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The stem plot for the given data is 3 4 5 6.

A stem and leaf plot, also known as a stem and leaf diagram, is a technique to arrange data such that it is simple to see how frequently certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

Arranging the given data in ascending order,

30, 34, 34, 35, 35, 36, 39, 39, 40, 40, 41, 42, 42, 43, 43, 43, 44, 46, 46, 48, 49, 49, 50, 52, 53, 58, 59, 61, 66, 68

The stem plot = 3 4 5 6

Calculated Statistics:

Minimum:30

Maximum:68

Range:38

Count:30

Sum:1365

Mean:45.5

Median:43

Mode:43

Standard Deviation:9.616

Variance:92.47

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Here acccording to the question,We are examining the conditions under which the sampling distributions of the sample proportions given.

Sampling distribution is a statistic that determines the probability of an event based on data from a small group within a large population. Its primary purpose is to establish representative results of small samples of a comparatively larger population. Since the population is too large to analyze, you can select a smaller group and repeatedly sample or analyze them. The gathered data, or statistic, is used to calculate the likely occurrence, or probability, of an event.

We are examining the conditions under which the sampling distributions of the sample proportions appear uniform, roughly normal, skewed to the left or skewed to the right.

When np10 and n(1p)10, where n is the sample size and p is the sample of proportions, are true, we know that the sampling proportions of the sample distributions will have a normal shape.

Aforementioned that our sample size is 300 people and that p = 0.45, we can use the given data to calculate

Successes anticipated: np= 300(0.45) = 135 10

Failures predicted: n(1p)=300 (10.45)=165 10

Since both of these statements are accurate, sample distribution sampling proportions will have a normal shape.

Because we anticipate each sample to have at least 10 successes and 10 failures, we have a normal sampling distribution.

As a result, the sample distribution has a roughly normal shape.

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Between the 100th and 400th kilometers, the average fuel consumption rate is 5/6 liters per kilometer.

A consequence of dividing the variation in a variable's function by the variation in the variable. For example The rate at which a distance changes in relation to time is known as velocity.

Given, Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.

Since in the domain [100, 400] graph shows somewhat linear properties.

from the graph Fuel consumption at 100 = 375 liters

Fuel consumption at 400 = 125 liters

rate in a linear function between two points = (y₂ - y₁)/ (x₂ - x₁)

thus rate between [100, 400] = (375-125)/400-100

rate between [100, 400]  = 250/300

rate between [100, 400] = 5/6litere per kilometer

therefore, the average fuel consumption rate, between the 100th kilometer and 400th kilometer is 5/6 liters per kilometer.

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The number of feet is dependent on the number of yards. The table is completed as shown in the attachment.

A variable whose value can be determined only if another variable's value is known is called a dependent variable. Thus the value of the variable depends on another variable.

In the given question, the number of feet can be known when that of yards is multiplied by a multiplicative factor. The value of the factor can be determined as;

multiplicative factor = 15/ 5

                                      = 3

So that feet is related to that of yards by this expression;

feet = multiplicative factor * yards

Thus,

when yards is 2, then;

feet = 3 * 2

       = 6

when feet = 12

12 = 3 * yards

yards = 12/ 3

         = 4

Thus the complete table is herewith attached to this answer for more clarifications.

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Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 - ∅), and cos = AB/AC = sin(90 - ∅).

The right triangle's angle serves as the domain input value for the six basic trigonometric operations, which produce a range of numbers as their results.Understanding the trigonometric functions of the four quadrants' graphs, domains, differentiation, and integration will be achievable.

Here,

Sinx = perp./hypo.

Cosx equals base/hypo.

So,

Sin = B/C

A= cos(90 -∅ ) = BC/AC

So,

Cos(90 -∅ ) = Sin(BC/AC)

And,

cos = AC/AB

AB/AC = sin(90 -∅ )

So,

cos AB/AC = sin (90 -∅ )

Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 -∅ ), and cos = AB/AC = sin(90 - ∅).

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Answer:2

Step-by-step explanation:

Answer:

Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.

Answer:

No, it is not a right triangle.

