7 divided by three-eighths

The time of motion of the frog after it jumped into air is determined as 0.8 second.

The time of motion of the frog is determined by solving the quadratic equation as follows;

60t - 75t² = 0

60t = 75t²

divide both sides by t

60 = 75t

divide both sides by 75

60/75 = t

0.8 s = t

Thus, the time of motion of the frog after it jumped into air is determined as 0.8 second.

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To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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The confidence interval useful and what went wrong is: A. The Nearly Normal Condition is not met since the data are extremely right-skewed. Because of the one outlier at $3,000,000, the standard deviation is very large, which makes the confidence interval too wide to be useful. The confidence interval does not encompass all of the data values in the sample.

The reason why the analysts did not find the confidence interval useful is because the Nearly Normal Condition is not met since the data are extremely right-skewed. This is due to the outlier at $3,000,000, which has a significant impact on the data distribution.

                                           Because of this outlier, the deviation is very large, which makes the t-interval too wide to be useful. Additionally, the confidence interval does not encompass all of the data values in the sample, which also decreases its usefulness.

                                            To improve the accuracy of the confidence interval, a different statistical model should have been used, such as the Student's t-model instead of the Normal model, since the standard deviation is unknown.      

                                                   Finally, the Independence Assumption is not met since the sample of cardholders is not representative of the population, which further decreases the reliability of the results. Therefore, it is important to consider all of these factors when interpreting the results of a statistical analysis.

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The 99% confidence interval estimating the proportion of all Ford Fusion drivers who are women is (0.40685, 0.67007). The closest option to this interval is option 2) (0.40385, 0.67307).

The answer is option 1) (0.41689, 0.66003). To design a new advertising campaign, Ford Motor Company conducted a sample survey of 91 Fusion owners and found that 49 of them were women. To estimate the proportion of all drivers who are women, a confidence interval is calculated. The formula for calculating the confidence interval is:

sample proportion ± z*(standard error)

where z is the critical value for the desired confidence level and the standard error is calculated as:

sqrt((sample proportion*(1 - sample proportion))/sample size)

For a 99% confidence interval, the critical value is 2.576. Plugging in the values from the sample, we get:

sample proportion = 49/91 = 0.5385
sample size = 91

Using the formula above, we can calculate the standard error as:

sqrt((0.5385*(1 - 0.5385))/91) = 0.0625

Finally, we can plug in the values into the confidence interval formula:

0.5385 ± 2.576*0.0625

which gives us the interval (0.41689, 0.66003). Therefore, option 1) is the correct answer.

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The mean is calculated by summing up all the values in the distribution and dividing it by the total number of values, while the median is the middle value when the data is arranged in ascending or descending order.

Another difference is that the mean is affected by outliers, meaning that extreme values can greatly influence its value. On the other hand, the median is not affected by outliers, as it only depends on the position of the middle value.

Therefore, to summarize, the mean is influenced by all values in the distribution and is affected by outliers, while the median is only influenced by the middle value and is not affected by outliers.

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Answer:

I think it's B, I'm not sure though

Step-by-step explanation:

The expression for arctan(4/3) in terms of π is a tan(4/3) / π.

To express arc tan(4/3) in terms of π, we can use the relationship between the trigonometric functions and the unit circle.

The tangent function (tan) is defined as the ratio of the length of the side opposite an angle to the length of the adjacent side in a right triangle. The inverse tangent function, arctan, gives the angle whose tangent is a given value.

In this case, arctan(4/3) represents the angle whose tangent is 4/3. To express this angle in terms of π, we can consider the unit circle.

For arctan(4/3), we can construct a right triangle in the unit circle with the opposite side equal to 4 and the adjacent side equal to 3.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:

hypotenuse² = opposite² + adjacent²

hypotenuse² = 4² + 3²

hypotenuse²= 16 + 9

hypotenuse²= 25

hypotenuse = 5

Now, let's denote the angle whose tangent is 4/3 as θ. In the right triangle we constructed, the sine of the angle θ is given by opposite/hypotenuse, which is 4/5, and the cosine of the angle θ is given by adjacent/hypotenuse, which is 3/5.

