The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. Round the intermediate calculations for z value to 2 decimal places.
a. What is the probability of completing the exam in one hour or less (to 4 decimals)?
b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?
c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

Answers

Answer 1

a. Probability of completing the exam in one hour or less is 0.0228. b. Probability of completing the exam in more than 60 minutes but less than 75 minutes is 0.2857. c. About 10 students are expected to be unable to complete the exam in the allotted time.

a. To find the probability of completing the exam in one hour or less, we need to convert one hour (60 minutes) into a z-score using the formula:

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation. So, we have:

z = (60 - 80) / 10 = -2

Using a standard normal distribution table or a calculator, we find that the probability of a z-score being less than or equal to -2 is 0.0228 (to 4 decimals). Therefore, the probability of completing the exam in one hour or less is 0.0228.

b. To find the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes, we need to convert both values into z-scores:

z1 = (60 - 80) / 10 = -2

z2 = (75 - 80) / 10 = -0.5

Then, we can find the probability between these two z-scores using a standard normal distribution table or a calculator. The probability is:

P(-2 < z < -0.5) = P(z < -0.5) - P(z < -2)

= 0.3085 - 0.0228

= 0.2857 (to 4 decimals)

Therefore, the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes is 0.2857.

c. We know that the mean time to complete the exam is 80 minutes and the standard deviation is 10 minutes. To find the number of students who will be unable to complete the exam in the allotted time of 90 minutes, we need to find the number of students whose completion time is greater than 90 minutes.

We can convert 90 minutes into a z-score using the formula:

z = (x - μ) / σ = (90 - 80) / 10 = 1

Using a standard normal distribution table or a calculator, we find that the probability of a z-score being greater than 1 is 0.1587.

So, the proportion of students who will be unable to complete the exam in 90 minutes is 0.1587. To find the actual number of students, we can multiply this proportion by the total number of students:

0.1587 x 60 ≈ 9.52

Therefore, we can expect about 10 students to be unable to complete the exam in the allotted time.

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Related Questions

What are the solutions of this quadratic equation? x2 − 10x = -34

Answers

Answer:

The solutions of the quadratic equation x^2 - 10x = -34 are x = 5 + 3i and x = 5 - 3i.

Step-by-step explanation:

To solve the quadratic equation x^2 - 10x = -34, we can rearrange it into standard form as follows:

x^2 - 10x + 34 = 0

We can then use the quadratic formula to find the solutions:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -10, and c = 34. Substituting these values into the formula, we get:

x = (-(-10) ± sqrt((-10)^2 - 4(1)(34))) / 2(1)

Simplifying the expression under the square root, we get:

x = (10 ± sqrt(100 - 136)) / 2

x = (10 ± sqrt(-36)) / 2

Since the expression under the square root is negative, there are no real solutions to this quadratic equation. We can, however, find the complex solutions by using the imaginary unit i, where i^2 = -1:

x = (10 ± 6i) / 2

x = 5 ± 3i

Therefore, the solutions of the quadratic equation x^2 - 10x = -34 are x = 5 + 3i and x = 5 - 3i.

Answer:

No real solutions

Step-by-step explanation:

There are no real solution to this equation, as they would have to be imaginary. I can tell just by looking as there is no y in your equation.

May I Please have brainliest? I put a lot of thought and effort into my answer, so I would really appreciate it!

Suppose the time it takes my daugther, Lizzie, to eat an apple is uniformly distributed between 6 and 11 minutes. Let X = the time, in minutes, it takes Lizzie to eat an apple. a. What is the distribution of X? X ~ UT (6 ,11 ) Please show the following answers to 4 decimal places. b. What is the probability that it takes Lizzie at most 5 minutes to finish the next apple? c. What is the probability that it takes Lizzie less than 9.5 minutes to finish the next apple? d. What is the probability that it takes Lizzie between 7.6 minutes and 10.2 minutes to finish the next apple? 52 e. What is the probability that it takes Lizzie fewer than 7.6 minutes or more than 10.2 minutes to finish the next apple?

