If sine= 2/3, which of the following are possible for the same value of ?

The rate of change for company A is 8.

The rate of change for company B is 15

Company A is better as it is charging less by a value of $18

What is rate of change?

Rate of change is the changes in the dependent variable when the independent variable changes by a unit value.

We are given 2 companies

A) equation for charges applied by company A is given by c=8h+10

Cost is a function of hours

To find the rate of change we differentiate the function

We get c' = 8

Rate of change for company A is 8

The cost for 4 hour rental is

c= 8(4)+10

c=32+10

c=$42

B) Company B charges $15 per hour

Rate of change for company B is 15

The cost for 4 hour rental is

c= 15(4)

c=$60

C) Company A is better to buy by $18 as the difference between the four hours price between company A and company B is $ 18

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We are given that the total number of sales is 35.

According to the question, his goal is to make add-on sales during 85% of sales.

Therefore, the add-on sales would be:

Hence, we will need to make 30 add-on sales to meet the goal.

Answer:

The midpoint is (-1,1)

Equation: y = -x -2

Step-by-step explanation:

Midpoint:

([tex]\frac{-5+3}{2}[/tex], [tex]\frac{-5 + 3 }{2}[/tex])  You are taking the averages of the x values and the y values.

([tex]\frac{-2}{2}[/tex],[tex]\frac{-2}{2}[/tex])  

(-1,-1)

Equation:

The slope of the 2 points given is

[tex]\frac{3 - -5}{3- - 5}[/tex] = [tex]\frac{8}{8}[/tex] = 1  The slope is the change of y over the change in x.  Points are given in the form (x,y)  So, I subtracted the y values on top and the x values on  the bottom of the fraction.

The equation that is created is perpendicular to the original line, so it slope is the negative reciprocal.

1 as a fraction is [tex]\frac{1}{1}[/tex].  negative reciprocal means turn the fraction upside down and take the opposite  value.  If I flip [tex]\frac{1}{1}[/tex] upside down, I get the same fraction which is equal to 1.  Now I will take the opposite sign.  Since it is positive, the new slope will be negative

slope  -1

x = -1

y = -1  

I am using the point that will be on the new line. This is the midpoint that we just found (-1,-1)  I am going to plug in the number that I know and solve for b or the y=intercept.

y =  mx + b

- 1 = -1(-1) + b

-1 = 1 + b  Subtract 1 from both sides of the equation

-2 = b

y = mx + b

y = -1x -2

or

y = -x -2

x = 3, y = 2

The equations are:

x + y = 5......................(1)

y - 2x = -4...................(2)

Make x the subject of the the formula

x = 5 - y...............(3)

Substitute equation (3) into equation (2)

y - 2(5 - y) = -4

y - 10 + 2y = -4

3y = -4 + 10

3y = 6

y = 6 / 3

y = 2

Substitute the value of y into equation (3)

x = 5 - 2

x = 3

Given:

The ship is moved from (-10,9) to (-1,-5) in the coordinate plane.

To find:

The transformation rule

Explanation:

The initial point can be written to obtain the terminal point as follow,

In general,

We write,

Final answer: Option C.

The flow of water can fill a 4-gallon container in 28 seconds.

Given:

Number of gallons = 4

Time = 28 seconds

Hence, the ratio of gallons to seconds will be 4 : 28

Therefore, the faucet fills the container at the rate of 1/7 gallon per second

Given:

radius of Ferris wheel = 40 ft

height of a car = 5 ft

height of a tent = 20 ft

no. of passenger cars = 20

time to load all cars = 12 minutes

time for 1 rotation = 2 minutes

time for all rotations = 8 minutes

What we want to know is how many degrees the car will have to travel along the circle before it reaches a height of 20 ft.

We can draw a triangle to represent the unknown and find the angle.

The total height from the ground to the center of the Ferris wheel is 45 ft (5ft car height + 40 ft radius). We deduct the 20ft height of the tent so we get the side of the right triangle we're using to solve for the missing angle. That height is 25 ft.

The radius also serves as the hypotenuse of the triangle.

We can then use the following to solve for the angle theta:

Now we know that the car must travel 51.3 degrees along the circle before it gets to a height where it can see above the tents. If one rotation is 360 degrees and it takes 2 minutes to complete one round, then to find the time it will take to travel 51.3 degrees, we use the following equation:

It will take them 17.1 to be able to start looking for their house.

Now every time the car goes around the path of the Ferris wheel, for 17.1 going up and another 17.1 seconds going down, they will not be able to look for their house.

17.1 seconds x 2 x 4 turns = 136.8 seconds

8 minutes - 136.8 seconds = 480 - 136.8 = 343.2 seconds or 5 minutes and 43.2 seconds

They have 5 minutes and 43.2 seconds to look for their house.

Answer:

The prime Factorization of 49 is 7.7

Step-by-step explanation:

Hope this helps! :))

Answer:

7

Step-by-step explanation:

The factors of 49 are 1, 7, and 49

Answer:

No Solution

Explanation:

Given the system of equations:

Using elimination, on subtracting, we have:

Therefore, the system of equations has No Solution.

Explanation

Part A

Given that x and y are related by the by the equation 90x + 2200 =y. We can find the change by comparing the formula with the original equation of a line.

Comparing the above with the given question, m becomes change in Lisa's pay for each copy of history is fun. Therefore,

Answer: 90 dollars

Part B

If Lisa does not sell any copies of history is fun, therefore, the value of x becomes zero. We can then have the total pay as

Answer: 2200 dollars

Given: A circle has a center point at the coordinates P(3,0) with a diameter line RT where R has the coordinates (-47,25).

Required: To determine the coordinates of T.

Explanation: The given circle is-

Let the coordinates of T be (x,y). Then the center of a circle is divided by the diameter in the ratio of 1:1. The section formula for a point (x,y) dividing a line segment in the ratio of 1:1 is-

Hence, for the given line RT, point P divided RT in 1:1. Thus-

Further solving for x and y as-

Final Answer: The coordinates of T are (53,-25).

The composition of the function, (g o h)(0) = 0.

To find the composition of a function, first, find the value of the inner function by plugging in the given value of x. The output of the inner function would now be used as the input to evaluate the outer function.

We are given the following:

g(x) = 5x

h(x) = √x

To find the composition of the function, (g o h)(0), first, find h(0). To find h(0), substitute x = 0 into the inner function, h(x) = √x:

h(0) = √0

h(0) = 0

Find (g o h)(0) by substituting x = 0 into g(x) = 5x:

(g o h)(0) = 5(0)

(g o h)(0) = 0

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The rational number is -91/100 or -0.91.

Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.

The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.

Given:

We have to find the rational number between -0.45 and -0.46

Now, make both decimal into fraction

-0.45 and -0.46

-45/100 and -46/100

Now, multiply 2

-45/100 x 2/2 and -46/100 x 2/2

-90/100 and - 92/100

Hence, the rational number is -91/100 or -0.91.

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The rational number is -91/100 or -0.91.

Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.

The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.

Given:

We have to find the rational number between -0.45 and -0.46

Now, make both decimal into fraction

-0.45 and -0.46

-45/100 and -46/100

Now, multiply 2

-45/100 x 2/2 and -46/100 x 2/2

-90/100 and - 92/100

Hence, the rational number is -91/100 or -0.91.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

assisted reproductive technology (ART) cycles:

pregnancies = 36%

pregnancies resulted in multiple births = 26%

Step 02:

a.

p (pregnancies) = 36% = 36/100 = 0.36

pregnancies resulted in multiple births = 26% = 26/100 = 0.26

p(pregnancies resulted in multiple births) = 0.36*0.26 = 0.0936

b.

p (pregnancy did not produce a multiple birth) = 1 - 0.0936 = 0.9064

c.

Indeed, the probability of multiple pregnancies is low 9.36%.

That is the full solution.

In order to calculate the new wage per hour, we just need to multiply the old value of $10.59 by 1.04, that is, an increase of 4%, so we have:

So the new wage per hour is $11.01.

Taylor's scored 22 points

Erin scored 18 points

Nya scored 54 points

Aaron scored 64 points

Let Taylor's point = x

Erin scored 4 less points than Taylor:

Erin's score = x - 4

Nya scored three times as many points as Erin:

Nya's score = 3(x - 4)

Aaron scored 10 more points than Nya:

Aaron's score = Nya's score + 10

= 3(x - 4) + 10

The total score of the four friend = 158 points

Taylor's score + Erin's score + Nya's score + Aaron's score = 158

x + (x - 4) + 3(x -4) + 3(x-4) + 10 = 158

Expand the parenthesis:

x + x -4 + 3x - 12 + 3x - 12 + 10 = 158

collect like terms:

x + x + 3x + 3x - 4 - 12 - 12 + 10 = 158

8x - 18 = 158

8x = 158 + 18

8x = 176

Divide both sides by 8:

8x/8 = 176/8

x = 22

Taylor's scored 22 points

Erin scored : x-4 = 22- 4 = 18 points

Nya scored : 3(x-4) = 3(22-4) = 3(18) = 54 points

Aaron scored: 3(x-4) + 10 = 54 + 10 = 64 points

Given the polynomial:

Let's factor the polynomial.

To factor, let's use the AC method.

Find a pair of numbers whose product is -18 and whose sum is 7.

We have the pair:

9 and -2

We have the factors:

(w + 9)(w - 2)

Therefore, the factored form of the polynomial is:

ANSWER:

Given:

The digit is 0.6295.

Required:

To find the 275th digit after the decimal point in the repeating decimal 0.6295.

Explanation:

For any non-negative integer, we have:

The 4n+1th digit after the decimal point is 6.

The 4n+2th digit after the decimal point is 2

The 4n+3th digit after the decimal point is 9

The 4n+4th digit after the decimal point is 5.

Since the repeating digit is 4 and we have to find the 275th digit.

Thus

It can be written as:

275 = 4. 68 + 3

That is 275th digit after the decimal point in the repeating decimal is 9 with n= 68.

Final answer:

Thus option k is the correct answer.

The triangle has a height of 19 meters.

