Justin is on a hiking trail goes north to south. If Justin hikes x miles north, his elevation, in feet, can be found using the function f(x)=(x+2)^2+100. Negative x values would find the elevation if Justin hikes south. Find and interpret the given function values and determine an appropriate domain for the function.

Answer:

For the first one:

\( \frac{8}{6} \\ \frac{12}{9} \\ \frac{16}{12} \)

for the second one:

\( \frac{6}{7} \\ \frac{24}{28} \\ \frac{36}{42} \)

For the third one:

\( \frac{2}{3} \\ \frac{4}{6} \\ \frac{12}{18} \)

To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.

Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:

a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.

Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.

b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.

Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.

c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).

Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.

d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).

Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.

Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.

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Answer:

yes

Step-by-step explanation:

The probability that a randomly chosen Latin student is a sophomore is 6/19, so the m + n is 25.

New schools have 40% freshmen with all freshmen taking Latin, 30% are sophomores with 80% sophomores taking Latin, 20% are juniors with 50% juniors taking Latin, and 10% are seniors with 20% seniors taking Latin.

So, the total students taking Latin is,

= 40%*100% + 30%*80% + 20%*50% + 10%*20%

= 76% of all students.

Then, the students that taking Latin is sophomore,

= 30% * 80%

= 24%

So the probability of a randomly chosen Latin student is a sophomore is,

m/n = chance event occurs / total event

= 24% / 76%

= 6 / 19

Since m is 6 and n is 19, so m + n is 6 + 19 or equal to 25.

Your question is incomplete, but most probably your full question was

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The value of m + n, where m and n are relatively prime positive integers, is 25.

We know that the percentage of students learning Latin are:

(40% * 100%) + (30% * 80%) + (20% * 50%) + (10% * 20%) = 76%

And the percentage of sophomore students learning Latin are:

30% * 80% = 24%

So, the desired probability is:

24 / 76 = 6 / 19

which means 6 is m and 19 is n.

Thus, m + n = 6 + 19 = 25.

Hence, the value of m + n, where m and n are relatively prime positive integers, is 25.

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Although part of your question is missing, you might be referring to this full question: In a new school 40 percent of the students are freshmen, 30 percent are sophomores, 20 percent are juniors, and 10 percent are seniors. All freshmen are required to take Latin, and 80 percent of the sophomores, 50 percent of the juniors, and 20 percent of the seniors elect to take Latin. The probability that a randomly chosen Latin student is a sophomore is m/n, where m and n are relatively prime positive integers. Find m+n.

Your current monthly income, before the effect of inflation, is approximately $2,129.63.

To determine your current monthly income, we need to account for the effect of inflation on the purchasing power of your income. Given that the inflation rate is eight percent, we can calculate the original income before the inflation adjustment.

Let's denote your current monthly income as "X."

The purchasing power after accounting for eight percent inflation is $2,300. This means that your original income, before the inflation adjustment, would have had a higher value. We need to find this original income.

Inflation reduces the purchasing power of your income, so we need to increase the current purchasing power by the inflation rate to find the original income. In this case, we'll increase $2,300 by eight percent:

Original Income = $2,300 / (1 + 0.08)

Original Income = $2,300 / 1.08

Original Income ≈ $2,129.63

Therefore, your current monthly income, before the effect of inflation, is approximately $2,129.63.

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Answer:

C: 800 x 20

Step-by-step explanation:

Basically, when you round 778 you see that the 7 and 8 are above 5, which means you round upwards. Therefore it would be best to round up to 800.

Then the 3 in 23 is below 5, meaning you round downwards. 20 Is the closest and best option.

So, C: 800 x 20 is best to do!

Answer:

Answer-C

Step-by-step explanation:

MARK ME BRAINLEST PLZ

a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.

b) The total interest that Rich will pay over the life of the loan is $4,914.20.

The interest on student loans is based on simple interest.

The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.

Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.

Capitalization refers to the addition of interest to the principal amount.

Period of student loan = 10 years

The amount of the federal unsubsidized student loan = $7,900

Interest rate = 4.29%

Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)

New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)

Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)

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Answer:

  10

Step-by-step explanation:

You want a number such that the square root of the sum of it and 8 is 3 times the square root of 2.

The relation in the problem statement is ...

  √(x +8) = 3√2

Squaring both sides, we have ...

  x +8 = 3²·2 = 18

  x = 10 . . . . . . . . . subtract 8

The number is 10.

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Chess is not a static game of complete information for several reasons. Firstly, the game is dynamic, meaning that the position of the pieces on the board changes constantly throughout the game.

Unlike in games like Tic Tac Toe or Connect Four, the state of the game at any given point is not fixed, and there are a vast number of possible outcomes. This means that players cannot simply memorize the best moves and outcomes for every situation, as they would in a game of complete information.

Secondly, chess is a game of imperfect information, as both players do not know what moves their opponent will make. Even with a complete understanding of the game's rules, players cannot predict with certainty the moves of their opponent, and must instead make strategic decisions based on their best assessment of their opponent's likely choices.

Finally, chess is a game of hidden information, as players do not know what their opponent is thinking or planning. A player may be able to predict their opponent's next move, but cannot know for sure what their long-term strategy is, making it difficult to make optimal decisions.

Overall, chess is a highly dynamic and complex game that is not static or complete in terms of information. Players must make strategic decisions based on incomplete and uncertain information, making it a challenging and rewarding game for those who play it.

Chess is a strategic board game played between two players, with each player starting with 16 pieces on a 64-square board. The game has been around for centuries and is considered one of the most popular and complex games in the world.

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Answer:

Center (7,2) and radius = 10

Step-by-step explanation:

Generally, we have the equation of a circle as follows;

(x-a)^2 + (y-b)^2 = r^2

where (a,b) represents the circle center and r represents the radius of the circle

Looking at the given equation of a circle, we have it that the center is (7,2) while the radius of the circle is 10

For nonnormal populations, as the sample size (n) increases, the distribution of sample means approaches a normal distribution.

This is known as the central limit theorem. The central limit theorem states that as the sample size increases, the distribution of sample means becomes more and more normal, even if the original population is not normal. The central limit theorem is a fundamental concept in statistics, as it allows us to use the normal distribution as an approximation for many statistical analyses, regardless of the underlying distribution of the population.

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Answer:

25

Step-by-step explanation:

so lets write our ratios.

Students that wear glasses to the whole class:

2 : 5

Students that wear glasses to those that dont:

2 : 3

And now if there are 15 kids in the class that dont wear glasses, that means that we have to multiply the second ratio by 5 to get the amount of students that don't wear glasses to 15. So now the second ratio will be

10 : 15

10 being amount of kids with glasses, and 15 kids without glasses. Now we just have to add them to get the answer of 25.

The equation (5)/(6)x+2=(7)/(8) when rewritten without fraction has a representation of 40x + 96 = 42

Given that we have the following

(5)/(6)x+2=(7)/(8)

When the brackets are removed, we have the following equation

5/6x + 2 = 7/8

Multiplying through the equation by 6

So, we have

6 * (5/6x + 2 = 7/8)

When the products are evaluated, we have

5x + 12 = 6 *  7/8

Multiplying through the equation by 8

So, we have

8 * (5x + 12 = 6 *  7/8)

When the products are evaluated, we have

40x + 96 = 42

Hence, the solution is 40x + 96 = 42

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Answer:

the aanswer is 1

Step-by-step explanation:

If the cost varies directly with the number of minutes Jalen talks on the phone, we can use the equation y = kx, where y represents the cost, x represents the number of minutes, and k is the constant of variation.

To determine the value of k, we can choose any of the given data points to substitute into the equation.

Let's use the first data point: Number of minutes, x = 150 and Cost, y = $7.50.

Substituting these values into the equation, we have:

$7.50 = k * 150

To solve for k, we divide both sides of the equation by 150:

k = $7.50 / 150

k = 0.05

Therefore, the equation that represents the variation is y = 0.05x.

Out of the given options, the equation y = 0.05x is the correct representation of the variation between the cost and the number of minutes Jalen talks on his mobile phone.

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Answer:

\(17\)

Step-by-step explanation:

\(\sqrt{285}\)

\(=16.8819430161\)

Answer:

Option D: \(y= -\frac34x+14\)

Step-by-step explanation:

In order for two lines to be perpendicular, the product of the slopes has to be \(-1\). That allows you to rule out A and C. Let's plug the coordinate of the point in B. If the equality holds, we found or line. Else, it's D.

\(11 =-\frac34(4) +8 \rightarrow 11 = -3+8 \rightarrow 11=5\) Which is obviously impossible. Our line has to be D

The required ratios are D/A = 0.62, N/E = 0.26, D+E = A. N/A = 0.1% D/A = 0.21, A-D=E. D/E = 4.69 D/A = 0.70, A=D+E. N/E = 7.3% and S/A = 7.6, N/S= .08, D/A = -55, A=D+E. N/A = 1.1%

The required ratios are given below:

D/A = 0.62

N/E = 0.26

D+E = A

From D+E = A, we get E = A - DD/A = 0.62A = D/0.62E = A - D

Substitute these values into N/E = 0.26

N/A = N/E * E/AN/A

N/A = 0.26 * (A - D)/A

Also, given that A = D+E and substituting the values of A and E in it, we get

A = 1.62D

From D/A = 0.21, we get

A = D/0.21

A-D = E

Substitute the value of E in terms of D and A. We get,

A = 1.21D

From D/A = 0.70, we get

A = D/0.70

A = D+E

Also, we have N/A = 0.17.

Substituting the values of A and E in terms of D and solving the above equations, we get

D = -127.82,

A = -222.93, and

E = 95.11.

Now N/E = 17/100, we get

N/E = 0.17.

Substituting the values of E and D, we get

N/A = 7.6 * 0.08 / 0.55

N/A = 1.10%

The values of the required ratios are summarized below:

D/A = 0.62,

N/E = 0.26,

D+E = A,

Find N/A = 0.1%

D/A = 0.21,

A-D=E,

Find D/E = 4.69

D/A = 0.70,

A=D+E,

Find N/E = 7.3% and

S/A = 7.6,

N/S= .08,

D/A = -55,

A=D+E,

N/A = 1.1%

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Answer:

x = 14

Step-by-step explanation:

30 = 3x - 12 (vertically opp)

30 + 12 = 3x

42 = 3x

42÷3 = x

14 = x

4.512 kg

Step-by-step explanation:

Answer:

the numbers are 5 and 7.

Step-by-step explanation:

The corresponding logistic model for the bacterial growth is W(t) = K / (1 + A * exp(-rt)), where W(t) represents the weight of the culture at time t, K is the maximum weight of the culture, A is a constant representing the initial conditions, r is the growth rate, and t is the time.

After 5 hours, the weight of the culture can be calculated using the logistic growth model. By plugging in the given values, we can solve for W(5). The logistic model equation will be: W(t) = 100 / (1 + A * exp(-rt)). We need to find the weight at t = 5 hours. To solve for this, we can use the information given in the question. We know that initially (t = 0), the weight of the culture is 10g, and at t = 2 hours, the weight is 25g. By substituting these values, we can solve for A and r.

To find the time when the culture's weight is 75g, we can again use the logistic growth model. By substituting the known values into the equation \(W(t) = 100 / (1 + A * exp(-rt)),\) we can solve for the time when W(t) equals 75g. This involves rearranging the equation and solving for t. By substituting the values for A and r that we found in part b, we can calculate the time when the culture's weight reaches 75g.

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Answer:

C. Find the sum of all the values and then divide by the number of values.

Answer:

angle 1=127 degree

angle 3=127 degree

angle 2=53 degree

angle 4=53 degree

angle 5=37 degree

angle 6=90 degree

angle 7=53 degree

angle 8=37 degree

angle 9=37 degree

angle 10=143 degree

angle 11=37 degree

angle 12=143 degree

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

The value of length SP for the two given similar triangles is 11.

Similar triangles are triangles that have the same shape but are different in size. In other words, their corresponding angles are equal, and their corresponding sides are proportional.

This means that if you were to take one of the similar triangles and enlarge or shrink it, while keeping the angles the same, it would still be a similar triangle.

The value of length SP is calculated by applying the following method;

|SP| = |ST|

3x + 2 = 5x - 4

3x - 5x = -4 - 2

-2x = - 6

x = 3

Length SP = 3x + 2

                 = 3(3) + 2

                 = 11

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δ10 is approximately equal to -25.5 ln(0.6) based on the given function a(t).

To calculate δ10, we need to evaluate the integral of a(t) from t = 0 to t = 10.

Let's break down the process step by step:

Given: \(a(t) = (1.02)t(1 - 0.04t)^{-1\)

Integrate the function a(t).

\(\int a(t) dt = \int(1.02)t(1 - 0.04t)^{-1} dt\)

Apply the substitution method.

Let u = 1 - 0.04t

Then, du = -0.04 dt, or dt = -du/0.04

Rewriting the integral with the substitution:

\(\int(1.02)t(1 - 0.04t)^{-1}dt = \int(1.02)t/u (-1/0.04) du\)

= -25.5 ∫ t/u du

Step 3: Integrate with respect to u.

-25.5 ∫ t/u du = -25.5 ln|u| + C

= -25.5 ln|1 - 0.04t| + C

Evaluate the definite integral.

To calculate δ10, we substitute the upper and lower limits of integration into the antiderivative:

δ10 = [-25.5 ln|1 - 0.04t|] from 0 to 10

= [-25.5 ln|1 - 0.04(10)|] - [-25.5 ln|1 - 0.04(0)|]

= [-25.5 ln|0.6|] - [-25.5 ln|1|]

= -25.5 ln|0.6|

Using a calculator, we can evaluate the natural logarithm:

δ10 ≈ -25.5 ln(0.6)

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Answer:

it should be -1,1

Step-by-step explanation: