The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?

The surface area of the cylinder can be expressed as 2g(r) + f(r)h/3.

A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Therefore the total surface area of a cylinder is the area of the circular tops + area of the sides of the cylinder.

Therefore the surface area of a cylinder can be expressed as;

area of the circular tops = πr²+πr² = 2πr²

area of the sides = πrh + πrh = 2πrh

Therefore the surface area of cylinder =

2πr( r+h)

f(r) = 6πr

g(r) = πr²

therefore the surface area = 2g(r) + f(r)h/3

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Algorithm Il always works correctly, but Algorithm I only works correctly when the maximum value is greater than or equal to - 1

=====================================================

Explanation:

Let's say we have the data set {-4,-3,-2}. The value -2 is the largest.

If we follow algorithm 1, then the max will erroneously be -1 after all is said and done. This is because the max is set to -1 at the start even if -1 isn't in the data set. Then we see if each data value is larger than -1.

Each statement being false means we do not update the max to its proper value -2. It stays at -1.

This is why we shouldn't set the max to some random value at the start.

It's better to use the some value in the data set to initialize the max. Algorithm 2 is the better algorithm. Algorithm 1 only works if the max is -1 or larger.

Therefore , the solution of the given problem of standard deviation comes out to be the CEO is informed that the mean scores for Cities A and B are identical.

Variance is a measure of difference used in statistics. The typical variance here between dataset and the mean is calculated using the multiplier of that figure. By comparing each figure to the mean, it incorporates those data points into its calculations, unlike other measurable measures of variability. Variations may result from internal or external factors and may include unintentional errors, inflated expectations, and changing economic or commercial circumstances.

Here,

It is clear that both offices share a comparable average score from the sentence "The CEO is informed that both City A or City B have the same mean score."

If City A is more reliable than City B, then City A will have a lower standard deviation.

A collection of data's variability or dispersion is measured by the standard deviation. The closer the data points are to the mean, the lower the standard deviation, and the less variable the data are.

So, the appropriate answer is:

The CEO is informed that the mean scores for Cities A and B are identical. However, due to the fact that City A's standard deviation is lower than City B's, City A is more reliable than City B.

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Option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B

According to the information given in the question,

A true proportion of 0.325 represents that the two simulations will be conducted for sampling proportions from a population

Simulation A -

Sample size - 100

Trials - 1500

Simulation B -

Sample size - 50

Trials - 2000

Now due to the relation of simulation A and simulation B, they are closely equal-

The total sample size of simulation A= 1500 x 100

= 150000

The total sample size of simulation B = 2000 x 50

= 100000

From the above calculations of simulations A and B, we can see that while comparing the,

Sample Size = Simulation A > Simulation B

Variability = Simulation B < Simulation B

Therefore, option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B is correct.

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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

The calculated value of standard deviation for the given data set is 2.236.

Standard deviation is the measure of dispersion of the observed values relative to the mean value. It indicates how far each value is apart from mean value.

we have data list 2 4 6 8

 the list is denoted by X and X² is the square of the data set

    X        X²

   2          4

    4         16

     6        36

     8         64

we add all the data, and the result is ∑X = 20

similarly, we add all the squared value, and the result is ∑X² = 120

Standard deviation is calculated by using the formula below

SD = √[∑X²/N - (∑X/N)²]

here, N denotes the amount of data set

hence, N= 4

SD = √[120/4 - (20/4)²] = 2.236

hence, standard deviation is 2.236

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Answer:

D

Step-by-step explanation:

i did it on khan

Answer:

D

Step-by-step explanation:

The value of x of the triangle is given by the trigonometric relation x = 30°

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔPQR

Now , the measure of side PQ = 48 cm

The measure of side PQ = 96 cm

The measure of ∠x is calculated by

From the trigonometric relations ,

sin x = opposite side / hypotenuse

On simplifying , we get

sin x = 48 / 96

sin x = 1/2

Taking inverse on both sides , we get

x = sin ⁻¹ ( 1/2 )

x = π/6

x = 30°

Therefore , the value of x is 30°

Hence , the angle of the triangle is 30°

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Answer:

Length is 32. 6 cm and width is 5.9 cm

Step-by-step explanation:

width(w)=w

perimeter(p)=78 cm

length(L) = 4w+9

p=2L+2w

78=2(4w+9)+2w

78=8w + 19 + 2w

10w=59

w=5.9 cm

L=4w+9

L=4(5.9)+9

L=32.6 cm

Therefore length is 32.6 cm and width is 5.9 cm

The total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.20.

To calculate the total cost, we need to determine the cost of each type of binder clip separately and then sum them up.

The cost of medium binder clips is $5 per pound, and Kayla purchased 0.1 pounds. Therefore, the cost of medium binder clips is 0.1 pounds * $5 per pound = $0.50.

The cost of jumbo binder clips is $6 per pound, and Kayla purchased 0.2 pounds. Thus, the cost of jumbo binder clips is 0.2 pounds * $6 per pound = $1.20.

Finally, to find the total cost, we add the individual costs together: $0.50 + $1.20 = $1.70.

