prime numbers that can be expressed as a sum and difference of 2 prime numbers
ASAP

V= (4d^2 - 48d + 96) / (-36(d - 1)^2) will be the expression for the volume of the following prism when the dimensions of the prism are given.

The quantity of space a three-dimensional figure occupies is measured by its volume. It is determined by multiplying the object's length, breadth, and height, and is generally symbolized by the letter "V". For example, the volume of a cube with sides of length 3 units is 3 x 3 x 3 = 27 units.

The formula 4/3r3 may be used to determine a sphere's volume, where r is the sphere's radius. The area of the base times the height of the cylinder, or r2h, yields the volume of a cylinder.

It's important to remember that the volume of a three-dimensions figure varies depending on its shape and size.

How to solve?

V = (d - 2/3d - 9) * (4/d - 4) * (2d - 6/2d - 4)

V = (d - 2/3d - 9) * (4/d - 4) * (4d - 24/4d - 16)

V = ((d - 2)/(3d - 9)) * (4/d - 4) * (4d - 24/4d - 16)

V = ((d - 2)/(3d - 9)) * (4/(d - 4)) * (4d - 24/(4d - 16))

V = ((d - 2)/(3d - 9)) * (4/(d - 4)) * (4d - 24/(4d - 16))

= ((d - 2) * 4 * (4d - 24)) / ((3d - 9) * (d - 4) * (4d - 16))

= (4d^2 - 48d + 96) / (12d^2 - 48d^2 + 144d - 36)

= (4d^2 - 48d + 96) / (-36d^2 + 144d - 36)

= (4d^2 - 48d + 96) / (-36(d^2 - 4d + 1))

= (4d^2 - 48d + 96) / (-36(d - 1)(d - 1))

V= (4d^2 - 48d + 96) / (-36(d - 1)^2)

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Answer:

80 and 120 for 3 pointers

Step-by-step explanation:

Answer:

her grade is 90

Step-by-step explanation:

a) In R^4, a set of 5 vectors is linearly dependent if the rank of the matrix formed by these vectors is less than 4. Otherwise, the set is linearly independent.(b) In R^6, a set of 5 vectors is linearly dependent if the rank of the matrix formed by these vectors is less than 5. Otherwise, the set is linearly independent.

a) To determine if the set of 5 vectors in R^4 is linearly dependent, we can check if the determinant of the matrix formed by these vectors is zero. If the determinant is zero, the vectors are linearly dependent. If the determinant is non-zero, the vectors are linearly independent. To check if they span R^4, we need to determine if every vector in R^4 can be expressed as a linear combination of these 5 vectors. If they can, then the set spans R^4. Lastly, if the vectors are linearly independent and span R^4, they form a basis for R^4. b) Similarly, to determine the linear dependence of a set of 5 vectors in R^6, we check if the determinant of the matrix formed by these vectors is zero. If it is zero, the vectors are linearly dependent. If the determinant is non-zero, they are linearly independent. To check if they span R^6, we need to verify if every vector in R^6 can be expressed as a linear combination of the given vectors. If they can, the set spans R^6. If the vectors are linearly independent and span R^6, they form a basis for R^6.

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Answer:

0.875 is the ratio from white to brown socks.

Answer:

Given function

#15 Find the inverse of h(x)

Substitute x with y and h(x) with x and solve for y:

The inverse is:

#16 The graph with both lines is attached.

The x- and y-intercepts of both functions have reversed values.

#17 Table of the inverse function  will contain same numbers with swapped domain and range.

Initial look is like this:

The rest of the table is filled in by finding the values:

Answer:

288 cm^3

Step-by-step explanation:

The fare for this flight was $542.50 which is calculated using least-squares regression line equation. Therefore, the correct answer 542.50

To find the fare for this flight, we will first use the provided least-squares regression line equation to predict the fare and then account for the residual.

Step 1: Use the least-squares regression line equation to predict the fare.
ŷ = 102.50 + 0.65x, where ŷ is the predicted fare and x is the distance in miles.

Step 2: Substitute the given distance (x = 500 miles) into the equation.
ŷ = 102.50 + 0.65(500)

Step 3: Calculate the predicted fare.
ŷ = 102.50 + 325
ŷ = 427.50

The predicted fare for a 500-mile flight is $427.50.

