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2 years ago

Based on the graph, what is the initial value of the linear relationship?

Mathematics

2 answers:

Mekhanik [1.2K]2 years ago

8 0

Based on the given figure above which is a coordinate, the initial value of the linear relationship would be 5. The answer is the last option. It would be 5 since given that the line passes through the x-axis at negative 3 and the y-axis at 5. Hope this is the answer that you are looking for.

bonufazy [111]2 years ago

4 0

Answer-

The initial value of the linear relationship is 5.

Solution-

The initial value, also know as y-intercept, is the output value when the input of a linear function is zero. It is the y-value of the point where the line crosses the y-axis or x=0 line.

As the line passes through the y-axis at 5, i.e 5 is the y intercept of the line.

Therefore, the initial value of the linear relationship is 5.

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A rectangular plot of land measures 120 feet by 96 feet. Which dimensions could not represent the plot on a scale drawing?

Tresset [83]

The answer is b. if you divide 120 and 96, you would get 20 inches.

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2 years ago

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Grades on a standardized test are known to have a mean of 1000 for students in the United States. The test is administered to 45

vovikov84 [41]

Answer:

a. The 95% confidence interval is 1,022.94559 < μ < 1,003.0544

b. There is significant evidence that Florida students perform differently (higher mean) differently than other students in the United States

c. i. The 95% confidence interval for the change in average test score is; -18.955390 < μ₁ - μ₂ < 6.955390

ii. There are no statistical significant evidence that the prep course helped

d. i. The 95% confidence interval for the change in average test scores is 3.47467 < μ₁ - μ₂ < 14.52533

ii. There is statistically significant evidence that students will perform better on their second attempt after the prep course

iii. An experiment that would quantify the two effects is comparing the result of the confidence interval C.I. of the difference of the means when the student had a prep course and when the students had test taking experience

Step-by-step explanation:

The mean of the standardized test = 1,000

The number of students test to which the test is administered = 453 students

The mean score of the sample of students, $\bar{x}$ = 1013

The standard deviation of the sample, s = 108

a. The 95% confidence interval is given as follows;

$CI=\bar{x}\pm z\dfrac{s}{\sqrt{n}}$

At 95% confidence level, z = 1.96, therefore, we have;

$CI=1013\pm 1.96 \times \dfrac{108}{\sqrt{453}}$

Therefore, we have;

1,022.94559 < μ < 1,003.0544

b. From the 95% confidence interval of the mean, there is significant evidence that Florida students perform differently (higher mean) differently than other students in the United States

c. The parameters of the students taking the test are;

The number of students, n = 503

The number of hours preparation the students are given, t = 3 hours

The average test score of the student, $\bar{x}$ = 1019

The number of test scores of the student, s = 95

At 95% confidence level, z = 1.96, therefore, we have;

The confidence interval, C.I., for the difference in mean is given as follows;

$C.I. = \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm z_{\alpha /2}\sqrt{\dfrac{s_{1}^{2}}{n_{1}}+\dfrac{s_{2}^{2}}{n_{2}}}$

Therefore, we have;

$C.I. = \left (1013- 1019 \right )\pm 1.96 \times \sqrt{\dfrac{108^{2}}{453}+\dfrac{95^{2}}{503}}$

Which gives;

-18.955390 < μ₁ - μ₂ < 6.955390

ii. Given that one of the limit is negative while the other is positive, there are no statistical significant evidence that the prep course helped

d. The given parameters are;

The number of students taking the test = The original 453 students

The average change in the test scores, $\bar{x}_{1}- \bar{x}_{2}$ = 9 points

The standard deviation of the change, Δs = 60 points

Therefore, we have;

C.I. = $\bar{x}_{1}- \bar{x}_{2}$ + 1.96 × Δs/√n

∴ C.I. = 9 ± 1.96 × 60/√(453)

i. The 95% confidence interval, C.I. = 3.47467 < μ₁ - μ₂ < 14.52533

ii. Given that both values, the minimum and the maximum limit are positive, therefore, there is no zero (0) within the confidence interval of the difference in of the means of the results therefore, there is statistically significant evidence that students will perform better on their second attempt after the prep course

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2 years ago

Graph the line that represents a proportional relationship between Y And x where the unit rate of change of y with their respect

aksik [14]

Answer:

$y=\frac{3}{8}x$

The graph in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Remember that

The unit rate of change is the same as the slope

In this problem

$m=\frac{3}{8}$

The linear equation is equal to

$y=\frac{3}{8}x$

To graph the line we need two points

we have (0,0) because the line passes through the origin

Determine other point

assume a value of x and calculate the value of y

For x=8

$y=\frac{3}{8}(8)=3$

The other point is (8,3)

Plot the points and join them to draw the line

The graph in the attached figure

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2 years ago

A scale model of a merry-go-round and the actual merry-go-round are similar. a. How many times greater is the base area of the a

Kipish [7]

The area ratio is the square of the linear dimension ratio. So if the merry-go-round base is circular, the area contains the square of the radius. If a polygon, the base can be divided into triangles. The area of each triangle involves the product of the base length and the height, so since both have the same change of length, the product will square the scaling ratio.
Let’s say the ratio of corresponding lengths is x:1 then the ratio of the base areas is x²:1.
The question doesn’t provide any figures.
Let’s put some in as an example. Let the actual merry-go-round be circular with a diameter of 20 feet, while the model is one foot in diameter. So the ratio of the actual ride and it’s model is 20:1. The area of the base of the actual ride is 100π sq ft. The area of the base of the model is π/4 sq ft. We expect the ratio of these areas to be 20²=400. 100π/(π/4)=400.

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2 years ago

The density of a certain material is such that it weighs 1 pound for every 3.5 cups of volume. Express this density in tons per

AnnZ [28]

Answer:

0.02 tons per cubic foot

Step-by-step explanation:

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2 years ago