Geometry.
Find the length of FG
Express your answer as a fraction times π

Answer:

The answer as follows

Step-by-step explanation:

Part I:

The graph of f(x) is a parabola with its vertex at the origin, opening upward.

To graph g(x), we can start by shifting f(x) 3 units to the right and 2 units up, according to the equation g(x) = (x - 3)² + 2. This means that the vertex of g(x) will be at the point (3, 2).

We can create a table of values for g(x) to plot some points and draw the graph:

| x  | g(x) |

|----|------|

| 0  | 11   |

| 1  | 8    |

| 2  | 5    |

| 3  | 2    |

| 4  | 5    |

| 5  | 8    |

| 6  | 11   |

Using these points, we can draw the graph of g(x) as a parabola that has the same shape as f(x), but is shifted to the right by 3 units and up by 2 units:

Part II:

The graph of g(x) is the graph of its parent function, f(x), shifted 3 units to the right and 2 units up. This means that every point on the graph of g(x) is 3 units to the right and 2 units up from the corresponding point on the graph of f(x).

In other words, the transformation that was applied to f(x) to get g(x) is a horizontal shift to the right by 3 units and a vertical shift up by 2 units. This is reflected in the equation g(x) = (x - 3)² + 2.

Based on the survey data, we can conclude that a higher proportion of teenagers own an iPod or MP3 player compared to young adults.

To determine if the difference is significant, we need to conduct a hypothesis test. We can begin by stating the null hypothesis as "there is no significant difference in the proportion of all teens and young adults who would say they own an iPod or MP3 player."

We can also state the alternative hypothesis as "there is a significant difference in the proportion of all teens and young adults who would say they own an iPod or MP3 player."

Next, we need to determine the test statistic and calculate the p-value to determine if the difference in the proportions is statistically significant. Assuming that the data follows a normal distribution, we can use a two-sample z-test to test our hypothesis.

Using a significance level of 0.05, we find that the test statistic is 3.07, and the p-value is 0.002. Since the p-value is less than the significance level, we can reject the null hypothesis and conclude that there is convincing evidence of a difference in the proportions of all teens and young adults who would say they own an iPod or MP3 player.

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There are 6,840 ways to award the prizes to the first three cars completing the race.

Since there are 20 cars within the race and the arrangement in which they wrap up is critical, a permutation equation can be utilized to decide the number of ways prizes are granted.

 There are his 20 ways to determine the winner of the first prize (because any of the 20 cars could be first).

He has 19 ways to determine the runner-up (because he has 19 cars left to be runner-up).

There are 18 ways to determine the 3rd place winner (because he has 18 cars left that could be 3rd place).

Using the multiplication principle, the total number of ways to award prizes is:

20 x 19 x 18 = 6,840

So there are 6,840 ways to award prizes to the top 3 cars that finish the race. 

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Step-by-step explanation:

sqrt (20) / sqrt(12)   =   sqrt(20*12) / 12 = 4 sqrt (15) / 12

   = sqrt (15) / 3  = 1.290994

Answer:

First, we need to find the radius of the cylinder. We know that:

V = πr^2h

And we are given that V = 1,130.97 cubic inches. We also know that a cylinder is symmetrical, which means that the height of the cylinder is equal to the diameter of the circle. In other words, h = 2r.

Therefore, we can rewrite the formula as:

V = πr^2(2r)

1,130.97 = πr^3

r^3 = 359.82

r = 7.12 inches (rounded to two decimal places)

Now we need to find the amount of space on either side of the cylinder. We know that the pedestal is 18 inches across, so the total width is 18 inches. If we want an even amount of space on either side, we need to subtract the diameter of the cylinder from the width of the pedestal, and then divide the result by two.

Diameter = 2r = 2(7.12) = 14.24 inches

Space on either side = (18 - 14.24)/2 = 1.88 inches (rounded to two decimal places)

Therefore, if Consuela places the cylinder on a pedestal that is 18 inches across, there will be 1.88 inches of space on either side.

Step-by-step explanation:

[tex] \frac{r - p}{7} = s \\ cross \: multiply \\ 7s = r - p \\ \: \: move \: the \: variable \: to \: the \: \\ right \\ - p = 7s - r \\ change \: the \: signs \\ p = - 7s + r \\ p = r - 7s[/tex]

Answer:

p= -7S+r

Step-by-step explanation:

p=-7S+r ( gotta write at least 20 characters)

The depth of the swimming pool s 8 feet

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

This means that

Depth = Volume/(length * width)

substitute the known values in the above equation, so, we have the following representation

Depth = 2000/(25 * 10)

Evaluate

Depth = 8

Hence, the depth is 8 feet

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The economic changes brought about by "rail-roads" are (a) Land prices rose and more land became available to settlers, (b) Copper mining developed as new technologies emerged, and (c) Transportation improved to bring the copper to market, So, correct option is (d).

The railroads brought about significant economic changes in several ways;

Option (a) : Land-prices rose and more land became available to settlers due to the expansion of railroads, making transportation faster, cheaper, and more reliable, thus leading to the settlement and development of previously unsettled or underdeveloped areas.

Option (b) : Copper mining developed as new technologies emerged, including steam-powered drills and machinery, which were made possible by the availability of rail transportation.

Option (c) : Transportation improved to bring the copper to market more quickly and efficiently than previously available methods, contributing to the growth of copper mining as a major industry.

Since, all are correct, the correct option is (d).

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The given question is incomplete, the complete question is

Select the economic changes brought about by the railroads.

(a) Land prices rose and more land became available to settlers.

(b) Copper mining developed as new technologies emerged

(c) Transportation improved to bring the copper to market

(d) All the options are correct.

The subtraction of Matrix B from Matrix A is represented as:

[tex]\[A - B = \begin{bmatrix}0 & -4 \\7 & -4 \\1 & 1\end{bmatrix}\][/tex]

Given Matrix:

[tex]\[ A = \begin{bmatrix}3 & -1 \\2 & 0 \\-3 & 3\end{bmatrix} \][/tex]  and  [tex]\[ B = \begin{bmatrix}3 & 3 \\-5 & 4 \\-4 & 2\end{bmatrix} \][/tex]

To find the result of subtracting Matrix B from Matrix A,

subtract the corresponding elements of the matrices.

Here is the subtraction result

[tex]\[A - B = \begin{bmatrix}3 - 3 & (-1) - 3 \\2 - (-5) & 0 - 4 \\(-3) - (-4) & 3 - 2\end{bmatrix} = \begin{bmatrix}0 & -4 \\7 & -4 \\1 & 1\end{bmatrix}\][/tex]

Therefore, the subtraction of matrices is:

[tex]\[A - B = \begin{bmatrix}0 & -4 \\7 & -4 \\1 & 1\end{bmatrix}\][/tex]

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Answer:

y-intercept = (0,0)

x-intercepts (0,0), (-2, 0)

Step-by-step explanation:

For y-intercept

If you think about a graph, when does the graph intercept/hit y.   What is your value for x.   Your y-intercept is usually (0, y)   So in order to find the y-intercept you need to plug in x=0 to find y.

Equation:

y=16x²+32x       substitute x=0

y=16(0)²+32(0)

y=0

y-intercept = (0,0)

For x-intercept

When you have an x intercept it looks like (x, 0), so you must solve for x when y=0

Because this is a quadratic equation(parabola), you will get 2 x-intercepts.

y=16x²+32x

0=16x²+32x      > In order to solver for x, you must factor but in this case

                            you can take out the greatest common factor (GCF) =16x

0=16x(x +2)       >Typically when you factor you get 2 parentheses and set

                            each parenthesis equal to 0, but instead we've pulled

                            an x on the outside.  When there is an x outside you set

                            the outside equal to 0 as well as the parenthesis to

                            solve for x.

16x = 0                 (x+2)=0

x=0                           x= -2

x-intercepts (0,0), (-2, 0)

The equation of exponential regression that fits the data is given as follows:

y = 1.5(2.5)^x.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

To obtain the equation of exponential regression, we must insert the points of the data-set into a calculator.

The points are given as follows:

(1, 3.75), (4, 9.375), (3, 23.438), (4, 58.594), (5, 146.484).

Inserting these points into a calculator, the equation is given as follows:

y = 1.5(2.5)^x.

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Answer:

54

Step-by-step explanation:

the first one is the only one I know from the top off my head I'll try and send it to you. but the first one is 53

5.48% of the people in line waited for more than 28 minutes

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

In a set with mean  and standard deviation , the z-score of a measure X

Given Mean waiting time of 20 minutes with a standard deviation of 5 minutes.

This means that percentage of the people in line waited for more than 28 minutes.

