Find the centroid of the region bounded by the curves f(x) = 4 – x² and g(x) = x + 2. Assume constant density.

Answer:

the answer is the one with the 5

Step-by-step explanation:

NUMBER 3

Answer:

\(A\approx\$880.68\)

Step-by-step explanation:

So, we know that Jolene bought an initial $750.

We also know that the purchase is increasing at an average rate of 5 1/2 %or 5.5%. In other words, this is being compounded.

So, we can use the compound interest formula, which is:

\(A=P(1+\frac{r}{n})^{nt}\)

Where A is the total amount, P is the principal value, r is the rate and n is the number of times compounded per year, and t is the amount of years.

So, substitute 750 for P. 5 1/2% is the same as 5.5% or 0.055 (you move the decimal two places to the left and remove the percent symbol) so substitute this for r. Since it's increasing yearly, n is 1. So, our formula is:

\(A=750(1+0.055)^t\)

Add:

\(A=750(1.055)^t\)

Since the stock was bought 3 years ago, the value now is t=3. So, substitute 3 for t and evaluate:

\(A=750(1.055)^3\)

Evaluate. Use a calculator:

\(A\approx\$880.68\)

And we're done!

Formula: A = P(1 + r/n)^t

We have these variables:

P = 750

r/n = 0.055

t = 3

Substitute and simplify:

A = 750(1 + 0.055)^3

A = 750(1.055)^3

A = 880.68

Best of Luck!

Answer:

I believe the answer is b. linear

Step-by-step explanation:

There were 89 points in the original data set.

To solve this problem, we can use the formula for the mean of a set of numbers:

Mean = (sum of all values) / (number of values)

Let's denote the number of points in the original data set as n.

The sum of the original data set is n  10 since the mean is 10.

When a point with a value of 100 is added, the new sum becomes n × 10 + 100.

The new mean is given as 11.

Using the formula for the mean, we can write the equation:

11 = (n × 10 + 100) / (n + 1)

To solve for n, we can multiply both sides of the equation by (n + 1):

11(n + 1) = n × 10 + 100

11n + 11 = 10n + 100

11n - 10n = 100 - 11

n = 89

Therefore, there were 89 points in the original data set.

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Answer:

See Below.

Step-by-step explanation:

We want to prove that:

\(\displaystyle \sin^2 A + \sin^2 B \cdot \cos 2A = \sin^2 B + \sin^2 A \cdot \cos 2B\)

Recall that double-angle identity for cosine:

\(\displaystyle \begin{aligned} \cos 2x &= \cos^2x - \sin^2 x \\ &= 2\cos^2x -1 \\ &= 1 - 2\sin^2 x\end{aligned}\)

Substitute cos(2A) for its third form:

\(\displaystyle \sin^2 A + \sin^2 B \cdot \left(1 - 2\sin^2 A\right) = \sin^2 B + \sin^2 A \cdot \cos 2B\)

Distribute:

\(\displaystyle \sin^2 A + \sin^2 B - 2\sin^2B \sin^2A = \sin^2 B + \sin^2 A \cdot \cos 2B\)

Rewrite:

\(\displaystyle \sin^2 B + \left(\sin^2 A - 2\sin^2 B\sin^2 A\right)\)

Factor:

\(\displaystyle \sin^2 B + \sin^2A\left(1 - 2\sin^2 B\right) = \sin^2 B + \sin^2A\cdot \cos 2B\)

Double-Angle Identity for cosine:

\(\displaystyle \sin^2 B + \sin^2 A \cdot \cos 2B \stackrel{\checkmark}{=} \sin ^2 B + \sin^2 A\cdot \cos 2B\)

Hence proven.

Answer:

30 = XY

Step-by-step explanation:

Angle Formed by Two Secants= 1/2(difference of Intercepted Arcs)

41 = 1/2 ( 112 - XY)

Multiply each side by 2

2*41 = 2*  1/2 ( 112 - XY)

82 = 112 - XY

Subtract 112 from each side

82 - 112 = -XY

-30 = -XY

Multiply by -1

30 = XY

Here’s what you need to know about intercepts. The x intercept of a graph has y coordinate zero. The y intercept of a graph has x coordinate zero.

AN EXAMPLE OF THIS IS:

So if you have a function y = 2x + 8 you would set x = 0 to find the y intercept. So we would get y = 8. To find the x intercept we would set y = 0 and get 0 = 2x + 8

or -8 = 2x or x = -4

Now if you have a more difficult like function y = 3x^2 + 10x - 4 we proceed the same way. To find the y intercept we would set x = 0 and get y = -4 so the y intercept is (0,-4)

To find the x intercept we would set y = 0 and get 3x^2 + 10x - 4 = 0. If you know the quadratic formula you could solve this by:

x = [-b +- SR(b^2 - 4*a*c] / 2a

so in our case x = [-10 +- SR(100 - 4*3*(-4))] / (2*3)

x = [-10 +- SR(100 + 48)] / 6

x = [-10 +- SR (148)] / 6

x = [-10 +- 12.2] / 6 approximately

x = [-10 - 12.2] / 6 or [-10 + 12.2 / 6]

x = -22.2/6 or 2.2/6

Answer: A

Step-by-step explanation:

Origin is at 0,0, and the arrow is pointing towards the center which is 0,0.

Step-by-step explanation:

The area of the floor of the scale drawing and the scale factor are 72 in² and 1/4 respectively

Actual Length = 36 feets

Actual width = 32 feets

Model width = 9 inches

The scale factor = 9 / 36 = 1/4

The length of the model canbe calculated thus :

Actual Length × scale factor

Model width = 32 × 1/4 = 8 inches

The Area of a rectangle can be calculated using the relation :

Area = Length × width

Area of floor = 8 inches × 9 inches = 72 inch²

Therefore, the area of the floor of the scale drawing is 72 in²

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The area of the rectangular floor in the scale drawing is A = 156 inches²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular floor in the scale drawing be A

Let the length of the rectangular floor be L = 26 feet

Now , the length of the rectangular floor in scale drawing = 13 inches = L/2

And , the width of the rectangular floor be W = 24 feet

So , the width of the rectangular floor in scale drawing = W/2 = 12 inches

Now , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

The area of the rectangular floor in the scale drawing A = 13 x 12

The area of the rectangular floor in the scale drawing A = 156 inches²

Hence , the area of rectangle is 156 inches²

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Step-by-step explanation:

given expression → x/y

we know,

x = 3 and y = 27

according to expression

3/27 → 1/9

therefore 1/9 is the answer.

Hope this answer helps you!

Answer:

1/9

Step-by-step explanation:

1. First, let's plug in the values of x and y.

2. Next, we have to simplify and find the greatest common factor between 3 and 27.

3. As you can see, 3 is the GCF of 3 and 27, so we divide both 3 and 27 by 3.

Therefore, the answer is 1/9!

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

t=2.18n

Step-by-step explanation:

Total cost is 6.54 for 3 tickets so divide 6.54 by 3 and you get price per ticket which is 2.18. Multiply that by how many tickets you want and you get your final price.

The coordinates of B' after the translation represented by (x - 4, y - 3) is (1, -2). See other solutions below

B is located at the point (5, 1) in the figure.

If we translate the point by (x - 4, y - 3), the new location of B, denoted by B', can be found by subtracting 4 from the x-coordinate and 3 from the y-coordinate.

Therefore, B' is located at (1, -2).

The given information provides us with a set of matching points, which are:

Preimage = (2, 1)

Image = (-1, 2)

These points can be represented by the equation:

(x, y) = (-y, x)

This equation indicates that the points have undergone a (d) clockwise rotation of 270 degrees.

Here, the smaller shape is created by scaling down a larger shape, the transformation is a dilation that results in a reduction.

The scale factor for this transformation could be either 1/2 or 1/4.

Given the points P = (3, -2) and S = (4, -5), we apply two transformations.

