Rewrite the given formula relating the area of a square to the length of its diagonal to solve for d. The 2nd screenshot is the formula sorry for the poor sc

y^2 = 90

y = √90 = 3√10

that's it

Answer:

The yellow region is 13.73 cm squared

Step-by-step explanation:

---

Area of square:

[tex]8 * 8 = 64 cm^2[/tex]

Area of the 4 quarter-circles:

[tex]4(\pi r^2)/4[/tex]

The fours cancel each other, we are left with:

[tex]\pi r^2[/tex]

r = 4, so substitute that, we get:

[tex]\pi 4^2 = 16 \pi cm^2[/tex]

Which can be approximated to 50.27 cm squared

Subtract the area of the circle from the square:

[tex]64 - 50.27 = 13.73 cm^2[/tex]

So the area of the yellow region is 13.73 cm squared

Answer:

its prime

Step-by-step explanation:

it can not be factored using foil

Applying mathematical operations, the greatest number of necklaces Georgia can make is 26.

The total number of beads available for making bracelets and necklaces is an addition operation between the beginning inventory of beads and the additional units purchased.

A subtraction operation is performed to determine the remainder after making bracelets.

Finally, a division operation determines the greatest number of necklaces to make.

The beginning inventory of beads = 322

The units purchased = 38 beads

The total number of beads that Georgia has = 360 (322 + 38)

The number of beads required to make bracelets = 120

The remainder after making bracelets = 240 (360 - 120)

The number of beads required for each necklace = 9

The greatest number of necklaces Georgia can make = 26 (240 ÷ 9)

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Answer:

a) 5

Step-by-step explanation:

the question say how many zero-dimensional objects are labeled on the object. so, you would count how many blue dots you see on the object, as you can see their are four dots on the the bottom, and one dot at the top.

so, 4 dots + 1 dot = ?

5 blue dots

so your answer is 5.

hopefully this helps, let me know if it doesn't.

we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.

How to solve the problem ?

The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.

To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.

Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.

Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.

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Answer:

Step-by-step explanation: 5

The ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is 4:3, or 4/3.

To find the ratio of the surface areas of the two similar cylinders, we need to consider the ratio of their corresponding dimensions. Since the two cylinders are similar, their radii are proportional to their heights. Let's denote the height of the smaller cylinder as h1, the height of the larger cylinder as h2, the radius of the smaller cylinder as r1, and the radius of the larger cylinder as r2.

Given:

h1 = 15 inches

h2 = 20 inches

The ratio of the heights is:

h2 / h1 = 20 / 15 = 4 / 3

Since the cylinders are similar, the ratio of their radii is the same as the ratio of their heights:

r2 / r1 = 4 / 3

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The p value based on the information will be E. P - value ≥ 0.20

Open Minitab 17. Select 'Stat' -> 'Basic Statistics' -> '2 - Sample t... Select 'Summarized data' from the dropdown menu.

Enter 5 in both Sample size of sample 1 and sample 2, 168 and 172 in Sample mean of Sample 1 and Sample 2. 5.4 and 7.5 in Standard deviation of Sample 1 and Sample 2.

Click on 'Options' and Enter 'Confidence level' 95.0(or the given Cofidence level) , 'Hypothesized difference' 0.0 , 'Alternative hypothesis' 'Difference \\neq Hypothesized difference'. Also the box 'Assume equal variance' can be ticked as requirement.

Click on 'Ok' -> 'Ok'.

Output: -

P - value = 0.361 i.e., P - value ≥ 0.20

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Answer:15

Step-by-step explanation:

The length of segment PQ is equals to the length of segment P'Q' divided by 1.5, that is:

PQ = P'Q'/1.5

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor for this problem is given as follows:

k = 1.5.

Hence the equation relating the lengths PQ and P'Q' is given as follows:

P'Q' = 1.5PQ

PQ = P'Q'/1.5

(as the length on the dilated figure is the original length multiplied by the scale factor).

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The value of the matrix 4G + 2F is [tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]

Matrices are an essential tool in mathematics and can be used to solve a variety of problems. In this case, we are given two matrices G and F, and we are asked to find the value of 4G + 2F.

To understand how to calculate the value of 4G + 2F, we first need to understand what it means to multiply a matrix by a scalar. When we multiply a matrix by a scalar, we simply multiply every element in the matrix by that scalar.

Now that we understand scalar multiplication, we can use it to find the value of 4G + 2F. We simply need to multiply each matrix by its respective scalar and then add the results element-wise.

[tex]4G = 4\begin{bmatrix}8 &-5 &8 &-2 &10 \\-6& -7&1 & 9& 2\\4&6 &3 &7 &5 \\-4 & -3& 0& -10& -9\end{bmatrix}= \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix}[/tex]

Now we have to find the value of 2[F]. that can be calculated as follows

[tex]2F = 2\begin{bmatrix}1 &8 &-2 &-5 &9 \\-9& 10&6 &-3&0\\4&5 &-4 &3 &7 \\2 &-10&-6 & -1& -8\end{bmatrix}= \begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]

Now we can add the two matrices element-wise to get the final result:

[tex]4G + 2F = \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix} +\begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]

[tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]

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The row operation is given as follows:

Division by 7 = multiplication by 1/7.

The matrix after the row operation is then given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

The element at row 1 and column 1 is given as follows:

7.

An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:

7/k = 1

k = 7.

The first row is given as follows:

7, -4 and 8.

Dividing every element of the first row by 7, the resulting matrix is then given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

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The statement that is true on the linear relationship between the brochures and cost of printing is A. the printing fee is $ 2.50.

To find the printing fee, find the difference between the total cost of two different numbers of brochures printed.

The printing fee is:

= ( Total cost of 43 - total cost of 40 ) / ( Difference between 43 and 40 )

= ( 607.50 - 600 ) / ( 43 - 40 )

= 7. 50 / 3

= $ 2. 50

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The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments

From the question, we have the following parameters that can be used in our computation:

The table of values

For the membership application, we have the following features

So, the function is

f(x) = 600 - 10x

For the membership available, we have the following features

So, the function is

g(x) = 20/3x

So, the functions are f(x) = 600 - 10x & g(x) = 20/3x

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The trigonometry functions when evaluated are shown below

In trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.

They are defined as follows:

sin A = opposite side/hypotenuse.

cos A = adjacent side/hypotenuse.

tan A = opposite side/adjacent side.

So, we have

Figure 1

Figure 2

Figure 3

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Answer:

d = $350

Step-by-step explanation:

If we allow d to represent the cost of the dryer and w to represent the cost of the washer, we know that the total cost of the washer and dryer is

d + w = 770.

Since we're told that the washer costs $70 more than the dryer, we know that

w = d + 70

We can substitute equation for w in the original equation to find d:

d + d + 70 = 770

2d + 70 = 770

2d = 700

d = 350

If you went on to find w, you'd see that it'd be 420 since 770 - d = w and 770 - 350 = 420

We know that the dryer costs $350 and the washer costs $420.  420 is indeed $70 more than $350 so our answer for the cost of the dryer is correct.

The calculated value of the fraction that is greater than the fraction by the model is 1/2

From the question, we have the following parameters that can be used in our computation:

Model fraction = 3/8

A fraction that is greater than the fraction by the model is represented as

Fraction > Model fraction

Substitute the known values in the above equation, so, we have the following representation

Fraction > 3/8

Add 1 to the numerator

So, we have

Fraction = 4/8

Simplify

Fraction = 1/2

Hence, the fraction that is greater than the fraction by the model is 1/2

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The degree of a polynomial is the highest exponent of the variable in the polynomial.

In this case, the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2 is 5, because the highest exponent of x is 5 (in the term -3x^5). Therefore, the answer is 5.

The quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.

To solve the above problem, we can use the following equation:

Rice + Milk + Sugar = 1 kg

Rice = 2/5 (1 kg) = 0.4 kg

Milk = 2/5 (1 kg) = 0.4 kg

Sugar = 1/6 (1 kg) = 0.167 kg

Therefore, the quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.

