Find the radius of a circle that has an area of 121 pi ft2.

The amount that was invested at the start of the 3 years that is the principal amount will be equal to $ 6051.098.

Let the principal amount that is invested be equal to x.

So, we get that:

P = x

Now, the time period t = 3 years.

Simple interest rate = r = 3.85 %

Amount after 3 years = A = $ 6750

A = P + ( P × r × t / 100)

6750 = x + ( x × 3.85 × 3 / 100)

6750 = x + 0.1155 x

6750 = 1.1155 x

x = 6750 / 1.1155

x = 6051.098

Therefore, we get that, the amount that was invested at the start of the 3 years that is the principal amount will be equal to $ 6051.098.

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Answer: this is not answer but it will help u with whoever does answer it

Step-by-step explanation:

we see here, slope is another version of finding the average rate of change. Average rate of change is finding the difference between the dependent variable (y-term) divided by the difference in the independent variable (x-term). Slope and average rate of change is exactly the same thing

Answer:Your answer would be -8 x - 17 y

Step-by-step explanation: x - 9 x would be - 8 x

                                               You would have to distribute the negative in the problem -(9 x- 8 y) which would make it -9 x +8 y and 9 y + 8 y is 17 y so there fore the answer is -8 x - 17 y

Answer:

-2, S, U, V. that was a good question.

Step-by-step explanation:

Thanks. You are known.

Answer:

(4,-4)

is the way from AtoB

Answer:

x= 5/12,y=− 5/4

​

Step-by-step explanation:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

6x−12y=24,4x+2y=8

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

6x−12y=24

Add 12y to both sides of the equation.

6x=12y+24

Divide both sides by 6.

x= 6/1 (12y+24)

Multiply  6

1 times 24+12y.

x=2y+4

Substitute 4+2y for x in the other equation, 4x+2y=8.

4(2y+4)+2y=8

Multiply 4 times 4+2y.

8y+16+2y=8

Add 8y to 2y.

10y+16=8

Subtract 16 from both sides of the equation.

10y=−8

Divide both sides by 10.

y=− 5/4

​Substitute − 5/4  for y in x=2y+4. Because the resulting equation contains only one variable, you can solve for x directly.

x=2(− 5/4 )+4

Multiply 2 times − 5/4 .

x=− 5/8 +4

Add 4 to − 5/8 .

x= 5/12

Answer:

Step-by-step explanation:

boy just include the unit rate of mph and make the question solvable as easy as that, or you could use the example and change the mph

6/7 of people are not having a disease, the whole is 1 so the difference is:

2/3 of those having a disease is:

15 people are the 1/7 fraction of total people referred to quarantine.

The total number is:

3/5 of 105 people are male, that is:

Number of female is:

Answer:

[tex]\sf (i) \quad \dfrac{1}{7}[/tex]

[tex]\sf (ii) \quad \dfrac{2}{21}[/tex]

[tex]\sf (iii) \quad 315\:people[/tex]

[tex]\sf (iv) \quad 126\: females[/tex]

Step-by-step explanation:

If 6/7 of people who are quarantined do not have the disease then the fraction of people that do have the disease is:

[tex]\begin{aligned} \implies 1-\dfrac{6}{7} & =\dfrac{7}{7}-\dfrac{6}{7}\\\\ & =\dfrac{7-6}{7}\\\\ & =\dfrac{1}{7}\end{aligned}[/tex]

Therefore, 1/7 of people in quarantine have the disease.

We are told that 2/3 of the people who have the disease come from abroad.  Therefore, the fraction of diseased people coming from abroad is 2/3rds of the diseased people:

[tex]\begin{aligned} \implies \dfrac{2}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{2}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{2 \times 1}{3 \times 7}\\\\ & = \dfrac{2}{21}\end{aligned}[/tex]

Therefore, the fraction of diseased people who have come from abroad is 2/21.

