The cost of one blanket after calculations sums up as $32.
Let b be the cost of one blanket and s be the cost of one scarf in dollars. We can set up a system of equations based on the information given:
2b + 5s = 104
3b + 4s = 128
We want to solve for the cost of one blanket, so we'll solve for b in terms of s. We can start by multiplying the first equation by 3 and the second equation by 2 to create a system of equations where the coefficients of b will cancel each other out when we subtract the two equations:
6b + 15s = 312
6b + 8s = 256
Subtracting the second equation from the first, we get:
7s = 56
Dividing both sides by 7, we get:
s = 8
Now we can substitute s = 8 into either of the original equations to solve for b:
2b + 5(8) = 104
2b + 40 = 104
2b = 64
b = 32
Therefore, one blanket costs $32.
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Sound travels at an approximate speed of [tex]3.43(10^2)[/tex] m/s. How far will sound travel in 2 minutes?
Answer:41,160 meters in 2 minutes at the speed of 343 meters per second.
Step-by-step explanation:
The speed of sound varies depending on the medium it's traveling through, but assuming you meant the speed of sound in air at room temperature, it's approximately 343 meters per second.
To find out how far sound will travel in 2 minutes (120 seconds), we can simply multiply the speed of sound by the time:
Distance = Speed x Time
Distance = 343 m/s x 120 s
Distance = 41,160 meters
Therefore, sound will travel approximately 41,160 meters in 2 minutes at the speed of 343 meters per second.
A box contains green marbles and blue marbles. Yosef shakes the box and chooses a marble at random. He records the color, then places the marble back into the box. Yosef repeats the process until he chooses 50 marbles. The table shows the count for each color. Write a probability model for choosing a marble.
green: 36
blue: 14
The probability model for choosing a marble from the box is P(green) = 36/50 and P(blue) = 14/50.
To create this probability model, first, count the total number of marbles chosen, which is 50. Then, count the number of green and blue marbles chosen, which are 36 and 14, respectively.
Divide the number of each color by the total number of marbles to find the probability of choosing a green or blue marble.
P(green) is calculated as 36/50 or 0.72, and P(blue) is calculated as 14/50 or 0.28. This model represents the likelihood of choosing a green or blue marble from the box based on Yosef's experiment.
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PLEASE HELP MEH
A 1,700-foot support wire is attached to
the top of an 800-foot radio tower.
1,700 ft
800 ft
А
B
A scale drawing of the tower and wire is
drawn using the scale 1 inch: 250 feet.
On the scale drawing, what is the length,
in inches, of AB? (8. 1B, 8. 1F)
F
15 in.
Make sure to
use the scale.
G 7. 5 in.
H
6 in.
J 18 in.
We know that the length of AB on the scale drawing is 10 inches
Using the scale of 1 inch: 250 feet, we can find the length of AB on the scale drawing by multiplying the actual length of AB by the scale factor.
The actual length of AB is the sum of the height of the tower (800 ft) and the length of the support wire (1,700 ft), which is 2,500 ft.
Multiplying 2,500 ft by the scale factor of 1 inch: 250 feet, we get:
2,500 ft ÷ 250 ft/inch = 10 inches
Therefore, the length of AB on the scale drawing is 10 inches.
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Aria ate the pictured slice of pizza. If the original
pizza was 8 inches in diameter, what is the area
of the slice she ate?
Answer:
Step-by-step explanation:
50.24n2
In a survey of 85 people, every fifth person had a pierced ear. How many people had a pierced ear? A 0.5 × 85 B 85 × 15 C 5÷85 D 85-4/5 E 85 × 0.25
Answer:
B
Step-by-step explanation:
Every fifth people means one person from 5 people in total. So when we convert that into numbers, it becomes [tex]\frac{1}{5}[/tex].
And in total there are 85 people involved, so the answer is
[tex]85[/tex] × [tex]\frac{1}{5}[/tex]
Answer:
Step-by-step explanation:
correct asnswer b
Earth's distance from the sun is 1. 496 x 108 km. Saturn's distance from the sun is 1. 4246 x 10 km. How many times further from the sun is Saturn? Explain how you arrived at your answer.
Saturn is approximately 9.52 times further from the sun than Earth.
