the question is in the picture :)

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e[tex].^{(-0.08(t-5)^2)}[/tex]  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e[tex].^{(-0.08u^2)}[/tex]  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e[tex].^{(-0.08u^2)}[/tex] du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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The height of the right triangular prism whose surface are is 480 square inches is equal to 9 inches.

Total surface area of the right prism = 480 square inches

Surface area of a right triangular prism is,

S = 2B + Ph

where S is the surface area,

B is the area of the triangular base,

P is the perimeter of the base,

and h is the height of the prism.

First, area of the triangular base.

Use the formula for the area of a triangle,

B = (1/2)bh

where b is the base of the triangle

and h is the height of the triangle.

⇒ B = (1/2) × 8 × 15

⇒ B = 60 in²

Since the base is a right triangle,

Use the Pythagorean theorem to find the length of the third side,

c² = 8² + 15²

⇒ c² = 64 + 225

⇒ c² = 289

⇒ c = 17

Perimeter of the base is,

⇒ P = 8 + 15 + 17

⇒ P = 40 inches

Surface area of right prism = 480

⇒ 2B +Ph = 480

⇒ 2×60 + 40h = 480

⇒40h = 480 - 120

⇒ h = 360 /40

⇒ h = 9 inches.

Therefore, the height of the right prism is equal to 9inches.

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The mathematical expression for the probability density function of the sales price is PDF(x) = 1/30,000 for 200,000 <= x <= 230,000.

Based on your question, we want to find the mathematical expression for the probability density function (PDF) of the sales price, given that the price is uniformly distributed between $200,000 and $230,000.

The function f(x) represents this probability density function, where the height of the function is 1/3000 (the width of the range of possible prices is 30,000, so the area under the function must equal 1), and it is 0 outside of that range.

For a uniform distribution, the probability density function is constant across the given range. To find the value of this constant, we can use the formula:

PDF(x) = 1 / (b - a)

where a is the lower limit of the range ($200,000), b is the upper limit of the range ($230,000), and x represents the sales price.

This is because the executive believes that the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and $230,000, which means that the probability is equal.

Plugging in the values, we get:

PDF(x) = 1 / (230,000 - 200,000)
PDF(x) = 1 / 30,000

So the mathematical expression for the probability density function of the sales price, if she leaves the house on the market for another month, is:

PDF(x) = 1/30,000 for 200,000 <= x <= 230,000

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Three different applications of linked list are mentioned here.

1. The most appropriate variation of a linked list for searching a list for a key and returning the keys of the two elements that come before it and the keys of the two elements that come after it would be a doubly linked list. A doubly linked list allows for bi-directional traversal, which means that it is easy to move forward and backward through the list. This makes it easy to locate the element with the key you are searching for and also retrieve the keys of the two elements that come before and after it.

2. The most appropriate variation of a linked list for creating a sorted list from a text file containing integer elements, one per line, sorted from smallest to largest would be a sorted linked list. A sorted linked list is a type of singly linked list that maintains its elements in a sorted order. As each element is added to the list, it is placed in its correct position to maintain the sorted order of the list.

3. The most appropriate variation of a linked list for a list that is short and frequently becomes empty, and is optimal for inserting an element into the empty list and deleting the last element from the list would be a circular linked list with header and trailer nodes. A circular linked list with header and trailer nodes is a type of singly linked list that has a special header node at the beginning of the list and a special trailer node at the end of the list. This type of linked list is optimal for inserting an element into an empty list because it is easy to update the header and trailer nodes to point to the new element. It is also easy to delete the last element from the list by updating the trailer node to point to the second-to-last element. Additionally, since this type of linked list is circular, it is easy to traverse the list repeatedly without having to worry about reaching the end of the list.

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Three different applications of linked list are mentioned here.

1. The most appropriate variation of a linked list for searching a list for a key and returning the keys of the two elements that come before it and the keys of the two elements that come after it would be a doubly linked list. A doubly linked list allows for bi-directional traversal, which means that it is easy to move forward and backward through the list. This makes it easy to locate the element with the key you are searching for and also retrieve the keys of the two elements that come before and after it.