Step-by-step explanation:

Right triangle fulfill the pythagorean theorem:

[tex]a^2+ b^2 = c^2[/tex]

Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.

[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]

Linear equations are equations that can be written in the form ax + b = c, where a, b, and c are real numbers and a ≠ 0.

The equation can be solved for the variable x by subtracting b from both sides and then dividing both sides by a. This will give the solution for x, which is x = (c - b) / a.

For example, consider the equation 2x + 4 = 10. This is a linear equation since it can be written in the form ax + b = c, where a = 2, b = 4, and c = 10. To solve for x, subtract b from both sides to get 2x = 6, and then divide both sides by a to get x = 3. Therefore, the solution to the equation is x = 3.

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Explanation:

Pick any two points on the line to apply the slope formula.

I'll select (-5,1) and (5,-1)

[tex](x_1,y_1) = (-5,1) \text{ and } (x_2,y_2) = (5,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - 1}{5 - (-5)}\\\\m = \frac{-1 - 1}{5 + 5}\\\\m = \frac{-2}{10}\\\\m = -\frac{1}{5}\\\\[/tex]

The slope as a fraction is -1/5

A slope of -1/5 means " go down 1, then to the right 5 units".

An example of this motion is when going from (-5,1) to (0,0)

Another example would be going from (0,0) to (5,-1)

----------

The "down 1, right 5" motion is because

If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.

If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.

0.48 + 0.3 = 0.78.

In other words, there is a 78% probability of her not being late.

Answer:

Both x - 5, and 4x-5-3x are equivalent to (1/3x+2x−5/3x)−(−1/3x+5)

Step-by-step explanation:

Let's reorganize the given expression:

(1/3x+2x−5/3x)−(−1/3x+5)

1/3x+2x−5/3x + 1/3x-5       [Expand the parentheses]

2/3x+2x−5/3x -5       [Combine like terms]

-3/3x+2x -5

-x + 2x - 5

x - 5                       One of the equivalent expressions

The option 4x-5-3x also reduces to x - 5

Answer:

(-9,0)  and (1,0)

Step-by-step explanation:

The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)  is 2x+y = -2.

The line between these locations' slopes must equal the negative reciprocal of the bisector's slope. It must go through the segment midway.

The slope of the line through the given points :

m = (y2 -y1)/(x2 -x1) = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2

Then, The slope of the required bisector:   m = -1/(1/2) = -2

The midpoint of the given segment:

((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)

Then the point-slope form of the equation of the bisector:

y -y1 = m(x -x1)

y -2 = -2(x -(-2))

y = -2x -4 +2

y = -2x -2 . . . . . . . slope-intercept form equation

2x +y = -2 . . . . . . .standard form equation

Thus, The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)  is 2x+y = -2.

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The length of the shortest piece is 5, and the longest piece is 13 feet by solving the equations.

The length of the shortest piece is 5, and the longest piece is 13 feet.

the solution is as follows,

Greg has a piece of rope that is 18 ft long.

He wants to cut it into two pieces so that the longer piece is 2 ft less than three times the length of the.

Let the length of the shorter piece be x.

And the length of the longer piece is 3x -2.

Greg has a piece of rope that is 18 ft long.

Then,

longest piece+ shorter piece = 18

x + 3x -2 = 18

4x - 2 =18

4x = 18+2

4x = 20

x= 20/4

x = 5.

Therefore,

The length of the shorter piece is x =5.

And the length of the longer piece = 3x -2 = 3(5)-2 = 15-2 = 13

Hence, the length of the shortest piece is 5, and the longest piece is 13 feet.

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The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)

From the question, we have the following expression that can be used in our computation:

–3(2x – 5) < 5(2 – x)

Divide bot sides of the inequality by -1

So, we have the following representation

3(2x – 5) > -5(2 – x)

Next, we open the brackets

This gives

6x – 15 > -10 + 5x

Hence, the representation is 6x – 15 > -10 + 5x

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Complete question

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

(a) 6x – 15 > -10 + 5x

(b) 6x – 15 < -10 + 5x

(c) 3(2x – 5) > -5(2 – x)

(d) 3(2x – 5) < -5(2 – x)

Answer: D

Step-by-step explanation:

In this problem, we are asked to find the domain of the function. Domain is finding the interval of the function of the x value.

