use the product to sum formula to help me solve this problem in trig

Answer: I believe it is D! hope this helps

Step-by-step explanation:

The standard deviation for the following set of numbers 29,31,37,42 is 34.75.

Why is there a standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Standard deviation:

= (29 + 31 +37 + 42 )/ 4

= 34.75

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The following equations can be solved in two different ways

On solving the equation we get the value as [tex]x=7[/tex]

What is an equation?

An equation is a formula that represents the equality between two expressions.

Method 1) : We are given an equation

[tex]5(x+2)=45[/tex]

Divide both sides by 5, we get

[tex]x+2=9[/tex]

Subtracting 2 from both sides we get,

[tex]x=7[/tex]

Method 2)

We are given an equation

[tex]5(x+2)=45[/tex]

On simplifying the equation we get

[tex]5x+10=45[/tex]

Subtracting 10 from both sides

[tex]5x=35[/tex]

Dividing both sides by 5 we get

[tex]x=7[/tex]

In the first method we first perform division then subtraction and in the second method we simplify the right side of the equation then subtract 10 and finally divide by 5.

Hence We solve the equation by 2 ways And in both cases we get the answer as 7

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1.

In order to calculate how much is 5% of the original value, let's use the following rule of three:

So the amount taken off is $0.32.

2.

Subtracting this amount from the original price, we have:

So the final value is $6.18.

3.

A solution in a sentence would be:

The final value after the discount is 0.95 * 6.5 = $6.18.

In this problem we have that

In the given right triangle

sin(x)=15/24 ------> by opposite side divided by the hypotenuse

using a calculator

x=38.68 degrees

sin(x)=15/24 ------> simplify

sin(x)=5/8

Answer

The new dimensions of the rectangle after dilation by scale factor of (9/4) include

New length = 72 feet

New width = 18 feet

Explanation

The relationship between new length, original length and scale factor of dilation is given as

New length = (Original length) × (Scale factor)

For this question,

Scale factor = (9/4)

Original length = 32 feet

New length = (Original length) × (Scale factor)

New length = 32 × (9/4) = 72 feet

New width = (Original width) × (Scale factor)

Original width = 8 feet

Scale factor = (9/4)

New width = (Original width) × (Scale factor)

New width = 8 × (9/4) = 18 feet

Hope this Helps!!!

Answer:

2,400 km

Step-by-step explanation:

1 km = 1000 m or 1 m = 10^-3 km

so 2,400,000 x 10^-3 = 2,400 km

I think it's 8- I did this before

We have the graph of the function h.

First, we must find h(-1)

To find h(-1) we must see which value takes the function when x = -1

In this case

We can see that when x = -1, the function is equal to 2.

So,

Second, to find one value of x for which h(x) = 5 we must see which value takes x when the function is equal to 5.

In this case

We can see when h(x) = 5, x takes the value of 1.

So,

Let the following variables represent the velocities of the plane and the wind:

When the plane travels with the wind, the total velocity is the sum of both velocities. When the plane travels against the wind, the resulting velocity will be the difference of both velocities.

When the plane travels with the wind, the following condition is satisfied:

When the plane travels against the wind, the following condition is satisfied:

This is a 2x2 system of equations. To solve it by the elimination method, add both equations:

Solve for the velocity of the wind from the first equation:

Therefore, the velocity of the plane is 62 miles per hour and the velocity of the wind is 18 miles per hour.

Answer:

ax^2 + bx + c = 0

Step-by-step explanation:

a, b, are the coefficients, c is the constant term, and x is the variable

Hope that helps

Given the table:

x f(x)

-5 -6

-4 -2

-3 0

-2 4

-1 4

0 0

1 -2

2 -6

3 -10

Let's find the best behaviour if the graph.

From the table, as the values of x increases, the values of f(x) decreases and as the values of y decreases, the values of f(x) decreases.

From the table of values, we can see that as x approaches negative infinity, f(x) approaches negative infinity.

Also, as x approaches infinity, f(x) approaches negative infinity.

Thus, we have the statement that best predicts the behaiour of the graph f(x):

As x ==> ∞, f(x) ==> -∞, and as x ==> -∞, f(x) ==> -∞

ANSWER:

If Emerson wants to fence a rectangular play area for his dog where he decides to make the length of the fence, 2feet more than the width, and he uses the complete 32feet fencing he had with himself, for this project, then the dimensions of the play area are 9ft in length and 7ft in width.