Since the sine is positive and the cosine is positive in the first quadrant of the unit circle, we can conclude that arctan(4/3) corresponds to an angle in the first quadrant.

Therefore, arctan(4/3) can be expressed as:

arctan(4/3) = θ

Since θ corresponds to an angle in the first quadrant, we can write:

arctan(4/3) = θ = tan(4/3)

Note that a tan(4/3) is an angle measure in radians. To express it in terms of π, we need to divide atan(4/3) by π:

arctan(4/3) = θ = tan(4/3) / π

So, the expression for arctan(4/3) in terms of π is a tan(4/3) / π.

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Answer:

7.85

Step-by-step explanation:

8÷7= 1.14285714

9- 1.14285714= 7.85714286

C(76.1) represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.

The function C(F) = (5/9)(F - 32) is used to convert temperatures from degrees Fahrenheit to degrees Celsius. In this case, the input of the function is 76.1, which represents the temperature in degrees Fahrenheit. By substituting this value into the function, we can calculate the corresponding temperature in degrees Celsius.

To convert 76.1 degrees Fahrenheit to degrees Celsius, we plug it into the function: C(76.1) = (5/9)(76.1 - 32). By performing the necessary calculations, we can find the value of C(76.1), which represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. Therefore, the correct answer is the first option: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.


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Answer:$9

Step-by-step explanation:Here's what we know:

2 * 24 + 3s = 75 (the pants ($24 each) and shirts all together is $75)

What we need to do is isolate s

Simplify:

48 + 3s = 75

subtract 48 from both sides:

48 + 3s - 48 = 75 - 48

3s = 27

Divide by 3:

3s / 3 = 27 / 3

s = 9

Shirts are $9 each.

Answer:

2 x 24 = 48

48 - 75 = 27

27 ➗ 3 = 9

so the cost of 1 shirt is $9

Step-by-step explanation:

Answer:f(6)=72

Step-by-step explanation:

In mathematics, linear programming is a technique for maximizing operations under certain restrictions.

Using the mathematical modeling technique of linear programming, a linear function is maximized or minimized depending on the restrictions it is subjected to. This method has proved helpful for directing quantitative judgments in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

In mathematics, linear programming is a technique for maximizing operations under certain restrictions. Maximizing or minimizing the numerical value is the primary goal of linear programming. It comprises of linear functions that are subject to restrictions in the form of inequalities or linear equations.

Therefore, the correct answer is option A. this is a binding constraint, so there is no slack or surplus.

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x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

am I supposed to do the picture one or the you type

Answer:

See Explanation

Step-by-step explanation:

The graphs are not given; however, I'll answer with the graph equation and also attach the graph...

Represent the boxes with x and the cash received with y.

When x = 5

y = 13.50

When x = 10

y = 27

First, we need to get the slope of the graph.

m = (y2 - y1)/(x2 - x1).

m = (27 - 13.5)/(10 - 5)

m = 13.5/5

m = 2.7

Next, is to determine the graph equation using

y - y1 = m(x - x1)

y - 13.5 = 2.7(x - 5)

y - 13.5 = 2.7x - 13.5

y = 2.7x - 13.5 + 13.5

y = 2.7x..

See Attachment for graph

The slope of the regression line predicting y from x is 0.30.

Given that,

x              y

29          215

62          225

75          173

99         129

108        111

So, the coordinate points are (29, 215) and (62, 225)

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (225-215)/62-29)

= 10/33

= 0.30

Therefore, the slope of the regression line predicting y from x is 0.30.

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Answer:

4b.

Step-by-step explanation:

Answer:

answer = 21

Step-by-step explanation:

2n - 2 = 40

2n - 2 + 2 = 40 + 2

2n = 42

2n/2 = 42/2

n = 21

The coordinates of the point on the parabola y = (x - 6)² that is closest to the origin, correct to six decimal places, are approximately (2.437935, 14.218164).