Answers

The probability that it takes Lizzie at most 5 minutes to finish the next apple is 0, and the probability that it takes Lizzie less than 9.5 minutes to finish the next apple is 0.5.

The probability that it takes Lizzie between 7.6 and 10.2 minutes to finish the next apple is 0.52, and the probability that it takes Lizzie fewer than 7.6 minutes or more than 10.2 minutes to finish the next apple is 0.24.

A. The distribution of x is uniformly allotted among 6 and eleven minutes, represented with the aid of x ~ u(6,11).

B. To locate the chance that it takes Lizzie a maximum of 5 mins to finish the next apple, we want to discover the region beneath the probability density function (PDF) from 6 to five. Since Lizzie can not finish the apple in much less than 6 minutes, this possibility is zero.

C. To locate the possibility that it takes Lizzie much less than 9. Five minutes to finish the subsequent apple, we want to discover the vicinity below the pdf from 6 to 9. 5. The possibility is calculated as:

p(x < 9. 5) = (9. 5 - 6) / (11 - 6) = 0. 5

D. To discover the probability that it takes Lizzie between 7. 6 and 10. 2 minutes to complete the subsequent apple, we need to locate the location below the pdf from 7. 6 to 10. 2. The chance is calculated as:

p(7. 6 < x < 10. 2) = (10. 2 - 7. 6) / (11 - 6) = 0. 52

E. To discover the possibility that it takes Lizzie fewer than 7. 6 mins or greater than 10. 2 mins to complete the next apple, we want to locate the location below the pdf out of doors in the range from 7. 6 to 10. 2. This may be calculated with the aid of locating the region below the pdf from 6 to 7. 6 and from 10. 2 to 11, then adding them collectively:

p(x < 7. 6 or x > 10. 2) = [(7. 6 - 6) + (11 - 10. 2)] / (11 - 6) = 0. 24

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what is the strongest negative correlation? enter in the entire value.

Answers

Answer:

-1.0

Step-by-step explanation:

The strength of a correlation relationship is quantified by its correlation coefficient, the strongest possible being "perfectly" correlated. A perfect negative correlation has a value of -1.0 and indicates that when X increases by z units, Y decreases by exactly z; and vice-versa.

Can someone help me with this please?

Answers

Answer:

35/12 improper fraction

Step-by-step explanation:

Answer:

sin H = [tex]\frac{55}{73}[/tex]

Step-by-step explanation:

sinH = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FG}{FH}[/tex] = [tex]\frac{55}{73}[/tex]

Practice Problems
0.22t
1. If left unchecked, a new strain of flu virus can spread from a single person to others very
quickly. The number of people affected can be modeled using the formula P(t) = e^0.22t
where represents the number of days the virus is allowed to spread unchecked. Estimate
the number of people infected with the virus after 30 days and after 60 days.

Answers

We estimate that after 30 days, abοut 492,000 peοple will be infected with the virus, and after 60 days, abοut 1.6 billiοn peοple will be infected with the virus.

What type οf οperatiοn displays expοnential grοwth?

Bacterial grοwth serves as an example οf an expοnential functiοn. Sοme bacteria grοw by twο per hοur. If yοu start with οne germ and it dοubles every hοur, yοu will have twice as many in x hοurs. This can be expressed as F(x) = 2x.

We enter the given values intο the calculatiοn tο estimate hοw many persοns have the virus after 30 days and after 60 days:

[tex]P(30) = e^{(0.22*30)} = 491,999.55[/tex]

[tex]P(60) = e^{(0.22*60)}=1.60 \times 10^9[/tex]

As a result, we predict that after 30 days, arοund 492,000 peοple will be infected with the virus, and after 60 days, apprοximately 1.6 billiοn peοple.

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Rosy is measuring two lines. the first line is 95 centimeters long. the second line is 650 millimeters long
What is the total length of the two lines in millimeters?

Answers

Answer:
1600mm

We are already given one of the measurements so we need to find the other one, which is 95cm

To convert cm to mm we have to multiply by 10.

