To find the probability that a student break lasts more than 7 minutes, we can use the z-score formula to standardize the break time and then use the standard normal distribution table or a calculator to find the probability. The probability that a student break lasts more than 7 minutes is approximately 0.3745 or 37.45%.
Step 1: Calculate the z-score.
The z-score formula is given by:
z = (X - μ) / σ
where X is the break time, μ is the mean, and σ is the standard deviation. In this case, X = 7 minutes, μ = 6.3 minutes,
and σ = 2.2 minutes. Plugging in these values:
z = (7 - 6.3) / 2.2 ≈ 0.32
Step 2: Find the probability using the standard normal distribution table or a calculator.
Now that we have the z-score, we can find the probability that a student break lasts more than 7 minutes. We want to find the area to the right of the z-score (0.32) since we are interested in break times longer than 7 minutes.
Using a standard normal distribution table or a calculator, we find that the area to the left of z = 0.32 is approximately 0.6255. However, we want the area to the right of z = 0.32, which is given by:
Area to the right of z = 1 - Area to the left of z
Area to the right of z ≈ 1 - 0.6255 ≈ 0.3745.
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What is the volume
of a pyramid with
sides of 22 inches and
30 inches, and a
of height of 15 inches?
Answer:
Base length=22
width=30
height=15
volume of pyramid= Lxwxh/3
=22x 30x 15/3 =3300in^3.
the shape below is made of two rectangles below 9cm,5cm,8cm
and 5cm
The area of the shape made of two rectangles is 85 square cm.
To find the area of the shape made of two rectangles with dimensions 9cm, 5cm, 8cm, and 5cm, follow these.
As per the given information,
Rectangle 1 has dimensions 9cm and 5cm.
Rectangle 2 has dimensions 8cm and 5cm.
For calculating the area of each rectangle using the formula:
Area = length × width
[tex]{Area\: of\: Rectangle} _1[/tex] = 9cm × 5cm = 45 square cm
[tex]{Area of Rectangle}_ 2[/tex] = 8cm × 5cm = 40 square cm
Add the areas of both rectangles to find the total area of the shape.
Total Area = [tex]{Area\: of\: Rectangle} _1[/tex] + [tex]{Area\: of\: Rectangle} _2[/tex]
Total Area = 45 square cm + 40 square cm
Total Area = 85 square cm.
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Question: The shape below is made of two rectangles joined together. 5 cm 9 cm 8 cm 5 cm Find the total area of the shape.
if a sample of shoppers showed stating that the supermarket brand was as good as the national brand, what is the p-value (to decimals)?
The p-value is 0.046, or 4.6% if a sample of shoppers showed stating that the supermarket brand was as good as the national brand.
To calculate the p-value, we use null and alternative hypotheses, as well as the test statistic and its distribution under the null hypothesis.
By the null hypothesis, we can say that supermarket brands are as good as national brands, and by the alternative hypothesis, we can say that supermarket brands are not as good as national brands.
This hypothesis can be tested by performing a two-tailed z-test for proportions.
In a sample of n shoppers, say that x shoppers say that supermarket brands are as good as domestic brands. The sample percentage can be calculated as follows:
p hat = x/n
in the null hypothesis, the sample proportion is equal to the hypothesized proportion, that is 0.5
The test statistic for a two-sided z-test for proportions is given by:
z = (p-hat - p0) / sqrt(p0(1-p0)/n)
where p0 is the hypothesized proportion under the null hypothesis.
In this case, we have:
p-hat = 0.5
p0 = 0.5
n = sample size
The null hypothesis states that the supermarket brand is as good as the national brand, so we would expect the proportion of shoppers who state this to be 0.5.
If the test statistic z falls in the rejection region (i.e., if |z| > 1.96 for a significance level of 0.05),
we would reject the null hypothesis and conclude that there is evidence to suggest that the supermarket brand is not as good as the national brand.