We are told that 15 people who have the disease do not come from abroad.  So if 2/3 of the people who have the disease come from abroad, then 1/3 of the people who have the disease do not come from abroad.  Remember that 1/7 of the total people have the disease.

[tex]\begin{aligned} \implies \dfrac{1}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{1}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{1 \times 1}{3 \times 7}\\\\ & = \dfrac{1}{21}\end{aligned}[/tex]

Therefore, 1/21 of the total number of people have the disease and do not come from abroad.

Therefore, 15 people are equal to 1/21 of the total number of people:  

[tex]\implies \sf Total\:number\:of\:people=15 \times 21 = 315[/tex]

Therefore, the total number of people in quarantine is 315.

If 3/5 of the total are male, then 2/5 must be female.

[tex]\begin{aligned} \implies \dfrac{2}{5} \textsf{ of }315 & = \dfrac{2}{5} \times 315\\\\ & = \dfrac{2 \times 315}{5}\\\\ & = \dfrac{630}{5}\\\\& = 126 \end{aligned}[/tex]

Therefore, 126 females are in quarantine.

The weight of the original sample from which all 14 batches in the task content is;  65.8 x 10-8 grams.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

WE have been given that Eli broke a cell sample into 14 batches, each weighing 4.7 x 10-8 grams. which follows that the task content; the weight of the original sample from which the eight batches were obtained be determined.

Hence, since each of the 14 batches weighs;

[tex]4.7 \times 10^{-8}[/tex]

Therefore, the weight of the original sample can be obtained as;

[tex]4.7 \times 10^{-8} \times 14\\\\65.8 \times 10^{-8}[/tex]

However, when the weight is expressed in scientific notation, thus the weight of the original sample is;

[tex]65.8 \times 10^{-8}[/tex]

Hence, The weight of the original sample from which all 14 batches which each weighed  4.7 x 10-8 grams are obtained as required in the task content is;  65.8 x 10-8 grams.

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Answer:

342 ÷ 23 = 14.869565217 or 14 r 20

Check step-by-step explanation below for 2 methods to solve.

14.869565217 method right below

14 r 20 method at the bottom in bold and underlined

Hope this helps :)

Step-by-step explanation:

divisor

↓ ? <------ quotient

23 | 342 <------ dividend

remainder = r (the number that the divisor can't go into.

1) 23 goes into 34 one time, so we write the one on top.

1

23 | 342

2) 23 • 1 = 23 so then we subtract 23 from 34 and get 11.

1

23 | 342

- 23

1 1

3) Now we carry down the 2 and get 112.

1

23 | 342

- 23 ↓

1 1 2

4) 23 goes into 112 four times, so we write the four on top.

1 4

23 | 342

- 23 ↓

1 1 2

5) 23 • 14 = 92 so we subtract 92 from 112 and get 20.

1 4

23 | 342

- 23 ↓

1 1 2

- 92

20

6) 23 can't go into 20 so we add a decinal and a zero to 342 (dividend) and add a decimal to 14 too.

1 4.

23 | 342.0

- 23 ↓

1 1 2

- 92

20

7) Repeat the same steps again (Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor (if greater use it if less than take the next number). Then divide it by the divisor and write the answer on top as the quotient. Subtract the result from the digit and write the difference below. Bring down the next digit of the dividend (if present). Repeat the same process.)

1 4.8

23 | 342.0

- 23 ↓↓

1 1 2

- 92

200

- 1 84

16

8) Keep repeating and then we get 14.8695652174

*However, if the directions say to not continue and add the decimal and zero then we must put a remainer (r).*

1 4 r 20

23 | 342

- 23 ↓

1 1 2

- 92

20

Answer:

6

Step-by-step explanation:

c is on -3 and A is on 3 -3 to 3 would be 6

The difference between -4/5 and -3/5 will be -7/5.

It should be noted that the difference between 4/5 and 3/5 will be illustrated thus:

= 4/5 - 3/5

= 1/5

Subtracting -3/5 from -4/5 will be:

= -3/5 - 4/5

It should be noted that they both have negative signs.