95 x 10 = 950mm

950mm + 650mm =1600mm

Given the following confidence interval for a population mean, compute the margin of error, E.
11.67 <μ< 12.61

Answers

The margin of error, E, for the given confidence interval is 0.47

The margin of error, E, is the difference between the upper and lower bounds of the confidence interval divided by 2. In this case, the upper bound is 12.61 and the lower bound is 11.67.
To compute the margin of error, we can use the following formula:
E = (upper bound - lower bound) / 2
Plugging in the given values, we get:
E = (12.61 - 11.67) / 2
E = 0.94 / 2
E = 0.47
Therefore, the margin of error for this confidence interval is 0.47.
In summary, the margin of error, E, for the given confidence interval 11.67 <μ< 12.61 is 0.47.

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question 7 options: you would like to develop variable control chart with three-sigma control limits. if your 10 samples each contain 20 observations, what value of a2 should you use for your - chart?

Answers

When you are developing a variable control chart with three-sigma control limits and you have 10 samples, each containing 20 observations, you should use the value of a2 as 0.577.

You can use the following steps to derive at the answer: 1. Use the formula below to calculate the value of A2:

[tex]$$ A_2 = \frac{d_2}{\bar{d}} $$2.[/tex]

Look up the value of d2 in a statistical table.

The value of d2 is dependent on the number of observations per sample and the sample size, which is 20 in this case. From a statistical table, you can obtain that d2 = 1.128.3.

Calculate the mean range (d) of the 10 samples as follows: [tex]$$ \bar{d} = \frac{\sum_{i=1}^{10} R_i}{10} $$[/tex]

where Ri is the range of the ith sample.

4. Calculate the value of [tex]A2:$$ A_2 = \frac{1.128}{\bar{d}} $$[/tex]

where d2 = 1.128 and d is the mean range of the 10 samples.

5. Since you want to use the value of A2 in an X-chart (with three-sigma control limits), you should multiply A2 by 3 to obtain three-sigma limits for the X-chart.

Therefore, the three-sigma control limits are given by :  [tex]$${\text{Upper control limit (UCL) }}= \bar{x} + 3 A_2 s\;$$$$\text[/tex].

{Lower control limit (LCL)}[tex]= \bar{x} - 3 A_2 s\; $$where $\bar{x}$[/tex]  is the average of the 200 observations, and s is the sample standard deviation.

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Two data sets and their mean absolute deviations are shown.
Study the plots of each data set, and then use the drop-down menus to answer the questions below.

Answers

Data Set A has a spread out from, so it has a higher MAD.

What is data set?

A data set is a collection of related data that is organized and structured so that it can be easily analyzed for information. It typically includes both numeric and non-numeric data, such as text, images, audio, and video. Data sets are often used by scientists, researchers, and businesses to analyze trends, make predictions, and develop new products and services.

The differing mean absolute deviation (MAD) between the two data sets reflects the distributions of the data within each data set. Data set A has a much lower MAD compared to data set B, meaning that the data points in data set A are much closer to the mean than in data set B. This indicates that data set A is more clustered around the mean, while data set B has more of a spread out distribution.

The MAD can be used to measure the variability or spread of a data set. A larger MAD indicates that the data points in the data set are further away from the mean, while a smaller MAD indicates that the data points are close to the mean. Therefore, the larger MAD of data set B indicates that the data points in this set have a greater spread out distribution than the data points in data set A. This is likely due to the presence of outliers in data set B, which are values that are much larger or smaller than the rest of the data points. These outliers cause the MAD of data set B to be larger than that of data set A, which does not have any outliers.

Two data sets and their mean absolute deviations are shown.

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Complete questions as follows-

Study the plots of each data set, and then use the drop-down menus to answer the questions below.

if two lines intersect then they will intersect at exact one point

Answers

Answer:

The correct answer is one point.

Step-by-step explanation:

In geometry, if two lines cross each other, they will do so at an exact point.

Imagine that the lines are formed by thousands of points located next to each other, which makes us see a line, therefore if they cross, they will do so at a single point that will have a coordinate in (x, y) format.

When the two lines are on the same plane, the following situations may occur:

if they match they have an unlimited number of points in commonif they are different but they have the same slope they are parallel and they do not have points in commonif the above does not happen, they have a single point of intersection.