2. The most appropriate variation of a linked list for creating a sorted list from a text file containing integer elements, one per line, sorted from smallest to largest would be a sorted linked list. A sorted linked list is a type of singly linked list that maintains its elements in a sorted order. As each element is added to the list, it is placed in its correct position to maintain the sorted order of the list.

3. The most appropriate variation of a linked list for a list that is short and frequently becomes empty, and is optimal for inserting an element into the empty list and deleting the last element from the list would be a circular linked list with header and trailer nodes. A circular linked list with header and trailer nodes is a type of singly linked list that has a special header node at the beginning of the list and a special trailer node at the end of the list. This type of linked list is optimal for inserting an element into an empty list because it is easy to update the header and trailer nodes to point to the new element. It is also easy to delete the last element from the list by updating the trailer node to point to the second-to-last element. Additionally, since this type of linked list is circular, it is easy to traverse the list repeatedly without having to worry about reaching the end of the list.

The solution is,  the distance between the two points to the (nearest tenth if nessacery) (7,3) (5,-4) is √53.

Here, we have,

We have information on the hypotenuse, now we must calculate the sides.

we have find the distance between the two points to the (nearest tenth if nessacery) (7,3) (5,-4)

we know that,

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

Using the x-coordinates of the points of the hypotenuse we obtain

7- (5) = 2

Using the y-coordinates of the points of the hypotenuse we obtain

3 - (-4) = 7

Now lets graph

Distance

d = √2² + 7²

  =√53

The distance would be √53.

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Based on the given information, I assume that you have a dataset and you are required to identify an appropriate transformed model for it. There are different types of transformations that can be applied to data such as logarithmic, square root, power, etc. The choice of the transformation depends on the nature of the data and the research question being addressed.

To identify an appropriate transformed model, you can start by examining the distribution of the response variable. If the distribution is skewed or has heavy tails, a transformation may be necessary to normalize the data. One way to assess the distribution is by creating a histogram or a density plot of the response variable.

Once you have identified an appropriate transformation, you can fit the transformed model to the data using regression analysis. The regression model will include the transformed response variable and one or more predictor variables.

After fitting the model, it is important to conduct the usual tests of model adequacy to ensure that the model is appropriate for the data. These tests include examining the residuals for normality, checking for homoscedasticity (i.e., equal variances), and testing for outliers and influential observations.

In summary, identifying an appropriate transformed model involves examining the distribution of the response variable and choosing a transformation that normalizes the data. Once the model is fitted, the usual tests of model adequacy should be conducted to ensure that the model is appropriate for the data.

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The average residential electrical power use refers to the amount of electrical energy consumed by households. It is typically measured in hundreds of watts per hour. By examining the provided table, you can identify the specific values for average power consumption in a residential setting.

According to the given table, the average residential electrical power use is measured in kilowatt-hours (kWh) per month, not hundreds of watts per hour. However, to convert it to the requested unit, we can divide the monthly average by the number of hours in a month (720 hours) and then multiply by 100 to get the average residential electrical power use in hundreds of watts per hour.

So, for example, if the monthly average is 600 kWh, the hourly average would be (600 kWh / 720 hours) x 100 = 83.33hundreds of watts per hour.

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If line passes through points (0,3) and (-3,0), then the slope calculated by Martin as "3" is incorrect because the correct slope is 1.

The "Slope" of a line is defined as measure of its steepness or inclination, and it describes how much the line rises or falls over a given distance in the horizontal direction.

To find the slope of a line passing through two points (x₁, y₁) and (x₂, y₂), we use the slope formula ⇒ slope = (y₂ - y₁) / (x₂ - x₁),

In this case, the two points are (0, 3) and (-3, 0). Substituting the coordinates in formula, we get:

⇒ slope = (0 - 3)/(-3 - 0),

⇒ Slope = -3/-3,

⇒ Slope = 1,

Therefore, the correct slope of the line passing through the points (0, 3) and (-3, 0) is 1, not 3 as Martin incorrectly said.

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The given question is incomplete, the complete question is

The line in the graph passes through the points (0,3) and (-3,0), Martin incorrectly said that the slope of this line is "3" . What is the correct slope?

Therefore, there are 4 vertices in this graph.