The proportion is 1 subtracted by the p-value of Z when X = 28. So

Z = 1.6

This has a p-value of 0.9452.

1 - 0.9452 = 0.0548.

As a percentage,

0.0548*100% = 5.48%

Thus 5.48% of the people in line waited for more than 28 minutes

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Answer:

y = -8x

Step-by-step explanation:

-2-6 = -8

the slope was -2 that decreased by 6 would be -8.

Helping in the name of Jesus.

To graph the line that passes through the coordinates (2, 3), (3, 4.5), (4, 6), and (6, 9), we can use the slope-intercept form of the equation of a line, which is y = mx + b.

To start, we can find the slope of the line using any two points on the line. Let's use the first and last points:

slope = (change in y) / (change in x) slope = (9 - 3) / (6 - 2) slope = 1.5

Now we can choose any of the four given points and plug in the slope to find the y-intercept, b. Let's use the second point:

4.5 = 1.5(3) + b b = 0.75

So the equation of the line is:

y = 1.5x + 0.75

To graph the line, we can plot the four given points and then connect them with a straight line. Alternatively, we can choose any two values of x and plug them into the equation of the line to find the corresponding values of y, and then plot the resulting points.

THIS LINE DOES PASS THROUGH THE ORIGIN

it is

NOT

proportional because the line passes through the origin

therefore the correct answer is:

A.

Answer:

[tex] {.2}^{4} = .0016[/tex]

Answer:

Step-by-step explanation:

0.2^4 is

0.2 x 0.2 x 0.2 x 0.2  =

0.04 x 0.04 =

0.0016

Answer:

Step-by-step explanation:

Of= x

So, we do 5x2+1

= 11/2= 5 1/2 then we start multiplying

11x2=22

2x3=6

so then that's 22/6

next, we divide 22 by 6

6 goes into 22 3 times remainder of

4

so its 3 4/6

In simplified form its 3 2/3

To calculate the total cost of shingling the roof, we first find the total square footage of the roof, which is 300 sq.ft. We then multiply this by the cost per square foot of the shingles, $2.13, to get a total cost of $639.

The first step is to calculate the total square footage of the roof. The given half measurement is 15ft by 10ft, so in-order to get square footage we multiply these two numbers (length * width). 15ft * 10ft = 150sq.ft. Since this is only half of the roof, we then multiply by 2 to get the total roof area. So, 150sq.ft * 2 = 300sq.ft.

The next step is to find the total cost. If the cost of 1 sq.ft. of shingles is $2.13, we just multiply the total area by the cost per square foot.  So, 300sq.ft. * $2.13/sq.ft = $639.

Therefore, it will cost $639 to shingle the entire roof.

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Spores forming bacteria include Clostridium botulinum, Clostridium perfringes and Bacillus cereus and when a food is frozen, it slows down bacteria activity.

2. Spore-forming bacteria include Bacillus (aerobic) and Clostridium (anaerobic) species. These species produce spores that are dormant bodies and take the genetic material present in the vegetative form, but do not have an active metabolism. They are very resistant against heat, dryness, and other negative ambient conditions than the vegetative form, and are used for survival during dryness. When the environmental conditions is conducive, spores germinate to vegetative Bacillus or Clostridium cells.

In the given question, the spore forming organisms are Clostridium botulinum, Clostridium perfringes and Bacillus cereus

3. What happens when a food is frozen?

When food is frozen, it does not kill the bacteria but rather slows down their reproductive activity and so, the amount of time it can be kept is extended compared to refrigeration.

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Answer:

Dear Kindergarten students,

Today, I am here to talk to you about place value and why it is important. Place value is the concept of understanding the value of a digit based on its position in a number. In other words, the position of a digit determines its value.

Let's take the number 123 for example. The digit 1 is in the hundreds place, the digit 2 is in the tens place, and the digit 3 is in the ones place. This means that 1 represents one hundred, 2 represents twenty, and 3 represents three. So when we put these digits together, we get the number 123.

Understanding place value is important because it helps us to read, write, and compare numbers. It also helps us to perform mathematical operations such as addition and subtraction more easily.

For instance, if we want to add two numbers such as 23 and 45, we need to line up the digits based on their place value. The ones place goes under the ones place, and the tens place goes under the tens place. Then we can add each column separately to get our answer of 68.

In summary, understanding place value is essential for working with numbers and performing mathematical operations accurately.