Since we are finding domain, we can eliminate A and B because those are looking at y interval, or range.

This leaves us with C and D. They are almost the same except for the ≤ in C and < in D. The difference between ≤ and < is the fact that ≤ includes and touches the point, and < doesn't.

The function has open circles at x=-3 and x=3. That means they don't touch and include x=-3 and x=3. The function only get's really close to those points, but not include them. This tells us that D is the answer.

The domain of the function is {x | −3 < x < 3}. Thus, Option D holds the truth.

The domain of a function refers to the interval of the x values of the function.

In this case, we are asked to find the domain of a linear function that is shown on a graph. The graph starts at an open circle at negative 3, negative 5 and ends at an open circle at 3, 7.

To find the domain, we need to look at the x interval of the function. Options A and B refer to the y interval or range and can be eliminated.

The remaining options, C and D, are similar, except for the fact that C includes and touches the point with "≤", while D doesn't with "<". The open circles at x=-3 and x=3 indicate that the function only gets close to these points, but does not include or touch them.

Thus, the correct answer is option D, {x | −3 < x < 3}.

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NA (There is not enough information given to determine the value of MZ)

In this question, we are given that WY is 4.6 for us to find the value of MZ We need more information to be in a position to answer this. More information includes maybe we know the value of M or at least having some relationship between WY and MZ for us to draw a conclusion and come up with the value of MZ. If at all we had a common value in WY and MZ say M then it could be easier to come to a conclusion and finally get the value of MZ.

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The measure of the angle ∠PQS will be 53°. Then the correct option is C.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

If angle ∠PQR measures 75°. And angle ∠PQS measures 22°.

Angle ∠SQR and angle ∠PQS are the adjacent angles. Then we have

∠PQS + ∠SQR = ∠PQR

∠PQS + 22° = 75°

∠PQS = 53°

The measure of the angle ∠PQS will be 53°. Then the correct option is C.

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Complete question is attached below.

The amount of money owned by JIm is $9

From the question, we have the following parameters that can be used in our computation:

The ratio of the amount owned by Tim tohe ratio of the amount owned by Jim is 6 : 1

This means that

Tim : Jim = 6 : 1

Also from the question, we have

Tim gets $54

This means that

Tim = 54

Substitute the known values in the above equation, so, we have the following representation

54 : Jim = 6 : 1

Multiply by 9

54 : Jim = 54 : 9

So, we have

Jim = 9

Hence, the amount is $9

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Answer:80

Step-by-step explanation:by5 will be this and 20 by 10 mulltiply 60 by 9

The degree of a polynomial is the highest power of each variable in the equation. In the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Therefore, the degree of this polynomial is 8.

1. Identify the highest power of each variable.

For 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z.

2. Add the highest powers of each variable.

2 + 3 + 4 = 9

3. Subtract 1 from the sum.

9 - 1 = 8

4. The degree of the polynomial is the result of the subtraction.

Therefore, the degree of the polynomial 7x2y3z4 is 8.

The degree of a polynomial is the highest power of each variable in the equation. To calculate the degree of a polynomial, you must identify the highest power of each variable and add them together. Then, subtract 1 from the sum to get the degree of the polynomial. For example, in the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Adding these powers together gives us 9. Subtracting 1 from this sum gives us 8, which is the degree of the polynomial. Therefore, the degree of the polynomial 7x2y3z4 is 8.

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The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works (independent variable) and the amount of money she earns (dependent variable).

The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works and the amount of money she earns. The number of hours worked is the independent variable because it is the variable that affects the amount of money earned. The amount of money earned is the dependent variable because this is the variable that is dependent on the number of hours worked.If she works 8 hours, she would earn $56.Jada earns $7 per hour, so if she works 3 hours, she would earn

$21 (3 x 7 = 21).

If she works 5 hours, she would earn

$35 (5 x 7 = 35).

If she works 8 hours, she would earn

$56 (8 x 7 = 56).

