Suppose that one person in 10,000 people has a rare genetic disease. There is an excellent test for the disease; 98.8% of the people with the disease test positive and only 0.4% of the people who don't have it test positive.
A) What is the probability that someone who tests positive has the disease?
B) What is the probability that someone who tests negative does not have the disease?

Answer:

Equation: 5t² − 10t + 13 = 0

Answer: No

Step-by-step explanation:

h(t) = -5t² + 10t + 22

When h(t) = 35:

35 = -5t² + 10t + 22

5t² − 10t + 13 = 0

This equation must have at least one real solution if the ball is to reach a height of 35 meters.  Which means the discriminant can't be negative.

b² − 4ac

(-10)² − 4(5)(13)

100 − 260

-160

The ball does not reach a height of 35 meters.

Answer:

Equation: 5t² − 10t + 13 = 0

Answer: No

Answer:

  41,055

Step-by-step explanation:

If there are 805 students in each of 51 schools, the total number of students is ...

  (805 students/school) × (51 schools) = 41,055 students

_____

We have to assume that all of the students in the county go to county schools. Apparently, we are to ignore the students that are dropouts or homeschooled, or that go to schools not in the county.

Answer: 41055

Step-by-step explanation:

51 schools, each has 805 kids

51*805=41055

Answer:

  8020 feet

Step-by-step explanation:

The tangent relation can be used to answer this question, since it relates the sides of a right triangle to the acute angle.

 tan(elevation angle) = (1472 ft)/(distance between)

Then ...

  distance between = (1472 ft)/tan(10.4°) ≈ 8020 ft

The skyscrapers are 8020 feet apart.

Using the tangent of the given angle of inclination and the height of skyscraper B, the horizontal distance between the bases of the two skyscrapers is calculated to be approximately 8077 feet.

The question is looking for the horizontal distance between the bases of two skyscrapers, given the height of one skyscraper and the angle of inclination from its base to the top of the other. This scenario forms a right triangle, where the height of skyscraper B is the opposite side, the distance between the skyscrapers is the adjacent side, and the angle of inclination is the given angle. We can use the tangent trigonometric function, which is the ratio of the opposite side to the adjacent side, to solve for the distance.

To calculate the distance (adjacent side) we can rearrange the equation: Tan(angle) = opposite/adjacent, to: Adjacent = opposite/tan(angle). Plugging in our given values we find: Distance = 1472 feet / tan(10.4 degrees) = approximately 8077 feet. Thus, the two skyscrapers are about 8077 feet apart.

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The circumference of circle with radius 18 inches in terms of pi is 36π inches

From the given figure, radius "r" = 18 inches

We have to find circumference of circle

circumference would be the length of the circle if it were opened up and straightened out to a line segment.

The circumference of circle is given as:

[tex]\text {circumference of circle }=2 \pi r[/tex]

Where "r" is the radius of circle

Substituting the value r = 18 inches in above formula,

[tex]\text {circumference of circle }=2 \times \pi \times 18=36 \pi[/tex]

Thus circumference of circle in terms of pi is 36π inches

Answer:

answer is 90 for first term

Step-by-step explanation:

Let the terms be  

First term x

We will use the formula s∞=x/1−r to find the sum of an infinite geometric series, where −1<r<1.  

We know the sum and the common ratio, so we'll be solving for x where r =4/5

s∞=x/1−r

450=x/1−4/5

450=x/1/5

450=5x

x=90

this is the first term x1 = 90

we know that common ratio is 4/5, so multiplying the first term by factor 4/5 to get the second term  

90 x 4/5=   72 second term  

Answer:

C) 90

Step-by-step explanation:

The sum of an infinite geometric series is:

S = a₁ / (1 − r)

where a₁ is the first term and r is the common ratio.

450 = a₁ / (1 − 4/5)

450 = a₁ / (1/5)

450 = 5a₁

a₁ = 90

Answer:

The length of the longer side is 4.48 inches.

Step-by-step explanation:

Given,

Length of diagonal = 6 in

Length of Short side = 4 in

Solution,

Let the length of long side be x.

Since the card is in the shape of rectangle. On drawing the diagonal the rectangle divides into two equal triangle.

So for find out the length of other side we use the Pythagoras theorem, which states that;

"In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides."

[tex]Hypotenuse^2=(Short\ side)^2+(Long\ side)^2[/tex]

[tex]\therefore 6^2=4^2+x^2\\36=16+x^2\\x^2=36-16=20\\x=\sqrt{20} =2\sqrt{5}[/tex]

[tex]x=2\times2.24=4.48\ in[/tex]

Thus the length of the longer side is 4.48 inches.

Answer:

2√26

Step-by-step explanation:

First, let's label side AB as y and side BP as h.

Then, using the Pythagorean Theorem, we can determine that for ΔABP,

5²+h²=y², which is equal to h² = y²- 25.

For ΔBPC, 8²+ h² = x², which is equal to h² = x²- 64.

Because both equations are equal to h², you can determine that y²- 25 = x²- 64. You can rewrite this equation as x²- y² = 39.

Then, for ΔABC, x²+ y² = (5+8)², which is equal to x²+ y² = 169.

Now, you can see that we have a system of equations. Using elimination, we can add the equations, getting:

2x² = 208

x² = 104

x = ±√104 which simplifies into ±2√26, but since x is a distance, and distance is always positive, the answer has to be 2√26.

Answer:

1)[tex]\mu=\frac{1}{2}(7.5+20) =13.75[/tex]

[tex]\sigma^2 = \frac{1}{12}(20-7.5)^2 =13.02[/tex]

2) [tex]F(x)=\big\{0, x<a[/tex]

[tex]F(x) =\big\{ \frac{x-a}{b-a}=\frac{x-7.5}{20-7.5}, a\leq x<b[/tex]

[tex]F(x)=\big\{1, x\geq b[/tex]

3) [tex]P(X<10)=F(10)=\frac{10-7.5}{20-7.5}=0.2[/tex]

[tex]P(10\leq X \leq 15)=F(15)-F(10)=\frac{15-7.5}{20-7.5} -\frac{10-7.5}{20-7.5}=0.6-0.2=0.4[/tex]

4) [tex]P(10.142\leq X \leq 17.358)=F(17.358)-F(10.142)=\frac{17.358-7.5}{20-7.5} -\frac{10.142-7.5}{20-7.5}=0.789-0.211=0.578[/tex]

[tex]P(6.534\leqX\leq 20.966)=P(6.534\leq X<7.5)+P(7.5\leq X \leq 20)+P(20<X\leq 20.966)=0+1+0=1[/tex]

Step-by-step explanation:

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability.

Part 1

If X is a random variable that follows an uniform distribution [tex]x\sim U(a,b)[/tex]. The mean for an uniform distribution is given by : [tex]\mu=\frac{1}{2}(a+b)[/tex]

On this case a=7.5 and b=20 so if we replace we got:

[tex]\mu=\frac{1}{2}(7.5+20) =13.75[/tex]

The variance for the uniform distribution is given by this formula:

[tex]\sigma^2 = \frac{1}{12}(b-a)^2 [/tex]

And replacing we have:

[tex]\sigma^2 = \frac{1}{12}(20-7.5)^2 =13.02[/tex]

Part 2

The cumulative distribution function is given by:

[tex]F(x)=\big\{0, x<a[/tex]

[tex]F(x) =\big\{ \frac{x-a}{b-a}=\frac{x-7.5}{20-7.5}, a\leq x<b[/tex]

[tex]F(x)=\big\{1, x\geq b[/tex]

Part 3

What is the probability that observed depth is at most 10?

We are interested on this probability:

[tex]P(X<10)=F(10)=\frac{10-7.5}{20-7.5}=0.2[/tex]

What is the probability that observed depth is between 10 and 15?

On this case we want this probability:

[tex]P(10\leq X \leq 15)=F(15)-F(10)=\frac{15-7.5}{20-7.5} -\frac{10-7.5}{20-7.5}=0.6-0.2=0.4[/tex]

Part 4

What is the probability that the observed depth is within one standard deviation of the mean value? within 2 standard deviations?

First we find the limits within one deviation from the mean:

[tex]\mu-\sigma= 13.75-3.608=10.142[/tex]

[tex]\mu-\sigma= 13.75+3.608=17.358[/tex]

And we want this probability:

[tex]P(10.142\leq X \leq 17.358)=F(17.358)-F(10.142)=\frac{17.358-7.5}{20-7.5} -\frac{10.142-7.5}{20-7.5}=0.789-0.211=0.578[/tex]

Now we find the limits within two deviation's from the mean:

[tex]\mu-2*\sigma= 13.75-2*3.608=6.534[/tex]

[tex]\mu-2*\sigma= 13.75+2*3.608=20.966[/tex]

But since the random variable is defined just between (7.5 and 20) so we can find just the probability on these limits.

