In a school, 3/4 of the students study a language. Of those who study a language, 3/5 study French. Find the ratio of students who study French to students who do not study French. Give your answer in its simplest form.

Answer:

x = 12

Step-by-step explanation:

The figure in the question was split into the triangles in the attachment to the solution.

Now applying the principle of similar triangles, we have:

[tex]\frac{16}{x} = \frac{x}{9}[/tex]

cross-multiplying, we have:

[tex]x^{2} = 16*9 = 144[/tex]

solving for x,

x = 12

The two numbers are 8,13.

Step-by-step explanation:

Let,

smaller number = x

Larger number = x+5

According to given statement;

Smaller number + Bigger number = 3x-3

[tex]x+(x+5)=3x-3\\x+x+5=3x-3\\2x+5+3=3x\\8 = 3x-2x\\8=x\\x=8[/tex]

Smaller number = 8

Larger number = 8+5 = 13

The two numbers are 8,13.

Keywords: algebraic equation, addition

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Answer:

The two numbers are 8,13.

Answer:

Step-by-step explanation:

A continuous function is one that has a set of unique solutions. a function is also said to be continuous if at every interval, there exist no sudden change in the assumed values otherwise the function will be discontinuous.

for example, the sine and cosine function are continuous over a set of real integers.

from the question, any assumed expression of x and integrating over the interval x and infinity will render the function continuous.

Assumed f(x) = cuberoot of x

Integrating and evaluating will prove that the function is continuous, as such a defined function is always a continuous function and not necessarily lipschitz.

Answer:

Step-by-step explanation:

area=4×22/7×14²=4×22×28=2464 units²

The surface area of a sphere with a radius of 14 is 2464 square units. When considering significant figures, this is rounded to 2500 square units to match the two significant digits of the given radius.

To find the surface area of a sphere with a radius of 14, using the given value of 22/7 for , the formula A = 4*pi*r2 is used. Plugging in the numbers:

A = 4 * (22/7) * (14)²

A = 4 * (22/7) * 196

A = 4 * 22 * 28

A = 88 * 28

A = 2464

Thus, the surface area of the sphere is 2464 square units.

Answer:

The answer to your question is 4x - 5

Step-by-step explanation:

                [tex](8x -10)\frac{1}{2}[/tex]

Distributive property, this property allows us to multiply two terms separately. That means that in this problem [tex]\frac{1}{2}[/tex]  will multiply the first term, and after that the second term. One half multiply 8x and also - 10.

                 [tex]\frac{8x}{2} - \frac{10}{2}[/tex]

Simplify and result

                [tex]4x - 5[/tex]

Using the distributive property on [tex](8x - 10) \times \frac{1}{2}[/tex], we get  [tex]4x-5[/tex]

Given: [tex](8x - 10) \times \frac{1}{2}[/tex]

To find: simplify using distributive property

Distributive property can be depicted by [tex]x(a+b) = xa + xb[/tex]

We can use this property and solve as follows:

[tex](8x - 10) \times \frac{1}{2} = [\frac{1}{2} \times 8x] - [10 \times \frac{1}{2}] = 4x -5[/tex]

We get the expression without parentheses [tex]4x-5[/tex]

Answer:

 42 mph

Step-by-step explanation:

If you start with the assumption that the answer is an integer, you can solve a problem like this by looking at the factors of 294.

  294 = 2·3·7² = 6·49 = 7·42

At 42 mph, the 294-mile trip took ...

   time = distance/speed = 294 mi/(42 mi/h) = 7 h

At a speed 7 mph faster, the 294-mile trip took ...

   (294 mi)/(49 mi/h) = 6 h . . . . . 1 hour less

The average speed of Imogene's car for the 294-mile trip was 42 miles per hour.

_____

Alternative solution

If you let s represent Imogene's speed, you can use the above time and distance relationship to write an equation relating the trip times:

  294/s = 294/(s+7) +1

Multiplying by s(s+7), we get ...

