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Answer:

Step-by-step explanation:= x+48=180 ( linier pair )

                                            = x=180-48

                                            = x=132

                                              = x+12=180 (liner pair)

                                              = x=180-12

                                              = x=168

Answer:1.25

Step-by-step explanation:

it just math

For the given numbers, 78 < 0. 708

To compare two numbers, we need to look at their values and determine which one is larger or smaller. In this case, we have 78 and 0.708. We can start by comparing their whole number parts, which are 78 and 0, respectively. Since 78 is greater than 0, we know that 78 is a larger number.

But what about the decimal parts of these numbers? To compare them, we need to look at the place value of each digit. The first digit after the decimal point in 78 is 0, and the first digit after the decimal point in 0.708 is 7. Since 7 is greater than 0, we know that 0.708 is a larger number than 0.78 in terms of their decimal parts.

Now that we have compared the whole number parts and decimal parts separately, we can combine the results to determine the final comparison. Since 78 is larger than 0 and 0.708 is larger than 0.78 in terms of their decimal parts, we can conclude that:

78 < 0.708

We use the symbol "<" here because 78 is smaller than 0.708.

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Answer:

Step-by-step explanation:

Change in Y/Change in X

5- -1/6- -2

5+1/6+2

6/8

3/4

Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters. 

Of all rectangles with an edge of 10 meters, the one that has the greatest zone(area) could be a square.

To see why, let's assume that a rectangle with a border of 10 meters has measurements of length L and width W.

At that point, we know that:

2L + 2W = 10

Rearranging this condition, we get:

L + W = 5

Presently, we need to discover the most extreme range encased by the rectangle, which is given by:

Area = L x W

Able to illuminate for one variable in terms of the other utilizing the condition L + W = 5:

L = 5 - W

Substituting this expression for L into the condition for the zone, we get:

Zone = (5 - W) x W

Extending and disentangling this expression, we get:

Area = 5W - W²

To discover the most extreme esteem of this quadratic expression, we will take its subsidiary with regard to W and set it to break even with zero:

dArea/dW = 5 - 2W =

Tackling for W, we get:

W = 2.5

Substituting this esteem back into the condition for the edge, we get:

L = 2.5

Hence, the measurements of the rectangle that has the greatest region are L = 2.5 meters and W = 2.5 meters, which implies it could be a square. The most extreme zone enclosed by the rectangle is:

Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters. 

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The expected profit if we assume that the contracts will be awarded independently is $44,400.

To calculate the expected profit, we'll multiply the profit from each contract by their respective probability and then sum the results.

Probability of getting the larger contract (P Larger) = 30% = 0.3

Profit from the larger contract (Profit Larger) = $60,000

Probability of getting the smaller contract (P Smaller) = 60% = 0.6

Profit from the smaller contract (Profit Smaller) = $20,000

Calculate the expected profit:

Expected Profit = (P Larger x Profit Larger) + (P Smaller x Profit Smaller) = $20,000 ) + (P Both x Profit Both) + (P None x Profit None)

Expected Profit = (0.3 x $60,000) + (0.6 x $20,000) + (0.18 x $80,000) + (0.28 x $0)

= $44,400

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No, the ratio of circumference to radius is not the same for every circle.

Ratio refers to the quantitative relation between two or more values, typically expressed in the form of a fraction or a proportion.

No, the ratio of circumference to radius is not the same for every circle. The ratio of circumference to diameter, also known as pi (π), is a constant value that remains the same for every circle. It is approximately equal to 3.14 or 22/7. However, the ratio of circumference to radius varies depending on the size of the circle.

The formula for circumference of a circle is C=2πr, where C is the circumference and r is the radius. Therefore, the ratio of circumference to radius is C/r = 2π. This means that for circles of different sizes, the ratio of circumference to radius will differ since the value of pi remains the same while the radius changes.

For example, if we consider two circles, one with a radius of 2 cm and the other with a radius of 4 cm, the ratio of circumference to radius for the first circle will be 2π (since C = 2πr = 2π x 2 = 4π) and for the second circle, it will be 2π (since C = 2πr = 2π x 4 = 8π). Thus, the ratio of circumference to radius is not the same for every circle.

