Steve and Jenna go door-to-door selling chocolate bars. Steve sells 23 chocolate
bars and Jenna sells 12 chocolate bars. Together they collect $210. How should
they divide the money so that each person gets a fair share?

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Answer:

x-intercept(s): (-28, 0)

y-intercept(s): (0, -20)

Step-by-step explanation:

Try This Answer.

Yes, Dimitri has enough gas to drive from Cincinnati to Toledo. To calculate this, we can multiply the fuel efficiency by the amount of gas in the tank.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Fuel efficiency: 21 miles per gallon

Gas in the tank: 12 gallons

So, the total distance that Dimitri can drive is:

= 21 miles per gallon x 12 gallons

= 252 miles

Since the distance from Cincinnati to Toledo is 202.4 miles, and the total distance that Dimitri can drive is 252 miles, we can conclude that he has enough gas to make the trip.

Dimensional analysis:

= 21 miles/gallon x 12 gallons

= 252 miles (correct dimensions)

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Answer:

Yes, Uncle Sonny is correct.

Step-by-step explanation:

If two figures are related by a dilation, then corresponding lines or line segments in the figures will be congruent. In a dilation, the ratio of the lengths of corresponding lines or line segments remains constant, which means they will have the same length. Therefore, they are congruent.

Answer:

bert had 60 paper clips, while ernie had 36 paper clips, when bert gives ernie 12 paper clips they both have 48 paper clips.

Step-by-step explanation:

b=bert clips; e=ernie clips;

5/3b=e; b-12=e+12; therefore there would have to be a difference of 24 between them, since at the lowest bert has 2 more paper clips than ernie to get a difference of 24 you multiply both sides by 12

Bert has 60 paper clips while Ernie has 36 paper clips.

Equation is used to show the relationship between two or more numbers and variables.

Let x represent the number of Bert paper clips and y represent the number of Ernie paper clip.

Bert has 5 paper clips for every 3 paper clips that Ernie has. Hence:

Also, If Bert gives Ernie 12 paper clips, they will have the same number of paper clips. Hence:

From solving equation 1 and 2 simultaneously:

x = 60, y = 36

Bert has 60 paper clips while Ernie has 36 paper clips.

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Answer:

133,860

Step-by-step explanation:

The baker was going to sell his house for 145,500 but he found that no one came to buy, so he decreased the amount by "8%".

* No we have our key elements:

- Starting amount = 145,500

- Rate of change = 8%

* We will get the "8%" of the number 145,500

- Firstly, "8%" means 8/100

- So, 0.08 will be our new rate of change.

* 145,500 will be multiplied by 0.08 to find the final answer because when we talk about the percentage of a number, we are going to talk about a part of it.

- 145,500 × 0.08 = 133,860 ; the same as

145,500 × 8/100 = 133,860

Answer:

The surface area is 12 square yards.

Step-by-step explanation:

answer

306.87 degrees and 666.87 degrees.

steps

4tanθ+5=0.

Subtract 5 from both sides to get 4tanθ=-5.

Divide both sides by 4 to obtain tanθ=-5/4.

θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:

θ = -53.13 + 360 = 306.87 degrees

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

Equation with tangent function.

Title: Solving an equation involving tangent function

Synopsis: We will solve the equation 4tanθ+5=0 on the interval [0,360).

Abstract: To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation. We start by subtracting 5 from both sides, giving us 4tanθ=-5. Then we divide both sides by 4, obtaining tanθ=-5/4. Finally, we take the arctangent (or inverse tangent) of both sides to find θ, remembering to specify the interval [0,360).

Numbered list:

Start with the equation 4tanθ+5=0.

Subtract 5 from both sides to get 4tanθ=-5.

Divide both sides by 4 to obtain tanθ=-5/4.

Take the arctangent (or inverse tangent) of both sides to find θ.

Specify the interval [0,360) when giving the solution.

Analogy: Solving this equation is like solving a puzzle where you need to rearrange the pieces to get the right picture.