If the test statistic falls in the non-rejection region (i.e., if |z| <= 1.96 for a significance level of 0.05),
we would fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that the supermarket brand is not as good as the national brand.
To calculate the p-value, we need to find the probability of getting a test statistic as extreme or more extreme than the one we observed, assuming the null hypothesis is true.
For a two-tailed test, the p-value is twice the observed area of the tails above the absolute value of the test statistic.
Assuming the sample size is large enough, the distribution of the test statistic can be approximated as a standard normal distribution under the null hypothesis.
Suppose in a sample of 100 shoppers, 50 said that supermarket brands are as good as domestic brands. after that:
p hat = 0.5
p0 = 0.5
n=100
The test statistic is:
z = (p hat - p0) / sqrt(p0(1-p0)/n) = 0 / sqrt(0.5 * 0.5 / 100) = 0
The p-value is the probability that the test statistic is extreme or more extreme than 0. This is the probability of getting further away from the 50/100 ratio or 0.5 in either direction.
p-value = P(p hat <= 0.4 or p hat >= 0.6) = 2 * P(p hat <= 0.4) = 2 * P(Z <= ( 0.4 - 0.5) / sqrt (0.5 * 0.5 / 100) ) = 2 * P(Z <= -2) ≈ 0.046
where Z is a standard normal random variable.
Therefore, the p-value is approximately 0.046, or 4.6%.
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which of the following is not a correct statement about the binomial and poisson distributions? group of answer choices when using the binomial distribution table, the number of trials must be greater than 30. the poisson distribution represents the random arrival of events per unit of time or space. only two outcomes are possible in a binomial situation. to use the poisson distribution tables, mu must be known or be able to be calculated.
The statement which is "The binomial distribution table, the number of trials must be greater than 30." is the not correct statement related to the binomial and Poisson distributions. Hence option a is the right choice.
a. "When using the binomial distribution table, the number of trials must be greater than 30"This is an incorrect statement.
There is no such rule stating that the number of trials must be greater than 30 for the binomial distribution.
b. "The Poisson distribution represents the random arrival of events per unit of time or space" This is the correct statement.
The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space, given a constant average rate of occurrence.
c. "Only two outcomes are possible in a binomial situation" This is correct statement.
A binomial distribution represents the number of successes in a fixed number of trials, each with only two possible outcomes (success or failure).
d. To use the Poisson distribution tables, mu must be known or be able to be calculated: This is correct.
In order to use the Poisson distribution tables, the mean number of events (represented by the symbol µ) must be known or calculable.
So, option a is right choice.
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Question :-
Which of the following is not a correct statement about the binomial and Poisson distributions?
a. When using the binomial distribution table, the number of trials must be greater than 30.
b. The Poisson distribution represents the random arrival of events per unit of time or space.
c. Only two outcomes are possible in a binomial situation.
d. To use the Poisson distribution tables, Mu must be known or be able to be calculated
at a financial services company, the mean percent allocation for bonds in a retirement portfolio is 26.9 percent with a population standard deviation of 3.6 percent. a random sample of 35 retirement plan participants was taken and the probability that the mean bond percent for the sample will be at least 28 percent was determined. was the probability a left-tail, right -tail or interval probability? what is the probability that the mean bond percent for the sample will be at least 28 percent? select all that apply below. select the two correct answers that apply below. you may use a calculator or the portion of the z-table given below. round your answer to three decimal places if necessary.
The probability in question is a right-tail probability because it is asking for the probability that the mean bond percent for the sample will be at least 28 percent, which is greater than the mean of 26.9 percent.
To calculate the probability, first find the z-score:
z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
z =[tex] (28 - 26.9) / (3.6 / sqrt(35))[/tex]
z = [tex] 1.1 / (3.6 / 5.916)[/tex]
z =[tex] 1.1 / 0.608[/tex]
z ≈ [tex] 1.809[/tex]
Using the z-table, the area to the left of this z-score is 0.965. Since we are looking for the right-tail probability, we need to subtract this value from 1:
Probability = 1 - 0.965
Probability ≈ 0.035
Thus, the probability that the mean bond percent for the sample will be at least 28 percent is approximately 0.035. The correct answers are right-tail probability and 0.035.
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Write the equation for the line through the given Q-points in slope-intercept form.
8. (5, 21) and (11,3)
9. (4, 8) and (12, 20)
As a result, the slope-intercept form equation for the line through points (5, 21) and (11, 3) is:
y = -3x + 36
Therefore, the equation of the line through (4, 8) and (12, 20) in slope-intercept form is:
y = (3/2)x + 2
The slope of the line must first be determined using the following formula to determine the equation of a line through two points in slope-intercept form:
slope[tex](m) =\frac {(y2 - y1)}{(x2 - x1)}[/tex]
where the coordinates for two points are (x1, y1) and (x2, y2).
The line's slope-intercept form is thus applicable, and it is as follows:
y = mx + b
where b is the y-intercept and m is the slope that we just discovered.
We possess
slope [tex](m) = \frac{(3-21)}{ (11-5)}[/tex],
m = -3
So, using one of our points, we can determine b:
y-21=-3(x-21)
As a result, the slope-intercept form equation for the line through points (5, 21) and (11, 3) is:
y = -3x + 36
9) (4, 8) and (12, 20)
The slope is
[tex]m= \frac{20-8}{12-4}\\m=\frac{12}{8}=\frac{3}{2}[/tex]
equation is (y-8)=1.5(x-4)
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For each of the figures write an absolute value equation that has the following solution set.
The absolute value equation that has the solution set with digits -18, 0, and X on a number line is :
|X| = X if X ≥ 0
|X| = -X if X < 0
What do you mean by term Equation?An equation is a mathematical statement that shows the equality of two expressions. It typically includes one or more variables (represented by letters) and may also include constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
If the solution set for the absolute value equation has digits -18, 0, and X on a number line, then the equation must have two separate cases: one where X is positive and one where X is negative. We can write the absolute value equation as:
|X| = X for X ≥ 0
|X| = -X for X < 0
To include the values -18 and 0 in the solution set, we need to check each case separately:
|X| = X if X is greater than 0 or zero. The equation X = a must therefore be resolved, where an is either -18 or 0. As X 0 is satisfied by only one value in the solution set, the case's solution is X = 0.
Example 2: X < 0
When X is negative, |X| equals -X. So, we must find a, where an is either -18 or 0, to solve the equation -X = a. This case's solution is X = 18, as it is the only value in the solution set that satisfies the condition X 0.
As a result, the absolute value equation whose answer is represented by the numbers -18, 0 and X on a number line is:
|X| = X if X ≥ 0
|X| = -X if X < 0
or
|X| = 0 if X = 0
|X| = 18 if X < 0
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The points
�
(
−
7
,
8
)
,
�
(
−
1
,
9
)
M(−7,8),N(−1,9), and
�
(
0
,
3
)
O(0,3) form a triangle. Find the desired slopes and lengths, then fill in the words that characterize the triangle.
Based on the lengths of the sides, we can see that the triangle is scalene. Based on the slopes of the sides, we can see that the triangle is acute since all the slopes are negative or less than 1.
What is triangle?A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
To find the desired slopes and lengths of the triangle formed by the points M(-7, 8), N(-1, 9), and O(0, 3), we can use the distance formula and the slope formula.