  294(s+7) = 294s +s(s+7)

  2058 = s^2 +7s . . . . . . . . . . . subtract 294s

We can complete the square by adding (7/2)^2 = 12.25 to both sides

  2070.25 = s^2 +7s +12.25 = (s +3.5)^2

  ±45.5 = s +3.5 . . . . . take the square root; next subtract 3.5

  -3.5 +45.5 = s = 42 . . . . use the positive solution

Imogene's average speed was 42 mph.

Imogene's average speed was 294 mph. We solve this by using the relationship between distance, speed, and time, and applying it to the specific constraints of the problem. By setting s = speed, we use two equations representing each scenario and solve for s.

Let's assign 's' to Imogene's average speed for the trip. The time taken at this speed is the distance traveled (294 mi) divided by 's' (speed = distance/time), making the time = 294/s. If the car was faster by 7 mph, the speed would be s+7 mph, and the time taken would then be 294/(s+7). The problem states that the second scenario would take 1 hour less, so 294/s = 294/(s+7) + 1.

Cross-multiplication and simplification of this equation result in (294s + 2058) = 294(s +7) or 294s + 2058 = 294s + 2058, which simplifies to 2058 = 7s, or s = 294 mph. Therefore, Imogene's average speed was 294 mph.

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Answer:

(x + 1)² + (y − 3)² = 41

Step-by-step explanation:

The center of the circle is the midpoint of the diameter.

(h, k) = ((x₂ + x₁)/2, (y₂ + y₁)/2)

(h, k) = ((3 + -5)/2, (-2 + 8)/2)

(h, k) = (-1, 3)

The radius is half the length of the diameter.

r = ½ √((x₂ − x₁)² + (y₂ − y₁)²)

r = ½ √((3 − -5)² + (-2 − 8)²)

r = ½ √(8² + 10²)

r = √41

Therefore, the equation of the circle is:

(x − h)² + (y − k)² = r²

(x + 1)² + (y − 3)² = 41

The standard form of equation of the circle is (x + 1) + (y - 3) = (6.40)².

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}

Given is that the endpoints of a diameter of a circle are (3, -2) and (-5, 8).

The center: (3-5/2, -2+8/2) = (-1, 3)

The diameter d = √{(x₂-x₁)² + (y₂-y₁)²}

d = √{(-5-3)² + (8 + 2)²}

d = √{64 + 100}

d = √164

d = 12.81

The radius r = 6.40

The standard form of equation of the circle is,

(x + 1) + (y - 3) = (6.40)²

Therefore, the standard form of equation of the circle is,

(x + 1) + (y - 3) = (6.40)²

To learn more about the distance between two points;

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Answer: d. Infinitely many solutions

Step-by-step explanation:

The given equation is expressed as

10-3x +10x-7 = 5x-5+2x+8

The first step is to make all the terms containing the variable to be on the left hand side of the equation and the constants to be on the right hand side of the equation.

10-3x +10x-7=5x-5+2x+8

10 - 7 + 10x - 3x = 5x + 2x - 5 + 8

7x + 3 = 7x + 3

Subtracting 7x and 3 from the left hand side and the right hand side of the equation, it becomes.

7x - 7x + 3 - 3 = 7x - 7x + 3 - 3

0 = 0

It has infinitely many solutions because as any value of x would satisfy both sides of the equation.

Answer:

The 4th graph

Step-by-step explanation:

To determine which graph corresponds to the  [tex]f(x) = \sqrt{x}[/tex]  we will start with inserting some values for x and see what y values we will obtain and then compare it with graphs.

[tex]f(1) = \sqrt{1} = 1\\f(2) = \sqrt{2} \approx 1.41\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3[/tex]

So, we can see that the pairs (1, 1), (2, 1.41), (4, 2), (3, 9) correspond to the fourth graph.