To find out how many times further from the sun Saturn is compared to Earth, we need to divide Saturn's distance from the sun by Earth's distance from the sun.
First, let's correct the distances given:
- Earth's distance from the sun: 1.496 x 10^8 km
- Saturn's distance from the sun: 1.4246 x 10^9 km (I assume you missed the exponent)
Now, let's calculate the ratio:
Ratio = (Saturn's distance) / (Earth's distance)
Ratio = (1.4246 x 10^9 km) / (1.496 x 10^8 km)
To make the calculation easier, let's factor out the common exponent (10^8):
Ratio = (1.4246 x 10) / (1.496)
Ratio ≈ 9.52
So, Saturn is approximately 9.52 times further from the sun than Earth.
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Can someone help me with 15 16 17 18?
Answer:15)5760.1 6)78. 17)582.4 18)112
Step-by-step explanation:
a time capsule has been buried 98m away from the cave at a bearing of 312 degrees how far west of the cave is the time capsule buried? give your answer in 1 decimal places
If a time capsule has been buried 98m away from the cave at a bearing of 312. the time capsule is buried about 82.2 meters west of the cave.
What is the time capsule?To find how far west the time capsule is buried, we need to find the horizontal component of the displacement vector that points from the cave to the location of the time capsule. We can use trigonometry to do this:
cos(312°) = adjacent/hypotenuse
The hypotenuse is the distance between the cave and the time capsule, which is 98m. The adjacent side represents the horizontal distance between the two points, which is what we want to find. Rearranging the equation, we get:
adjacent = cos(312°) x hypotenuse
adjacent = cos(312°) x 98
adjacent ≈ 82.2
Therefore, the time capsule is buried about 82.2 meters west of the cave.
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Jane moved from a house with 78 square feet of closet space to an apartment with 47.58 square feet of closet space. what is the percentage decrease of jane's closet space?
Jane's closet space decreased by approximately 38.97%.
To find the percentage decrease of Jane's closet space, we need to first calculate the amount of decrease and then express it as a percentage of the original value.
The amount of decrease is the difference between the original closet space and the new closet space:
Decrease = Original closet space - New closet space
Decrease = 78 - 47.58
Decrease = 30.42
So Jane's closet space decreased by 30.42 square feet.
To express this decrease as a percentage of the original value, we use the following formula:
Percentage decrease = (Decrease / Original value) x 100%
Substituting the values, we get:
Percentage decrease = (30.42 / 78) x 100%
Percentage decrease ≈ 38.97%
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Which cardboard box can hold the greatest number of 1 in x 2 in x 4 in sponges
The cardboard box with the largest volume can hold the greatest number of 1 in x 2 in x 4 in sponges.
To find the box with the largest volume, first determine the volume of each sponge: V_sponge = 1 in x 2 in x 4 in = 8 cubic inches. Next, find the volume of each box by multiplying its length, width, and height (V_box = L x W x H).
To determine how many sponges each box can hold, divide the volume of the box by the volume of the sponge (V_box / V_sponge). The box with the highest resulting quotient can hold the most 1 in x 2 in x 4 in sponges.
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The radius of a base is 9 cm. The height is 12 cm . What is the volume of the cone?
volume =πr^2h
=π(9)^2*12
=π81*12
=972πcm^3
During a lab experiment, the
temperature of a liquid changes
from 63 °f to 102°f.
what is the percent of increase
in the temperature of the
liquid?
The percent increase in temperature of the liquid is 61.9%. This means that the temperature increased by 61.9% of its original value.
What is the percentage increase in temperature of a liquid that changes from 63°F to 102°F during a lab experiment?When we want to calculate the percent increase in a value, we need to compare the new value to the old value.
In this case, the old value is the initial temperature of the liquid, which is 63 °F, and the new value is the final temperature of the liquid, which is 102 °F.
To calculate the percent increase, we use the formula I mentioned earlier, which subtracts the old value from the new value, divides the result by the old value.
And then multiplies the quotient by 100% to express the result as a percentage.
So, for this experiment, we can calculate the percent increase in temperature as:
((102 - 63) / 63) x 100% = 61.9%
This means that the temperature of the liquid increased by 61.9% of its original value. Alternatively, we can also say that the final temperature is 161.9% of the initial temperature.
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Find the Lap lace transform of
f(t) = 6u (t- 2) + 3u(t-5) - 4u(t-6)
F(s)=
To find the Laplace transform of f(t), we use the formula:
L{f(t)} = ∫[0,∞) [tex]e^(-st)[/tex] f(t) dt
where L{f(t)} denotes the Laplace transform of f(t) and u(t) is the unit step function.
Using the linearity of the Laplace transform, we can find the Laplace transform of each term separately and add them up.
L{6u(t-2)} = [tex]6e^(-2s)[/tex] / s (applying the time-shift property)
L{3u(t-5)} = [tex]3e^(-5s)[/tex] / s (applying the time-shift property)
L{-4u(t-6)} = -[tex]4e^(-6s[/tex]) / s (applying the time-shift property)
Therefore, the Laplace transform of f(t) is:
F(s) = L{f(t)} = 6[tex]e^(-2s)[/tex] / s + [tex]3e^(-5s)[/tex] / s - [tex]4e^(-6s)[/tex]/ s
= [tex](6e^(-2s) + 3e^(-5s) - 4e^(-6s)) / s[/tex]
Hence, the Laplace transform of f(t) is F(s) = [tex](6e^(-2s) + 3e^(-5s) - 4e^(-6s)) / s.[/tex]
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Find the area of the shaded region. Round your answer to the nearest hundredth.
Answer:
The radius of the circle is 5/√2 = (5√2)/2 inches.
Area of circle = π((5√2)/2)^2
= 25π/2 square inches
Area of triangle = (1/2)(5√2)((5√2)/2)
= 25/2 square inches
Area of shaded region
= (25/2)(π - 1) = 26.77 square inches
Make sure to include your null and alternative hypothesis, your test statistic, your p-value, decision, and conclusion in the context in your response. A poll conducted by the General Social Survey asked a random sample of 1325 adults in the United States how much confidence they had in banks and other financial institutions. A total of 149 adults said they had a great deal of confidence. An economist claims that less than 15% of US adults have great confidence in banks. Use a= 0. 05 can you conclude that the economist's claim is true?Use a=0. 01 can you conclude that the economist's claim is true?
At both the 5% and 1% significance levels, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.
Null Hypothesis: The proportion of US adults who have great confidence in banks is 15% or higher.
Alternative Hypothesis: The proportion of US adults who have great confidence in banks is less than 15%.
We can use a one-tailed z-test to test the economist's claim.
The test statistic is
z = (P - p) / √(p * (1-p) / n)
where P is the sample proportion, p is the hypothesized proportion, and n is the sample size.
Using the sample data, we have
P = 149/1325 = 0.1121
p = 0.15
n = 1325
The test statistic is
z = (0.1121 - 0.15) / √(0.15 × (1-0.15) / 1325) = -3.196
Using a significance level of α = 0.05, the critical value for a one-tailed test is -1.645. Since our test statistic is less than the critical value, we reject the null hypothesis.
The p-value for this test is P(Z < -3.196) = 0.0007. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.
At the 5% significance level, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.
Using a significance level of α = 0.01, the critical value for a one-tailed test is -2.33. Since our test statistic is less than the critical value, we reject the null hypothesis.
The p-value for this test is P(Z < -3.196) = 0.0007. Since the p-value is less than the significance level of 0.01, we reject the null hypothesis.
At the 1% significance level, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.
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(x+2)^1/2-5=-2
Answers is x=7
SHOW WORK
[tex](\text{x}+2)^{1/2}-5 = -2\\\\\sqrt{\text{x}+2}-5 = -2\\\\\sqrt{\text{x}+2} = -2+5\\\\\sqrt{\text{x}+2} = 3\\\\(\sqrt{\text{x}+2})^2 = 3^2\\\\\text{x}+2= 9\\\\\text{x}= 9-2\\\\\text{x}= 7\\\\[/tex]
-----------------------
Check:
[tex](\text{x}+2)^{1/2}-5 = -2\\\\\sqrt{\text{x}+2}-5 = -2\\\\\sqrt{7+2}-5 = -2\\\\\sqrt{9}-5 = -2\\\\3-5 = -2\\\\-2 = -2 \ \ \ \checkmark\\\\[/tex]
The answer is confirmed.
-----------------------
Answer: x = 7Maria is currently taking quantitative literacy course. The instructor often gives quizzes. Each quiz is worth
10 points. Maria got the following scores: 10, 9, 10, 9, 10.
(a) Calculate the average of her quizzes. Round your answer to the nearest tenth (if needed).
(b) Calculate standard deviation of her quizzes. Round your answer to the nearest tenth.
Maria's average quiz score is 9.6.
B. The standard deviation of her quizzes is approximately 0.5 (rounded to the nearest tenth).
What is the average?(a) The average of Maria's quizzes can be found by adding up all her scores and dividing by the total number of quizzes:
Average = (10 + 9 + 10 + 9 + 10) / 5 = 9.6
Therefore, Maria's average quiz score is 9.6.
(b) To calculate the standard deviation of her quizzes, we first need to find the variance. We can do this by finding the average of the squared differences between each score and the mean:
[(10 - 9.6)² + (9 - 9.6)² + (10 - 9.6)² + (9 - 9.6)² + (10 - 9.6)²] / 5 = 0.24
So the variance is 0.24. To find the standard deviation, we take the square root of the variance:
√0.24 ≈ 0.5
So the standard deviation of her quizzes is approximately 0.5 (rounded to the nearest tenth).
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Which geometric term would you use to describe the crossing sign shown below?
An X- shaped rail road crossing sign is shown.
A.
perpendicular lines
B.
parallel lines
C.
intersecting lines
D.
points
The geometric term that can be used to describe the crossing sign shown is intersecting lines.
What are intersecting lines geometry?In geometry, intersecting lines are two lines that cross one another at a location known as the point of intersection. It is possible to use the point of intersection to solve issues concerning angles, segments, and geometric shapes because it is the sole point that both lines share.
Two pairs of opposite angles that are equal to one another are formed when two lines connect, giving rise to four angles.
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Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points. for this one, use substitution method.
The value of X and y when substitution method is used to solve the given quadratic equation would be = 8 and 2 respectively.
How to calculate the unknown values using the substitution method?The equations that are given is listed below:
X - 3y = 2 ---> equation 1
2x - 6y = 6 ----> equation 2
In equation 1, make X the subject of formula;
X = 2 + 3y
Substitute X = 2 + 3y into equation 2,
2( 2 + 3y) - 6y = 6
4 + 6y - 6y = 6
y = 6-4
y = 2
Substitute y = 2 into equation 1;
x - 3(2) = 2
X = 2 + 6
X= 8
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Question 1(Multiple Choice Worth 2 points)
(Circle Graphs MC)
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 3(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Question 5(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Answer 1: Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
How to solveThe circle graph shows the percentage of residents who prefer each transportation method, and the total sample size is 400.
For streetcar, (15/100) x 400 = 60 residents prefer it, and for cable car, (27/100) x 400 = 108 residents prefer it.
Together, Streetcar and Cable Car are the preferred transportation for 60 + 108 = 168 residents.
Answer 2: The median is the best measure of center, and it equals 19.
The box plot shows the distribution of the number of tickets sold for a school dance.
The median is the middle value of the data when arranged in order, and it is represented by the line in the box. In this case, the median is 19. The mean, on the other hand, can be influenced by extreme values, and we cannot determine it from the box plot alone.
Answer 3: Median, because Sunny Town is skewed.
When comparing the data, we need to consider the measure of center that is less affected by extreme values, and that is the median.
The median is the middle value of the data when arranged in order. The histogram for Sunny Town is skewed to the right, which means that there are some very high values that are affecting the mean.
Therefore, the median is the better measure of center to determine which location typically has the cooler temperature.
Answer 4: The IQR of 13 is the most accurate to use, since the data is skewed.
The histogram shows the frequency of donations received by a charity, and the data is skewed to the right.
The IQR (Interquartile Range) is the difference between the third quartile (Q3) and the first quartile (Q1), which represents the middle 50% of the data.
The IQR is less sensitive to extreme values and is a better measure of variability for skewed data. In this case, the IQR is 49 - 42 = 7, which is the most accurate measure of variability to use.
Answer 5: There were about 15 principals in attendance.
In the exhibit room, out of 80 people, 15 are principals.
We can assume that the proportion of principals in the exhibit room is the same as the proportion of principals in the conference.
Therefore, the estimated number of principals in the conference is (15/80) x 900 = 168.75, which is approximately 169.
Answer 6: Histogram
The teacher wants to represent the subject preferences of 100 students. A histogram would be the best graphical representation to use because it shows the frequency distribution of a continuous variable, which in this case could be the number of students who prefer each subject.
A stem-and-leaf plot is used for small datasets, and a box plot is used to display the distribution of a continuous variable across categories. A circle graph is more appropriate for displaying categorical data, such as the percentage of students who prefer each subject.
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n a circle, a 180 degree sector has area 162\pi in Superscript 2. What is the radius of the circle?
The radius of the circle is 10 inches.
Area of a sector.A sector is a part of a given circle which is made from two radii and an arc. It's area can be determined by;
area of a sector = θ/360*πr^2
where θ is the measure of its central angle, and r is its radius.
Then from the given question, we have;
area of a sector = θ/360*πr^2
162 = 180/360 *3.14*r^2
= 1.57r^2
r^2 = 162/1.57
= 103.1847
So that;
r = (103.1847)^1/2
= 10.16
The radius of the circle is approximately 10 inches.
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HELP DUE IN 5 min Area=?
Answer:
The answer to your problem is, 39
Step-by-step explanation:
In order to find the area of the triangle use the formula down below:
A = [tex]\frac{h_{b} b}{2}[/tex]
Base = 13
Height = 6
Replace them equals:
= [tex]\frac{6*13}{2}[/tex] = 39
Thus the answer to your problem is, 39
Find the critical mumbers for g(x) = 2 sin r- r on (0,7). Then find the absolute maximum and minimum values for g(x) on (0,7). Give exact answers, not decimal approximations."
2 cos x - 1 = 0, cos x = 1/2, and x = π/3 or 5π/3. These are the critical numbers of g(x) on (0,7). the absolute maximum value of g(x) on (0,7) is √3 - π/3 and the absolute minimum value is -√3 - 5π/3.
To find the critical numbers for g(x) = 2sin(r) - r on the interval (0, 7), follow these steps:
1. Find the derivative of g(x): g'(x) = 2cos(r) - 1
2. Set the derivative equal to zero: 2cos(r) - 1 = 0
3. Solve for r: r = cos^(-1)(1/2)
Now, find the absolute maximum and minimum values for g(x) on the interval (0, 7):
1. Evaluate g(x) at the critical numbers: g(cos^(-1)(1/2)) = 2sin(cos^(-1)(1/2)) - cos^(-1)(1/2)
2. Evaluate g(x) at the endpoints of the interval: g(0) = 2sin(0) - 0, g(7) = 2sin(7) - 7
3. Compare the values from steps 1 and 2 to find the maximum and minimum values.
The critical numbers for g(x) = 2sin(r) - r on the interval (0, 7) are r = cos^(-1)(1/2). The absolute maximum and minimum values for g(x) on the interval (0, 7) can be found by comparing g(cos^(-1)(1/2)), g(0), and g(7).
To find the critical numbers of g(x) = 2 sin x - x on (0,7), we first need to find its derivative:
g'(x) = 2 cos x - 1
Setting g'(x) = 0, we get:
2 cos x - 1 = 0
cos x = 1/2
x = π/3 or 5π/3
These are the critical numbers of g(x) on (0,7).
To find the absolute maximum and minimum values of g(x) on (0,7), we need to evaluate g(x) at the critical numbers and at the endpoints of the interval (0,7).
g(0) = 0
g(π/3) = 2 sin(π/3) - π/3 = √3 - π/3
g(5π/3) = 2 sin(5π/3) - 5π/3 = -√3 - 5π/3
g(7) = 2 sin(7) - 7
To determine the absolute maximum and minimum values, we compare these values:
The absolute maximum value is √3 - π/3, which occurs at x = π/3.
The absolute minimum value is -√3 - 5π/3, which occurs at x = 5π/3.
Therefore, the absolute maximum value of g(x) on (0,7) is √3 - π/3 and the absolute minimum value is -√3 - 5π/3.