Distance formula:
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Using this formula, we can find the lengths of the sides of the triangle:
Length of MO:
d(MO) = √((0 - (-7))² + (3 - 8)²) = √(7² + 5²) = √(74)
Length of NO:
d(NO) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)
Length of MN:
d(MN) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)
Slope formula:
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Using this formula, we can find the slopes of the sides of the triangle:
Slope of MO:
m(MO) = (3 - 8) / (0 - (-7)) = -5/7
Slope of NO:
m(NO) = (9 - 8) / (-1 - (-7)) = 1/6
Slope of MN:
m(MN) = (9 - 8) / (-1 - (-7)) = 1/6
Characterization of the triangle:
Based on the lengths of the sides, we can see that the triangle is scalene (no two sides have the same length). Based on the slopes of the sides, we can see that the triangle is acute (all angles are less than 90 degrees) since all the slopes are negative or less than 1. Additionally, we can see that the side MO is the longest side of the triangle, and since the slope of MO is negative, we can conclude that the angle opposite side MO is the largest angle in the triangle.
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what’s the answer????
Answer:
The vertex of the quadratic function f(x) = -2x^2 + 8x is (2, 8).
Step-by-step explanation:
To find the vertex of the quadratic function f(x) = -2x^2 + 8x, we first need to find the x-coordinate of the vertex using the formula:
x = -b / 2a
where a = -2 and b = 8. Substituting these values, we get:
x = -8 / 2(-2) = 2
Now, to find the y-coordinate of the vertex, we can substitute this value of x back into the equation: f(2) = -2(2)^2 + 8(2) = 8
can yall help me with this pls?
Answer:
Step-by-step explanation:
[tex]-\frac{8}{35}[/tex]
Given: w ∥ x and y is a transversal. prove: ∠3 and ∠5 are supplementary. parallel and diagonal lines w and x are cut by horizontal transversal y. on line w where it intersects with line y, 4 angles are created. labeled clockwise, from uppercase left, the angles are: 1, 3, 4, 2. on line x where it intersects with line y, 4 angles are created. labeled clockwise, from uppercase left, the angles are: 5, 7, 8, 6. use the drop-down menus to complete the proof. given that w ∥ x and y is a transversal, we know that ∠1 ≅∠5 by the . therefore, m∠1 = m ∠5 by the definition of congruent. we also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the . by the , m∠3 m ∠1 = 180. now we can substitute m∠5 for m∠1 to get m∠3 m∠5 = 180. therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary.
we use the definition of supplementary angles again to conclude that ∠3 and ∠5 are supplementary.
To prove that ∠3 and ∠5 are supplementary, we can use the following steps:
Given: w ∥ x and y is a transversal.
∠1 ≅ ∠5 by the corresponding angles postulate.
By definition, ∠3 and ∠1 are a linear pair, so they are supplementary.
Therefore, m∠3 + m∠1 = 180 by the definition of supplementary angles.
Substituting m∠5 for m∠1, we get m∠3 + m∠5 = 180.
Therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary.
In step 1, we use the corresponding angles postulate, which states that when two parallel lines are cut by a transversal, the pairs of corresponding angles are congruent. In step 2, we use the definition of a linear pair, which states that when two angles form a line, they are supplementary. In step 3, we use the definition of supplementary angles, which states that the sum of two supplementary angles is 180 degrees. In step 4, we substitute m∠5 for m∠1, since we know that ∠1 ≅ ∠5. Finally, in step 5, we use the definition of supplementary angles again to conclude that ∠3 and ∠5 are supplementary.
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according to the text, 69 percent of all 6- to 11-year-olds in the united states: please choose the correct answer from the following choices, and then select the submit answer button. answer choices are harmonious and stable. are chronically poor. live with one parent. live with two parents.
Two parents are present in 69% of all families with children ages six to eleven. Option d is correct.
Option d is the correct choice, which states that 69 percent of all families with children aged six to 11 have two parents. This information is supported by various studies and statistics, which have consistently shown that the majority of families in the United States consist of two-parent households. While single-parent families do exist, they are less common than families with two parents.
This information is important in understanding the dynamics and structure of families in the US, as well as in developing policies and programs that support and strengthen families.