The first transformation (x - 2, y) is defined as shifting the x-coordinate of each point left by 2 units, while keeping the y-coordinate the same.

This results in new points P' = (1, -2) and S' = (2, -5).

The second transformation involves reflecting the new points across the x-axis, which changes the sign of their y-coordinates.

The resulting points are P'' = (1, 2) and S'' = (2, 5).

In this context, we are given the coordinates of point A as (-2, -5).

This implies that if we scale down the original coordinates by a factor of 1/2, we get the new coordinates of point A, which become (-1, -2.5).

Therefore, the coordinates of point A' are (-1, -2.5).

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Answer:

hope you have understood

The total cost for Beck to attend the fair and go on 4 rides can be calculated as follows:

Cost of admission: $10

Cost of 4 rides: 4x

Total cost: $10 + 4x

Since we are not given the value of x, we cannot calculate the total cost. However, we know that each ride costs x dollars, so we can use this information to find the cost of each ride if we are given the total cost. Alternatively, if we are given the cost of each ride, we can find the total cost by substituting the value of x into the equation.

As the question does not provide any information about the value of x or the total cost, we cannot provide a specific answer to this question.

Sabrina's difference in interest is approximately $7,050.68, and she will pay approximately $23,050.68 on March 9, 2020.

To calculate Sabrina's difference in interest and the amount she will pay on March 9, 2020, we need to consider the interest calculations for both Janeen and Sabrina.

a. Sabrina's Difference in Interest:

Since Sabrina's terms are exact interest, the interest is calculated based on the exact number of days.

First, let's determine the number of days between April 5, 2019, and March 9, 2020:

Number of days = 365 (days in a year) - 31 (days in March) - 4 (days in April) = 330 days

Now we can calculate Sabrina's interest:

Interest = Principal x Rate x Time

Interest = $16,000 x 65% x (330/365)

Interest = $16,000 x 0.65 x 0.90410958904

Interest ≈ $7,050.68

b. Sabrina's Payment on March 9, 2020:

To find the total amount Sabrina will pay, we need to add the interest to the principal.

Total Payment = Principal + Interest

Total Payment = $16,000 + $7,050.68

Total Payment ≈ $23,050.68

Therefore, Sabrina's difference in interest is approximately $7,050.68, and she will pay approximately $23,050.68 on March 9, 2020.

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The correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.

Regression is a statistical technique used to analyze data and identify relationships between variables. It is used to predict the value of a dependent variable based on one or more independent variables. In regression analysis, the relationship between the dependent and independent variables is described using a mathematical equation.

This sine regression model is based on the data given in the question. The model is in the form y = a* sin(bx + c) + d.
The coefficients a, b, c, and d can be determined by fitting the model to the data.
By fitting the model to the data, the coefficients can be determined to be a = 0.508, b = 0.212, c = 1.529, and d = -0.512.
Therefore, the correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.

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For a painting with frame, the quadratic equation can be ued too determine the thickness of the frame x is equals to the

4x² + 26x - 3 = 0. So, option(b) is right one.

There is defined that katie wants to hang a painting in a galery. See the above figure. Total area of the painting and frame must be equal to 45 square feet. Let the dimensions of painting be L and W that is length and width.

The width of painting, W = 6 feet

Length of painting, L = 7 feet

The thickness of the frame = x feet.

So, the new length of painting and frame, L' = (6 + 2x ) feet

The new width of painting and frame, W' = (7 + 2x ) feet

We have to determine the quadratic equation for thickness of the frame x. Using the area formula for rectangular, A = length × width

Area of rectangular painting and frame, A'

= new length × new width = L'× W'

= ( 6 + 2x) ( 7 + 2x)

From the scenario, A' = 45 sq. feet

=> ( 6 + 2x) ( 7 + 2x) = 45

=> 42 + 12x + 14x + 4x² = 45

Simplify the above expression,

=> 4x² + 26x = 3

=> 4x² + 26x - 3 = 0

Hence, required quadratic equation is

4x² + 26x - 3 = 0.

