Danessa needs to compare the area of one large circle with a diameter of 8 to the total area of 2 smalle

diameter one-half that of the large circle.

Which statements about the areas are true? Select three options.

The area of the large circle is 16

The area of one small circle is 4

The area of one small circle will be one-half of the area of the large circle.

The total area of the two small circles will equal that of the large circle

The total area of the two small circles will be one-half of the area of the large circle

Answer:

Option C is correct.

Alex earned about $60 more than Joaquin did.

Step-by-step explanation:

The linear regression equation

y = 0.18 x + 320.22

is used to predict the weekly salary, y, of an employee who sells x dollars worth of merchandise.

Joaquin sold $1500 worth of goods. Meaning that x for that week for Joaquin is 1500.

Joaquin' s salary for that week is then given as

y = 0.18x + 320.22

y = 0.18(1500) + 320.22 = 590.22

Hence, Joaquin's salary for that week = $590.22

Alex earns $650 that week. Meaning that y for Alex in that week = 650

y = 0.18x + 320.22

650 = 0.18x + 320.22

0.18x = 650 - 320.22 = 329.78

x = (329.78/0.18) = 1832.1

Hence, Alex sold goods worth $1832.1 that week.

Joaquin sold goods worth $1500

Joaquin earned $590.22

Alex sold goods worth $1832.1

Alex earned $650

From this calculation, it is evident that 'Alex earned about $60 more than Joaquin did' is the correct option as $650 is about $60 more than $590.22

Hope this Helps!!!

Answer:

the answer is C :)

Step-by-step explanation:

Answer:

The rate at which the radius is increasing

dr/dt = 1.91 cm/s

Step-by-step explanation:

The circumference C of a circle can be written as;

C = 2πr .....1

Where;

r = radius

The rate at which the circumference of the circle

is increasing can be written as dC/dt;

Differentiating equation 1, we have;

dC/dt = 2π dr/dt

Making dr/dt the subject of formula;

dr/dt = (dC/dt)/2π

Given;

dC/dt = 12cm/s

Substituting the value of dC/dt;

dr/dt = 12/2π

dr/dt = 1.909859317102 = 1.91 cm/s

The rate at which the radius is increasing dr/dt is 1.91 cm/s

Answer:

Option (1).

Step-by-step explanation:

Amount of water hold by both the pitchers (Large + small) = 12 cups

Let the small pitcher holds the water = S cups

If the water hold by the large pitcher is twice the size of the small pitcher, then the amount of water hold by large pitcher = 2S

Total amount water hold by both = S + 2S

Equation for this situation will be,

S + 2S = 12

Therefore, Option (1) will be the answer.

Answer:

B: 3/2x - 7 + 3 = 0

Step-by-step explanation:

Answer: C

Step-by-step explanation:

General form is in Ax+By+C. To do this, you move everything onto one side.

[tex]\frac{3}{2}x -y+3=0[/tex]

This should be the general form, but this is not correct in these answer choices! Let's try this another way to get Ax+By+C by making Ax not a fraction.

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

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

[tex]2(y+3)=3x[/tex]

[tex]2y+6=3x[/tex]

[tex]3x-2y-6=0[/tex]

This may seem incorrect, but we can always check our answer by plugging in numbers.

In our slope intercept form, let's say x=2. What would be our y?

[tex]y=\frac{3}{2} (2)-3[/tex]

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

[tex]y=0[/tex]

Now we know our coordinates should be (2, 0). When we rewrite the slope-intercept form, we should still get 0 when we plug in x=2 and y=0. Let's check on all answer choices to see which one works.

A. Correct

-3(2)+2(0)+6

-6-6=0

0=0

B. Incorrect

3/2(2)-(0)+3

3+3=6

6≠0

C. Correct

3(2)-2(0)-6

6-6=0

0=0

D. Incorrect; not general form

2(0)=3(2)-6

0=6-6

Now, you can see that A and C are both correct, but the main difference, is that you want to make A positive. The only option where A is positive is in answer C.

Answer:

C:

Step-by-step explanation:

In the attached file

Answer:

B. h=S/πr²

Step-by-step explanation:

The question lacks options. Here is the complete question.

Which of the following equations is equivalent to S = πr²h

a. h=S-πr^2

b. h=S/πR^2

C. h= πr^2/S

D. h=S+ πr^2

To know the equation equivalent to πr²h, we will make h the subject of the formula as shown from the one given in equation.

