72° (x+4)° Write an equation that can be used to find the value of x.​

Answer: 162

Step-by-step explanation:

so you will have to do 62+28+75=162

15 member enjoy both dancing and hiking.

The likelihood of the preceding event is multiplied by the probability of the subsequent, or conditional, occurrence to determine the conditional probability. Conditional probability examines the likelihood that one event will occur given the likelihood that a related event will occur beforehand.

We have,

Member enjoy dancing, n(D) = 62

Member enjoy hiking, n(H) = 28

Member enjoy dancing or hiking, n(D ∪ H) = 62

Using Conditional probability

n (D ∪ H) = n(D) + n(H) - n (D ∩ H)

75 = 62 + 28 - n (D ∩ H)

75 - 90 = - n (D ∩ H)

n (D ∩ H) = 15

Thus, 15 member enjoy both dancing and hiking.

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The formula for the volume of a cylinder is:

V = πr^2h

where r is the radius and h is the height of the cylinder.

Substituting the given values, we get:

V = π(7^2)(13)

= 1274π

≈ 3993.87 cubic inches (rounded to the nearest hundredth)

Therefore, the volume of the cylinder is approximately 3993.87 cubic inches.

Answer:

19.25

Step-by-step explanation:

You add up all three sides which would be 10+3.25+6 to get the awnser 19.25

The set of inequalities that expresses the given relationships are -6 < -2 and -2 > -4. The correction is second option -6 < -2 and -2 > -4

From the question, we are to determine the set of inequalities that expresses the relationships

From the given information,

The given relationships are:

A score of -6 is lower than a score of -2. A score of -2 is higher than a score of -4.

First, we will write the first relationship as an inequality

A score of -6 is lower than a score of -2

This means that -6 is less than -2.

Using inequalities symbols, we can write that

-6 < -2

Now,

For the second relationship :

A score of -2 is higher than a score of -4

This means, -2 is greater than -4

Using inequalities symbols, we can write that

-2 > -4

Hence,

The inequalities that express the relationships are -6 < -2 and -2 > -4

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Answer:

Step-by-step explanation:

18

A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611

B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362

The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.

The formula for calculating the standard error of the mean is

SE = σ/√n

where SE is the standard error, σ is the population standard deviation, and n is the sample size.

For n = 30, SE = 4,000/√30 = 729.16

A. For a sample size of n = 60, SE = 4,000/√60 = 516.40

To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error.

For a range of +/- $500, the z-scores are

z = ($51,300 - $51,800) / 516.40 = -0.969

z = ($52,300 - $51,800) / 516.40 = 0.969

Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.

B. For a sample size of n = 120, SE = 4,000/√120 = 368.93

Following the same steps as above, the z-scores for a range of +/- $500 are

z = ($51,300 - $51,800) / 368.93 = -1.364

z = ($52,300 - $51,800) / 368.93 = 1.364

Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.

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We may infer from the box plots that Super Fast Food, with its smaller IQR, is better equipped to predict wait times than Burger Quick.answer is option (a).

When values are sorted in order of magnitude, the median, a measure of central tendency, is the middle value in the collection.

BX charts are a common approach to visually depict a distribution of data, such as wait times at a drive-through restaurant. The bx in a bx plot depicts the interquartile range (IQR), or the middle 50% of the data, with the bttm and tp of the bx standing in for the first quartile (25th percentile) and third quartile (75th percentile), respectively. A line inside the box represents the median, or the value that splits the data into equal halves.

Although the range, which is the difference between the data's highest and minimum values, can also be used as a consistency indicator, its accuracy is lower than that of the IQR due to its sensitivity to extreme values and outliers. In this instance, Burger Quick's range is 30 - 2 = 28 minutes, while Super Fast Food's range is 27 - 3 = 24 minutes. Despite the fact that the range for Super Fast Food is narrower, it is still unreliable as a measure of consistency since it is significantly impacted by the outlier at 27 minutes, which is considerably outside the range of the data.