Thank you for listening!

Step-by-step explanation:

That what I would say

By Unitary method, 3 gallons = 12 quarts

We know that the  the unit conversion,

one liquid gallons is equals to the four liquid quarts

i.e., 1 gallon = 4 quarts

We need to find the 3 gallons to quarts.

Let us assume that x represents the required amount of liquid quarts.

By Unitary method,

⇒ x = 3 × 4

⇒ x = 12 quarts of liquid

Therefore, the unit conversion 3 gallons equals to 12 quarts.

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The angles that can be obtained by trigonometry are shown below.

The Greek words "trigonon" (triangle) and "metron" are the origins of the word "trigonometry" (measure). Trigonometry is the study of triangles, specifically the lengths of their sides and the sizes of the angles that connect them.

1) Cos 32 = x/14

x = 14 Cos 32

= 11.9

2) Sin 54 = 22/x

x = 22/Sin 54

x = 27.2

3) Tan 75 = 17/x

x = 17/Tan 75

x = 4.6

4) Cos 43 = 31/x

x = 31/Cos 43

x = 42.4

5) Tan x = 9/12

x = Tan-1(9/12)

x = 36.9

6) Sin x = 11/35

x = Sin-1 (11/35)

x = 18.3

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To find the quotient of whole number divided by a unit fraction the steps are discussed below.

We have to divide a whole number by a unit fraction.

let the whole number be 10 and fraction is 1/2.

So, division is

= 10 / (1/2)

Now, Reciprocate the fraction in the denominator as

= 10 x 2/1

= 20

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The total value of the investment after 20 years with continuous compounding is $2,917.76.

Given information:

P = principal = $1000.

R = 5.5%

t = 20 years.

First, convert R as a percent to 'r' as a decimal

r = R/100

r = 5.5/100

r = 0.055 rates per year,

Then solve the equation for A:

The total value of the investment can be calculated using the formula:

A = P(1 + r/n[tex])^{nt}[/tex]

A = 1,000.00(1 + 0.055/1[tex])^{(1)(20)}[/tex]

A = 1,000.00(1 + 0.055[tex])^{(20)}[/tex]

A = $2,917.76

The total amount accrued, principal plus interest, with compound interest on a principal of $1,000.00 at a rate of 5.5% per year compounded 1 time per year over 20 years is $2,917.76.

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The angles which are equivalent to sin [tex]\theta[/tex] = √2/2 are,

Given sin [tex]\theta\\[/tex] =  √2/2 the theta value is equal to 45° which is present in the first quadrant.

To find out equivalent theta values, we will find out all 45° equivalent values in each quadrant.

From the above analysis, the equivalent angles are 45°, 225°, 135° and 315°. So, the option A is correct.

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The given question is missing options. The complete question is,

Select all angle measures for which sin theta= -sqrt2/2

A) 45°, 225°, 135°, and 315°

B) 45°, 225°, 280° and 325°

C)60°, 90°, 225° and 135°

D)75°, 135°, 250° and 315°

The simplification of the given expression is:

[tex]\sqrt[3]{\frac{6c}{-125} } = -\frac{\sqrt[3]{6c} }{5}[/tex]

Here we have an expression with a cube root:

[tex]\sqrt[3]{\frac{6c}{-125} }[/tex]

We can distribute the cube root over the fraction, then we will get:

[tex]\sqrt[3]{\frac{6c}{-125} } = \frac{\sqrt[3]{6c} }{\sqrt[3]{-125} } = \frac{\sqrt[3]{6c} }{-5}[/tex]

That is the expression simplified.

We can't keep simplifying this, because 6 is not a perfect cube and c is just a variable.

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In a series circuit, charges follow a single path, meaning that they flow through each component of the circuit one after another.

What is series circuit?

A series circuit is an electric circuit in which the components (such as resistors, capacitors, and inductors) are connected in a single path so that the current flows through each component in turn without branching off.

In a series circuit, charges follow a single path, meaning that they flow through each component of the circuit one after another. This means that the current passing through each component is the same, and the voltage is split between the components. If one component fails, the circuit is broken, and no current can flow.

In contrast, in a parallel circuit, charges have multiple paths to flow through. The current splits up and passes through each path independently, meaning that the current through each component is not necessarily the same.

The voltage across each component is the same, and the total current is the sum of the current through each path. If one component fails, the current can still flow through the other paths, and the circuit remains complete.

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