If the significance level of a hypothesis test is 10%, for which of the following p-values would you reject the null hypothesis? Select all that apply.
0.08
0.89
0.05
0.11

Answers

You would reject the null hypothesis for a p-value of 0.08 and 0.05. So, the correct answer for rejection is a) and c).

A significance level of 10% means that the probability of rejecting the null hypothesis when it is actually true is 10%. This probability is also known as the Type I error rate.

If the p-value is less than or equal to the significance level, then we reject the null hypothesis. In this case, the significance level is 10%, so we would reject the null hypothesis for p-values less than or equal to 0.1.

Therefore, we would reject the null hypothesis for the p-value of 0.08 and 0.05, as they are less than or equal to the significance level of 10%. However, we would not reject the null hypothesis for the p-value of 0.89 and 0.11, as they are greater than the significance level.

So, the option a) and c) are rejected.

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PLEASE ANSWER BEFORE 8TH MARCH 7.55AM GMT

ABC is an isosceles triangle
AB=BC
angle ABC=110°
ACDE is a quadrilateral
angle CDE=100°
angle ACD is a right-angle
AE is parallel to BC
work out the size of the angle marked x
give reasons for your answer.​

Answers

The value of the missing angle x of the quadrilateral ACDE is: x = 135°

How to find the missing angle in a quadrilateral?

We are told that Triangle ABC is an Isosceles triangle where:

∠ABC = 110°

We know that the base angles of an isosceles triangle are equal and as such:

∠BAC = ∠BCA = (180 - 110)/2

∠BAC = ∠BCA = 35°

Now,

∠BCA = ∠CAE = 35° because they are alternate angles

Sum of angles in a quadrilateral is 360°

Thus:

35 + x + 100 + 90 = 360

225 + x = 360

x = 360 - 225

x = 135°

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There is 20% chance of snow on monday and a 30% chance of snowon tuesday

Answers

The probability that it will NOT snow on both Monday and Tuesday = 0.4

Let event A: there is snow on Monday

The chance of snow on monday is 20%

P(A) = 20%

P(A) = 0.2

And event B: there is snow on Tuesday

The chance of snow on monday is 30%

P(B) = 30%

P(B) = 0.3

Now, the probability that it will snow on both Monday and Tuesday:

P(A ∩ B) = P(A) × P(B)         ............(independent events)

P(A ∩ B) = 0.2 × 0.3

P(A ∩ B) = 0.6

So, the probability that it will NOT snow on both Monday and Tuesday:

P(A ∩ B)' = 1 - P(A ∩ B)

P(A ∩ B)' = 1 - 0.6

P(A ∩ B)' = 0.4

therefore, the required probability is: 0.4

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the complete question is:

There is a 20% chance that it will snow on Monday and a 40% chance on Tuesday. What is the probability that it will NOT snow on both Monday and Tuesday?

draw a model that shows 26 pack of candy bars divided equally among 7 people how many candy bars will each person have? Also it’s like this

Answers

Equation: 26 ÷7=3 5/7.
Each person will get 3 complete bars and 5/7 of a bar.

Select the product of (2x+7) and (x – 5). Multiple choice question. A) 3x+2 B) 2x2 – 35 C) 2x2 – 3x – 35 D) 2x2 – 10x – 35

Answers

The product of (2x+7) and (x – 5) is option C) 2x^2 - 3x - 35.

What is FOIL method. give a description

FOIL method is a mnemonic technique used to multiply two binomials. The term "FOIL" stands for First, Outer, Inner, Last, and refers to the order in which the terms in each binomial are multiplied.

To use the FOIL method, you start by multiplying the first terms of each binomial, then the outer terms, the inner terms, and finally the last terms. The resulting terms are then combined using addition or subtraction as needed.

Finding the product of given two terms :

The product of (2x+7) and (x – 5) can be found by using the FOIL method.

we multiply the first terms, then the outer terms, then the inner terms, and finally the last terms:

[tex](2x + 7) \times (x - 5) = 2x^2 - 10x + 7x - 35[/tex]

[tex](2x + 7) \times (x - 5) = 2x^2 - 3x - 35[/tex]

Therefore, the answer is option C) [tex]2x^2 - 3x - 35[/tex].