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Complete question:

katie wants to hang a painting in a galery. the painting and framemust have an area of 45 square feet. the painting is 6 feet wide by 7 feet long. which quadratic equation can be ued too determine the thickness of the frame x?

a) 4x^2 + 26x + 45 = 0

b) 4x^2 + 26x − 3 = 0

c) x^2 + 13x − 3 = 0

d)x^2 + 13x + 45 = 0

In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.

The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.

The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.

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Answer:

Im not too sure but it might be d?

Use the scaling factor equation: greater length over smaller length to go from a smaller to a larger figure. Use the formula scale factor = smaller length over larger length if you're scaling down from a larger to a smaller figure.

What is scale factor in math?

How can I calculate the scale factor?

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Answer:

Step-by-step explanation:

The given equation is not instandard form. First standard form is neccesary.

The result is 3x + 108 = 12y which is equal to 12y = 3x + 108

The slope is represented in this form as m (Y = mx + b)

(with b as the initial value)

Therefore, 3 is the slope.

To find its perpendicular slope.

To find it's perpendicular, know that it is the negative reciprocal.

FInally, the slope perpendicular to the line whose equation is 3x - 12y = -108 is \(\frac{1}{-3\\}\)

The linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.

What is a function?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable

solution:

The linear function:

  C(x) =  1.25x + 500

For revenue function:

  R(x) = 3.50x

R(50) = 3.50(50)

         = $175

Using the C(x) and revenue function we can find the number of slushies and profit.

Thus, the linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.

Hence the linear and revenue functions are C(x) =  1.25x + 500 and  R(x) = 3.50x

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The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw is 0.39.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, can be calculated using conditional probability.

P(A|B) = P(A and B) / P(B)

P(A and B) = P(T or P on second draw and F on first draw) = P(T on second draw and F on first draw) + P(P on second draw and F on first draw)

= (3/9) x (4/10) + (2/9) x (4/10) = 14/90

To find P(B), we know that it is 0.4.

Therefore, the conditional probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is:

P(A|B) = P(A and B) / P(B) = (14/90) / 0.4 ≈ 0.39

So the probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is approximately 0.39.

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Answer:

A)-7

B)2

C)-2

D)-4

Step-by-step explanation:

Answer:

well the (a) is -3 and (c) is 2

Step-by-step explanation:

Answer:

This is a true statement

Step-by-step explanation:

If you were to refer to a number line, The more you go to the -10, -11, -12 you are getting smaller, the more you go to 0, 1, 2 then you are getting bigger.

Key: The more you go left on a number line, you are getting smaller and probably ending on negatives

The more you go right on a number line you are getting bigger and probably ending on positives.

-1 is most likely going right to the number line meaning it is big

-11 is going to the left on the number line so it is getting smaller

Therefore, -11 is less than -1

The 85% confidence interval for the mean time at lunch is (31.84, 39.36) minutes.

In a random sample of fourteen people, the mean time at lunch was 35.6 minutes.

Standard deviation of 8.2 minutes.

A common method to calculate the confidence interval for the mean of a normal distribution is to use the Z-score. For a 85% confidence interval, the Z-score is 1.44. Therefore, the confidence interval can be calculated as:

The confidence interval formula in statistics is used to describe the amount of uncertainty associated with a sample estimate of a population parameter.

Where,

n= Number of terms

\($\overline{\mathrm{x}}\)= Sample Mean

\($\sigma\)=Standard Deviation

\($z_{\alpha / 2}\)= Value corresponding to a2 in z table

\($t_{\alpha / 2}\)= Value corresponding to a2 in t table

\($\alpha\)=(1 - Confidence Level /100)

So for the given data, the confidence interval would be:

35.6 ± 1.44 * 8.2 / √14

35.6 ± 1.44 * 8.2 / 3.74

35.6 ± 3.76

Therefore, the 85% confidence interval for the mean time at lunch is (31.84, 39.36) minutes.

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Answer:

12.9

Step-by-step explanation:

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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