algebra ...........................

Algebra ...........................

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given that y is inversely proportional to x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion

(a)

To find k use the condition when y = 7 , x = 9, that is

7 = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )

63 = k

y = [tex]\frac{63}{x}[/tex] ← equation of proportion

(b)

When x = 21, then

y = [tex]\frac{63}{21}[/tex] = 3


Related Questions

A business operated at 100% of capacity during its first month and incurred the following costs: Production costs (19,900 units): Direct materials $172,700 Direct labor 221,400 Variable factory overhead 265,400 Fixed factory overhead 92,800 $752,300 Operating expenses: Variable operating expenses $134,100 Fixed operating expenses 43,700 177,800 If 1,500 units remain unsold at the end of the month, the amount of inventory that would be reported on the absorption costing balance sheet is

Answers

Answer:

Ending inventory cost= $56,700

Step-by-step explanation:

Giving the following information:

Production costs (19,900 units):

Direct materials $172,700

Direct labor 221,400

Variable factory overhead 265,400

Fixed factory overhead 92,800

Total= $752,300

The absorption costing method includes all costs related to production, both fixed and variable. The unit product cost is calculated using direct material, direct labor, and total unitary manufacturing overhead.

Total unitary production cost= 752,300/19,900= $37.80

Units in ending inventory= 1,500

Ending inventory cost= 1,500*37.8

Ending inventory cost= $56,700

Hurrryy!!!
What is the value of x in the solution to the system of linear equations?
y=3x+2
y=x-4
O-7
O-3
0 1
O 5

Answers

Answer:

-3

Step-by-step explanation:

I'm not sure what the 0s are all about, but I can help with the equation;

To do this, we can do substitution. By equaling x-4 to 3x+2, we get

x-4=3x+2

By isolating the x, we get

-2x=6

x=-3

Hope this helped!

Read the passage.
(1) I think that schools should switch from using paper textbooks to using computer tablets. (2)
Textbooks were effective in the pre-digital age, but now we live in a technology-based society, so
schools need to get with the program and adopt a modern approach to learning. (3) In fact, the chair
of the Federal Communications Commission said that "it's time for the next stage" of learning with
tablets and pointed out how textbooks are often out of date. (4) Opponents argue that tablets aren't
a good choice because initially they're very expensive. (5) The secretary of education pointed out
that tablets can be updated regularly, which saves money in the long run. (6) Not to mention the
pluses of having the latest and greatest info! (7) Many experts agree that switching to tablets is
important for the future of education.
To improve the logical flow of the paragraph, the bestplace to move sentence 7 is before

Answers

This question is incomplete because the options are missing; here is the question statement and options:

To improve the logical flow of the paragraph, the best place to move sentence 7 is before

A. Sentence 1.

B. Sentence 3.

C. Sentence 5.

D. Sentence 6.

The correct answer is B. Sentence 3

Explanation:

The paragraph develops an argument through different sections. This includes the thesis statement "schools should switch from using paper textbooks to using computer tablets", reasons and evidence that support this thesis, the explanation of one counterclaim, and finally, reasons to disprove the counterclaim and confirm the claim.

In the case of sentence 7 "Many experts agree that switching to tablets is  important for the future of education" this provides a reason that supports the argument and due to this, it is more appropriate this sentence is placed after the thesis and before the counterclaim "Opponents argue that tablets ...".

In this context, this sentence should be placed before sentence 3 that belongs to the evidence provided to support the claim. Moreover, sentence 7 would appropriately introduce sentence 3 as they are both related to the opinion of experts about this issue.

The 7th sentence can be placed before the first, third, and fifth.

Decision making

The process of making an important decision is known as decision making.

Given

7 statement is there.

To find the position of the 7th sentence.

How to place 7th sentences?

7th sentence can be placed before the first because it seems that the conversation is starting.

7th sentence can be placed before the third because you can say as an update will be done by  Federal Communications Commission.

7th sentence can be placed before the fifth because the secretary wants to implement it in his system due to its regular update.

Thus, the 7th sentence can be placed before the first, third, and fifth.

More about the decision-making link is given below.

https://brainly.com/question/3369578

Teresa is investigating if grade level has any effect on time spent studying. What is the response variable?

Answers

Answer:

The time spent studying is the response variable.

Step-by-step explanation:

The response variable, also known as the dependent variable is the main question which the experiment wants to provide an answer for. Usually, the predictors determine or affect the response variable.  In the study where Teresa investigates the effect of grade level on time spent studying, the response variable is the time spent studying, while the predictor which is the grade level provides an explanation as to the time spent studying.