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--The complete question is, According to your text, 69 percent of all families with children aged six to 11:
a) are harmonious and stable.
b) have one parent.
c) are chronically poor.
d) have two parents.
Link to the text is, open.maricopa.edu/devpsych/chapter/chapter-9-early-adulthood/--
what is the ordered pair of 2x-5y ≥10
Step-by-step explanation:
This is the equation for a AREA greater than or equal to a line
2x-10 >= 5y
y <= 2/5 x -2 there are infinite answers
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
the correct answer is: Wide Awake, with a median value of 4.5 gallons. Thus, option A is correct.
What is the medians?Based on the data given, the correct measure of center to determine which shop typically sells the most amount of coffee per hour would be the median.
Calculating the medians for both coffee shops:
For Coffee Ground:
[tex]1.5, 12, 11, 9.5[/tex] (sorted data)
Median [tex]= (11 + 12)/2 = 11.5[/tex]
For Wide Awake:
[tex]2.5, 18, 3, 6[/tex] (sorted data)
Median [tex]= (3 + 6)/2 = 4.5[/tex]
Comparing the medians, we can see that Wide Awake has a median value of 4.5 gallons, which is higher than the median value of 11.5 gallons for Coffee Ground.
Therefore, the correct answer is: Wide Awake, with a median value of [tex]4.5[/tex] gallons.
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Answer: Coffee Ground typically sells more coffee per hour than Wide Awake.
Step-by-step explanation:
Given that:
Coffee ground :
Hour 1: 1.5
Hour 2: 20
Hour 3: 3.5
Hour 4: 12
Hour 5: 2
Hour 6: 5
Hour 7: 11
Hour 8: 7
Hour 9: 2.5
We add up all of these numbers and divide by the total number of hours to find the mean:
(1.5 + 20 + 3.5 + 12 + 2 + 5 + 11 + 7 + 2.5) / 9 = 7.222
therefore mean is 7.2
Median:
Arranging them in Ascending or descending order, we get:
1.5,2,2.5,3.5,5,7,11,12,20
As we know, The median of discrete data is :
((n+1)/2)th element if the number of elements is odd
Average of (n/2) th and ((n+1)/2)th element if the number of elements is even. the value
Here the number of elements is odd, so the median is:
((n+1)/2)th =(9+1)/2 = 5th element
i.e., the median is 5.
Wide Awake:
Given that:
Hour 1: 2.5
Hour 2: 10
Hour 3: 4
Hour 4: 18
Hour 5: 4
Hour 6: 3
Hour 7: 6.5
Hour 8: 5
Hour 9: 15
We add up all of these numbers and divide by the total number of hours to find the mean:
(2.5 + 10 + 4 + 18 + 4 + 3 + 6.5 + 5 + 15) / 9 = 7.056
therefore mean is 7.1
Median:
Arranging them in Ascending or descending order, we get:
3,6.5,5,4,4,2.5,10,18,15
Here the number of elements is odd, so the median is:
((n+1)/2)th =(9+1)/2 = 5th element
i.e., the median is 4.
As we can observe, the mean and median of coffee ground is high.
So we can conclude that the Coffee Ground shop has sold more coffee.
The radius of a circle is 4 meters. What is the circle's area? r=4 m
Answer:
Step-by-step explanation:
Luther's class recorded how many states each student has visited.
States visited
) Number of states
) Name
Luther
Amelia
Oliver
Katie
Emilio
Joe
Dustin
2
5
2
3
1
) What is the median of the numbers?
The median of the given numbers is 2.5.
its formula and examples are explained. In Mathematics, the median is defined as the middle value of a sorted list of numbers. The middle number is found by ordering the numbers. The numbers are ordered in ascending order. Once the numbers are ordered, the middle number is called the median of the given data set.
Given, Number of states visited by the students in Luther's class are:
Luther - 2 states
Amelia - 5 states
Oliver - 2 states
Katie - 3 states
Emilio - 1 state
Joe - 0 states
Dustin - 0 states
Arranging these numbers in ascending order, we get:
0, 0, 1, 2, 2, 3, 5
The median is the middle number when the numbers are arranged in order.
