What expression is equal to6 e + 3 (e-1)

Answer:

height of the candle after 6 hours= 18.6 centimeters

Step-by-step explanation:

the function gives a line with a slope of −0.4.

the height of the candle after 11 hours is 16.6 centimeters.

after 6 hours, the height will be

But slope= y2-y1/x2-x1

Y2 is the unknown

Y1 = 16.6

X1= 11 hours

X2= 6 hours

y2-y1/x2-x1= -0.4

(Y2-16.6)/(6-11)= -0.4

(Y2-16.6)/(-5)= -0.4

(Y2-16.6)= -5( -0.4)

(Y2-16.6)= 2

Y2 = 2+16.6

Y2 = 18.6 centimeters

height of the candle after 6 hours= 18.6 centimeters

Answer:

C.Scatter Plot of Residuals vs Yhat

Step-by-step explanation:

Answer:

4b + .60a

Step-by-step explanation:

b represents the number of bunches of bananas

a represents the number of apple

Multiply the cost by the number purchased of each item and add them together

4b + .60a

Answer:

[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]

Step-by-step explanation:

Bananas represented by b

1 banana costs $4 so b bananas will cost $ 4 b

Apples represented  by a

1 apples costs 0.60 $ so a apples will cost $ 0.60 a

Totally, they will cost:

=> $ (4 b + 0.60 a)

Find the circumference:

Circumference = 2 x PI x radius:

Circumference = 2 x 3.14 x 16 = 100.48 inches.

A full circle is 360 degrees, a 45 degree angle is 1/8 of a full circle.

Arc length = 100.48 / 8 = 12.56 inches.

Answer:

300%

Step-by-step explanation:

1 year = 12 months

percent = part/whole * 100%

percent = 12/4 * 100% = 300%

Answer:

please can u follow me I've started following you

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

Answer:

[tex]\boxed{108d}[/tex]

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³.  Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

[tex]\frac{216}{108}=2[/tex]

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is [tex]\boxed{108d}[/tex].

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) = [tex]\dfrac{1}{6}[/tex]

P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in the first dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]

= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]

= [tex]6 \times ( \dfrac{1}{6})^4[/tex]

= [tex](\dfrac{1}{6})^3[/tex]

= [tex]\dfrac{1}{216}[/tex]

The probability of two 1's and two 4's in the second  dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]

= [tex]\dfrac{9}{216}[/tex]

∴

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]

By applying  Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]

P(second die (green) | two 1's and two 4's )  = 0.9

Thus; the probability the die chosen was green is 0.9

Answer:

Rational

Step-by-step explanation:

Rational number consists of

-5/6 is a Fraction and we can also simply it to a Decimal.

Hope this helps ;) ❤❤❤

Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:

[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]

[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]

To test it, use F-test statistics and compare variances of each treatment.

Calculate F-value:

[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]

[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]

[tex]F=\frac{1.5876}{0.8649}[/tex]

F = 1.8356

The critical value of F is given by a F-distribution table with:

degree of freedom (row): 20 - 1 = 19

degree of freedom (column): 20 - 1 = 19

And a significance level: α = 0.05

[tex]F_{critical}[/tex] = 2.2341

Comparing both values of F:

1.856 < 2.2341

i.e. F-value calculated is less than F-value of the table.

Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.

Answer:

Step-by-step explanation:

50 : 10 = 5 speaks French only

50 -5= 45 the remainder

4/5 * 45= 36 speaks French and English

45 - 36= 9 speaks English only

The number of students who speak:

i) French only = 5 students,

ii) both French and English = 36 students,

iii) English only = 9 students.

Step 1: Find the number of students who speak French only.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Step 3: Find the number of students who speak both French and English.

Step 4: Find the number of students who speak English only.

Let's calculate it step by step:

Step 1: Find the number of students who speak French only.

1/10 of 50 pupils speak French only:

French-only speakers = (1/10) * 50 = 5 students.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Remaining students = Total students - French-only speakers

Remaining students = 50 - 5 = 45 students.

Step 3: Find the number of students who speak both French and English.

4/5 of the remaining students speak both French and English:

Both French and English speakers = (4/5) * 45 = 36 students.