The changes or variations on time spent studying depends on the grade level. This means that the grade level provides an explanation of the length of time dedicated to studying.

Q1. 12.5g of medicine cost 1,075 naira. What is the cost of 1g of medicine. Q2. What is the total pay for someone who works 42 hours and gets 645 naira per hour

Answers

Step-by-step explanation:

Q1. 1,075÷12.5 =8

So Therefore 1g of medicine cost 8 naira

Q2.645÷42=15.3

so therefore 1 hour cost 15.3 naira

The cost of 1g of medicine is 86 naira and the total pay for someone who works 42 hours  is 27090 naira.

What is Division?

A division is a process of splitting a specific amount into equal parts.

Given that 12.5g of medicine cost 1,075 naira.

We have to find the cost of 1g of medicine.

12.5g=1075 naira

1g=1075/12.5

1g=86 naira.

the total pay for someone who works 42 hours and gets 645 naira per hour

The cost for 42 hours

42×645

27090 naira

Hence,  the cost of 1g of medicine is 86 naira and the total pay for someone who works 42 hours  is 27090 naira.

To learn more on Division click:

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Find the radius of the cylinder when volume is 304 cm^3 and height is 10 cm

Answers

Answer:

3.11 cm

solution,

Volume of cylinder=304 cm^3

height=10 cm

Radius=?

Now,

[tex]volume = \pi {r}^{2} h \\ or \: 304 = 3.14 \times {r}^{2} \times 10 \\ or \: 304 = 31.4 \times {r}^{2} \\ or \: {r}^{2} = \frac{304}{31.4} \\ or \: {r}^{2} = 9.68 \\ or \: r = \sqrt{9.68} \\ or \: r = \sqrt{ {(3.11)}^{2} } \\ r = 3.11 \: cm[/tex]

Hope this helps..

Good luck on your assignment..

what is the answer to 263·24−164·24+24

Answers

Answer:

2400

Step-by-step explanation:

You have to follow PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction).  Based off of this, you have to do the multiplication first, and then add.

263 × 24 - 164 × 24 + 24

6312 - 3936 + 24

2376 + 24

2400

The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.

What is the value of the expression?

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The expression is given below.

⇒ 263 · 24 − 164 · 24 + 24

Simplify the expression, then the value of the expression is given as,

⇒ 263 · 24 − 164 · 24 + 24

⇒ 6312 − 3936 + 24

⇒ 6336 − 3936

⇒ 2400

The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.

More about the value of the expression link is given below.

https://brainly.com/question/23671908

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The public radio show "A Prairie Home Companion," features news from the fictional town of Lake Wobegon, MN, home to many Norwegian bachelor farmers, and where "all the women are strong, all the men are good looking, and all the children are above average." Suppose average means average for the town. Such a town could not possibly exist, because (select all that apply)

a. not all women are strong

b. not all the children can be above average

c. not all Norwegian bachelor farmers are good looking

d. half the children must be below average

Answers

Answer:

b. not all the children can be above average

d. half the children must be below average

Step-by-step explanation:

In theory, all women could be strong and all men could be good looking, however, since the average is calculated based on the town children, it is not possible for all children to be above average.

Assuming a normal distribution, half the children must be at or below average, while the other half must be at or above the average.

Therefore, the correct answers are:

b. not all the children can be above average

d. half the children must be below average

Answer:

Second and last options are correct choices.

Step-by-step explanation:

If all the children are above average, then the average should not include the average of the children. Because it is impossible for a data set to be have values greater than it's average.

Best Regards!

Which equation has a constant of proportionality equal to 10 choose 1 answer a, y=2/20x b, y=30/3x c, y=12/2x d, y=5/5x

Answers

Answer:

b

Step-by-step explanation:

30/3x=10

Find the width of a photograph whose length is 8 inches and whose proportions are the same as a photograph that is 18 inches wide by 24 inches long.

Answers

Answer:

6 Inches

Step-by-step explanation:

First Photograph

Length:Width = 24:18

Second Photograph

Let the unknown width =x

Length:Width = 8:x

Since the proportions of the two photographs are the same

[tex]8:x=24:18\\\\\dfrac{8}{x}= \dfrac{24}{18}\\\\24x=8 \times 18\\\\x=(8 \times 18) \div 24\\\\x=6$ inches[/tex]

The width of the photograph is 6 inches.

Write the value of the money in dollars 4-8 Brainliest Awnser gets 7 points for greatness

Answers

4. 12 cent

5. $2.06

6. $1.56

7. $1.30

8. 86 cent

ab = cde


In order to solve the equation above for c, you must multiply both sides of the equation by the same expression

ab x _? = cde x _?

The resulting equation is

C= _?

Answers

Answer:

1) We have to multiply both sides by  1/(de)

2) c=ab/(cd)

Step-by-step explanation:

We have to achieve the right side expression be c only.  To do that we have to multiply cde by   1/(de) .  However we have to multiply the left side by

1/(de) as well.

So the resulting left side expression is:

ab *1/(de)=ab/(de)

So c= ab/(de)

Given equation in the question is,

ab = cde

To solve the given equation for the value of c, follow the algebraic rules,

1). Multiply both the sides of the equation with [tex]\frac{1}{de}[/tex],

   [tex]ab\times \frac{1}{de} = \frac{cde}{de}[/tex]

   [tex]\frac{ab}{de}= \frac{cde}{de}[/tex]

   [tex]\frac{ab}{de}=c[/tex]

Therefore, resulting equation for c will be,

[tex]c=\frac{ab}{de}[/tex]

Learn more,

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what is the solution set of y= x^2+2x+7 and y= x+7 ?

Answers

Answer:

(-1, 6)

(0, 7)

Step-by-step explanation:

Easiest and fastest way to do this is to graph both equations and analyze the graph for when they intersect each other.

Karen, Pete, Rose, and David are comparing their solutions to a homework problem below.
(+ + 8
(-2)
1
Select the student who correctly subtracted the rational expressions,
Karen:
Pete:
+ 8 - 7
2
2)
5
(1 + 8)(x + 5) - 7
(1 - 2)(+ 5)
12 + 135 + 40 - 77 + 14
2 + 3x - 10
1? +61 + 54
12 + 91 - 10
Rose:
David:
(1 + 5
(1 + 8)
(r
+3+*5
(+216-6= x2 + 35 – 10
1 + 1
x2 + 3x - 10
7: + 8) + (x - 2)(= + 5)
7(: - 2)
II
75 + 8 + 12 + 91 - 10
78 14
2 + 101 - 2
70 - 14

Answers

Answer:pete

Step-by-step explanation:

A taxi charges a flat rate of $3.00 plus $1.50 per mile. If Xander has $45.00, which inequality represents m, the distances in miles he can travel in the taxi? m less-than-or-equal-to 10 m greater-than-or-equal-to 10 m less-than-or-equal-to 28 m greater-than-or-equal-to 28

Answers

Answer:

  m less-than-or-equal-to 28

Step-by-step explanation:

Xander's charge for m miles will be (3 +1.50m). He wants this to be no more than $45, so ...

  3 +1.50m ≤ 45

  1.50m ≤ 42 . . . . . . subtract 3

  m ≤ 28 . . . . . . . . . .divide by 1.5

Answer: M is less than or equal to 28 or C

Step-by-step explanation:

GOT RIGHT ON E D G

divide
a) 21564÷2
b)40565÷5
c)6365÷8
d)1436÷7



answer please fast ​

Answers

Answer:

21564 ÷ 2 = 10782

40565 ÷ 5 = 8113

6365 ÷ 8 = 795.625

1436 ÷ 7 = 205.142857143

You and 3 of your friends decide to sell lemonade around town, and then split the money you make evenly. You decide to sell each cup of lemonade for 50 cents. In total, you all sell 120 cups of lemonade. How much money will each of you earn? Write an expression for the problem too.


Expression:


Answers

Answer:

$15

Step-by-step explanation:

Each cup is 50 cents which is basically $0.50

Multiply $0.50 by 120= $60

Because you and your three friends equal 4 total people,

divide 60 by 4 to get your own profit:

60/4=15

Solve 56000(1+1.8%)^5

Answers

Answer:

The solution to this expression is 61,224.74

Step-by-step explanation:

To solve we initially have to convert the percentage to a decimal:

[tex]1.8\% = \frac{1.8}{100} = 0.018[/tex]

So

56000*(1+1.8%)^5 = 56000(1+0.018)^5 = 56000(1.018)^5 = 61,224.74

The solution to this expression is 61,224.74

What is the slope of the line between (−4, 4) and (−1, −2)?

Answers

Answer:

-2

Step-by-step explanation:

The slope of a line is

m = (y2-y1)/(x2-x1)

   = (-2 -4)/(-1 - -4)

   = -6/ ( -1 +4)

   = -6 /3

    =-2

Answer:

[tex]= - 2 \\ [/tex]

Step-by-step explanation:

[tex]( - 4 \: \: \: \: \: \: \: \: \: \: \: 4) = > (x1 \: \: \: \: \: \: y1) \\ ( - 1 \: \: \: \: - 2) = > (x2 \: \: \: \: \: \: y2)[/tex]

Now let's find the slope

[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{4 - ( - 2)}{ - 4 - ( - 1)} \\ = \frac{4 + 2}{ - 4 + 1} \\ = \frac{6}{ - 3} \\ = - 2[/tex]

hope this helps you.

brainliest appreciated

good luck! have a nice day!

According to an​ airline, flights on a certain route are on time 80​% of the time. Suppose 17 flights are randomly selected and the number of​ on-time flights is recorded.

Required:
a. Explain why this is a binomial experiment.
b. Find and interpret the probability that exactly 11 flights are on time.
c. Find and interpret the probability that fewer than 11 flights are on time
d. Find and interpret the probability that at least 11 flights are on time.
e. Find and interpret the probability that between 9 and 11 flights, inclusive, are on time.

Answers

Answer:

a) Check Explanation

b) Probability that 11 out of the 17 randomly selected flights are on time = P(X = 11) = 0.0680

c) Probability that fewer than 11 out of the 17 randomly selected flights are on time

= P(X < 11) = 0.0377

d) Probability that at least 11 out of the 17 randomly selected flights are on time

= P(X ≥ 11) = 0.9623

e) Probability that between 9 and 11 flights, inclusive, out of the randomly selected 17 are on time = P(9 ≤ X ≤ 11) = 0.1031

Step-by-step explanation:

a) How to know a binomial experiment

1) A binomial experiment is one in which the probability of success doesn't change with every run or number of trials. (Probability of each flight being on time is 80%)

2) It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (It's either the flights are on time or not).

3) The outcome of each trial/run of a binomial experiment is independent of one another.

All true for this experiment.

b) Probability that exactly 11 flights are on time.

Let X be the random variable that represents the number of flights that are on time out of the randomly selected 17.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 17 randomly selected flights

x = Number of successes required = number of flights required to be on time

p = probability of success = Probability of a flight being on time = 80% = 0.80

q = probability of failure = Probability of a flight NOT being on time = 1 - p = 1 - 0.80 = 0.20

P(X = 11) = ¹⁷C₁₁ (0.80)¹¹ (0.20)¹⁷⁻¹¹ = 0.06803777953 = 0.0680

c) Probability that fewer than 11 flights are on time

This is also computed using binomial formula

It is the probability that the number of flights on time are less than 11

P(X < 11) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0376634429 = 0.0377

d) Probability that at least 11 out of the 17 randomly selected flights are on time

This is the probability of the number of flights on time being 11 or more.

P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17)

= 1 - P(X < 11)

= 1 - 0.0376634429

= 0.9623365571 = 0.9623

e) Probability that between 9 and 11 flights, inclusive, are on time = P(9 ≤ X ≤ 11)

This is the probability that exactly 9, 10 or 11 flights are on time.

P(9 ≤ X ≤ 11) = P(X = 9) + P(X = 10) + P(X = 11)

= 0.0083528524 + 0.02672912767 + 0.06803777953

= 0.1031197592 = 0.1031

Hope this Helps!!!

Bruce goes hiking every 2 days and swimming every 11 days . He did both kinds of exercise today . How many days from now will he next go both hiking and swimming again.

Answers

To find out this answer, we will find the LCM of 2 and 11.

LCM= 22

So, Bruce will go for hiking and swimming together after another 22 days.

Hope it helps
Please mark my answer as BRAINLIEST

Answer:

22 more days

Step-by-step explanation:

so basically you have to find out the LCM of 2 and 11. which is 22. And that means they go hiking AND swimming in the same day the next 22 days. (basically what the other person said lol)

AND that is basically your answer :D

3. What is the explicit formula for the arithmetic sequence 2, 7, 12, 17, ...?

Answers

Step-by-step explanation:

The given sequences are;

2,7,12,17......

difference =5

by using formula,

we get,

tn=a+(n-1)d

tn= 2+(n-1)5

Therefore, tn is 5n-3 is required formula for this arithmetic sequences.

Hope it helps....

Please answer this correctly

Answers

Answer:

75%

Step-by-step explanation:

There are 3 numbers that fit this rule, 3, 5, and 6. There is a 3/4 chance spinning one or a 75% chance.