We may therefore deduce from the box plots that Super Fast Food, due to its smaller IQR, is able to estimate their wait time more reliably than Burger Quick.

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The complete question is,

The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.

Which drive-thru is able to estimate their wait time more consistently and why?

Burger Quick, because it has a smaller IQR

Burger Quick, because it has a smaller range

Super Fast Food, because it has a smaller IQR

Super Fast Food, because it has a smaller range

Answer:

a=60 (12*5=60)

b=7 (45/9=5 5+2=7)

c=62

d=25 (11*5=55 55-30=25)

a) A recurrence relation, aₙ = aₙ₋₂ + aₙ₋₃

is for the different signals that can be sent in n microseconds.

b) Initial conditions are a₀ = 0, a₁ = a₂ = 1

c) The number of messages sent in 12 microseconds are equal to 16.

A recurrence relation is an equation form for nth term of a sequence of numbers which is equal to some combination of the previous terms. We have a messages are sent over a communications channel using two different signals. Let an be different number of messages that can be transmitted in n microseconds. In case of First signal, it required 2 microsecondes time to tramissmit the signals. So, the different number of signals that can be transmitted in 2 microseconds are [tex]a_{n - 2} [/tex]

In case of second signal , Time required by second signal to to transmit signal = 3

microsecondes

So, different number of messages that can be transmitted in 3 microseconds are

[tex]a_{n - 3} [/tex]

Each signal of a message is transmitted one by one.

a) A recurrence relation for the number of different signals that can be sent in n microseconds is written as

[tex]a_n = a_{n - 2} + a_{n - 3}[/tex]

hat is an us sum of different signals transmitted by each signals.

b) recurrence relation is

[tex]a_n = a_{n - 2} + a_{n - 3}[/tex]

so, the initial conditions of the recurrence relation in part (a) is n = 3 , [tex]a_3 = a_1 + a_0 [/tex]

a₀ = 0, a₁ = 1 , a₂ = 1

c) Different messages can be sent in 12 microseconds is determined by plugging the value in recurrence relation, a₃

= a₁ + a₀ = 1 + 0 = 1

a₄ = 1 + 1 = 2

a₅ = 1 + 1 = 2

a₆ = 2 + 1 = 3

a₇ = 2 + 2 = 4

a₈ = 3 + 2 =5

a₉= 4 + 3 = 7

a₁₀= 5 + 4 = 9

a ₁₁ = 7 + 5 = 12

a₁₂ = 9 + 7 = 16

Hence, required value is 16.

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Answer:

1. The parameter of interest is the proportion of students in the school who think of their parents or guardians as “strict”. A statistic that the students could use to estimate the parameter is the proportion of students in their sample who think of their parents or guardians as “strict”.

2. The best design for this study is a sample survey. An experiment would involve manipulating the parents' behavior and observing the effect on the students, which is not ethical. An observational study would only observe the behavior without manipulation, but it is not clear what behavior to observe in this case.

3. Here are three questions that could provide objective data related to strictness:

4. An appropriate method for obtaining a sample of 100 students is random sampling. The students could assign each student in the school a number, and then use a random number generator to select 100 numbers. They could then survey the students corresponding to those numbers. Another method could be stratified sampling, where the students divide the school into groups based on grade level, and then randomly sample a proportionate number of students from each group.

Answer:

60

Step-by-step explanation:

5x4x3=60 therefor you would get 60 3 digit numbers

Answer:

color cube

Step-by-step explanation:

To rewrite the equation of the circle in graphing form, we need to complete the square for both the x and y terms.

x² + 6x + y² - 4y = -9

Step 1: Move the constant term to the right side of the equation.

x² + 6x + y² - 4y + 9 = 0

Step 2: Group the x terms and the y terms separately.

(x² + 6x) + (y² - 4y) + 9 = 0

Step 3: Complete the square for the x terms. To do this, take half of the coefficient of x (which is 6), square it, and add and subtract it inside the parentheses.

