Olivia, Nicholas, Chloe, and Ethan each took many samples from the same
population of students. The number of students in each of their samples is
shown in the table below. Which person's sampling distribution is most likely
to closely approximate the population distribution?
Person taking sample Number of students in each sample
Olivia
29
Nicholas
70
Chloe
56
Ethan
91
A. Olivia
B. Chloe
C. Ethan
D. Nicholas

The division technique can be used to evaluate the given expression

12.75÷1. 5

The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are  (÷) and (/).

“p divided by q” can be written as: (p÷q) or (p/q).

The method of verification can be expressed as:

Dividend = (Divisor × Quotient) + Remainder.

The given equation is:12.75÷1.5

We'll first write the above decimal numbers in fractional form.

12.75÷1.5

1275/100÷15/10

2. Now we'll divide it further.

⇒1275/100÷15/10

⇒1275/100×15/10

⇒1275/10×15

⇒225/10×3

⇒88/10

3. And finally, we'll write our quotient in decimal form.

⇒88/10

⇒8.8

ㅤ

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Rate of speed of each cyclist is:

Alisha 10mi/hr

Jose 15mi/hr

Raul 10mi/hr

Ruthie 16mi/hr

Data given of each cyclist;

Formula used: [tex]r=\frac{d}{t}[/tex]

here,

r=rate of speed

d=distance

t=time

Alisha: Distance=40mi; Time=4hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{40}{4} =10mi/hr[/tex]

Jose: Distance=30mi; Time=2hr

applying the formula

[tex]r=\frac{d}{t}\\ r=\frac{30}{2} =15mi/hr[/tex]

Raul: Distance=40mi; Time=4hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{40}{4}=10mi/hr[/tex]

Ruthie: Distance=80mi; Time=5hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{80}{5} =16mi/hr[/tex]

Alisha= 10mi/hr

Jose= 15mi/hr

Raul= 10mi/hr

Ruthie= 16mi/hr

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The given sequence represents the sales of a product over time. The sum of the first 6 terms is 693.75, which is calculated by multiplying each term in the sequence by its respective exponent.

The sum of the first 6 terms of the geometric sequence is calculated as follows:

[tex]a_1 = 125 \left(\frac{1}{5}\right)^{1-1} = 125 \\[/tex]

[tex]a_2 = 125 \left(\frac{1}{5}\right)^{2-1} = 25 \\[/tex]

[tex]a_3 = 125 \left(\frac{1}{5}\right)^{3-1} = 5 \\a_4 = 125 \left(\frac{1}{5}\right)^{4-1} = 1 \\a_5 = 125 \left(\frac{1}{5}\right)^{5-1} = \frac{1}{5} \\a_6 = 125 \left(\frac{1}{5}\right)^{6-1} = \frac{1}{25} \\[/tex]

Total sum = 125 + 25 + 5 + 1 +[tex]\frac{1}{5} + \frac{1}{25}[/tex] = 693.75

The geometric sequence a_n=12[tex]5\left(\frac{1}{5}\right)^{n-1}[/tex]represents the sales of a product over time, where n is the number of years after its release. The sum of the first 6 terms is calculated by multiplying each term in the sequence by its respective exponent. This gives us the following 6 terms: a_1 = 125, a_2 = 25, a_3 = 5, a_4 = 1, a_5 = 1/5, and a_6 = 1/25. The sum of these 6 terms is 693.75.

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Answer:

sum up the numbers and divide by the numbers of values.

80+84+79+44+87+73+89+90+82+89+93+97+77+71 / 14

1135/14

= 81•1 is the mean

Answer: 1/36

Step-by-step explanation: 2/9 x 1/8 =2/72 = 1/36

It’s angle 1 and angle 8

The pair of angles that are formed on the other side of the pearl lines, but on the opposite side of the transversal

goodluck

Answer:

Nonlinar assosion

Step-by-step explanation:

Answer:

Its B

Step-by-step explanation:

The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached

The values of the constants in the sinusoidal function, h = a + b·(c·t) are;

a = 30

b = -20

c = π/1.5

A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.

The diameter of the Ferris wheel = 40 m

The location of the axle above the ground = 30 m

The time it takes to make a complete a rotation = 3 minutes

The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;

h = a + b·cos(c·t)

The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.

Therefore;

At t = 0, h = 30 - 40/2 = 10

h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b

a + b = 10

Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;

a = 30

a + b = 10, therefore;

b = 10 - a

b = 10 - 30 = -20

b = -20

At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50

50 = a + b·cos(1.5·c)

50 = 30 - 20 × cos(1.5·c)

20 × cos(1.5·c) = 30 - 50 = -20

cos(1.5·c) = -1

cos(π) = -1

Therefore; 1.5·c = π

c = π/1.5

The equation is therefore;

h = 30 - 20·cos((π/1.5)·t)

a = 30, b = -20, c = π/1.5

Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel

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Answer:

2 x 13 x 9 = 234 cm3 is your answer.

Step-by-step explanation:

Whenever given 3 side lengths of a rectangular prism you ALWAYS have to multiply those in order to get the volume..

Answer:

B

Step-by-step explanation:

Answer:

1. So $7 per hour

For 24 hour =7×24= $168

28-24=4

4×7=28

168+28=$196

or

For 28 hour

7×28

= $196

2. 7×112

=$784

3. To find the difference subtract

784-196=$588

Answer:

196; 784; 588

Step-by-step explanation:

Function 3x²+24x-6 does not belong with the other three

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the option we have to simplify each function

a. f(x)=3x²+6x-24

b. f(x)=3x²+24x-6

c. f(x)=3(x-2)(x+4)

=3(x²+4x-2x-8)

=3x²+6x-24

d. f(x)=3(x+1)²-27

3(x²+1+2x)-27

3x²+3+6x-27

3x²+6x-24

So function 3x²+24x-6 does not belong with the other three

Hence, function 3x²+24x-6 does not belong with the other three

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Answer:

Median

Step-by-step explanation:

Mean: Add up all the numbers, then divide by how many numbers there are.

Median: Arrange your numbers in numerical order. Count how many numbers you have. Go to the number in that position and average it with the number in the next higher position to get the median.

Mode: Put the numbers in order from least to greatest and count how many times each number occurs.

Range: The difference between the smallest and highest numbers

Answer:

Mean:

[tex]mean = \frac{(45 + 39 + 49 + 37 + 3 + 51)}{6} \\ = 37.3[/tex]

Median:

[tex]3 \: \: 37 \: \: 39 \: \: 45 \: \: 49 \: \: 51 \\ median = ( \frac{n}{2} + 1) {}^{th} \\ = ( \frac{6}{2} + 1) {}^{th} \\ = 4 {}^{th} \: value \\ median = 45[/tex]

Mode:

[tex]mode = none \\ all \: digits \: are \: repeated \: once[/tex]

Range:

[tex]range = 51 - 3 \\ = 48[/tex]

Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

The result of the operation between two mixed numbers are listed below:

Mixed numbers are real numbers with special notation to transform improper fractions into a combination of integers and fractions. That is:

a b / c = a + b / c

Where a, b, c are integers and c is a non-zero number.

The procedure to simplify the operation is described below:

Case 1

1 3 / 8 ÷ 1 4 / 9

(1 + 3 / 8) ÷ (1 + 4 / 9)

(11 / 8) ÷ (13 / 9)

(11 / 8) / (13 / 9)

99 / 104

Case 2

2 1 / 3 ÷ 1 3 / 4

(2 + 1 / 3) ÷ (1 + 3 / 4)

(7 / 3) ÷ (7 / 4)

(7 / 3) / (7 / 4)

28 / 21

4 / 3

Case 3

4 1 / 5 ÷ 3 1 / 2

(4 + 1 / 5) ÷ (3 + 1 / 2)

(21 / 5) ÷ (7 / 2)

42 / 35

6 / 5

Case 4

5 1 / 5 ÷ 2 1 / 2

(5 + 1 / 5) ÷ (2 + 1 / 2)

(26 / 5) ÷ (5 / 2)

(26 / 5) / (5 / 2)

52 / 25

Case 5

9 1 / 2 ÷ 9 4 / 6

(9 + 1 / 2) ÷ (9 + 4 / 6)

(19 / 2) ÷ (58 / 6)

114 / 106

57 / 53

Case 6

2 2 / 10 ÷ 6 2 / 3

(2 + 2 / 10) ÷ (6 + 2 / 3)

(22 / 10) ÷ (20 / 3)

(22 / 10) / (20 / 3)

(66 / 200)

33 / 100

Case 7

2 1 / 4 ÷ 4 1 / 2

(2 + 1 / 4) ÷ (4 + 1 / 2)

(9 / 4) ÷ (9 / 2)

(9 / 4) / (9 / 2)

18 / 36

1 / 2

Case 8

2 2 / 3 ÷ 1 2 / 3

(2 + 2 / 3) ÷ (1 + 2 / 3)

(8 / 3) ÷ (5 / 3)

(8 / 3) / (5 / 3)

8 / 5

Case 9

5 3 / 5 ÷ 1 2 / 5

(5 + 3 / 5) ÷ (1 + 2 / 5)

(28 / 5) ÷ (7 / 5)

(28 / 5) / (7 / 5)

28 / 7

4

Case 10

4 2 / 3 ÷ 3 1 / 2

(4 + 2 / 3) ÷ (3 + 1 / 2)

(14 / 3) ÷ (7 / 2)

(14 / 3) / (7 / 2)

28 / 21

4 / 3

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The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.