As there are an odd number of numbers, there is only one number that is exactly in the middle, which is 2.
Therefore, the median of the given numbers is 2.5.
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a 2-column table with 4 rows. column 1 is labeled situation with entries increasing, difference, finding part of a total, sharing or grouping. column 2 is labeled operation with entries , minus, times, divided by. filipe practiced 12 fewer hours than bianca. if filipe practiced for 16 hours, how long did bianca practice? bianca practiced for hours.
Bianca practiced 28 hours a day whereas Filipe practiced 12 fewer hours than Bianca, if Filipe practiced for 16 hours
below are the situations and the operations used
Rising = +
difference = -
to find the part of the grand total= ÷
Sharing or Grouping = *
Since "Filipe trained 12 hours less than Bianca" and "Filipe trained 16 hours", we can use rising(+) to find the amount of time Bianca trained.
it is calculated by using the following formula
Bianca's training time = Filipe's training time + 12
Bianca practice hours = 16 + 12
Bianca Practice Hours = 28
So Bianca practiced 28 hours a day.
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Simon is taking A trip from Orlando Fl, to sacremento, California which is about 2,804 miles. On average his car gets 48.6 miles for every 2 gallons of gas. How many gallons of gas does Simon need for his trip? Round your answer to the nearest tenth.
Simon needs approximately 48.6 gallons of gas for his trip from Orlando, FL to Sacramento, CA.
To calculate the number of gallons of gas Simon needs for his trip, you can use the following formula:
Gallons = Miles / Miles per gallon
First, convert the distance of 2,804 miles to miles per gallon by dividing by the car's average mileage per 2
gallons:2,804 / 48.6 = 57.75 mpg
Then, use this value to calculate the number of gallons of gas Simon needs for his trip:
Gallons = Miles / Miles per gallon
Gallons = 2,804 / 57.75
Gallons ≈ 48.6 gallons
Therefore, Simon needs approximately 48.6 gallons of gas for his trip from Orlando, FL to Sacramento, CA.
The answer should be rounded to the nearest tenth, so the final answer is 48.6 gallons.
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(1)/(x^(2)-6x)=(x)/(x^(2)-36)+2 Solve for x Please and thank you yall r life savers <3
Answer:
you need an equally
Step-by-step explanation:
Make x the subject of the formula 3x + a = b(x+5)
Answer:
x=[tex]\frac{5b-a}{3-b}[/tex]
Step-by-step explanation:
3x+a=b(x+5)
3x+a=bx+5b
3x-bx=5b-a
x(3-b)=5b-a
x=[tex]\frac{5b-a}{3-b}[/tex]
PLEASE HELP!!!!
Question: Write the equation of a line parallel to y = x -5 that goes through (7,0).
To find the equation of a line parallel to y = x - 5 that goes through (7,0), we need to use the fact that parallel lines have the same slope.
The slope of the line y = x - 5 is 1, since the coefficient of x is 1. Therefore, the slope of the parallel line we want to find is also 1.
Using the point-slope form of a line, we can write the equation of the parallel line as:
y - y1 = m(x - x1)
where (x1, y1) is the point (7,0) and m is the slope of the line, which we know is 1.
Plugging in the values, we get:
y - 0 = 1(x - 7)
Simplifying, we get:
y = x - 7
Therefore, the equation of the line parallel to y = x - 5 that goes through (7,0) is y = x - 7.
Answer:
y = x - 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 5 ← is in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes , then
y = x + c ← is the partial equation
to find c substitute (7, 0 ) into the partial equation
0 = 7 + c ( subtract 7 from both sides )
- 7 = c
y = x - 7 ← equation of parallel line
Pleaseeeee helppp meee
Answer: The missing side e is approximately 21.1 units long. So, the correct answer is E. None of the above
Solve this question for me
Answer:
d
Step-by-step explanation:
12 - 9.5 = 2.5
DO NOW:
The central angle ABC and central angle DEF are both right angles.