Step 4: Adjust for the residual.
The residual for this flight is 115.0, which means the actual fare is $115 higher than the predicted fare.

Step 5: Add the residual to the predicted fare to find the actual fare.
Actual fare = Predicted fare + Residual
Actual fare = 427.50 + 115
Actual fare = 542.50

The fare for this flight was $542.50.

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Divide the amount of tip by amount charged:

10 / 80 = 0.125

Multiply by 100:

0.125 x 100 = 12.5 %

The tip was 12.5 %

Translate:

Twice a number increased by 2 is at least 10.

     2 · n                               +2           ≥             10

Solve:

   2n + 2 ≥ 10

         2n ≥ 8

           n ≥ 4

As long as you pick a number that's 4 or greater, you'll satisfy that statement.

Answer:

The answer is 9x² + 3x - 2.

Step-by-step explanation:

1) Collect like terms.

\((7x^{2} + {2x}^{2} ) + ( - 2x + 5x) + (8 - 10)\)

2) Simplify.

\( {9x}^{2} + 3x - 2\)

Therefor, the answer is 9x² + 3x - 2.

The total number of ways in which the group of seven people can be seated together in a row are 1440.

The group of seven people are attending the movie together and two of them are insisting that they will sit side by side to each other.

Now if all the people were to be seated in any random order then the number of positions would have been seven but now as two people are sitting side by side so we will consider only six positions in which we have to make the combinations.

And as we know that the seven people will be unique and there will be no repetition total number of ways in which the seven can be fitted together in a row is,

= 6 x 5 x 4 x 3 x 2 x 1 x 2

= 1440

It is to be noted that we have multiplied by the number of positions with to because the two people who are sitting together can be seated in two possible ways.

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Answer:

The equations that have infinitely many solutions are;

Explanation:

For an equation to have infinitely many solutions, the left-hand side of the equation and the right side of the equation must be equivalent/equal.

That means that the expression before the equal sign must be equivalent to the expression after the decimal.

such as;

From the given equation, the equations that have their left and right sides equivalent are;

Therefore, the equations that have infinitely many solutions are;

Answer:

  16.6°

Step-by-step explanation:

The triangle can be solved using the Law of Cosines to find the side opposite the given angle, then the Law of Sines to find the missing angle from the given sides.

__

We choose to use a=10, b=4, C=29°.

  c² = a² +b² -2ab·cos(C) . . . . . law of cosines

  c² = 10² +4² -2·10·4·cos(29°) ≈ 46.0304

  c ≈ √46.0304 ≈ 6.78457

Then angle B (opposite side b) is ...

  sin(B)/b = sin(C)/c . . . . . . . . . law of sines

  sin(B)/4 = sin(29°)/6.78457

  B = arcsin(4/6.78457×sin(29°)) ≈ 16.6085°

The missing acute angle is about 16.6°.

The real values of $c$ for which $x^2 + 16x + c$ is the square of a binomial are $64$ and $0$.

To find these values, we can use the concept of completing the square. For a quadratic expression to be the square of a binomial, the coefficient of the linear term ($16x$) must be twice the product of the square root of the constant term ($c$) and the square root of the coefficient of the quadratic term ($1$). In this case, the coefficient of the linear term is $16$ and the coefficient of the quadratic term is $1$. So, we have $16 = 2\sqrt{c}\sqrt{1}$.

Simplifying this equation gives $16 = 2\sqrt{c}$. Dividing both sides by $2$ yields $\sqrt{c} = 8$. Squaring both sides gives $c = 64$. Thus, $c = 64$ is one possible value.

Additionally, if we consider the case when $c = 0$, the quadratic expression becomes $x^2 + 16x + 0 = (x + 8)^2$. Therefore, $c = 0$ is another possible value.

In summary, the real values of $c$ for which $x^2 + 16x + c$ is the square of a binomial are $64$ and $0$.

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The answer is :

Explanation

Here is the answer.

When we subtract two numbers, the result is called the difference.

So if we have 37 - 7 = 30, 30 is the difference.

When we add two numbers, the result is called the sum.

So if we have 30 + 7 = 37, 37 is the sum.

