The red car is actually traveling along the road at a speed of approximately 26.67 feet per second.
We can start by drawing a diagram of the situation:
P (police car)
|
|
|
40 | S (stop sign)
-------|--------------------
| 160
| R (red car)
Let's use the Pythagorean theorem to find the distance between the police car and the red car at any time t:
d(t)² = 40² + (160 - v*t)²
Where v is the speed of the red car in feet per second, and d(t) is the distance between the police car and the red car at time t.
We want to find how fast the red car is actually traveling along the road, so we need to find v when the distance between the police car and the red car is decreasing at a rate of 100 feet per second:
d'(t) = -100
We can take the derivative of the equation for d(t) with respect to time:
2d(t)d'(t) = 0 + 2(160 - v*t)(-v)
Simplifying and plugging in d'(t) = -100, we get:
-4000 + 2v²t = -100(160 - vt)
Solving for v, we get:
v = 80/3 ≈ 26.67 feet per second
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During one week, Sheila made several changes to her bank account. She made four withdrawals of 40$ each from an ATM she also used her check card for a 156$ purchase then she deposited her paycheck of $375
The amount change in her bank account during that week after withdrawals and deposit is equal to $59.
Total number of withdrawals made by Sheila = 4
Amount made at the time withdrawals using ATM = $40
Amount withdraw using check card to purchase = $156
Amount deposited using paycheck = #375
Let us calculate the total amount of money Sheila withdrew from her bank account using ATM,
4 withdrawals of $40 each
= 4 x $40
= $160
So, she withdrew $160 and made a $156 purchase, meaning she spent a total amount of,
= $160 + $156
= $316
Sheila also deposited her paycheck of $375, so the total amount of money in her account changed by is equal to,
$375 - $316 = $59
Therefore, the amount in Sheila's account increased by $59 during that week.
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The above question is incomplete, the complete question is:
During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?
Flying Home for the Holidays Does the airline you choose affect when you'll arrive at
your destination? The dataset DecemberFlights contains the difference between actual and
scheduled arrival time from 1000 randomly sampled December flights for two of the major North
American airlines, Delta Air Lines and United Air Lines. A negative difference indicates a flight
arrived early. We are interested in testing whether the average difference between actual and
scheduled arrival time is different between the two airlines.
a. Define any relevant parameter(s) and state the null and alternative hypotheses.
b. Find the sample mean of each group, and calculate the difference in sample means.
c. Use StatKey or other technology to create a randomization distribution and find the p-value.
d. At a significance level of a = 0. 01, what is the conclusion of the test? Interpret the conclusion in
context.
a
Relevant parameter is the difference between actual and scheduled arrival time. Also the difference in sample means is -1.70 minutes. We get a p-value of 0.017 and the conclusion is that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.
a. Relevant parameter: the difference between actual and scheduled arrival time.
Null hypothesis: The average difference between actual and scheduled arrival time is the same for Delta Air Lines and United Air Lines.
Alternative hypothesis: The average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.
b. Sample mean for Delta Air Lines: -2.31 minutes
Sample mean for United Air Lines: -4.01 minutes
Difference in sample means: -1.70 minutes
c. To create a randomization distribution, we can pool the data from both airlines and randomly assign them to two groups with the same sample sizes as Delta Air Lines and United Air Lines. We then calculate the difference in sample means for each random assignment. Repeating this process many times gives us a randomization distribution. Using StatKey with 10,000 iterations, we get a p-value of 0.017, which is less than 0.01.
d. At a significance level of 0.01, we reject the null hypothesis and conclude that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines. Specifically, the average difference for United Air Lines is greater than that of Delta Air Lines. This could have implications for travelers who prioritize arriving on time, as they may wish to consider
Delta over United.
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An experiment was conducted to test the effect of a new dietary supplement for weight loss. Ten men and ten women were given the supplement daily for a month; then the amount of weight each person lost was determined. A significance test was conducted at the α = 0. 05 level for the mean difference in the number of pounds lost between men and women. The test resulted in t = 2. 178 and p = 0. 3. If the alternative hypothesis in question was Ha: μm − μw ≠ 0, where μm equals the mean number of pounds lost by men and μw equals the mean number of pounds lost by women, what conclusion can be drawn? (2 points)
options:
There is not a significant difference in mean weight loss between men and women.