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The length of PR of the triangle is 3√2 units

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The triangle PQR can be drawn as shown in the attached image. Thus, we can say:

sin 45° = 3/PR   (sine = opposite/hypotenuse)

1/√2 = 3/PR     (Remember: sin 45° = 1/√2)

PR = 3 * √2

PR = 3√2 units

Thus, the length of PR is 3√2 units

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To find the probability of drawing a face card or a red card, we first need to determine the total number of favorable outcomes and then divide it by the total number of possible outcomes (52 cards in a deck).

A face card can be a King, Queen, or Jack, and there are 12 face cards in a deck (3 face cards x 4 suits). There are 26 red cards in a deck (13 cards from hearts suit and 13 cards from diamonds suit). However, we must subtract the red face cards from the total, as they are already included in the 12 face cards. There are 6 red face cards (3 face cards x 2 red suits).

So, the total number of favorable outcomes is 12 face cards + 26 red cards - 6 red face cards = 32 cards.

The probability of drawing a face card or a red card is the number of favorable outcomes divided by the total number of possible outcomes: 32/52 ≈ 0.6154, or approximately 61.54%.

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The surface soil of the entire garden within the fencing that needs to be turned prior to planting is approximately 176.625 square feet.

To calculate the area of the circular garden, we need to know the radius of the garden. We can find the radius by using the formula for the circumference of a circle, which is

C = 2πr

Where C is the circumference and r is the radius.

In this problem, we are given that the circumference of the garden is 47.1 feet, so we can set up the equation as

47.1 = 2πr

Solving for r, we get

r = 47.1 / (2π)

r ≈ 7.5 feet

Now that we know the radius, we can calculate the area of the garden using the formula for the area of a circle, which is

A = πr²

Substituting the value we found for r, we get:

A = 3.14 × (7.5)²

A ≈ 176.625 square feet

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The probability that the sample mean would be greater than 87.78 wpm is  0.8933.

The problem  provides information on the mean and variation of the amount of words per minute (wpm) read by sixth graders, and it asks for the likelihood of receiving a sample mean wpm bigger than a particular value if a random sample of 94 sixth graders is collected.

By using a standard normal distribution table or calculator and estimating the sampling distribution of the sample means as being normal using the central limit theorem, we can find the standard deviation of the sampling distribution and calculate the probability of obtaining a sample mean wpm that is less than or equal to the given value by subtracting this value from 1.

Calculations result in a likelihood of 0.8933, which means there is a good chance the sample mean wpm will be higher than the value provided.

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Answer:

Step-by-step explanation:

we do not have enough information to calculate the margin of error, as we are missing values such as the sample mean, sample size, and population standard deviation.

Let's calculate the margin of error for the confidence interval and check if the value of  [tex]32.1[/tex] inches falls within the range.

Given:

Confidence interval: [tex](28, 32)[/tex] inches

Confidence level: [tex]80%[/tex]

Sample mean (x): Unknown

Sample size (n): Unknown

Population standard deviation (σ): Unknown

Belief: Population average height is  [tex]32.1[/tex] inches

To determine if [tex]32.1[/tex]  inches falls within the confidence interval, we need to calculate the margin of error (ME) for the confidence interval. The formula for the margin of error is:

ME = (Critical value) * (Standard deviation of the sample statistic)

Therefore, , we do not have enough information to calculate the margin of error, as we are missing values such as the sample mean, sample size, and population standard deviation.

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The total amount of money in the account at the end of 5 years, compounded monthly, is $2,329.48.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To find the total amount of money in the account, we can use the formula for compound interest:

A = [tex]P*(1 + r/n)^{(n*t)}[/tex]

where:

A is the total amount of money in the account

P is the principal or initial amount of money in the account

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

In this case, P = $2,000, r = 0.03 (since 3% is equivalent to 0.03), n = 12 (since the interest is compounded monthly), and t = 5.

So, plugging in the values, we get:

A = [tex]2000*(1 + 0.03/12)^{(125)}[/tex]

A = [tex]2000(1.0025)^{60}[/tex]

A = $2,329.48 (rounded to the nearest cent)

Therefore, the total amount of money in the account at the end of 5 years, compounded monthly, is $2,329.48.

