John has taken six quizzes in his statistics class. His
scores on these quizzes are listed below.
71, 75, 76, 80, 85, 87
He finds that the mean is 79.0 and the median is 78.0
for these six quiz scores. If John earns a 100% on the
next exam, what will the new mean and median be?
O The new mean will be 82.0 and the new median will
be 78.0.
O The new mean will be 82.0 and the new median will
be 80.0.
O The new mean will be 89.5 and the new median will
be 78.0.
O The new mean will be 89.5 and the new median will
be 80.0

The unit rate that corresponds to the proportional relationship shown in the graph is: 4/3 cm/s.

A proportional relationship is a mathematical relationship in which two variables are directly proportional to each other, meaning that the ratio of their values is always constant. The unit rate of a proportional relationship is the constant of proportionality, also known as the coefficient of proportionality. It is a number that relates the two variables in the relationship and it is also the slope of the line in the graph representation of the relationship.

For example, in a proportional relationship of y = kx, where y and x are the two variables and k is the constant of proportionality, the unit rate is k. It tells us how much y changes for each unit change in x. For example, if k=2, then for each increase of 1 in x, y will increase by 2.

Using a point on the graph, (12, 16):

Unit rate = y/x = 16/12 = 4/3 cm/s.

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The inequality to represent this situation is (11x+300)≤650

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

Here, given that,

The school marching band has a budget of up to $650.00 to cover 11 new uniforms.

and competition fees that total $300.00.

Let, the cost of each new uniform = $x

Then cost for 11 uniforms = $11x

i.e. total cost = $ (11x + 300)

hence, we get,

$(11x+300)≤$650

(11x+300)≤650

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Answer:

48x - 32

Step-by-step explanation:

8(6x-4)

We want to distribute the 8 to each term inside the parentheses

8 *6x - 8* 4

48x - 32

[tex] \longmapsto \: 8(6x - 4 )[/tex]

[tex] \longmapsto \: 48x - 32[/tex]

A represents the p region, B represents the (q∩p) region and C represents the q region.

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

Given is a Venn diagram,

Studying the Venn diagram, we get that,

A represents the region occupied by p, that means A is representing the region that belongs to p.

B is the region B includes the area which commonly lies both in p AND q at the same time that means B displays the region in which both p AND q.

C represents the region occupied by q, that means C is representing the region that belongs to q.

Hence, A's region is p, B's region is (q∩p) and C's region is q.

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Answer:kkkkkkk

Step-by-step explanation:

The 3 fraction models are the area model, which uses a shaded area to represent the fraction; the number line model, which uses a line to represent the fraction; and the set model, which uses a set of objects to represent the fraction.

1. Area Model: A visual representation of a fraction that shows a shaded area representing a whole, and the fraction is represented by the shaded area in relation to the whole.

2. Number Line Model: A visual representation of a fraction that uses a line to represent the whole, and the fraction is represented by a point on the line in relation to the whole.

3. Set Model: A visual representation of a fraction that uses a set of objects to represent the whole, and the fraction is represented by the number of objects in relation to the whole.

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The 3 fraction models are as follows;-

1- the area model- A visual representation of a fraction that shows a shaded area representing a whole, and the fraction is represented by the shaded area in relation to the whole.

2-the linear  model-A visual representation of a fraction that uses a line to represent the whole, and the fraction is represented by a point on the line in relation to the whole.

3- the set model- A visual representation of a fraction that uses a set of objects to represent the whole, and the fraction is represented by the number of objects in relation to the whole.

fraction model

A fraction bar model is where you draw a long rectangle and divide it into equal parts to show a fraction.

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Answer:

The first one is 1/5

Step-by-step explanation: because there are 5 sides and the second one is 50 feet

Answer:

calculate the perimeter of the circle base using C = 2πR. multiply this value by the cylinders height to get its lateral surface area A= 2πRH

Step-by-step explanation:

The correct statement regarding whether juniors and earbuds are independent events are given as follows:

Yes, because P(A|B) = P(A).

If two events are independent, the multiplication of the probabilities of each event is equals to the probability of both events, that is:

P(A and B) = P(A) x P(B).

The conditional probability formula is given as follows:

P(B|A) = P(A and B)/P(A).

Hence, for independent events, we have that:

P(B|A) = P(B).

And also:

P(A|B) = P(A).

A probability of an event is calculated as the division of the number of total outcomes by the number of desired outcomes.

Out of 32 students, 16 are juniors, hence the probability of a junior student is given as follows:

P(A) = 16/32 = 0.5.

Out of 8 students with earbuds, 4 are juniors, meaning that the conditional probability is given as follows:

P(A|B) = 4/8 = 0.5.

