The legs of a right triangle are x and 15 while the hypotenuse is 17.

Which equation can be used to determine the value of x using the Pythagorean Theorem?

Answer: Paul is 18 years old and Gary is 12 years old.

Step-by-step explanation:

Let x represent the age of Paul.

Paul is six years older than Gary. This means that Gary's age would be

x - 6

The sum of their ages is 30. This means that

x + x - 6 = 30

2x - 6 = 30

Adding 6 to the left hand side and the right hand side of the equation, it becomes

2x - 6 + 6 = 30 + 6

2x = 36

Dividing the left hand side and the right hand side of the equation by 2, it becomes

2x/2 = 36/2

x = 18

Therefore, Paul is 18 years old.

Gary is 18 - 6 = 12 years old.

Answer: m= $25/10 r

Step-by-step explanation:

Let m= money

r= raffle ticket

Then according to the statement

m= $25 for 10 tickets

so 10 tickets= $25

Or the equation goes,

m= $25/10 r

Answer:

20%.

Step-by-step explanation:

I = PRT

300 = 3000*R * 0.5

300 =  1500R

R = 300 / 1500

R =  3/15 = 1/5

As a percentage it is  100 * 1/5

= 20%.

Answer: 20%

Step-by-step explanation: Notice that in this problem we're asked to find the interest rate not the interest so our answer will be a percent rate of interest.

Let's start this problem by writing the interest formula shown below.

Interest = principal · rate · time

Now we fill in the formula.

The interest earned is $300 so we substitute 300 into the formula.

The principal is the amount invested or $3,000.

We don't know the rate so we can use the variable r.

The time is 0.5 which is equivalent to 1/2

so we can substitute 1/2 in for t.

So we have the equation 300 = (3,000)(r)(1/2).

Simplifying on the right side of the equation, 3,000 · 1/2 is 1,500.

So we have 300 = 1,500r

Now to solve for r since r is being multiplied by 1,500, we need to divide by 1,500 on both side of the equation.

On the right side of the equation, the 1,500's cancel and we have r and on the left side of the equation we have 300 divided by 1,500 or 0.2.

This means that 0.2 = r.

Remember however that the interest rate is a percent so we need to change our decimal to a percent by moving the decimal point 2 places to the right to get 20%. So the interest rate is 20%.

Answer: The system of equations required is

x + y = 20

40x + 70y = 1220

Step-by-step explanation:

Let x represent the number of small boxes of paper shipped and

Let y represent the number of large boxes of paper shipped.

A total of 20 boxes of paper were shipped. This is expressed as

x + y = 20

Each small box of paper weighs 40 pounds and each large box of paper weighs 70 pounds. The total weight of the large and small boxes of paper that were shipped is 1220 pounds altogether. This is expressed as

40x + 70y = 1220

We define x as the number of small boxes and y as the number of large boxes. The first equation, x + y = 20, is based on the total number of boxes. The second equation, 40x + 70y = 1220, is based on the total weight of the boxes.

We need to find a system of equations that represents the given situation. We will use two variables. Let's say x represents the number of small boxes and y represents the number of large boxes for your problem.

The first equation can be based on the total number of boxes, which is 20. So, the equation is: x + y = 20.

The second equation will be based on the total weight of the boxes, which is 1220 pounds. A small box weighs 40 pounds and a large box weighs 70 pounds. So, the equation will be: 40x + 70y = 1220.

So, we have the system of equations:

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Final answer:

Rosa saves 30% of her weekly earnings for college, which is calculated by dividing the amount saved ($36) by her total weekly earnings ($120) and then multiplying by 100%.

Explanation:

To determine the percentage of her earnings that Rosa saves, we will use the formula for calculating percentage: Percentage saved = (Amount saved ÷ Total earnings) × 100%.

First, we identify the total earnings and the amount saved: Rosa's total weekly earnings are $120, and she saves $36 each week.

Next, we calculate the percentage: Percentage saved = ($36 ÷ $120) × 100% = 0.3 × 100% = 30%.

Therefore, Rosa saves 30% of her weekly earnings for college.

Answer: d

Step-by-step explanation: Both country A and B has equal number of workers,physical capital, human capital and access to natural resources.

Non is higher than the other.

Yo sup??

y=-3/x+4

cross multiply

x+4=-3/y

x=-3/y-4

f(y)=-3/y-4

or

f(x)=-3/x-4

=-4x-3/x

The correct answer is option 4

Hope this helps.