There is sufficient evidence that there is a difference in mean weight loss between men and women.
There is sufficient evidence that, on average, men lose more weight than women.
The proportion of men who lost weight is greater than the proportion of women.
There is insufficient evidence that the proportion of men and women who lost weight is different
The null hypothesis (H0) is that there is no significant difference in mean weight loss between men and women, or μm - μw = 0. The alternative hypothesis (Ha) is that there is a significant difference in mean weight loss between men and women, or μm - μw ≠ 0.
Is there sufficient evidence to support the claim that there is a difference in mean weight loss between men and women in the dietary supplement experiment?The p-value of 0.3 indicates that there is no significant difference in mean weight loss between men and women. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we can conclude that there is not a significant difference in mean weight loss between men and women.The t-value of 2.178 indicates that there is some difference in the mean weight loss between men and women, but the p-value of 0.3 indicates that this difference is not statistically significant. In other words, the observed difference in mean weight loss could have occurred by chance, and we cannot reject the null hypothesis that there is no difference in mean weight loss between men and women. Therefore, we conclude that there is not a significant difference in mean weight loss between men and women.Learn more about experiment,
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For the function f(x) = 2x^4 In x, find f'(x).
To find the derivative (f'(x)) of the function f(x) = 2x^4 In x, we will need to use the product rule and the chain rule of differentiation.
Using the product rule, we have:
f'(x) = [2(In x)](4x^3) + [2x^4](1/x)
Simplifying this expression, we get:
f'(x) = 8x^3 In x + 2x^3
Therefore, the derivative of f(x) is f'(x) = 8x^3 In x + 2x^3.
Hi! To find the derivative f'(x) of the function f(x) = 2x^4 * ln(x), we'll use the product rule. The product rule states that if you have a function h(x) = u(x)v(x), then h'(x) = u'(x)v(x) + u(x)v'(x). In this case, u(x) = 2x^4 and v(x) = ln(x).
First, find the derivatives of u(x) and v(x):
u'(x) = d(2x^4)/dx = 8x^3
v'(x) = d(ln(x))/dx = 1/x
Now, apply the product rule:
f'(x) = u'(x)v(x) + u(x)v'(x)
f'(x) = (8x^3)(ln(x)) + (2x^4)(1/x)
Simplify the expression:
f'(x) = 8x^3 * ln(x) + 2x^3
This is the derivative of the given function.
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.the function f(x) = 5^x is stretched vertically by a scale factor
of 2, shifted 3 units to the left and down 1 unit to produce the
function g(x). find g(x).
please help :d
The transformation of the function g(x) is g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, a shift of 3 units to the left, and a downward shift of 1 unit applied to the original function f(x) = 5^x.
- Vertical stretch by a scale factor of 2: Multiply the output by 2.
- Shift 3 units to the left: Replace x with x + 3.
- Shift 1 unit down: Subtract 1 from the output.
Thus, the function g(x) can be written as:
g(x) = 2 * f(x + 3) - 1
Substituting f(x) = 5^x, we get:
g(x) = 2 * 5^(x + 3) - 1
Simplifying:
g(x) = 2 * 125 * 5^x - 1
g(x) = 250 * 5^x - 1
The function g(x) is given by g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, followed by a shift of 3 units to the left, and a downward shift of 1 unit, applied to the original function f(x) = 5^x.
The transformation increases the steepness of the graph, shifts it to the left, and shifts it downward. The expression 250 * 5^x represents the vertical scaling, and the -1 accounts for the vertical shift downward. Overall, g(x) is a modified version of f(x) with these transformations applied.
Therefore, the function g(x) is g(x) = 250 * 5^x - 1.
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in the coordinate plane, point b is located at (2, -3), Point C is reflected across the y-axis. Plot and label points b and C in the coordinate plane.
Thus, we can label the points B and C' in the coordinate plane as follows
|
|
C' |
|
------B(2, -3)
|
|
|
Coordinate plane calculation.To reflect a point across the y-axis, we keep the x-coordinate the same but change the sign of the y-coordinate.
