A random sample of n people selected from a large population will be asked whether they have read a novel in the past year. Let the random variable R represent the number of people from the sample who answer yes. The variance of random variable R is 6. Assume the responses are independent of each other. If the proportion of people from the population who read a novel in the past year is 0.40, which of the following is the best interpretation of random variable R ?

1. A binomial variable with 15 independent trials
2. A binomial variable with 25 independent trials
3. A variable that is not binomial with 25 independent trials
4. A binomial variable with 40 independent trials
5. A variable that is not binomial with 40 independent trials

Answer: Random sampling

Step-by-step explanation:

In the given situation , the population of interest is "all adults"

Since the man got selected randomly from entire population of adults by the marketing company, it means the type of sampling method was used is random sampling technique.

Hence, the correct answer is "random"

Question is not proper, Proper question is given below;

36% of the beans in Pythagoras's soup are lentils, and 33 1/3% of those lentils are green.

If Pythagoras removes all green lentils from his soup, then x% of the original beans remain. What is x?

Answer:

88% of the original beans remains [tex](x)[/tex] after removing green lentils.

Step-by-step explanation:

Given:

Let the Original beans be 'n'.

Now given:

36% of the beans in Pythagoras's soup are lentils.

So we can say that;

Amount of lentils = [tex]\frac{36}{100}n=0.36n[/tex]

Also Given:

33 1/3% of those lentils are green

Amount of green lentils = [tex]33\frac{1}{3}\%\ \ Or \ \ \frac{100}{3}\%[/tex]

Amount of green lentils = [tex]\frac{100}{3}\times 0.36n\times\frac{1}{100}= 0.12n[/tex]

Now we need find the percentage of original beans remain after removing green lentils.

Solution:

percentage of original beans remain  ⇒ [tex]x\%[/tex]

To percentage of original beans remain after removing green lentils we will subtract Amount of green lentils from Original beans  and then multiplied by 100.

framing in equation form we get;

[tex]x\%[/tex] = [tex](n-0.12n)\times 100=88n \ \ \ Or \ \ \ 88\%[/tex]

Hence 88% of the original beans remains [tex](x)[/tex] after removing green lentils.

Answer:

x = 88

Step-by-step explanation:

We know that 36% of the letters are vowels. Of these, one-third are Os

(Since 33 1/3% = 33 1/3 divided by 100 = 1/3.) One-third of 36% is 12%, so 12% of the total letters in Pythagoras' soup are Os. When these are removed from the soup, 100 - 12=88% of the original letters remain.

So, x = 88

Hope this helps!

Answer:

Step-by-step explanation:

The Chef bought he had 8 cartons with 36 eggs in each carton. This means that the total number of eggs that the Chef bought is

36 × 8 = 288 eggs

He uses 2/5 for Fridays breakfast. This means that the number of eggs that he used on Friday is

2/5 × 8= 16/5 cartons

The remaining number of cartons would be

8 - 16/5 = 24/5 cartons

He used 3/8 of the remaining for Saturdays breakfast. This means that the number of eggs that he used on Saturday is

3/8 × 24/5 = 9/5 cartons

Total number of cartons that he used is

16/5 + 9/5 = 25/5 = 5 cartons

Since one carton contains 36 eggs, then the total number of eggs that the Chef used is

5 × 36 = 180 eggs

Question:

Ana participated in a charity walk. She raised $0.25 for each 1/2 mile that she walked.The first day Ana walked 11 miles.The second day, she walked 14 miles.How much money did Ana raised?

Answer:

Ana raised $ 12.5

Solution:

From given question,

First day walk = 11 miles

Second day walk = 14 miles

Let us first calculate the total distance she walked

Total distance = first day walk + second day walk

Total distance = 11 + 14 = 25 miles

Thus she walked for 25 miles

Given that,

She raised $0.25 for each 1/2 mile that she walked

[tex]\frac{1}{2} \text{ mile} = 0.25 \text{ dollars }[/tex]

Therefore, for 1 mile we get,

[tex]\frac{1}{2} \times 2 \text{ mile} = 0.25 \times 2 \text{ dollars }\\\\1 \text{ mile } = 0.5 \text{ dollars }[/tex]

Now calculate for 25 miles

[tex]25 \text{ mile } = 25 \times 0.5 = 12.5 \text{ dollars }[/tex]

Thus she raised $ 12.5

A line is a set of all points that : C. are the same distance from two points.

