Looking for help finding the area to show work

Answer:

2x-2

Step-by-step explanation:

2(x-1)=

Distribute

2x* -2*1

2x-2

Answer:

[tex]2x - 2[/tex]

Solution,

[tex]2(x - 1) \\ = 2 \times x - 2 \times 1 \\ = 2x - 2[/tex]

hope this helps..

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.

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.

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

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.

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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Answer:

Volume of the sphere= 113.112 cubic inch(Inch ³)

Step-by-step explanation:

First of all the formula for the volume of a sphere Is given as 4πr³

Already the radius r is already given as 3 inches

While π = 3.142

Volume of the sphere = 4/3πr³

Volume of the sphere = 4/3(3.142)(3)³

Volume of the sphere= 4/3(3.142)(27)

Volume of the sphere= 4/3(84.834)

Volume of the sphere= 339.336/3

Volume of the sphere= 113.112 Inch ³

Volume of the sphere= 113.112 cubic inch

Answer:

b

Step-by-step explanation:

30/3x=10

4. 12 cent

5. $2.06

6. $1.56

7. $1.30

8. 86 cent

Answer:

Hey there!

We have x+2y=5, and x-2y=5.

x+2y=5

x-2y=5

Add the x's to get 2x and the 2y's to get 0. Finally add the 5's to get 10.  

Thus, we have 2x+0=10, or 2x=10.

x=5

y=0

Hope this helps :)

Answer:

x=3,y=1

Step-by-step explanation:

x+2y = 5

x-2y = 1

Add the two equations together to eliminate y

x+2y = 5

x-2y = 1

----------------------

2x +0y = 6

Divide by 2

2x/2 = 6/2

x = 3

Then solve for y

x+2y = 5

3 + 2y =5

2y = 5-3

2y = 2

Divide by 2

2y/2 = 2/2

y =1

x=3,y=1

Check

3+2(1) = 5

5=5

3-2(1)=1

1=1

Answer:

The probability of the infected is more than 8 in a hour is 0.00384

Step-by-step explanation:

Given that the Mean of the arrival rate of the infect follows a Poisson distribution =   x`= 3 / hour

The Poisson distribution formula is given by

P(X) = e-ˣ` x`ˣ/ x!

The mean is 3 and we have to find the probability of 8 or more which means

1 -X  where X takes the values of 0,1,2,3,------,8.

P( more than 8 ) = 1- P( X ≤ 8 ) =1- {e-³ (3)⁸/8! +e-³ (3)⁷/7! +e-³ (3)⁶/6! +e-³ (3)⁵/5! +e-³ (3)⁴/4! +e-³ (3)³/3! +e-³ (3)²/2!+ e-³ (3)¹/1! +e-³ (3)⁰/0!}

Putting the Values

P( more than 8 ) = 1- P( X ≤ 8 ) =1- [ 0.04979*6561 / 40320 +0.04979*2187 / 5040 + 0.04979*729 / 720 +0.04979*243 / 120+0.04979*81 / 24 + 0.04979 *27 / 6 + 0.04979 *9 /2 + 0.04979*3/ 1 + 0.04979*1/1 }

Solving

P( more than 8 ) = 1- P( X ≤ 8 ) =1- [ 0.0081 + 0.0216 + 0.0504 + 0.1008 + 0.1680 + 0.2240 + 0.2241+ 0.14937 + 0.04979]

P( more than 8 ) = 1- P( X ≤ 8 ) =1-0.99616

P( more than 8 ) = 1- P( X ≤ 8 ) =0.00384

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!!!

Answer:

The Empirical Rule

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

So the answer to this question is the Empirical Rule

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.

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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Great Question!

The problem we have at hand is known to be a function, which maps elements from one set of objects, ( the domain ) onto another, the range. If we were to consider an ordered pair, say ( x, y ), then the function would map x onto y. The inverse function is simply the reverse. Take the ordered pair (-4,0). Function g would map - 4 onto 0, such that [tex]g( - 4 ) = 0[/tex]. Therefore, the inverse function would map 0 onto - 4, resulting in [tex]g^{-1}( 0 ) = - 4[/tex]. And there you have it! Our first part is answered!