Point B is located at (2, -3), so it looks like
|
|
|
|
------B(2, -3)
|
|
|
|
To reflect point C across the y-axis, we change the sign of the y-coordinate, but keep the x-coordinate the same. If point C is located at (x, y), then its reflected image, C', would be located at (-x, y).
Since we don't have the coordinates for point C, we cannot plot it accurately. However, we know that its reflected image would be located at (-x, y), so we can label it as C' for now.
So, the reflected image of point C across the y-axis, C', would be located at (-x, y). Thus, we can label the points B and C' in the coordinate plane as follows
|
|
C' |
|
------B(2, -3)
|
|
|
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Ms. Grant recorded the numbers of students in her homeroom class who
participated in spirit week.
The table shows the number of students who dressed up each day.
Day
Mon Tues. Wed. Thurs. Fri. Total
Number of students O
1
4
5
5
15
Find the mean and the median of the data set.
Determine which of these values is greater.
A. The median, 4, is greater than the mean, 3.
B. The mean, 4, is greater than the median, 3.
C. The mean, 4, is greater than the median, 2.
D. The median, 5, is greater than the mean, 0.
The mean and the median of the data set is given as the median, 4, is greater than the mean, 3. The correct answer is option a.
To find the mean of the data set, we add up all of the numbers and divide by the total number of days. So, the mean is (1+4+5+5+1+5+5)/6 = 3.
To find the median, we first need to put the numbers in order from least to greatest: 1, 1, 4, 5, 5, 5. The median is the middle number, which in this case is 4.
Now we need to determine which value is greater. The options are:
A. The median, 4, is greater than the mean, 3.
B. The mean, 3, is greater than the median, 4.
C. The mean, 4, is greater than the median, 2.
D. The median, 5, is greater than the mean, 0.
We can eliminate options B and D because they don't make sense. The mean cannot be less than 0, and the median cannot be less than the mean.
Option A is correct. The median, 4, is greater than the mean, 3. This makes sense because there are two 1's in the data set, which bring down the mean. However, the median is not affected by outliers like this, so it remains higher.
Option C is incorrect because the mean is not 4, it is 3.
In summary, the mean of the data set is 3 and the median is 4. The median is greater than the mean, which is represented by option A.
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Question 10(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 11(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12(Multiple Choice Worth 2 points)
The answer to the first question is: Burger Quick, because it has a larger median.
The answer to the second question is: Histogram, because it can show the frequency distribution of the continuous variable "number of carbohydrates" and group the data into intervals.
What is a histogram?A histogram is a graphical representation of a distribution of numerical data. It consists of a series of bars, where each bar represents a range of values of the data and the height of the bar indicates the frequency or count of data points falling within that range.
In a histogram, the horizontal axis represents the range of values or intervals of the data, called bins, and the vertical axis represents the frequency or count of data points falling within each bin. The bins can be of equal or unequal width depending on the nature of the data.
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Select all the correct answers.
Isosceles trapezoid ABCD is shown.
Which three statements are correct?
In the given Isosceles trapezoid ABCD, the following three statements are correct:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths. Non-parallel sides on isosceles trapezoids have the same lengths. Hence, AD ≅ BC
A triangle with two equal sides is said to be isosceles. The two angles facing the two equal sides are also equal. Hence, ∠ADC ≅ ∠BCD.
The diagonals of the isosceles trapezoid are also equal. Hence, AC ≅ BD.
Thus, three correct statements in the given question are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
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What is the sum of the heights of the two trees?
Round your answer to the nearest whole number
The sum of the heights of the two trees with given volumes and radius is equal to 9 cm (nearest whole number ).
Volumes of the cylindrical trunks of first tree = 904.78 cm³
and Volumes of the cylindrical trunks of first tree =113 cm³.
radius of the first tree = 6cm
Radius of the second tree = 6cm
The formula for the volume of a cylinder is V = πr²h,
where r is the radius of the cylinder,
h is the height of the cylinder,
and π is the constant approximately value equal to 3.14.
For the first tree,
⇒904.78 = π(6)²h
⇒h = 904.78 / (π(6)²)
⇒h ≈ 8.004 cm
For the second tree, we have,
⇒113 = π(6)²h
⇒h = 113 / (π(6)²)
⇒h ≈ 0.9996 cm
This implies,
The sum of the heights of the two trees is equal to,
= 8.004 + 0.9996
= 9.003 cm
= 9 cm ( nearest whole number)
Hence, the sum of the heights of the two trees is approximately 9 cm nearest whole number.
