How many people Mark and Heather can invite to the party?

The value of x = 9 (back)

The value of x = 12 (orange)

The value of x = 8 (purple)

The value of x = 12.75 (green).

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

10 and 2x - 8 are parallel lines.

10 = 2x - 8

10 + 8 = 2x

18 = 2x

x = 9 (black)

7 and -17 + 2x are the two parts of a line separated by a midpoint.

7 = -17 + 2x

7 + 17 = 2x

2x = 24

x = 12 (orange)

7 and x + 15 are two parts of a line separated by a midpoint.

7 = x + 15

7 - 15 = x

x = 8 (purple)

m∠2 = 4x + 8

one angle = 45°

Other angle = 180 - 104 = 76°

The sum of the triangles is 180.

45 + 4x + 8 + 76 = 180

4x = 180 - 129

4x = 52

x = 12.75 (green)

Thus,

The value of x = 9 (back)

The value of x = 12 (orange)

The value of x = 8 (purple)

The value of x = 12.75 (green).

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A box-and-whisker plot which represents the given data is: B. A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.

In Mathematics, a boxplot is also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

By using an online box-and-whisker plot calculator, the five-number summary for the given data set include the following:

By critically observing the box-and-whisker plots (see attachment), we can logically deduce that boxplot A correctly represents the given data set.

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Complete Question:

Which box-and-whisker plot represents this data: 6,9, 13, 13, 18, 20, 24, 25, 26, 28, 30, 30?

By using slope intercept form of equation of line, the graph of

h(x) = [tex]-\frac{2}{5}x + 4[/tex] has been shown

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Let the independent variable be x and dependent variable be h(x)

The dependent variable decreases 2 units for every 5 units the independent variable increase.

Slope = [tex]-\frac{2}{5}[/tex]

So,

h(x) = [tex]-\frac{2}{5}x + c[/tex]

Now,

h(0) = 4

So, c = 4

h(x) = [tex]-\frac{2}{5}x + 4[/tex]

The graph has been attached here-

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The total surface area of the solid object is the sum of the surface area of the cylinder and the surface area of the cone.

The surface area of the cylinder is 2πr(r+h), where r is the radius of the cylinder and h is its height.

The surface area of the cone is πr(l+r), where r is the radius of the cone and l is its slant height.

Since the cylinder and the cone have the same radius, we can call this radius r.

The total surface area of the solid object is therefore 2πr(r+h) + πr(l+r).

We are told that this total surface area is equal to 6336/210 = 30 sq. cm.

Thus, we can set up the equation: 2πr(r+h) + πr(l+r) = 30.

We are trying to find the value of l, which is the slant height of the cone. We are given the value of h, which is the height of the cylinder. We can substitute this value into the equation to get:

2πr(r+30) + πr(l+r) = 30.

This equation can be rearranged and solved for l to find the slant height of the cone.

l = sqrt(900 - 60r).

Since we are given that the slant height of the cone is 26 cm, we can substitute this value into the equation to solve for the radius of the cone:

26 = sqrt(900 - 60r)

Solving for r, we find that the radius of the cone is 15 cm.

Substituting this value back into the equation for the slant height of the cone, we find that the height of the cone is:

l = sqrt(900 - 60(15)) = sqrt(300) = 17.67 cm.

Thus, the height of the cone is approximately 17.67 cm.

The area of the paper that remains is 375.04cm².

What is an area?

The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

We take it that the semicircles cover the full width of the paper.

So the radius is 16/2 = 8 cm

Since there are two of them, the area is full circle.

First, we find the area of the rectangle before the cuts were made.

Area = L * W

L = 36

W = 16

Area = 36×16 = 576 cm²

Now, we find the area of the circle cutouts.

r = 8

Area = pi * r²

Area = 3.14 * 8²

Area = 3.14 * 64

Area = 200.96cm²

Now, we find the total area left

Total Area Left = rectangle - circle

Total Area Left = 576 - 200.96

Total Area left = 375.04cm².

Hence,  the area of the paper that remains is 375.04cm².

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If  hose fills a hot tub at a rate of 3.49 gallons per minute. Then 1.64 hours will it take to fill a 343​-gallon hot​ tub

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

A hose fills a hot tub at a rate of 3.49 gallons per minute.

We need to find how many  hours will it take to fill a 343​-gallon hot​ tub

3.49/1=343/x

Apply cross multiplication

x=343/3.49

x=98.28 minutes

1 hr=60 minutes

So divide 98.28/60

1.64

Hence, it takes 1.64 hours to fill the hot tub.

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The current ratio and acid-test ratio for the business is 3.50 and 0.90.

What is Working Capital?

Working capital is a gauge of a company's liquidity. This is crucial because it aids the business in making decisions about its current assets and liabilities.