S = πr²h

To get h, we will divide both sides by the coefficient of h (i.e πr²)

S/πr² = πr²h/πr²

S/πr² = h

h = S/πr²

This shows that h = S/πr² is equivalent to S = πr²h

Answer:

she will purchase 8 pounds of potatoes.

But if she had on $3.0

She will purchase only two pounds

Step-by-step explanation:

first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30.

1.5+1.14+1.05+0.30=$ 3.99

6-3.99= 2.01

If the rest cost 0.5

Then there are 4 pounds of 0.5 in 2.01.

So total she will purchase 8 pounds of potatoes.

But if she had on $3.0

She will purchase only two pounds, as it will only purchase1.5+1.14+= 2.64 worth of potatoes.

With $6 Janice can get a total of 10.7 pounds, but with $3  she will be able to afford the first two pounds only

Given Data

Amount at hand = $6

First Pound cost = $1.50

Second Pound cost = $1.14

Third Pound cost = $1.05

Total = 1.5+1.14+1.05 =  3.69

Balance  = 6-3.69 = $2.31

Hence the number of pound we can get with $2.31 for subsequent purchase will be

= 2.31/0.3

= 7.7 pounds

This means that the total number of pounds will be

= 3+7.7

=10.7pounds

subsequent Pound cost = $0.3

Learn more about algebra here:

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Answer: 30 in^2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I put the answer in an atachement

Answer:

B.

Step-by-step explanation:

In the attached file

Answer:

-7 goes in the box

Step-by-step explanation:

x^ -3 = x^4 * x^n

We know that a^b * a^c = a^ (b+c)

x^-3 = x^(4+n)

When the bases are the same the exponents are the same

-3 = 4+n

Subtract 4 from each side

-3 -4 = 4+n-4

-7 = n

Answer:

36

Step-by-step explanation:

Answer:

The answer is 2/9

Step-by-step explanation:

2(2)^0 (3)^-2 = 2(1)/(3)^2 = 2/9

Answer:

D. (X + 3 ) ( X +1 )

process:

x² + 4x + 3

= x² + (3 + 1)x +3

= x² + 3x + x + 3

= X (x+3) + 1 (X+3)

= (X + 3 ) ( X +1 )

Answer:

The point estimate is 0.3488.

The 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day is (0.3114, 0.3862).

Step-by-step explanation:

In a sample with a number n of people surveyed with a point estimate of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1078, \pi = \frac{376}{1078} = 0.3488[/tex]

The point estimate is 0.3488.

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3488 - 2.575\sqrt{\frac{0.3488*0.6512}{1078}} = 0.3114[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3488 + 2.575\sqrt{\frac{0.3488*0.6512}{1078}} = 0.3862[/tex]

The 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day is (0.3114, 0.3862).

Answer:

C. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

The company should choose the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

We have given that,

A sports company wants to package a ball with a 1.5-inch radius in sets of two.

They have two options a cylinder or a square prism.

2 balls are inside of a cylinder and 2 balls are inside of a square prism. The cylinder has a height of 6 inches and a radius of 1.5 inches.

A square prism is basically a cuboid, that has square bases. It has four rectangular faces and two square-shaped ends. In Geometry, we have studied various three-dimensional shapes called solid shapes or solids.

The square prism has base lengths of 3 inches and the prism has a height of 6 inches.

The company wants to use the package that has the least amount of wasted space.

Therefore, The company should choose the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

To learn more about the cylinder or a square prism visit:

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Answer:

Answers are below

Step-by-step explanation:

The center coordinates of the circle are at (0,0).

The radius of the circle is 20

I graphed the circle on the graph below to show you how I got my answers.

The center of the equation x² + y² = 400 is, (0, 0).

And, The radius is 20.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The equation is,

⇒ x² + y² = 400

Now, We know that;

The standard for of the equation of circle is,

⇒ (x - h)² + (y - k)² = r²

Where, (h, k) is the center of the circle and 'r' is the radius of the circle.

Hence, By comparing we get;

⇒ x² + y² = 400

⇒ (x - 0)² + (y - 0)² = 20²

The center of the equation x² + y² = 400 is, (0, 0).

And, The radius is 20.