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The given question is incomplete, I answer the question in general according to my knowledge:
The two trees trunk are in cylindrical shape. one with radius 6cm and volume 904.78 cm³ and another one with radius 6cm and volume 113 cm³.
What is the sum of the heights of the two trees? Round your answer to the nearest whole number
Which of the following tables represents a linear relationship that is also proportional?
Answer:
Step-by-step explanation:
proportional means the graph passes through the origin, also known as (0,0). In this case, the only table with both 0’s in the x and y is the second one from the top.
3. la mamá de jordan compró 7 cajas de envases de jugo para después del entrenamiento del equipo. cada caja tenía 8 envases de jugo. después que el equipo bebió todo el jugo que quiso, quedaron 29 envases de jugo. el equipo abrió una nueva caja solo después de beber todo el jugo de la caja anterior. ¿cuántas cajas de jugo abrió el equipo?
Answer:
Step-by-step explanation:
The team drank a total of 7 x 8 = 56 juice boxes, and there were 29 remaining, so the team opened 56 - 29 = 27 juice boxes.
Since the team only opened a new box after finishing the previous one, the team opened 27 - 1 = 26 boxes of juice in total.
To explain this solution in more detail, we can use basic arithmetic. We know that the mom bought 7 boxes of juice, each containing 8 juice boxes,
so the total number of juice boxes is 7 x 8 = 56. After the team drank all the juice they wanted, there were 29 juice boxes remaining. This means that the team drank 56 - 29 = 27 juice boxes.
Since the team only opened a new box of juice after finishing the previous one, the number of boxes opened will be one less than the total number of juice boxes consumed.
Therefore, the team opened 27 - 1 = 26 boxes of juice in total. It is important to note that this assumes that the team opened all the boxes they consumed and did not drink any juice directly from the remaining boxes.
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Sam has a cylindrical storage container 7 inches tall with a radius of 5 inches.
How much cat litter will fit in the container?
Use 3. 14 for π. Round your answer to the nearest tenth.
Answer: _____________ cubic inches
The cylindrical storage container can hold 549.5 cubic inches of cat litter.
To find the volume of the cylindrical storage container, we need to use the formula:
V = πr²h
Where:
π is a constant approximately equal to 3.14
r is the radius of the container
h is the height of the container
Substituting the given values, we get:
V = 3.14 x 5² x 7
V = 549.5 cubic inches
Since we know that the vessel can hold549.5 boxy elevation of cat waste, we can use this value to determine how important cat waste can fit in the vessel in other units. For illustration, if we want to know how numerous liters of cat waste can fit in the vessel, we can convert boxy elevation to liters using the conversion factor 1 liter = 61.02 boxy elevation. boxy elevation61.02 boxy elevation per liter = 8.998 liters thus, the spherical storehouse vessel can hold roughly 9 liters of cat waste.
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Hiroshi is 6 years older than Kaido. Saitama is three times as old as Hiroshi. The sum of their three ages is 79 Find the ratio of Kaido's age to Hiroshi's age to Saitama's age. (Use the letter x for any algebraic method) 14°C Heavy rain soon Optional working Search Answer: Total marks: 4 hp
The ratio of Kaido's age to Hiroshi's age to Saitama's age is 5:8:24.
How to find the ratio of there ages?Hiroshi is 6 years older than Kaido. Saitama is three times as old as Hiroshi. The sum of their three ages is 79.