Do not be confused with the third graph - you can see that on the third graph there are also negative y values, which cannot be the case with the [tex]f(x) =\sqrt{x}[/tex], the range of that function is  [tex][0, \infty>[/tex], so there are only positive y values for [tex]f(x) = \sqrt{x}[/tex]

Answer:

if your on edge its the last one

Step-by-step explanation:

use the graphing calculator and input the equation and it will be fourth graph

Sean reads 60 minutes on wednesday

Solution:

Given that,

Let "x" be the number of minutes read on monday

Let "y" be the number of minutes read on tuesday

Let "z" be the number of minutes read on wednesday

He reads 3 times as many minutes on Tuesday as he does on Monday

Number of minutes read on tuesday = 3 times the number of minutes read on monday

y = 3x --------- eqn 1

He reads 4 times as many minutes on Wednesday as he does on Monday

Number of minutes read on wednesday = 4 times the number of minutes read on monday

z = 4x ------- eqn 2

Sean reads 45 minutes on Tuesday

y = 45

Substitute y = 45 in eqn 1

45 = 3x

x = 15

Substitute x = 15 in eqn 2

z = 4(15)

z = 60

Thus he reads 60 minutes on wednesday

Final answer:

Sean reads for 60 minutes on Wednesday, calculated by knowing he reads four times as many minutes on Wednesday as on Monday, and he reads 45 minutes on Tuesday which is three times his Monday reading time.

Explanation:

Since Sean reads 3 times as many minutes on Tuesday as he does on Monday, and he reads 45 minutes on Tuesday, we can determine that he reads 45 minutes ÷ 3 = 15 minutes on Monday. Sean then reads 4 times as many minutes on Wednesday as he does on Monday. So, he must read 15 minutes × 4 = 60 minutes on Wednesday.

Answer:

The answer to your question is width = 8ab³

Step-by-step explanation:

Data

Area = 32a³b⁴ u²

length = 4a²b   u

Formula

Area of a rectangle = width x length

Solve for width

                           width = [tex]\frac{Area}{length}[/tex]

Substitution

                          width = [tex]\frac{32a^{3}b^{4}}{4a^{2}b}[/tex]

Simplify using rules of exponents, just remember that in a division we subtract the exponents and divide the coefficients normally.

                          width = 8 a²b³

Answer:

Step-by-step explanation: 32a^3 is -8 < a < - 8 axis interceptions 32a^3            vertical asymphotes None Extreme points of a32a^3 0,0

Answer: to suggest or accept that a theory or idea is true as a starting point for reasoning or discussion.

Step-by-step explanation:

Here's an example: Astronomers postulate that the comet will reappear in 4000 years.

Answer: The equation that would help members to find how much they would pay per month is

40 + 12x = 460

Step-by-step explanation:

Let x represent the amount of money that members would pay per month.

Let y represent the number of months for which a member uses the gym.

There is a fee of $40 when you join, and the rest is paid monthly. This means that the cost of using the gym for x months would be

40 + xy

A one year membership to metro gym costs $460. Therefore are 12 months in a year. Therefore,

40 + 12x = 460

12x = 460 - 40 = 420

x = 420/12 = 35

The equation that would help members to find how much they would pay per month is

The problem can be solved using combinatorics, specifically the permutation of a multiset. Using the formula P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is total number of operations and n1, n2,... are the number of each identical operation, the number of different possible sequences to complete the manufacturing operation are 35.

The number of sequences of the operations can be found by using the formula for permutations of multiset - a concept in combinatorics part of mathematics. Permutations of a multiset are the number of ways in which we can arrange all the elements of the multiset considering the repetition of elements. We have 7 operations in total: three identical notches (type A) and four identical bends (type B). The formula is:

P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is the total number of items(7 in this case), n1,n2,...,nk are the number of each type of item.

Therefore, the number of different possible sequences to complete the manufacturing is: P(7 ; 3, 4) = 7! / (3! * 4!). This evaluates to 35.

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Answer:

$ 213.50

Step-by-step explanation:

From the question;

Albert spent;

We are required to determine Albert's monthly allowance;

Then;

Deducting $35.5, we get,

$(x/2 - 35.5)

Then, 3/5 of the remainder is on a book

Thus, 1 - 3/5 = 2/5 of the remainder (represents the amount that remained after buying a book and a shirt.