In this problem we find the area of a triangle, in square meters, and the relationship between its height (h) and its base length (b), both in meters. We must solve the following expression to determine the height:

A = (1 / 2) · b · h

h = 3 + 2 · b

A = 76

Then,

76 = (1 / 2) · b · (3 + 2 · b)

152 = b · (3 + 2 · b)

152 = 3 · b + 2 · b²

2 · b² + 3 · b - 152 = 0

Finally, we find the roots of the polynomial by quadratic formula:

b₁ = 8, b₂ = - 19 / 2

Since, lengths are non-negative real numbers, the only possible solution is b = 8 and the height of the triangle is:

h = 3 + 2 · 8

h = 19

The height of the triangle is 19 meters.

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Given:

Graph opes upwards.

Let the vertex be (h,k)

Axis of symmetry is

y- intercept

x=0,

y=1

There is no x intercept .

Domain:

Range:

The function is increasing:

The function is decreasing:

Let's call x to the bags of peanuts. One bag has a variable cost of $1.83, then the variable cost of x bags is 1.83x dollars.

The total cost of production for the corporation is obtained by adding fixed and variable costs. In this case, the total cost is 18,200 + 1.83x dollars.

The revenue for the corporation of 1 bag is $3.43, then of x bags is 3.43x dollars.

When the revenue and the total cost are equal, the breakeven point is reached, in this case:

18,200 + 1.83x = 3.43x

18,200 = 3.43x - 1.83x

18,200 = 1.6x

18,200/1.6 = x

11375 = x

The cost of production of 11375 bags is:

Total Cost = 18,200 + 1.83*11375

Total Cost = 18,200 + 20816.25

Total Cost = 39016.25

Pete’s breakeven point is (11375, 39016.25), or, 11375 bags and $39,016.25

To derive f(x) = -67x, we can use the Power Rule.

In the given term, our n = 1 since x¹ = x. So, following the power rule, we will multiply the exponent 1 to the constant term -67, then subtract 1 from the exponent 1, hence x¹ will become x⁰.

Then, simplify.

Therefore, the first derivative of f(x) = -67x is -67.

Answer:

To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced.

So x = 10

Explanation:

Given the below equation;

To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced;

1) Note that we need to find a perpendicular line. Perpendicular lines have reciprocal and opposite slopes. So we know that the slope we need is -3

2) We also know that it must pass through (-2,-6), so let's plug the slope -3 the point (-2,-6) so that we can find the linear coefficient:

ANSWER

EXPLANATION

Recall, the formula for calculating the surface area of a cone is;

Given;

Substitute the values into the formula;

Given the function

We want to evaluate this function at x = 2.

When we evaluate a function at a given value, we just need to substitute the terms with a variable by the given value.

The values of x and y obtained by inverse matrix method are 2 and 3 respectively

An inverse of a matrix, A, is a matrix [tex] A^{-1}[/tex], that multiplies matrix A to give an identity matrix.

The inverse matrix method involves defining and making use of a coefficient matrix, A, a variable matrix, X, and a constant matrix, B, which are obtained from the system of equations as follows;

A·X = B
The system of equations is presented as follows;

3·x + 4·y = 18

4·x - y = 5

From the above system of equations, we have:

[tex]The \ coefficient \ matrix, \ A = \begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex]

[tex]The \ variable \ matrix, \ X = \begin{bmatrix} x \\ y \end{bmatrix}[/tex]

[tex]The \ constant \ matrix, \ B = \begin{bmatrix} 18 \\ 5 \end{bmatrix}[/tex]

From the equation, A·X = B, we have;

[tex]\therefore X = \dfrac{B}{A} = A^{-1} \times B[/tex]

Where: A⁻¹ is the inverse matrix of A, which is found as follows;

[tex]If\ A = \begin{bmatrix} a&b \\ c&d \end{bmatrix}[/tex]

[tex]Then, \ A^{-1} = \dfrac{1}{a\cdot d-b\cdot c} \cdot \begin{bmatrix} d& -b \\ -c& a \end{bmatrix}[/tex]

Which gives the value of A⁻¹ obtained from the coefficient matrix, A = [tex]\begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex] as follows;

[tex]A^{-1} = \begin{bmatrix} 3 & 4 \\ 4 & - 1 \end{bmatrix}^{ - 1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix}[/tex]

[tex]A^{-1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} & \dfrac{ - 4}{ - 19} \\\\ \dfrac{ - 4}{ - 19} & \dfrac{3}{ - 19} \end{bmatrix}[/tex]

The variable matrix, [tex]X = A^{-1} \times B[/tex], which gives the value of the variables in the solution is therefore;

[tex]X = \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} &\dfrac{ - 4}{ - 19} \\ \\\dfrac{ - 4}{ - 19} &\dfrac{3}{ - 19} \end{bmatrix} \times \begin{bmatrix} 18 \\ 5 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]

[tex]\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]

Therefore;

x = 2 and y = 3

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• The total surface area of a cylinder is given by:

where r = 1.75 cm

h = 3 cm

Hence:

• The volume of a cylinder is given by:

Hence:

ANSWER

surface area = 57.7 cm²

volume = 28.9 cm³