Starting with x_0 = 1, we will iteratively apply Newton's method:

D(x) = √(x² + ((x - 6)²)²)

D'(x) = (1/2) * (x² + ((x - 6)²)²)^(-1/2) * (2x + 4(x - 6)³)

x_1 = x_0 - (D(x_0) / D'(x_0))

= 1 - (√(1² + ((1 - 6)²)²) / ((1/2) * (1² + ((1 - 6)²)²)^(-1/2) * (2(1) + 4(1 - 6)³)))

≈ 2.222222

The difference |x_1 - x_0| ≈ 1.222222 is greater than the desired tolerance, so we continue iterating:

x_2 = x_1 - (D(x_1) / D'(x_1))

≈ 2.424972

The difference |x_2 - x_1| ≈ 0.20275 is still greater than the desired tolerance, so we continue:

x_3 = x_2 - (D(x_2) / D'(x_2))

≈ 2.437935

The difference |x_3 - x_2| ≈ 0.012963 is now smaller than the desired tolerance. We can consider this as our final approximation of the x-coordinate.

To find the corresponding y-coordinate, substitute the final value of x into the equation y = (x - 6)²:

y ≈ (2.437935 - 6)²

≈ 14.218164

Therefore, the coordinates of the point on the parabola y = (x - 6)² that is closest to the origin, correct to six decimal places, are approximately (2.437935, 14.218164).

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Answer:

Step-by-step explanation:  

So briefly corresponding angles are angles that have the same position as another angle on the same figure. In your example there a multiple figures. The only pair that is NOT a corresponding angle is 1 and 11 because they have no lines in common they are not on the same figure! Hope this helps!

A ray has only one endpoint. A segment has two endpoints.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. In everyday language, a line segment with two points designating its ends is also referred to as a "line."

A ray and a segment are parts of a line.

This line segment has two fixed-length endpoints, A and B. The distance between this line segment's endpoints A and B is its length.

In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length.

A line segment's length can be calculated using either metric units like millimeters or centimeters or conventional units like feet or inches.

Ray has only one endpoint and the other ends go infinity.

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The graph that represents the situation is required.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Graphs are a popular tool for graphically illuminating data connections. A graph serves the objective of presenting facts that are either too many or complex to be fully expressed in the text while taking up less room.

Here the  X- axis denotes the number of hours and

Y- axis denotes the pounds of ice.

The given ordered pair is

\(\left(\frac{1}{2}, 1 \frac{1}{2}\right)=(0.5,1.5)\)

At zero hours the ice produced will be zero so, the third and fourth options are incorrect.

The only graph where the line passes through (0.5,1.5).

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Answer: D

Sorry if it is not.

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

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A) The measure of central tendency that best describes the data for time spent on the internet (min/day) is the median.

The median is the middle value in a set of data when the data is arranged in numerical order. In this case, the data arranged in numerical order is 38, 43, 48, 52, 65, 75, 120. The median value is 52, which is the middle value in the data set.

B) The measure of central tendency that best describes the data for the weight of books (oz) is the mode. The mode is the value that occurs most frequently in a data set. In this case, the data is 12, 10, 9, 15, 16, 10. The mode is 10, as it occurs twice in the data set and is the most frequent value.

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Answer:

Step-by-step explanation:

A: $0.1(x) + 25(y) = x + 25

B: $0.05(x) + $40(y) = x + 40

Because they didn't give a certain amount of miles traveled, we have to go with we do know.

**this is probably wrong.

Answer:

  (c)  105°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

  (5x +15) +(4x +3) = 180

  9x +18 = 180 . . . . . simplify

  x +2 = 20 . . . . . . . divide by 9

  x = 18 . . . . . . . . . . subtract 2

Angle RST is ...

  5x +15 = 5(18) +15 = 105

The measure of angle RST is 105°.

Answer:

2(7(9) + 9(10) + 7(10)) = 2(63 + 90 + 70) = 2(223) = 446 square meters

The p-value of the test claim is calculated as; p < 0.00001.

The z-score between two samples is expressed as;

z =  (x₁ – x₂)/√(σ₁²/n₁) + (σ₂²/n₂)

The parameters given are;

Sample mean 1: x₁ = 23.38

Sample mean 2: x₂ = 18.69

Sample standard deviation 1: σ₁ = ?