Current ratio = Current Assets / Current Liabilities

Current ratio = 460,500 / 131,500

Current ratio = 3.5 times

Quick ratio

Quick ratio = Quick Assets \ Current Liabilities

Quick ratio = 118,000 / 131,500

Quick ratio = 0.90

Cash 52,000

Short-term investments 12,000

Accounts receivable 54,000

Inventory 325,000

Prepaid expenses 17,500

Total Current Assets 460,500

Total Quick assets 118,000

Accounts payable 106,500

Other current payables 25,000

Total Current Liabilities 131,500

Quick assets include Cash, Short term investments and accounts receivables

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Answer:

67°

Step-by-step explanation:

Th sum of the interior angles of a triangle is 180.  Set the measurements of the three sides to 180 and solve for x.  Then substitute in the value for x in 4x  +11

4x + 11 + 2x + 1 + 7x -14 = 180  Combine like terms

13x - 2 = 180  Add 2 to both sides

13x = 182  Divide both sides by 13

x = 14

Plug this in for x

4x + 11

4(14) + 11

56 + 11

67

Answer:

4 6 8 10

Are the ans

Step-by-step explanation:

Plus 2 each time

The solution of linear equations in two variables gives the following results.

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Given:

Total number of tables in dining hall = 20 people

The number of people who can seat at long table = 10 people

The number of people who can seat at the round table = 10 people

According to the question, let’s assume a linear equation in two variables

number of long tables = x

number of round tables = y

⇒ x +y=20 ………… (1)

⇒10 x + 8 y=182 ………...(2)

Multiply equation (1) by 8 and subtract it from equation 2.

⇒ 10x+8y=182 ………… (2)

⇒ 8x+8 y=160 ………....(1)

⇒2x=22

⇒x=11

now put the value of x in equation (1) we get,

⇒11+y=20

⇒y=20-11

⇒y=9

Therefore, the number of long tables = 11

The number of round tables = 9  

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The ratio of Marcus's point to Scott's point will be = 1 : 2

According to the table given attached below,

We can find the ratio of the squares,

First, let us know about the definition of Ratio and Proportion.

The ratio is defined as the comparison between the two similar quantities

The fraction can also be represented as a ratio using the ' : ' sign

For example, let us consider two numbers a and b

In fraction, we could write it as = [tex]\frac{a}{b}[/tex]

Writing it as a ratio = a : b

According to the table given below,

Marcus's points = 7

Scott's points = 14

The ratio of Marcus's points to Scott's points = [tex]\frac{Marcus}{Scott}[/tex]

14 / 7

2 / 1

2 : 1

Therefore, The ratio of Marcus's point to Scott's point will be = 1 : 2

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The inverse of the expression represented as 12/(x-1) is (12/x) + 1

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

12/(x - 1)

The given parameter is an expression

Also, we can see that the above expression is a quotient expression

So, we start by expressing it as an equation

This is represented as

y = 12/(x - 1)

Swap/Switch the positions of the variables x and y

So, we have the following representation

x = 12(y - 1)

This gives

y - 1 = 12/x

Make y the subject

y = (12/x) + 1

Hence, the inverse is (12/x) + 1

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The distance traveled by train would be 300 miles.

What is the relation between speed, distance, and time?

You can use the equivalent formula d = rt which means distance equals rate times time. To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

A train travels for 3.75 hours at 80 miles per hour.

The distance traveled = speed * time

                                     = 3.75 * 80

                                     = 300 miles.

Hence, the distance traveled by train would be 300 miles.

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Probability that a card is chosen is not blue is 3/5

Probability means possibility.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.topic. One is the probability of every event in a sample space.

According to the probability formula, the likelihood that an event will occur is equal to the proportion of favorable outcomes to all outcomes.

probability that an event will occur P(E) = Number of favorable outcomes/Total Number of outcomes

Total number of cards in the box is 5+8+7=20 cards

Number of cards that are not not blue = 5 + 7 = 12 cards

Probability that a card is chosen is not blue = Number of favorable outcomes/Total Number of outcomes = 12/20 = 3/5

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Probability that a card is chosen is not blue is 3/5

What is Probability?

Probability means possibility. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. topic. One is the probability of every event in a sample space.

According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.
probability that an event will occur P(E) = Number of favorable outcomes/Total Number of outcomes
Total number of cards in the box is 5+8+7=20 cards
Number of cards that are not not blue = 5 + 7 = 12 cards
Probability that a card is chosen is not blue = Number of favorable outcomes/Total Number of outcomes = 12/20 = 3/5

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Answer:

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

The probability of getting a 10 or a jack from a deck of poker cards (52 cards) is 15.38%.

Probability is concerning about numerical description  

Is how likely is an event is occur or how likely it is true.

As per the given sequence -

there are four 10 cards and  four jack cards respectively

4+4=8

If you want to get one from the  52 cards, so it's 8 out of 52. 8/52

To calculate the percentage, you must  multiply 8 by 100, then divide by 52.