Step-by-step explanation:

A line is defined as a set of all points that are the same distance from two given points. For a line to form, you must connect points, thus its correct to say a line is formed when you draw a locus of a given point.

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Keywords: line, set , points

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Answer: 1) Percentage, Probability, Proportion

Step-by-step explanation:

In statistics,

▪Proportion means a fraction of the total.

▪Percentage means a number or a ratio, expressed as a fraction of 100. Here, the total is 100.

▪Probability which may look slightly different from the other two means a number between 0 and 1, showing the exact likelihood of an event happening. Which in context can mean, a number showing a fraction of an event happening out of the whole (0 to 1).

▪Critical value means a point in hypothesis testing on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

In the four definitions, the odd one out is Critical Value.

So the option without critical value in it is option 1) Percentage, Probability, Proportion since we can use the three interchangeable.

Answer:

1. Percentage, Probability, and Proportion

Step-by-step explanation:

Proportion means a portion of a whole e.g. 2/5

Percentage means a ratio of a number expressed as a fraction of 100 e.g 20/100

Probability- This means the likelihood of an event to occur e.g 1/2

All these three terms are usually expressed as a Fraction of a Number which makes them similar.

Answer:

In terms of negative correlation, I would say it's the longer you exercise, the more you sweat.

Answer:

Its D. The younger the child, the more sleep they need.

Step-by-step explanation:

–21 + x

Explanation:

Step 1: Given expression: –4 + (–17) + x

Step 2: In the algebraic property, positive × negative = negative

So, –4 + (–17) + x = –4 – 17 + x

Step 3: Add two negative numbers, the result will be sum with minus sign

–4 – 17 + x = –21 + x

Hence,  –21 + x is the required equation.

Answer:

160m/s

Step-by-step explanation:

The object can hit the ground when t = a; meaning that s(a) = s(t) = 0

So, 0 = -16a² + 400

16a² = 400

a² = 25

a = √25

a = 5 (positive 5 only because that's the only physical solution)

The instantaneous velocity is

v(a) = lim(t->a) [s(t) - s(a)]/[t-a)

Where s(t) = -16t² + 400

and s(a) = -16a² + 400

v(a) = Lim(t->a) [-16t² + 400 + 16a² - 400]/(t-a)

v(a) = Lim(t->a) (-16t² + 16a²)/(t-a)

v(a) = lim (t->a) -16(t² - a²)(t-a)

v(a) = -16lim t->a (t²-a²)(t-a)

v(a) = -16lim t->a (t-a)(t+a)/(t-a)

v(a) = -16lim t->a (t+a)

But a = t

So, we have

v(a) = -16lim t->a 2a

v(a) = -32lim t->a (a)

v(a) = -32 * 5

v(a) = -160

Velocity = 160m/s

Using movement concepts, it is found that:

----------------------------------

The height of the object after t seconds, dropped from a height of 500 feet, is given by:

[tex]h(t) = -16t^2 + 500[/tex]

----------------------------------

It hits the ground when [tex]h(t) = 0[/tex], thus:

[tex]h(t) = 0[/tex]

[tex]-16t^2 + 500 = 0[/tex]

[tex]16t^2 = 500[/tex]

[tex]t^2 = \frac{500}{16}[/tex]

[tex]t = \sqrt{\frac{500}{16}}[/tex]

[tex]t = 5.59[/tex]

The object hits the ground after 5.59 seconds.

----------------------------------

The velocity is the derivative of the position, thus:

[tex]v(t) = h^{\prime}(t) = -32t[/tex]

The velocity when it impacts the ground is v(5.59), thus:

[tex]v(5.59) = -32(5.59) = -178.88[/tex]

The object hits the ground at a velocity of -178.88 feet per second.

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The mean score of all the students together, after calculating the combined total score and dividing by the total number of students, is 83.1.