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Answer:

[tex]f(2\pi) = 32\pi^3 - 2[/tex]

Step-by-step explanation:

Main steps:

Step 1: Use integration to find a general equation for f

Step 2: Find the value of the constant of integration

Step 3: Find the value of f for the given input

Step 1: Use integration to find a general equation for f

If [tex]f'(x) = g(x)[/tex], then [tex]f(x) = \int g(x) ~dx[/tex]

[tex]f(x) = \int [12x^2 - sin(x)] ~dx[/tex]

Integration of a difference is the difference of the integrals

[tex]f(x) = \int 12x^2 ~dx - \int sin(x) ~dx[/tex]

Scalar rule

[tex]f(x) = 12\int x^2 ~dx - \int sin(x) ~dx[/tex]

Apply the Power rule & integral relationship between sine and cosine:

[tex]f(x) = 12*(\frac{1}{3}x^3+C_1) - (-cos(x) + C_2)[/tex]

Simplifying

[tex]f(x) = 12*\frac{1}{3}x^3+12*C_1 +cos(x) + -C_2[/tex]

[tex]f(x) = 4x^3+cos(x) +(12C_1 -C_2)[/tex]

Ultimately, all of the constant of integration terms at the end can combine into one single unknown constant of integration:

[tex]f(x) = 4x^3 + cos(x) + C[/tex]

Step 2: Find the value of the constant of integration

Now, according to the problem, [tex]f(0) = -2[/tex], so we can substitute those x,y values into the equation and solve for the value of the constant of integration:

[tex]-2 = 4(0)^3 + cos(0) + C[/tex]

[tex]-2 = 0 + 1 + C[/tex]

[tex]-2 = 1 + C[/tex]

[tex]-3 = C[/tex]

Knowing the constant of integration, we now know the full equation for the function f:

[tex]f(x) = 4x^3 + cos(x) -3[/tex]

Step 3: Find the value of f for the given input

So, to find [tex]f(2\pi)[/tex], use 2 pi as the input, and simplify:

[tex]f(2\pi) = 4(2\pi)^3 + cos(2\pi) -3[/tex]

[tex]f(2\pi) = 4*8\pi^3 + 1 -3[/tex]

[tex]f(2\pi) = 32\pi^3 - 2[/tex]

Answer:

[tex]f(2 \pi)=32\pi^3-2[/tex]

Step-by-step explanation:

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given:

If g(x) is the first derivative of f(x), we can find f(x) by integrating g(x) and using f(0) = -2 to find the constant of integration.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]     [tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $\sin x$}\\\\$\displaystyle \int \sin x\:\text{d}x=-\cos x+\text{C}$\end{minipage}}[/tex]

[tex]\begin{aligned} \displaystyle f(x)&=\int f'(x)\; \text{d}x\\\\&=\int g(x)\;\text{d}x\\\\&=\int (12x^2-\sin x)\;\text{d}x\\\\&=\int 12x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\int x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\cdot \dfrac{x^{(2+1)}}{2+1}-(-\cos x)+\text{C}\\\\&=4x^{3}+\cos x+\text{C}\end{aligned}[/tex]

To find the constant of integration, substitute f(0) = -2 and solve for C:

[tex]\begin{aligned}f(0)=4(0)^3+\cos (0) + \text{C}&=-2\\0+1+\text{C}&=-2\\\text{C}&=-3\end{aligned}[/tex]

Therefore, the equation of function f(x) is:

[tex]\boxed{f(x)=4x^3+ \cos x - 3}[/tex]

To find the value of f(2π), substitute x = 2π into function f(x):

[tex]\begin{aligned}f(2 \pi)&=4(2 \pi)^3+ \cos (2 \pi) - 3\\&=4\cdot 2^3 \cdot \pi^3+1 - 3\\&=32\pi^3-2\\\end{aligned}[/tex]

Therefore, the value of f(2π) is 32π³ - 2.

Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

Since the containers were not given in the question, In a case whereby Ruth has a cylindrical cup that is filled with water where the cup has a diameter of 2 inches and a height of 6 inches,  the  volume of cylinder cup is 18.85inch^3.

Note that ; the container were not given in the question, so  we will just need to calculate the volume of the cylindrical cup to know how much water it can hold .