Therefore, the value will be -7/5 or - 1 2/5.

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Answer:

8/5 or 1 3/5

Step-by-step explanation:

Answer:

Exact form: 8/5
Mixed Number form: 1 3/5

Step-by-step explanation:

First, let's cancel the common factor of 3

4/3 * 6/5
4 * (3*2/5)
4 * 2/5

Next, lets combine 4 and 2/5

4*2/5
8/5

We can finish this off by simplifying 8/5

8/5 = 1 3/5

Answer:

  x = 21

Step-by-step explanation:

You are given expressions (x+63)° and (4x)° for alternate interior angles at a transversal crossing parallel lines. You want to know the value of x.

Where a transversal crosses parallel lines, alternate interior angles are congruent. That means ...

  (4x)° = (x +63)°

  3x = 63 . . . . . . . . divide by °, subtract x

  x = 21 . . . . . . . . . divide by the coefficient of x

H = S/2πr + r or (S + 2πr²)/2πr simplified and solved for the value  S = 2πr² + 2πrh

Here given that S = 2πr² + 2πrh

Lets simply the equation

⇒ S = 2πr² + 2πrh

⇒ S = 2πr(r + h)

⇒ S/2πr = r + h

⇒ h = S/2πr + r or (S + 2πr²)/2πr

In mathematics, an equation is a formula that indicates the equality of two expressions by connecting them with the equals sign =.

The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.

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An absolute value inequality for given graph is |x| ≤ 6

In this question, we have been given a graph of a number line.

We need to write an absolute value inequality for given graph.

From the given graph, we can observe that the value of x lies between -6 to 6.

i.e., -6 ≤ x ≤ 6

We know that, for a real number 'm', the absolute value function for m would be,

|±m| = m

So, -6 ≤ x ≤ 6

|x| ≤ 6, which is required inequality.

Therefore,  an absolute value inequality for given graph is |x| ≤ 6

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ABCD and ABEC are parallelograms becayse a parallelogram can be divided into congruent triangles of different orientations

The pre-image of the rotations are given as:

The image of the rotations are given as:

Notice that the triangles ABC and CDA have a common line segment AC, while the triangles ABC and ECB have a common line segment CB

The above is true, because the triangle is rotated by 180 degrees through its own midpoint

When the images of the rotations are viewed as a single shape, the view of the shape is a parallelogram

Because a parallelogram can be divided into congruent triangles of different orientations, then ABCD and ABEC are parallelograms

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Complete question

Triangle CDA is the image of triangle ABC after a 180º rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180º rotation around the midpoint of segment BC.

Explain why ABCD and ABEC are parallelograms.

See attachment for image

1. The line passing through (-14,-9) and (7,9) has the equation:

y = 6/7x + 3/2

2.The line passing through (0,-3) and (0,15) has the equation:

since the slope is undefined, hence equation of the line is not formed.

3.The line passing through (-24,-16) and (-8,-6) has the equation:

y = 5/8x - 1

4.The line passing through (-8,-12) and (12,13) has the equation:

y = 5/4x - 2.

Given we have the pair of points, through which we need to determine the equation of the line:

1.  (-14,-9) and (7,9)

first we need to find the slope

(-14,-9) = (x₁,y₁)

(7,9) = (x₂,y₂)

m= y₂₋y₁/x₂₋x₁

= 9-(-9)/7-(-14)

= 18/21

m= 6/7

Use the slope and one of the points to find the y-intercept b:

(7,9) and m= 6/7

substitute in y=mx+b

9=6/7(7) + b

b = 9/6

b= 3/2

now substitute m=6/7 and b= 3/2 in slope intercept form.

y = 6/7x + 3/2

2. (0,-3) and (0,15)

first we need to find the slope

(0,-3) = (x₁,y₁)

(0,15) = (x₂,y₂)

m= y₂₋y₁/x₂₋x₁

= 15-(-3)/0-0

= undefined

hence  we can't frame the equation of the line.

