Find the area of a circle with radius, r = 9cm.
Give your answer in terms of π .

Answer:

18 + 81 = 9(x² + 6x + 9)

11 = (x + 3)²

When we are completing the square, we are going to move the value of c across the equals.  We will do that by adding, and end up with

18=9(x²+6x)

We take the value of b (the coefficient of x), divide it by 2 and square it:

(6/2)²=3²=9

This is the value that completes the square.  However, since the entire square is multiplied by 9, this value must be multiplied by 9 before we can add it across the equals:

18+9(9) = 9(x²+6x+9)

18+81=9(x²+6x+9)

99=9(x²+6x+9)

Dividing both sides by 9, we have:

11=x²+6x+9

11=(x+3)²

Answer:

18 + 81 = 9(x2 + 6x + 9) and 11 = (x + 3)2

Step-by-step explanation:

EDG

Answer:

49

Step-by-step explanation:

25²-24²

625-576

=49

use calculator lah dehh

Answer:

Step-by-step explanation:

Hi,

for n =0, so at the beginning we have 125 individuals

for n=1 the population is decreasing by 4%

it means that we got 125 - 124*0.04 = 125*(1-0.04)=125*0.96

for n = 2 we got [tex]125*0.96*0.96=125*0.96^2[/tex]

for n >= 1 we got [tex]125*(0.96)^n[/tex]

so the correct answer is A

do not hesitate if you need further explanation

hope this helps

Answer:

the quotient is 9 because a negative divided by a negative is a positive

Answer:

y = (-3/4)x + 7/4

Step-by-step explanation:

Step 1: Define general form of equation of line

An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept

Step 2: Set up the system to solve for parameters of equation of line

(solve for M and b)

That equation passes 2 points, which are represented in form of (x, y), (5, -2) and (-3, 4).

Substitute these values of x and y into the original equation in step 1:

-2 = 5M + b

4 = -3M + b

Step 3: Solve the system of equations in step 2 for M and b

Subtract 1st equation from 2nd equation:

     6 = -8M

=> M = -6/8 = -3/4

Substitute M back into 1st equation:

=> -2 = 5*(-3/4) + b

=>  b = -2 + 15/4

=>  b = 7/4

=>  The equation of the line that passes through (5, -2) and (-3, 4):

      y = (-3/4)x + 7/4

Hope this helps!

:)

Answer:

Y= -4/3(x-7/2)

Step-by-step explanation:

So first calculate the difference between them,

changes by 8 x units, and -6 y units.

Then substitute them into y/x to find gradient

-6/8 = -4/3

so now we have a part of the equation:

Y= -4/3(x-a)

substitute Y= -2 and x=5 (from (5,-2))

-2= -4/3(5-a)

-2= -20/3+4a/3

Multiply by 3 on both sides

-6= -20+4a

add 20 on both sides

14=4a

a=7/2

use this as the value of a

Y= -4/3(x-7/2)

Answer:

The probability that the event will not happen is [tex]\frac{4}{17}[/tex]

Step-by-step explanation:

The occurrence of an event can be divided into two parts, the event would occur or the event would not occur. But the probability of an event is 1.

From the given question;

The probability of the event = 1

The probability that the event will happen, P = [tex]\frac{13}{17}[/tex]

Thus,

The probability that the event will not happen = probability of the event - probability that the event will happen

                                               = 1 - P

                                               = 1 - [tex]\frac{13}{17}[/tex]

                                               = [tex]\frac{17 - 13}{17}[/tex]

                                               = [tex]\frac{4}{17}[/tex]

Thus, the probability that the event will not happen is [tex]\frac{4}{17}[/tex].

Answer:

$638641.33

Step-by-step explanation:

Adam earns $45,000 in his first year.

His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.

This is a geometric sequence where the:

(a)

Sum of  geometric series[tex]=\dfrac{a(r^n-1)}{r-1}[/tex]

Substituting the given values, Adam's total earnings over n years

[tex]=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}[/tex]

(b)When n=12 years

[tex]\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)[/tex]

Answer:

i hope this helps you

The Equation of the line is 2y = -x.

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

Given Points of the line are (0,0) and (4,-2).

Since we are given two points.

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\\\(y - (-2)) = \dfrac{-2- 0}{4 - 0} (x -4)\\\\\\(y - (-2)) = \dfrac{-1}{2} (x -4)\\\\2(y + 2) =-1(x -4)\\\\2y + 4 = -x + 4\\\\2y = -x\\\\[/tex]

Therefore, Equation of the line is 2y = -x.