Proof

Provide the missing reasons for the proof of part of the triangle midsegment theorem.

Given: K is the midpoint of MJ.

           L is the midpoint of NJ.

Prove: MN = 2KL

The complete answer is attached in the diagram below.

The complete answer for the missing reasons is attached below in the diagram.

Please check the figure.

Keywords: statement, proof, reason

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Answer:

A=4000, B=80, C=24

Step-by-step explanation:

You forgot to put the correct area model, I attached it to the answer.

We have the fact that Mountain Q is 4 times the height of Mountain P. That's the "4" we have in the left side of our model. It's like having a multiplication table, next to the "4" we have "A" and upper this we have "1000", the only thing we have to do is multiplify 4*1000=4000. The next letter we have is B and below it we have "320", we divided it by 4, 320/4=80. The last letter we have is C, and is below a "6", we only have to multiplify it by 4, 6*4=24.

At the end we only sum our

The missing values in the model for the area are:

A = 4,000

B = 80

C = 24

A model is a mathematical system that represents a real life concept in an easy to understand manner.

Given the model in this question, we can find the missing values as shown below:

A = 4 × 1000 = 4,000

B = 320/4 = 80

C = 4 × 6 = 24

Therefore, the missing values in the model for the area are:

A = 4,000

B = 80

C = 24

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For Janay's art project, the blue wire must be longer than 4 inches and shorter than 10 inches to create a triangle. This is based on the Triangle Inequality Theorem, which states that the length of any side of a triangle should be less than the sum of the lengths of the other two sides, but more than the difference of the two sides' lengths.

To determine how long the blue wire should be for Janay's art project, we need to understand a rule in geometry related to triangles, specifically the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.

Here, we have side lengths of 3 inches (purple wire) and 7 inches (pink wire), so the blue wire can be any length that is less than 3+7=10 inches, and more than |7-3|=4 inches. So the blue wire should be more than 4 inches and less than 10 inches to form a triangle.

This ensures that Janay will be able to form a valid triangle for her art project. If the length of the blue wire is less than 4 inches or greater than 10 inches, a triangle cannot be formed.

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Answer:

Option C) 88                                          

Step-by-step explanation:

We are given the following in the question:

Unit cost of sweatpants = $7

Unit cost of jackets = $14

Let x be the number of sweatpants sold and y be the number of jackets sold.

Customers bought 8 times as many sweatpants as jackets

Then, we can write,

[tex]x = 8y[/tex]

Total sales = $6,160

[tex]7x + 14y = 6160[/tex]

Substituting the values, we get,

[tex]7(8y) + 14y = 6160\\70y = 6160\\y = 88\\x = 704[/tex]

Thus, 88 jackets were sold.

Option C) 88

Answer:

Probability so see one falling star over half an hour is 0.25

Step-by-step explanation:

An hour can be taken as two half hours so we can write the probability to see a falling star as

(1-P)*(1-P) = 1 - 0.44

( 1 - P )² = 0.56

1 - P = [tex]\sqrt{0.56}[/tex]

P = 1 - [tex]\sqrt{0.56}[/tex]

P = 0.25

Answer:

Step-by-step explanation:

The formula for determining the total surface area of a cylinder is expressed as

Total surface area = 2πr² + 2πrh

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

Assuming that the cylindrical cup is open at the top, the formula becomes

Area = πr² + 2πrh

From the information given,

Radius = 1.8 inches

Height = 4 inches

Therefore, the surface area of the coffee cup is

(3.14 × 1.8²) + (2 × 3.14 × 1.8 × 4)

= 10.1736 + 45.216

= 55.4 inches² to the nearest tenth.

Answer:

55.4 :))

Step-by-step explanation:

Debra's cows produced [tex] 2 \frac{7}{24}[/tex] more gallons than Hank's cows.

Hank's cows :

Debra's Cows :

The difference in amount of Milk produced :

Sum of Debra's cow - Sum of Hank's cows

Now we have:

11⅙ - 8⅞

67/6 - 71/8 = (536 - 426) / 48

67/6 - 71/8 = 110/48

110/48 = [tex] 2 \frac{7}{24}[/tex]

Hence, Debra's cows produced [tex] 2 \frac{7}{24}[/tex] more gallons than Hank's cows.