As the probability is equal, these two events are independent, and the first statement is correct.

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Answer:

A

Step-by-step explanation:

Answer:

she is going to make $408.90 in 18.2518.25 hours

Answer:

The correct inequality to represent this scenario is: C. 35 + 4x ≤ 75

Explanation: Penelope has a fixed fee of $35 to rent the kayak and an hourly fee of $4. To find the maximum number of hours she can rent the kayak, we need to find the value of x that makes the inequality 35 + 4x ≤ 75 true. In this inequality, 35 is the fixed fee and 4x represents the total cost of renting the kayak for x hours. To solve for x, we need to subtract 35 from both sides of the inequality to get 4x ≤ 40. Then, we need to divide both sides by 4 to get x ≤ 10. This means that Penelope can rent the kayak for a maximum of 10 hours.

Therefore , as a result, A = 84.3 sq unit is the answer to the pentagon presented challenge.

In geometry, a penta is a polygon having five sides. A simple pentagon's interior angles add up around 540°. It is possible to create simple or self-intersecting pentagons. A regular pentagon that intersects itself is a pentagram. A 2D polygon with five sides and 5 corners is called a pentagon. The English word "five" is derived from the Greek terms "gon" and "penta." The outcome of mixing the two syllables "Penta + Gon" is Pentagon.

Here,

The equation that is widely used to determine the area of the any regular hexagon that use the apothem or side is

Area for normal polygons = 1/2 perimeter the polygon apothem.

Thus ,area of pentagon

=> A = 1/4 * √5(5+2√5)

=>A  = 84.3 sq unit

Therefore , the solution of the given problem of pentagon comes out to be  A = 84.3 sq unit

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You can dilate a line centered at the origin by using its coordinates of origin.

Dilating a line centered at the origin is a useful tool in geometry. To do this, you need to first identify the coordinates of the origin, or (0,0). Then, you need to identify the equation of the line.

Once you have these two points, you can calculate the coordinates of the line when you multiply the equation by a certain number, which is known as the scale factor.

This scale factor will determine the amount of dilation that needs to be applied to the line. Finally, you can plot the new points on a graph and draw the line to see the new shape.

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g(-2)= -25

[tex]g(x)=-2x^2+7x-3\\\\g(-2)= -2(-2)^2+7(-2)-3\\g(-2)=-2(4)-14-3\\g(-2)=-8-17\\g(-2)=-25[/tex]

Plug in -2 into x and solve as shown above.

Based on the data above, what is the median number of grams of sugar in a chocolate cake at these bakeries is equal to: A. 108.

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

First of all, we would sort the number of grams from the least to greatest as follows:

87, 98, 106, 107, 108, 119, 134, 134, 135

Therefore, the median number of grams of sugar is equal to the middle number:

Median = 108.

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Complete Question:

A nutritional company analyzed the amount of sugar in a chocolate cake in nine different bakeries in Toledo. The values in the list below represent the number of grams of sugar in a chocolate cake at each of these bakeries. 134, 108, 106, 119, 134, 107, 135, 87, 98.

Based on the data above, what is the median number of grams of sugar in a chocolate cake at these bakeries?

108

110

111

114

134

The given statement opposite sides of a parallelogram are equal is true.

Proof,

We can see that RUTS is a parallelogram

here it is given that ,RU=TS and PQ = UT.

bringing the diagonal RT into scene we can see that,

∠URT = ∠STR

∠UTR=∠SRT

as these are the pairs of alternate angles.

RU || ST and PQ || UT

RT=TR  , being the common side.

Therefore,

ΔRUT ≅ ΔTSR

by AAS theorem

Hence , we can say that PQ=UT matches the sides of congruent triangles.

Therefore proved that the opposite sides of a parallelogram are equal.

A triangle can be proved congruent by using SAS , ASA, RHS or SSS, AAA etc congruency rules.

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False. The reason in line 2 of the proof would be "opposite angles of a parallelogram are equal. "

Given: rstu is rsqp

To prove: pq = ut

1. Draw a parallelogram with vertices r,s,q,p

2. Since rstu is rsqp, opposite angles of the parallelogram are equal

3. Therefore, by the property of a parallelogram, opposite sides of the parallelogram are equal

4. Thus, pq = ut

The reason in line 2 of the proof is that opposite angles of a parallelogram are equal, not opposite sides, which is the reason given in line 3.

False. The reason in line 2 of the proof would be "opposite angles of a parallelogram are equal. "

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Answer: any number that can divide by 4 so 4, 8, 12, 16 would all work

Step-by-step explanation: there are 4 groups each has somthing in it if you take everything out of all of the groups it will be divisible by 4 because they all have the same amount of things so any number divisible by 4 will work

Answer:

16 percent increase in the number of train passengers from 2010 to 2012.