One-sentence summary: We solve the equation 4tanθ+5=0 by subtracting 5, dividing by 4, taking the arctangent, and specifying the interval [0,360).

To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation.

Subtracting 5 from both sides gives us: 4tanθ = -5

Dividing both sides by 4: tanθ = -5/4

Taking the arctangent (or inverse tangent) of both sides, we get: θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

However, we need to specify the interval [0,360), which means we need to add 360 degrees to the negative solution, giving us 306.87+360 = 666.87 degrees (which is equivalent to 306.87-360 = -53.13 degrees in this interval).

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

Sure, here's just the math:

4tanθ + 5 = 0

Subtracting 5 from both sides:

4tanθ = -5

Dividing both sides by 4:

tanθ = -5/4

Taking the arctangent (or inverse tangent) of both sides:

θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:

θ = -53.13 + 360 = 306.87 degrees

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

ChatGPT

The exponential function is used to determine that:

1. A 0.5 percent.

b) 940.

bacteria (9000)

The substitution method entails substituting the values of the function's variables to arrive at the function's value. The system of linear equations is solved using the replacement approach.

Modeling an exponential function involves:

n(t) = n (0)ekt

that where:

The initial value is n(0).

The constant growth rate is k.

The model in this issue is:

n(t) = 940 e^ 0.5 t

Hence, k= 0.5, 940  and

a) 45 percent.

b) 940.

So 9000 bacteria.

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Answer: E ( (17)(50)/88 )

Step-by-step explanation:

(Row total * column total) / table total

Answer:

15

Step-by-step explanation:

Answer:

200 detective phones.

Step-by-step explanation:

Write the proportion where x is the number of detective phones.

cross multiply

divide both sides by 60

The side x of the triangular base prism is 0.4 centimetres.

The diagram above is a triangular prism. The triangular base of the prism is a right triangle. Therefore, the unknown side x can be found using Pythagoras's theorem,

c²= a² + b²

where

Therefore,

x² = 0.5² - 0.3²

x² = 0.25 - 0.09

x = √0.16

x = 0.4 cm

Therefore,

x = 0.4 centimetres.

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Given statement solution is :- "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)).

"f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)).

The expressions "F(g(x)) g(f(x))" and "f(g(x)) g(f(x))" are compositions of functions. The answer to the question posed would depend on the specific functions F(x) and g(x), as well as f(x) and g(x) in the second expression.

To provide a brief response:

For the expression "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)). The order of composition is F(g(x)) first, followed by g(f(x)).

For the expression "f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)). The order of composition is f(g(x)) first, followed by g(f(x)).

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Answer:

No slope.

Step-by-step explanation:

There is no such thing as a vertical slope, meaning that there is no slope. I hope this helps! :)

Answer:

No slope

Step-by-step explanation:

The line is going straight up :)

Brainliest pls?

True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

Given,

In the question:

To see the graph :

Mark all the statement that are true.

Now, According to the question:

From the graph,

Equations are expressions of two mathematical expressions t such as two numbers, functions. An equality between quantities and operations, usually with an equal sign "=".

Functions is a correspondences between two sets that are not empty each element in the set of input values can corresponds to a element in a set of output values that is unique.

Hence, True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

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Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

Answer:

A. {seagull, crow}

Step-by-step explanation:

sorry im late but hopefully this helps anyone!

The option A is correct {seagull, crow}.

Chance is represented by probability. A part of math manages the event of an irregular occasion. The value is expressed as a number from 0 to 1. Likelihood has been acquainted in Math's with anticipate how likely occasions are to occur. The extent to which something is likely to occur is basically what probability means. The probability distribution is also based on this fundamental probability theory.

Given a table shows relation in  Animals  is a bird and can fly

where, Let event A = The animal is a bird

Let event B = The animal can fly.

to find the  outcomes are in A and B

According to the table, each of the two events provided by the problem describes a condition that must be verified. The first event specifies that it must be a bird, while the second event specifies that it must fly.