The subject of this question is the computation of the mean score of all students. The first step is to find the total score of both sets of students. For the first group, the total score is the mean score multiplied by the number of students, which is 93.2 * 32 = 2974.4. For the second group, total score is 63.4 * 16 = 1014.4. The combined total score is 2974.4 + 1014.4 = 3988.8. Since there are 32 + 16 = 48 students in total, the mean score of all students is calculated by dividing the combined score by the total number of students. So, the mean score of all the students together is 3988.8 / 48 = 83.1 (rounded to one decimal place).

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Answer:

10 stereos must the salesperson sell to make the same amount of money with both plans.

Step-by-step explanation:

Let the Number of stereo sold = x

According to Plan A

250 + 25X

According to Plan B

50X

According to given condition

250 + 25X = 50X

250 = 50X - 25X

250 = 25X

X = 250/25

X= 10

Answer:

the answer is a

Step-by-step explanation:

Answer:

Nt=10 (m=4,n=6)

Step-by-step explanation:

we have that m = amount of time used by the large washing machine to wash a load of clothes and n = amount of time used by the small washing machine to wash a load of clothes, so

[tex]m=\frac{Tt}{Tpm}=\frac{2h}{\frac{1h}{2}}=4\\n=\frac{Tt}{Tpn}=\frac{2h}{\frac{1h}{3}}=6[/tex]

Nt=m+n=10

where Tt = time frame, Tpm= m' time frame, Tpn = n' time frame and Nt = total number of charges

Answer: Total laundry done in 2hours=110

Step-by-step explanation:

Let m be large washing machines

Let n be small washing machines

Load of laundry for large machine=30mins

Load of laundry in small machine=20 mins

2 hours laundry =2×60=120mins

For m in 2hrs=120/30=4

For n in 2hrs=120/20=6

m loads in 2hrs=4m

n loads in 2hrs=6n

1st statement:n=3m

Substituting

4m+6(3)=x

4m+18m=x

X=22m

Value of m cannot be determined because statement 1 is insufficient

From the 2nd statement: 2m+3n=55

Multiply both sides by2

4m+6n=110

Answer:

the probability that the average loss from fire in the sample is no greater than $275 is 0.9938

Step-by-step explanation:

given information:

mean, μ = $250

std deviation, σ = $1000

random sample, n = 10000

x = $275

P([tex]x[/tex] ∠_ 275) = P(z < (z ∠ (x - μ)/(σ/√n))

                    = P (z ∠ (275 - 250)/(1000/√10000)

                    = P(z ∠ 2.5)

                     =  0.9938

The probability that the average loss from fire in the sample is no greater than $275 is 99.38%.

the probability that the average loss from fire in the sample is no greater than $275,

[tex]P(z\leq x)=P[z< \dfrac{(x-\mu )}{(\dfrac{\sigma}{\sqrt n})}][/tex]

[tex]P(z\leq 275)=P[z< \dfrac{(275-250 )}{(\dfrac{1000}{ \sqrt {10000}})}][/tex]

[tex]P(z\leq 275)=P[z< \dfrac{(25 )}{(10)}][/tex]

[tex]P(z\leq 275)=P[z< {(2.5)}][/tex]

[tex]P(z\leq 275)=0.9938[/tex]

P(x ≤ $275) = 99.38%

Hence, the probability that the average loss from fire in the sample is not greater than $275 is 99.38%.

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Final answer:

The magnitude of vector B is 1. There is no valid direction angle theta for vector B.

Explanation:

Part A:

The magnitude of vector B can be found using the formula for the magnitude of the vector product:

|A x B| = |A||B|sin(theta)

Given |A x B| = 12, |A| = 8, and |B| = ?

Using the formula above, we can solve for |B|:

12 = 8 * |B| * sin(theta)

sin(theta) = 12 / (8 * |B|) = 1.5 / |B|

Sine of any angle lies between -1 and 1, therefore 1.5 / |B| should lie in this range

|-1| <= 1.5 / |B| <= |1|

1 <= 1.5 / |B| <= 1

1.5 <= |B| <= 1

The magnitude of vector B is 1.

Part B:

The direction angle theta can be found using the formula:

cos(theta) = Bz / |B|

Given Bz = |B| and sin(theta) = 1.5 / |B|

1.5 / |B| = sqrt(1 - sin^2(theta)) = sqrt(1 - 1) = sqrt(0) = 0

This implies that sin(theta) = 1.5 / |B| = 0, which is not possible

Hence, there is no valid direction angle theta for vector B.