Let V be the number of vertices in the graph. The sum of the degrees of all vertices in an undirected graph is twice the number of edges, so in this case, the sum of degrees is 2 * 10 = 20.

We know that two vertices have degree 4, so the degrees of the remaining vertices must add up to 20 - 2 * 4 = 12.

If there are v vertices of degree 3, then the total degree contributed by those vertices is 3v, so we have:

3v + 2 * 4 = 20

3v = 12

v = 4

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The total amount of money in the purse was approximately 23 ducats. A man finds a purse with an unknown number of ducats in it. After he spends 1/4, 1/5, and 1/6 of the amount, 9 ducats remain. To find the initial amount in the purse, let's represent it as "x".

He spent (1/4)x, (1/5)x, and (1/6)x. The sum of these fractions plus the remaining 9 ducats equals the total amount:

(1/4)x + (1/5)x + (1/6)x + 9 = x

To solve this equation, first find a common denominator for the fractions, which is 60. Rewrite the equation with the common denominator:

(15/60)x + (12/60)x + (10/60)x + 9 = x

Combine the fractions:

(37/60)x + 9 = x

Now, isolate x on one side of the equation:

9 = (23/60)x

To find x, divide both sides by (23/60):

x = 9 / (23/60)

x = 9 * (60/23)

x = 540/23

Since x represents the number of ducats, it should be a whole number. So, we round it to the nearest whole number:

x ≈ 23

Therefore, there were approximately 23 ducats in the purse initially.

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Answer:

Step-by-step explanation:

first, you have to find the interest.

formula: Principal × Rate × Time ÷ 100

Principal - $1500

Rate - 5%

Time - 5 yrs

I=PRT÷100

= $1500 × 5% × 5yrs ÷ 100

= 1500 × 5 × 5÷ 100

= 37500 ÷ 100

= $ 375

That's the interest.

Amount = Principal + Interest

              = $ 1500 + $375

               =$ 1875

That's the total amount you'll have to pay back.

The Explanation for product of powers rule works and multiply exponents when raising a power to a power is shown below.

1. We know,

When the terms with the same base are multiplied, the powers are added.

So, 7² x 7³

Here the base is same (7) and multiplication applied here then the powers get added.

So, [tex]7^{2+3[/tex]

= [tex]7^5[/tex]

2. Now, According to the power to the power rule, when a base is raised to a higher power, the two powers are multiplied while the base stays the same.

So, (7²)³

= [tex]7^{2 .3}[/tex]

= [tex]7^6[/tex]

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The linear equation on the graph is the one in option D:

3y +x = -6

On the given graph, we can see a linear equation that passes through the the y-axis at the value y = -2

Then the line is of the form:

y = ax - 2

Where a is a negative value.

Also, notice that each 3 units moved in x, there is a decrease of 1 unit in the y-value, then the slope is -1/3, the line is:

y = (-1/3)*x - 2

We can rewrite that as:

3y = -x - 6

3y +x = -6

Then we can see that the correct option is D.

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Answer: L = 2 * (x + y) = 120

We frame the questions using the provided information:

1a. To help Max devise an equation for the area (A) of their campsite in terms of x and y, first recall that the area of a rectangle is given by the formula A = length * width.

Let x represent the length of the campsite and y represent the width. Now, write an equation for the area (A) in terms of x and y.

Answer: A = x * y

1b. To help Max devise an equation for the length of the yellow caution tape (L) in terms of x and y, first consider that the length of the tape should be equal to the perimeter of the campsite. The perimeter of a rectangle can be found using the formula P = 2 * (length + width). In this case, the length of the yellow caution tape (L) is given as 120 ft.

Let x represent the length of the campsite and y represent the width.

Write an equation for the length of the yellow caution tape (L) in terms of x and y.

Answer: L = 2 * (x + y) = 120

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Answer:

​

Answer: x>1

Step-by-step explanation:

9x-3>6

move the 3 over so: 9x>6+3, 9x>9

divide both sides by 9: (9x)/9>9/9, x>1

and bam, that's your answer x>1

The confidence interval around the sample mean value is (31.66, 35.26). This means that we can be 95% confident that the true mean age of all Native American inmates in state correctional facilities falls within this range.