Answer: speed at the equator =

1047.33 miles per hour

Step-by-step explanation:

The radius of earth is 4000miles

The earth rotates on its axis, hence we calculate the circumference at the equator

Circumference, C = 2 π R

C = 2 x 3.142 x 4000miles

C = 25,136 miles

Since the total time of one complete rotation about it's axis is 24hours

Hence, the speed at the equator is

speed = 25,136/24 = 1047.33 miles per hour

The speed of the person on the equator due to daily rotation of the earth is;

Speed = 1047.221 miles per hour

Formula for circumference is;

C = 2πR

Thus;

C = 2 × π × 4000miles

C = 25,132.74 miles

C ≈ 25133 miles

We know that formula for speed is;

speed = distance/time

Thus;

Speed on the equator is;

speed = 25133/24 = 1047.221 mph

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Answer:

The correct answer is C. 30 = 9x + 7

Correct statement and question:

Elena is cutting a 30-foot piece of ribbon for a craft project. She cuts off 7 feet, and then cuts the remaining piece into 9 equal lengths of x feet each.

Answer choices:

A. 7x + 9 = 30

B. 30x + 7 = 9

C. 30 = 9x + 7

D. 9x - 7 = 30

Source:

https://quizizz.com/admin/quiz/5c94aa300d3459001a4ef259/unit-6-lesson-4-equations-and-word-problems

Step-by-step explanation:

1. Information given to us to answer the problem correctly:

Length of the piece of ribbon for a craft project = 30 feet

First cut = 7 feet

Remaining piece cut into 9 equal lengths of x feet each

2. Let's find the right equation to solve for x:

9x + 7 = 30

The nine equal pieces of x feet each plus the piece of 7 feet add up to 30 feet

The correct answer is C. 30 = 9x + 7

The area would be 8 2/3* 5 3/4 which according to my calculator is 49 5/6

So the area is 49 5/6 ft^2.

Hope this helped!

Answer:

Step-by-step explanation:

A yard of lace costs w cents a yard and fabric costs $.40 more than the lace. This means that the cost of a yard of fabric would be

w + 0.5

Kimberly wants to buy one yard of lace and 2 yards of fabric. This means that the total amount of money that she would have to pay for the lace is is

0.4 × 1 = 0.40

Amount that she would spend on the fabric is 2(w + 0.5) = 2w + 1

Total cost would be

0.4 + 2w + 1

Final answer:

Kimberly will need a total of 3w + 80 cents to purchase one yard of lace and two yards of fabric, where w is the cost of one yard of lace in cents.

Explanation:

To calculate how much money Kimberly will need to buy one yard of lace and two yards of fabric, first we identify the cost of one yard of lace as w cents. The fabric costs $0.40 more than the lace per yard, so the cost of one yard of fabric is w cents + 40 cents. Kimberly wants to buy two yards of fabric, so we multiply the cost of one yard of fabric by 2, which gives us 2(w + 40) cents.

Adding together the cost of the lace and the two yards of fabric, we get: w + 2(w + 40). Simplifying this expression, we have: w (cost of one yard of lace) + 2w (twice the cost of lace per yard for two yards of fabric) + 80 (twice the additional cost of fabric per yard)

w + 2w + 80 cents

3w + 80 cents

Therefore, Kimberly will need a total of 3w + 80 cents to purchase one yard of lace and two yards of fabric.

Answer:

  78

Step-by-step explanation:

You want to know the sum of two 2-digit numbers such that one differs from the other by a multiple of 10, and the difference of their squares is 2340.

The difference of squares is the product of the sum and difference of the two numbers. Here, the difference must be a multiple of 10, so we want factorizations of 2340 that have a multiple of 10 as a factor. These are ...

  2340 = 10(234) = 20(117) = 30(78)

where the first factor (the difference) is less than the second factor (the sum).

The sum of two 2-digit numbers cannot be more than 200, and it must be even if they both have the same units digit. The only viable product from the above list is 30 × 78, where 30 is the difference of the numbers and 78 is their sum.

The sum of the numbers is 78.

__

Additional comment

The two numbers are 54 and 24. The difference of their squares is ...

  2916 -576 = 2340

Difference of squares: a² -b² = (a -b)(a +b).

Answer: 8 cups of white paint is used.