Final answer:

The magnitude of vector B is 1.5 m. The direction angle θ of vector B measured from the +y-direction to the +z-direction is 90°.

Explanation:

Part A: To find the magnitude of vector B, we need to use the relationship between the magnitude of the vector product A x B and the magnitudes of vectors A and B. According to the given information, the magnitude of the vector product A x B is 12.0 m². Since the vector product is in the +z-direction, we can conclude that the magnitudes of vectors A and B multiplied by the sine of the angle between them equals 12.0 m².

Let's use this information to find the magnitude of vector B:

|A x B| = |A||B|sin(θ)

12.0 m² = 8.0 m * |B| * sin(90°)

|B| = 12.0 m² / (8.0 m * sin(90°))

|B| = 12.0 m² / 8.0 m = 1.5 m

Therefore, the magnitude of vector B is 1.5 m.

Part B: To find the direction angle θ of vector B measured from the +y-direction to the +z-direction, we can use the relationship between the components of vectors A and B and the direction angle θ:

tan(θ) = By / Bz

Substituting the given information into the equation:

tan(θ) = 0 / Bz

Since vector B has no x-component, we know that Bx = 0. Therefore, we only need to find the value of Bz to determine the direction angle θ.

Recall that |B| = 1.5 m. Using the Pythagorean theorem, we can find the value of Bz:

|B|² = Bx² + By² + Bz²

(1.5 m)² = (0)² + (0)² + Bz²

Bz² = (1.5 m)²

Bz = 1.5 m

Since Bz > 0, we know that the direction angle θ is in the positive range. In this case, the direction angle θ is 90° measured from the +y-direction to the +z-direction.

Answer:

$6.83

Step-by-step explanation:

To start off, we would want to graph the points.

Once we have our graph, we see our correlation is positive, meaning that every year past 1950, the price of 1 movie ticket increases.

Our next step would to figure out the linear regression, or to guess a best line of fit. Once we do so, we should see where the movie tickets should approxametly rise to.

We then use the best line of fit to estimate the price in 2015, or when x = 65 (65 years after 1950).

The answer closest to the estimate would be 6.83. Attached image is the graph on Desmos.

Answer:

Arianna multiplied the dividend by the divisor instead of finding the reciprocal.

Step-by-step explanation:

The fraction division problem Arianna solved is [tex]\frac{2}{3}\div \frac{4}{5}[/tex]

Adrianna's next step is  [tex]\frac{2}{3}\times \frac{4}{5}[/tex]

We are supposed to choose from the options the most accurate description of Arianna's work.

The mistake Arianna committed is that, she did not reciprocate the [tex]\frac{4}{5}[/tex] before multiplying.

Therefore the correct answer is:

Arianna multiplied the dividend by the divisor instead of finding the reciprocal.

Only option 1: 3y+3z is equivalent to given expression

Step-by-step explanation:

In order to find the equivalent expression to given expression, we have to simplify each of the options to compare with the given expression

Given expression is:

[tex]3y+3z[/tex]

Option 1:

[tex]3(y+z)\\= 3y+3z[/tex]

Option 2:

[tex]3y+z[/tex]

Option 3:

[tex]10y+2z+y+z\\= 10y+y+2z+z\\= 11y+3z[/tex]

Option 4:

[tex]6+y+3z[/tex]

Hence,

Only option 1: 3(y+z) is equivalent to given expression

Keywords: Polynomials, expressions

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Answer:

heterozygous (Aa) are 0.085 = or 8.54%

Step-by-step explanation:

The heterozygous individuals are carriers of the sickle cell trait. They have a genotype of Aa and are represented by the 2pq term

in the H-W equilibrium equations.