When we multiply two numbers, the result is called the product.

So if we have 6 × 6 = 36, 36 is the product.

Finally, when we divide two numbers, the result is the quotient.

So if we have 36 ÷ 2 = 18, 18 is the quotient.

Answer: coordinates of the y-intercept is (0, -21)

Step-by-step explanation:

I'm assuming that you are asking for the coordinates of the y-intercept of the function

f(x)=(x-7)(x+3).

Well the y-intercept occurs when x=0, so plugging this value into f(x) yields f(0)=(-7)(3)=-21.

Answer is 6.

Explaination:

When subtracting a negative number, the number becomes positive and the minus sign to a plus sign.

you do 479 x 2 = 958 there is your answer your welcome

Answer:

15

Step-by-step explanation:

10.5 x (20/14)=14.99999999999...=15

Pythagoras theorem - The length of the third side is 6.71unit

What is Pythagoras theorem ?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The Pythagoras theorem's equation is as follows:

H² = P² + B²

The triangle's third side will be the following length:

Let x represent the triangle's third side's length.

9² = 6² + x²

81 = 36 + x²

x² = 45

x = 6.708

x = 6.71 units

Hence, the third side of the triangle is 6.71unit

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Answer:

take the numbers in the () and turn them into a equation  slope

Step-by-step explanation:

Answer:

\(14z+8\)

Step-by-step explanation:

\(2(7z+4)\\\\\boxed{14z+8}\\\\\left \{ {{2*7z=14z} \atop {2*4=8}} \right.\)

Hope this helps.

Answer:

2

Step-by-step explanation:

Given expression:

\(\log_82+3\log_82+\dfrac{1}{2}\log_816\)

\(\textsf{Apply the Power law}: \quad n\log_ax=\log_ax^n\)

\(\implies \log_82+\log_82^3+\log_816^{\frac{1}{2}\)

Simplify:

\(\implies \log_82+\log_88+\log_84\)

\(\textsf{Apply the Product law}: \quad \log_ax + \log_ay=\log_axy\)

\(\implies \log_88+\log_8(2 \cdot 4)\)

\(\implies \log_88+\log_88\)

\(\implies 2\log_88\)

\(\textsf{Apply log law}: \quad \log_aa=1\)

\(\implies 2 \cdot 1\)

\(\implies 2\)

please look above for your answer .

EXPLANATION

Since the initial amount of money was of $29,820, and the account earns interest rate by a reason of 7% per year, we can use the simple interest rate equation as shown as follows:

Where P=Principal= 29,820, r=rate in decimal form=7/100=0.07 , t=time in years=4,

Plugging in the numbers into the expression:

Multiplying numbers:

Adding the Interest to the Initial Capital: 29,820+8,349 = 38,169

In conclusion, Colin will have $38,169 after 4 years

The given expression y=cos x is solved using the arc length formula. And, the required integral or curve length is \(L=\int\limits^{2\pi}_0 \sqrt{1+\sin^2x} \, dx\).

The length of the curve or the arc length helps to determine the distance between one point to another point in the curve. This is calculated by using the integral formula between two given points,

\(L=\int\limits^b_a \sqrt{1+\left(\frac{dy}{dx}\right)^2} \, dx\)

The given expression is y=cosx and the limit is 0≤x≤2π. First, differentiate the given expression concerning x, we get,

dy/dx= -sin x

Then, squaring both sides of the above expression,

(dy/dx)²= sin²x

Now, substituting (dy/dx)² in the formula, we get,

\(L=\int\limits^{2\pi}_0 \sqrt{1+\sin^2x} \, dx\)

Therefore, the above expression is the required answer.

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The complete question is -

Set up, but do not evaluate, an integral for the length of the curve y=cosx, 0≤x≤2π.

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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Answer:

27

Step-by-step explanation:

Since the exponents are negative, what we need to do is switch up the places so that it's positive.

\(\frac{3^{-9} }{3^{-12} }\)

\(\frac{3^{12} }{3^{9} }\)

Now, we can use the \(\frac{x^a}{x^b} = x^a^-^b\) rule to solve for the answer.

\(3^{12-9}\)

3³

27

Answer:

Z= -150

Step-by-step explanation: