Compare problems 1 and 2. What similarities do you see? What differences do you
notice?

(Algebra/geometry terms)

You must explicitly state that the null hypothesis is demonstrated to be true in cases where there is insufficient evidence to disprove it.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H₀

Even though we are unable to rule out the null hypothesis, this does not always imply that it is accurate. The reason for this is that a hypothesis test cannot tell which hypothesis is true or even which is more likely. It just evaluates whether there is sufficient evidence to disprove the null hypothesis.

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The equation to the parabola that passes through the points (0,4), (2,4) and (-2,8) is y = 6x+8.

A parabola is a mirror-symmetrical, nearly U-shaped planar curve in mathematics. It correlates to a multitude different statistical equations that appears to be superficially distinct and yet all define the exact same arcs. A point and a line are used in one definition of a parabola. the intersection of a right circular cone with a plane parallel to an element of the cone; a plane curve produced by a point moving so that its distance from a fixed point is equivalent to its length from a dedicated line. Anything resembling a bowl (such as an antenna or microphone reflector). A parabola graph shows a quadratic function as a U-shaped curve. A parabola is one of the conic sections in mathematics and is created by the intersection of a right circle .

y= ax²+ bx +c

Always begin with the coordinates which has 0 in it

(0,4)

4=a(0)² + b(0) + c

4=c

y = ax²+ bx + 4

The next set of coordinates (2,4)

4 = a(2)² + b(2) + 8

4 = 4a + 2b + 8

-4 = 4a + 2b

The other set of coordinates(-2,8)

8 = a(-2) + 2-2b +  8

0 = 4a-2b

Add the two above equations together...

0 = 8a

0 = a

Subtract the two equations from each other...

= 0 + 4b

24 = 4b

6 = b

y = 6x+8

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The value of d i.e. the diameter will be 8 inches when the circumference is 25.12 inches.

The distance a circle's circumference extends from one end to the other is known as the diameter.

The circumference of a circle is the distance of its outer length.

According to the formula, c = πd, c is the circumference of the circle and d is the diameter of the circle.

Value of π is 3.14

When c = 25.12 inches, the value of d will be

d = c/π

d = 25.12/3.14

d = 8 inches

The diameter will be 8 inches when circumference is 25.12 inches.

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Answer:

a) 0.25% b) 99.75%

Step-by-step explanation:

the chance that one bulb is defective is 0.05, so two bulbs being defective has a chance of 0.05 * 0.05 which equals 0.25%

For at least 1 bulb to work, both bulbs can't be broken. We already know that the chance for both bulbs being broke is 0.25%, so 100%-0.25% would equal the chance that at least one light bulb works, which is 99.75%

If a researcher uses u.s. census data to examine changes in the number of individuals in each racial group across states over time, she is using stratified sampling.

Samples may be classified as:

For this problem, we have that the population is divided into groups, according to their racial group, and then parts of the sample are surveyed, hence stratified sampling is used.

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if an organization wants to test whether a minority of its employees are dissatisfied with their bonuses, the null hypothesis would be that the true population proportion would be equal to 0.5

This is further explained below.

Generally, The null hypothesis is a common kind of statistical theory that proposes there is no statistical link and significance between two sets of observed data and measurable phenomena in a set of provided single observable variables.

In conclusion, In the event that a company is interested in determining whether or not a subset of its workers are unsatisfied with the incentives they get, the null hypothesis would state that the actual population percentage would be equal to fifty percent.

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CQ

If an organization wants to test whether a minority of its employees are dissatisfied with their bonuses, the nult hypothesis would be that the true population proportion would be: less than 5 OOOO greater than 5 not equal to 5 .5

The inequality representing the shaded region is given by 2y - x < 4.

For the given question, the graph is shown,

Consider two coordinates from the graph and find the slope using them.

(x₁, y₁) = (0, 2)

(x₂, y₂) = (4, 4)

slope m = (y₂ - y₁)/(x₂ - x₁)

Put the values.

m = (4 - 2)/(4 - 0)

m = 1/2

Put the value of slope in the equation of line in slope intercept form.

y - y₁ = m(x - x₁)

Put the values;

y - 2 = 1/2(x - 0)

Simplifying;

2y - 4 = x

2y - x = 4

Now, from the graph, as the origin of the coordinate axis and the shaded region region of the graph lies on the same side, the inequality is less than.

2y - x < 4, only less than as the graph is made with dotted lines.

Thus, the inequality representing the shaded region is given by 2y - x < 4.

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Answer:

==========================

Equation of surface area:

Substitute and calculate:

Equation of volume:

Substitute and calculate:

a. The equation of the perimeter is x + x + x + 2x + 2x = 42. Option A

b. x = 6 centimeters

c. The lengths are 6 centimeters , 6 centimeters , 6 centimeters  , 12 centimeters  and 12 centimeters respectively.

It is important to note that the formula for calculating the perimeter of a pentagon is expressed as;

Perimeter = 5a

Where: 'a' represents the length of one of its side

From the information given, we have that the perimeter of the geometrical figure is the sum of its sides.

Given the sides;

x , x , x, 2x , 2x

Now, substitute the values into the formula for perimeter

x + x + x + 2x + 2x = 42

collect like terms and add them

7x = 42

Now, make 'x' the subject of formula by dividing both sides by the coefficient of the variable 'x'

We have;

7x/7 == 42/7

x = 6 centimeters

But the length of the sides is determined by substituting the value of x as 6

x = 6 centimeters

x = 6 centimeters

x = 6 centimeters

2x = 2(6) = 12 centimeters

2x = 2(6) = 12 centimeters

Hence, the lengths are 6, 6, 6 , 12 and 12 centimeters respectively.

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Answer:

x =10

Step-by-step explanation:

Equation

-(2x + 5.9) +8.3 = 4+3(-x+ 2.8)             Carefully remove both sets of brackets

Solution

-2x - 5.9 + 8.3 = 4 + -3x + 8.4             Combine like terms on both sides

-2x + 2.4 = -3x + 12.4                           Add 3x to both sides

-2x+3x + 2.4 = -3x+3x + 12.4               Combine

x + 2.4 = 12.4                                        Subtract 2.4 from both sides

x + 2.4 - 2.4 = 12.4 - 2.4                       Combine

x = 10

Answer:

A straight line is represented by a linear equation.

The possible equations are:

\mathbf{3y = 2x + 4}3y=2x+4 .

\mathbf{y = \frac 23x + \frac{4}{3}}y=

3

2

x+

3

4

.

\mathbf{y = \frac 23(x - 1) + 2}y=

3

2

(x−1)+2 .

\mathbf{y = \frac 23(x - 4) + 4}y=

3

2

(x−4)+4

The points are given as:

\mathbf{(x,y) = \{(1,2),(4,4)\}}(x,y)={(1,2),(4,4)}

Start by calculating the slope (m)

\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}m=

x

2

−x

1

y

2

−y

1

So, we have:

\mathbf{m = \frac{4-2}{4-1}}m=

4−1

4−2

\mathbf{m = \frac{2}{3}}m=

3

2

The equation in slope intercept form is then calculated as:

\mathbf{y = m(x - x_1) + y_1}y=m(x−x

1

)+y

1

So, we have:

\mathbf{y = \frac 23(x - 1) + 2}y=

3

2

(x−1)+2

or

\mathbf{y = \frac 23(x - 4) + 4}y=

3

2

(x−4)+4

Expand \mathbf{y = \frac 23(x - 1) + 2}y=

3

2

(x−1)+2

\mathbf{y = \frac 23x - \frac 23 + 2}y=

3

2

x−

3

2

+2

Take LCM

\mathbf{y = \frac 23x + \frac{-2 + 6}{3}}y=

3

2

x+

3

−2+6

\mathbf{y = \frac 23x + \frac{4}{3}}y=

3

2

x+

3

4

Multiply through by 3

\mathbf{3y = 2x + 4}3y=2x+4

So, the possible equations are:

\mathbf{3y = 2x + 4}3y=2x+4 .

\mathbf{y = \frac 23x + \frac{4}{3}}y=

3

2

x+

3

4

.

\mathbf{y = \frac 23(x - 1) + 2}y=

3

2

(x−1)+2 .

\mathbf{y = \frac 23(x - 4) + 4}y=

3

2

(x−4)+4

Graph is plotted below.

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x, y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line. A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Coordinates are:

(-6,-8)

(1,--8)

(10,-8)

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Answer: The value of f/5 is 4.

Step-by-step explanation:  This question can be solved by using substituting the value of f( which is 20) in the earlier given expression ( which is f/5).

Here are the steps to solve this question:-

Step 1. Expression = f/5 ( according to the question)

Step 2. Value of f=20 ( according to the question)

Step 3. Using the value of f in step 2 in the equation given in step 1,

                        f/5=20/5

                         f/5=4

Thus, the value of expression f/5 is 4.

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Answer:

m= 3

Step-by-step explanation:

In the slope-intercept form (y= mx +c), the coefficient of x (when the coefficient of y is 1) is the slope.

y= x +5

Slope of line= 1

Parallel lines have the same slope, hence the slope of 3y -mx +3= 0 is also equal to 1.

Let's rewrite the equation into slope-intercept form.

Keep the y term on the left-hand side, bring the others to the right.