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PLEASE HELPPPP!! 20pts Students in the Drama Club are purchasing accessories for a play. They shop at two different stores over the span of three days. The items purchased at Store A al cost the same amount. The tems pur
⢠Day 1: Students spent $30. They purchased 4 items from Store A and 7 items from Store B.
⢠Day 2: Students spent $22. They purchased 3 items from Store A and 5 items from Store B.
On Day 3 students will need to buy 10 items from Store A and 17 items from Store B. What is the amount of money the students will need on the third day?
Part A: Write a system of equations to model the situations
The students will need $74 on the third day.
Let x be the cost of one item at Store A and y be the cost of one item at Store B. Then the system of equations to model the situation is:
4x + 7y = 30
3x + 5y = 22
To find the cost on Day 3, we need to solve for x and y, and then use those values to calculate:
10x + 17y = ?
Part B: Solve the system of equations to find x and y
To solve the system of equations, we can use elimination or substitution. Here, we'll use substitution.
From the first equation, we can solve for x:
4x + 7y = 30
4x = 30 - 7y
x = (30 - 7y)/4
Substitute this expression for x into the second equation:
3x + 5y = 22
3((30 - 7y)/4) + 5y = 22
(90 - 21y)/4 + 5y = 22
90 - 21y + 20y = 88
-y = -2
y = 2
Now that we know y = 2, we can substitute this value back into either equation to find x:
4x + 7y = 30
4x + 7(2) = 30
4x + 14 = 30
4x = 16
x = 4
So x = 4 and y = 2.
Part C: Calculate the amount of money needed on Day 3
Finally, we can use these values to calculate the amount of money needed on Day 3:
10x + 17y = 10(4) + 17(2) = 40 + 34 = 74
Therefore, the students will need $74 on the third day.
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In nop, the measure of zp=90°, the measure of zn=39, and pn = 72 feet. find the length of op to the nearest tenth of a foot?
The length of OP to the nearest tenth of a foot is approximately 41.5 feet
To find the length of OP, we can use the Pythagorean theorem since we have a right triangle.
OP^2 = PN^2 - ON^2
First, we need to find ON using the trigonometric ratio of tangent.
tan(39) = ON/PN
ON = PN * tan(39)
ON = 72 * tan(39)
ON ≈ 53.4 feet
Now we can plug in our values:
OP^2 = 72^2 - 53.4^2
OP^2 ≈ 1720.84
OP ≈ 41.5 feet (rounded to the nearest tenth of a foot)
Therefore, the length of OP to the nearest tenth of a foot is approximately 41.5 feet.
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Two random samples 4. 49, 7. 68, 5. 97, 0. 97, 6. 88, 6. 07, 03. 08, 04. 02, 03. 83, 6. 35, and 4. 59, 3. 39, 3. 79, 6. 89, 5. 07, 07. 41, 0. 44, 2. 47, 4. 80, 7. 23 were obtained independently from distributions with the same mean. Perform a permutation test to test the hypothesis that the variability in both populations is the same against the alternative that it is larger in the second population. As a test statistic use: (i) The difference of sample ranges. (ii) The ratio of sample variances. (iii) Compare both results
A. Main Answer:
The hypothesis that the variability in both populations is the same against the alternative that it is larger in the second population, we can perform a permutation test using two different test statistics:
(i) the difference of sample ranges and
(ii) the ratio of sample variances. By comparing the results of both test statistics, we can draw conclusions about the variability in the populations.
(i) Difference of Sample Ranges:
1. Calculate the sample range for each sample. The sample range is the difference between the maximum and minimum values in the sample.
Sample 1 Range = Maximum value - Minimum value for Sample 1
Sample 2 Range = Maximum value - Minimum value for Sample 2
2. Calculate the observed difference of sample ranges, which is the difference between the sample range of Sample 2 and Sample 1.
3. Pool the data from both samples and shuffle them randomly, keeping the same sample sizes.
4. Calculate the difference of sample ranges for the shuffled data.
5. Repeat steps 3 and 4 many times (e.g., 1000 permutations) to obtain a distribution of the difference of sample ranges under the null hypothesis (where variability is the same in both populations).
6. Compare the observed difference of sample ranges from step 2 with the distribution obtained from the permutations.
(ii) Ratio of Sample Variances:
1. Calculate the sample variance for each sample.
2. Calculate the observed ratio of sample variances, which is the ratio of the sample variance of Sample 2 to the sample variance of Sample 1.