Do you think the LENGTH of the intercepted arc will have the same measurement? Why or Why not?
Answer:
Yes, the length of the intercepted arc will have the same measurement. When a central angle intercepts an arc of a circle, the measure of the angle is equal to the measure of the intercepted arc. In this case, both angles ABC and DEF are right angles, which means that they each intercept half of the circle. Therefore, the length of the intercepted arcs will be the same.
What fraction do you get from putting together 8 copies of the unit fraction 1/2? Explain how you found the numerator.
When you put together 8 copies of the unit fraction 1/2, you are essentially adding 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2.
To add fractions, you need to make sure the denominators are the same. In this case, all the fractions already have the same denominator of 2.
So, we can add the numerators together:
1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 8/2
Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
8/2 = 4
Therefore, putting together 8 copies of the unit fraction 1/2 gives us a fraction of 4/1, or simply 4.
Please help and show process for any of these questionss
Using equations,
8. The original dimensions of the rectangle are:
Length = 6m and Width = 2m.
9. The meter contains the following:
Value of nickels = 0.63
Value of dime = 2.26
Value of quarters = 0.21
10. Volume of the sphere is V. So, the value of r will be:
r = ∛ (3v/4π)
11. Solving for the linear equation we can get the value of m = -1
Define equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation.
In the question,
1. Let the length of the rectangle be = x.
Let the width of the rectangle be = w.
Given,
l = 3w
When the width is increased by 4 meters, (w + 4) meters is the width now.
Then, the rectangle becomes a square.
That means length and width are equal.
l = w+4
Using l from the 1st equation,
3w = w + 4
Subtracting w from both sides,
⇒ 3w - w = 4
⇒ 2w = 4
Diving both sides by 2,
⇒ w = 2 meters.
We know, l = 3w
l = 3 × 2
l = 6 meters.
2. Here,
Let nickels be n.
Let dimes be d.
Let quarters be q.
Given,
Triple the number of quarters as nickels, so:
3q = n
Solving this for q,
q = n/3
Dimes is one than double the times of nickels, so:
d = 2n + 1
Total value of coins = $3.10
So, n + d + q = 3.10
Substituting the value of q and d,
⇒ n + 2n + 1 + n/3 = 3.10
⇒ 3n + n/3 = 3.10 - 1
⇒ (9n+n)/3 = 2.10
⇒ 10n = 6.3
⇒ n =0.63.
We can now find,
d = 2n + 1
= 2 × 0.63 + 1
= 1.26 + 1
= 2.26
q = n/3
= 0.63/3
= 0.21
3. Given,
Volume of sphere,
V = 4/3 × π × r³
Solving for r,
Multiply 3/4 on both sides,
⇒ 3v/4 = π r³
Divide both sides by π,
⇒ 3v/4π = r³
Now, taking cube root on both sides we get,
r = ∛ (3v/4π)
4. Now given a linear equation,
[tex]y=-2x^{m+2}[/tex]
As the equation is a linear equation,
The value of (x, y) we can take as (0,0)
So, 1 = m +2
⇒ m = -1
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or watch a video clare streams a classical music station while she's doing chores on the weekends. here are the types of musical pieces she has listened to so far this weekend: overture, symphony, sonata, concerto, symphony, sonata, overture, symphony, opera, sonata, concerto based on the data, what is the probability that the next piece clare listens to will be a concerto?
If Clare streams a classical music station while doing chores, then probability that next piece will be a concerto is 2/11.
In order to calculate the probability that the next-piece Clare listens to will be a concerto, we count the number of concertos in the list of pieces she has already listened to and divide by the total number of pieces.