It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Consequently, it follows that the greatest possible quotient as required is; 25.

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Answer:

Length and Width

Plotting method is the graphical representation of mathematical expression.

A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.

At first, we need to choose the coordinate system by which we plot the point.

suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.

besides, we need to determine the required value that will be plotted on the plan.

if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.

we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.

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The lower left-hand corner of the graph is the third quadrant.

It contains the negative values of both x and y.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.

Cartesian system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

coordinates

Coordinates are numbers which determine the position of a point or a shape in a particular space.

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Answer:y=1.19x

Step-by-step explanation: Since each pound of tomato costs 1.19, you multiple the price by the amount of pounds to get the total cost.

Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).

Let the given points be,

A = (3, 2), B = (-2, -3) and C = (2, 3)

The formula for the distance between two points:

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 [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].

Therefore,

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)

[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex]  units

B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex]  units

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex]  units

By using the Pythagorean theorem:

According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Now, we can see that,

[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]

[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]

Therefore, the given triangle is a right angled triangle.

Therefore, option(A) s correct.

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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

A. right triangle

B. equilateral triangle

C. isosceles triangle

D. none of these

7 gallons of 76% solution contain 0.76×(7 gal) = 5.32 gal of sugar

10 gal of c% solution (c for concentration) contain c/100×(10 gal) = c/10 gal of sugar

(for example, if you have 10 gal of 50% solution, then it contains 50/10 = 5 gal of sugar)

Mixing the two gives a new solution with a total volume of 17 gal. If its concentration ends up at 64%, then it must contain 0.64×(17 gal) = 10.88 gal of sugar. This means

(sugar in 76% solution) + (sugar in c% solution) = 10.88 gal

5.32 gal + c/10 gal = 10.88 gal

c/10 gal = 5.56 gal

c = 50.56 ≈ 51

which makes the answer A.

Answer:

d. 56

Equation:

Let x = the percent of the 10 gallon sugar solution

10x + 76(7) = 64(10 + 7)

10x + 532 = 1088

10x = 1088 - 532

10x/10 = 556/10

x = 55.6

55.6 is closest to 56, therefore, the answer is 56%

Answer:

28 cm^2

Step-by-step explanation:

a^+21^2=36^2

a^2+441=1225

a=28

Answer:

7

Step-by-step explanation:

So first you substitute A in

15-|-4(2)|

Then you multiply first because of GEMDAS or PEMDAS

15-|-8|

And because absolute value means how far away it is from 0, -8 is 8 away from 0 , thus |-8| is 8. So we simplify the equation

15-8

=7

Answer:

12.25

Step-by-step explanation:

Solution for What is 35 percent of 35:

35 percent *35 =

( 35:100)*35 =

( 35*35):100 =

1225:100 = 12.25

Now we have: 35 percent of 35 = 12.25

Question: What is 35 percent of 35?

Percentage solution with steps:

Step 1: Our output value is 35.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 35 = 100%

Step 4: Similarly, x = 35%

Step 5: This results in a pair of simple equations:

35 = 100% (2)

x = 35% (2)

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both equations have the same unit (%); we have

[tex]\frac{35}{x} =\frac{100}{35}[/tex] (with % for 100 and 35)

Step 7: Again, the reciprocal of both sides gives

[tex]\frac{x}{35} =\frac{35}{100}[/tex]

⇒ x=12.25

Therefore, 35% of 35  is 12.25

Answer:

a= -2,3*4,-1

b=u

c=w

Step-by-step explanation:

The volume of the pyramid as calculated from the data given is found to be as 21.33 cubic units .

The distance from a corner to the center is 8 , and from the corner to the top of the pyramid is 8, because it is given that the tringles are equilateral.

so the height becomes,

√3a/2 = 4√3

The area of the hexagon is calculated using the formula ,

=3√3/2 x a²

=3√3/2 x 64

= 963√3

=332.553 square units.

Volume of a pyramid is calculated as ,

1/3 x base x height

= 1/ 3 x 8 x 8

= 1/3 x 64

=21.33 cubic units answer.

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