Find the surface area of the cylinder
8 cm
3 cm
The surface area of the cylinder is cm?
(Simplify your answer. Type an exact answer in terms of r.)
Enter your answer in the answer hoy

Answer:

5.4 = 7.56

1.5 = 2.1

Step-by-step explanation:

Just find the answer for 40% of the given meters.

The restrictions on the width is that it must be between 14.1 yards and 17.3 yards

From the question, we have the following parameters that can be used in our computation:

Area = between 240 yd² and 360 yd²

Also, we have

Length = 1.2 times the width

This means that

l = 1.2w

The area is then calculated as

Area = lw

So, we have

Area = 1.2w²

This means that

240 < 1.2w² < 360

Divide through by 1.2

200 < w² < 300

Take the square roots

14.14 < w < 17.32

Approximate

14.1 < w < 17.3

Hence, the width must be between 14.1 yards and 17.3 yards

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Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

Answer:

The question is incomplete

Answer:

It was 1/3 before

Step-by-step explanation:

Answer:

0.0778 = 7.78% probability that the average age at death of these nine participants will exceed 68 years

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

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

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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.

Central Limit Theorem

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

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

Approximately normal with mean equal to 66.3 years and standard deviation equal to 3.6 years.

This means that \(\mu = 66.3, \sigma = 3.6\)

Sample of 9:

This means that \(n = 9, s = \frac{3.6}{\sqrt{9}} = 1.2\)

What is the probability that the average age at death of these nine participants will exceed 68 years?

This is 1 subtracted by the pvalue of Z when X = 68. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{68 - 66.3}{1.2}\)

\(Z = 1.42\)

\(Z = 1.42\) has a pvalue of 0.9222

1 - 0.9222 = 0.0778

0.0778 = 7.78% probability that the average age at death of these nine participants will exceed 68 years

Answer:

it will be one out six to roll a four

Step-by-step explanation:

there is one being rolled to be a 4 out of six

Answer:

A survey shows that the probability that an employee gets placed in a suitable job is 0.65. So, the probability he is in the wrong job is 0.35.The test has an accuracy rate of 70%. So, the probability that the test is inaccurate is 0.3. Thus, the probability that someone is in the right job and the test predicts it wrong is The probability that someone is in the wrong job and the test is right is 

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

The mean prior to the given set of numbers would be \(58.8\).

How So?

1. Knowing this, first order the set from least to greatest.

\(22, 35, 44, 63, 63, 71, 80,92\)

2. Then, add up all the values.

\(22+35+44+63+71+80+92=470\)

3. Finally, divide 470 by 8 (the number of values in the set).

\(470\) ÷ \(8 = 58.75\)

4. Round 58.75, leaving you with the following solution:

\(58.75=58.8\) ←Our Final Solution / Mean

______________________________________________

Hope this helps!

Answer: answer is step by step

Step-by-step explanation:

A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true.

Hello there! I hope my answer will help you!

Look:

x+2=0

x=0-2

x=-2

Actually, it's Mental Math! :)

\(GraceRosalia\)

Answer:

42 minues 5 seconds to do 17 laps.

Step-by-step explanation:

it takes her 2 minuetes and 50 seconds to do 1 lap if you multiply 2.5x17=

42 munites and 5 secondesto do 17 laps

Answer:

It would take 42.5 min

Step-by-step explanation:

4/10 = 2.5(unit rate for every lap it takes 2.5 min)

17 x 2.5 = 42.5

After cοmpleting the task, we can state that The whοle number clοsest tο  expressiοn 7.141 is 7. Therefοre, √51 is clοsest tο the whοle number 7.

The whοle numbers are the part οf the number system which includes all the pοsitive integers frοm 0 tο infinity. These numbers exist in the number line. Hence, they are all real numbers. We can say, all the whοle numbers are real numbers, but nοt all the real numbers are whοle numbers.

