Means if a number is bigger than other number.
Divide 647,457 by 325,712,318
3. Adam is 20 years younger than Brian. In two years Brian will be twice as old as
Adam is now. How old
are they now? Solve the problem using the elimination method.
Answer:
Here,
Let the age of Adam be x
and ,Brian be y
so,x=y+20.........eqn 1
and ,2(y+2)=x
or,2y+4=x......eqn 2
Now ,
subtracting eqn1 and eqn 2
so, x=y+20
x=2y+4
- - -
______________
0 = -y+16
so,y=16 and x=y+20 =16+20=36 .
so Adam is 36 years old and brian is 16.
What is the range of the given function ?
The range of the function is y ≤ 3.
What is the range of the function?The set of a function's potential output values is known as its range.
Given, the graph of the function.
The range of a function is the set of values of y the function can take.
The maximum y value of the function is 3, and the graph is going down both sides infinitely.
Therefore, the range of the function is y ≤ 3.
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In how many ways can a person order one ice cream cone with 3 different flavors of ice cream if there are 11 flavors to choose from and it matters to the person how the 3 flavors are stacked on the one cone? That is, which flavor is on top, middle, and bottom.
Answer:
I think the answer is 33?
Select the correct rational numbers.
-4 2/3 ,-3 2/3, -1 2/3 2/3
ASAPPPPP PLEASE HELPPP!!!!!!!!!!
Between 50 and 100 books are stored on a shelf. Exactly 20 percent of them are textbooks. Exactly one-seventh of them are novels. Can the exact number of books on the shelf now be determined? Why or why not?
Answer:
no
Step-by-step explanation:
the percentage has nothing to do with how many of them there are, forgive me if im wrong
The exact number of books on the shelf cannot be determined based on the information given.
What is an expression?An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.
We know that between 50 and 100 books are stored on a shelf, so let's assume the number of books is some integer value between 50 and 100, inclusive. Let's call this value "n".
Exactly 20% of the books are textbooks, which means there are 0.2n textbooks on the shelf.
Exactly one-seventh of the books are novels, which means there are (1/7)n novels on the shelf.
We know that n, 0.2n, and (1/7)n are all integers because they represent whole numbers of books. We can write this as:
n = a
0.2n = b
(1/7)n = c
where a, b, and c are integers.
From the second equation, we know that 0.2n is a multiple of 1/10. From the third equation, we know that n is a multiple of 7. Therefore, we can rewrite these equations as:
n = 10b
n = 7c
Since n is equal to both 10b and 7c, we know that n must be a multiple of the least common multiple of 10 and 7, which is 70.
So, n must be a multiple of 70, and therefore must be one of the integers 50, 70, or 90. However, we cannot determine which of these three values is the correct one based on the information given, because all three satisfy the conditions in the problem:
If n=50, then 20% of the books (i.e., 10 books) are textbooks, and 1/7 of the books (i.e., 7.14 books, which we round down to 7) are novels.
If n=70, then 20% of the books (i.e., 14 books) are textbooks, and 1/7 of the books (i.e., 10 books) are novels.
If n=90, then 20% of the books (i.e., 18 books) are textbooks, and 1/7 of the books (i.e., 12.86 books, which we round down to 12) are novels.
Therefore, the exact number of books on the shelf cannot be determined based on the information given.
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Find the exact arc length of f(x)=√2x+1 0≤x≤4
The exact arc length of f(x)=√2x+1 is 4.5.
The arc length is the separation between two points along a curve segment. The arc length of a function f(x) is given by the formula,
[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx[/tex]
Where f'(x) is derivative of function f(x). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.
Finding the arc length of f(x)=√2x+1 0≤x≤4, using the formula,
First finding the derivative of function,
[tex]f'(x)=\frac{d(\sqrt{2x+1})}{dx} \\\\=\frac{2}{2\sqrt{2x+1}} \\\\=\frac{1}{\sqrt{2x+1}}[/tex]
Now, putting the derivative of function f(x) in the formula of arc length L,
[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+(\frac{1}{\sqrt{2x+1}})^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+\frac{1}{2x+1}}}\\\\L=\int\limits^4_0 {\sqrt{\frac{2x+1+1}{2x+1}}}\\L=\int\limits^4_0 {\sqrt{\frac{1}{2x+1}}}\\\approx4.5[/tex]
Therefore, the exact arc length of f(x)=√2x+1 is 4.5.
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write an expression using division that could be used to find the width of the rectangle
The expression used to find the width using division is:
W = A/L
Which expression can be used to find the width?We know that for a rectangle of width W and length L, we know that the area is given by the product between these two dimensions, then:
A = L*W
We want a expression using division that can be used to find the width, so, suppose we know the values of the area and the length, the we can divide both sides by L to get:
A/L = W
This expression gives the width.
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Weight of pennies.
The distribution of weights of United States pennies is approximately normal with a mean of 2.4 grams and a standard deviation of
0.04 grams.
What is the probability that a randomly chosen penny weighs less than 2.4 grams? 6%
What is the probability that the mean weight of 15 pennies is less than 2.4 grams?
1) The probability that a randomly chosen penny weighs less than 2.4 grams is; 0.00621.
2) The probability that the mean weight of 15 pennies is less than 2.4 grams is; 0
How to apply the central limit theorem?The central limit theorem in statistics tells us that the sampling distribution of the mean will usually be normally distributed, provided that the sample size is large enough.
We are given the following parameter;
Population mean; μ = 2.4 grams
Standard deviation; σ = 0.04 grams
1) The probability that a randomly chosen penny weighs less than 2.4 grams is: P(X < 2.4)
Formula for z-score is;
z = (X - μ)/σ
z = (2.4 - 2.5)/0.04
z = -2.5
The p-value from z-score calculator is; p = 0.00621.
2) The standard deviation for these 15 pennies will now be;
σ' = 0.04/√15
σ' = 0.0103
The probability that the mean weight of 15 pennies is less than 2.4 grams is expressed as;
P(X' < 2.4)
z = (2.4 - 2.5)/0.0103
z = -9.709
The p-value from z-score calculator is; p = 0
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If each standard room cdn fill 2 guests what is the maximum number of guests that all standard rooms can accommodate
The maximum number of guests that can fill all the standard rooms is twice the number of the standard rooms
How to find the number of guests that can fill the standard roomsInformation from the question
each standard room can fill 2 guests
the maximum number of guests that all standard rooms can accommodate = ?
The problem is solved by multiplication
each standard room (1) = 2 guests
all standard rooms = ?
cross multiplying
? * 1 = 2 * all standard rooms
? = all standard rooms times two
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parallel lines, traversal, and algebra
need help!
The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;
x = 4°, y = 10°
11. x = 9°, y = 12°
12. x = 14°, y = 5°
13. x = 8°, y = 11°
14. x = 16°, y = 23°
15. x = 9°, y = 13°
What are parallel lines?Parallel lines are lines that maintain the same distance from each other along their lengths.
From the figure, we get;
(29·x - 3) and (15·x + 7) are linear pair angles, therefore;
(29·x - 3) + (15·x + 7) = 180°
44·x + 4 = 180
x = (180 - 4)/44 = 4
x = 4°
(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;
(15·x + 7) + (13·y - 17) = 180°
(15×4 + 7) + (13·y - 17) = 180°
67 + 13·y - 17 = 180°
50 + 13·y = 180
13·y = 180 - 50 = 130
y = 130 ÷ 13 = 10
y = 10°
11. (18·x - 44)° and (8·x - 10)° are same side exterior angles, therefore;
(18·x - 44)° + (8·x - 10)° = 180°
26·x - 54 = 180
x = (180 + 54)/26 = 9
x = 9°
(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;
(8·x - 10)° + (13·y - 38)° = 180°
(8 × 9 - 10)° + (13·y - 38)° = 180°
62 - 38 + 13·y = 180
13·y = 180 - (62 - 38) = 156
y = 156 ÷ 13 = 12
y = 12°
12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;
(9·x - 2)° = (5·x + 54)°
(9·x - 2)° = (5·x + 54)°
9·x - 5·x = 54 + 2 = 56°
4·x = 56°
x = 56° ÷ 4 = 14°
x = 14°
(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;
(9·x - 2)° + (10·y + 6)° = 180°
(9 × 14 - 2)° + (10·y + 6)° = 180°
124 + 6 + 10·y = 180
10·y = 180 - 130 = 50
y = 50 ÷ 10 = 5
y = 5°