____

This second bit here is interesting. Let [tex]y = h( x )[/tex] -

[tex]y = 4x + 3[/tex] - Switch x and y,

[tex]x = 4y + 3[/tex] - And now solve this equation for y,

[tex]x - 4y = 3,\\- 4y = - x + 3,\\y = 1 / 4x - 3 / 4[/tex]

As you can see, we have taken the inverse of h( x ). As y = h( x ), we can thus conclude the following -

[tex]h^{-1}(x) = 1 / 4x - 3 / 4[/tex]

____

The composition (h^-1 o h)(-5) is, in other words, h^-1(h(-5)). We can therefore calculate h(-5) and then take it's inverse -

[tex]h(-5) = 4(-5) + 3,\\h(-5) = - 20 + 3,\\h(-5) = - 17[/tex]

Now we can take it's inverse -

[tex]h^{-1}(-17) = 1 / 4( - 17 ) - 3 / 4,\\- 17 / 4 - 3 / 4,\\= - 5![/tex]

Our solution for this last bit is - 5. And, if you don't feel like reading through this entire explanation just take a look at the " summed up " answer below,

[tex]g^{-1}( 0 ) = - 4,\\\\h^{-1}( x ) = 1 / 4x - 3 / 4,\\\\( h * h^{-1} )( - 5 ) = - 5[/tex]  I do hope that helps you!

Answer:

Or 50

Step-by-step explanation:

Answer:

a) The normal distribution function for the IQ of a randomly selected individual is presented in the first attached image to this solution.

b) The probability that the person has an IQ greater than 105 = P(X > 105) = 0.3707

The sketch of this probability is presented in the second attached image to this solution.

c) The minimum IQ needed to qualify for the Mensa organization = 130.81. Hence, P(X > 131) = 2%

The sketched image of this probability is presented also in the second attached image to the solution. The shaded region is the required probability.

d) The middle 40% of IQs fall between 92 and 108 IQ respectively.

P(x1 < X < x2) = P(92 < X < 108) = 0.40

The sketched image of this probability is presented in the third attached image to the solution. The shaded region is the required probability.

Step-by-step explanation:

The IQ of an individual is given as a normal distribution withh

Mean = μ = 100

Standard deviation = σ = 15

If X is a random variable which represents the IQ of an individual

a) The distribution of X will then be given as the same as that of a normal distribution.

f(x) = (1/σ√2π) {e^ - [(x - μ)²/2σ²]}

The normal distribution probability density function is more clearly presented in the first attached image to this question

b) Probability that the person has an IQ greater than 105.

To find this probability, we will use the normal probability tables

We first normalize/standardize 105.

The standardized score of any value is that value minus the mean divided by the standard deviation.

z = (x - μ)/σ = (105 - 100)/15 = 0.33

P(x > 105) = P(z > 0.33)

Checking the tables

P(x > 105) = P(z > 0.33) = 1 - P(z ≤ 0.33) = 1 - 0.6293 = 0.3707

The sketch of this probability is presented in the second attached image to this question. The shaded region is the required probability.

c) Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization.

We need to find x for P(X > x) = 2% = 0.02

Let the corresponding z-score for this probability be z'

P(X > x) = P(z > z') = 0.02

P(z > z') = P(z ≤ z') = 1 - 0.02 = 0.98

From the normal distribution table, z' = 2.054

z = (x - μ)/σ

2.054 = (x - 100)/15

x = 2.054×15 + 100 = 130.81 = 131 to the nearest whole number.

The sketched image of this probability is presented also in the second attached image to the solution. The shaded region is the required probability.

d) The middle 40% of IQs fall between what two values?

P(x1 < X < x2) = 0.40

Since the normal distribution is symmetric about the mean, the lower limit of this IQ range will be greater than the lower 30% region of the IQ distribution and the upper limit too is lesser than upper 30% region of the distribution.

P(X < x1) = 0.30

P(X > x2) = 0.30, P(X ≤ x2) = 1 - 0.30 = 0.70

Let the z-scores of x1 and x2 be z1 and z2 respectively.

P(X < x1) = P(z < z1) = 0.30

P(X ≤ x2) = P(z ≤ z2) = 0.70

From the normal distribution tables,

z1 = -0.524

z2 = 0.524

z1 = (x1 - μ)/σ

-0.524 = (x1 - 100)/15

x1 = -0.524×15 + 100 = 92.14 = 92 to the nearest whole number.

z2 = (x2 - μ)/σ

0.524 = (x2 - 100)/15

x2 = 0.524×15 + 100 = 107.86. = 108 to the nearest whole number.

The sketched image of this probability is presented in the third attached image to the solution. The shaded region is the required probability.

Hope this Helps!!!

Answer:

x=3, y=-2, z=1

Step-by-step explanation:

I solved by substitution

Answer:

x = 3; y = -2; z = 1.

Step-by-step explanation:

-x + 2y + 4z = -3

x – 2y - 3z = 4

(-x + x) + (2y - 2y) + (4z - 3z) = (-3 + 4)

0 + 0 + z = 1

z = 1

x - 2y - 3(1) = 4

x - 2y - 3 = 4

x - 2y = 7

x = 2y + 7

2(2y + 7) + y - (1) = 3

4y + 14 + y - 1 = 3

5y + 13 = 3

5y = -10

y = -2

x = 2(-2) + 7

x = -4 + 7

x = 3

So, your answer is (3, -2, 1).

Hope this helps!