Learn more about linear equations here:

https://brainly.com/question/27465710

#SPJ2

Answer:

About 38 feet

Step-by-step explanation:

The formula for a circle's circumference is 2 times pi times r, which is the radius.

Since the diameter is 12, the radius is half the diameter, so the radius is 6.

2 times pi times 6 is about 37.7 feet, or 38 feet.

Hope this helped.

Answer:

M.

Step-by-step explanation:

Answer:

There is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks

Step-by-step explanation:

The slope (0.2) is the rate of change in Y-hat for each unit change in x.

In this specific case, since Y-hat is the revenue, in millions, and x is the number of clicks, in thousands, the best interpretation is that there is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks

Answer:  b) 1/3

Step-by-step explanation:

The numbers LESS THAN 3:  1, 2

[tex]\dfrac{\text{Quantity of numbers less than 3}}{Total\ number}\quad =\dfrac{2}{6}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]

Answer:

a). r = [tex]\frac{6}{7}[/tex]

b). At least 5 terms should be added.

Step-by-step explanation:

Formula representing sum of infinite geometric sequence is,

[tex]S_{\inf}=\frac{a}{1-r}[/tex]

Where a = first term of the sequence

r = common ratio

a). If the sum is seven times the value of its first term.

    [tex]7a=\frac{a}{1-r}[/tex]

    [tex]7=\frac{1}{1-r}[/tex]

    7(1 - r) = 1

    7 - 7r = 1

    7r = 7 - 1

    7r = 6

    r = [tex]\frac{6}{7}[/tex]

b). Since sum of n terms of the geometric sequence is given by,

    [tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]

If the sum of n terms of this sequence is more than half the value of the infinite sum.

[tex]\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}[/tex] >  [tex]\frac{7a}{2}[/tex]

[tex]\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}[/tex]

[tex]\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}[/tex]

[tex]1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}[/tex]

[tex]1-(\frac{6}{7})^{n}> \frac{1}{2}[/tex]

[tex]-(\frac{6}{7})^{n}> -\frac{1}{2}[/tex]

[tex](\frac{6}{7})^{n}< \frac{1}{2}[/tex]

[tex](0.85714)^{n}< (0.5)[/tex]

n[log(0.85714)] < log(0.5)

-n(0.06695) < -0.30102

n > [tex]\frac{0.30102}{0.06695}[/tex]

n > 4.496

n > 4.5

Therefore, at least 5 terms of the sequence should be added.

Answer:

The width or range of the confidence interval with sample size 200 will be about half of that of the confidence interval with sample 50.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)

- For the two random samples, of sizes 50 and 200, the Central limit theorem allows us to say that the sample mean is approximately equal to the population mean as this random sample satisfies the condition of being a simple random sample and a distribution obtained from a normal distribution.

- Making the right assumption that population standard deviation is known and z-distribution is used to find the critical value

Critical value for 95% = 1.96

The critical value for both samples are the same then.

- Standard Error of the mean = σₓ = (σ/√n)

where σ = population standard deviation

n = sample size

For the two distributions

Confidence Interval = (Sample mean) ± [(Critical value) × (Standard Error of the mean)

(Sample mean)₅₀ = (Sample mean)₂₀₀

(Critical value)₅₀ = (Critical value)₂₀₀

(Standard Error of the mean)₅₀ = (σ/√50) = 0.1414σ

(Standard Error of the mean)₂₀₀ = (σ/√200) = 0.0707σ

0.1414σ = 2 × 0.0707σ

(Standard Error of the mean)₅₀ = 2 × (Standard Error of the mean)₂₀₀

(Standard Error of the mean)₅₀ > (Standard Error of the mean)₂₀₀

Hence,

(Margin of Error)₅₀ > (Margin of Error)₂₀₀

(Margin of Error)₅₀ = 2 × (Margin of Error)₂₀₀

Confidence Interval = (Sample mean) ± (Margin of error)

Hence, the width or range of the confidence interval with sample size 50 will be about two times larger than the confidence interval with sample 200.

Hope this Helps!!!