As per the question statement, Emerson wants to fence a rectangular play area for his dog and he decides to make the length of the fence, 2feet more than the width, for which, he uses the complete 32feet fencing he had with himself.

We are required to calculate the dimensions the play area from the above-mentioned data.

To solve this question, we need to know the formula to calculate the perimeter of rectangle which goes as [p = 2(l + b)]

Where, "p" is the perimeter of the rectangle, "l" is the length and "b" is the breadth of the rectangle.

Here given that, length of the fence will be 2feet more than width of the same. So, let us assume that width of the fence is "x" ft, and the length of the fence should be (x + 2)ft.

Also since, Emerson uses the complete 32feet fencing he had with himself, the perimeter of the play-area will be 32ft.

Substituting our assumptions in the above mentioned formula to calculate the perimeter of rectangle, we get, [32 = 2{x + (x + 2)}], which is a linear equation. Therefore, solving this equation for x, we will obtain our desired answer.

[32 = 2{x + (x + 2)}]

Or, [32 = 2(x + x + 2)]

Or, [32 = 2(2x + 2)]

Or, (32 = 4x + 4)

Or (4x = 32 - 4)

Or, (4x = 28)

Or, [x = (28/4)]
Or, (x = 7).

Therefore, (x + 2) = (7 + 2) = 9ft.

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The matrix X is [tex]X = A^{-1} B[/tex]

What are invertible matrix?

A square matrix is invertible if and only if the determinant is not equal to zero. A n × n matrix is only invertible if the determinant of the matrix is not zero and has inverse. If the determinant is zero, then the matrix is not invertible and has no inverse.

Given that the two matrix A, B are invertible, therefore the inverse of the matrix exists.

Now given that,

AX = B                 …(1)

Multiplying [tex]A^{-1}[/tex] on both the side of the equation (1), we get

[tex]A^{-1} A X = A^{-1} B[/tex]

We know that [tex]AA^{-1} = 1[/tex]

⇒ [tex]X = A^{-1} B[/tex]

Therefore, the matrix will be [tex]X = A^{-1} B[/tex]

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Given:

Required:

To write the steps to solve the given equation and to find the value of x.

Explanation:

(A)

Consider

First multiply 6,

Next subtract 15 from 61, we get

Add 51 to the above equation

Subtract 3x we get

Divide 9 on both side, we get

(B)

x = 7 makes the equation true.

Final Answer:

The value of x = 7 makes the equation true.

Hence, the inequality which symbolizes when a student's average cost of tutoring is no more than $22.207 is:

Answer:

0.0324

Step-by-step explanation:

0.36x0.09=0.0324

Then

4 | x + 1| + 2 > 6

Substract 2 , at left and right

4 |x+1 | > 6-2 = 4

Now divide by 4

(4 |x + 1| )/4 > 4/4

Then

| x + 1| > 1

Now solve this equation, by way of 2 equations

x + 1 > 1

and

- (x + 1) < 1

Solution for first iis

x > 1 - 1

x > 0

And solution for second inequality is

- x - 1 < 1

x < -1 - 1

x < -2

THEN ANSWER interval for this is

(-OO, -2) U (0, OO)

ANSWER IS OPTION B)

Interval notation is

x > 0 ( 0, infinite)

x < -2 ( - infinite, -2)

You have the following system of equations:

3x - 3y + 3z = 0 (1)

2x - y - 3z = 2 (2)

-7x + 6y - 2z = -2 (3)

In order to determine if the previous system has solution or not, proceed as follow:

Add equation (1) and (2):

3x - 3y + 3z = 0

2x - y - 3z = 2

5x - 4y = 2 (5)

Multiply the equation (3) by -3 and the equation (2) by 2:

(-7x + 6y - 2z = -2)(-3)

21x - 18y + 6z = 6

(2x - y - 3z = 2)(2)

4x -2y - 6z = 4

Add the previous results:

21x - 18y + 6z = 6

4x -2y -6z = 4

25x - 20y = 10 (6)

You can notice that equation (6) is five times equation (5). It means that there is no way of getting a solution for x or y with equations (5) and (6).

the previous situation also means that there is no solution to the system of equations.