13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;
(8·x - 1)° is congruent to angle (11·x - 25)°
(8·x - 1)° = (11·x - 25)°
11·x - 8·x = 25 - 1 = 24
3·x = 24
x = 24 ÷ 4 = 8
x = 8°
Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;
(15·y - 48)° + (8·x - 1)° = 180°
(15·y - 48)° + (8 × 8 - 1)° = 180°
(15·y - 48)° + 63° = 180°
15·y + 15° = 180°
15·y = 180° - 15° = 165°
y = 165° ÷ 15 = 11°
y = 11°
14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;
(4·x + 4)° = (7·x - 44)°
7·x - 4·x = 44° + 4° = 48°
3·x = 48°
x = 48° ÷ 3 = 16°
x = 16°
The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°
Therefore;
39 + 8·y - 43 = 180°
8·y = 180 + 43 - 39 = 184
y = 184 ÷ 8 = 23
y = 23°
15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;
(15·x - 26) = (12·x + 1)
(15·x - 12·x) = (26 + 1)
3·x = 27
x = 27 ÷ 3 = 9
x = 9°
The vertical angle to (2·x + 1) is therefore;
12·x + 1 = 12 × 9 + 1 = 109
The angle sum property indicates that we have;
28° + 109° + (4·y - 9)° = 180°
(4·y - 9)° = 180° - (28° + 109°) = 43°
(4·y - 9)° = 43°
(4·y)° = 43° + 9° = 52°
y = 52°/4 = 13°
y = 13°
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An earthworm accelerates from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m. How long did it take?
By using the formula of acceleration, it can be calculated that
Time taken by an earthworm to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s
What is acceleration?
At first, it is important to know about velocity
Distance travelled by a body per unit interval of time in a particular direction is called Velocity
The rate of change of velocity is called acceleration.
Acceleration is a vector quantity as the direction is taken into account.
Initial velocity of earthworm (u)= 0.01 m/s
Final velocity of earthworm (v) = 0.02 m/s
Distance (s) = 0.9 m
We know,
[tex]v^2 = u^2 + 2as\\0.02^2 = 0.01^2 + 2 \times a \times 0.9\\0.02^2 - 0.01^2 = 1.8a\\(0.02 + 0.01)(0.02 - 0.01) = 1.8a\\a = \frac{0.03 \times 0.01}{1.8}\\a = 0.000167 \ ms^{-2}[/tex]
Again,
v = u + at
0.02 = 0.01 + 0.000167[tex]\times[/tex] t
t = [tex]\frac{0.02 - 0.01}{0.000167}[/tex]
t = 59.88 s
Time taken by an earthworm to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s
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Can anyone help me in this question? pls.........
Answer: A
Step-by-step explanation :
HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )
I need help with Part 2 only
A bottle maker assumes that 24% of his bottles are defective. If the bottle maker is right, what is the probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4%? Round your answer to four decimal places.
The probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4% is: 10.9069.
What is the probability that the population proportion will be greater than 4%?To obtain the correct value, we need to use the formula for the Z score. This formula requires that we subtract the average or mean value from the data point provided and divide the remaining value by the standard deviation.
Here is the formula:
z = (x-μ)/σ
First population proportion = 0.24
The sample proportion, hat p = 0.04
Z score =
[tex]0.04 - 0.24 / \sqrt 0.24 (1 - 0.24) / 546[/tex]
So, the Z score will
= -10.9469
So, when the z score = - 10.9469, the probability that Z is greater than - 10.9469, is = 10.9069
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What is the relationship between Figure A and Figure B?
-Figure A was translated left 2 units and up 4 units
-Figure A was reflected over the y-axis
-Figure A was translated right 4 units and up 2 units
-Figure A was dilated by a scale factor of 2
Answer:
Figure A was translated right 4 units and up 2 units
a body of mass 10.5 kg fell to the ground . calculate the weight of the body.
Answer:
103 N
Step-by-step explanation:
we use the equation: w = mg
where m is mass, W is weight and g is gravitational field strength
w = ?
m= 10.5 kg
g = 9.81 ms‐² (for earth)
so,
w = 10.5 × 9.81
w = 103.005
w ≈ 103 Newtons
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
Using polar coordinates, volume of the given solid is, 32√3π.
What is volume of solid?