Answer:

75%

Step-by-step explanation:

The numbers 6 or odd are 3, 5, and 6.

3 numbers out of a total of 4 numbers.

3/4 = 0.75

Convert to percentage.

0.75 × 100 = 75

P(6 or odd) = 75%

The relative frequency distribution of the number of phobias reported by a hypothetical sample of 500 college students is given as follows.

0–2 0.48
3–5 0.26
6–8 0.12
9–11 0.09
12–14 0.05

Required:
a. What is the probability that a college student expresses fewer than three phobias?
b. What is the probability that a college student expresses more than eight phobias?
c. What is the probability that a college student has between 3 and 11 phobias?

Answers

Answer:

a. 0.48

b. 0.14

c. 0.47

Step-by-step explanation:

Data provided in the question

0 - 2        0.48

3 - 5        0.26

6 - 8        0.12

9- 11        0.09

12- 14       0.05

Based on the above information

a. The probability for fewer than three phobias is

= P( x < 3)

= 0.48

b.  The probability for more than eight phobias is

= P( x >8)

= 0.09 + 0.05  

= 0.14

c. Probability between 3 and 11 phobias is  

= P(3 < x < 11)

= 0.26 + 0.12  + 0.09

= 0.47

The confidence interval on estimating the heights of students is given as (5.4, 6.8). Find the sample mean of the confidence interval.

Answers

Answer:

The sample mean is 6.1

Step-by-step explanation:

Margin of Error (E) = (upper limit - lower limit)/2 = (6.8 - 5.4)/2 = 1.4/2 = 0.7

Sample mean = lower limit + E = 5.4 + 0.7 = 6.1

A cone-shaped paper drinking cup is to be made to hold 33 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.) height cm radius cm

Answers

Answer:

The height and the radius of the cylinder are 3.67 centimeters and 5.19 centimeters, respectively.

Step-by-step explanation:

The volume ([tex]V[/tex]) and the surface area ([tex]A_{s}[/tex]) of the cone, measured in cubic centimeters and square centimeters, respectively, are modelled after these formulas:

Volume

[tex]V = \frac{h\cdot r^{2}}{3}[/tex]

Surface area

[tex]A_{s} = \pi\cdot r \cdot \sqrt{r^{2}+h^{2}}[/tex]

Where:

[tex]h[/tex] - Height of the cylinder, measured in centimeters.

[tex]r[/tex] - Radius of the base of the cylinder, measured in centimeters.

The volume of the paper drinking cup is known and first and second derivatives of the surface area functions must be found to determine the critical values such that surface area is an absolute minimum. The height as a function of volume and radius of the cylinder is:

[tex]r = \sqrt{\frac{3\cdot V}{h} }[/tex]

Now, the surface area function is expanded and simplified:

[tex]A_{s} = \pi\cdot \sqrt{\frac{3\cdot V}{h} }\cdot \sqrt{\frac{3\cdot V}{h}+ h^{2}}[/tex]

[tex]A_{s} = \pi\cdot \sqrt{\frac{9\cdot V^{2}}{h^{2}} + 3\cdot V\cdot h }[/tex]

[tex]A_{s} = \pi\cdot \sqrt{3\cdot V} \cdot\sqrt{\frac{3\cdot V+ h^{3}}{h^{2}} }[/tex]

[tex]A_{s} = \pi\cdot \sqrt{3\cdot V}\cdot \left(\frac{\sqrt{3\cdot V + h^{3}}}{h}\right)[/tex]

If [tex]V = 33\,cm^{3}[/tex], then:

[tex]A_{s} = 31.258\cdot \left(\frac{\sqrt{99+h^{3}}}{h} \right)[/tex]

The first and second derivatives of this function are require to determine the critical values that follow to a minimum amount of paper:

First derivative

[tex]A'_{s} = 31.258\cdot \left[\frac{\left(\frac{3\cdot h^{2}}{\sqrt{99+h^{2}}}\right)\cdot h - \sqrt{99+h^{3}} }{h^{2}}\right][/tex]

[tex]A'_{s} = 31.258\cdot \left(\frac{3\cdot h^{3}-99-h^{3}}{h^{2}\cdot \sqrt{99+h^{2}}} \right)[/tex]

[tex]A'_{s} = 31.258\cdot \left(\frac{2\cdot h^{3}-99}{h^{2}\cdot \sqrt{99+h^{2}}} \right)[/tex]

[tex]A'_{s} = 31.258\cdot \left[2\cdot h\cdot (99+h^{2}})^{-0.5} -99\cdot h^{-2}\cdot (99+h^{2})^{-0.5}\right][/tex]