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The relationship between the input  and output  is that the perimeter of a square is always equal to four times the length of one of its sides.

The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S

1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.

2.Yes, the function can be represented with an equation. The equation would be:

Perimeter = 4 × Side Length.

Side Length (input) 1  2  3  4  5

Perimeter (output)  4 8 12 16 20

This equation states that the perimeter of a square is equal to four times the length of one of its sides.

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The various statements regarding the given scatter plot is checked and found to be true or false.

What is a scatter plot?

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.

1)The equation of the line is y = 2500x - 125.

From the graph we can take two points on the line,

( 2,2250) and ( 10,1250)

Standard equation of line is y = mx + b

where b is y - intercept and m is slope

m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125

From graph, b = 2500

Equation of line is

y = -125x + 2500

Therefore the given equation is false.

2) The group of hikers descends about 250 feet every minute.

      From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.

So the hikers descend 250 feet every minute.

Therefore the given statement is true.

3) The hikers began at the elevation of 2500 feet.

     The x-intercept of the graph is 2500 feet.

      So the beginning elevation is 2500 feet.

 Therefore the statement is true.

4) The graph shows a negative association.

Since the line in the graph is going down and the slope is negative, the graph shows a negative association.

Therefore the statement is true.

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The probability that the mean mpg for a random sample of 25 light vehicles is 0.042341

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

z = (x-μ)/σ/n, where

x is the raw score = 20 mpg

μ is the population mean = 21 mpg

σ is the population standard deviation = 2.9

n = random number of samples [tex]x < 20[/tex]

[tex]= z = 20 - 21/2.9/\sqrt{25} \\= z = -1/2.9/5\\= z = -1.72414\\[/tex]

P-value from Z-Table:

[tex]P(x < 20) = 0.042341[/tex]

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Answer:

--------------------------

Distributive Property is:

Apply it to the given expression:

The matching choice is C.

Answer:

[tex] \sf \: c) \: 30 - 6q[/tex]

Step-by-step explanation:

Given expression,

→ 6(5 - q)

Let's simplify the expression,

→ 6(5 - q)

→ 6(5) - 6(q)

→ (6 × 5) - (6 × q)

→ (30) - (6q)

→ 30 - 6q

Hence, option (c) is correct.

The transformation of the function is given by reflection along y axis and a translation of 5 units up

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the transformation be represented as A

Now , the equation will be

Let the triangle be represented as ΔODG

Now , the coordinates of ΔODG is

O = O ( -1 , -2 )

D = D ( -5 , -3 )

G = G ( -2 , -4 )

Now , the transformed triangle is ΔACT

The coordinates of ΔACT is

A = A ( 1 , 3 )

C = C ( 5 , 2 )

T = T ( 2 , 1 )

Now , on reflecting the triangle ΔODG along y axis , we get

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse

So , the coordinates of triangle O'D'G' , we get

O' = O' ( 1 , -2 )

D' = D' ( 5 , -3 )

G = G' ( 2 , -4 )

Now , translating the triangle ΔO'D'G' up by 5 units , we get

The y coordinate of the triangle gets incremented by 5

So ,

A = O' ( 1 , -2 + 5 )

C = C ( 5 , -3 + 5 )

T = T ( 2 , -4 + 5 )

And , the coordinates of the triangle ΔACT is

A = A ( 1 , 3 )

C = C ( 5 , 2 )

T = T ( 2 , 1 )

Hence , the transformation is reflection along y axis and followed by translation of 5 units up

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Answer:

5 hours

Step-by-step explanation:

Olivia needs to make 700 - 15 = <<700-15=685>>685 cupcakes.

So she needs to work for 685 / 137 = <<685/137=5>>5 hours

Answer:

4(3p - 7)

Step-by-step explanation:

First find the factors of 12 and 28:

12: 1, 2, 3, 4, 6, 12

28: 1, 2, 4, 7, 28

Notice any common factors: 1, 2, 4

Now, out of these factors, 4 is the GCF since it is the greatest common factor, so divide 12 and 28 by 4:

12/4 = 3.  28/4 = 7.

Hence, 12p-28 = 4(3p - 7)