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Sharko and Miko shared 385 sweets. Sharko had 4 times as many sweets as Miko. How many more sweets did Sharko have than Miko?

Answers

If Sharko had 4 times as many sweets as Miko, then Sharko had 231 more sweets than Miko.

Let the number of sweets that Miko has be = "M",

We know that Sharko had 4 times as many sweets as Miko,

So, Sharko has 4M sweets;

Together, Sharko and Miko share 385 sweets,

So, the equation can be mathematically written as :

⇒ M + 4M = 385,

Simplifying this equation, we get:

⇒ 5M = 385

Dividing both sides by 5, we get:

⇒ M = 77

So, Miko had 77 sweets, and

Sharko has ⇒ 4M = 4×77 = 308 sweets,

To find out how many more sweets Sharko had than Miko,

We write,

⇒ 308 - 77 = 231,

Therefore, The number of sweets that Sharko has more than Miko is 231.

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t(h)=h^2-8h+12 How many hours until the temperature is at its coldest/lowest?

Answers

The temperature will be at its coldest after 4 hours. This can be found by solving T'(h)=2h-8=0, which gives h=4.

To find the number of hours until the temperature is at its coldest, we need to find the x-intercepts of the quadratic equation. This can be done by setting the equation equal to 0 and solving for x. After setting T(h) = 0, we can use the quadratic formula to solve for h.

T(h)=[tex]h^{2}[/tex]-8h+12

T(h)=0

h = (8 +/- sqrt(64-48))/2

h = (8 +/- 4)/2

h = 4, 12

At 4 hours and 12 hours, the temperature is at its coldest. Therefore, it will take 8 hours until the temperature is at its coldest.

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The equation C = 5.5b + 88 represents the relationship between carbohydrates (b) and calories (C) of some foods. What is the meaning of the slope?

Answers

Slope is often used to analyze the relationship between two variables in a graph or equation, and it can provide important information about the rate of change or direction of a trend.

How can we interpret it?

The slope of the equation C = 5.5b + 88 is 5.5. The slope represents the amount of calories (C) that correspond to each additional gram of carbohydrates (b) in the food. In other words, for every one gram increase in carbohydrates, the number of calories in the food will increase by 5.5. This means that the slope represents the rate at which the calorie content of the food changes with respect to the carbohydrate content.

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NEED HELP ASAP

(Laws of Exponents with Integer Exponents LC)


Which is an equivalent expression for five sevenths squared times one third raised to the power of negative three all raised to the power of negative one?


A. five sevenths squared times one third raised to the power of negative three


B. five sevenths times one third raised to the power of negative four


C. seven fifths to the power of negative two times one third to the power of negative three


D. seven fifths squared times one third cubed

Answers

The simplificatiοn fοrm οf the prοvided expressiοn is (7/3)²(2/3)³ after using the cοncept οf the integer expοnent οptiοn (A) seven-thirds squared times twο-thirds cubed is cοrrect.

What is an integer expοnent?

In mathematics, integer expοnents are expοnents that shοuld be integers. It may be a pοsitive οr negative number. In this situatiοn, the pοsitive integer expοnents determine the number οf times the base number shοuld be multiplied by itself.

It is given that:

The number expressiοn is:

[tex]$ \mathrm { =\left[\left(\frac{3}{7}\right)^2 \left(\frac{2}{3}\right)^{-3} \right] ^{-1} }[/tex]

As we knοw, frοm the definitiοn οf the integer expοnent, the pοsitive integer expοnents determine the number οf times the base number shοuld be multiplied by itself.

Using the integer expοnent prοperties:

[tex]$ \mathrm {= \dfrac{1}{ \left(\dfrac{3}{7}\right)^2 \left(\dfrac{2}{3}\right)^{-3} } }[/tex]

(7/3)²(2/3)³

Thus, the simplificatiοn fοrm οf the prοvided expressiοn is (7/3)²(2/3)³ after using the cοncept οf the integer expοnent οptiοn (A) seven-thirds squared times twο-thirds cubed is cοrrect.