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The only statement that is true is b, which states that the quadrilateral is a rectangle.

A quadrilateral is a polygon with four sides and four vertices. The sum of the interior angles of a quadrilateral is always 360 degrees. Quadrilaterals can have sides of different lengths and angles of different measures, giving rise to many different types of quadrilaterals with different properties.

First, we find the lengths of the sides of the quadrilateral:

AB = √[(7-6)² + (-1+4)²] = √10

BC = √[(4-7)² + (0-0)²] = 3

CD = √[(3-4)² + (-3+0)²] = √10

AD = √[(6-3)² + (-4+1)²] = √26

Then, we find the slopes of each pair of opposite sides:

AB: (7-6)/(−1+4) = 1/3

BC: (4-0)/(0-(-1)) = 4/1 = 4

CD: (-3-(-4))/(0-(-3)) = 1/3

AD: (6-3)/(-4-(-1)) = -1/5

Now we can analyze each statement:

a.) Rhombus

A rhombus is a quadrilateral with all sides of equal length. We found that AB = CD and AD ≠ BC, so not all sides are of equal length. Therefore, statement a is false.

b.) Rectangle

A rectangle is a quadrilateral with all angles equal to 90 degrees. We can find the slopes of adjacent sides and check if they are opposite reciprocals:

AB: 1/3

BC: 4

CD: 1/3

AD: -1/5

We can see that AB and CD have slopes of 1/3 and are opposite reciprocals, and BC and AD have slopes of 4 and -1/5, respectively, and are also opposite reciprocals. Therefore, all angles of the quadrilateral are 90 degrees. Also, since AB = CD and AD ≠ BC, the quadrilateral is a rectangle. Therefore, statement b is true.

c.) Square

A square is a special type of rectangle with all sides of equal length. We found that AB ≠ AD, so not all sides are of equal length. Therefore, statement c is false.

d.) None

We have determined that the quadrilateral is a rectangle, so it is not "none". Therefore, statement d is false.

Therefore, the only statement that is true is b, which states that the quadrilateral is a rectangle.

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To find the surface area of an object, we need to calculate the area of all its faces and add them up.

Assuming that "W" stands for the width, "l" for the length, and "h" for the height, the surface area of the object would be:

Area of the bottom face = length x width = 17' x 21' = 357 square feet

Area of the top face = same as the bottom face = 357 square feet

Area of the front and back faces = height x width = 19' x 17' = 323 square feet (each)

Area of the left and right faces = height x length = 19' x 21' = 399 square feet (each)

Therefore, the total surface area of the object would be:

357 + 357 + 323 + 323 + 399 + 399 = 2158 square feet.

So, the surface area of the object is 2158 square feet.

The maximum number of guests that Marshall can invite with a total budget cost of $81.90 is 63 guests.

Cost can refer to a variety of measures used to quantify the expense or effort required to solve a problem or perform a task.

For example, in optimization problems, the cost function represents a mathematical function that measures the objective or goal that needs to be minimized or maximized, subject to certain constraints.

First, we can find the cost per guest for the retirement party, which is $15.60 ÷ 12 guests = $1.30 per guest.

Next, we can use this unit rate to find the maximum number of guests that Marshall can invite with a total budget of $81.90:

Maximum number of guests = Total budget ÷ Cost per guest

Maximum number of guests = $81.90 ÷ $1.30 per guest

Maximum number of guests = 63 guests (rounded down to the nearest whole number)

Therefore, the maximum number of guests that Marshall can invite with a total budget of $81.90 is 63 guests.

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Answer:

Step-by-step explanation:

You want to know if the fractions (2 1/2)/(6.5) and (5/8)/(1 5/8) are in a proportional relationship, and the simplest form of each.

Equivalent fractions can be found by multiplying numerator and denominator by the same number.

  (2 1/2)/(6.5) = 2·(2 1/2)/(2·6.5) = 5/13

  (5/8)/(1 5/8) = 8(5/8)/(8·(1 5/8)) = 5/(8+5) = 5/13

Both fractions are equivalent to 5/13, so their relationship is proportional.

Answer:

The longer pole is approximately 55.4 ft tall

Step-by-step explanation:

Modeling the description will help you visualize and find the answer easier. By alternate interior angles theorem, the angle at the bottom (shown in picture below) is congruent to the angle of depression. Therefore, we can use tangent to find x.

tan 28=x/90

x=90*tan 28 (isolate the variable)

x is approx 47.9

to find the pole's height, you must add the shorter pole's height as well

h is approx 47.9+7.5

therefore, the longer pole's height is approx 55.4 ft tall

The correct statement is that a fairly strong negative linear relationship exists between the x and y variables.

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

In this case, the correlation coefficient is -0.88, which indicates a strong negative linear relationship between the x and y variables. This means that as the value of x increases, the value of y decreases in a predictable manner.

The negative sign of the correlation coefficient indicates that the relationship is negative, meaning that as one variable increases, the other variable tends to decrease. The absolute value of the correlation coefficient, 0.88, indicates a strong relationship, meaning that the values of the two variables are closely related and can be used to predict each other's values.

Therefore, the correct statement is that a fairly strong negative linear relationship exists between the x and y variables.

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The value of the angle is 10.81° ( nearest hundredth). ( optionA)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

The value of sin(tetha) = opposite/hypotenuse.

This means that if sin x = 3/16 , then 3 is the opposite and 16 is the hypotenuse. and the inverse of sin is sin^-1 . Same thing is applied to other functions like cos and tan.

If sinx = 3/16

sin x = 0.1875

x = sin^-1(0.1875)

x = 10.81° ( nearest hundredth)

therefore the missing value is 10.81°.

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The critical value of the chi-square distribution corresponding to a sample size of 5 and a confidence level of 98% is given as follows:

0.297 and 13.277.

To obtain a critical value, we need three parameters, given as follows:

Then, with the parameters, the critical value is found using a calculator.

The parameters for this problem are given as follows:

Using a chi-square distribution calculator, the critical values are given as follows:

0.297 and 13.277.

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D) 81 is equivalent to 27^(4/3).

The expression 27^4/3 can be simplified using the rule that (a^m)^n = a^(m*n). Therefore, we can write,

27^(4/3) = (3^3)^(4/3)

Using the power of a power rule, we can simplify further,

(3^3)^(4/3) = 3^(3*4/3)

Simplifying the exponent, we get,

3^(4)

To check the other answer choices,

A. 4^3 is not equivalent to 27^4/3.

B. (27^1/3)^4 is equivalent to 27^(4/3), which we already simplified to 3^4. Therefore, this expression is also equivalent to 3^4.

C. 3^1/4 is not equivalent to 27^4/3.

D. 81 is equivalent to 3^(4).

Therefore, the expression 27^4/3 is equivalent to 3^4, which is answer choice D) 81.

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The measure of the center is 19.

we can predict that about 169 principals

A pie chart shows how the whole is divided into parts

A bar graph with the title favorite sport and the x-axis labeled sport and the y-axis labeled the number of students,

the proportion of students in the sample who prefer ice cream:

81/225 = 0.36

we can predict that about 1440 students prefer ice cream.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

Answer to Question 2:

The appropriate measure of the center for the given box plot is the median, and its value is 19.

Answer to Question 5:

Since 15 out of 80 people in the exhibit room are principals, we can estimate that 15/80 of the total attendees are principals. To estimate the total number of attendees who are principals, we can multiply this fraction by the total number of attendees:

15/80 x 900 = 168.75

So, we can predict that about 169 principals were in attendance at the conference.

Answer to Question 6:

Since the teacher gathered data on the subject that students preferred, a pie chart would be the best graphical representation of the data. A pie chart shows how the whole is divided into parts, which is exactly what the teacher is trying to show.

Answer to Question 7:

A bar graph with the title favorite sport and the x-axis labeled sport and the y-axis labeled the number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44 correctly displays the data.

Answer to Question 8:

A circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent correctly represents the data in the table.

Answer to Question 9:

To estimate the number of students who prefer ice cream, we can use the proportion of students in the sample who prefer ice cream:

81/225 = 0.36

We can estimate the total number of students who prefer ice cream by multiplying this proportion by the total number of students:

0.36 x 4000 = 1440

So, we can predict that about 1440 students prefer ice cream.