3.  (-24,-16) and (-8,-6)

first we need to find the slope

(-24,-16) = (x₁,y₁)

(-8,-6) = (x₂,y₂)

m= y₂₋y₁/x₂₋x₁

= -6-(-16)/-8-(-24)

= -6+16/-8+24

= 10/16

m= 5/8

Use the slope and one of the points to find the y-intercept b:

(-8,-6) and m= 5/8

substitute in y=mx+b

-6=5/8(-8) + b

b = -1

now substitute m=5/8 and b= -1 in slope intercept form.

y = 5/8x - 1

4. (-8,-12) and (12,13)

first we need to find the slope

(-8,-12) = (x₁,y₁)

(12,13) = (x₂,y₂)

m= y₂₋y₁/x₂₋x₁

= 13-(-12)/12-(-8)

= 25/12+8

= 25/20

m= 5/4

Use the slope and one of the points to find the y-intercept b:

(12,13) and m= 5/4

substitute in y=mx+b

13=5/4(12) + b

b = -2

now substitute m=5/4 and b= -2 in slope intercept form.

y = 5/4x - 2.

hence we get the acquired results.

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The lengths of the scaled copy of rectangle is 18 inches by 30 inches .

Scaled by a factor : Whenever something is scaled by a factor it means that it is multiplied by that factor .

For Example , if 3  is scaled by a factor of 2 , means 3 is multiplied by 2 that is 3*2=6.

In the given question

length of rectangle = 3inches

it is scaled by factor of 6 , that means

length of scaled copy of rectangle = 3*6= 18inches.

breadth of the rectangle = 5 inches

it is scaled by factor a factor of 6 , that means

breadth of scaled copy of rectangle = 5*6 = 30inches.

Therefore , the lengths of the scaled copy of the rectangle will be 18inches by 30inches.

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The area of the screen to the nearest square centimeter is 0.103 m².

Given, that the length of the computer screen is = 16 inches

width of the computer screen = 10 inches

we know that 1 inch = 0.0254 m

Width = 10 inches = 10 × 0.0254 m

= 0.254 m

Length = 16 inches = 16 × 0.0254 m

= 0.4064 m

By definition,

Area =  length × width

        = 0.254 × 0.4064 m²

        = 0.103 m²

hence we get the area of the computer screen as 0.103 m²

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From the data given, we have that:

1. The linear regression equation is given by:y = 0.69684x - 1.43675.

2. 21 users during the 32th week.

To find the equation, we need to insert the points (x,y), given in a scatter plot or in a table, in the calculator. We also have to identify the type of data that models the situation, such as linear, quadratic or exponential.

For this problem, the data is increasing somewhat linearly, hence linear regression is used.

The points of the function, from the table, are given as follows:

(1, 1.5), (4, 2.2), (6, 2.4), (10, 3.9), (12, 5.5), (15, 6.8), (20, 12.3), (24, 16.4), (25, 17.6).

Hence the the linear equation that models the data is:

y = 0.69684x - 1.43675

The value during the 32th week is found when x = 32, hence:

y = 0.69684(32) - 1.43675 = 21 (rounded up, as the first decimal digit is greater than 0.5).

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Answer:

768

Step-by-step explanation:

The numbers are multiplying by 4 each time, Therefore the next number will be 768.

The values of x satisfying the condition of the quadratic function (f o g)(x) = 17 is; (2, 4)

We are given the functions;

f(x) = 2x - 3

g(x) = x² - 6x + 18

Thus;

(f o g)(x) = 2(x² - 6x + 18) - 3

= 2x² - 12x + 36 - 3

= 2x² - 12x + 33

Now, we want to find the value of x when (f o g)(x) = 17. Thus;

2x² - 12x + 33 = 17

2x² - 12x + 16 = 0

Factorizing this gives us;

(2x - 8)(x - 2) = 0

Thus;

2x - 8 = 0 or x - 2 = 0

x = 4 or 2

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The component form of the given magnitude and direction is 7.4 +  6.7i.