The equivalent expression to 45÷(2-x) is 45/(2-x).

According to the question,

We have the following expression:

45÷(2-x)

Or in other words, it can be said that 45 is divided by (2-x).

Now, when we are finding the equivalent expression of any expression for that matter then the final expression after solving any expression should be equal to the original one.

For example, the equivalent expression for 3/5 is 6/10 because when we divide the second fraction by we will get 3/5.

Now, in this case, the equivalent expression will be:

45/(2-x)

Because the fraction also means division.

Hence, the correct option is A.

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Answer: 0.6

Step-by-step explanation:

m = 6/10

m = 0.6

The explicit formula for this sequence exists as = (-9) + (n-1)6

We can use an explicit formula, as previously discussed, to determine the nth term in a series. The simplest meaning of explicit is precise or unambiguous. The reason the formula is explicit is that, if properly used, it can be used to find the nth term.

An arithmetic sequence can be expressed explicitly as a = a + (n - 1)d, and each term of the sequence can be computed without knowledge of the other parts. The nth term of an arithmetic, geometric, or harmonic series is usually the explicit formula.

Given: -9, -3, 3, 9, 15. ​

Because it is an arithmetic series, the supplied sequence.

Therefore, there is no difference between two consecutive terms.

For example, 3-(-3)=6 and (-3)-(-9)=6.

The nth term is now equal to a+(n-1)d.

as, a=-9

So, = -9+(n-1)6

= -9+6n-6

= 6n-15

so that =-9+(n-1)6.

The answer is option D

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Given:

Since n is greater or equal to -1, we are to use a closed dot.

To draw the number line, make a closed circle at point -1, and move the red line left (because n is less than or equal to -1).

Therefore the number line that shows the inequality is the third number line.

The diagram is below

we have the expression

step 1

Factor 2

step 2

Simplify

Answer: 539.9

Step-by-step explanation: Since 2004 is our starting year, 9 years have passed since 2004 and 2013. 9 would be the “x” in the equation.

y = 20.1(9) + 359

y = 180.9 + 359

y = 539.9

The next year's expected profit to quote is $19,386.97

Given,

Net profit for 1st year = $14,250

Net profit for 2nd year = $15,390

Net profit for 3rd year = $16,621.21

Net profit for 4th year = $17,950.90

We have to find the expected profit in the next year.

For that, first we have to find the profit percentage of 4 years.

Profit % for 1st year =( 15,390 - 14,250 )/14250 × 100 = 0.08 × 100 = 8%

Profit % for 2nd year =( 16,621.21 - 15,390 )/15,390 × 100 = 0.08 × 100 = 8%

Profit % for 3rd year =( 17,950.90 - 16,621.21)/16,621.21 × 100 = 0.08 × 100 = 8%

So the profit percentage is consistent for the years.

Then we can find next years profit by;

Net profit for 4th year × 1.08 = 17,950.90 × 1.08 = 19,386.97

That is,

The next year's expected profit to quote is $19,386.97

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Answer:

d. $19,386.97

The box has the shape of a cuboid.

The volume of the box is given by the formula:

We now find the number of cubes that make up the length, width, and height

Hence, the volume of the box can be calculated by:

Therefore, the volume is 72 ft³

Answer

The point of intersection is the solution point for the system equation

The point of intersection is the solution

The final answer

x = 4

y= -3

Given

d = 1/4 inch

d = diameter

Procedure

P(x) = (x4+2x3-7x2+4x) = 0.1 or an expression of more than two algebraic terms, particularly the sum of numerous phrases that contain different powers of the same variable, p(x)=0.1 x4 + 0.2 x3 - 0.7x2 + 0.4x (s).

Zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function are the four most prevalent types of polynomials used in precalculus and algebra.

For instance, the polynomial 2x+5 has an exponent of 1.

The following are a few illustrations of each kind of polynomial function:

continuous operation. Example: The linear polynomial function y = 1. For instance, the quadratic polynomial function 5y + 10 Consider the Cubic Polynomial Function 14x2 + 2x – 6. Example: Quartic polynomial function 4y3 + 5y2 + 2. Eg: 3y4 + 5

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