QUESTION ONE
(a) If the mean of five values is64, find the sum of the values
(b) If the mean of five values is 8.2 and four of the values are 6, 10, 7, and 12, find the fifth vaue.
(c) Find the mean of 10, 20, 30, 40, and 50.
i) Add 10 to each value and find the mean.
ii) Subtract 10 from each value and find the mean.
iii) Multiply each value by 10 and find the mean.
iv) Divideeach value by 10 and find the mean.
v) Make a general statement about each situation.

QUESTION TWO
a)Find the mean deviation for these data. 5, 9, 10, 11, 11, 12, 15, 18, 20, 22

b)The mean marks in statistics of 100 students in a class was 72 per cent. The mean marks of boys
was 75 per cent, while their number was 70 per cent. Find outthe mean marks of girls in the
cass.

c)The weighted geometric mean of the four numbers 20, 18, 12, and 4 is 11.75. If the weights of
the first three numbers are 1, 3, and 4, respectivey, find the weight of the fourth number

QUESTION THREE
a)For a group of 50 male workers, the mean and standard deviation of their monthly wages
are $6300 and $900 respectively. For a group of 40 female workers, these are $ 5400 and $
600 respectively. Find the standard deviation of monthly wages for the combined group of
workers.

b)A study of the age of 100 persons grouped into intervals 20–22, 22–24, 24–26..., revealed
the mean age and standard deviation to be 32.02 and 13.18 respectivey. While checking it
was discovered that the observation 57 was misread as 27. Cacuate the correct mean age and standard deviation

QUESTION FOUR
The weekly sales of two products A and B were recorded as given below:
Product A : 59 75 27 63 27 28 56
Product B : 150 200 125 310 330 250 225
Find out which of the two shows greater fluctuation in sales

The sine of angle B is obtained dividing the length of the opposite side to angle B by the length of the hypotenuse.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined on the bullet points below:

The problem is incomplete, hence the general procedure to obtain the sine of angle B is presented.

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The minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.

Now, For the minimum height of the second beaker, we need to find its volume first.

The volume of the first beaker is given by;

⇒ V₁ = πr₁²h₁

where r₁ is the radius and h₁ is the height.

Substituting the given values, we get:

V₁ = π(1.8)²(4.6)

V₁ ≈ 66.85 cubic inches

Since, the first beaker is filled to the top, its volume equals the volume of the solution.

Therefore, the volume of the solution is also 66.85 cubic inches.

To find the minimum height of the second beaker, we need to use the formula for the volume of a cylinder:

V₂ = πr₂²h₂

where r₂ is the radius and h₂ is the height of the second beaker.

We want to find h₂ such that V₂ is equal to 66.85 cubic inches.

Dividing both sides of the equation by πr₂², we get:

h₂ = V₂ / (πr₂²)

Substituting the given value for r₂, we get:

h₂ = 66.85 / (π(1.25)²)

h₂ ≈ 13.5 inches

Therefore, the minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.

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By expanding and simplifying the algebraic expression (y + 7)(y - 5), we have the result y² + 2y - 35

To expand an algebraic expression in brackets, we need to use the distributive property to make is easy for simplification, thus we expand and simplify the expression as follows:

(y + 7)(y - 5) = y(y - 5) + 7(y - 5) {distributive property}

(y + 7)(y - 5) = y² - 5y + 7y - 35

by simplification, we have;

(y + 7)(y - 5) = y² + 2y - 35

Therefore, the expansion and simplification of the algebraic expression (y + 7)(y - 5), gives the result y² + 2y - 35.

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False. When Jane turns left 40 degrees and walks 60 meters, she is farther away from her starting position than when she crossed the finish line.

If Jane turns left 90 degrees or 120 degrees, then she will also be farther away from her starting position than when she crossed the finish line. Turning left 90 degrees or 120 degrees will take her in a different direction, and thus she will be farther away from her starting position than when she crossed the finish line.

Therefore, the given statement is false.

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The required mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.

The original mean is the sum of the ages divided by the number of students:

Mean = (10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15) / 10

Mean = 124 / 10

Mean = 12.4

If another student of age 15 joins the class, the new sum of the ages is:

Sum = 10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 15

Sum = 139

The new mean is the new sum of ages divided by the new number of students:

New mean = Sum / (Number of students + 1)

New mean = 139 / 11

New mean = 12.63636... or about 12.6 (rounded to one decimal place)

Therefore, the mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.

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Let's start by finding how many bags of lemons Rachel used on Monday. We know she used a whole number of bags plus a fraction, so we'll need to convert the mixed number to an improper fraction:

1 2/5 = 7/5

So Rachel used 7/5 bags of lemons on Monday.

On Tuesday, Rachel used 1 1/4 times as many lemons as on Monday. To find out how many bags of lemons that is, we can multiply the amount Rachel used on Monday by 1 1/4:

1 1/4 = 5/4

5/4 times 7/5 = 35/20 = 7/4

So Rachel used 7/4 bags of lemons on Tuesday, which is the same as 1 3/4 bags of lemons.

Therefore, Rachel used 1 3/4 bags of lemons on Tuesday.

The only graph that represents a function is: Graph D

A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs.  Each input has only one output. The function is the description of how the inputs relate to the output.

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.

From the graphs, we can see that:

Graph A has 2 outputs at x = -2

Graph B has 2 outputs at x = 0

Graph C has two outputs at x = -1

Graph D has a unique output for every input and as such it is a function

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Answer:

  3013.5 cm³

Step-by-step explanation:

Given a ball with a circumference of 56.3 cm, you want to know its volume.

The formula for circumference is ...

  C = 2πr

Solving for radius, we get ...

  r = C/(2π) = 56.3 cm/(2π) ≈ 8.96042 cm

The volume of a sphere is given by ...

  V = 4/3πr³

  V = 4/3π(8.96042 cm)³ ≈ 3013.5 cm³

The ball's volume is about 3013.5 cubic centimeters.

__

Additional comment

Alternatively, we could use the formula ...

  V = C³/(6π²)

to get the same result.

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The measure of the missing dimension is 8 meters.

We are given that;

Volume= 2288 cubic meters

Height= 13meter

Length= 22meter

Now,

To find the width.

You can rearrange the formula to solve for width by dividing both sides by length and height:

Width = Volume / (length × height)

Plug in the given values:

Width = 2288 / (22 × 13)

Simplify:

Width = 2288 / 286

Width = 8

Therefore, by the given rectangular prism the answer will be 8 meters.

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Answer:250

Step-by-step explanation:

I think they just want you to multiply the 25 and the 10 (radius squared times the height)

The solution to the system of equations in this problem is given as follows:

(-1, -5).

The system of equations in the context of this problem is defined as follows:

The x-coordinate of the solution in the context of this problem is obtained equaling the two equations, as follows:

x - 4 = -3x - 8

4x = -4

x = -1.

Hence the y-coordinate of the solution is obtained as follows:

y = -1 - 4

y = -5.

Thus the solution is:

(-1, -5).

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The correct option is D, the equation has two complex solutions.

Here we can see that we have the graph of a quadratic equation.

It opens upwards, and we can see that it has a vertex at (1, 4), which intercepts the y-axis at y = 5.

Now, we say that the solutions of a quadratic are the values of x such that the function becomes zero.

Particualrly, in this graph we can see that the graph never intercepts the x-axis, that means that this equation has no real roots.

Then the correct option is:

"Function f has exactly two complex solutions."

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The percentage of Dinesh’s time spent on Project X is 36.90%.

We have,

From the table,

The total time spent on the X-project each week is given as:

= 23(1/3) + 16(1/3) + 9.33 + 4.20

= 23.33 + 16.33 + 9.33 + 4.20

= 53.19

This is the time spent on X-project for the month.

Now,

The total time spent on all the events in the table.

= 144.13

The percent of Dinesh’s time spent on Project X.

= 53.19/144.13 x 100

= 36.90%

Thus,

The percentage of Dinesh’s time spent on Project X is 36.90%.

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Answer:

The three numbers are -4, 0, and 1.

Step-by-step explanation:

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The measure of the third outgoing current will be 0.5 amperes.

We know that,

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.

Then the measure of the third outgoing current will be

We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.

Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆.

Then we have

I₁ + I₂ + I₃ = I₄ + I₅ + I₆

0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆

1.85 = 1.35 + I₆

I₆ = 0.5

Thus, the measure of the third outgoing current will be 0.5 amperes.

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complete question:

The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current

The equation of smallest degree with integer coefficients will be f(x) = x^2 - (3 + √7)x + 3√7

It should be noted that to begin, let us establish the following:

x = √(8 - 1) which is equal to √7.

y = √(8 + 1) which is equivalent to √9. Therefore, y equals 3.

For the value of x, its conjugate coincides with √7; hence:

(x - x') × (x - y') = (x - √7)(x - 3)

Equation expansion yields:

f(x) = x^2 - (3 + √7)x + 3√7

By substituting for both values x and y in the equation above, we can show that f(x) satisfies the given specifications:

When x takes on a value of √7:

f(√7) = (√7)^2 - (3 + √7)√7 + 3√7 = 7 - 7 = 0

With an input value of 3:

f(3) = 3^2 - (3 + √7)(3) + 3√7 = 9 - 9 - 3√7 + 3√7 = 0

The lowest degree polynomial with rational coefficients having √(8 - 1) and √(8 + 1) as its roots is: f(x) = x^2 - (3 + √7)x + 3√7

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Answer:0.98

2.17 are correct

Step-by-step explanation:

-u^2 - 4u + 4 = 0

Multiplying both sides by -1, we get:

u^2 + 4u - 4 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 4, and c = -4. Substituting these values, we get:

u = (-4 ± sqrt(4^2 - 4(1)(-4))) / 2(1)

u = (-4 ± sqrt(32)) / 2

u = (-4 ± 4sqrt(2)) / 2

u = -2 ± 2sqrt(2)

Therefore, either:

length LD = 6 units

length DF = 9 units

length HF = 6 units

length LH = 9 units

length L'D' = 2 units

length D'F' = 3 units

length H'F' = 2 units

length L'H' = 3 units

Dilation is the scaling of an object, where it gets bigger or smaller.

Scale factor = new dimension/old dimension

length LD = 15-9 = 6units

length DF = 6-(-3) = 9units

length HF = 15-9 = 6 units

length LH = 6-(-3) = 9 units

Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.

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The measure of angle 3 is 52⁰.

The measure of angle 5 is 38⁰.

The measure of angle 6 is 52⁰.

The measure of angle 3, 5 and 6 is calculated as follows;

angle 1 + angle 2 + angle 3 = 180 (sum of angles in straight line )

90 + 38 + angle 3 = 180

angle 3 = 180 - 128

angle 3 = 52⁰

The measure of angle 5 is calculated as follows;

angle 5 = angle 2 (vertical opposite angles are equal)

angle 5 = 38⁰

The measure of angle 6 is calculated as follows;

angle 6 = angle 3 (vertical opposite angles are equal)

angle 6 = 52⁰

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The number of ways of selecting 3 items from a total of 7 items, where order does not matter is (a) 35 ways.

The number of ways to choose three items from a group of seven, where order does not matter, is given by the combination formula:

⇒ C(n,r) = n!/(r! × (n-r)!),

where n is = total number of items, and r is = number of items to be chosen,

We have, total items (n) = 7 and items to be selected (r) = 3.

Substituting the values,

We get;

⇒ C(7,3) = 7!/(3! × (7-3)!),

⇒ 7!/(3! × 4!),

⇒ (7 × 6 × 5)/(3 × 2 × 1),

⇒ 35 ways.