Therefore, the total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.70.

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The simplified expression for the cost of renting the apartment for n months is 900n + 1350.

We have,

To simplify the expression 900(n + 1) + 450, we can start by using the distributive property of multiplication over addition, which states that:

a(b + c) = ab + ac.

So, we have:

900(n + 1) + 450

= 900n + 900(1) + 450 (applying the distributive property)

= 900n + 900 + 450

= 900n + 1350

Therefore,

The simplified expression for the cost of renting the apartment for n months is 900n + 1350.

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The control limits are set at 3-sigma (z=3), we know that the LCL will be 3 times the standard deviation below the c-bar value. The Lower Control Limit (LCL) for the C-bar chart, is approximately 0.235.

The Lower Control Limit (LCL) for the C-bar chart can be calculated by subtracting 3 times the standard deviation from the c-bar value.

Since the control limits are set at 3-sigma (z=3), we know that the LCL will be 3 times the standard deviation below the c-bar value.

To calculate the standard deviation, we need to divide the c-bar value by the square root of the number of observations (n). In this case, n=8. So, the standard deviation is equal to c-bar divided by the square root of 8.

Next, we multiply the standard deviation by 3 to get the amount by which the LCL is below the c-bar value. Subtracting this value from the c-bar value gives us the LCL for the C-bar chart.

Therefore, the LCL is equal to the c-bar value minus (3 times the standard deviation). Plugging in the values, the LCL is equal to 3.44 minus (3 times c-bar divided by the square root of 8).

Calculating this, we get the LCL to be approximately 0.235.

Therefore, the correct answer is b. 0.235.

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The value of x is 10.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Parallelogram has the property that the consecutive or adjacent angles of a parallelogram are supplementary.

That is, they sum up to 180°.

Here, (6x)° and (12x)° are supplementary.

6x + 12x = 180

18x = 180

x = 10

Hence the value of x is 10.

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We can conclude that both probabilities in parts (a) and (b) are approximately 0.95, regardless of the sample size.

Assuming that the population is normally distributed with a mean of 100 and a standard deviation of 15, we can use the central limit theorem to approximate the sampling distribution of the sample means as normal, regardless of the sample size.

Since we're interested in the probability that the sample mean falls within a certain range, we can standardize the sampling distribution of the sample means using the formula:

z = (\(\bar X\) - μ) / (σ / √n)

where \(\bar X\) is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For both parts (a) and (b), we want to find P(90 < \(\bar X\) < 110), which we can rewrite as P((90 - 100) / (15 / √n) < (\(\bar X\) - 100) / (15 / √n) < (110 - 100) / (15 / √n)).

Simplifying this expression, we get P(-2√n < z < 2√n), where z is a standard normal random variable.

The probability that a standard normal random variable falls within ±2 standard deviations of the mean is approximately 0.95. Therefore, we can conclude that both probabilities in parts (a) and (b) are approximately 0.95, regardless of the sample size.

This is because the sample size n only affects the standard deviation of the sampling distribution of the sample means (i.e., σ / √n), but not its shape or center. Therefore, the probability that the sample mean falls within a certain range is largely determined by the width of that range relative to the standard deviation of the sampling distribution, which is approximately constant regardless of the sample size.

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Answer:

-9 and +4 are the factors

Step-by-step explanation:

-9 times +4 is -36 and if you add +4 to -9, you get -5.

After this your function will look like this:

\(x^2-9x+4x-36\)

and then:

\(x(x-9)+4(x-9)\)

so the answer is:

\((x-9)(x+4)\)

Answer:

1.75

Step-by-step explanation:

h(t) = -16t² + 56t

h'(t) = -32t + 56

To find time at max height equate h' to 0

0 = -32t + 56

t = 56/32 = 1.75 s

It takes 1.75 s to reach max highest point

The best deal is to buy 12 pounds. Winnie should buy the 12 pound bags.

Given that, there are 4 deals, i.e.

To get the best deal, calculating the cost of one pound for each deal.

For deal 1, Cost of one pound is \(\dfrac{\$4.99}{4.2} = \$1.19\)

For deal 2, Cost of one pound is \(\dfrac{\$9.27}{8.5} = \$1.09\)

For deal 3, Cost of one pound is \(\dfrac{\$11.04}{12} = \$0.92\)

For deal 4, Cost of one pound is \(\dfrac{\$18.99}{20} = \$0.95\)

Here the lowest cost of one pound is $0.92 which is deal 3.

So, the best deal is to buy 12 pounds. Winnie should buy the 12 pound bags.

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Answer:

y - 2 = (-3)(x - 5)

Step-by-step explanation:

Solving the given equation for y enables us to determine the slope of this line:

3y = x + 12, or y = (1/3)x + 4.

Any line perpendicular to this line has slope -3, which is the negative reciprocal of 1/3.

The desired equation (of the perpendicular line through (5,2 ) is then

y - 2 = (-3)(x - 5)

The equations of the graph from the figure are y = 4 and y = -2

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

The graph

On the graph, we can see that

We have two horizontal lines that pass through the points y = 4 and y = -2

This means that the equations represented on the graph are y = 4 and y = -2

So, we can conclude that none of the options are true from the options

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Answer: 20 days

Step-by-step explanation:

First find out the number of miles Carson rides every day.

If he goes at 12 every 3 days, in one day he goes:

= 12 / 3

= 4 miles per day

Going at 4 miles a day, the number of days it would take to ride 80 miles is:

= 80 / 4

= 20 days

Answer: slope  

=

−

1

3

y-intercept  

=

2

Explanation:

the equation of a line in  

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange  

x

+

3

y

=

6

into this form

subtract x from both sides

x

−

x

+

3

y

=

6

−

x

⇒

3

y

=

−

x

+

6

divide all terms by 3

⇒

y

=

−

1

3

x

+

2

←

in slope-intercept form

⇒

slope  

=

−

1

3

and y-intercept  

=

2

graph{-1/3x+2 [-10, 10, -5, 5]}

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

X=Y /2+ 5/2

Answer:

Volume of rectangular prism = 1200 cubic inches

Step-by-step explanation:

Given that:

Length of rectangular prism = 10 inches

Width of rectangular prism = 8 inches

Height of rectangular prism = 15 inches

Volume of rectangular prism = Length * Width * Height

Volume = 10 * 8 * 15

Volume = 1200 cubic inches

Hence,

Volume of rectangular prism = 1200 cubic inches

Range = max- min= 3

acc to our question-

max = 4

min = 1

range max - min

4-1 = 3

Hence,  range: 3

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Answer:

C) 135° and 10°

Step-by-step explanation:

180°-45°= 135°

180°-135°-35°= 10°

Answer:

C) 135, 10

Step-by-step explanation:

The bottom angle has to equal 180 so subtract 45 and you get 135. The other triangle must also equal 180 so you add 135 and 35 and you get 170. The last angle has to be 10

Answer:

A. contract

Step-by-step explanation:

The total number of probability options will be 8 options.

1. Red plain and Red striped.

2. Blue plain and Blue striped.

3. Yellow plain and Yellow striped.

4. Green plain and Green striped.

5. Red plain and Blue striped.

6. Blue plain and Yellow striped.

7. Yellow plain and Green striped.

8. Green plain and Red striped.

There are 8 socks in the basket, and you can choose 1 plain sock and 1 striped sock.

This means that there are 8 possible combinations of socks you could choose.

Count the number of socks in the basket. There are 8 total socks (4 plain and 4 striped).

The number of options: There are 8 possible combinations of socks you could choose, so you have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.

Therefore,

You have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.

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At hour 9, the temperature recorded was = 75 degrees

At hour 13, the temperature recorded was = 95 degrees

The rate of change = Change in the temperature / Change in the time

⇒ The rate of change = 95 - 75 degrees / 13 - 9 hour

⇒ The rate of change = 20 degrees / 4 hours

⇒ The rate of change = 5 degrees per hour

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Answer:

r = 115°

s = 130°

t = 115°

Step-by-step explanation:

1) Angles on a straight line equal 180°.

So, to find angle 'r' you must do 180° - 65° to get 115°.

2) The two dashes on the side represent that the angle equivalent to 65° is equal to the angle next to angle 't'.

So you do 180° - 65° again to get 115°, to work out angle 'r'. This means that both the exterior angles are 115°.

3) The interior angles of a triangle add up to 180°.

So you must do 65° + 65° = 130°

180° - 130° = 50°

Then to work out angle 's' do 180° - 50° = 130°.

So the final answers are:

r = 115°

s = 130°

t = 115°

(Extra information: Exterior angles always add up to 360°, so if the angles on the outside of the shape don't add up to 360°, then you might have slipped up somewhere)

Answer:

Line of symmetry: Yes (It has 2, Diagonally, and vertically)

Parallel sides: Yes (Side 1 and side 2 and top line 1 and top line 2 are parallel)

Perpendicular sides: No (No right angles are present by the connecting lines)

Obtuse angles: Yes (All the touching lines are obtuse angles)

The statements about the study are:

Let's analyze each statement:

1) This study uses random sampling.

This is true, as the children are randomly selected, so there is no bias.

2) This study uses a repeated measures design.

Is really important to repeat any given study, and this one does it, so this option is correct. This study was repeated 4 times, so this is true.

3) This study uses blinding.

Blinding is when the participants of the study don't know all the important information for the study. Here there is no clarification of blinding being used, so we assume this is false.

4) This study uses blocking.

Blocking is when the sample is divided in "blocks" that are similar between them, as you can see, in this study the children are divided in blocks, so this is true.

5) This study uses a control group.

The control group would be a group that is left alone and "don't participate" in the experiment, so then the results can be compared after. In this experiment, the control group is the one that has no screen time, so this statement is correct.

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Answer:

B

Step-by-step explanation:

point slope uses the form y - y1 = m(x - x1)

m stand for slope. in this case it is -3

x1 is -1 and y1 is 6

when you plug it in, you get

y - 6 = -3(x - [-1])

which simplifies to your final answer: y - 6 = -3(x + 1)