An object's space requirement is expressed in terms of its volume. The amount of unit cubes required to completely fill the solid is how much it weighs. We have a total of 30 unit cubes in the solid, so the volume is as follows: 2 units 3 units 1 unit Equals 30 cubic units
We have to find the volume of the solid Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4 using polar coordinates.
So, the volume is
[tex]2\int\limits\int\limits_D {\sqrt{16-x^2-y^2} } \, dA[/tex]
[tex]2\int\limits^2^\pi _0 {\int\limits^4_2 {\sqrt{16-r^2} } rdrdtheta[/tex]
[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(16-r^2)_2^4 } \, dtheta[/tex]
[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(-2\sqrt{3}) } \, dtheta[/tex]
[tex]\int\limits^2^\pi _0 {16\sqrt{3} } \, dtheta[/tex]
[tex]32\sqrt{3}\pi[/tex]
Hence, the volume of the given solid using polar coordinates is, [tex]32\sqrt{3}\pi[/tex].
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factorize 6x²y-10xy+15x-25
The factors of 6x²y-10xy+15x-25 are (3x-5)(2xy+5).
According to the question,
We have the following expression:
6x²y-10xy+15x-25
In this expression, we can not use any identity to solve it further.
Now, in order to find the factors of this expression, we will find the common terms from the first two terms and one common factor from the last two terms.
Taking 2xy as a common factor from first two terms and 5x as a common factor from the last two terms:
2xy(3x-5)+5(3x-5)
Taking (3x-5) as a common factor from the above expression:
(3x-5) (2xy+5)
Hence, the factors of 6x²y-10xy+15x-25 are (3x-5)(2xy+5).
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lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. Work out how much money Elliot received. Elliot received £
If lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. The amount that Elliot received is £56.
How to find the amount received?Given data;
Sharing ratio 8:5
Amount Elliot got = 21
In order to determine the amount that Elliot received we need to formulate and equation and then use the formulated equation to find the amount received.
Equation
21 × 8 ÷ (8-5)
Hence,
£21 × 8 ÷ (8-5)
£168 ÷ 3
= £56
Therefore Elliot received £56.
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If using the method of completing the square to solve the quadratic equation
x² - 13x +31 = 0, which number would have to be added to "complete the
square"?
To make a square using the method of completing the square.
[ (a + b)² = a² + 2ab + b² ]
[ (a - b)² = a² - 2ab + b² ]
x² - 13x + 31 = 0
(x - 13/2)² + (293/4) = 0
The number added to complete the square is 293/4.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
x² - 13x + 31 = 0
To make a square using the method of completing the square.
[ (a + b)² = a² + 2ab + b² ]
[ (a - b)² = a² - 2ab + b² ]
x² - 2 x (13/2)x + (13/2)² - (13/2)² + 31 = 0
(x - 13/2)² + 169/4 + 31 = 0
(x - 13/2)² + (293/4) = 0
Thus
The number added to complete the square is 293/4.
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Find the value of x.
(x + 8)
Answer:
52°
Step-by-step explanation:
This is an equilateral triangle. Therefore all the sides and angles are equal to each other.
We know that,
the sum of the interior angles in a triangle is 180° and in equilateral triangles each angle measured 60° ( 180°/3 ).
Accordingly,
x + 8 = 60
Subtract 8 from both sides.
x = 60 - 8
x = 52°
A number c divided by 3 is greater than -20
The solution of the given statement will be inequality c > -60.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
We have been given the statement "number c divided by 3 is greater than -20".
As per the given statement, we can represent this algebraic form with inequality as:
⇒ c / 3 > -20
Inequality by multiplying both sides of the inequality by 3:
⇒ 3 × c / 3 > 3 × -20
⇒ c > -60
Thus, the solution of the given statement will be inequality c > -60.
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The question seems to be incomplete the correct question would be
Find the solution if a number c divided by 3 is greater than -20.
Given that a geometric progression has a = -2 and r = -0.5, Determine values for the: (i) fifth term of the GP. [3 marks] (ii) sum of the first 20 terms [4 marks]
The fifth term of the geometric progression is -0.125 and the sum of the first 20 terms is [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]
What is a geometric Progression?A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio.