Therefore, the ratio of Kaido's age to Hiroshi's age to Saitama's age can be calculated as follows:
Hence,
let
x = Kaido age
Hiroshi age = 6 + x
Saitama age = 3(6 + x) = 18 + 3x
Therefore,
x + 6 + x + 18 + 3x = 79
5x = 79 - 24
5x = 50
x = 50 / 5
x = 10
Therefore,
x = Kaido age = 10 years
Hiroshi age = 6 + x = 6 + 10 = 16 years
Saitama age = 3(6 + x) = 18 + 3x = 18 + 3(10) = 48 years
Hence, the ratio of there ages are as follows:
10:16:48
Let's divide through by 2
5:8:24
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A student usally saves $20 a month. He would like to reach a goal of saving $350 in 12 months the students writes the equation 350=12(x + 20) to represent this situation
Answer: x=55/6 or 55 over 6
Step-by-step explanation: Step 1: Distribute:
- 350= 12(x+20)
- 350= 12x + 240
Step 2: Subtract 240 from both sides:
- 350-240= 12x+240-240
Step 3: Simplify:
Subtract the numbers: 350-240= 12x+240-240= 110=12x+240-240
Subtract again: 110=12x+240-240= 110=12x
Step 4: Divide both sides by the same factor:
110=12x= 110/12= 12x/12
Step 5: Simplify:
- Divide the numbers: 110/12=12x/12= x=55/6=12x/12
- Cancel terms that are in both the numerator and denominator: 55/6=12x/12= 55/6=x
- Move the variables to the left: 55/6=x = x=55/6
Answer: x=55/6 or 55 over 6
in each hand of a card game, there is a 54% chance of winning 3 points and a 46% chance of losing 4 points. is the game a fair game? explain
Answer: yes, the game is fair.
Step-by-step explanation:
The game is fair because:
a. you are playing with multiple players, and they have equal odds
b. the odds of winning are higher, so there is balance since you earn less points.
Give brainliest please!
W X Y Z is a kite. Find the measure of angle W.
The measure of angle W in the kite WXYZ is 0 degrees.
To find the measure of angle W in the kite WXYZ, we can use the properties of kites. In a kite, the two opposite angles formed by the intersection of the diagonals are equal. Let's denote the measure of angle W as "x."
Step 1: Start with the given information that WXYZ is a kite.
Step 2: Recall that the diagonals of a kite intersect at right angles. Let's label the intersection point of the diagonals as point P.
Step 3: Draw the diagonals WX and YZ, which intersect at point P.
Step 4: Recognize that angles WXP and ZYP are congruent. Therefore, the measure of angle WXP is also x.
Step 5: Observe that the sum of the angles in a triangle is 180 degrees. Since triangle WXP is a triangle, we can write the equation: x + 90 + 90 = 180.
Step 6: Simplify the equation: x + 180 = 180.
Step 7: Subtract 180 from both sides: x = 0.
Step 8: Analyze the result. The measure of angle W, denoted by x, is equal to 0 degrees.
Therefore, the measure of angle W in the kite WXYZ is 0 degrees.
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A pitcher contains 13 cups of iced tea. You drink 1. 75 cups of the tea each morning
and 1. 5 cups of the tea each evening. When will you run out of iced tea?
The duration of days after which the individual will run out of iced tea is 4 days, under the condition that a pitcher can hold 13 cups of iced tea. The individual drinks 1. 75 cups of the tea every morning and 1. 5 cups of the tea each evening.
So to solve this problem we have to relie on the basic principles of division
Total amount of tea consumed per day = 1.75 cups (morning) + 1.5 cups (evening)
= 3.25 cups
Total amount of tea in the pitcher = 13 cups
Number of days before running out of iced tea = 13 cups / 3.25 cups per day
= 4 days
Then, the duration of days until the iced tea runs out is 4 days.
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PLEASE HELP
A survey was done that asked people to indicate whether they prefer saltwater fishing or freshwater fish in the results of the survey are shown in the two way table
complete a relative frequency table from this data.
enter your answer is rounded to the nearest 10th of a percent in the boxes
According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.
To find the percentage of people that make up each group, we must find the total number of people who were surveyed:
228 + 245 + 242 + 285 = 1,000
Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:
Age 30 and younger and Saltwater fishing:
1,000 = 100%
228 = ?%
Hence, We get;
228 x 100 / 1,000 = 22.8%
Age 30 and younger and Freshwater fishing:
1,000 = 100%
245 = ?%
245 x 100 / 1,000 = 24.5%
Over 30 years old and Saltwater fishing:
1,000 = 100%
242 = ?%
242 * 100 / 1,000 = 24.2%
Over 30 years old and Freshwater fishing:
1,000 = 100%
285 = ?%
285 * 100 / 1,000 = 28.5%
To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:
Age ranges
228 + 245 = 473
242 + 285 = 527
1,000 = 100%
473 = ?%
473 * 100 / 1,000 = 47.3%
1,000 = 100%
527 = ?%
527 * 100 / 1,000 = 52.3%
Fishing mode preferences
228 + 242 = 470
245 + 285 = 530
1,000 = 100%
530 = ?%
530 * 100 / 1,000 = 53%
1,000 = 100%
547 = ?%
470 * 100 / 1,000 = 47%
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A tennis court in the shape of a rectangle has an area of 7200 square
feet. One pair of sides measures twice the length of the other pair of
sides. What are the dimensions of the tennis court?