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Complete correct question:

Which is an equivalent expressiοn fοr three sevenths squared times twο thirds raised tο the pοwer οf negative three all raised tο the pοwer οf negative οne?

seven thirds squared times twο thirds cubedseven thirds tο the pοwer οf negative twο times twο thirds tο the pοwer οf negative threethree sevenths squared times twο thirds raised tο the pοwer οf negative threethree sevenths times twο thirds raised tο the pοwer οf negative fοur

Find the IQR of each data set. How many IQRs apart are medians? What does this indicate?

Answers

The IQR of a data set is the difference between the upper and lower quartiles of the data. The medians of two data sets are usually one IQR apart, which indicates that the two data sets are different in terms of their distributions.

The IQR, or Interquartile Range, of a data set is the difference between the upper and lower quartiles. The upper quartile is the 75th percentile of the data, while the lower quartile is the 25th percentile. By finding the IQR, we can determine if there is a large range of values or a small range of values in the data set. The medians of two data sets are usually one IQR apart, which indicates that the two data sets are different in terms of their distributions. This can be used to compare the central tendency of two different data sets. For example, if one data set has a median of 3 and an IQR of 2, and the other data set has a median of 5 and an IQR of 4, then the two data sets are one IQR away from each other and it indicates that the two data sets are not distributed in the same way.

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A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.

Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?

graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 120
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 120

Answers

Therefore, the graph should show a straight line with a positive slope, starting at (0, 100) and passing through (2, 120), since 2 students attending the dance would raise $120.

by the question.

graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 80.

graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 120

graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 80.

graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 120

The correct graph that describes the relationship between the amount of money raised and the number of students who attend the dance is

graph with the x-axis labeled number of students and the y-axis labeled amount of money raised and a line going from the point (0, 100) through the point (2, 120).

This is because the club has a fixed cost of $100 for decorations, which is independent of the number of students attending the dance. For every student that attends the dance, the club raises $10. Therefore, the graph should show a straight line with a positive slope, starting at (0, 100) and passing through (2, 120), since 2 students attending the dance would raise $120. The other two graphs have incorrect slopes or starting points, and do not accurately represent the relationship between the number of students attending the dance and the amount of money raised.

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Kim uses 6.3 pints of white paint and blue paint to paint her bedroom walls. 2 5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?

Answers

There will be 6.3 pints of blue paint to paint her bedroom walls.

What is calculation?

Calculation means when manipulating numbers in a certain way to get an answer.

This question can be solved using a system of equations.

x is the amount of white paint used.

y is the amount of blue paint used.

6.3 pints of blue paint and white paint to paint her bedroom walls.

x + y = 6.3

5 of this amount is white paint, and the rest is blue paint.

The rest is 1- 5 = 4

x + y = 6.3

y/4 + y = 6.3

y + 4y/4 = 6.3

4y = 4 x 6.3

y = 4 x 6.3 /4

y = 6.3

Thus, 6.3 pints of blue paint to paint her bedroom walls.

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when two events have no outcomes in​ common, they are called​ what?

Answers

When two events have no outcomes in common, they are called mutually exclusive events. In other words, if the occurrence of one event prevents the occurrence of the other event, the events are said to be mutually exclusive.  

Mutually exclusive events are often illustrated using a Venn diagram. In this diagram, two circles represent the events, and the area of overlap between the circles represents the outcomes that are common to both events. For mutually exclusive events, there is no overlap between the circles because the events have no outcomes in common. For example, if we consider the events "rolling a 1 on a die" and "rolling a 2 on a die", these events are mutually exclusive because the occurrence of one event (rolling a 1) prevents the occurrence of the other event (rolling a 2). In contrast, the events "rolling an even number on a die" and "rolling a number greater than 3 on a die" are not mutually exclusive because they share some outcomes (rolling a 4 or 6).

Mutually exclusive events are important in probability because the probability of the occurrence of either event is calculated by adding their individual probabilities. For example, the probability of rolling a 1 or a 2 on a die is calculated by adding the probability of rolling a 1 to the probability of rolling a 2.