Thus,

8*100/52=15.38

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a) The null hypothesis is: [tex]H_0: p \leq 0[/tex]

b) The alternative hypothesis is: [tex]H_1: p > 0[/tex]

c) The test statistic is: z = 9.71.

d) The correct option is of: A. Yes.

e) The confidence interval is of: 0.0819 < p < 0.1336.

At the null hypothesis, it is tested if there is not enough evidence that the proportion for men is greater, that is, the subtraction is not greater than 0:

[tex]H_0: p \leq 0[/tex]

At the alternative hypothesis, it is tested if there is evidence that the proportion for men is greater, that is, if the subtraction is greater than 0, hence:

[tex]H_1: p > 0[/tex]

We have a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.01, hence the critical value is of:

z = 2.327.

Thus the decision rule regarding the test statistic is given as follows:

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the mean by the standard error of the sampling distribution of the difference of sample proportions, hence:

z = 0.1078/0.0111 = 9.71.

z > 2.327 -> enough evidence that the proportion is greater.

The confidence interval is obtained as the mean plus/minus the multiplication of the standard error and of the critical value.

Then the bounds of the interval are:

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Answer:x=$7.31

Step-by-step explanation:6lbs  

$12.90 x

6lbs x=($12.90 )(3.4 lbs)

6lbs x=43.86$lbs

6lbs x/6lbs=43.86$lbs/6lbs

The equivalent form of the compound inequality is -9>-x≥-10.

A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. It is when the solution sets for the various statements cross over or intersect. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true. It consists of the union or combination of the solution sets for the various statements. A conjunction is a compound inequality that contains the word "and." Even though "and" and "or" are considered to be conjunctions of speech, their meanings in mathematics are distinct from their grammatical counterparts. The conjunction (part of speech) "or"—when used to demonstrate this point—is whenever used in a compound inequality, it creates a disjunction, as the name suggests. Simply keep in mind that "con" stands for "with another" and "dis" for "one OR the other."

Given -33>-3x-6≥-36.

Dividing everything by 3 we get -11>-x-2≥-12.

Now adding to every side we get compound inequality as -9>-x≥-10.

The equivalent form of the compound inequality is -9>-x≥-10.

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Write this set of rational numbers from least to greatest -11 3/4, 7, -7, 13, -13:

Answer:

-13 , -11 , -7 , 3/4 , 7 , 13

a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0,-6) is y = -1/m * x - 6

b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2,-2) is y = -1/m * x - 2

what is intercepts?

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0, -6) can be written as:

                                    y = mx + b

  where m is the slope and b is the y-intercept.

Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-6).

Therefore, the equation of the line is y = -1/m * x - 6

b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2, -2) can be written as:

                                  y = mx + b

  where m is the slope and b is the y-intercept.

Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-2).

Therefore, the equation of the line is y = -1/m * x - 2

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Answer:

to much money to buy a car I try to work it down to 10k

Confidence interval for given data is (82.156,88.843)

The confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.

The alpha value determines the confidence level, which is the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.

general form of a confidence interval is: 

                              point estimate + Z SE (point estimate)

    Formula for confidence interval is given by

                                          [tex]X[/tex] ±  [tex]Z\frac{s}{\sqrt{n} }[/tex]

Where:

   X is the mean

   Z is the chosen Z-value from the table above

   s is the standard deviation

   n is the number of observations

In given ques

X = 85.5, Z=1.960, s =+ 12.3, n= 52

confidence interval = 85.5± (1.960×12.3/√52)

(82.156,88.843)

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Answer:

-12,-17

Step-by-step explanation:

Answer:

multiplication

Step-by-step explanation:

you multiply. I know this because I am in pre algebra right now and we learned about this again. If you are doing division then it’s the opposite same for subtraction as well as addition.

The plane is perpendicular to the axis but does not go through the vertex. The plane intersects the double cone at only the vertex is ellipse.

A planar curve that has two focal points is normally called an ellipse on the condition that at every point on the curve, it will be seen that the sum of the two distances from the focal points is constant. This generalizes the shape of a circle, which is a unique variety of an ellipse whereby the two focus points coincide.

The plane is said to not be intersecting with the vertex, not parallel to the axis nor perpendicular to the axis, then not parallel to the side of the cone, but it intersects only one cone is called a circle.

A circle is defined as a closed, two-dimensional object whereby every point in the plane is seen to be equally spaced from a central point. The line of reflection symmetry is seen to be formed by all lines that transverse the circle. Additionally, every angle has rotational symmetry around the center.

Thus, the conclusion is that the first two options are properties of an ellipse.

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Answer:

10.35 miles/hour

Step-by-step explanation:

Hence, Sam ran at the rate of 10.35 miles/hour .