Answer:
60 x 120
Step-by-step explanation:
2x(x) = 7200
2[tex]x^{2}[/tex] = 7200 divide both sides by 2
[tex]x^{2}[/tex] = 3600
[tex]\sqrt{x^{2} }[/tex] = [tex]\sqrt{3600}[/tex]
x = 60
This is one of the dimensions. The other dimension is twice 60 or 120.
a = lw
a = (60)(12)
a = 7200
Helping in the name of Jesus.
Find area bounded by y = in(x)/x, y = 0, and x = e¹⁹. (Express numbers in exact form. Use symbolic notation and fractions where needed.)
The area bounded by y = in(x)/x, y = 0, and x = e¹⁹ is 361/2 square units.
To find the area bounded by the curves y = ln(x)/x, y = 0, and x = e¹⁹, we need to integrate the function ln(x)/x with respect to x over the interval [1, e¹⁹].
∫[1, e¹⁹] ln(x)/x dx
To solve this integral, we use integration by parts with u = ln(x) and dv/dx = 1/x dx.
∫ ln(x)/x dx = ∫u dv = uv - ∫v du
where v = ln(x) and du/dx = 1/x dx.
∫ ln(x)/x dx = ln(x)^2/2 |[1, e¹⁹] - ∫[1, e¹⁹] (1/x)(ln(x)/2) dx
Evaluating the definite integral at the limits gives:
ln(e¹⁹)²/2 - ln(1)²/2 = 361/2
So the area bounded by the curves y = ln(x)/x, y = 0, and x = e¹⁹ is 361/2 square units.
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Find point p in terminal sides 2,-5
The location of the point P that is 2/5 of the way from A to B on the directed line segment AB is A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).
How do we determine the location of a point within a line segment?A line segment is generated from two distinct points set on a plane, The location of the point P within the line segment can be found by means of the following vectoral formula below:
P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)], 0 < k < 1 (1)
Where:
A(x, y) = Initial point
B(x, y) = Final point
k = Distance factor
We have that A(x, y) = (- 8, - 2), B(x, y) = (6, 19) and k = 2/5, then the location of the point P is:
P(x, y) = (- 8, -2) + (2/5) · [(6, 19) - (- 8, -2)]
P(x, y) = (- 8, -2) + (2/5) · (14, 21)
P(x, y) = (- 12/5, 32/5)
In conclusion, the location of the point P that is 2/5 of the way from A to B on the directed line segment AB is A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).
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#complete question:
Find the point P that is 2/5 of the way from A to B on the directed line segment AB if A (-8, -2) and B (6, 19).
It has been reported that 48% of teenagers play video games on their phones. A
random sample of 60 teenages is drawn. Find the probability that the proportion of
teenagers in the sample who play videos games on their phone is less than 0. 489
The probability is less than 0.489 is approximately 0.8980 or 89.80% that the proportion of teenagers in the sample who play videos games on their phone is less than 0. 489
First, we need to calculate the mean and standard deviation of the sampling distribution of the sample proportion:
Mean = p = 0.48
Standard deviation = sqrt((p*(1-p))/n) = sqrt((0.48*0.52)/60) = 0.071
Next, we need to standardize the sample proportion using the formula:
z = (sample proportion - population proportion) / standard deviation
z = (0.489 - 0.48) / 0.071 = 1.27
Finally, we need to find the probability that the standardized sample proportion is less than 1.27 using a standard normal distribution table or calculator. This probability is approximately 0.8980.
Therefore, the probability that the proportion of teenagers in the sample who play video games on their phones is less than 0.489 is approximately 0.8980 or 89.80%.