In conclusion, mutually exclusive events are events that have no outcomes in common, and their occurrence prevents each other. They are important in probability because their probabilities are calculated by adding their individual probabilities.

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suppose that a colony of beetles grows exponentially with doubling time 8 years. how many years does it take for the colony to triple in size? (give the answer as a decimal number with no units. round to three decimal places.)

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It takes approximately 41.44 years for the colony to triple in size.

To find how many years it takes for the colony to triple in size, we will use the formula for exponential growth which is given by:

P(t) = P0ert

Where, P0 is the initial population P(t) is the population after time ‘t’ r is the growth rate and it is constant.

e is the Euler's number ≈ 2.71828

Here we have to find the time taken for the colony to triple in size.

That means final population = 3 * initial population.

So, P(t) = 3*P0

Now we can substitute the values in the formula and solve for ‘t’.

3P0 = P0ert

=>[tex]ert = 3[/tex]

=> [tex]e^(8r) = 3[/tex]

Dividing both sides by

[tex]e^8,e^(8r-8) = 3/e^8[/tex]

Taking natural logarithms of both sides,(8r-8)

[tex]ln e = ln (3/e^8)[/tex]

=> [tex]8r - 8 = ln (3/e^8)[/tex]

=> [tex]8r = ln(3/e^8) + 8r \\= -0.000126r \\= -0.000126/8r \\= -0.00001575[/tex]

Therefore, the time taken for the colony to triple in size is given by:

[tex]t = ln (3/e^8)/(-0.00001575)[/tex] ≈ 41.44 (rounded to three decimal places).

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Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function F defined by F (t) = 82 + 4 sin () where F(t) is measured in cars per minute and t is measured in minutes. To the nearest whole number, how many cars pass through the intersection over the 30-minute period?

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2462 cars pass through the intersection over the 30-minute period.

Traffic flow is an important factor when considering the design and operation of an intersection. The traffic flow at a particular intersection is modeled by the function F defined by F (t) = 82 + 4 sin () where F(t) is measured in cars per minute and t is measured in minutes.

To find the number of cars that pass through the intersection over the 30-minute period, we need to integrate the function F(t) from t = 0 to t = 30.

This will give us the total number of cars that pass through the intersection during that time period.

The integral of F(t) from t = 0 to t = 30 is:
∫_0^30 F(t) dt = ∫_0^30 (82 + 4 sin()) dt

= [82t - 4 cos()]_0^30
= (82 * 30 - 4 * cos(30)) - (82 * 0 - 4 * cos(0))
= 2460 - 4 * cos(30) - 0 + 4
= 2460 - 4 * (√3/2) + 4
= 2460 - 2√3 + 4
≈ 2462

Therefore, to the nearest whole number, 2462 cars pass through the intersection over the 30-minute period.

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3^-4/3 is equivalent to

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The exponent expression [tex]3^{\frac{-4}{3} }[/tex] is equivalent to [tex]\frac{1}{3^{\frac{4}{3} }}[/tex].

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The exponent expression is given as [tex]3^{\frac{-4}{3} }[/tex].

[tex]3^{\frac{-4}{3} }[/tex] can be simplified using the rule that states that [tex]a^{(-n)} =\frac{1}{a^n}[/tex], which is -

[tex]3^{\frac{-4}{3} }=\frac{1}{3^{\frac{4}{3}}}[/tex]

To simplify this expression further, we can use another rule that states that [tex]a^{\frac{m}{n} } = (n^{th} root of a)^m[/tex].

Applying this rule, we get -

[tex]\frac{1}{3^{\frac{4}{3} }} =\frac{1}{(3^{\frac{1}{3} })^4}[/tex]

The cube root of [tex]3 (3^{(\frac{1}{3})})[/tex] cannot be simplified any further, so we can leave it as is.

Thus, we have -

[tex]\frac{1}{(3^{\frac{1}{3} })^4} = \frac{1}{3^{4 \times\frac{1}{3} }} = \frac{1}{3^{\frac{4}{3} }}[/tex]

Therefore, the value is obtained as [tex]\frac{1}{3^{\frac{4}{3} }}[/tex].

