El valor de "x" que es solución de la ecuación 5x + 22 = 2x + 29 es:

Answers

Answer 1

Answer:

x =7/ 3

Step-by-step explanation:

5x+  22=  2x+  29

⇔5x - 2x= 29 - 22

⇔3x = 7

⇔x = 7/3


Related Questions

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds. For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23. Find the P-value of the test statistic.

Answers

Answer:

The p-value of the test statistic is 0.2019.

Step-by-step explanation:

Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.

At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:

[tex]H_0: \mu \leq 384[/tex]

At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:

[tex]H_1: \mu > 384[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

384 is tested at the null hypothesis:

This means that [tex]\mu = 384[/tex]

For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.

This means that [tex]n = 41, X = 387, \sigma = 23[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}[/tex]

[tex]z = 0.835[/tex]

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.

Looking at the z-table, z = 0.835 has a p-value of 0.7981.

1 - 0.7981 = 0.2019

The p-value of the test statistic is 0.2019.

Draw clearly the graph of the linear equation. y=1/2x, where x= (-4 -2, 0, 2, 4)​

Answers

Answer:

(in attachment)

Step-by-step explanation:

you can find the points by inputting the x-values into the equation to solve for the y-values, then connecting the plotted points to create the line.

When x=-4

y=1/2(-4)

y=-2

(-4,-2)

Repeat for all values.

Solve for x:
|3x-1|=4

Answers

Answer:

x = 5/3  x= -1

Step-by-step explanation:

|3x-1|=4

There are two solutions to the absolute value equation, one positive and one negative

3x-1 =4  and 3x-1=-4

Add 1 to each side

3x-1+1 = 4+1   3x-1+1 = -4+1

3x=5             3x = -3

Divide by 3

3x/3 = 5/3     3x/3 = -3/3

x = 5/3  x= -1

Select the correct answer. Solve the equation using the method of completing the square. 2r2 + 16r - 8 = 0​

Answers

Answer:

r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]

Answer:

r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

It was right for me

A random sample of n1 = 296 voters registered in the state of California showed that 146 voted in the last general election. A random sample of n2 = 215 registered voters in the state of Colorado showed that 127 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance.

Answers

Answer:

The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

California:

Sample of 296 voters, 146 voted. This means that:

[tex]p_{Ca} = \frac{146}{296} = 0.4932[/tex]

[tex]s_{Ca} = \sqrt{\frac{0.4932*0.5068}{296}} = 0.0291[/tex]

Colorado:

Sample of 215 voters, 127 voted. This means that:

[tex]p_{Co} = \frac{127}{215} = 0.5907[/tex]

[tex]s_{Co} = \sqrt{\frac{0.5907*0.4093}{215}} = 0.0335[/tex]

Test if the population proportion of voter turnout in Colorado is higher than that in California:

At the null hypothesis, we test if it is not higher, that is, the subtraction of the proportions is at most 0. So

[tex]H_0: p_{Co} - p_{Ca} \leq 0[/tex]

At the alternative hypothesis, we test if it is higher, that is, the subtraction of the proportions is greater than 0. So

[tex]H_1: p_{Co} - p_{Ca} > 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = p_{Co} - p_{Ca} = 0.5907 - 0.4932 =  0.0975[/tex]

[tex]s = \sqrt{s_{Co}^2+s_{Ca}^2} = \sqrt{0.0291^2+0.0335^2} = 0.0444[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.0975 - 0}{0.0444}[/tex]

[tex]z = 2.2[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.0975, which is 1 subtracted by the p-value of z = 2.2.

Looking at the z-table, z = 2.2 has a p-value of 0.9861.

1 - 0.9861 = 0.0139.

The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.

From past experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain one defective transistor, 3% contain two defective transistors, and 2% contain three defective transistors. About how many extra transistors per day would the company need to replace the defective ones if it used 10 cartons per day?

Answers

Answer:

Ungrouped data refers to the data that is first gathered from a study, it is a raw data that is, i.e it has not sorted into categories or grouped. To calculate the mean of ungrouped data we use the formula

Step-by-step explanation:

Which of the following tables represent valid functions?​

Answers

Answer:

Step-by-step explanation:

A relation may or may not represent a function.

Table (a), (c) and (d) represent a function

The tables represent a relation

For a relation to be a function, then:

The y values must have unique (or distinct) x-values.

From the list of tables, we have the following observations

All y values in table (a), have different corresponding x valuesy values 3 and 6 in table (b), point to the same x value (2)All y values in table (c), have different corresponding x valuesAll y values in table (d), have different corresponding x values

Hence, all the tables represent a valid function, except table (b)

Read more about functions and relations at:

https://brainly.com/question/6241820

Select the correct statement about what data scientists do during the Data Preparation stage.

a. During the Data Preparation stage, data scientists define the variables to be used in the model.
b. During the Data Preparation stage, data scientists determine the timing of events.
c. During the Data Preparation stage, data scientists aggregate the data and merge them from different sources.
d. During the Data Preparation stage, data scientists identify missing data.
e. All of the above statements are correct.

Answers

Answer:

e. All of the above statements are correct.

Option e is correct. All of the above statements are correct.

What is Data science?

Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data

Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.

During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.

Hence, All of the above statements are correct, Option e is correct.

To learn more on Data science click:

https://brainly.com/question/20815848

#SPJ5

A teacher calculates for the test grades in
Class A, mean = 32 and sd = 4
Class B, mean = 32 and sd = 8
a. If the teacher was going to guess what any student in his/her class would earn, what is the best score
to guess?
b. Which of the classes has more consistency in their scores? Why?

Answers

Answer:

a. best score to guess would be 33

b. Standard deviation simplifies the square root of the mean so makes it closer to 1 has more consistency as the mean of 32 when squared is sqrt 32  is Class A as class a = 4 and is closer to 5.65685425

as 5.65685425^2 = 32

Step-by-step explanation:

If you are comparing two normally-distributed variables on the same measurement scale then yes, you can regard the standard deviation as an indicator of how reliable the mean is--the smaller the standard deviation, the better able you are to "zero in" on the actual population mean.

a. proofs;

We find  32/6 = 5.333 and 32/5 = 6.4 and 6.4 is closer to both sd 4 and 8 than 5.33 is. As 6.4 it is closer to 6

But when we use 33/6 = 5.5 and therefore shows close range 6

therefore the two sd  proves it is slightly high 32 score average for both classes A + B when joined and high 32 = 33 mean when classes A+B are joined or you could say 32/8 = 4 is class B becomes lower tests scores as 32/4 = 8 of class A that has higher test scores.

In this exercise we have to use probability and statistics to organize the students' grades, so we have:

A) best score is  33

B) Class A

In the first part of the exercise we have to analyze the grades of each class, like this:

A)Class A: 32/4

Class B: 32/8

Dividing each of them we have:

[tex]32/4=8 \\32/8=4[/tex]

B) With the information given above, we can say that the best class is A.

See more about statistics at  brainly.com/question/10951564

Bill works for a large food service company. In one hour he can make 19 sandwiches or he can make 40 salads. Bill works 7 hours per day. If Bill needs to make 30 sandwiches then how many salads can he make

Answers

Answer:

[tex]x=216 salads[/tex]

Step-by-step explanation:

One Hour:

Salad=40

Sandwich=19

Total work time[tex]T=7[/tex]

Generally

Time to make 30 sandwiches is

[tex]T_s=\frac{30}{19}[/tex]

[tex]T-s=1.6hours[/tex]

Therefore

Bill has 7-1.6 hours to make salads and can make x about of salads in

[tex]x=(7-1.6)*40[/tex]

[tex]x=5.4*40[/tex]

[tex]x=216 salads[/tex]

can u guys help me pls

Answers

Answer:

350cm

Step-by-step explanation:

to turn metres in centimetres, multiply by 100

so: 3.5 x 100 = 350

g From a distribution with mean 38 and variance 52, a sample of size 16 is taken. Let X be the mean of the sample. Show that the probability is at least 0.87 that X is in (33, 43)

Answers

Answer:

[tex]P=8.869[/tex]

Step-by-step explanation:

From the question we are told that:

Mean [tex]\=x =38[/tex]

Variance [tex]\sigma=52[/tex]

Sample size [tex]n=16[/tex]

[tex]X=(33, 43)[/tex]

Generally the equation for Chebyshev's Rule  is mathematically given by

[tex]A=(1-\frac{1}{k^2})*100\%[/tex]

Where

[tex]k=\frac{\=x-\mu}{\frac{\sigma}{\sqrt n}}}}[/tex]

[tex]k=\frac{43-38}{\frac{52}{\sqrt 16}}}}[/tex]

[tex]k=2.77[/tex]

Therefore

Probability

[tex]P=(1-\frac{1}{2.77^2})[/tex]

[tex]P=8.869[/tex]

A soft drink machine outputs a mean of 29 ounces per cup. The machine's output is normally distributed with a standard deviation of 4 ounces. What is the probability of filling a cup between 33 and 35 ounces? Round your answer to four decimal places.

Answers

Answer:

0.8919 = 89.19% probability of filling a cup between 33 and 35 ounces.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

A soft drink machine outputs a mean of 29 ounces per cup. The machine's output is normally distributed with a standard deviation of 4 ounces.

This means that [tex]\mu = 29, \sigma = 4[/tex]

What is the probability of filling a cup between 33 and 35 ounces?

This is the p-value of Z when X = 35 subtracted by the p-value of Z when X = 33.

X = 35

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 29}{4}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

X = 33

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33 - 29}{4}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.0413.

0.9332 - 0.0413 = 0.8919

0.8919 = 89.19% probability of filling a cup between 33 and 35 ounces.

Answer:

0.1598

Step-by-step explanation:

Solve For X any and all help is appreciated (:

Answers

Answer:

x is 3

Step-by-step explanation:

You use proportions to figure out x, what you first do is set up the proportion of the big triangle, then the small triangle.

[tex]\frac{(9+3)}{3}[/tex]= [tex]\frac{12}{x}[/tex]

By setting up this proportion, you would then cross multiply, and get 12x = 36. This is when you divide by 12 on both sides and get x=3

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

See this attachment

[tex]\boxed{\boxed{\sf{ x=3 }}}[/tex] [tex]\sf{ }[/tex]

Suki makes and sells denim jackets in a small store at the mall. She has found that
the following system of equations represents the expenses and the revenue for
running her store.
C = 520 + 31n
C = 96n
Determine the minimum number of jackets she must sell to make a profit.

Answers

Answer:

8

Step-by-step explanation:

96n = 520 + 31n

65n=520

n=8

Hope this helps :)

et f(x)=6(2)x−1+4. The graph of f(x) is translated 7 units to the left to form the graph of g(x). Enter the equation for g(x) in the box.

Answers

Answer:

[tex]g(x) = 6(2)^{x -8}+ 4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 6(2)^{x - 1}+ 4[/tex]

Required

Find g(x)

From the question, f(x) is translated 7 units left;

The rule of translation is: [tex](x,y) \to (x-7,y)[/tex]

So, we have:

[tex]g(x) = f(x - 7)[/tex]

[tex]g(x) = 6(2)^{x -7- 1}+ 4[/tex]

[tex]g(x) = 6(2)^{x -8}+ 4[/tex]

What is the solution of this system of linear equations?
3y = 3 y equals StartFraction 3 over 2 EndFraction x plus 6.x + 6
y – StartFraction one-half EndFraction y minus StartFraction 1 over 4 EndFraction x equals 3.x = 3

Answers

Answer:

[tex]x = 4[/tex]

[tex]y = 4[/tex]

Step-by-step explanation:

Given

[tex]3y = \frac{3}{2}x + 6[/tex]

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

Required

The solution

Multiply the second equation by 3

[tex]3 * [y-\frac{1}{4}x = 3][/tex]

[tex]3y-\frac{3}{4}x = 9[/tex]

Rewrite as:

[tex]3y =\frac{3}{4}x + 9[/tex]

Subtract this from the first equation

[tex][3y = \frac{3}{2}x + 6]- [3y =\frac{3}{4}x + 9][/tex]

[tex]3y - 3y = \frac{3}{2}x - \frac{3}{4}x + 6 - 9[/tex]

[tex]0 = \frac{3}{4}x -3[/tex]

Rewrite as:

[tex]\frac{3}{4}x =3[/tex]

Multiply both sides by 3/4

[tex]x =3*\frac{4}{3}[/tex]

[tex]x = 4[/tex]

Substitute [tex]x = 4[/tex] in [tex]3y = \frac{3}{2}x + 6[/tex]

[tex]3y = \frac{3}{2} * 4 + 6[/tex]

[tex]3y = 6 + 6[/tex]

[tex]3y = 12[/tex]

Divide both sides by 3

[tex]y = 4[/tex]

Answer:

C. no solution

Step-by-step explanation:

did it on edge2021

Consider points a, b, and c in the graph. Determine which of these points is relative minima on the interval x = –1 and x = –2 in the graph.

Answers

Answer:

C.

Step-by-step explanation:

1) note, the point "а" belongs to the given interval only, then

2) the correct answer is C) a.

Answer:

as we can see here point {\color{Red}a} lies on the interval (-2, -1)

so option A is correct

Step-by-step explanation:

Given a set of data that is skewed-left, there is at least _____ % of the data within 2 standard deviations.

Answers

Answer:

75

Step-by-step explanation:

For non-normal distributions, we use Chebyshev's Theorem.

Chebyshev Theorem

The Chebyshev Theorem states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Within 2 standard deviations of the mean, so 75%.

i’ll make brainliest
look at the photo and check my work?
also tell me the answer to the ones i didn’t do
thanks :)

Answers

First of all, your work all seems to be correct.

2. =, this is because in decimals 100% and 1 are the same.

3. Measure of center is the mean, median, and mode, as they are all ways to interpret the center of the data.

5. The lines do not appear to be congruent as they are of different lengths.


Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
The person above is correct but gives me Brainliest because I’m want it mores then they can, but I don’t want too do wrk

Eight students are running for three positions in
the student council: president, vice president,
and secretary. Which represents the total
number of ways that three students can be
selected if each student can be elected to only
one position?

Answers

Answer:

Step-by-step explanation:

Total number of outcome are  

1320

.

Explanation:

It is apparent that there are  

12

ways in which the post of President can be filled. Once President's post is filled, there are  

11

ways to fill the post of Vice President and then  

10

ways to fill the post of Secretary,

Hence a total of  

12

11

10

or  

1320

ways or outcomes.

Answer:

1320

Step-by-step explanation:

Which of the following is an arithmetic sequence?
O 1,-3,9,-27...
0-2, 4, -6, 8, ...
-8, -6, -4,-2....
O2, 4, 8, 16, ...

Answers

9514 1404 393

Answer:

  (c)  -8, -6, -4, -2, ...

Step-by-step explanation:

An arithmetic sequence has sequential terms that have a common difference.

The first differences of the offered sequences are ...

  a) -4, 12, -36

  b) 6, -10, 14

  c) 2, 2, 2 . . . . . . constant, so an arithmetic sequence

  d) 2, 4, 8

__

The arithmetic sequence is -8, -6, -4, -2, ....

Find the probability that a randomly selected point within the square falls in the blue shaded area (circle). r = 2 in [? ]% Round to the nearest tenth of a percent.​

Answers

Answer:

78.5 %

Step-by-step explanation:

the probability = π(2)² / (4×4) ×100%

= 4π /16 × 100%

= π/4 ×100%

= (π×25)%

= 3.14 × 25 %

= 78.5 %

The blue Sox baseball won 40 games out of 48 games played. The Green Sox won 27 games of 45 games played. Which team won the greater percentage of the game? By what percent?

Answers

Step-by-step explanation:

40 won dividend 48 games

= 40/48 x 100

83.33% Win

Green Sox

27/45 x 100

60%

so Conclusion

The most Won Greatest Between Blue & Green are

Sox Have 83.33% Won

I need help with this

Answers

Answer:

Yes because 5^2 + 12^2 = 13^2

Step-by-step explanation:

We can check using the Pythagorean theorem

a^2 + b^2 = c^2

5^2 + 12^2 = 13^2

25+ 144= 169

169 = 169

9514 1404 393

Answer:

  D.  Yes, because 5² +12² = 13²

Step-by-step explanation:

To determine if a triple of three numbers will form a right triangle, see if they satisfy the Pythagorean theorem. If they do, the sum of the squares of the smaller two numbers will equal the square of the largest.

Here, we have ...

