61) If an ellipse has vertices at (-7.0). (7.0), (0.4), and (0-4), what is its domain? What is its range?

the result is approximately: [tex]0.32608695652173913 x 10^(-10)[/tex]

To divide 300 million by 9.2 quintillion, you can use the following calculation:

[tex]300[/tex] million ÷  [tex]9.2[/tex] quintillion

First, let's convert 300 million to scientific notation:

[tex]300 million = 300,000,000 = 3 \times 10^8[/tex]

Next, let's convert 9.2 quintillion to scientific notation:

[tex]9.2 quintillion = 9.2 \times 10^18[/tex]

Now, we can perform the division:

[tex](3 x 10^8) ÷ (9.2 x 10^18)[/tex]

When dividing numbers in scientific notation, we subtract the exponents:

[tex]3 ÷ 9.2 = 0.32608695652173913[/tex]

And we subtract the exponent of 10:

[tex]10^(8-18) = 10^(-10)[/tex]

Therefore, Putting it all together, the result is approximately: [tex]0.32608695652173913 x 10^(-10)[/tex]

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1. Find the radius. The pizza has a diameter of 16, which means it has a radius of 8.
2. Put (8) into the area of a circle formula. A = πR2 or A = π(8)2
3. Find area. 201.06 square inches.
4. Divide by 12. 201.06 ÷ 12 = 16.755.
5. Multiply by 4 (since they each ate 4 slices). 16.755 × 4 = 67.020

Therefore, each boy ate 67 square inches of pizza.

Answer: 6.02

Step-by-step explanation:

use SOH CAH TOA, or in this case SOH

the Sine equals Opposite over Hypotenuse, which in this case is sin37=x/10.

Plug into a calculator and you get 6.02 after rounding.

Hope this helps :)

(and thanks for answering one of my questions)

The value of x is 6.01815 cm.

Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.

We have,

Angle = 37

Hypotenuse = 10 cm

Using Trigonometry

sin 37 = P/ H

0.601815 = x/ 10

x= 6.01815 cm

Thus, the value of x is 6.01815 cm.

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Answer:

No

Step-by-step explanation:

No, because 10 times around the route is 4200 yards, which is less than 3 miles

Based on an exponential model of the data, the predicted value of variable 2 when variable 1 = 2 is: A. variable 2 ≈ 128.

In order to determine an exponential equation for the line of best fit that models the data points contained in the graph (scatter plot), we would have to use a graphing calculator (Microsoft Excel).

Based on the scatter plot (see attachment) which models the relationship between the x-values (variable 1) and y-values (variable 2), an exponential equation for the line of best fit is given by

[tex]y = 137.93e^{-0.03x}[/tex]

Now, we can determine the predicted value of variable 2 when variable 1 = 2;

[tex]y(2) = 137.93e^{-0.03\times 2}\\\\y(2) = 137.93e^{-0.06}[/tex]

y(2) ≈ 128.

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Answer:

2%

Step-by-step explanation:

2/100 = 0.02

Then we can convert the decimal to a percentage by multiplying by 100:

0.02 x 100 = 2%

So 2/100 as a percentage is 2%. I hope this helps!

Answer:

12 × 4 × 18 = 864

( Use the volume formal L × W × H to help in all volume equations )

Answer:

a = 40°

Step-by-step explanation:

An isosceles triangle has two sides that are the same size. The angles opposite from those sides are equal (they are called base angles.) And, the three angles in a triangle add up to 180°

So,

100 + a + a = 180

combine like terms

100 + 2a = 180

subtract 100

2a = 80

divide by 2

a = 40

Answer:

( Use this formula below to help you find the volume of all equations using volume)

Volume formal = L × W × H

Volume formal = 24 × 15 × 5

Answer = 24 × 15 × 5 = 1,800

The total number of possible outcomes is n = 16

Given data ,

Let the total number of digits be represented as A

Now , the value of A = { 8 , 4 , 3 , 2 }

So , the total number of possible two digits numbers are

n = 2⁴

n = 16 outcomes

Let the outcomes be represented as B

B = { 82 , 83 , 84 , 88 , 42 , 43 , 44 , 48 , 22 , 23 , 24 , 28 , 32 , 33 , 34 , 38 }

Hence , the number of outcomes is n = 16

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4. The Federal Reserve System does d. all of these central bank functions.

5. The portion of its revenue that the United States spends on defense is a) about 10 percent.

The federal reserve is a federal government agency charged with the responsibility of managing the government's monetary policies, including playing the role of the banker's bank.

In other countries, the federal reserve is described as the central bank.

Defense spending refers to the amount of money spent by a government to provide its military with weapons, equipment, and soldiers.

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1) A and D are linear equations while B and C are non linear

2) The rule of the equation is given by option C

3) The solution is option C

4) The area is option B

5) The standard form expressions are shown by option C

We know that;

y = x + 3

-2x + y = 1

Then

x - y = -3 ---- (1)

-2x + y = 1 ---- (2)

x = -3 + y --- (3)

Substitute (3) into (2)

-2(-3 + y) + y = 1

6 - 2y + y = 1

6 -y = 1

-y = 1 -6

y = 5

Substitute y = 5 into (1)

x - 5 = -3

x = -3 + 5

x = 2

Thus the solution is (2, 5)

a^2 = 10^2 - 8^2

a = √100 - 64

a = 6

A = 1/2bh

A = 0.5 * 8 * 6

A = 24cm^2

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the equation representing an employee's monthly earnings is y = 0.16x + 1250 where x is the monthly sales and y is the monthly earnings, the true statement is c) Employees receive 16% commission on their total monthly sales..

An equation is an algebraic statement of the equality or equivalence of mathematical expressions.

While equations use the equal symbol (=), mathematical expressions combine variables with numbers, constants, values, and mathematical operands.

Let the monthly earnings of an employee = y

Let the monthly sales = x

y = 0.16x + 1,250

Thus, from this equation, 0.16 represents 16% commission on sales, therefore, the correct option is Option C.

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a) The monthly salary of an employee is $1,250.

b) The slope is 1,250 and the y-intercept is 0.16.

c) Employees receive 16% commission on their total monthly sales.

d) The monthly salary of an employee is 12.50%.

Answer:

1/2

Step-by-step explanation:

The probablility of any number on a die is 1/6.

So the numbers 4, 2, and 1 each have a probability of 1/6 meaning that each have a total probability of: 1/2. 3 is not accounted for due to our restriction.

Answer:

No

Step-by-step explanation:

to grap (-5,5) do not start at (0,0)

-5 is at the x axis so start it at (-0) then for 5 its juts (0) so (-0,0)

The equations which represents circles that have a diameter of 12 units and a center that lies on the y-axis are; x² + (y – 3)² = 36 and x² + (y + 8)² = 36.

Recall, the equation of a circle takes the form;

(x - h)² + (y – k)² = r² where r = radius = diameter/2 and (h, k) is the center.

Therefore, if diameter is; 12, the radius of the circle is; 6 so that; r² = 36 and if the center lies on the y-axis, the value of h must be 0.

Ultimately, the equations that satisfy the given conditions are; x² + (y – 3)² = 36 and x² + (y + 8)² = 36.

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The square inches of pizza each boy eats to the nearest whole square inch is 67 square inches.

The correct answer choice is option D.

A pizza has the shape of a circle

Area of a circle = πr²

Radius, r = diameter / 2

= 16/2

= 8 inches

Area of a circle = πr²

= 3.14 × 8²

= 3.14 × 64

= 200.96 square inches

The pizza was cut into 12 equal slices

Area of each slice = 200.96 square inches / 12

= 16.75 square inches

Area of pizza each boy eats = 16.75 square inches × 4

= 66.99 square inches

Ultimately, the square inches of pizza each boy eats is approximately, 67 square inches.

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Answer:

Step-by-step explanation:

since there is one square and 4 circles, the answer is 1/4

Answer:  the volume of the box is 31.25 cubic feet.

Step-by-step explanation: The volume of the box can be found by multiplying the area of the square base by its height:

Volume = Base Area x Height

Since the base of the box is a square with 2.5 feet wide on a side, its area can be calculated as:

Base Area = Side Length x Side Length = 2.5 ft x 2.5 ft = 6.25 sq. ft

And since the height of the box is 5 feet, the volume can be calculated as:

Volume = Base Area x Height = 6.25 sq. ft x 5 ft = 31.25 cubic feet

Therefore, the volume of the box is 31.25 cubic feet.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59[/tex]

Answer:

Adeline has 60 notebooks and 4 children.

Step-by-step explanation:

Let's assume that Adeline has 'x' notebooks and 'y' children.

According to the given information, if Adeline gives 13 notebooks to each child, she will have 8 notebooks left. This can be represented by the equation:

x - 13y = 8 ...(1)

Similarly, if she gives 15 notebooks to each child, they will have zero notebooks left, which can be represented by the equation:

x - 15y = 0 ...(2)

We now have two equations with two variables. To solve for 'x' and 'y', we can use the method of elimination. Multiplying equation (1) by 15 and equation (2) by 13, we get:

15x - 195y = 120 ...(3)

13x - 195y = 0 ...(4)

Subtracting equation (4) from equation (3), we get:

2x = 120

x = 60

Substituting the value of 'x' in equation (2), we get:

60 - 15y = 0

y = 4

Therefore, Adeline has 60 notebooks and 4 children.

To the nearest whole dollar, the antique dresser was purchased by Danielle as follows: A. purchase price: $120, advertised price: $300.