Based on the information provided, the mean age of Native American inmates in state correctional facilities is 33.46, which is higher than the mean age of the entire inmate population (31.84). However, because this is only a sample of Native American inmates, we need to calculate a confidence interval to estimate the true mean age of all Native American inmates in state correctional facilities.

To create a 95% confidence interval, we will use the formula:

Confidence Interval = Sample Mean +/- (Critical Value x Standard Error)

The critical value for a 95% confidence interval with 111 degrees of freedom (n-1) is 1.98. The standard error can be calculated using the formula:

Standard Error = Standard Deviation / Square Root of Sample Size

Plugging in the values, we get:

Standard Error = 9.62 / Square Root of 112 = 0.91

Confidence Interval = 33.46 +/- (1.98 x 0.91) = 33.46 +/- 1.80

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The  Surface area of Composed figure is 1,341 square feet.

First, Surface Area of Prism

= (9 + 9 + 9)15 + (9)(6)

= 27 x 15 + 54

= 405 + 54

= 459 square feet

Now, Surface area of Cuboid

= 2 (105 + 210+ 126)

= 2(441)

= 882 square feet

Thus, the Surface area of Composed figure

= 459 + 882

= 1,341 square feet

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Answer:

g = 13/4 or 3.25

Step-by-step explanation:

Step 1:  First we can distribute the 2 on the right-hand side (rhs) of the equation:

[tex]\frac{2*5-2*g}{3}\\\\ \frac{10-2g}{3}[/tex]

Step 2:  We can also rewrite this fraction since we have two inverse operations, namely multiplication and division:

[tex]\frac{10}{3}+\frac{-2g}{3}\\ \\ \frac{10}{3}-\frac{2g}{3}\\ \\ \frac{10}{3}-\frac{2}{3}g[/tex]

Step 3:  We can convert both sides into whole numbers by multiplying both sides by the least common denominator (lcd), which is essentially the lowest multiple shared by the denominators 6 and 3.

The lowest multiple shared by the two numbers is 6 as 6*1 = 6 and 3*2 = 6

Thus, we multiply both sides by 6:

left-hand side (lhs)

[tex]\frac{7}{6}*\frac{6}{1}\\ \\ \frac{42}{6}\\ \\ 7[/tex]

right-hand side (rhs)

[tex](\frac{10}{3}-\frac{2}{3}g)*\frac{6}{1}\\ \\ (\frac{10}{3}*\frac{6}{1})+(-\frac{2}{3}g*\frac{6}{1})\\ \\ \frac{60}{3}-\frac{12}{3}g\\ \\ 20-4g[/tex]

Since we have simplified both sides, we can now solve for g:

[tex](7=20-4g)-20\\(-13=-4g)/-4\\13/4=g\\3.25=g[/tex]

You can keep the mixed number or use the decimal answer as both are the same answer in different forms.

For such a problem, it can be helpful to check by plugging in 3.25 for g in the equation

[tex]\frac{7}{6}=\frac{2(5-3.25)}{3}\\ \\ \frac{7}{6}=\frac{2(1.75)}{3}\\ \\ \frac{7}{6}=\frac{3.5}{3}\\\\ 1.167=1.167[/tex]

If quadrilateral RSTU is reflected across the line x = 1, then the coordinates of R’, S’, T’, and U’ are (-3, 2), (-2, 4), (-3, 6) and (-4, 4) respectively.

To reflect a point across the line x = 1, we can use the formula (2a - x, y), where (a, b) is the original point and x = 1 is the line of reflection.

Using this formula, we can find the coordinates of the reflected points as follows:

The x-coordinate of the line of reflection is 1, so the new x-coordinate for each point will be 2(1) - x = 2 - x.

The y-coordinate for each point will remain the same.

Therefore, the reflected coordinates are:

R' = (2(1) - 5, 2) = (-3, 2)

S' = (2(1) - 4, 4) = (-2, 4)

T' = (2(1) - 5, 6) = (-3, 6)

U' = (2(1) - 6, 4) = (-4, 4)

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Hackman Corporation will record interest expense of $58822 on each interest payment date for the life of the bonds.

