Which solution set is graft on the number line

Answer:

Step-by-step explanation:

45000 x %22 = 9900 per year

9900/12=825 per month

The linear regression equation that represents this data set is equal to y = 120.8x + 2,114.

First of all, we would determine the slope of the given data set by using this formula:

[tex]Slope = \frac{\sum (x-\bar x)(y-\bar y)}{\sum (x-\bar x)^2}[/tex]

For the sample mean (years), we have:

[tex]\bar x = \frac{0\;+\;1+\;2\;+\;3\;+4}{5} \\\\\bar x =\frac{15}{4} \\\\\bar x =3.75[/tex]

For the sample mean (cases), we have:

[tex]\bar y = \frac{904\;+\;900+\;833\;+\;837\;+754}{5} \\\\\bar y =\frac{4,228}{4} \\\\\bar y =1057[/tex]

The sums are given by:

∑(x - |x|) = (0 - 3.75) + (1 - 3.75) + (2 - 3.75) + (3 - 3.75) + (4 - 3.75)

∑(x - |x|) = - 3.75 - 2.75 - 1.75 - 0.75) + 0.25

∑(x - |x|) = -8.75.

∑(x - |x|)² = (-8.75)² = 76.5625.

∑(y - |y|) = (904 - 1057) + (900 - 1057) + (833 - 1057) + (837 - 1057) + (754 - 1057)

∑(y - |y|) = -153 - 157 - 224 - 220 - 303

∑(y - |y|) = -1,057‬.

∑(x - |x|)(y - |y|) = -8.75 × -1057

∑(x - |x|)(y - |y|) = 9,248.75.

Now, we can determine the slope:

Slope = 9,248.75/76.5625

Slope = 120.8‬.

Therefore, the equation is given by:

y = 120.8x + a

Next, we would find the value of a:

1057 = 120.8(-8.75) + a

a = 1057 + 1,057

a = 2,114.

Hence, the linear regression model is given by:

y = 120.8x + 2,114.

Since the new cases would reach 579, the calendar year would be calculated as follows:

579 = 120.8x + 2,114

120.8x = 579 - 2,114

120.8x = -1,535

x = -1,535/120.8

x = -12.71.

Year = 2014 + 12.71

Year = 2026.71 ≈ 2027.

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Answer:

A

Step-by-step explanation:

if you say x=0 than y=2

if you say y=0 then x=2/5

you observe those values in the first graph

Answer:

Volume of the Earth is about 16.67 times bigger than Mercury's volume.

Step-by-step explanation:

Given:

[tex]V_E = 1 \times 10^{12} \text{ km}^3\\V_M = 6 \times 10^{10} \text{ km}^3[/tex]
[tex]V_E[/tex] is the volume of the Earth and [tex]V_M[/tex] is the volume of the Mercury.

Divide volume of the Earth with the volume of Mercury.

[tex]\frac{V_E}{V_M} = \frac{1 \times 10^{12} \text{ km}^3}{6 \times 10^{10} \text{ km}^3} = \frac{1 \times 10^{2}}{6} = \frac{100}{6} = \frac{50}{3} \approx 16.67[/tex]

Volume of the Earth is about 16.67 times bigger than Mercury's volume.

Answer:

Yes

Step-by-step explanation:

Natural numbers are positive integers such as 1, 2, 3, etc., (sometimes zero as well). As such, they are indeed whole numbers, so the statement is true.

The correct answer is option B which is the pool must have been the same depth at the start of the interval as it was at the end of the interval.

The rate of change is defined as the changes that occur in any data with respect to time like changing of level of water respect to time. Changing of the position of any object with respect to time that is speed.

Here in the question, it is given that Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. The meaning of this statement is that the level of the water in the pool is the same as that of the level two weeks ago.

Therefore the correct answer is option B which is the pool must have been the same depth at the start of the interval as it was at the end of the interval.

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Box and whisker plot has shown in the picture which shows different measures of the data set.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have data:

45, 51, 53, 55, 55, 65, 75, 81, 84, 87, 93, 93, 95, 96, 100

Sample size: 15

A  = (c) The Lowest value (45)

B = (e)Lower quartile Median (55)

C = (b) Median (81)

D = (d) Upper quartile (93)

E = (a) The Highest value (100)

Thus,  box and whisker plot has shown in the picture which shows different measures of the data set.