Thus, we can define whοle numbers as the set οf natural numbers and 0. Integers are the set οf whοle numbers and negative οf natural numbers. Hence, integers include bοth pοsitive and negative numbers including 0. Real numbers are the set οf all these types οf numbers, i.e., natural numbers, whοle numbers, integers and fractiοns.

√51 is apprοximately equal tο 7.141. The whοle number clοsest tο 7.141 is 7.

Therefοre, √51 is clοsest tο the whοle number 7.

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Answer:

a) h(x; 7, 5, 12) = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)

b) 2.92

Step-by-step explanation:

a)

Here

Number of interviewees = N = 12

Number of job openings = M = 5

Interviews schedules for the first day =  n = 7

N − M = 12 - 5 = 7

Using hypergeometric distribution:

Let X be the no. top four candidates interviewed on first day.

The probability mass function of X:

P(X = x) = \((^{M} C_{x})\)   \((^{N-M} C_{n-x})\) /  \((^{N} C_{n})\)

It can be written as:

h(x; n, M, N)  =  \((^{M} C_{x})\)   \((^{N-M} C_{n-x})\) /  \((^{N} C_{n})\)    

                    = (5Cx) (7C7-x) / (12C7)

                    = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)

h(x; 7, 5, 12) = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)

b)

The expectation is: E(X) = np

E(X) = n * M/N

              = 7 * 5/12

              = 7 * 0.41667

              = 2.9167

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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Answer:

Step-by-step explanation:

Although you can start with 4x^2-2x-4=0, it's just slightly easier to reduce the coefficients.  4x^2-2x-4=0 becomes 2x^2 - x - 2 = 0.

The discriminant (part of the quadratic formula) is b^2 - 4ac.  Using b = -1. a = 1 and c = -2, we get (-1)^2 - 4(2)(-2), or 17.

                                                       -b ± √(b^2 - 4ac)

Then the quadratic formula   x = ---------------------------

                                                                 2a

                                         -(-1) ± √17           1 ± √17

takes on the values  x = -----------------  =  ---------------

                                                  4                      4

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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Answer: 9.44 seconds

Step-by-step explanation:

A movement equation in the vertical axis is usually written as follows:

p(t) = (-g/2)*t^2 + v0*t + p0

where:

g is the gravitational acceleration, in this case is 32 ft/s^2, then -g/2 = -16ft/s^2

v0 is the initial velocity, in this case, 24 ft/s

p0 is the initial height, in this case, 1200ft

Then, when p(t)  = 0ft will mean that the pebble will hit the ground, then we need to calculate:

p(t) = -16t^2+24t+1200  = 0

and find the value of t, this is a quadratic equation, then we can use the Bhaskara equation to find the two solutions, these are:

\(t = \frac{-24 +- \sqrt{24^2 - 4*(-16)*1200} }{2*-16} = \frac{-24 +- 278.2}{-32}\)

Then the two solutions are:

t = (-24  + 278.2)/-32 = -7.94 seconds (we can discard this one, because the negative time is not really defined)

t = (-24 - 278.2)/-32 = 9.44 seconds

Then the pebble needs 9.44 seconds to hit the ground

TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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The estimated area of Laurens's circle is 642 squared.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Parker:

Area = 40 squared

This means,

πr² = 40

r² = 40/3.14

r² = 12.74

r = √12.74

r = 3.6

Laurens:

r = 4 x 3.6

r = 14.3

Area = πr²

Area = 3.14 x 14.3 x 14.3

Area = 642

Thus,

Laurens's circle area is 642 squared.

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To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of y = 7, a second point by going up 3 and over y = 10, and then draw a line through the points.

How to know if a point lies in the graph of a function?

All the points (and only those points) which lie on the graph of the function satisfy its equation. Thus, if a point lies on the graph of a function, then it must also satisfy the function.

Given that:

y = 3/4x + 7

At x = 0

y = 7.

Going over by 3 then,

7 + 3 = 10.

So, now y = 10

10 = 3/4x +7

3/4x = 10-7

3/4x = 3

x = 4.

Now,

To draw a graph of 3/4x + 7, a person can draw c point x of 0 and y of 7, a second point by going over 3 and up 4.

Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of 7, a second point by going over 3 and up 10 and then draw a line through the points.

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The method of proof required to prove the statements are are as follows:(a) proof by contradiction. (b)  proof by construction. and (c) proof by contrapositive.

a) To prove the statement "there are no integers x and y such that x is a prime greater than 5 and x 6y 3", we can use proof by contradiction.

The proof starts by assuming that there exist integers x and y such that x is a prime greater than 5 and x 6y 3. We then show that this assumption leads to a contradiction, i.e., a statement that cannot be true.

Suppose that x is a prime greater than 5 and x 6y 3 for some integers x and y. Then, we can write x as x = 6y + 3 = 3(2y + 1). This means that x is divisible by 3 and hence cannot be a prime greater than 5, contradicting our initial assumption. Therefore, our assumption that there exist integers x and y such that x is a prime greater than 5 and x 6y 3 is false, and the statement is proven.

b) To prove the statement "for all integers n, if n is a multiple of 3, then n can be written as the sum of consecutive integers", we can use proof by construction.

The proof starts by taking an arbitrary integer n that is a multiple of 3. We then construct a sequence of consecutive integers whose sum is equal to n.

Let k = n/3 be an integer. Then, we can write n as n = 3k. We can now construct a sequence of consecutive integers starting from k - (k-1) = 1 and ending at k + (k-1), such that their sum is n. For example, if k = 4, then the sequence is 1, 2, 3, 4, 5, 6, 7, and their sum is 3k = 12 = 1+2+3+4+5-6-7. Since we can construct such a sequence for any integer n that is a multiple of 3, the statement is proven.

c) To prove the statement "for all integers a and b, if a 2 b 2 is odd, then a or b is odd", we can use proof by contrapositive.

The contrapositive of the statement is: "if both a and b are even, then a 2 b 2 is even". To prove this, we can use the properties of even numbers, which can be written in the form 2k for some integer k.

Suppose that both a and b are even. Then, we can write a = 2m and b = 2n for some integers m and n. Substituting these values into the expression a 2 b 2, we get:

a 2 b 2 = (2m)2 (2n)2 = 4m2n2 = 2(2m2n2).

Since 2m2n2 is an integer, we have shown that a 2 b 2 is even. Therefore, the contrapositive statement is true.

Since the contrapositive statement is true, the original statement "for all integers a and b, if a 2 b 2 is odd, then a or b is odd" must also be true, because it is the logical equivalent of the contrapositive.  

Therefore, the mentioned statements are proved with the methods of contradiction, construction, and contrapositive.

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Answer: Coupon B is more profitable

Answer:

w= (-6/7)

Step-by-step explanation:

Answer:

w = -6/7

Step-by-step explanation:

−

10

7

(

−

7

a

10

)

=

−

10

7

⋅

3

5

Answer:

yes

Step-by-step explanation:

12+3=5x-3+3

15=5x

15=5(3)

15=15

Answer: The equation used to find the value of x is 5x - 4 = 3x + 10. The value of x is determined to be 7.

Step-by-step explanation:

Four less than the product of a number (x) and 5 = 5x - 4

8 more than 2 added to 3 times the number = 3x + 2 + 8 = 3x + 10

Four less than the product of a number (x) and 5 is equal to 8 more than 2 added to 3 times the number => 5x - 4 = 3x + 10

                                                         5x - 3x = 10 + 4

                                                         2x = 14

                                                         x = 14/2

                 therefore,                      x = 7

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The maximum height reached by each stone is 40.5 meters.

The height of each stone above the ocean is given by the function:

h = -2t² + 2t + 40

This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.

The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.

The t-coordinate of the vertex is given as:

t = -b / 2a

Substitute the values of a and b,

t = -2 / (2×(-2)) = 0.5

So the maximum height is reached 0.5 seconds after the stone is thrown.

To find the maximum height, substitute the value of t into the function:

h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters

Therefore, the maximum height reached by each stone is 40.5 meters.

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