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Answer:

The correct answer will be:

[tex]-\dfrac{62}{23}[/tex]

Step-by-step explanation:

It is given that :

Initial temperature, [tex]T_1 = 0^\circ F[/tex]

Final temperature,

[tex]T_2 = -15\dfrac{1}{2}^\circ F\\\Rightarrow T_2 = -\dfrac{15\times 2+1}{2} ^\circ F\\\Rightarrow T_2 = -\dfrac{31}{2} ^\circ F[/tex]

Time taken :

[tex]5\dfrac{3}{4}\ hrs = \dfrac{5 \times 4+3}{4}\ hrs = \dfrac{23}{4}\ hrs[/tex]

Change in temperature per hour:

[tex]\dfrac{\text{Difference of temperature}}{\text{Total Time Taken}}\\\Rightarrow \dfrac{T_2-T_1}{\text{Total Time Taken}}[/tex]

Putting the values of temperatures and time:

[tex]\dfrac{\dfrac{-31}{2}-0}{\dfrac{23}{4}}\\\Rightarrow \dfrac{\dfrac{-31}{2}}{\dfrac{23}{4}}\\\Rightarrow \dfrac{-31 \times 4}{2 \times 23}} \text{---- Error done by Wen at this step}\\\Rightarrow \dfrac{-31 \times 2}{23}}\\\Rightarrow \dfrac{-62}{23}}[/tex]

The error done by Wen was during calculating the values of fraction.

So, the correct answer is :[tex]\frac{-62}{23}}[/tex] instead of [tex]\frac{-713}{8}[/tex]

Answer:

C. Wen did not take the reciprocal of the divisor

Step-by-step explanation:

Answer:

67.5

Step-by-step explanation:

right angle =90 degree

total = 360 degree

360-90=270

270÷4=67.5

Answer: choice B

Step-by-step explanation:

Events A and B are independent if the equation P(B)=P(B|A) or P(A∩B) = P(A) · P(B) holds true.

in this example

p(A)=1/6    {5}

p(B)=1/2   {1,3,5}

P(B|A)=1

so

P(B)≠P(B|A)

=>A and B are dependent

Answer:

[tex]\chi^2 =\frac{10-1}{18} 23.04 =11.52[/tex]

The degrees of freedom are:

[tex] df =n-1=10-1=9[/tex]

Now we can calculate the critical value taking in count the alternative hypotheis we have two values:

[tex]\chi^2_{\alpha/2}= 2.70[/tex]

[tex]\chi^2_{1-\alpha/2}= 19.02[/tex]

Since the calculated value is between the two critical values we FAIL to reject the null hypothesis and we can't conclude that the true variance is different from 18

Step-by-step explanation:

Information given

[tex]n=10[/tex] represent the sample size

[tex]\alpha=0.05[/tex] represent the confidence level  

[tex]s^2 =4.8^2= 23.04 [/tex] represent the sample variance obtained

[tex]\sigma^2_0 =18[/tex] represent the value to verify

System of hypothesis

We want to verify if the true variance is different from 18, so the system of hypothesis would be:

Null Hypothesis: [tex]\sigma^2 = 18[/tex]

Alternative hypothesis: [tex]\sigma^2 \neq 18[/tex]

The statistic would be given by:

[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]

And replacing we got:

[tex]\chi^2 =\frac{10-1}{18} 23.04 =11.52[/tex]

The degrees of freedom are:

[tex] df =n-1=10-1=9[/tex]

Now we can calculate the critical value taking in count the alternative hypotheis we have two values:

[tex]\chi^2_{\alpha/2}= 2.70[/tex]

[tex]\chi^2_{1-\alpha/2}= 19.02[/tex]

Since the calculated value is between the two critical values we FAIL to reject the null hypothesis and we can't conclude that the true variance is different from 18

Answer:

Step-by-step explanation:

The standard error of the mean is defined as the ratio of standard deviation to the square root of the sample size of a data. The standard error of the mean is mathematically expressed as shown below;

[tex]X = \frac{\sigma}{\sqrt{n} }[/tex]

X is the standard error of the mean

[tex]\sigma[/tex] is the standard deviation

n is the sample size.

Given;

[tex]\sigma = 121\\n = 256[/tex]

On substitution into the formula we have;

[tex]X = \frac{121}{\sqrt{256} }[/tex]

[tex]X = \frac{121}{16} }\\[/tex]

X ≈ 7.56

Answer:

The time (t) = 2.6 years

Step-by-step explanation:

To calculate the time for earning a compound interest, compounded on a certain amount of present value (PV), compounded periodically, the following formula is used:

[tex]FV=PV(1+\frac{i}{n} )^{n*t}[/tex]

where:

FV = future value = $6,100

PV = present value = $5,000

i = interest rate in decimal = 7.5% = 0.075

n = number of compounding periods per year = quarterly = 4 (4 quarters a year)

t = time of compounding in years = ???