According to the question 0.2% of the population is affected with sickle cell anemia, thus q^2

= 0.2% = 0.002 in decimal. So, q =

sqr(q^2)

or sqr(0.002) =

0.04472

and p + q = 1, thus p = 1 – q = 1 – 0.04472 = 0.96

Thus, A allele has a frequency of 0.96 and the a allele has a frequency of 0.04472. Therefore, the

percentage of the population that is heterozygous (Aa) and are carriers is = 2pq = 2× 0.04472× 0.96 =0.085 = or 8.54%

Answer:

[tex]y=\frac{5}{3} x-\frac{38}{3}[/tex]

the value of b is -38/3

Step-by-step explanation:

[tex]y=\frac{5}{3} x+b[/tex] goes through the point (7,-1)

we need to find out b for the given equation using (7,-1)

Plug in 7 for x  and -1 for y

[tex]y=\frac{5}{3} x+b[/tex]

[tex]-1=\frac{5}{3} (7)+b[/tex]

[tex]-1=\frac{35}{3}+b[/tex]

subtract 35/3 from both sides

[tex]-1 -\frac{35}{3} =b[/tex]

[tex]\frac{-38}{3} =b[/tex]

Replace it in the original equation

[tex]y=\frac{5}{3} x-\frac{38}{3}[/tex]

Answer: the rate of the car is 50mph

Step-by-step explanation:

Let x represent the average speed of the bus.

Let y represent the distance travelled by the bus.

The average speed of the car is 30 mph slower than twice the speed of the bus. This means that the average speed of the car would be

2x - 30

Distance = speed × time

Time = distance/speed

Therefore, In 2 hours time,

2 = y/x

2x = y

In two hours the car is 20 miles ahead of the bus. Therefore

2 = (y + 20)/(2x - 30)

2(2x - 30) = y + 20

4x - 60 = y + 20 - - - - - - - - -1

Substituting y = 2x into equation 1, it becomes

4x - 60 = 2x + 20

4x - 2x = 20 + 60

2x = 80

x = 80/2 = 40

The speed of the car would be

2x - 30 = 2 × 40 - 30

= 80 - 30 = 50 mph

Answer:

[tex]h'=\frac{dh}{dr}=-\frac{2}{r^3\pi}[/tex]

Step-by-step explanation:

Assuming the dough is of cylindrical shape and that the volume must stay the same the equation for the volume of the cylinder is the following:

[tex]V=r^2\pi h[/tex]

where V is the volume, r the radius and h the height of the cylinder. If you get h to the left hand side you get the following equation:

[tex]h=\frac{V}{r^2\pi}[/tex]

To find the rate of change of the height you need to derive the above equation with respect to r:

[tex]h'=-\frac{2}{r^3\pi}[/tex]

Rate of change is simply how much a quantity changes, over another.

The expression for the rate of change of the dough in terms of height h and radius r is [tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]

From the complete question, we have:

[tex]\mathbf{V = \pi r^2h}[/tex]

Next, we make h the subject

[tex]\mathbf{h = \frac{V}{\pi r^2}}[/tex]

Rewrite as:

[tex]\mathbf{h = \frac{V}{\pi}r^{-2}}[/tex]

Differentiate with respect to r

[tex]\mathbf{h' = -2\times \frac{V}{\pi}r^{-2-1}}[/tex]

[tex]\mathbf{h' = -2\times \frac{V}{\pi}r^{-3}}[/tex]

Rewrite as:

[tex]\mathbf{h' = \frac{-2V}{\pi r^3}}[/tex]

Remove V, to leave the answer in terms of r and h

[tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]

Hence, the expression for the rate of change of the dough in terms of height h and radius r is [tex]\mathbf{h' = \frac{-2}{\pi r^3}}[/tex]

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The required function is: [tex]f(t) = -0.05t+12[/tex]

Step-by-step explanation:

We have to write a function for the remaining figurines Colin has to paint.

Here

f is the function that represents number of figurines remaining

t represents time in minutes as the unit of measurement is minutes

f will be a function of t

It is mentioned in the problem that after working for 60 minutes, he has 9 figurines left to paint.