Answer:

[tex]x^2-4x+4[/tex]

Step-by-step explanation:

[tex](x - 2)^2[/tex]

[tex](x - 2)(x - 2)[/tex]

[tex]x(x-2)-2(x-2)[/tex]

[tex]x^2-2x-2x+4[/tex]

[tex]x^2-4x+4[/tex]

Answer:

[tex]{x}^{2} - 4x + 4 \\ [/tex]

Step-by-step explanation:

[tex] {(x - 2)}^{2} \\ (x - 2)(x - 2) \\ x(x - 2) - 2(x - 2) \\ {x}^{2} - 2x - 2x + 4 \\ {x}^{2} - 4x + 4[/tex]

hope this helps you

Answer:

The lines would intersect at: (6, -4)

Step-by-step explanation:

I graphed both lines.

Answer:

(4,-2)

Step-by-step explanation:

The equation for the graphed line is [tex]y=\frac{1}{2} x-4[/tex] as it has a slope of [tex]\frac{1}{2}[/tex] and a y-intercept of -4.

Now that we have the two equations, we can set them equal to each other to find the x-value at which they intersect

[tex]\frac{1}{2} x-4=-x+2[/tex]

First, we can add 4 to each side

[tex]\frac{1}{2} x=-x+6[/tex]

Then we can add x to each side

[tex]\frac{3}{2} x=6[/tex]

Now we need to divide both side by [tex]\frac{3}{2}[/tex], which is the same thing as multiplying by [tex]\frac{2}{3}[/tex]

[tex]x=6*\frac{2}{3} \\\\x=\frac{12}{3} \\\\x=4[/tex]

Now that we have the x-value, we can plug it into one of the equations to see the y-value for where they intersect.

[tex]y=-x+2\\\\y=-(4)+2\\\\y=-2[/tex]

This means that the coordinates for the intersection of these two lines would be [tex](4,-2)[/tex]

Step-by-step explanation:

Take the $50 and quit.

(Each game as outlined by drwls has an expected value of $1.50.

You are playing it 5 times, so the expected return is $7.50.

Your choice was to either accept $50 or play the game)

Answer: Answer choices 1, 3, 4

Step-by-step explanation:

As long as it ends in .0, .2, .4, .6, or .8 it's fine. Therefore the first and last 2 work, since 0.2 can end in either of those 5 values.

Hope that helped,

-sirswagger21

Answer:

Step-by-step explanation:

a. Two methods of fund raising is being tested here in the first case study. To make a completely randomized experiment. I would use and randomly assign half the population of the 1000 donor sample that will be sent literature about the successful activities of the charity and asked to make another donation to one of the two treatment conditions: which is a sent literature about the successful activities of the charity. While the placebo group would be the other 500 donors contacted by phone and asked to make another donation with no influence whatever from the charity.

b. For the second case study, To make a completely randomized experiment. I would use and randomly assign 43 particupants which are to be given a gel that contains the tooth-whitening chemicals to the treatment condition containing the tooth-whitening chemicals while the placebo group would be the remaining 42 which are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals.

c. Using three blocks: the completely randomized design experiment would be:

Donors younger than 30 years old:

Sent literature: Yes No

Contact by phone: Yes No

Donors 30 to 59 years old:

Sent literature: Yes No

Contact by phone: Yes No

Donors 60 and older:

Sent literature: Yes No

Contact by phone: Yes No

(Yes means yes to another donation and No means no to another donation)

Answer:

Step-by-step explanation:

a. Two methods of fund raising is being tested here in the first case study. To make a completely randomized experiment. I would use and randomly assign half the population of the 1000 donor sample that will be sent literature about the successful activities of the charity and asked to make another donation to one of the two treatment conditions: which is a sent literature about the successful activities of the charity. While the placebo group would be the other 500 donors contacted by phone and asked to make another donation with no influence whatever from the charity.

b. For the second case study, To make a completely randomized experiment. I would use and randomly assign 43 particupants which are to be given a gel that contains the tooth-whitening chemicals to the treatment condition containing the tooth-whitening chemicals while the placebo group would be the remaining 42 which are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals.

c. Using three blocks: the completely randomized design experiment would be:

Donors younger than 30 years old:

Sent literature: Yes No

Contact by phone: Yes No

Donors 30 to 59 years old:

Sent literature: Yes No

Contact by phone: Yes No

Donors 60 and older:

Sent literature: Yes No

Contact by phone: Yes No

(Yes means yes to another donation and No means no to another donation)

Answer:

The answer is D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

  3/2

Step-by-step explanation:

The graph rises 3 feet for each 2 seconds to the right. The slope is ...

  rise/run = (3 ft)/(2 s) = (3/2) ft/s

The numerical value of the slope is 3/2 or 1.5. The associated units are feet per second.