Therefore the time is calculated thus:

[tex]6100=5000(1+\frac{0.075}{4} )^{4*t}[/tex]

[tex]6100=5000(1+0.01875 )^{4t}[/tex]

[tex]6100=5000(1.01875 )^{4t}[/tex]

Next, let us divide both sides of the equation by 5000

[tex]\frac{6100}{5000} = \frac{5000(1.01875)^{4t} }{5000}[/tex]

1.22 = [tex](1.01875)^{4t}[/tex]

Taking natural logarithm of both sides

㏑(1.22) = ㏑[tex](1.01875)^{4t}[/tex]

㏑(1.22) = 4t × ㏑(1.01875)

0.1989 = 4t × 0.01858

4t = [tex]\frac{0.1989}{0.01858} = 10.71[/tex]

∴ 4t = 10.71

t = 10.71 ÷ 4 = 2.6 years

Answer:

(a)p(3,3)=0.0416

(b)p(4,11)=0.0002

Step-by-step explanation:

Number of Customers, X

[tex]\left\begin{array}{|c|ccccc|}X&0&1&2&3&4\\P(X)&0.1&0.2&0.3&0.25&0.15.\end{array}\right[/tex]

Y = the total number of packages to be wrapped for the customers waiting in line

[tex]\left\begin{array}{|c|ccccc|}Y&1&2&3\\P(Y)&0.55&0.35&0.1\end{array}\right|[/tex]

a. P(X = 3, Y = 3)

p(3,3) means that there are 3 customers with one gift each

The probability of this event happening:

[tex]0.25 \times 0.55^3=0.0416[/tex]

p(3,3)=0.0416

b. p(4,11)

For 4 people to have a total package of 11, there must be 3 customers with 3 packages each and 1 customer with 2 packages,

The probability of this happening is:

[tex]p(4,11)=0.15\times^4C_1\times0.1^3\times0.35\\p(4,11)=0.0002[/tex]

Answer:

51.38% probability that they requested regular gas

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question, we have that:

Event A: Not filling the tank

Event B: Regular gas

40% of the customers request regular gas

This means that [tex]P(B) = 0.4[/tex]

Of those customers requesting regular gas, 70% only fill up part of their tank.

This means that [tex]P(A|B) = 0.7[/tex]

Probability of not filling the tank:

70% of 40%(regular gas)

100 - 60 = 40% of 35%(unleaded gas).

100 - 50 = 50% of 25%(premium gas).

So

[tex]P(A) = 0.7*0.4 + 0.4*0.35 + 0.5*0.25 = 0.545[/tex]

What is the probability that they requested regular gas?

[tex]P(B|A) = \frac{0.4*0.7}{0.545}[/tex] = 0.5138

51.38% probability that they requested regular gas

Answer:

To the nearest tenth of a degree

∠E= 47.9°

Step-by-step explanation:

ΔDEF , let's recognize that it's a right angle triangle because of the presence of ∠F=90°.

Other important measurements are

DE = 82 feet, and EF = 55 feet.

We are to find ∠E

Let's find the missing side first

Side DF

DF² = DE² - EF²

DF²= 82²_55²

DF²=6724-3025

DF²= 3699

DF= 60.82 feet

Let's use the sine formula to look for the angle.

DF/sin ∠E= DE/sin 90

Sin 90= 1

DE= 82

DF= 60.82

Sin ∠E= DF/DE

Sin ∠E= 60.82/82

Sin ∠E= 0.7417

∠E= sin^-1 (0.7417)

∠E= 47.8764

To the nearest tenth of a degree

= 47.9°

Answer:

29/5 =x

Step-by-step explanation:

25 = 5x − 4

Add 4 to each side

25+4 = 5x − 4+4

29 = 5x

Divide each side by 5

29/5 = 5x/5

29/5 =x

Answer:

The answer is 6

Step-by-step explanation:

:)

Answer:Y=x3

2nd answer: Just add it all up and divide by how many things you had to add. For an example: (2+2+2+2)/4.

Step-by-step explanation:

Answer:

A. Step 2

Step by step explanation:

It was applied in Step 2 where 9 was added to both sides of the equation.

Answer:

50

Step-by-step explanation:

7850/3.14

Square root 2500

50

Answer:

1.25

Step-by-step explanation:

Lets sum up the values

24

and then divide by their number (8)

we get 3 on average

now let's see how much each data point varies from that average (this is always a positive value)

1, 1, 2, 1, 1, 1, 3, 0

Let's sum and divide by 8 again

10/8 = 1.25

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