Step-by-step explanation:

In a lilac paint mixture 40% of the mixture is white paint 20% is blue and the rest is red. This means that the percentage of red paint in the mixture is 100 - (40 + 20) = 40%

There are four cups of blue paint used in a batch of lilac paint. This means that 20% of the total number of cups of paint used in a batch of lilac paint is 4.

Assuming that the total number of cups of paint in the mixture is x, then,

20/100 × x = 4

0.2x = 4

x = 4/0.2 = 20

Therefore, the number of cups of white paint used is

40/100 × 20 = 0.4 × 20

= 8 cups

Final answer:

In the lilac paint mixture, for every 4 cups of blue paint, which accounts for 20% of the mixture, there are 8 cups of white paint, corresponding to 40% of the mixture.

Explanation:

The question involves determining the amount of white paint used in a batch of lilac paint given that 40% of the paint mixture is white, 20% is blue, and the remainder is red. We're told that 4 cups of blue paint are used. Since blue paint represents 20% of the mixture, we can use this information to find out the total amount of the paint mixture and then calculate the amount of white paint needed.

First, find the total amount of the paint mixture by calculating the full 100% that the 4 cups of blue paint (20%) contribute to. This calculation is as follows:

Now that we know the total paint mixture is 20 cups, we can determine the amount of white paint, which is 40% of the total mixture:

Therefore, 8 cups of white paint are used in the mixture.

Since a silicon (Φ = 7.77 × 10-19 J) surface is irradiated with UV radiation with a wavelength of 235 nm. Assume an electron was a mass of 9.11 x 10-31 kg, the kinetic energy of the emitted electrons is 6.9 × 10⁻²⁰ J

The kinetic energy of emitted electron in photoelectric effect is given by

K = hc/λ - Φ where

Since a silicon (Φ = 7.77 × 10-19 J) surface is irradiated with UV radiation with a wavelength of 235 nm. Assume an electron was a mass of 9.11 x 10-31 kg. To determine the kinetic energy of the emitted electrons, we proceed as follows

Since the kinetic energy of the emitted electrons is

K = hc/λ - Φ

Given that

So, substituting the values of the variables into the equation, we have that

K = hc/λ - Φ

K = (6.63 × 10⁻³⁴ Js × 3 × 10⁸ m/s)/235 × 10⁻⁹ m - 7.77 × 10⁻¹⁹ J

K = (19.89 × 10⁻²⁶ Jm)/235 × 10⁻⁹ m - 7.77 × 10⁻¹⁹ J

K = 0.0846 × 10⁻¹⁷ J - 7.77 × 10⁻¹⁹ J

K = 8.46 × 10⁻¹⁹ J - 7.77 × 10⁻¹⁹ J

K = 0.69 × 10⁻¹⁹ J

K = 6.9 × 10⁻²⁰ J

So, the kinetic energy is K = 6.9 × 10⁻²⁰ J

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Answer:

44.4%

Step-by-step explanation:

Additional amount they were adding to equipment cost is $900

Percentage of $900 that is $400 = $400/$900 × 100 = 44.4%

$400 is approximately 44.44% of the additional $900 being added to the equipment cost.

To calculate what percent $400 is out of the additional $900 being added to the equipment cost, we can use the following formula:

In this case, the part is $400, which is the predicted additional profit from advertising, and the whole is the total additional amount of $900 being added to the equipment cost.

Using the formula:

So, $400 is 44.44% (approximately) of the additional $900 that the brothers were planning to add to the equipment cost.

Answer:

Absolute magnitude

Step-by-step explanation: Astronomy deals with the study of stars and other heavenly bodies. Astronomers use apparent magnitude to define how bright a star appears and shines from the earth.

Answer: 3/8

Step-by-step explanation:

Firstly, let's look at the possible outcome when 3 coins are tossed.

If two coins are first tossed, the possible outcome will be,

{HH, HT, TH, TT}

if one more coin is tossed together with the two to make it 3coins, the possible outcome will be gotten by matching the H and T of the third coin with the set of sample space above to give us,

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

This gives a total sample space of 8.