Hackman Corporation issued$ 1 million face value 12 bonds dated January 1, 2019, for$. The bonds pay interest semiannually on June 30 and December 31 and are due December 31, 2023. Hackman uses the straight- line amortization  system to  regard for the bond  decoration. The periodic  decoration amortization is$ 2,300, and the semiannual  decoration amortization is$ 1,150.

Annual effective interest rate = (Face value of the bonds × Coupon rate) / Issue price of the bonds

Annual effective interest rate = ($1,000,000 × 12%) / $1,023,000 = 11.76%

Effective interest rate for the period = (1 + (11.76% / 2))^(6 / 12) - 1 = 5.75%

Interest expense = $1,023,000 × 5.75% = $58,822.50

Therefore, the amount of interest expense that Hackman Corporation should recognize on June 30, 2019, is approximately $58,822.50.

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The length of the base of the triangular base is 4 feet.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The formula for the volume of a triangular prism is:

V = (1/2)bh x h

where b is the base of the triangular base, h is the height of the triangular base, and h is the height of the prism.

Substituting the given values, we get:

72 = (1/2)(x) x 3 x 12

Simplifying, we get:

72 = 18x

Dividing both sides by 18, we get:

x = 4

Therefore,

The length of the base of the triangular base is 4 feet.

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Answer:

The length, x, of the base of the triangular base of the prism is 4 ft.

Step-by-step explanation:

The volume of a regular prism can be found by multiplying the area of its base by its height.

[tex]\boxed{\textsf{Volume of a regular prism}=\textsf{Base area} \times\textsf{height}}[/tex]

The base of a triangular prism is a triangle.

The area of a triangle is half the product of its base and height.

Given that b = x and h = 3, the area of the triangular base of the prism is:

[tex]\begin{aligned}\textsf{Area of triangular base}&=\dfrac{1}{2} bh\\\\&=\dfrac{1}{2} \cdot x \cdot 3\\\\&=\dfrac{3}{2}x\; \sf ft^2\end{aligned}[/tex]

To find the value of x, substitute the given volume, v = 72 ft³, the given height, h = 12 ft, and the found area of the base into the formula for volume, and solve for x:

[tex]\begin{aligned}\textsf{Volume}&=\textsf{Base area} \cdot \textsf{Length}\\\\\implies 72&=\dfrac{3}{2}x \cdot 12\\\\72&=\dfrac{36}{2}x \\\\2 \cdot 72&=2 \cdot \dfrac{36}{2}x \\\\144&=36x\\\\\dfrac{144}{36}&=\dfrac{36x}{36}\\\\4&=x\end{aligned}[/tex]

Therefore, the value of x is 4 feet.

Answer:

23/28

Step-by-step explanation:

1/4 + 4/7

make them have same denominator of 28

7/28 + 16/28

=23/28

Answer:

23/28

Step-by-step explanation:

Hope this helps! Pls give brainliest!

The option that is the correct form after substituting a, b, and c into the quadratic formula is; x = (-7 ± √(7² - 4·(1)·(8)))/((2)·(1))

The quadratic formula which can be used to solve the quadratic equation of the form f(x) = a·x² + b·x + c = 0

The quadratic formula is; x = (-b ± √(b² - 4·a·c))/(2·a)

The quadratic equation x² + 7·x + 8 = 0, evaluated using the quadratic formula can be expressed as follows;

The values of a, b, and c obtained from the specified quadratic equation are; a = 1, b = 7, and c = 8, therefore;

x = (-7 ± √(7² - 4×1×8))/(2×1)

The correct option is therefore; x = (-7 ± √(7² - 4×1×8))/(2×1)

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Answer: We can use the Pythagorean theorem to solve this problem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have:

a = -10

b = 24

c = ?

Using the Pythagorean theorem, we can solve for c:

c^2 = a^2 + b^2

c^2 = (-10)^2 + 24^2

c^2 = 676

c = sqrt(676)

c = 26

Therefore, the length of the missing side of the right triangle is 26 units.