Therefore, the correct option is (a).

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Answer:

112 yards

Step-by-step explanation:

The center of the Ferris wheel is 61 yards above the ground and the radius is 51 yards. When Jack is at the 9 o'clock position, he is at a distance of 112 yards from the center of the Ferris wheel (51 yards from the center plus 61 yards above the ground). Let θ be the angle that Jack has swept out measured from the 9 o'clock position, in radians.

The function g that represents Jack's vertical distance above the ground in yards in terms of the angle θ is:

g(θ) = 61 + 51sin(θ)

where sin(θ) represents the vertical component of the distance Jack has traveled.

Note that when θ = 0, sin(θ) = 0, which means Jack is at the very top of the Ferris wheel, 112 yards above the ground. When θ = π/2, sin(θ) = 1, which means Jack is at the 12 o'clock position, 112 + 51 = 163 yards above the ground. Similarly, when θ = π, sin(θ) = 0, which means Jack is at the very bottom of the Ferris wheel, 112 yards above the ground.

Answer: The point that satisfies the equation is E. (-3, -4).

Explanation:

To determine which point lies on the circle represented by the equation (x − 3)² + (y + 4)² = 6², we can substitute the coordinates of each point into the equation and see which one satisfies the equation.

A. (9, -2): (9 − 3)² + (-2 + 4)² = 6²

(6)² + (2)² = 36

36 + 4 = 40 ≠ 36

B. (0, 11): (0 − 3)² + (11 + 4)² = 6²

(-3)² + (15)² = 36

9 + 225 = 234 ≠ 36

C. (3, 10): (3 − 3)² + (10 + 4)² = 6²

(0)² + (14)² = 36

0 + 196 = 196 ≠ 36

D. (-9, 4): (-9 − 3)² + (4 + 4)² = 6²

(-12)² + (8)² = 36

144 + 64 = 208 ≠ 36

E. (-3, -4): (-3 − 3)² + (-4 + 4)² = 6²

(-6)² + (0)² = 36

36 + 0 = 36

The point that satisfies the equation is E. (-3, -4).

Answer:

B.

Step-by-step explanation:

We can use the given formula to find the time it takes for the rocket to reach a height of 10 feet:

10 = -16t^2 + 22t + 6

Rewriting the equation in standard quadratic form:

16t^2 - 22t + 4 = 0

Using the quadratic formula:

t = (22 ± sqrt(22^2 - 4(16)(4)))/(2(16))

t = (22 ± sqrt(36))/32

t = 3/4 or 1/4

Since the rocket reaches a height of 10 feet at two different times (3/4 and 1/4 seconds), it must pass through that height twice during its flight. Therefore, the rocket will reach a height of 10 feet. The correct answer is B.

Based on the information, HH is a subset of Ha, which is a subset of aH, which is a subset of H, which is a subset of HH

It should be noted that to demonstrate this theory, we must show that each of these collections are components of the others and consequently all are equivalent.

At first, let's evaluate HH. As H is a subgroup of G, it is dependent on multiplication so for any two elements h1, h2 in H, the product h1h2 is also in H. Thus, every entity within HH can be expressed as the aggregate of h1h2 for certain elements h1, h2 from H. Since H is a subgroup, it is also subject to inverse property, so h2^-1h1^-1 remains inside H. Clearly, h1h2 thus translates to h'(h2^-1h1^-1)h'', where h', h'' are members of H.

This illustrates that every component of HH can be presented as h'h'' for a pair of h', h'' which exist in H, therefore approximating with accuracy the definition of H. Thus, we have demonstrated that HH is part of H.

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Answer: 2x + 12

Step-by-step explanation:

Let the cost of each sweater be x.

since she's buying 2, the total cost of the sweaters will be 2x.

Just tack on the + 12 at the end for the sunglasses :)