This means that

f(60) = 9

It is also given that he takes 20 minutes to paint one figurine which means in 60 minutes he will have painted 3 figurines

So at start total figurines that needed to be painted will be:

9+3 = 12

Which means that

f(0) = 12

By using these two points we can find the slope of the function

[tex]m = \frac{Change\ in\ figurines}{Change\ in\ time}\\m = \frac{9-12}{60-0}\\m = \frac{-3}{60}\\m = -0.05[/tex]

The function will be:

[tex]f(t) = mt+b[/tex]

Putting the value of slope

[tex]f(t) = -0.05t+b[/tex]

b is the initial value of figurines so

[tex]f(t) = -0.05t+12[/tex]

Keywords: Functions, slope

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Answer:

B )  -2

Step-by-step explanation:

slope of given points

slope [tex]m= \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }[/tex]

The given points are

[tex]m = \frac{-4-8}{5-(-1)}[/tex]

[tex]m=\frac{-12}{6}[/tex]

[tex]m=-2[/tex]

final answer :-

slope of the line is m=-2

Answer:

product of the constants P will be

P = 12

Step-by-step explanation:

the quadratic equation

F= x² + t*x - 9

has as solution

a and b= [-t  ± √( t² - 4*1*(-9)) ] /2]

then

a - b = -t/2

a= b - t/2

since b is an integer , then t/2 should be an integer , then t=2*n , where n is any integer

also

a and b= [-t  ± √( t² - 4*1*(-9)) ] /2] = [-2*n  ± √(4*n²+36 )] /2  = -n  ± n √ (1+9/ n²]

since n are integers , then √ (1+9/ n²]  should be and integer and therefore

9/ n² should be an integer. Then the possible values of n are

n=1 and n=3

therefore the possible values of t are

t₁=2*1 = 2

t₂=2*3 = 6

the product of the constants P will be

P=t₁*t₂ = 12

Answer:

729

Step-by-step explanation:

Hi, your question was incomplete hence I have attached the complete version of the question below.

Answer:

5x^3 y^2

Step-by-step explanation:

Using the property of the product of the exponents on the base and removing the parentheses,

(125x^9y^6)^(1/3) = (125)^(1/3) * (x^9)^(1/3) * (y^6)^(1/3)

= (125)^(1/3) * (x)^9*(1/3) * (y)^6*(1/3)

= 5 * (x)^3 * (y)^2                                                    

= 5 x^3 y^2

hence the required result is 5 x^3 y^2

Answer:

0.5 seconds

Step-by-step explanation:

Two rockets are launched at the same time, but from different heights.

[tex]y = -16t^2+ 150t + 5[/tex]

[tex]y = -16t^2 + 160t[/tex]

when the heights are same then y are equal. So equation both equations and solve for t

[tex]-16t^2+ 150t + 5= -16t^2+ 160t[/tex]

Add -16t^2 on both sides

[tex]+ 150t + 5=160t[/tex]

Subtract 150 t from both sides

[tex]5=10t[/tex]

Divide 10 on both sides

t=0.5 seconds

Answer:

The answer to your question is    5x + 6y - 42 = 0  

Step-by-step explanation:

Data

y-intercept = 7

parallel to -5x - 6y = 1

Process

1.- Find the slope

                             - 6y = 5x + 1

                                 y = -5/6 x - 1/6

As the lines are parallels, the slope is the same in both lines

                                 m = -5/6

2.- Find the equation of the new line

If the line has a y-intercept of 7, it means that the point is (0, 7)

                       y - y1 = m(x - x1)

Substitution

                      y - 7 = -5/6 (x - 0)

Simplification

                      y - 7 = -5/6x

Equal to zero

                     5/6x + y - 7 = 0

Multiply by 6

                     5x + 6y - 42 = 0           This is the equation of the line

Answer:

6y = -5x + 42

Step-by-step explanation:

-5x - 6y = 1

-6y = 5x + 1---------------------(i)

y = -5x/6 - 1/6

comparing the equation above with y = mx + c, we have;

m = -5/6

for condition of parallelism

the gradient of the new line = -5/6

Using the formula

y = mx + c

y = -5x/6 + 7

6y = -5x + 42

Hi there! Since the ratios of students at Hanover High School are in different scales, we need to scale them up! First, let's take the ratio 1:2. This can be scaled up to 5:10. Now, combine the two ratios to find the ratio of freshmen to sophomores. 3:10 + 5:10 = 8:10. The remaining number is 2, since 8 + 2 = 10, so the ratio of freshmen to sophomores is 2:10!

Hope this was helpful!

The graph of y=|x| would look like graph A

The reflected graph (mirrored image) would be graph D