The length of the missing side of the right triangle is 26.  To find the length of the missing side of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

The formula is:

[tex]c² = a² + b²[/tex]

In this problem, a = 10 and b = 24. To find the length of the missing side (the hypotenuse, c), we can plug these values into the formula:

c² = 10² + 24²
c² = 100 + 576
c² = 676

Now, we take the square root of both sides to find the length of the missing side:

c = √676
c = 26

So, the length of the missing side (the hypotenuse) of the right triangle is 26.

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The test statistic and p-value for the slope of the regression line are t = 26 and p-value = 0.00.

Based on the given information, the analysis is focused on determining whether there is a linear relationship between GRE score and the chance of admission. The pattern observed in the scatterplot shows a linear pattern in the data, indicating a potential linear relationship between the two variables.

To test this hypothesis, a regression analysis was performed, which yielded a coefficient table with estimates for the intercept and slope of the regression line. The p-value for the slope test was found to be 0.00, which suggests strong evidence for a significant linear relationship between GRE score and the chance of admission.

Furthermore, a 95% confidence interval for the slope was calculated, which did not include the null value of zero. This means that we can reject the null hypothesis and conclude that there is a linear relationship between the GRE score and the chance of admission.

In summary, based on the analysis and statistical tests performed, there is evidence to support a linear relationship between the GRE score and the chance of admission.
The test statistic and p-value for the slope of the regression line are t = 26. ,an  p-value = 0.00.
A 95% confidence interval for the slope on the line is (0.01, 0.01). Since 0 is not found in the confidence interval and our alternative hypothesis is two-sided, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and the chance of admission.

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Blaise will make $1575 at the end of weeks on his personal pay schedule.

Step 1: determine the number of days in weeks

They're five working days in a per week, so then there are a total of 10 working days in a weeks.

Step 2: Calculate Blaise's profits for every day

using the given pay schedule, Blaise's profits for the primary 10 days would be:

Day 1: $115

Day 2: $125

Day 3: $135

Day 4: $145

Day 5: $155

Day 6: $165

Day 7: $175

Day 8: $185

Day 9: $195

Day 10: $205

Step 3: Now we will addition of Blaise's profits

adding up the profits from the first 10 days, we get:

$115 + $125 + $135 + $145 + $155 + $165 + $175 + $185 + $195 + $205 = $1575

Therefore On his own pay plan, Blaise will earn $1575 at the end of each week.

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Step-by-step explanation:

Area of ENTIRE (360 degrees) circle = pi r^2 = 144 pi  cm^2

  you want 60 degrees of this out of the 360 degrees

         60 / 360   *   144 pi = 1/6 * 144 pi =    24 pi cm^2  <=====exact answer

C. The more reliable survey would be: Tamira's survey is more reliable than Denise's survey, and approximately 1,500 residents of the town would likely be in favor of the construction of a new baseball stadium.

Tаmirа's survеy is mоre reliаble bеcаusе shе survеyed rеsidеnts frоm diffеrеnt sectiоns оf thе town, whiсh is а mоre representаtive sаmple оf thе entire populаtiоn. Denise's survеy, оn thе othеr hаnd, wаs cоnducted аt а bаsebаll gаme, whiсh might hаve introduced а biаs towаrds people who аre mоre likеly to bе in fаvor оf thе new stаdium.

Bаsed оn Tаmirа's survеy, 30 out оf 150 rеsidеnts (20%) аre in fаvor оf thе cоnstructiоn.

If we extrаpolаte this percentаge to thе entire populаtiоn оf 7,500 rеsidеnts, we cаn estimаte thаt аpproximаtely 1,500 rеsidеnts (20% оf 7,500) would likеly bе in fаvor оf thе new bаsebаll stаdium.

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True. The mathematical equations that describe simple harmonic motion (SHM) involve sine and cosine functions. For example, if the block is released at a distance from its equilibrium position, its displacement x varies with time t according to the equation x = a cos(ωt), where ω is the angular frequency of the motion.

True. Due to the periodic properties of Simple Harmonic Motion (SHM), the mathematical equations that describe this motion involve sine and cosine functions. If the block is released at a distance A from its equilibrium position, its displacement x varies with time t according to the equation:

x(t) = A * cos(ωt + φ)

where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. Both sine and cosine functions are used to describe the displacement, velocity, and acceleration of an object in SHM because of their periodic nature.

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