Hence, the answers to all question are:

the measure of the center is 19.

we can predict that about 169 principals

A pie chart shows how the whole is divided into parts

A bar graph with the title favorite sport and the x-axis labeled sport and the y-axis labeled the number of students,

the proportion of students in the sample who prefer ice cream:

81/225 = 0.36

we can predict that about 1440 students prefer ice cream.

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A statement that represents a system of equations that could be used to determine the cost of a DVD and a CD, in dollars include the following: C. the system of equations is d = 3.2c and d = 5c - 8.50, for c, the cost of a CD, d, the cost of a DVD.

In order to write a system of linear equations to describe this situation, we would assign variables to the cost of a CD and cost of a DVD, and then translate the word problem into an algebraic equation (linear equations) as follows:

Since the cost of a DVD is 3.2 times the cost of a CD, or $8.50 less than 5 CDs, a system of linear equations that models the situation is given by;

d = 3.2c

d = 5c - 8.50.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The length from point A to point B on the clock is approximately 24.083 cm, which is closest to 24 cm. This is calculated using the Pythagorean theorem.

Using the Pythagorean theorem, we can calculate the length from point A to point B as follows

First, we need to find the length of the vertical line segment from point D to point A. This is equal to the radius of the clock, which is 24 cm.

Next, we can find the length of the horizontal line segment from point D to point B. This is equal to the distance from the top of the clock at point D to the hanger at point B, which is given as 2 cm.

Now, we can use the Pythagorean theorem to find the length from point A to point B

AB² = AD² + DB²

AB² = (24 cm)² + (2 cm)²

AB² = 576 cm² + 4 cm²

AB² = 580 cm²

AB ≈ 24.083 cm

Therefore, the length from point A to point B is approximately 24.083 cm, which is closest to 24 cm.

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Answer:

The length from point A to point B on the clock is approximately 24.083 cm, which is closest to 24 cm. This is calculated using the Pythagorean theorem.

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The probability that the golfer will hit at least 6 times in his next 10 attempts is A. 20 %

To estimate the probability of the golfer hitting at least 6 times in his next 10 attempts using a table of random numbers, we can perform a simulation.

Let's use the given table of random numbers to simulate 10 attempts for each trial. We can consider each pair of digits as one attempt. We will perform 10 trials and count how many times the golfer hits at least 6 times in 10 attempts.

Now count the number of trials with at least 6 hits:

Trial 2, Trial 5, and Trial 9 have at least 6 hits. That's 3 out of 10 trials.

To estimate the probability, divide the number of successful trials (at least 6 hits) by the total number of trials:

Probability = (Number of successful trials) / (Total number of trials)

Probability = 3 / 10 = 0.3

The estimated probability that the golfer will hit at least 6 times in his next 10 attempts is 30%. There is no exact match among the possible answers, but the closest one is 20%.

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The given statement "The radical expressions √2 and √12 can be combined to become one radical expression through addition or subtraction. " is true because a single radical expression that represents the two original expressions.

When we simplify a radical expression, we try to write it in its simplest form. For example, we know that √4 is equal to 2 because 2 multiplied by itself gives us 4. Similarly, we know that √9 is equal to 3 because 3 multiplied by itself gives us 9.

We can simplify radical expressions further by combining them using addition or subtraction. For example, √4 + √9 is equal to √13 because we can add 2 and 3 to get 5 and take the square root of 5 to get √5.

Now, let's look at √2 and √12. We can simplify √12 to √(4 × 3) because 4 is a perfect square. This gives us √4 × √3, which simplifies to 2√3.

Therefore, we can write √2 + √12 as √2 + 2√3. This is one radical expression that combines the two original expressions using addition. We can also subtract √12 from √2 to get √2 - 2√3, which is another radical expression that combines the two original expressions using subtraction.

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The mean is 120

The mode is 126
The median is 123
The range is 21

How to calculate the mean, mode, median and range?

Mean= 126 + 128 + 107 + 113 + 120 + 126/6

= 720/6

= 120

Mode= 126

Median= 120 + 126/2

= 246/2

= 123

Range= Highest-lowest

= 128-107

= 21

Hence the mean is 120, the mode is 126, the median is 123 and the range is 21

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