The side length of one side of the square is 8n¹⁸

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

Area = 64 n Superscript 36square units

Express the area expression properly

So, we have the following representation

Area = 64n³⁶ square units

Take the square roots of both sides to calculate the side length

This gives

Side length = 8n¹⁸

Hence, the side length is 8n¹⁸

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The third side is the hypotenuse of a right angle triangle and the length is equal to 4.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

We shall represent the length of the third side with the letter x, such that by Pythagoras rule we evaluate for the hypotenuse as follows:

x² = 3² + (√7)²

x² = 9 + 7

x² = 16 {take square root of both sides}

x = √16

x = 4.

Therefore, the length of the third side which is also the hypotenuse is equal to 4 using the Pythagoras rule.

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The probability that three segments were chosen could form a triangle [tex]\frac{7}{20}[/tex] .

Using the probability concept, it is found that there is a  probability that the three segments selected could form a triangle.

The number of desired outcomes divided by the number of total outcomes is called probability.

In this problem, the order in which the sides of the segments are selected is not important, hence, the combination formula is used to find the number of total outcomes.

Combination formula:

[tex]C_{n.x}[/tex] is the number of different combinations of x objects from the set of n elements, given by:

            [tex]C_{n,x} = \frac{n !}{x ! ( n - x) !}[/tex]

Total outcomes:

Three segments from a set of six lengths, hence:

[tex]C_{6,3} = \frac{6 !}{3 ! 3 !} = 20[/tex]

Desired outcomes:

Then :

p = [tex]\frac{D}{T} = \frac{7}{20}[/tex]

 [tex]\frac{7}{20}[/tex] -the probability that the three segments selected could form a triangle.

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Answer:

200%

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8 cm}\underline{Percent change formula}\\\\$\rm Percent\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$\\ \end{minipage}}[/tex]

Given values:

Substitute the values into the percent change formula to find the percent increase in car sales:

[tex]\begin{aligned} \implies \textsf{percent change}&=\dfrac{450000-150000}{150000}\times 100\\\\&=\dfrac{300000}{150000}\times 100\\\\ &=2\times 100\\\\&=200\%\end{aligned}[/tex]

Therefore, the percent increase in car sales was 200%.

The average rate of change on the interval -1 ≤ x ≤ 4 for the equation y = x^2 + 4x + 1 is 13/5.

What is the rate of change?

The rate of change refers to how much a function's output (y) changes with respect to a change in its input (x).

To find the average rate of change on the interval -1 ≤ x ≤ 4 for the equation y = x^2 + 4x + 1, we can use the formula:

average rate of change = (y2 - y1) / (x2 - x1)

Where y2 and y1 are the function values at x2 and x1 respectively.

So, we have:

average rate of change = (f(4) - f(-1)) / (4 - (-1))

where f(4) = 4² + 44 + 1 = 17 and f(-1) = (-1)² + 4(-1) + 1 = 4

Therefore,

average rate of change = (17 - 4) / (4 - (-1)) = 13 / 5

Hence, The average rate of change on the interval -1 ≤ x ≤ 4 for the equation y = x^2 + 4x + 1 is 13/5.

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Therefore , the solution of the given problem of triangle comes out to be and MB or x = √106.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

Given :  A right triangle ,

=>  2√53 =  BH

=> MH = √106

∠m / ∠MHB = 45°

Using Pythagoras theorem :

=> ( 2√53)² = (√106)² + x²

=> 4 * 53 - 106 = x²

=> x² =  212 -106

=>  x = √106

Therefore , the solution of the given problem of triangle comes out to be

and MB or x = √106.

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Answer:

104 students

Step-by-step explanation:

This is an example of a proportion problem. However, its only 5 out of 8, we need it to say 65 out of x. We can solve this by multiplying both the top and bottom by 13. (Because to get 65 from 5, we need to multiply by 13)

5 bikes   x  13    =  65 bikes

____                          

8 students x 13 =  104 students

Answer: -4.2c+4.8d

Step-by-step explanation:

If i'm not missing anything this looks like a distributive property question.

Multiply the outside number by the inside numbers (with their variables)

So

-7c*0.6 = -4.2c

8d*0.6 =  4.8

so the answer is -4.2c+4.8d

Answer:

x = 2

Step-by-step explanation:

If ΔCAB≅ΔIPS, the PS=AB

11x + 6 = 4(2x + 3)

11x + 6 = 8x + 12

3x = 6

x = 6/3 = 2