The purchase price of the antique dresser can be determined by reversing the solution from the discounted price.

The discounted price is divided by the discount factor to calculate the advertised or marked price.

Let the purchase price of the antique dresser = x

Markup = 250%

Discount = 15%

Discounted price = $255

Discount factor = 0.85 (1 - 0.15)

Marked up or advertised price = $300 ($255 ÷ 0.85)

Purchase price = $120 ($300 ÷ 2.5)

Thus, the correct option is Option A.

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Answer:

x = 80

Step-by-step explanation:

using the rules of logarithms

log x - log y = log ([tex]\frac{x}{y}[/tex] )

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

log5x - log4 = 2

log ([tex]\frac{5x}{4}[/tex] ) = 2

note that log is actually [tex]log_{10}[/tex]

then

[tex]log_{10}[/tex] ( [tex]\frac{5x}{4}[/tex] ) = 2

[tex]\frac{5x}{4}[/tex] = 10² = 100 ( multiply both sides by 4 to clear the fraction )

5x = 400 ( divide both sides by 5 )

x = 80

Answer:

Step-by-step explanation:

Step 1: FOIL

Step 2: Simplification

Step 3: Getting ready to combine like terms

Answer:

The domain of the function in the graph is option B, 6≤k≤11.

In the given graph, the horizontal axis represents k and the vertical axis represents j. The graph shows a line segment connecting the points (6, 120) and (11, 80). The domain of a function is the set of all possible values of the independent variable (input) for which the function is defined. In this case, k is the independent variable and j is the dependent variable (output).

The line segment in the graph represents a linear function, where the value of j depends on the value of k. The function is defined only between the values of k that correspond to the endpoints of the line segment, which are k = 6 and k = 11. Therefore, the domain of the function is 6≤k≤11.

Answer:

Step-by-step explanation:

3x = 90 + 46 - 14

3x = 122

x=[tex]\frac{122}{3}[/tex]≈40,7

Answer: 40.6 repeated

Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated

The possible zeros from the function would be zero.

To find all possible zeros of the polynomial f(x) = 2x³ + 3x² - 10x + 7, we can use the Rational Root Theorem.

We can test these possible zeros by plugging them into the polynomial:

f(1) = 2(1)³ + 3(1)² - 10(1) + 7 = 2

f(-1) = 2(-1)³ + 3(-1)² - 10(-1) + 7 = 12

f(7) = 2(7)³ + 3(7)² - 10(7) + 7 = 776

f(-7) = 2(-7)³ + 3(-7)² - 10(-7) + 7 = -732

f(1/2) = 2(1/2)³ + 3(1/2)² - 10(1/2) + 7 = -0.5

f(-1/2) = 2(-1/2)³ + 3(-1/2)² - 10(-1/2) + 7 = 8.5

f(7/2) = 2(7/2)³ + 3(7/2)² - 10(7/2) + 7 = 89.75

f(-7/2) = 2(-7/2)³ + 3(-7/2)² - 10(-7/2) + 7 = -83.75

None of the possible rational zeros are actual zeros of the polynomial f(x) = 2x³ + 3x² - 10x + 7.

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The full question is:

Find all possible zeros. (Enter your answers as a comma-separated list.) f(x) = 2x3 + 3x2 − 10x + 7

Answer: 0.2461

Step-by-step explanation:

There are 16 balls in total, and 9 of them are purple. If the first ball drawn is replaced before the second is drawn, then the number of purple balls and the number of total balls in the urn remain the same for the second draw.

The probability of drawing a purple ball on the first draw is 9/16. Since the ball is replaced, the probability of drawing a purple ball on the second draw is also 9/16.

The probability that the second ball drawn is a purple ball, given that the first ball drawn was replaced and was a green ball:

(7/16) * (9/16) = 63/256 ≈ 0.2461

Answer:

$2,602.44

Step-by-step explanation:

To find the monthly payments and the total interest for Loan A, we can use the formula for the present value of an installment loan:

PV = PMT x [1 - (1 + r/n)^(-nt)] x (n/r)

where PV is the present value of the loan, PMT is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years of the loan.

For Loan A, we have:

PV = $14,000

r = 0.051 (5.1% as a decimal)

n = 12 (monthly payments)

t = 3

Substituting these values into the formula and solving for PMT, we get:

PMT = PV / ([1 - (1 + r/n)^(-nt)] x (n/r))

= 14000 / ([1 - (1 + 0.051/12)^(-12*3)] x (12/0.051))

= $417.79

So the monthly payment for Loan A is $417.79.

To find the total interest paid over the life of the loan, we can simply multiply the monthly payment by the total number of payments and subtract the original loan amount:

Total interest = PMT x (nt) - PV

= 417.79 x (3 x 12) - 14000

= $2,602.44

Therefore, the total interest paid for Loan A is $2,602.44.