Therefore;

2/5 (x/2 - 35.5) = 28.5

We get;

x/2 - 35.5 = 28.5 (5/2)

x/2 - 35.5 = 71.25

 x/2 = 71.25 + 35.5

  x/2  = $ 106.75

    x = $ 106.75 × 2

       = $ 213.50

Therefore, Albert's monthly allowance is $ 213.50

Answer:

B) 6 units

Step-by-step explanation:

The formula of the volume of the Pyramid is 1/3×area of the base×height

1/3×70×height=140

Dividing both sides by 70

1/3×height=2

Multiplying both sides by 3

Height = 6

Final answer:

The height of a right square pyramid with a rectangular base area of 70 square units and a volume of 140 cubic units is 6 units, by using the volume formula of the pyramid.

Explanation:

The question asks us to find the height of a right square pyramid with a given base area and volume. To find the height, we need to use the formula for the volume of a pyramid, which is given by the formula: Volume = (Base Area * Height) / 3. We are given the base area as 70 square units and the volume as 140 cubic units.

Using the formula to solve for the height we get:
Height = (Volume * 3) / Base Area = (140 * 3) / 70 = 6 units. Therefore, the height of the pyramid is 6 units.

Answer:he would arrive 0.2 miles faster.

Step-by-step explanation:

Distance = speed × time

Time = distance/speed

William cycles at a sped of 15 miles per hour. He cycles 12 miles from home to school. This means that the time it takes William to get to school from home would be

12/15 = 0.8 hours

If he increases his cycling speed by 5 miles per hour, his new speed becomes

15 + 5 = 20 miles per hour

Therefore, the new time it takes William to get to school from home would be

12/20 = 0.6 hours

The difference in both times is

0.8 - 0.6 = 0.2 hours

Therefore, he would arrive 0.2 miles faster.

Answer:

E.) 1

Step-by-step explanation:

Firstly we will solve for L.H.S.

L.H.S. =[tex]Csc^2\theta[/tex]

Since we know that [tex]Csc^2\theta[/tex] is the inverse of [tex]Sin^2\theta[/tex].

So we can say that;

[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex]

Now For R.H.S.

[tex]Cot^2\theta+1[/tex]

Since we  can rewrite [tex]cot^2\theta[/tex] as [tex]\frac{cos^2\theta}{sin^2\theta}[/tex].

Now we can say that the R.H.S. is;

[tex]\frac{cos^2\theta}{sin^2\theta}+1[/tex]

Now we add the fraction and get;

[tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}[/tex]

Now according to trigonometric identity;

[tex]cos^2\theta+sin^2\theta=1[/tex]

So, [tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}[/tex]

Here,

[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex]   and     [tex]Cot^2\theta+1[/tex] = [tex]\frac{1}{sin^2\theta}[/tex]  

L.H.S. = R.H.S.

Hence [tex]csc^2\theta=cot^2\theta+1[/tex]

Answer:

33 hearts sold, 48 roses sold

Step-by-step explanation:

x- number of roses sold

y- number of hearts sold

x=15+y <- " The number of bouquets sold was 15 more than the number of hearts sold"

5x+3y=339

5(15+y)+3y=339

75+5y+3y=339

8y=339-75

8y=264

y=33

x=15+33=48

The number of chocolate hearts sold was 33, and the number of bouquets sold was 48 for a total revenue of $339.

Let's assume the number of chocolate hearts sold was 'x'. Since the number of bouquets sold was 15 more than the number of hearts sold, the number of bouquets sold would be 'x + 15'.

The price of each rose bouquet is $5, so the total revenue from selling bouquets would be '5(x + 15)'.

Similarly, the price of each chocolate heart is $3, so the total revenue from selling hearts would be '3x'.

Since the total revenue collected was $339, we can set up an equation: '5(x + 15) + 3x = 339'.

Simplifying the equation, we get '8x + 75 = 339'.

Subtracting 75 from both sides of the equation, we get '8x = 264'.

Dividing both sides of the equation by 8, we get 'x = 33'.

Therefore, 33 chocolate hearts were sold, and the number of bouquets sold would be '33 + 15 = 48'.

Answer: Ballwin Bears

Step-by-step explanation:

Answer:

The Ballwin Bears are taller on average, and the Aviation Aces have players whose are more consistent.