(x² + 6x + 9 - 9) + (y² - 4y) + 9 = 0

(x + 3)² - 9 + (y² - 4y) + 9 = 0

(x + 3)² + (y² - 4y) = 0

Step 4: Complete the square for the y terms. To do this, take half of the coefficient of y (which is -4), square it, and add and subtract it inside the parentheses.

(x + 3)² + (y² - 4y + 4 - 4) = 0

(x + 3)² + (y - 2)² - 4 = 0

Step 5: Move the constant term to the right side of the equation.

(x + 3)² + (y - 2)² = 4

The equation is now in graphing form, which is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Comparing the equation to the graphing form, we see that the center of the circle is (-3, 2) and the radius is 2. Thus, the graph of the circle is centered at (-3, 2) with a radius of 2.

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After answering the presented question, we may conclude that  So the surface area of the ramp, including the front and sides, is 42 square feet.

The surface area of an object indicates the overall space occupied by its surface. The surface area of a three-dimensional form is the entire amount of space that surrounds it. The surface area of a three-dimensional form refers to its full surface area. By summing the areas of each face, the surface area of a cuboid with six rectangular faces may be computed. As an alternative, you may use the following formula to name the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total amount of space occupied by the surface of a three-dimensional object (a three-dimensional shape contains height, breadth, and depth).

To find the surface area of the ramp, we need to calculate the area of each face and add them up.

The front face is a rectangle with dimensions 6 ft by 4 ft, so its area is:

Area of front face = length * width = 6 ft * 4 ft = 24 ft²

The two side faces are right triangles with base 6 ft and height 3 ft. The area of each triangle is:

Area of one side face = 1/2 * base * height = 1/2 * 6 ft * 3 ft = 9 ft²

Since there are two side faces, the total area of the side faces is:

Area of side faces = 2 * Area of one side face = 2 * 9 ft² = 18 ft²

Therefore, the total surface area of the ramp is:

Surface area = Area of front face + Area of side faces = 24 ft² + 18 ft² = 42 ft²

So the surface area of the ramp, including the front and sides, is 42 square feet.

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Zip line B's total length requires 301 feet of cable using the distance between trees and change in height.

To determine the length of cable needed, we need to calculate the horizontal and vertical distances between the trees, and then apply the constraints.

Let's start by labeling the trees and their distances:

Tree 1: 120 ft from Tree 2, 150 ft from Tree 3

Tree 2: 140 ft from Tree 3

Zip line B is the longest, so calculate the length of cable needed for that option.

Horizontal distance: Tree 2 to Tree 3 is 140 ft.

Vertical distance: The starting platform needs to be 16 ft above the ground, and the harness hangs down 4 ft below the cable, plus an additional 3 ft for the rider's legs. So the total height difference is 16 + 4 + 3 = 23 ft.

Using the slope constraint, we want a vertical change of 6 to 8 feet for every 100 feet of horizontal change. For a horizontal distance of 140 ft, we want a vertical change of:

(6/100) x 140 = 8.4 ft

(8/100) x 140 = 11.2 ft

So the zip line needs to have a vertical drop of between 8.4 and 11.2 ft.

Using the slack constraint, we need to add 5% slack to the length of the cable:

140 ft x 1.05 = 147 ft

Adding 7 ft of extra cable at each end, the total length of cable needed is:

140 ft + 147 ft + 7 ft + 7 ft = 301 ft

Therefore, the total length of cable needed for Zip line B is 301 ft.

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Complete question:

Designing a Zip Line You and your friend Latisha work at the community center. You will be counselors at a summer camp for middle school students. The camp director has asked you and Latisha to design a zip line for students to ride while at camp. A zip line is a cable stretched between two points at different heights with an attached pulley and harness to carry a rider. Gravity moves the rider down the cable. The zip line will be secured to two trees. The camp has a level field with three suitable trees to choose from. All three trees are on level ground. • Tree 1 is 120 feet from Tree 2. • Tree 2 is 140 feet from Tree 3. • Tree 1 is 150 feet from Tree 3. Tree 2 Tree 3 Tree 1 120 ft 140 ft acer Tree 1 is 120 feet from Tree 2. • Tree 2 is 140 feet from Tree 3. Tree 1 is 150 feet from Tree 3. - Tree 2 Tree 3 Tree 1 120 ft 140 ft 150 ft There are three possible zip line locations: Zip line A between Tree 1 and Tree 2, Zip line B between Tree 2 and Tree 3, or Zip line C between Tree 1 and Tree 3. acer Tree 2 Tree 1 Tree 3 Zip line A Zip line 8 Zip linec A professional company will be hired to install the zip line. They will build platforms at the two trees used for starting and ending the zip line. The starting platform will require the cable to start at a height 16 feet above the ground You and Latisha researched how to build a zip line. There are four basic constraints for your design. • Slope Constraint: The slope of the zip line should be 6 to 8 feet of vertical change for every 100 feet of horizontal change. • Slack Constraint: The zip line should have a 5% slack in it. acer • Harness Constraint: The cable must be high enough that the rider, while buckled into the harnese dnes not touch the ground. • The harness hangs down 4 feet below the cable. • An additional 3 feet must be used to allow for a rider's legs to hang down below the harness. • Brake Constraint: A brake must be placed on the cable to ensure the rider does not hit the tree. A bungee cord connects the brake to an anchor in the ground. . The length of the bungee cord is 24 feet. • The bungee cord stretches to a maximum of 175% of its original length. Harness Constraint Brake Constraint Rider 4 ft Rider Brake 3 ft Harness Bungee cord Brake anchor acer Rider 4 ft Rider Brake 3 ft Harness Bungee cord Brake anchor Your task is to choose which zip line to build, Zip line A, Zip line B, or Zip line C, and to design this zip line within the given constraints. acer The camp director is ready to purchase the cable. Use the distance between the trees and the change in height of the cable to determine the length of cable needed. Be sure to include: • the required 5% slack in the line, and • 7 extra feet of cable at each end to wrap around each tree. Enter the total length, in feet, of cable needed.

The incorrect measurements of the right triangle is 36² + 60² = 48²

Given data ,

Let the triangle be represented as ABC

Now , let the height of the triangle be AB = 36 miles north

Let the base of the triangle be BC = 48 miles east

Now , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , 36² + 48² = 60²

So , the incorrect option from the data is 36² + 60² = 48²

Hence , the triangle is formed

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Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

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A good prediction for the number of times a 5 will be rolled out of 50 rolls of a 6-sided number cube is 8 times.

Assuming the number cube is fair and each outcome has an equal probability of occurring, we can use the concept of probability to make a prediction for the number of times a 5 will be rolled.

Since there are six possible outcomes, each with a probability of 1/6, the expected frequency of rolling a 5 in one roll is:

1/6 x 50 = 8.33

This means that if the number cube is rolled 50 times, we would expect to see a 5 appear approximately 8.33 times. However, since we cannot roll a fraction of a time, we need to round this number to the nearest whole number.

Rounding 8.33 to the nearest whole number, we get:

8

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Complete question is:

A 6-sided number cube with sides labeled 1,2,3,4,5, and 6 is rolled 50 times. What is a good prediction for the number of times a 5 will be rolled?

The simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.

To find the ratio of corydoras catfishes to the total number of fish, we need to add up the number of corydoras catfishes to the total number of fish, and express the ratio as a simplified fraction.

The total number of fish is 7 + 12 + 4 + 11 = 34.

The ratio of corydoras catfishes to the total number of fish is 9:34.

To simplify this ratio, we can divide both sides by the greatest common factor, which is 1 in this case.

So the simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.

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Answer:

152 cm, 161 cm, and 162 cm

Answer:

240 tickets sold

Step-by-step explanation:

first, you would set up the proportion by writing [tex]\frac{228}{95} =\frac{x}{100}[/tex]

with "x" being the number of seats that needs to be sold

then, you would cross multiply

and you get

[tex]95x=228*100[/tex]    next, you simplify to get the inequality [tex]95x=22800[/tex]

then divide both sides by 95

[tex]x=240[/tex]

so 240 tickets to fill all the seats

hope this helps ;)

Answer: 0.5

Step-by-step explanation:

1/2% is equal to 50 out of 100, or 50/100.