3. Pool the data from both samples and shuffle them randomly, keeping the same sample sizes.
4. Calculate the ratio of sample variances for the shuffled data.
5. Repeat steps 3 and 4 many times (e.g., 1000 permutations) to obtain a distribution of the ratio of sample variances under the null hypothesis.
6. Compare the observed ratio of sample variances from step 2 with the distribution obtained from the permutations.
By comparing the results of both test statistics, we can assess whether the variability in the second population is significantly larger than the first population. If both test statistics consistently indicate larger variability in the second population, it provides evidence against the null hypothesis and suggests that the variability in the second population is indeed larger.
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Just explain how to do it with the answer please.
The measures of the angles JIK and JIL are 67 degrees and 157 degrees
Calculating the measures of the angles JIK and JIL?From the question, we have the following parameters that can be used in our computation:
Tangent at point IDiameter = IKThe measure of IJ = 46 degreesThe inscribed angle opposite to the same arc is half of the external angle
Using the above as a guide, we have the following:
JIK = 90 - 46/2
JIK = 67 degrees
Also, we have
JIL = 90 + JIK
So, we have
JIL = 90 + 67
JIL = 157 degrees
Hence, the measure of the angle JIL is 157 degrees
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b. use the overhead rate in (a) to determine the amount of total and per-unit overhead allocated to each of the three products, rounded to the nearest dollar.
The amount of total and per-unit overhead allocated to each of the three products using overhead rate is equal to,
Total Per Unit Factory Overhead , Cost Factory Overhead Cost
Flutes $530 $1,060,000
Clarinets $795 $1,192,500
Oboes $397.5 $695,625
Total $1,722.5 $2,948,125
Budgeted factory overhead cost = $2,948,125
The single plantwide overhead rate
= Dividing the budgeted factory overhead cost by the total budgeted direct labor hours.
For this,
Flutes= 2,000×2
= 4,000 hours
Clarinets= 1,500×3
= 4,500 hours
Oboes= 1,750×1.5
= 2,625 hours
Total direct labor hours = 11,125
Substitute the value we have,
⇒ Single plantwide overhead rate = $2,948,125 / (2,000 x 2.0 + 1,500 x 3.0 + 1,750 x 1.5)
= $2,948,125 / 11,125
= $265 per direct labor hour
To allocate overhead to each product
=Multiply the overhead rate by the budgeted direct labor hours per unit for each product.
Substitute the value we have,
Flutes,
$265 x 2.0 = $530 total overhead cost, $265 per unit
Clarinets,
$265 x 3.0 = $795 total overhead cost, $265 per unit
Oboes,
$265 x 1.5 = $397.5 total overhead cost, $265 per unit
And
Total factory overhead cost allocated = Estimated manufacturing overhead rate× Actual amount of allocation base
For,
Flutes
= 4,000× 265
= $1,060,000
Clarinets
= 4,500×265
= $1,192,500
Oboes
= 2,625×265
= $695,625
This implies,
The total and per-unit overhead allocated to each product, rounded to the nearest dollar is,
Total Per Unit Factory Overhead , Cost Factory Overhead Cost
Flutes $530 $1,060,000
Clarinets $795 $1,192,500
Oboes $397.5 $695,625
Total $1,722.5 $2,948,125
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The above question is incomplete, the complete question is:
Bach Instruments Inc. makes three musical instruments: flutes, clarinets, and oboes. The budgeted factory overhead cost is $2,948,125. Overhead is allocated to the three products on the basis of direct labor hours. The products have the following budgeted production volume and direct labor hours per unit:
Budgeted Production Volume Direct Labor Hours Per Unit
Flutes 2,000 units 2.0
Clarinets 1,500 3.0
Oboes 1,750 1.5
a. Determine the single plantwide overhead rate.
$ per direct labor hour
b. Use the overhead rate in (a) to determine the amount of total and per-unit overhead allocated to each of the three products, rounded to the nearest dollar.
Total Per Unit
Factory Overhead Cost Factory Overhead Cost
Flutes $ $
Clarinets
Oboes
Total $
What is the area of the sector bounded by the arc?