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Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
Point B is the image of point A under a rotation about the origin.
Describe Rotation?Rotation is a transformation in which an object or a point is turned around a fixed point or a fixed axis. The fixed point or axis is called the center of rotation, and the angle of rotation specifies the amount and direction of the turn. When an object is rotated, its orientation changes but its shape and size remain the same.
For example, if you rotate a square by 90 degrees around its center, it will look the same as before, but it will be oriented differently. Similarly, if you rotate a point in a coordinate system around the origin, its position will change, but its distance from the origin will remain the same.
Rotations are commonly used in geometry, physics, and engineering to describe the motion of objects, such as the rotation of the Earth around its axis or the rotation of a wheel on an axle. They are also used in computer graphics to create animations and in robotics to control the movement of robotic arms and other devices.
When point A is rotated about the origin to form point B, the distance between the origin and each point remains the same. The direction from the origin to point A and the direction from the origin to point B are related by the angle of rotation. Specifically, point B is the image of point A under a rotation about the origin.
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7. For the function f(x) = -5.5 sin x + 5.5 cos x on a. Find the intervals for which f is concave up and concave down on [0,2π]. CCUP_________ CC DOWN______
b. Identify the coordinates of any points of inflection for fon [0,2π].
a. For the function, the interval for which f is concave down on [0,2π] is (π/4, 5π/4).
CCUP: (0, π/4) and (5π/4, 2π)
CCDOWN: (π/4, 5π/4)
b. The coordinates of the points of inflection are (π/4, 2.45) and (5π/4, -5.95).
a. To find the intervals for which f is concave up and concave down on [0,2π], we need to determine the second derivative of the function f(x):
f(x) = -5.5 sin x + 5.5 cos x
f'(x) = -5.5 cos x - 5.5 sin x
f''(x) = 5.5 sin x - 5.5 cos x
To find where f is concave up (CCUP), we need to find where f''(x) > 0. Thus, we solve the inequality:
5.5 sin x - 5.5 cos x > 0
sin x > cos x
This inequality holds for 0 < x < π/4 and 5π/4 < x < 2π. Therefore, the intervals for which f is concave up on [0,2π] are (0, π/4) and (5π/4, 2π).
To find where f is concave down (CCDOWN), we need to find where f''(x) < 0. Thus, we solve the inequality:
5.5 sin x - 5.5 cos x < 0
sin x < cos x
This inequality holds for π/4 < x < 5π/4. Therefore, the interval for which f is concave down on [0,2π] is (π/4, 5π/4).
Thus, we have:
CCUP: (0, π/4) and (5π/4, 2π)
CCDOWN: (π/4, 5π/4)
b. To find the coordinates of any points of inflection for f on [0,2π], we need to find where the concavity changes, i.e., where f''(x) = 0 or is undefined. Thus, we solve the equation:
5.5 sin x - 5.5 cos x = 0
sin x = cos x
This equation holds for x = π/4 and x = 5π/4.
To determine the concavity at these points, we can examine the sign of f''(x) in the intervals surrounding these points:
For x in (0, π/4), f''(x) < 0, so f is concave down.
For x in (π/4, 5π/4), f''(x) > 0, so f is concave up.
For x in (5π/4, 2π), f''(x) < 0, so f is concave down.
Therefore, the points of inflection for f on [0,2π] are (π/4, f(π/4)) and (5π/4, f(5π/4)).
To find the coordinates of these points, we can substitute π/4 and 5π/4 into the original function:
f(π/4) = -5.5 sin(π/4) + 5.5 cos(π/4) = -2.75 + 5.5/√2 ≈ 2.45
f(5π/4) = -5.5 sin(5π/4) + 5.5 cos(5π/4) = -2.75 - 5.5/√2 ≈ -5.95
Therefore, the coordinates of the points of inflection are (π/4, 2.45) and (5π/4, -5.95).
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Pyramid A (shown below) has a volume of 20 cubic units and a height of 4 units. What is the area of its base? Rectangular pyramid Group of answer choices 80 square units 5 square units 45 square units 15 square units
The base area of the pyramid is 5 units squared.
How to find the base area?The pyramid has a volume of 20 cubic units and the height of the pyramid is 4 units.