  5² + 12² ?? 13²

  25 +144 ?? 169

  169 = 169 . . . . . . these side lengths will form a right triangle

_____

Additional comment

Three integer numbers like these that will satisfy the Pythagorean theorem are called a "Pythagorean triple." A few such triples that are commonly seen in algebra and trig problems are ...

  (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)

It is worthwhile to remember a few of these, as you will see them again.

Which of these are related functions. Plato

Answers

Answer:

◦•●◉these are related functions



Suppose 50.7 liters of water came out of a faucet today. If 2.6 liters of water come out each minute, for how many minutes was the faucet on?

Answers

I believe the answer is 19.5 (or 19m 30s), 50.7/2.6=19.5, 2.6x19.5=50.7

A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide. If one bag of gravel covers 10 square feet, how many bags are needed to cover the path? Round your answer to the nearest tenth. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. ​

Answers

Answer:

[tex] \displaystyle 4[/tex]

Step-by-step explanation:

we are given that A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide.since together the width of Vegetable garden and path is 11 ft, the width of the vegetables garden will be the difference between the total width and the width of path Thus,

[tex] \displaystyle \rm W _{ garden} = 11 - 2[/tex]

simplify substraction:

[tex] \displaystyle \rm W _{ garden} = 9[/tex]

recall that, every single side of a square is equal to each other therefore the the area of the garden will be

[tex] \displaystyle {9}^{2} [/tex]

simplify square:

[tex] \displaystyle 81[/tex]

together the garden and path makes a square of every side length 11 ft saying that the area will be:

[tex] \displaystyle {11}^{2} [/tex]

simplify square:

[tex] \displaystyle 121[/tex]

the area of path will be the difference between the total area and the garden area therefore,

[tex] \displaystyle 121 - 81[/tex]

simplify addition:

[tex] \displaystyle 40[/tex]

to figure out how many bags are needed to cover the path. we just need to divide the area of the path by the area of a bag of gravel and that yields:

[tex] \displaystyle \frac{40}{10} [/tex]

simplify division:

[tex] \displaystyle \boxed{\rm4}[/tex]

hence,

4 bags are needed to cover the path.

According to records from a large public university, 88% of students who graduate from the university successfully find employment in their chosen field within three months of graduation. What is the probability that of nine randomly selected students who have graduated from this university, at least six of them find employment in their chosen field within three months

Answers

Answer:

0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they found employment, or they did not. The probability of a student finding employment is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

88% of students who graduate from the university successfully find employment in their chosen field within three months of graduation.

This means that [tex]p = 0.88[/tex]

Nine randomly selected students

This means that [tex]n = 9[/tex]

What is the probability that of nine randomly selected students who have graduated from this university, at least six of them find employment in their chosen field within three months?

This is:

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{9,6}.(0.88)^{6}.(0.12)^{3} = 0.0674[/tex]

[tex]P(X = 7) = C_{9,7}.(0.88)^{7}.(0.12)^{2} = 0.2119[/tex]

[tex]P(X = 8) = C_{9,8}.(0.88)^{8}.(0.12)^{1} = 0.3884[/tex]

[tex]P(X = 9) = C_{9,9}.(0.88)^{9}.(0.12)^{0} = 0.3165[/tex]

Then

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0.0674 + 0.2119 + 0.3884 + 0.3165 = 0.9842[/tex]

0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.

A trough is 12 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 4 inches deep

Answers

Answer:

[tex]\frac{dh}{dt}=0.5ft[/tex]

Step-by-step explanation:

From the question we are told that:

Length [tex]l=12[/tex]

Top length [tex]l_t=3ft[/tex]

Height [tex]h=1ft[/tex]

Rate [tex]R=14 ft3/min[/tex]

Water rise [tex]w=4[/tex]

Generally the equation for Velocity is mathematically given by

[tex]V=frac{1}{2}wh'(l)\\\\V=frac{1}{2}wh'(12)[/tex]

[tex]V=18h'^2[/tex]

Therefore

[tex]R=18(2h)(\frac{dh}{dt})[/tex]

Where

[tex]h=\frac{3}{4}[/tex]

Therefore

[tex]\frac{dh}{dt}=\frac{R}{18(2h)}[/tex]

[tex]\frac{dh}{dt}=\frac{14}{18(2.3/4)}[/tex]

[tex]\frac{dh}{dt}=0.5ft[/tex]

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