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.

Answer:

A repeating decimal is not a rational number and The product of two irrational numbers is always rational

Step-by-step explanation:

One statement that is not true is "The product of two irrational numbers is always rational". Take for example the irrational numbers √2 and √3. Their product is √6 which is also irrational.

The other false statement is "A repeating decimal is not a rational number". Take for example the repeating decimal 0.33333..... It can be written as 1/3 which is a rational number.

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

Answer:

21564 ÷ 2 = 10782

40565 ÷ 5 = 8113

6365 ÷ 8 = 795.625

1436 ÷ 7 = 205.142857143

Answer:

-5°C < 5°C

The temperature was higher on Wednesday than on Tuesday.

Answer:

150/250 or 3/5 or a 60% chance

Step-by-step explanation:

Why?

because you need to calculate the number of balls that are a three-digit number and they will not be a three-digit number up until you get to 100 so what is 250-100? its 150  so your fraction is  150/250 or 3/5 if you need it simplified. To get a percent you need to divide 150 by 250 to get 0.6 and then you multiply by 100.

Answer:

a) This t-value obtained (2.92) is in the rejection region (t > 1.69), hence, the sample does not support the cofdee industry's claim.

b) p-value for this test = 0.006266

c) The p-value obtained for this test is lesser than the significance level at which the test was performed, hence, we can reject the nuĺl hypothesis and say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Step-by-step explanation:

a) Degree of freedom = n - 1 = 34 - 1 = 33

The critical value of t for a significance level of 0.10 and degree of freedom of 33 = 1.69

Since we are testing in both directions whether the the average U.S. adult drinks 1.7 cups of coffee per day using our sample,

The rejection region is t < -1.69 and t > 1.69

So, we compute the t-statistic for this sample data to test the claim.

t = (x - μ)/σₓ

x = sample mean = 1.95 cups of coffee per day

μ₀ = The standard we are comparing against = 1.7 cups of coffee per day

σₓ = standard error = (σ/√n)

σ = standard deviation = 0.5 cups

n = Sample size = 34

σₓ = (0.5/√34) = 0.0857492926 = 0.08575

t = (1.95 - 1.70) ÷ 0.08575

t = 2.9154759464 = 2.92

This t-value obtained is in the rejection region, hence, the sample does not support the cofdee industry's claim.

b) Checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 34 - 1 = 33

Significance level = 0.10

The hypothesis test uses a two-tailed condition because we're testing in both directions.

p-value (for t = 2.92, at 0.10 significance level, df = 33, with a two tailed condition) = 0.006266

c) To use PHStat, the claim that the average U.S. adult drinks 1.7 cups of coffee per day is the null hypothesis.

The alternative hypothesis is that the real number of cups of coffee that the average U.S. adult drinks as obtained from the sample data, is significantly different from the 1.7 in the coffee industry's claim.

The p-value obtained from PHstat = 0.0063

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.10

p-value = 0.0063

0.0063 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Hope this Helps!!!

Answer:

60

Step-by-step explanation:

We are using sigma notation to solve for a sum of arithmetic sequences:

The 5 stands for stop at i = 5 (inclusive)

The i = 1 stands for start at i = 1

The 12 stands for expression of each term in the sum

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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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

Answer:

C.

Step-by-step explanation:

Easiest and quickest way to do this is to plug it into your calc. Using the Binomial Theorem would be a time killer for this question, especially when it's an evaluation question.

Answer:

The answer is option C

Step-by-step explanation:

I just got it right

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.

Answer: 9

Step-by-step explanation:

Apex

Answer:

The functions that represent this situation are A. [tex]f(n)=3\cdot 2^{n-1}[/tex] and C. [tex]a(n)=a(n-1)\cdot 2; a(1)=3[/tex].

Step-by-step explanation:

A geometric sequence goes from one term to the next by always multiplying or dividing by the same value.

In geometric sequences, the ratio between consecutive terms is always the same. We call that ratio the common ratio.

This is the explicit formula for the geometric sequence whose first term is k and common ratio is r:

                                                [tex]a(n)=k\cdot r^{n-1}[/tex]

This is the recursive formula of that sequence:

                                                 [tex]a(1)=k\\\\a(n)=a(n-1)\cdot r[/tex]

We know that the first term is k = 3 and the common ratio is r = 2. Therefore,

The explicit formula is [tex]f(n)=3\cdot 2^{n-1}[/tex] and the recursive formula is [tex]a(n)=a(n-1)\cdot 2; a(1)=3[/tex].

Answer:

Step-by-step explanation:

To solve for x we use sine

sin ∅ = opposite / hypotenuse

From the question

38 is the hypotenuse

20 is the opposite

So we have

sin x = 20/38

sin x = 10/19

x = sin-¹ 10/19

x = 31.75

Hope this helps you