Answer:

The answer is 508

Step-by-step explanation:

Solution

First of all, the proportion of B is exceeds 0.5 in total.

Now,

To find the total of A it we have A =314 +512 = 826

The number of employed that choose B = 356

For us to have the proportion of B to be higher than the 0.5, the unemployed B from what is shown here should exceed the difference between total A and B employed

what this suggest is that the employed B is greater than 826-356 = 470

So,

The respondent that are unemployed that choose B  must be greater than 470

Thus,

We recall that the B proportion among the unemployed respondent is lesser than .50

Thus suggests that the respondent that are unemployed who choose be is lesser than 512

The conditions becomes

470 lesser than the number of unemployed respondents who selected B lesser than 512

Hence  the needed number of the number of unemployed respondents who chose B should be between 470 and 512

So, possible answer here is 508.

Answer:

The answer is y = -3x - 2.

Step-by-step explanation:

Given that in slope-form equation, m represents gradient and c is y-intercept. So you have to sbustitute the values into the equation :

[tex]y = mx + c[/tex]

[tex]let \: m = - 3 \\ let \: c = - 2[/tex]

[tex]y = - 3x - 2[/tex]

Answer:

There are 60 marbles in the bag

Step-by-step explanation:

The total number of marbles  times the probability of red marbles = number of red marbles

total * 7/10 = 42

Multiply each side by 10/7

total * 7/10 * 10/7 = 42*10/7

total

60

There are 60 marbles in the bag

Answer:

  B = R/x -A

Step-by-step explanation:

  [tex]\text{Divide the equation by x:}\\\\\dfrac{R}{x}=A+B\\\\\text{Subtract A:}\\\\\dfrac{R}{x}-A = B\\\\\text{The solution is ...}\\\\\boxed{B=\dfrac{R}{x}-A}[/tex]

Answer:

[tex] b = \frac{r - ax}{x} \\ [/tex]

Step-by-step explanation:

[tex]r = x(a + b) \\ r = ax + bx \\ r - ax = bx \\ \frac{r - ax}{x} = b[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

48

Step-by-step explanation:

Esinam shere a common ratio hence,

the lcm of 3 and 5 is 15

Kissi:Esinam= 9:15 and Esinam:Lariba=15:25

Combining; 9:15:25

Let x be the ages such that,

Kissi=9x and Esinam=15x and Lariba=25x

9x+15x+25x=147

49x=147

x=3

Youngest; Kissi=9x=9(3)=27

Oldest; Lariba=25x=25(3)=75

Difference 75-27=48

Answer:

22%

Step-by-step explanation:

Car's price is reduced by 8% or 0.92 times a year

after 3 years it will make:

or

Answer:

Hello!

Here is your answer:

22%

I hope I was able to help you.  If not, please let me know!

Step-by-step explanation:

Answer:

B. Complements of congruent angles are congruent.

Step-by-step explanation:

Angles <DCF and <FEG have angles measures that are complementary to to angles E and C.

Answer:

x =30.4 seconds

Step-by-step explanation:

We can use ratios to solve

20 drops           8 drops

---------------  = ----------------

76 seconds      x seconds

Using cross products

20x = 8*76

20x =608

Divide each side by 20

20x/20 = 608/20

x =30.4 seconds

Answer:

30.4 secs = 30secs

Step-by-step explanation:

20 drops fall in 76s

Hence 1 drop is 76/20

Therefore 8 drops would be ;

76/20 × 8 = 30.4 secs

Answer:

1:0.4641

Step-by-step explanation:

We are told that the scale of the model with respect to the real world is 0.1 cubic meter. This means that for every 1 cubic meter in the real world the model represents 0.1.

They tell us that the real world volume is 100,000, that if we assume a cube, we have to:

V = l ^ 3

l = 100000 ^ (1/3)

l = 46.41

46.41 meters would be each side, now the volume of the model would be:

100,000 * 0.1 = 10,000

Which means that its sides would be:

V = l ^ 3

l = 100000 ^ (1/3)

l = 21.54

We calculate the scale of the sides:

21.54 / 46.41 = 0.4641

Which means that for every 1 meter in the real world the model represents 0.4641 meters.