[tex]P(6.534\leqX\leq 20.966)=P(6.534\leq X<7.5)+P(7.5\leq X \leq 20)+P(20<X\leq 20.966)=0+1+0=1[/tex]

The probability of the observed depth being at most 10 is 0.295 and between 10 and 15 is 0.295. The probability that the observed depth is within one standard deviation of the mean is 0.525.

To find the mean and variance of the depth, we use the formula:

Mean = (a + b) / 2 = (7.5 + 20) / 2 = 13.75 cm

To find the variance, we use the formula:

Variance = (b - a)^2 / 12 = (20 - 7.5)^2 / 12 ≈ 12.1875 cm^2

The cumulative distribution function (CDF) of depth can be calculated by finding the probability that the observed depth is less than or equal to a certain value. In this case, since the depth follows a uniform distribution, the CDF is:

CDF(x) = (x - a) / (b - a)

To find the probability that the observed depth is at most 10, we substitute x=10 into the CDF formula:

CDF(10) = (10 - 7.5) / (20 - 7.5) = 0.295

To find the probability that the observed depth is between 10 and 15, we subtract the CDF of 10 from the CDF of 15:

Probability = CDF(15) - CDF(10) = (15 - 7.5) / (20 - 7.5) - (10 - 7.5) / (20 - 7.5) = 0.59 - 0.295 = 0.295

To find the probability that the observed depth is within one standard deviation of the mean value, we need to find the range between Mean - Standard Deviation to Mean + Standard Deviation. Since the variance is the square of the standard deviation, we take the square root of the variance to find the standard deviation:

Standard Deviation = √Variance = √12.1875 ≈ 3.49 cm

Hence, the range is (Mean - Standard Deviation, Mean + Standard Deviation):

Range = (13.75 - 3.49, 13.75 + 3.49) = (10.26, 17.24) cm

To find the probability within this range, we calculate the difference between the CDF of 17.24 and the CDF of 10.26:

Probability = CDF(17.24) - CDF(10.26) = (17.24 - 7.5) / (20 - 7.5) - (10.26 - 7.5) / (20 - 7.5) ≈ 0.82 - 0.295 ≈ 0.525

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Answer with Step-by-step explanation:

We have to prove that

[tex]sin 2\theta=2sin\theta cos\theta[/tex] by using Euler's formula

Euler's formula :[tex]e^{i\theta}=cos\theta+isin\theta[/tex]

[tex]e^{i(2\theta)}=(e^{i\theta})^2[/tex]

By using Euler's identity, we get

[tex]cos2\theta+isin2\theta=(cos\theta+isin\theta)^2[/tex]

[tex]cos2\theta+isin2\theta=(cos^2\theta-sin^2\theta+2isin\theta cos\theta)[/tex]

[tex](a+b)^2=a^2+b^2+2ab, i^2=-1[/tex]

[tex]cos2\theta+isin2\theta=cos2\theta+i(2sin\theta cos\theta)[/tex]

[tex]cos2\theta=cos^2\theta-sin^2\theta[/tex]

Comparing imaginary part on both sides

Then, we get

[tex]sin2\theta=2sin\theta cos\theta[/tex]

Hence, proved.

Answer:

The worth of 375 Croatian Kuna  = $ 55.54

Step-by-step explanation:

Here, given:

The worth of  121.32 Croatian Kuna   = $18

Now, let us assume the worth of 375 Croatian Kuna  = $ m

As, both have same units in conversion at the same rate,

So, by the RATIO OF PROPORTION:

[tex]\frac{18}{121.32 }   = \frac{m}{375}[/tex]

Solving for the value of m, we get:

[tex]m = \frac{18}{121.32}  \times 375  = 55.64[/tex]

or, m = $55.64

Hence, the worth of 375 Croatian Kuna  = $ 55.54

Answer: Robert's present age is 10 years

Robert father's present age is 40 years

Step-by-step explanation:

Let r = Robert's current age

Let y = Robert father's current age

Robert's father is 4 times as old as robert. This means that

y = 4x

After 5 years, Robert's father will be three times as old as Robert. This means that

y + 5 = 3(x+5)

y + 5 = 3x + 15 - - - - - - - ;1

We will substitute y = 4x into equation 1. It becomes

4x + 5 = 3x + 15

Collecting like terms,

4x - 3x = 15 - 5

x = 10

y = 4x

Substituting x = 10,

y = 4× 10 = 40 years

Answer:

The true statement is that the expression is satisfied for n = -2.