From the given list,
The total number of pieces of music = 11;
The number of concerto is = 2;
So, probability that next piece Clare listens to will be a concerto is:
⇒ P(concerto) = (number of concertos)/(total number of pieces);
⇒ 2/11
Therefore, the required probability is 2/11.
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The given question is incomplete, the complete question is
Clare streams a classical music station while she's doing chores on the weekends. here are the types of musical pieces she has listened to so far this weekend :
{overture, symphony, sonata, concerto, symphony, sonata, overture, symphony, opera, sonata, concerto}
Based on the data, What is the probability that the next piece Clare listens to will be a concerto?
What is the missing length?
area
A. 8 m
B. 4 m
C. 12 m
D. 18 m
Find w.
12 m
15 m
area = 114 m²
The missing length is 8m which is option A.
Length calculation.
To find the missing length, we need to use the formula for the area of a rectangle:
area = length x width
We are given the area as 114 m² and the width as 15 m. Let's substitute these values into the formula:
114 = length x 15
Solving for length, we get:
length = 114/15
length = 7.6
Therefore, the missing length is approximately 7.6 m.
However, none of the given answer choices match this value exactly. The closest answer is A. 8 m, which is off by only 0.4 m. Therefore, A. 8 m is the best answer choice.
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a line segment is divided so that the lesser part is to the greater part as the greater part is to the whole. if is the ratio of the lesser part to the greater part, then the value of
The problem involves a line segment divided into two parts in a specific ratio. The ratio of the length of the lesser part to the length of the greater part is found to be (√2 - 1).
Let the length of the whole line segment be x, and let y be the length of the greater part. Then the length of the lesser part is (x - y).
According to the problem statement, the ratio of the lesser part to the greater part is the same as the ratio of the greater part to the whole. Mathematically, we can write this as:
(x - y)/y = y/x
Simplifying this equation, we get:
x^2 - y^2 = y^2
x^2 = 2y^2
Taking the square root of both sides, we get:
x = y√2
Therefore, the value of the ratio of the lesser part to the greater part is:
(x - y)/y = (√2 - 1)
So, the answer will be (√2 - 1).
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HELP!!
Sally Brown bought a house with a 10% adjustable rate mortgage for 20 years. She was paying $9.66 monthly per thousand on her original loan. At the end of 4 years she owes the bank $55,000. Interest has now gone up to 12%, the bank can renew the mortgage at this rate or Sally can pay the full $55,000. Sally renews the mortgage and will pay $11.02 monthly per thousand on this loan.
What is the amount of the old and new monthly payment? What is the percent of increase in her new monthly payment (to the nearest tenth)?
old payment = $
new payment = $
% increase
As a result, the percentage decrease in her new monthly payment is 18.1%. (to the nearest tenth).
How to calculate the monthly payment?To begin, we must determine the original loan amount. Using the information provided, we can construct the following equation:
$55,000 = P(1 + 0.10)^4
P denotes the original loan amount.
When we solve for P, we get:
P = $38,574.09
The old monthly payment is calculated as follows:
$38,574.09 / 1000 x $9.66 = $372.64
We must now compute the new loan amount. Because Sally renewed her mortgage at a 12% interest rate, we can apply the same formula as before, but with a new time period of 16 years (since 4 years have already passed):
Now, we need to calculate the new loan amount. Since Sally renewed the mortgage at a 12% interest rate, we can use the same formula as before, but with a new time period of 16 years (since 4 years have already passed):
$55,000 = P(1 + 0.12)^16
Solving for P, we get:
P = $27,703.25
The new monthly payment can be calculated as:
$27,703.25 / 1000 x $11.02 = $305.23
To find the percent increase, we can use the following formula:
percent increase = ((new value - old value) / old value) x 100
Plugging in the values, we get:
percent increase = (($305.23 - $372.64) / $372.64) x 100 = -18.1%
So the percent of decrease in her new monthly payment is 18.1% (to the nearest tenth).
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