Step 4: Find the number of students who speak English only.

To find the English-only speakers, subtract the total number of French-only speakers and both French and English speakers from the total number of students:

English-only speakers = Total students - (French-only speakers + Both French and English speakers)

English-only speakers = 50 - (5 + 36) = 50 - 41 = 9 students.

To know more about French:

https://brainly.com/question/34246494

#SPJ2

Complete question is:

There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only, find the number of students who speak​

i) French only,

ii) both French and English,

iii) English only,

Answer:

4

Step-by-step explanation:

"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.

Answer:

The answer is

[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]

Step-by-step explanation:

Since the Earth's moon is a sphere

Surface area of a sphere from the question is given by

A = 4πr²

where r is the radius

To find the radius using the diameter we use the formula

radius = diameter / 2

[tex]radius \: = \frac{3.8 \times {10}^{8} }{2} [/tex]

[tex]radius = 1.9 \times {10}^{8} \: m[/tex]

π = 3.14

Substitute these values into the above formula

That's

[tex]A = 4 \times 3.14 \times ({1.9 \times {10}^{8} })^{2} [/tex]

We have the final answer as

[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]

Hope this helps you

Answer:

20 cm

Step-by-step explanation:

20 cm

8/2 = 4

6/2 = 3

3 and 4 are the sides of the triangle (four triangles in rhombus)

a²+b²=c²

4³+3²=c²

c = 5

5 x 4 = 20

Hope this helped

Answer:

perimeter = 20 cm

Step-by-step explanation:

consider breaking the rhombus into four equal parts.

and that gives you a triangle.

(refer to image attached for more clarification)

let a = 3, b = 4

to get the side c, use Pythagorean theorem = c² = a² + b²

c = sqrt (3² + 4²)

side c = 5

therefore,

perimeter = 4 x sides (c)

perimeter = 4 x 5

perimeter = 20 cm

The arc length is

[tex]S=\displaystyle\int_C\mathrm ds[/tex]

where C is the given curve and ds is the line element. C is defined on 0 ≤ t ≤ 3π by the vector function,

[tex]\mathbf r(t)=(t\cos t,t\sin t)[/tex]

so the line element is

[tex]\mathrm ds=\left\|\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}\right\|\,\mathrm dt[/tex]

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm d(t\cos t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm d(t\sin t)}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

[tex]\mathrm ds=\sqrt{1+t^2}\,\mathrm dt[/tex]

So we have

[tex]S=\displaystyle\int_0^{3\pi}\sqrt{1+t^2}\,\mathrm dt\approx46.132[/tex]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Temp. 174 176 177 178 178 179 180 181

Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74

Temp. 184 184 184 184 184 185 185 186

Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94

Temp. 186 186 186 188 188 189 190 192

Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16

A)

Using the online linear regression calculator, the lie of best fit which models the data above is :

ŷ = 0.09386X - 15.55523

Where ;

X = independent variable

ŷ = predicted or dependent variable

- 15.55523 = intercept

0.09386 = gradient / slope

B)

Point estimate when tank temperature is 186

ŷ = 0.09386(186) - 15.55523

ŷ = 17.45796 - 15.55523

ŷ = 1.90273

C)

Residual error (y - ŷ), ŷ = 1.90273 when x = 186

(0.94 - 1.90273) = −0.96273

(1.85 - 1.90273) = −0.05273

(2.02 - 1.90273) = 0.11727

(2.64 - 1.90273) = 0.73727

D)

To determine the proportion of observed variation in efficiency ratio, we find the Coefficient of determination R^2, which can be found using the online Coefficient of determination calculator : the r^2 value obtained is 0.4433.

Answer:

After 7 days the crystals will be 57.57 grams.

Step-by-step explanation:

In this the continuous exponential growth formula will be used.

y = A e ^rt

Where A = original amount = 10 grams

y is the growth after 7 days

e is Euler's number= 2.719

t is the time in hours , weeks, years etc.= 7 days

r  is the rate in decimals = 25% = 0.25

Putting the values in the formula:

y = A e ^rt

y = 10 e ^0.25 (7)

Calculating with the calculator

y = 10* 2.719^1.75

y= 57.57 grams.