To find the component form of  magnitude 10 and direction 42°:
component form = x + iy

Then,

Therefore, 7.4 + 6.7i is the component form of the given magnitude and direction

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Answer: $1200

Step-by-step explanation:

The equation to find out the price of the couch on sale is:

972=x*0.81

(0.81 is the same as 81% or 100% - 19%)

Then this equation can be arrange to figure out x

972=x*0.81

972/0.81=x

x=1200

Answer:

$1200

Step-by-step explanation:

Given the following question:

A couch when on a 19% discount
The new price of the couch was 972 dollars

We are trying to find the original price of the couch. To find that answer we are going to use the formula to calculate the percentage.

19% of 1200
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{19\times1200}{100}[/tex]
[tex]19\times1200=22800[/tex]
[tex]22800\div100=228[/tex]

Now check our answer by subtracting 228 from our original price 1200:

[tex]1200-228=972[/tex]
[tex]=972[/tex]

Our original price is "$1200."

Hope this helps.

The 107th derivative of f(x) =cos(x) is sin(x).

The derivative of y = f(x) function is the rate of change of  y  with respect to the independent variable x.

Derivative is represented by [tex]\frac{d}{dx}[/tex] and

First derivative to y is given by  [tex]\frac{d}{dx}f(x) = \lim_{h\to \00} \frac{f(x+h)-f(x)}{h}[/tex]

Second derivative [tex]\frac{d^{2}y }{dx^{2} } = \frac{d}{dx} (\frac{dy}{dx} )[/tex] and so on higher derivatives can be defined.

[tex]\frac{d(sinx)}{dx} = cosx\\\frac{d(cosx)}{dx} = -sinx[/tex]

Given f(x) = cos(x)

Then the first derivative of cos(x) is [tex]\frac{d(cosx)}{dx} = -sinx[/tex]

The second derivative of cos(x) is [tex]\frac{d^{2}(cosx) }{dx^{2} } = \frac{d}{dx} (\frac{dcosx}{dx} ) = \frac{d(-sinx)}{dx} =-cosx[/tex]

Third derivative [tex]\frac{d^{3}(cosx) }{dx^{3} } = \frac{d }{dx } (\frac{d^{2} cosx}{dx^{2} } ) = \frac{d(-cosx }{dx } = sinx[/tex]

[tex]\frac{d^{4}(cosx) }{dx^{4} } = \frac{d(sinx) }{dx } = cosx\\\frac{d^{5}(cosx) }{dx^{5} } = \frac{d(cosx) }{dx } = -sinx\\\\\frac{d^{6}(cosx) }{dx^{6} } = \frac{d(-sinx) }{dx } = -cosx\\\\\frac{d^{7}(cosx) }{dx^{7} } = \frac{d(-cosx) }{dx } = sinx\\[/tex]

Eighth derivative if cos(x) is  cos(x)

and so on

Therefore , the first , fifth , ninth ,... derivative of f(x) =cos(x)  is -sin(x)

The second, sixth, tenth.... derivative of f(x) =cos(x)  is -cos(x)

The fourth , eighth , 12th,... derivative of f(x) =cos(x)  is cos(x)

We can say that very multiple of fourth derivative of f(x) =cos(x)  is cos(x)

We can write 107 as 104 + 3

As 104 is multiple of 4 therefore 104th derivative of cos(x) is cos(x)

[tex]\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3} }{dx^{3} } (\frac{d^{104} cosx}{dx^{104} } ) \\\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3}(cosx) }{dx^{3} } = sinx[/tex]

Therefore, the 107th derivative of f(x) =cos(x) is sin(x).

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Answer:

2,025,000,000

Step-by-step explanation:

(3×10)⁴×(5×10)

8810000×2500

2,025000,000