Outcomes that has at least two consecutive heads in the sequence are {HHH, HHT, THH} which is the possible outcome i.e 3

Probability that the outcome has at least two consecutive heads in the sequence will be;

Possible outcome/total outcome

= 3/8

Part (1) : The solution is [tex]729[/tex]

Part (2): The solution is [tex]$\frac{1}{16 x^{8}}$[/tex]

Part (3): The solution is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]

Explanation:

Part (1): The expression is [tex]3^{2} \cdot3^{4}[/tex]

Applying the exponent rule, [tex]$a^{b} \cdot a^{c}=a^{b+c}$[/tex], we get,

[tex]$3^{2} \cdot 3^{4}=3^{2+4}$[/tex]

Adding the exponent, we get,

[tex]3^{2} \cdot3^{4}=3^6=729[/tex]

Thus, the simplified value of the expression is [tex]729[/tex]

Part (2): The expression is [tex]$\left(2 x^{2}\right)^{-4}$[/tex]

Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,

[tex]$\left(2 x^{2}\right)^{-4}=\frac{1}{\left(2 x^{2}\right)^{4}}$[/tex]

Simplifying the expression, we have,

[tex]\frac{1}{2^4x^8}[/tex]

Thus, we have,

[tex]$\frac{1}{16 x^{8}}$[/tex]

Thus, the value of the expression is [tex]$\frac{1}{16 x^{8}}$[/tex]

Part (3): The expression is [tex]$\frac{2 x^{4} y^{-4} z^{-3}}{3 x^{2} y^{-3} z^{4}}$[/tex]

Applying the exponent rule, [tex]$\frac{x^{a}}{x^{b}}=x^{a-b}$[/tex], we have,

[tex]\frac{2x^{4-2}y^{-4+3}z^{-3-4}}{3}[/tex]

Adding the powers, we get,

[tex]\frac{2x^{2}y^{-1}z^{-7}}{3}[/tex]

Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,

[tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]

Thus, the value of the expression is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]

Answer:

2.5 pounds pounds of sulfur and 1 pound of lead should be removed each day in order to minimize net cost.

Step-by-step explanation:

Given model of cost:

[tex]C(x, y) = 7,000 + 100x^2 + 50y^2[/tex]

Government clean-air subsidies amount for sulfur = 500 $/pound

Government clean-air subsidies amount for lead = 100 $/pound

Subsidies amount for x pounds of sulfur = x500 $

Subsidies amount for y pounds of lead= y100 $

Model of subsidy amount :

[tex]S(x,y)=500x+100y[/tex]

Net cost(N) = Cost - Subsidy = C(x,y)-S(x,y)

[tex]N=7,000 + 100x^2 + 50y^2-500x-100y[/tex]..[1]

Differentiating above [1] in with respect to dx :

[tex]\frac{dN}{dx}=\frac{7,000 + 100x^2 + 50y^2-500x-100y}{dx}[/tex]

[tex]\frac{dN}{dx}=200x-500[/tex]..[2]

Putting [tex]\frac{dN}{dx}=0[/tex]:

[tex]0=200x-500[/tex]

x = 2.5

Now taking second derivative of [2]:

[tex]\frac{d^N}{dx^2}=200[/tex]

[tex]\frac{d^N}{dx^2}>0[/tex] (minima)

Differentiating above [1] in with respect to dy :

[tex]\frac{dN}{dy}=\frac{7,000 + 100x^2 + 50y^2-500x-100y}{dy}[/tex]

[tex]\frac{dN}{dy}=100y-100[/tex]..[3]

Putting [tex]\frac{dN}{dy}=0[/tex]:

[tex]0=100y-100[/tex]

y = 1

Now taking second derivative of [3]:

[tex]\frac{d^N}{dy^2}=100[/tex]

[tex]\frac{d^N}{dy^2}>0[/tex] (minima)

2.5 pounds pounds of sulfur and 1 pound of lead should be removed each day in order to minimize net cost.

The amounts of sulfur and lead the firm should remove are 2.5 pounds and 1 pound respectively to minimize the net cost.

Given to us

cost of controlling emissions, C(x, y) = 7,000 + 100x² + 50y²

amount to $500 per pound of sulfur

$100 per pound of lead removed

We know that the net cost can be written as,

T(x, y) = 7,000 + 100x² + 50y² -500x -100y

where x and y is the amount of sulfur and lead emission reduced respectively.

To find the minimum of x differentiate the value of net cost with respect to x,

[tex]\dfrac{dT}{dx} = \dfrac{ 7,000 + 100x^2 + 50y^2 -500x -100y}{dx}[/tex]

    [tex]= \dfrac{ 7,000 + 100x^2 + 50y^2 -500x -100y}{dx}\\\\= 0+ 100(2x) + 0 + 500 + 0\\\\ = 200x+500[/tex]

Substitute against 0, to get the minimum value of x,

0 = 200x+500

x = 2.5

Differentiate again,

[tex]\dfrac{d^2T}{dx^2} = \dfrac{d(200x+500)}{dx}[/tex]

      [tex]=200+0[/tex]

As the value of differentiation is positive, therefore, the slope of the function will be going towards the positive.