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Answer:

The answer is -2/3

Step-by-step explanation:

Multiply by the reciprocal:

7/3 / 1/4 x 2

Simplify expression:

7/3 x 4/7 -2

Calculate:

1/3 x 4 -2

4/3 - 2

= -2/3

Answer:

See below ~

Step-by-step explanation:

Question 18

Question 19

#1

Length of diameter

Length of radius=10/2=5

#2

Solution set

Answer:

Angle H is 133

Step-by-step explanation:

(h-48)+95=180

solve it and you will get 133

Answer:

133°

Step-by-step explanation:

from the diagram,

(h- 48)° +95°= 180° ( angles on a straight line)

h-48+95 = 180°

h+47 = 180

collect like terms

h = 180-47= 133°

Answer:

Step-by-step explanation:

Remove full rotations of [tex]2\pi[/tex]  until the angle is between 0 and [tex]2\pi[/tex].

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

The exact value of [tex]cos(\frac{\pi }{3})[/tex] is [tex]\frac{1}{2}[/tex].

[tex]\frac{1}{2}[/tex]

The result can be shown in multiple forms.

Exact Form:

[tex]\frac{1}{2}[/tex]

Decimal Form:

[tex]0.5[/tex]

Vocabulary:

Rotation

A transformation in which a figure is rotated through a given angle, about a point.

Angle

The union of two rays with a common endpoint, called the vertex.

Considering it's vertex, the quadratic equation that could be represented on the plane is given as follows:

f(x) = (x - 8)² - 6.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Researching the problem on the internet, it is found that the given graph has vertex at (8,-6), hence h = 8, k = -6 and considering a = 1 the equation is given as follows:

f(x) = (x - 8)² - 6.

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Answer:

24 because it is the middle number

Step-by-step explanation:

Answer:

slope =.25

Step-by-step explanation:

I assume this is asking to find the slope?

graph this equation and you'll see that the run is 16 and the rise is 4.

rise/run

4/16 = .25

Answer:

The right one is ........

Answer:

Yes

Step-by-step explanation:

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

Answer:

solution: (x,y)=(-2,8)

Step-by-step explanation:

1) 3x+3y=18

  2x+y=4

2) -x-y=-6

  2x+y=4

3) x=-2

4) 2x(-2)+y=4

5) y=8

6) (x,y)=(2,8)

and that is :D

Answer:

1. False

2. True

3. False (Not sure about this one)

4. True

5. False

Answer:

..........................

Based on the triangle inequality theorem, the possible length of the third side of the triangle is: 9 < x < 51

The triangle inequality theorem states if a and b are two sides of a triangle, the possible length of the third side would be: a + b < x < a - b.

Two given sides of the triangle are 30 ft and 21 ft. The possible length of the third side of the triangle would be:

30 - 21 < x < 30 + 21

9 < x < 51

Possible length of the third side would range between: 9 < x < 51

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Answer:

Step-by-step explanation:

Answer:

choice 2

Step-by-step explanation:

Arithmetic sequences arare linear. The common difference is the slope. The points given are (3,10) And (5,26).

The slope is the change of y (26-10=16) over the change of x (5-3=2); this is 16/2=8.

The equation of line in slope-intercept form whose slope is given as 8 is y=8x+b.

We may plug in a point to solve for b.

Let's plug in (3,10):

10=8(3)+b

10=24+b

10-24=b

-14=b

So the equation we are lookinlooking for is y=8x-14 which is choice 2.

Answer:

D

Step-by-step explanation:

Given :

Solving :

Hence :

Answer:

D. [tex]\huge 2x^2y\sqrt[5]{7xy^3}[/tex]

Step-by-step explanation:

Answer: 3π in terms of pi or 9.42 if in π or pi= 3.14

Step-by-step explanation:

The volume of the shaded part in cubic units is  4/3π(20)³ -  4/3π(4)³

The sphere is a a solid 3-dimensional object. THe formula for calculating its volume is expressed as:

V = 4/3πr³

where:

r is the radius of the sphere

For the outer sphere:

V = 4/3π(20)³

For the inner sphere:

V = 4/3π(4)³

The volume of the shaded part in cubic units is  4/3π(20)³ -  4/3π(4)³

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Answer:

D

Step-by-step explanation:

Answer:

a) 9 ft.

Step-by-step explanation:

The  bath and the tent along with their shadows and the ground make 2 similar  triangles. So:

4/6 = 6/x

4x = 36

x = 9 ft.

Answer:

88 m^2

Step-by-step explanation:

We can split the parallelogram into three shapes. 1 square and 2 triangles.

To find the area of a square, multiply one side by another side that does not face it. To find the area of a triangle, divide the base by half OR multiply the base by 0.5, and then multiply by the height.

Since these shapes are all pieces of the parallelogram, add together their total areas to get the area of the parallelogram.

Square: 7 x 8

Triangle: 0.5 x 4 x 8 or 4/2 x 8

(7 x 8) + 2 x (0.5 x 4 x 8)

56 + 2 x (2 x 8)

56 + 2 x 16

56 + 32

56 + 32 = 88 m^2