The given circle has a radius of 3 m and the shaded
section has an arc length of 47 m.
nº
Arc length
Circumference
360°
3 m
WIN
nº
360°
arc length
40 m
nº
Area = (97)
360°
Area = { (97)
bem?
The area of the sector is approximately 23.24 m^2.
How to find the area?To find the area of the sector, we first need to find the central angle of the sector.
The entire circumference of the circle is given by 2πr, where r is the radius of the circle. In this case, the circumference is 2π(3) = 6π m.
The arc length given is 47 m, which we can use to find the central angle of the sector:
central angle = (arc length / circumference) × 360°
central angle = (47 / 6π) × 360°
central angle ≈ 299.02°
Now that we have the central angle, we can use the formula for the area of a sector:
area of sector = (central angle / 360°) × πr^2
area of sector = (299.02 / 360) × π(3)^2
area of sector ≈ 7.43π m^2
Rounding to two decimal places, the area of the sector is approximately 23.24 m^2.
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A study was conducted to determine the relationship existing between the grade in english and the grade in mathematics. a random sample of 10 cte students in uc were taken and the following are the results of the sampling th a)compute for the pearson( r) - 10pts b) state null and alternative hypothesis- 5pts b)find equation of regression line- 5pts c) interpret and conclude results - 5pts student 1 2 3 4 5 6 7 8 9 10 english 75 83 80 77 89 78 92 86 93 84 mathematics 78 87 78 76 92 81 89 89 91 84
a) The Pearson correlation coefficient is 0.76.
b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)
Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)
c) The regression line is: y = 0.64x + 34.18
d) Interpretation and conclusion: The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.
Correlation analysis:
Using the Pearson correlation coefficient to measure the strength and direction of the linear relationship between two variables.
Hypothesis testing:
Setting up null and alternative hypotheses, and using the t-test to determine whether the correlation coefficient is statistically significant.
Linear regression:
Finding the equation of the regression line that best describes the relationship between the two variables.
Interpretation and conclusion:
Using the results of the analysis to draw meaningful conclusions about the relationship between the two variables and the sample population as a whole.
Here we have
A study was conducted to determine the relationship existing between the grade in English and the grade in mathematics. a random sample of 10 students in uc was taken and the following are the results of the sampling
Student 1 2 3 4 5 6 7 8 9 10
English 75 83 80 77 89 78 92 86 93 84
Mathematics 78 87 78 76 92 81 89 89 91 84
a) To compute the Pearson correlation coefficient (r), first calculate the mean, standard deviation, and covariance of the two variables:
Mean of English grades (x)
= (75+83+80+77+89+78+92+86+93+84)/10 = 83.7
Mean of Math grades (y)
= (78+87+78+76+92+81+89+89+91+84)/10 = 84.5
The standard deviation of English grades (Sx)
= √((75-83.4)²+(83-83.4)²+...+(84-83.4)²)/9) = 6.52
The standard deviation of Math grades (Sy)
= √((78-84.4)²+(87-84.4)²+...+(84-84.4)²)/9) = 5.47
Covariance of the two variables
= ((75-83.4)(78-84.4)+(83-83.4)(87-84.4)+...+(84-83.4)(84-84.4))/9 = 26.6
Using the formula, r = cov(X,Y)/(SxSy),
we can calculate the correlation coefficient as follows
r = 26.6/(6.52*5.47) = 0.76
Therefore,
The Pearson correlation coefficient is 0.76.
b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)
Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)
c) To find the equation of the regression line, we need to calculate the slope (b) and the intercept (a) of the line. The formula for the slope is:
b = r(Sy/Sx) = 0.76(5.47/6.52) = 0.64
The formula for the intercept is:
=> a = y - bx = 84.4 - 0.64(83.4) = 34.18
Therefore,
The equation of the regression line is:
y = 0.64x + 34.18
Interpretation and conclusion:
The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.
The p-value associated with this correlation coefficient can be used to test the null hypothesis.
The equation of the regression line shows that for every one-point increase in the English grade, the predicted increase in the Mathematics grade is 0.64 points.
Therefore,
a) The Pearson correlation coefficient is 0.76.
b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)
Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)
c) The regression line is: y = 0.64x + 34.18
d) Interpretation and conclusion: The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.
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