Sample standard deviation 2: σ₂ = ?

Sample size 1: n₁ = 40

Sample size 2: n₂ = 35

standard error = sample standard deviation /√(sample size)

σ₁ = 23.38/√40

σ₁ = 3.697

σ₂ = 18.69/√35

σ₂ =  3.159

Thus;

z = (23.38 – 18.69)/√(3.697²/40) + (3.159²/35)

z = (23.38 – 18.69)/0.792

z = 5.92

From online p-value from z-score calculator, p < 0.00001.

Thus, the p-value is less than the significance value and the results are significant and alternate hypothesis is accepted.

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The solution to the given initial-value problem is:

\(x(t) = $\frac{1}{2}$e$^{-2t}$ $\begin{bmatrix}2\ -1\end{bmatrix}$ + $\frac{3}{2}$e$^{5t}$ $\begin{bmatrix}1\ 3\end{bmatrix}$ + $\begin{bmatrix}2\ -1\end{bmatrix}$\).

To solve the given initial-value problem:

\(x' = $\begin{bmatrix}-1 & -2\ 3 & 4\end{bmatrix}$x + $\begin{bmatrix}5\ 5\end{bmatrix}$, x(0) = $\begin{bmatrix}-3\ 7\end{bmatrix}$\)

First, we find the solution to the homogeneous system:

\(x' = $\begin{bmatrix}-1 & -2\ 3 & 4\end{bmatrix}$x\)

The characteristic equation is:

\(|$\begin{bmatrix}-1-\lambda & -2\ 3 & 4-\lambda\end{bmatrix}$| = $\lambda^2-3\lambda-10 = 0$\)

Solving the above quadratic equation, we get:

\(\lambda_1 = -2$ and $\lambda_2 = 5$\)

The corresponding eigenvectors are:

\(v_1 = $\begin{bmatrix}2\ -1\end{bmatrix}$ and v_2 = $\begin{bmatrix}1\ 3\end{bmatrix}$\)

Therefore, the general solution to the homogeneous system is:

\(xh(t) = c1e$^{-2t}$ $\begin{bmatrix}2\ -1\end{bmatrix}$ + c2e$^{5t}$ $\begin{bmatrix}1\ 3\end{bmatrix}$\)

Next, we find the particular solution to the non-homogeneous system. We assume the solution to be of the form:

xp(t) = A

Substituting this in the given equation, we get:

\(A = $\begin{bmatrix}-1 & -2\ 3 & 4\end{bmatrix}$A + $\begin{bmatrix}5\ 5\end{bmatrix}$\)

Solving for A, we get:

\(A = $\begin{bmatrix}2\ -1\end{bmatrix}$\)

Therefore, the particular solution is:

\(xp(t) = $\begin{bmatrix}2\ -1\end{bmatrix}$\)

The general solution to the non-homogeneous system is given by:

\(x(t) = xh(t) + xp(t) = c1e$^{-2t}$ $\begin{bmatrix}2\ -1\end{bmatrix}$ + c2e$^{5t}$ $\begin{bmatrix}1\ 3\end{bmatrix}$ + $\begin{bmatrix}2\ -1\end{bmatrix}$\)

Using the initial condition \(x(0) = $\begin{bmatrix}-3\ 7\end{bmatrix}$,\)we get:

\(c_1$\begin{bmatrix}2\ -1\end{bmatrix}$ + c_2$\begin{bmatrix}1\ 3\end{bmatrix}$ + $\begin{bmatrix}2\ -1\end{bmatrix}$ = $\begin{bmatrix}-3\ 7\end{bmatrix}$\)

Solving for c₁ and c₂, we get:

\(c_1 = $\frac{1}{2}$ and c_2 = $\frac{3}{2}$\)

Therefore, the solution to the given initial-value problem is:

\(x(t) = $\frac{1}{2}$e$^{-2t}$ $\begin{bmatrix}2\ -1\end{bmatrix}$ + $\frac{3}{2}$e$^{5t}$ $\begin{bmatrix}1\ 3\end{bmatrix}$ + $\begin{bmatrix}2\ -1\end{bmatrix}$.\)

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