Therefore, the area of the base can be calculated as follows:
Hence,
volume of the pyramid = base area × height of the prism
20 = base area × 4
Therefore,
base area of the pyramid = 20 / 4
base area of the pyramid = 5 units squared.
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A triangular frame is being built as the support for a ramp. The longest part of the
frame will sit on the ground. The second longest side is 2'3" and forms an 18°
angle with ground. The smallest side is 10" long. Determine the angle the
smallest side will make with the ground.
The smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.
To determine the angle the smallest side will make with the ground, we can use the law of sines. The law of sines states that for any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.
Let's label the sides of our triangle as follows:
The longest side (sitting on the ground) is side c
The second longest side is side b
The smallest side is side a
We know that side b is 2'3" long, which is equivalent to 27 inches. We also know that side a is 10 inches long. We can use the law of sines to solve for the angle opposite side a:
sin(A) = (a/c) * sin(C)
We can solve for sin(C) by using the fact that the sum of the angles in any triangle is 180 degrees:
C = 180 - A - B
We know that angle B is 18 degrees, so we can substitute that into our equation for C:
C = 180 - A - 18
C = 162 - A
Substituting this expression for C into our equation for sin(A), we get:
sin(A) = (a/c) * sin(162 - A)
We know that c is the longest side of the triangle and therefore opposite the largest angle. Since we are interested in the angle opposite side a, we can assume that angle A is the smallest angle in the triangle. We can use this assumption to simplify our equation for sin(A):
sin(A) = (a/c) * sin(162)
Plugging in the values for a, c, and sin(162), we get:
sin(A) = (10/27) * 0.951
sin(A) = 0.352
Taking the inverse sine of both sides, we get:
A = sin^-1(0.352)
A ≈ 20.6 degrees
Therefore, the smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.
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cos 14° -sin 14°/ cos 14° + sin 14° = cot 59
Answer:
To solve this trigonometric identity, we need to use the definitions of the trigonometric functions and some algebraic manipulation. Here's how we can do it:
cos 14° - sin 14°/ cos 14° + sin 14°
= (cos 14°/cos 14°) - (sin 14°/cos 14°)/(cos 14°/cos 14°) + (sin 14°/cos 14°) (multiplying the numerator and denominator of the second term by cos 14°)
= 1 - tan 14°/1 + tan 14° (using the definitions of cosine and sine, and dividing both terms by cos 14°)
= (1 - tan²14°)/(1 + tan 14°) (using the identity 1 + tan²θ = sec²θ)
= 1/cot 14° - cot 14° (using the definition of cotangent and simplifying the numerator)
= cot 90° - cot 14° (using the identity cot(90° - θ) = tan θ)
= cot (90° + 14°) (using the identity cot(θ + 90°) = -tan θ)
= cot 104°
Since cot(104°) = cot(180° - 76°) = -cot 76°, we can also write the final answer as -cot 76°.
Therefore, the given identity is true, and we have shown that:
cos 14° - sin 14°/ cos 14° + sin 14° = cot 59 = -cot 76°.
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Dolly went to the Walmart and he buy 14 teddy bears and 3 dolls for 158 $ and her sister went to the Gwinnett place mall and she buy 8 teddy bears and 12 dolls for 296 $. If they both buy same brand bears and dolls, then what is price of one teddy bear and one doll? (use matrices multiplication to solve system of equations. ) (Show work)
According to formed equations, the price of one teddy bear and one doll is $7 and $20 respectively.
Let us represent the teddy bear as x and dolls as y. Now, framing the equation for Dolly and Gwinnett.
Cost of teddy bear × number + cost of dolls × number = total expenditure
14x + 3y = 158 : equation 1
8x + 12y = 296 : equation 2
Divide the equation by 4
2x + 3y = 74 : equation 3
Subtraction equation 3 from equation 1
14x + 3y = 158
- 2x + 3y = 74
12x = 84
x = 84/12
x = $7
So, the cost of teddy bear = $7
keep the value of x in equation 3 to find the cost of y
2×7 + 3y = 74
14 + 3y = 74
3y = 74 - 14
3y = 60
y = 60/3
y = $20
Thus, the cost of teddy bear and dolls are $7 and $20.
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Y – 84 = -11(x – 6)
What is the point and slope