All terms of a geometric progression have a common multiple called the common ratio.
if a = -2, which is first term
r = -0.5 which is common ration,
Then fifth term = a[tex]r^{4}[/tex]
substitute a and r into the above equation, you have
fifth term = (-2)([tex](-0.5)^{4}[/tex] = - 0.125
sum of G.P when the common ratio is less than 1, we have
[tex]\frac{a(1 - r^{n} )}{1 - r}[/tex]
where n = number of terms = 20
sum = [tex]\frac{-2(1 - (-0.5)^{20}) }{1--0.5}[/tex] = [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]
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An airplane travels 3582 kilometers against the wind in 6 hours and 4482 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
Answer: Let us assume speed of jet in still air =x
speed of wind =y
Jet flying against the wind
Relative speed of the jet = speed of jet in still air -speed of the wind=x-y
distance covered =3426
time =6 hours
distance = speed * time
3426=(x-y)*6
x-y =3426/6
x-y=571——(1)
Jet flying with the wind
Relative speed of the jet = speed of jet in still air +speed of the wind=x+y
distance covered =4026
time =6 hours
distance = speed * time
4026=(x+y)*6
x+y =4026/6
x+y=671———-(2)
solving 1 and 2 we get
x+y=671
x-y=571
x=621
y=50
speed of jet in the still air =x= 621 miles per hour
Step-by-step explanation:
What is 8% off of 12$?
Answer:
11.04 U.S. dollarsStep-by-step explanation:
because it is the answer I looked it up (;-;)PLEASE HELP! ALGEBRA 1 HW I WILL GIVE BRAINLYEST FOR ANSWER!!
In the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.
What do we mean by equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.So, the values of C are:
Equation: 12.5x + 5y = CCalculate as follows:
(A) When x = -2 and y = 15.
12.5(-2) + 5(15) = CC = 50(B) When x = 0 and y = 10.
12.5(0) + 5(10) = CC = 50(C) When x = 2 and y = 5.
12.5(2) + 5(5) = CC = 50(D) When x = 4 and y = 0.
12.5(4) + 5(0) = CC = 50Therefore, in the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.
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Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is 22 1 4 cm 22 4 1 cm22, start fraction, 1, divided by, 4, end fraction, start text, c, m, end text tall. It has a rectangular shape and an area of 890 cm 2 890cm 2 890, start text, c, m, end text, squared. How wide across is Keala's book cover? cm
The width across Keala book cover is 40cm
What is a rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees
From the question,
The length of the cover
= 22 1/4
= 89/4
The area of the cover
=890 cm²
From the formula
Area of a Rectangle = Length x Breadth
890=89/4×Breadth
Breadth = 890×4/89
Breadth=40cm
Hence, the width of the book cover is 40cm
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Evergreen Landscaping bought 7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270. The next week the firm bought 5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015. Pea gravel costs $28 less per ton than topsoil. Find the cost per ton for each item.
The cost of topsoil per ton would be $48.
The cost of pea gravel per ton is $20.
The cost of mulch per ton is $479.
What is the linear equations in two variable?
A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equation.
We have,
7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270.
5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015.
Let,
cost of topsoil per ton = x
cost of pea gravel per ton = x - 28
cost of mulch per ton = m
7x + 6m + 3(x - 28) = 3270
7x + 6m + 3x - 84 = 3270
10x + 6m = 3270 + 84
10x + 6m = 3354 -------------(i)
5x + 5m + 5(x - 28) = 3015
5x + 5m + 5(x - 28) = 3015
10x + 5m = 3015 - 140
10x + 5m = 2875 -----------(II)
Subtracting equation (II) from (I), we get
10x + 6m = 3354
- 10x + 5m = 2875
Solving we get
m = 479
Put m = 479 in equation(I), we get
10x + 6m = 3354
10x + 6(479) = 3354
10x = 480
x = 480/10
x = 48
Hence,
The cost of topsoil per ton would be = x = $48.
The cost of pea gravel per ton = x - 28 = 48 - 28 = $20.
The cost of mulch per ton = m = $479.
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In the first five math quizzes, Patty had an average score of 8. She got a 7 and a 5 on the next two quizzes. After the eighth quiz, her
average stood at 7.5. What was her score on the eighth quiz?
*
Answer: 8
Step-by-step explanation:
(Sum of first 5 quizzes) / 5 quizzes = 8
Sum of 1st 5 quizzes = 8 x 5 = 40
let x = score on the 8th quiz
(40 + 7 + 5 + x) / 8 = 7.5
52 + x = (7.5)(8) = 60
x = 60 - 52 = 8