After 7 days the crystals will be 57.57 grams.

Answer:

57.55g

Step-by-step explanation:

Use the formula f(t) = aert, where a = 10, r = 0.25, and t = 7. This gives f(7) = 10e(0.25)(7) = 10e1.75 ≈ 10(5.755) ≈ 57.55.

Answer:

135 degrees

Step-by-step explanation:

3x+15 = 5x - 5 because of the alternate interior angles theorem.

20 = 2x

x = 10

3(10) + 15 = 30+15 = 45

Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.

180-45 = 135.

Answer:

z=65

Step-by-step explanation:

supplementary angles means sum of those angles is 180 degrees

so,

z+z+50=180

2z=130

z=65

I did the best I could, I'm 12 don't judge me.

Answer:

The answer is

Step-by-step explanation:

First factor (x+1)² out of the expression

That's

[tex] \frac{ ({x + 1})^{2} (6 \cos( \frac{\pi}{3} )) {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) }{ ({x + 1})^{2} } [/tex]

Reduce the expression by (x + 1)²

We have

[tex]6 \cos( \frac{\pi}{3} ) \times {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) [/tex]

Using trigonometric values table

[tex] \cos( \frac{\pi}{3} ) = \frac{1}{2} [/tex]

[tex] \sin( \frac{\pi}{2} ) = 1[/tex]

So we have

[tex]6 \times \frac{1}{2} \times {x}^{2} - {x}^{3} \times 2 \times 1[/tex]

Simplify

We have the final answer as

[tex] {3x}^{2} - 2 {x}^{3} [/tex]

Hope this helps you

Answer:

5/36 ; 1/12 ; 2/9 ; yes

Step-by-step explanation:

Given the following :

Roll of two fair dice : green and red

Probability = (number of required outcomes / number of total possible outcomes)

(a) What is the probability of getting a sum of 6?

Number of required outcomes = 5

P(sum of 6) = 5/36

b.) What is the probability of getting a sum of 10?

Number of required outcomes = 3

P(sum of 10) = 3 / 36 = 1/12

c.) What is the probability of getting a sum of 6 or 10?

P(getting a sum of 6) + P(getting a sum of 10)

(5/36) + (1/12) = (5 + 3) / 36

= 8/36 = 2/9

The events are mutually exclusive because each event cannot occur at the same time.

Answer:

1/2 mi

Step-by-step explanation:

Fairfax to Greenwood is equal to one mile

Now think of it as an equation and substitute 1/2 for fairfax and x for greenwood

1/2 + x = 1

This means that x = 1/2

Because of this from Arcadia to Greenwood it is 1/2 mi

Answer:

the least integer for n is 2

Step-by-step explanation:

We are given;

f(x) = ln(1+x)

centered at x=0

Pn(0.2)

Error < 0.01

We will use the format;

[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01

So;

f(x) = ln(1+x)

First derivative: f'(x) = 1/(x + 1) < 0! = 1

2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1

3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2

4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6

This follows that;

Max|f^(n+1) (c)| < n!

Thus, error is;

(n!/(n + 1)!) × 0.2^(n + 1) < 0.01

This gives;

(1/(n + 1)) × 0.2^(n + 1) < 0.01

Let's try n = 1

(1/(1 + 1)) × 0.2^(1 + 1) = 0.02

This is greater than 0.01 and so it will not work.

Let's try n = 2

(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267

This is less than 0.01.