[tex]A'_{s} = 31.258\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-0.5}[/tex]

Second derivative

[tex]A''_{s} = 31.258\cdot \left[(2+198\cdot h^{-3})\cdot (99+h)^{-0.5}-0.5\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-1.5}\right][/tex]

Let equalize the first derivative to zero and solve the resultant expression:

[tex]31.258\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-0.5} = 0[/tex]

[tex]2\cdot h - 99 \cdot h^{-2} = 0[/tex]

[tex]2\cdot h^{3} - 99 = 0[/tex]

[tex]h= \sqrt[3]{\frac{99}{2} }[/tex]

[tex]h \approx 3.672\,cm[/tex]

Now, the second derivative is evaluated at the critical point:

[tex]A''_{s} = 31.258\cdot \{[2+198\cdot (3.672)^{-3}]\cdot (99+3.672)^{-0.5}-0.5\cdot [2\cdot (3.672) - 99\cdot (3.672)^{-2}]\cdot (99+3.672)^{-1.5}\}[/tex]

[tex]A''_{s} = 18.506[/tex]

According to the Second Derivative Test, this critical value leads to an absolute since its second derivative is positive.

The radius of the cylinder is: ([tex]V = 33\,cm^{3}[/tex] and [tex]h \approx 3.672\,cm[/tex])

[tex]r = \sqrt{\frac{3\cdot V}{h} }[/tex]

[tex]r = \sqrt{\frac{3\cdot (33\,cm^{3})}{3.672\,cm} }[/tex]

[tex]r \approx 5.192\,cm[/tex]

The height and the radius of the cylinder are 3.672 centimeters and 5.192 centimeters, respectively.

If this procedure is repeated 100 times, what is the probability that the number of times that the coin lands tails will be less than 40

Answers

Answer:

1.79% probability that the number of times that the coin lands tails will be less than 40

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

100 times

[tex]n = 100[/tex]

Then

[tex]\mu = E(X) = np = 100*0.5 = 50[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5[/tex]

What is the probability that the number of times that the coin lands tails will be less than 40

Using continuity correction, this is [tex]P(X < 40 - 0.5) = P(X < 39.5)[/tex], which is the pvalue of Z when X = 39.5.

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

[tex]Z = \frac{39.5 - 50}{5}[/tex]

[tex]Z = -2.1[/tex]

[tex]Z = -2.1[/tex] has a pvalue of 0.0179

1.79% probability that the number of times that the coin lands tails will be less than 40

Use x=1 to identify the value of each expression.

Answers

Answer:

[tex] {9}^{1} = 9 \\ {3}^{1} = 3 \\ {1}^{3} = 1[/tex]

Beverly drove from the Atlantic City to New York she drove 284 miles at a constant speed of 58 mph how long did it take Beverly to complete the trip

Answers

Answer:

4.9 hours = 4 hours 54 minutes

Step-by-step explanation:

speed = distance/time

time * speed = distance

time = distance/speed

time = (284 miles)/(58 mph) = 4.9 hours

4.9 hours - 4 hours = 0.9 hours

0.9 hours * (60 minutes)/(1 hour) = 54 minutes

4.9 hours = 4 hours 54 minutes

Follow the directions to solve the system of equations by elimination. 8x + 7y = 39 4x – 14y = –68 Multiply the first equation to enable the elimination of the y-term. Add the equations to eliminate the y-terms. Solve the new equation for the x-value. Substitute the x-value back into either original equation to find the y-value. Check the solution.

Answers

Answer:

x=½

y=5

Step-by-step explanation:

(8x+7y=39)2

16x+14y=78

4x-14y=-68 add the two equations

20x=10.

divide both sides by 20

x=½

8x+7y=39

4+7y=39

7y=39-4

7y=35

y=5

The value of x and y in the system of equation using elimination method is 1 / 2and 5 respectively.

8x + 7y = 39

4x – 14y = –68

Multiply the first equation to enable the elimination of the y-term:

Multiply by 2

16x + 14y = 78

Add the equations to eliminate the y-terms:

-14y + 14y = 0

4x + 16x = 20x

-68 + 78 = 10

Solve the new equation for the x-value

20x = 10

x = 1 / 2

Substitute the x-value back into either original equation to find the y-value

8(1 / 2) + 7y = 39

4 + 7y = 39

7y  = 35

y = 35 / 7

y = 5

learn more on system of equation here: https://brainly.com/question/3861421?referrer=searchResults

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