To find the minimum of y differentiate the net cost with respect to y,

[tex]\dfrac{dT}{dy} = \dfrac{ 7,000 + 100x^2 + 50y^2 -500x -100y}{dy}[/tex]

     [tex]= 0+0+50(2y)-100\\\\=100y-100\\\\=100(y-1)[/tex]

Substitute against 0 to get the minimum value of y,

0 = 100(y-1)

y = 1

Differentiate again,

[tex]\dfrac{d^2T}{dy^2} = \dfrac{d(100y-100)}{dy}[/tex]

       [tex]=100[/tex]

As the value of differentiation is positive, therefore, the slope of the function will be going towards the positive.

Hence, the amount of sulfur and lead the firm should remove is 2.5 pounds and 1 pound respectively to minimize the net cost.

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Answer:

3

Step-by-step explanation:

the initial statement is  

y ∝ 1 /x

 to convert to an equation multiply by k the constant

of variation

y = k × 1 /x = k /x

to find k use the given condition

y = 5  when  x = 6

y = k/ x ⇒ k = y x = 5 × 6 = 30

y = 30 /x

when  

x = 10

then

y = 30 /10 = 3

Answer: y = 3

Step-by-step explanation:

In inverse variation, as one variable increases, the other variable decreases and as one variable decreases, the other increases.

We would introduce a constant of proportionality, k. Therefore,

y = k/x

When y = 5 , x = 6

Therefore,

5 = k/6

Cross multiplying by 6, it becomes

k = 6 × 5 = 30

The expression becomes

y = 30/x

Therefore, when x is 10,

y = 30/10

y = 3

Answer:

[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}= \frac{0.113}{0.343}= 0.329[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the age of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(37.5,6.2)[/tex]  

Where [tex]\mu=37.5[/tex] and [tex]\sigma=6.2[/tex]

We are interested on this probability:

[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}[/tex]

We can begin finding [tex] P(X>40)[/tex] using the z score formula given by:

[tex] z = \frac{a-\mu}{\sigma}[/tex]

Using this formula we have:

[tex] P(X>40)= P(Z>\frac{40-37.5}{6.2}) = P(Z>0.403)[/tex]

And using the complement rule and the normal standard table or excel we have this:

[tex]P(Z>0.403)=1-P(Z<0.403)= 1-0.657= 0.343[/tex]

Now we can find [tex] P(X>45)[/tex] using the z score formula given by:

[tex] z = \frac{a-\mu}{\sigma}[/tex]

Using this formula we have:

[tex] P(X>45)= P(Z>\frac{45-37.5}{6.2}) = P(Z>1.210)[/tex]

And using the complement rule and the normal standard table or excel we have this:

[tex]P(Z>1.210)=1-P(Z<1.210)= 1-0.887= 0.113[/tex]

And replacing into our original probability we got:

[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}= \frac{0.113}{0.343}= 0.329[/tex]

Answer:

The answer to your question is the probability to select a yogurt of raspberry is 1/4 or 25%.

Step-by-step explanation:

Data

Number of cartons = 12

Number of cartons of raspberry = 3

To solve this problem, just use the formula of probability and simplify it to get the result.

Formula

P(A) = [tex]\frac{Number of favorable outcomes to A}{Total number of outcomes}[/tex]

Substitution

P(A) = 3/12

Simplification

P(A) = 1/4 or 25%

Final answer:

By setting up an equation with x representing the number of correct answers, we find that Peter answered 11 questions correctly on his quiz.

Explanation:

To determine how many questions Peter answered correctly on his quiz, we first need to set up an equation to represent the situation. Let's let x be the number of questions Peter got right, and since he answered 15 questions in total, it means he got (15 - x) questions wrong. Since he gets 3 points for each correct answer and loses 1 point for each wrong answer, we can write the equation as:

3x - (15 - x) = 29

Now, we will solve for x:

3x - 15 + x = 29

4x - 15 = 29

4x = 29 + 15

4x = 44

x = 44 / 4

x = 11

So, Peter answered 11 questions correctly.