Step-by-step explanation:

Given:

[tex]4n = \frac{1}{2}\times (2n-12)[/tex]

To check:

Left hand side = Right-hand side ( for n = -2)

Proof :

For n = -2

Consider  Left hand side of the equation given above.

∴ Left hand side = 4n

                            = 4×(-2)   ......................for n = -2

                            = -8

Consider Right-hand side of the equation given above

∴ Right-hand side = [tex]\frac{1}{2}\times (2n-12)[/tex]

                              [tex]=\frac{1}{2}\times (2\times(-2) - 12) \\= \frac{1}{2}\times (-4 - 12)\\ =\frac{1}{2}\times (-16)\\ =-8[/tex]

Now we get Left hand side equal to Right hand side

i.e. Left hand side = Right hand side

i.e. [tex]4n = \frac{1}{2}\times (2n-12)[/tex] is true for n = -2

Answer:

Step-by-step explanation:

Refer to attached graph

Parent function:

Transformations

1. Reflection over x-axis: f(x) →  -f(x)

2. Horizontal shift 4 units to the right: g(x) → g(x - 4)

3. Vertical shift 3 units up: h(x)  → h(x) + 3

This is the final function

The system of equations that represents the number of each vehicle rented is: x + y + z = 155, x = 9y, and y = 3z.

The question represents a system of linear equations. With the agreed notations: Let x represent cars, let y represent vans and let z represent trucks. We are given that:

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The answer is (1,-5).

The solution to the linear-quadratic system of equations is found by substituting y from the linear equation into the quadratic equation and solving for x, then back-solving for y. The system has two solutions: (-5, -3) and (1, 3).

To solve the linear-quadratic system of equations:

First, let's use substitution. The second equation can be rearranged to y = x + 2. Substituting this into the first equation gives us:

x + 2 = x2 + 5x - 3

Let's move all terms to one side to make it a quadratic equation:

x2 + 5x - x - 3 - 2 = 0

x2 + 4x - 5 = 0

This is a quadratic equation that can be factored into:

(x + 5)(x - 1) = 0

Setting each factor equal to zero gives us the solutions for x:

Now we'll substitute these x-values back into y = x + 2 to find the corresponding y-values:

Therefore, the system has two solutions: (-5, -3) and (1, 3).

If we needed to use the quadratic formula, it would be in the context of an equation that is not easily factorable.

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Answer:

  > 6 cm

Step-by-step explanation:

Let b represent the length of the base in cm. Then the perimeter is ...

  b + (b -2) + (b +3) > 19

  3b +1 > 19 . . . . . . collect terms

  3b > 18 . . . . . . . . subtract 1

  b > 6  . . . . . . . . . divide by 3

The length of the base is greater than 6 cm.

The length of the base of the triangle is greater than 6 cm.

To find the length of the base of the triangle, let's assume that the base is x cm. According to the question, one side is 2 cm shorter than the base, so its length would be (x - 2) cm. The other side is 3 cm longer than the base, so its length would be (x + 3) cm. The perimeter of a triangle is the sum of all its sides, so we can set up an equation: x + (x - 2) + (x + 3) > 19. Solving this inequality will give us the value of x, which is the length of the base.

Therefore, the length of the base of the triangle is greater than 6 cm.

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Answer:

Triangles A B C and X Y Z are shown. The length of side A B is 6 and the length of side B C is 5. The length of side X Y is 1.5, the length of side Y Z is 1.25, and the length of X Z is 1. Angles A B C and X Y Z are congruent. Angles B C A and Y Z X are congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C. Line m is shown below both triangles.

Which sequence of transformations could map △ABC to △XYZ?

wrong answer a reflection across line m and a dilation  

wrong answer a dilation by One-fourth and a reflection across line m

wrong answer a rotation about C and a dilation

Right answer a dilation by One-fourth and a translation

Step-by-step explanation:

Answer:

a dilation by One-fourth and a translation

Step-by-step explanation:

Total sales are 200 tickets

Step-by-step explanation:

the formula for percentage will be used for this situation

Given

Sold tickets on first day = 44

Percentage = 22%

Let x be the total sales

Then

[tex]Tckets\ sold\ on\ first\ day = 22\%\ of\ x\\44=0.22*x\\x=\frac{44}{0.22}\\x=200[/tex]

Total sales are 200 tickets

Keywords: Percentage

Learn more about percentage at:

#LearnwithBrainly

Answer:

200 (tickets)

Answer:

 2115751

Step-by-step explanation:

Count the number length of string of lowercase letter. one String has 26 letter.