So,the least integer for n is 2

In this exercise we have to use the knowledge of Taylor Polynomial to calculate the requested function, this way we will have;

the least integer for n is 2    

The function given in this exercise corresponds to:

[tex]f(x) = ln(1+x)[/tex]

knowing that the x point will be centered on:

[tex]x=0\\Pn(0,2)\\Error < 0.01[/tex]

By rewriting the equation we have to:

[tex][[Max(f^{(n+1)} (c))]/(n + 1)!] *0.2^{(n+1)} < 0.01[/tex]

So doing the derivatives related to the first function given in the exercise we have to:

[tex]f(x) = ln(1+x)[/tex]

Following this we have to:

[tex]Max|f^{(n+1)} (c)| < n![/tex]

Thus, error is;

[tex](n!/(n + 1)!) * 0.2^{(n + 1)} < 0.01[/tex]

[tex](1/(n + 1))* 0.2^{(n + 1)} < 0.01[/tex]  

Let's try n = 1

[tex](1/(1 + 1)) *0.2^{(1 + 1)} = 0.02[/tex]

This is greater than 0.01 and so it will not work. Let's try n = 2

[tex](1/(2 + 1)) * 0.2^{(2 + 1)} = 0.00267[/tex]

This is less than 0.01. So,the least integer for n is 2.

See more about Taylor polynomial at brainly.com/question/23842376

Answer:

Step-by-step explanation:

The sequence of the problem above is an arithmetic sequence

For an nth term in an arithmetic sequence

F(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

To find the equation first find the common difference

0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15

The first term is 0.5

Substitute the values into the above formula

That's

f(n) = 0.5 + (n - 1)0.15

f(n) = 0.5 + 0.15n - 0.15

The final answer is

Hope this helps you

Answer:

Step-by-step explanation:

Took the math test on edge

Answer:

The Taylor series of f(x) around the point a, can be written as:

[tex]f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....[/tex]

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

[tex]fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}[/tex]

In this exercise we must calculate the Taylor series for the given function in this way;

[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]

The Taylor series of f(x) around the point a, can be written as:

[tex]f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....[/tex]

Here we have:

[tex]f(x) = 4cos(x)\\a = 7\pi[/tex]

Then, let's calculate each part:

[tex]f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4[/tex]

Here we already can see two things:

1) The odd derivatives will have a sin(x) function that is zero when evaluated in [tex]x=7\pi[/tex].

2) We also can see that the sign will alternate between consecutive terms.

So we only will work with the even powers of the series:

[tex]f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....[/tex]

So we can write it as:

[tex]f(x)=\sum f_n[/tex]

Such that the n-th term can written as:

[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]

See more abour Taylor series at: brainly.com/question/6953942

[tex]10[/tex] divisions between $20$ and $20.1$ so each division is $\frac{20.1-20.0}{10}=0.01$

A is 2nd division from $20.0$, so, A is $20.0+2\times 0.01=20.02$

similarly, C is one division behind $20.0$ so it is 19.99

and B is $20.14$

Answer:

8 feet deep

Step-by-step explanation:

volume = length x width x depth

3496 = 23 x 19 x d

3496 = 437 x d

divide both sides by 437

d = 8

Answer:

(3x+11)/ (5x-9)

Step-by-step explanation:

The numerator is what is on the top of the bar in the middle

(3x+11)/ (5x-9)

Answer:

[tex]\large \boxed{\mathrm{Option \ B}}[/tex]

Step-by-step explanation:

The numerator of a fraction is the top section of the fraction.

Answer:

The second option.

Step-by-step explanation:

The first option consists of a line that extends at both opposite sides to infinity, with no precise end.

The third option is a ray that has an endpoint of A, and extends to infinity towards B.

The fourth option is a line segment. It has two endpoints, B and A.

The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.

The answer is the 2nd option.

Answer:

sin(4π/21)

Step-by-step explanation:

Step 1: Rearrange expression

sin(π/3)cos(π/7) - cos(π/3)sin(π/7)

Step 2: Use sin(A ± B)

sin(π/3 - π/7)

Step 3: Evaluate

sin(4π/21)

And we have our answer!

Answer:

a)  z (score) 1,53

b)  z ( score) - 1,96

c) 200 students

Step-by-step explanation:

Normal Distribution N ( 74;10)

a) From z-table, and for 6,3 %  ( 0,063 ) we find the z (score) 1,53

Note : 6,3 % or 0,063 is the area under the curve, the minimum score neded to get A

b) To fail   2,5 %  ( 0,025 ) from z-table  get - 1,96

c) If the group of  student who did not pass the course (5) correspond to 2,5 % then by simple rule of three

5                 2,5

x ?               100

x = 500/2,5

x = 200