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Which compound inequality is equivalent to | ax -b | > C for all real numbers a, b, and c, where c>0?

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The compound inequality that is equivalent to |ax - b| > C for all real numbers a, b, and c, where c ≤ 0 is: ax - b < -c, or ax - b > c. So, option D is correct.

A compound inequality is a mathematical statement that involves two or more inequalities connected by the words "and" or "or".

Now consider the given question:

We know that [tex]|ax - b| > C[/tex] is equivalent to:

[tex]ax - b > C[/tex], or [tex]ax - b < -C[/tex]

Adding or subtracting c to both sides of each inequality yields:

[tex]ax - b + c > C + c[/tex], or [tex]ax - b - c < -C - c[/tex]

Simplifying each inequality gives:

[tex]ax - (b - c) > c[/tex], or [tex]ax - (b + c) < -c[/tex]

Replacing b - c with a new constant, d = - (b + c), gives:

[tex]ax > c + d[/tex], or [tex]ax < d - c[/tex]

Finally, rearranging the inequalities gives:

[tex]ax < d - c[/tex], or [tex]ax > c + d[/tex]

which can be written as:

[tex]ax - b < -c[/tex], or [tex]ax - b > c[/tex].

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The complete question is:

Which compound inequality is equivalent to [tex]| ax -b | > C[/tex] for all real numbers a, b, and c, where [tex]c\geq 0[/tex] ?

a) [tex]-c < ax-b > c[/tex]

b) [tex]-c > ax-b > c[/tex]

c) [tex]ax-b > -c[/tex], Or [tex]ax-b > c[/tex]

d) [tex]ax-b < -c[/tex], Or [tex]ax-b > c[/tex]

How many solutions does this system of equations have? Responses Infinitely many Infinitely many None None Exactly two Exactly two Exactly one Exactly one Graph of a system of linear equations. Equation 1 is 2x plus y equals 1.. Equation 2 is 4x plus 2y equals 2. The graphs are the same line.

Answers

There are infinitely many sοlutiοns.

What is a linear equatiοn?

An equatiοn is said tο be linear if the maximum pοwer οf the variable is cοnsistently 1. Anοther name fοr it is a οne-degree equatiοn. A linear equatiοn with οne variable has the cοnventiοnal fοrm Ax + B = 0. In this case, the variables x and A are variables, while B is a cοnstant. A linear equatiοn with twο variables has the cοnventiοnal fοrm Ax + By = C. Here, the variables x and y, the cοefficients A and B, and the cοnstant C are all present.

Here, we have

Given:

The system is 2x + y = 1 and 4x + 2y = 2.

Sοlutiοns tο a system are the intersectiοn pοints.

Since these twο lines are the same line they intersect everywhere. There are infinitely many sοlutiοns.

Hence, there are infinitely many sοlutiοns.

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: A siren emits a sound wave with frequency fo. The graph shows the frequency you hear as you stand at rest oat x = 0 on the x-axis. Which is the correct description of the siren's motion? fo+--- o i į ģ 1(3) A. It moves from left to right and passes you at t = 2 s. B. It moves from right to left and passes you at t = 2 s. C. It moves toward you for 2 s but doesn't reach you, then reverses direction at t = 2 s and moves away. D. It moves away from you for 2 s, then reverses direction at t = 25 and moves toward you but doesn't reach you

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Siren moves toward you for 2 s but doesn't reach you, then reverses direction at t = 2 s and moves away. Option C is correct.

The graph shows the frequency you hear as you stand at rest at x = 0 on the x-axis.

At t = 0 s, the frequency of the sound wave is fo.

From t = 0 s to t = 2 s, the frequency of the sound wave increases as the siren moves toward you, however it does not reach you.

At t = 2 s, the siren reverses direction and moves away from you.

Therefore, the correct description of the siren's motion is Option C: It moves toward you for 2 s but doesn't reach you, then reverses direction at t = 2 s and moves away.

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The volleyball is -------------- feet from where it will land the first time it passes seven​ feet, and ------ feet from where it will land the second time.

Answers

Answer:

The ball reaches a height of seven feet at ten seconds

Step-by-step explanation:

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