So you turn that into a decimal (fifty one hundredths).

0.50

You can get rid of the 0 at the end.

0.5

Hope this helps!!! :)

The length of wire per unit length is 8.168 cm.

Its function is to produce a regulated magnetic field through a coil twisted into a compact helix. The solenoid is a sort of electromagnet.

The magnetic field inside a solenoid is given by:

B = u*n*I

where B is the magnetic field, u is the permeability of free space, n is the number of turns per unit length, and I is the current.

The number of turns in a solenoid is given by:

N = n*L

where N is the total number of turns, L is the length of the solenoid, and n is the number of turns per unit length.

Therefore, the magnetic field can be written as:

B = u*N*I/L

Rearranging this equation, we get:

L = u*N*I/B

Substituting the given values, we get:

L = (4*pi*10⁻⁷)*(N=?) * (I=18.0 A) / (B=23.0 mT)

The number of turns per unit length is not given, so we cannot determine the total number of turns N. However, we can calculate the length of wire per unit length by using the formula for the circumference of a circle:

C = 2*pi*r

where r is the radius of the solenoid.

Substituting the given values, we get:

C = 2*pi*(d/2) = pi*d = 8.168 cm

Therefore, the length of wire per unit length is 8.168 cm.

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Answer: The outlier is 93 is an outlier. Since an outlier exists, median and IQR are the best measures of center and variation to represent this data set

The inequality to find the number of tablespoons of flour actually used in a recipe is |t - 48| <= 4. The correct answer is D.

Since the recipe calls for 3 cups of flour with a variation of up to 4 tablespoons, the total amount of flour used can vary between 3 cups - 4 tablespoons and 3 cups + 4 tablespoons. Converting tablespoons to cups, this becomes 3 cups - 1/4 cup and 3 cups + 1/4 cup.

Thus, the range of cups of flour used is [3 - 1/4, 3 + 1/4], which is [2.75, 3.25]. Multiplying by 16 to convert back to tablespoons, we get the range [44, 52].

So, the inequality that could be used to find the number of tablespoons of flour actually used in the recipe is

|t - 48| <= 4

where t is the number of tablespoons of flour used. So, the correct option is D).

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Matching of the equation will be:

A) x= -7

B) x= 3

C) x= 9

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

A) 3(x-5) = 2(x-11) has x= -7 as the solution.

B) 4(3x+7) -5 = 12x +8 has x= 3 as the solution.

C) 3(x+1) -2x = x+3 has x= 9 as the solution.

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A cone with a height of 9 in and a base diameter of 6 in has the volume 84.78 cubic inches.

The formula for the volume of a cone is:

V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius of the base and h is the height.

In the question it is given height = 9 in and a base diameter = 6 in.

Radius = diameter/2

r = d/2 = 6/2 = 3 inches

Substituting the values in the formula:

V = (1/3)π[tex](3\ in)^2[/tex](9 in)

Simplifying the expression:

V ≈ 84.78 [tex]in^3[/tex]

Rounding to the nearest hundredth, we get:

V ≈ 84.78 [tex]in^3[/tex]

Therefore, the approximate volume of the cone is 84.78 cubic inches.

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The standard deviation of the sampling distribution of the sample mean is 0.02.

The standard deviation of the sampling distribution of the sample mean can be calculated using the formula:

σ/√n

Where σ is the population standard deviation and n is the sample size.

In this case, the population standard deviation (σ) is 0.2 and the sample size (n) is 100. Substituting these values in the formula gives:

0.2/√100

Simplifying, we get:

0.2/10 = 0.02

This means that if we were to take multiple random samples of size 100 from the population, the mean of each sample would vary around the population mean of 3.2, with a standard deviation of 0.02.

This is because the standard deviation of the sampling distribution represents the amount of variation in sample means around the population mean.

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