Step-by-step explanation:

(This is the correct answer on Knewton-alta)

Answer:

Therefore, we use the  linear depreciation and we get is 17222.22 .

Step-by-step explanation:

From Exercise we have that  is boat  $250,000.

The straight line depreciation for a boat  would be calculated as follows:

Cost  boat is $250,000.  

For  $95,000 Deep Blue plans to sell it after 9 years.

We use the formula and we calculate :

(250000-95000)/9=155000/9=17222.22

Therefore, we use the  linear depreciation and we get is 17222.22 .

To calculate the annual depreciation expense for Deep Blue's boat using the straight-line method, subtract the salvage value from the purchase price and divide by the number of years of useful life, resulting in an annual depreciation expense of $17,222.22.

To determine the annual depreciation, subtract the salvage value from the purchase price and divide by the useful life of the asset in years:

Subtract the salvage value from the purchase price: $250,000 - $95,000 = $155,000.

Divide the result by the number of years of useful life: $155,000 / 9 years = $17,222.22.

Therefore, Deep Blue would record an annual depreciation expense of $17,222.22.

Answer:

Step-by-step explanation:

Answer: a=6 b=9 c=8

Step-by-step explanation:

The problem consists of finding the roots of the quadratic equations:

[tex]x^2+15x+54=0\\[/tex]

[tex]x^2-17x+72=0\\[/tex]

The roots can be found with the following equation for solving quadratic equations:

[tex]x_{12}=\frac{-B\pm\sqrt{B^2-4AC}}{2A}[/tex]  for equation: [tex]Ax^2+Bx+C=0[/tex]

After solving the equations you can write the result as:

[tex]x^2+15x+54=(x+6)(x+9)\\[/tex]

[tex]x^2-17x+72=(x-9)(x-8)[/tex]

Answer:

b = 9

a = 6

c= 8

Therefore, a,b,c = 6,9,8

Question:

The expression $x^2 - 15x - 54$ can be written as $(x-a)(x-b),$ and the expression $x^2 - 17x + 72$ written as $(x - b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a b c$?

Step-by-step explanation:

To determine the values of a,b and c.

We need factorize the two equations.

i) x^2 -15x +54

x^2 -6x -9x +54

x(x-6) -9(x-6)

=(x-6)(x-9)

ii) x^2 -17x +72

x^2 -9x -8x +72

x(x-9) -8(x-9)

=(x-9)(x-8)

From the question:

Comparing

(x-a)(x-b) to (x-6)(x-9)

And

(x-b)(x-c) to (x-9)(x-8)

We can see that b is common in the two cases and also 9 is common in the two factorised equations.

So,

b = 9

a = 6

c= 8

Therefore, a,b,c = 6,9,8

Answer:

Option A) inferential statistics        

Step-by-step explanation:

We describe inferential statistic as:

Inferential Statistic:

Thus, the correct answer is

Option A) inferential statistics.

Answer:

Step-by-step explanation:

Answer:

Population : all the steaks Tessa can cook

Parameter : minimum internal temperature of 160 degrees Fahrenheit

Sample : two random thermometer readings

Statistic : minimum sample reading of 165 degrees Fahrenheit

Step-by-step explanation:

Let's recall the definitions of these statistical concepts and match it with the information that were provided to us:

Answer:

800 months

Step-by-step explanation:

The formula for interest is:

(Capital * saving account * time) / 100

So:

(10000 * 0.06 * x) / (100) = 4800

We clear x:

(10000 * 0.06 * x) = (100) * 4800

x = 480,000 / (10000 * 0.06)

x = 800 months (66.67 years)

To determine the duration for which the deposited $10,000 at 6% interest grew to a total of $14,800 ($10,000 principal + $4,800 interest), the formula for compound interest can be re-arranged to solve for the time variable. You'll use the amount of money accumulated, the principal amount, the annual interest rate, and the assumption that the interest is compounded annually. Plug these values into the formula to calculate the number of years.