The volume of a cylinder can be caluculated using te exppresion  π r² h

Then from the question the  diameter = 2 inches radius = 2/2 = 1 inches

height =6 inches

π r² h

=π  * 1^2 * 6

=18.85inch^3

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Answer:

It is called as triangular numbers

Step-by-step explanation:

these numbers can be represented as a triangle of dots

The evaluation of the trigonometric identities to find the sine of the sum of angles A and B, using the values for cos(A) and sin(B) indicates;

15. sin(A + B) = -52/85

16. A + B is in Quadrant III

Trigonometric identities are equations involving trigonometric ratios that are true for the values of the input variables.

15. cos(A) = -15/17, sin(B) = 4/5

The trigonometric identity for the sine of the  addition of two angles, the addition formula indicates that we get;

sin(A + B) = sin(A)·cos(B) + cos(A)·sin(B)

cos(B) = √(1 - (4/5)²) = √(1 - 16/25) = 3/5

sin(A) = √(1 - (-15/17)²) = 8/17

Therefore; sin(A + B) = (8/17) × (3/5) + (-15/17) × (4/5) = -52/85

16. π/2 < A < π, and 0 < B < π/2

Therefore; π/2 + 0 < A + B < π + π/2

The solution from the previous question indicates that we get;

sin(A + B) = -52/85

The sine of an angle is negative in the third and fourth quadrant

The fourth quadrant is; π + π/2 < θ < 2·π

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Answer:

C. (x + 3)² + (y - 4)² = 9

Step-by-step explanation:

The equation for a circle is r² = (x - a)² + (y - b)² where "r" is the radius and (a, b) is the center.

We are given that (-3, 4) is the center and the radius is 3, so that means a = -3, b = 4, and r = 3. Insert the values to their respective places in the equation:

3² = (x - (-3))² + (y - 4)²

9 = (x + 3)² + (y - 4)²

Answer:

equation of a circle: (x-a)²+(y-b)²=r²

(x-(-3))²+(y-4)²=3²

(x+3)²+(y-4)²= 9

(x+6x+9)+(y-8y+16) =9

x+6x+9+y-8y+16=9

x+y+6x-8y+9+16-9=0

x+y+6x-8y+16 =0

Note that the graph of the function ((x+1)²+(y+2)²=9) is attached accordingly

A coordinate graph is one that has two axes that are perpendicular to each other. These two axes are known as the x- and y-axes. The y-axis is represented by the vertical line, while the x-axis is represented by the horizontal line. A coordinate plane, a Cartesian plane, and a Cartesian coordinate system are other names for it.

The given circle has a radius of 3 units and centre is (-1,-2).

This circle can thus be drawn by first plotting the point (-1,-2) and then with this point as centre draw a circle of radius 3.

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Full question:

graph the circle

((x+1)²+(y+2)²=9)

The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

We can derive an inequality from the problem statement which is:

8X + 12Y >= 1000

This inequality represents the amount of money the basketball team needs to raise by selling donuts.

X is the number of half dozen boxes sold

Y is the number of full dozen boxes sold.

To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:

If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:

8(50) + 12(50) = $400 + $600 = $1000

So this is a valid solution that meets the fundraising goal.

If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:

8(100) + 12(0) = $800

This is not enough to meet the fundraising goal, so it is not a valid solution.

If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:

8(0) + 12(100) = $1200

This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.

Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

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The loan have a higher monthly payment Because the lease is riskier to the financing company.

To Determine the costs of buying versus leasing a motor vehicle, we need to consider the total costs associated with each option. For buying, the total cost is the sum of the down payment, loan payments, and the estimated value at the end of the loan, minus the resale value of the car.

On the other hand, for leasing, the total cost can be calculated as the sum of the security deposit, lease payments, and end-of-lease charges. We also need to consider the opportunity cost of investing the down payment and the security deposit.

We know that Melisha can pay for her vehicle with a 4-year loan or with a lease with the same down payment and same interest rate.

Therefore, the loan have a higher monthly payment Because the lease is riskier to the financing company.

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Answer:

Step-by-step explanation:

2x2x2 = 2^3

2^3 = 8

2^x + 4 = 8

so x= 2