26 letters in the lowercase.

Same as in the next string.So number of length of 5 string is = 26^5

Lets count the length of string that does not have x then string of lowercase is containing 25 letters.

25 letters and same is in the next string. So length of 5 string is = 25^5

Hence

The string of 5 lowercase letters are with at least one x = 26^5 -25^5

                                                                                             =   2115751

To find the number of strings of 5 lower case English letters that have the letter x in them, we can subtract the number of strings that don't have an x from the total number of strings. The total number of strings of length 5 is 26^5, and the number of strings that don't have an x is 25^5. Therefore, the number of strings that have the letter x is 26^5 - 25^5 = 45,651.

To find the number of strings of 5 lower case English letters that have the letter x in them somewhere, we can first count the number of strings that don't have an x in them and subtract it from the total number of strings of length 5.

The total number of strings of length 5 is 26^5 since each letter can be any of the 26 lower case English letters.

Now, to count the number of strings that don't have an x in them, we can consider each position in the string. For the first position, we have 25 options (all the letters except x). Similarly, for the second position, we also have 25 options, and so on. Therefore, the total number of strings that don't have an x in them is 25^5.

Finally, we can find the number of strings that have the letter x in them by subtracting the number of strings that don't have an x from the total number of strings: 26^5 - 25^5 = 45,651.

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Answer:yes

Step-by-step explanation:

Please show me the question and I am gonna answer It

Answer:

2.47 m/s

Step-by-step explanation:

A girl flies a kite at a height 34 m above her hand.

It is vertical height of kite, 34 m

The horizontal rate of kite, [tex]\dfrac{dx}{dt}=3/ m/s[/tex]

Let the length of string released be s m

In right triangle using pythagoreous theorem

[tex]s^2=34^2+x^2[/tex]

For s = 60 m ,

[tex]60^2=34^2+x^2[/tex]

[tex]x=49.44[/tex] m

Differentiate the equation  [tex]s^2=34^2+x^2[/tex]  w.r.t  t

[tex]2s\dfrac{ds}{dt}=0+2x\dfrac{dx}{dt}[/tex]

[tex]2\cdot 60\cdot \dfrac{ds}{dt}=2\cdot 49.44\cdot 3[/tex]

[tex]\dfrac{ds}{dt}=\dfrac{296.62}{120}[/tex]

[tex]\dfrac{ds}{dt}=2.47[/tex] m/s

Hence, the rate of string letting out 2.47 m/s

Answer:

Step-by-step explanation:

In order to buy the new car, Nancy

paid $1,500 up front and took out a loan for the rest of the amount.

Let x = The amount of loan that she took.

The interest rate on the loan is 5%.

This means that she paid interest of 5/100 × x = 0.05 × x

= 0.05x

If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02,

It means that

1,500 + x + 0.05x is greater than 16,213.02

1500 + 1.05x = 16213.02

1.05x = 16,213.02 - 1500

1.05x = 114713.02

x = 114713.02/1.05

x = $109250 .49524

The amount that Nancy borrowed is greater than $109250 .49524

Answer:

amount borrowed + interest = x+5% of x

                                               = x + 5/100x

                                               = x + 0.05x

                                               = 1.05x

The expression 1.05x represents the sum of the amount Nancy borrowed and the interest she owes on that amount.

Step-by-step explanation:

Answer:

The value of x is [tex]\frac{10}{3}[/tex] hours.

Step-by-step explanation:

Machine A = 5 hours

Machine B = x hours

Machine A and B = 2 hours

Using the formula: [tex]\frac{T}{A}  + \frac{T}{B} = 1[/tex]

where:

T is the time spend by both machine

A is the time spend by machine A

B is the time spend by machine B

[tex]\frac{2}{5}  + \frac{2}{x}  = 1[/tex]

Let multiply the entire problem by the common denominator (5B)

[tex]5x(\frac{2}{5}  + \frac{2}{x} = 1)[/tex]

2x + 10 = 5x

Collect the like terms

10 = 5x - 2x

10 = 3x

3x = 10

Divide both side by the coefficient of x (3)

[tex]\frac{3x}{3}  = \frac{10}{3}[/tex]

[tex]x = \frac{10}{3}[/tex] hours.