You deposited $10,000 into a savings account at 6% interest. To determine how long it took for you to earn $4,800 in interest, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:

In this case, we can rearrange the formula to solve for t, because you want to find out how many years it took for your investment to turn into A = $10,000 + $4,800 = $14,800. Assuming the interest is compounded annually (n = 1), the formula becomes:

t = ln(A/P) / n * ln(1 + r/n)

Plugging in the numbers gives us:

t = ln($14,800 / $10,000) / ln(1 + 0.06)

By calculating this, you can get the number of years you had the money in the savings account.

I'm not sure of whether or not you're aware of this, but you asked this question in the math section. Nevertheless, I remember in 5th grade I did a project on whether or not it is possible to use solar energy to heat up different colored bags filled with water, and to determine which one would heat up the quickest. If that one doesn't pique your interest, you can go to sciencebuddies.com and search through a variety of project ideas if you'd like. That's where I found mine.

Final answer:

A good science fair project for 5th graders could be the 'Race of the Cans' experiment. Students can collect cans with different types of food and predict which can will win a race down an inclined plane.

Explanation:

A good science fair project for 5th graders could be the 'Race of the Cans' experiment. In this experiment, students can collect several cans containing different types of food and predict which can will win the race down an inclined plane. They can then explain their prediction and see if it is correct. Another option is to collect empty cylindrical containers of the same size and fill them with different materials like wet or dry sand to see how it affects the race.

Answer:

the machine is mixing the nuts are not  in the ratio 5:2:2:1.

Step-by-step explanation:

Given that a machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1.

A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans.

Create hypotheses as

H0: Mixture is as per the ratio 5:2:2:1

Ha: Mixture is not as per the ratio

(Two tailed chi square test)

Expected values as per ratio are calculated as 5/10 of 500 and so on

Exp        250      100    100       50        500

Obs       269      112       74       45         500

O-E          19        -12      -26       -5           0

Chi          1.343   1.286  9.135   0.556   12.318

square

df = 3

p value = 0.00637

Since p value < alpha, we reject H0

i.e. ratio is not as per the given

We perform a chi-square goodness of fit test to analyze if the machine is mixing nuts according to the ratio. We set a null and alternate hypothesis, calculate expected frequencies for each group, calculate chi-square test statistic and compare it with the critical value. If the calculated chi-square is greater than the critical value, we reject the null hypothesis.

This question asks about hypothesis testing using chi-squared tests. In this particular case, we're testing the observed distribution of mixed nuts against the expected distribution given by the ratio 5:2:2:1.

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Answer:

Pan is closest to Paris when she gets to Florence when she is 35 miles away

Step-by-step explanation:

With Paris at (0,0), Rome is 40miles west which is on the negative x axis.

Florence is 35 miles closer (east to Paris) so we have -45 + 35 = -10

and 55 mikes north of Rome which is on the positive y-axis. So Florence is at point (-10,55)

The distance between the two points Florence and Paris is √(x2 - x1)^2 + (y2 - y1)^2

x1 = 0, y1 = 0

x2 = -10, y2 = 55

So we have

√(-10-0)^2 + (55-0)^2

= √(-10)^2 + (55)^2

= √ 100 + 3025

= √3125

= 55.9 mikes from Paris

Pam is closest to Paris when she gets to Florence when she is 35 miles away

Pam gets closest to Paris when she is 5 miles away, which occurs when she travels directly east from Rome before heading north to Florence.

Pam is taking a train from Rome to Florence, and we need to find out how close she gets to Paris along the way. Rome is 40 miles due west of Paris, and Florence is 35 miles east and 55 miles north of Rome. While traveling from Rome to Florence, Pam would initially get closer to Paris as she travels east, but as she moves north, the closest point to Paris would be directly east from Rome before moving north.

Answer:P(A/B)=0.08

Step-by-step explanation:

The probability formula to find p(A/B) is :

P(A/B) = p(A n B) / p(A)

Which means that B is contain in A and p(A n B) is p(B)

p(A n B)=p(B)=0.05

p(A)=0.625

Therefore

P(A/B) = p(A n B) / p(A)=p(B) / p(A)

P(A/B)=0.05 / 0.625

P(A/B)=0.08