3y= mx -3

Divide both sides by 3:

[tex]y = \frac{m}{3} x - 1[/tex]

Given that the slope is 1,

[tex] \frac{m}{3} = 1[/tex]

Multiply both sides by 3:

m= 1(3)

m= 3

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Answer:

b = 64°

Step-by-step explanation:

The sum of interior angles of a polygon is 180°(n - 2), where "n" is number of sides.

~~~~~~~~~~

180°(6 - 2) = 720°

114° + (b + 49°) + (2b - 25°) + 142° + (b + 39°) + (3b - 47°) = 720°

7b + (114° + 49° - 25° + 142° + 39° - 47°) = 720°

7b + 272° = 720°

7b = 448°

b = 64°

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient so equation of line is y = -3x + c.

Substitute (1,7) into the equation to find c.

7 = -3(1) + c

c = 10

Hence equation of line is y = -3x + 10

The polynomial that represents the volume of the rectangular box is 3x² - x - 24 = 0

The dimension of the rectangular box are 9 inches, 8 inches and 3 inches.

The volume of the rectangular box can be expressed as follows:

volume of the rectangular box = l w h

where

Therefore,

w = x inches

l = 3x

h = 3x - 1

volume of the rectangular box = 72x

Therefore, the polynomial that represents the volume of the rectangular box is as follows:

72x = 3x × x × (3x - 1)

72x = 3x²(3x - 1)

72x = 9x³ - 3x²

9x³ - 3x² - 72x = 0

3x(3x²- x - 24) = 0

3x² - x - 24 = 0

Therefore,

x = 3 or - 8 / 3

we can only use positive values.

Hence, the dimension of the rectangular box is as follows:

w = 3 inches

l = 3(3) = 9 inches

h = 3(3) - 1 = 8 inches

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Answer:

y = 1.25x - 2.5

Step-by-step explanation:

To write the equation of a line in line in slope intercept form,

                  we can use y = mx + c

According to the question, writing the given equation in slope intercept form makes y the subject.

5x - 4y = 10

First, subtract 5x from both sides.

- 4y = 10 - 5x

Now, divide both sides by -4.

[tex]\frac{-4y}{-4}=\frac{10-5x}{-4} \\\\y = \frac{-5x}{-4}+\frac{10}{-4}\\\\y= 1.25x-2.5[/tex]

Step-by-step explanation:

1 f(x) = ax (x − a)² + 1

Take the derivative

f'(x) = d/dx ( a x( x -a) ²+1

Use differentiation rules

f' x = ax2 x-a +0

Simplify

= f'(x)=2ax-2a²

answer

The absolute value equation representing all numbers x whose distance from 8 is 6 units will be x = {2, 14).

Based on the information given, it should be noted that the distance of x, positive or negative from 8 can be expressed as |x - 8|.

Since the distance is equal to 6, our equation will be:

|x - 8| = 6

x = 8 + 6 = 14

or

- |x - 8| = 6

-x + 8 = 6

-x = 6 - 8

-x = -2

x = 2

Therefore, the appropriate equation is x = {2, 14).

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A Energy t = 54.70 min could it sustain a current.

What does energy mean according to science?

apply power  = energy/time  =  Vi

so energy  E    = vit

time t  =  E/vi

t  =  6400/(1.3* 1.5)

t  = 6400/1.95 sec

t  =  3282.05 sec

t = 54.70 min

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The number of terms of the second arithmetic progression is 46.

The two arithmetic progression have the same first and last terms.

The first arithmetic progression has 21 terms with a common difference of 9.

The second arithmetic progression have common difference of 4.

Therefore,

using the first arithmetic progression,

a + (n - 1)d = nth term

a + 20(9) = last term

last term = a + 180

using the second arithmetic progression,

a + (n - 1)d = nth term

They have the same last and first term,

Hence,

a + 180 = a + (n - 1)4

a + 180 = a + 4n - 4

180 + 4 = 4n

184 = 4n

n = 184 / 4

n = 46

Therefore, the number of terms is 46

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Answer: 7. 140°  8. 60°

Step-by-step explanation:

7.

A internal angle of a convex poligon is:

[tex]\displaystyle\\x=\frac{(n-2)180^0}{n} \\\\n=9\\\\So,\\\\x=\frac{(9-2)180^0}{9} \\\\x=7*20^0\\\\x=140^0[/tex]

8.

[tex]\displaystyle\\x=\frac{(n-2)180^0}{n} \\\\n=3\\\\So,\\\\x=\frac{(3-2)180^0}{3} \\\\x=1*60^0\\\\x=60^0[/tex]

The statements which best describes the value of the expression 18x – 35, when x = 2 is that the result is a whole number that is neither prime nor composite and is denoted as option D.

This is referred to as the number which is divided by one and itself and there must be exactly two numbers involved.

18x – 35 =  18(2) – 35

                = 36 - 35 = 1

In the case of 1, the numbers involved is just one which 1 which is why it isn't regarded as a prime number. A composite number can be formed with two small integers and the formation of 1 is 1 × 1 which is why 1 isn't.

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Answer:

The Answer Is: D.! The Results is A Whole Number That is Neither Prime nor Composite

Step-by-step explanation:

Hope This Helped! You Have a Great Day!

Answer: 60.96 pi or just 60 pi rounded to the nearest whole and the base is a circle , the shape is a cylinder

Step-by-step explanation:

Answer: x> -99/4

Step-by-step explanation:

−2/5x −9 < 9/10

Multiply Both Sides

-4x-90<9

Move the constant to the right

-4x < 9 + 90

Calculate

-4x < 90

Divide both sides

Answer x> -99/4

Answer:

1/4

Step-by-step explanation:

17/20, 14/20, 11/20, 8/20, 5/20

5/20 = 1/4