Therefore, Machine B will fill the same lot in [tex]\frac{10}{3}[/tex] hours.

Answer:

  23°

Step-by-step explanation:

Let the interior angles of ΔABC be referenced by A, B, and C. The definition of point D means that ΔDAB is an isosceles triangle, so we have the relations ...

  A + B + 118 = 180 . . . . interior angles of ΔABC

  A = B +16 . . . . . . . . . . base angles of ΔDAB

Using the expression for A in the second equation to substitute into the first equation, we get ...

  (B+16) +B +118 = 180

  2B + 134 = 180 . . . . . collect terms

  2B = 46 . . . . . . . . . . . subtract 134

  B = 23 . . . . . . . . . . . . divide by 2

m∠ABC = 23°

Answer:

12

Step-by-step explanation:

5x-3/3x+2 = 60/40

=> x = 12

Hope it's helpful ;)

Final answer:

The average speed of the flock of birds over 5 hours is 9 miles per hour, calculated by dividing the distance function f(x) by the time function g(x) at x equal to 5.

Explanation:

The student asked to solve f divided by g of 5 for the given functions f(x) = 2x + 26 and g(x) = x − 1. This will give us the average speed of the flock of birds over the time interval when x equals 5.

First, we substitute x with 5 in both functions:

f(5) = 2(5) + 26 = 10 + 26 = 36 miles

g(5) = 5 − 1 = 4 hours

Next, we divide the outcome of function f by the outcome of function g:

\(\frac{f(5)}{g(5)} = \frac{36}{4} = 9 \) miles per hour

This result represents the average speed of the flock of birds over the time interval when x equals 5 hours.

Answer:

Step-by-step explanation:

The price of the 8 ounce box is $2.48, we will determine the price per ounce for the 8 ounce box

If 8 ounce = $2.48

1 ounce will be 2.48/8 = $0.31

The price of the 14 ounce box is $3.36

we will also determine the price per ounce for the 14 ounce box

If 14 ounce = $3.36

1 ounce will be 3.36/14 = $0.24

To determine how much greater is the cost per ounce of cereal in the 8 ounce box than in the 14 ounce box, we will subtract the unit cost of the 14 ounce box from the 8 ounce box. It becomes

$0.31 - $0.24= $0.07

Answer: Norm Alpina did better with z-score 0.79

Step-by-step explanation:

Z score formula = (raw score - mean) / standard deviation

For Jack Hartig,

score = 4; mean = 2.9; standard deviation = 2.1

Hence, Z score = (4 - 2.9) /2.1

= 1.1/2.1

= 0.52

For Norm Alpina,

score = 8; mean = 6.5; standard deviation = 1.9

Hence, Z score = (8 - 6.5) /1.9

= 1.5/1.9

= 0.79

Relatively, Norm Alpina did better for having Z score 0.79

By calculating z-scores for both students, which represent the number of standard deviations their scores are from the mean, Norm Alpina has a higher z-score and hence performed relatively better compared to Jack Hartig on their respective quizzes.

In order to determine which student did relatively better on their quizzes, we need to calculate the z-scores for each student. A z-score indicates how many standard deviations an observation is above or below the mean. The formula for a z-score is Z = (X - μ) / σ, where X is the score, μ(mu) is the mean, and σ(sigma) is the standard deviation.

For Jack Hartig:

Z = (4 - 2.9) / 2.1
 = 1.1 / 2.1
 = 0.524

For Norm Alpina:

Z = (8 - 6.5) / 1.9
 = 1.5 / 1.9
 = 0.789

Norm Alpina's z-score is higher, indicating that, relatively speaking, he performed better than Jack Hartig on the quiz based on how their scores relate to their respective class means and standard deviations.

Question #1:

To find the percentage of boy's in the class, divide.

9 / 36 = 0.25

0.25 * 100% = 25% (boys in the class)

We can write this proportion as 9/36 since this is the same as 25%.

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Question #2:

We know that the ear buds in both options cost $125.

The earbuds online are on a 20% discount.

The earbuds in store are on a 90$ sale

Lets find the discount for the online pair.

20% = 0.2

125 * 0.2 = 25

125 - 25 = $100 (price after discount)

After solving we can see that the earbuds in store are a better price. So, you will purchase the ear buds in store.

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Best Regards,

Wolfyy :)