Accordingly, the creatures that have the two occasions confirmed in the table are he seagull and crow.

Hence the  {seagull, crow} are  outcomes are in A and B.

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The length of the leg of the windows are 6ft and 2ft

The perimeter of the shape is the sum of its external measures

Perimeter. = x + x + x + x/3

20 = 3x + x/3

Determine the value of x

60 = 9x + x

10x = 60

x = 6

For the smallest leg

S = x/3

S = 6/3

S = 2ft

Hence the length of the leg of the windows are 6ft and 2ft

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Let the present age of student be x

Present of teacher will be 4x

After 20 years,

Age of student = x + 20

Age of teacher = 4x + 20

According to the given condition after 20 years,

x + 20 = (4x + 20)/2

x + 20 = 2x + 10

2x - x = 20 - 10

x = 10

So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.

Hope This Helps You!

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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Answer:

20 cm^2

Step-by-step explanation:

A = 1/2 * d1 * d2 = 1/2 * 8 * 5 = 1/2 * 40 = 20cm^2

Answer:

If you've more doubts you can ask :)

Step-by-step explanation:

If the centre of a circle is (a, b) and radius r, then the equation of the circle is :

\((x - x)^2 + (y-b)^2 = r^2\)

First we will find the centre, (a , b):

\(a = \frac{3+(-1)}{2} = \frac{2}{2} = 1\\\\b = \frac{-2 + 4}{2} = \frac{2}{2} = 1\)

Find radius:

\(Radius, r = \frac{Diameter}{2}\)

Diameter is the distance between (-1, 4) and (3, -2)

\(diameter = \sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2} \\\\\)

             \(= \sqrt{(3-(-1)^2 + (-2-4)^2} \\\\=\sqrt{16 + 36}\\\\=\sqrt{52}\\\\=\sqrt{4 \times 13}\\\\=2\sqrt{13} \ units\)

Therefore , \(r = \frac{2 \times \sqrt{13} }{2} = \sqrt{13} \ units\)

Equation of the circle is :  

                                 \((x - 1)^2 +(y-1)^2 = 13\)

Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

9514 1404 393

Answer:

  -0.67, -0.68, -0.69, -0.70, -0.71

Step-by-step explanation:

There are an infinite number of ways to do this.

Perhaps the simplest is to do it in decimal.

 -4/5 = -0.8

  -2/3 = -0.666... (repeating 6)

Any negative decimal number between these values will do. For example, ...

  -0.67, -0.68, -0.69, -0.70, -0.71

__

If you want to choose fractions that are evenly spaced between the given values, you can find their difference, then divide that difference into 6 parts (1 more than the number of numbers you need).

  -2/3 -(-4/5) = 4/5 -2/3 = (12 -10)/(5·3) = 2/15 . . . . length of interval

  1/6 of this difference is ...

     (1/6)(2/15) = 2/90 = 1/45

The interval end point nearest 0 is ...

  -2/3 = -30/45

so the 5 intermediate values will be that value with -1/45 repeatedly added:

  -31/45, -32/45, -33/45 = -11/15, -34/45, -35/45 = -7/9

_____

Additional comment

The fractions we came up with could be referred to as "5 arithmetic means between -2/3 and -4/5." There is nothing in the problem statement suggesting the values need to be evenly spaced.

When doing this in decimal, you can obtain a new value simply by adding more digits to the decimal fraction:

  -0.68, -0.685, -0.6853, -0.68531, -0.799

Answer:

It is warm.

Step-by-step explanation:

Answer:

Subtraction property of equality

Step-by-step explanation:

In mathematics that are various types of properties that can be used to solve for questions

In the above question:

If 3x - 14 = 12

then 3x = 26

The property that is applied here is the Subtraction property of equality.

The subtraction property of equality states that when we subtract from one side of and algebraic expression, we must subtract from the other side

a = b

a - c = b - c

a = 3x

b = 26

c = 14

3x = 26

3x - 14 = 26 - 14

then 3x - 14 = 12