If g(6) = 3 - 5(6), what is g(x)?

Answers

Answer 1

Step-by-step explanation:

g(6) = 3 - 5(6) = 3 - 30 = -27

We know the value of function g at 1 single point, g(6) = -27.

That is not enough to know what function g is.

Since the problem states that g(6) = 3 - 5(6), the problem is trying to guide you into answering that g(x) = 3 - 5x, but this is simply an assumption.


Related Questions

Using the following data, determine if the normal distribution gives a reasonable approximation: 71 42 77 84 46 93 94 63 82 88 57 32 79 67 68 83 60 65 58 70 Calculate the mean and standard deviation for these data using the appropriate equations. Compare these values to those you would get from the distribution line that you draw through the data by eye.

Answers

Hi, I'm glad to help you with this question. To determine if the normal distribution gives a reasonable approximation using the given data, we need to calculate the mean and standard deviation. Here are the steps:

1. Calculate the mean (average): Add all the data points together and divide by the number of data points.
(71+42+77+84+46+93+94+63+82+88+57+32+79+67+68+83+60+65+58+70) / 20 = 1380 / 20 = 69

Mean = 69

2. Calculate the standard deviation: First, find the difference between each data point and the mean, square the differences, and then find the average of those squared differences. Finally, take the square root of that average.
a. Differences from the mean: (-2, 27, 8, 15, -23, 24, 25, -6, 13, 19, -12, -37, 10, -2, -1, 14, -9, -4, -11, 1)
b. Squared differences: (4, 729, 64, 225, 529, 576, 625, 36, 169, 361, 144, 1369, 100, 4, 1, 196, 81, 16, 121, 1)
c. Average of squared differences: (4520) / 20 = 226
d. Square root of the average: √226 ≈ 15.03

Standard Deviation ≈ 15.03

Now that we have the mean (69) and the standard deviation (15.03), you can compare these values to the distribution line that you draw through the data by eye. If the distribution line follows a bell-shaped curve with the mean at the center and the data points spread around it following the standard deviation, then the normal distribution provides a reasonable approximation for this data set.

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A1 Let p, q E Z>1. Let A : RP → R9 be an affine function. Then there exists some c ERP and some R-linear transformation L : RP → R9 such that for every x ERP, we have A(x) = c+L(x). = Prove that for every a ERP, the function A is differentiable at a with dA(a) = L.

Answers

Means that the derivative of A at a, dA(a), is equal to L. Hence, A is differentiable at a with dA(a) = L.

To prove that the function A is differentiable at a with dA(a) = L, we need to show that:

lim(x→a) [A(x) - A(a) - L(a)(x-a)] / ||x-a|| = 0

We know that A(x) = c + L(x) for all x in RP, where c is a constant and L is a linear transformation from RP to R9.

Then, we have:

A(a) = c + L(a)

L(a)(x-a) = L(x-a) + L(a-a) = L(x-a)

Substituting these into the limit expression, we get:

lim(x→a) [c + L(x) - c - L(a) - L(x-a)] / ||x-a||

= lim(x→a) [L(x) - L(a)] / ||x-a||

Since L is a linear transformation, it is continuous. Therefore, we can write:

lim(x→a) [L(x) - L(a)] / ||x-a|| = L( lim(x→a) [x-a] / ||x-a|| )

But lim(x→a) [x-a] / ||x-a|| = u, a unit vector in the direction of x-a.

Therefore, we have:

lim(x→a) [L(x) - L(a)] / ||x-a|| = Lu

This means that the derivative of A at a, dA(a), is equal to L. Hence, A is differentiable at a with dA(a) = L.

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In a state's lottery, you can bet $4 by selecting three digits, each between 0 and 9 inclusive If the same three numbers are drawn in the same order, you win and collect $500. Complete parts (a) through (e) a. How many different selections are possible? b. What is the probability of winning? (Simplify your answer.) c. If you win, what is your net profit?___ $ (Type an integer or a decimal. Do not round) d. Find the expected value for a $4 bet.___ $ (Type an integer or a decimal. Do not round) e. If you bet $4 on a certain casino game, the expected value is -1.7¢ Which bet is better in the sense of producing a higher expected value a $4 bet on the state's loftery or a S4 bet on the casino game? Explain. O A. Neither bet is better because both games have the same expected value O B. It is impossible to compare the values because they have different units. C. The casino game is a better bet because it has a larger expected value.

Answers

The expected value of a $4 bet on the state's lottery is -$0.84 and the expected value of a $4 bet on the casino game is -1.7¢ (which is equivalent to -$0.017), the state's lottery is a better bet in terms of producing a higher expected value.

a. There are 10 possible choices for each of the three digits, so the total number of different selections is 10 x 10 x 10 = 1000.

b. Since there is only one winning combination out of the 1000 possible selections, the probability of winning is 1/1000.

c. If you win, your net profit would be $500 - $4 = $496.

d. The expected value is the sum of the products of each possible outcome and its probability. In this case, the expected value is (1/1000) x $500 + (999/1000) x (-$4) = -$0.84.

e. Since the expected value of a $4 bet on the state's lottery is -$0.84 and the expected value of a $4 bet on the casino game is -1.7¢ (which is equivalent to -$0.017), the state's lottery is a better bet in terms of producing a higher expected value.

This is because the expected loss for the state's lottery is smaller than the expected loss for the casino game.

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The table below shows the number of hours ten students spent studying for a test and their scores.

Hours Spent Studying(x):0,1,2,4,4,4,6,6,7,8
Test Scores(y):35,40,46,47,70,82,88,82,95

Write the linear regression equation for this data set. Round all values to the nearest hundredth.

State the correlation coefficient of this line, to the nearest hundredth.

Explain what the correlation coefficient suggests in the context of the problem.

Answers

The correlation coefficient of 0.88 reveals that there is an intense linear connection between the two variables.

How to explain the correlation

It should be noted that to ascertain the correlation coefficient, we can utilize the formula:

r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

Retaining the same numeric values from before, we can compute:

r = (9(976) - (36)(605)) / sqrt[(9(182) - (36)^2)(9(11681) - (605)^2)] ≈ 0.88

Therefore, the correlation coefficient is fairly close to 0.88.

The correlation coefficient implies a strong positive relationship between hours expended studying and test outcomes. As the quantity of hours committed to studying increases, the test scores will tend to keep up accordingly. A correlation coefficient of 0.88 reveals that there is an intense linear connection between the two variables, and the line of best fit serves as a desirable standard representation of the data.

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Answer:

y = 34.27 + 7.79xr = 0.98Strong positive correlation: The more hours of studying for a test a student does, the higher their test score.

Step-by-step explanation:

It appears there is an error in the table. The correct table is:

[tex]\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-11}\vphantom{\dfrac12}\textsf{Hours spent studying $(x)$}&0&1&2&4&4&4&6&6&7&8\\\cline{1-11}\vphantom{\dfrac12}\textsf{Test score $(y)$}&35&40&46&65&67&70&82&88&82&95\\\cline{1-11}\end{array}[/tex]

The simplest method to find the linear regression equation and the correlation coefficient for this data set is to use a statistical calculator.

After entering the data into a statistical calculator we get:

a = 34.272727...b = 7.79220779...r = 0.981574157...

The regression line of y on x is y = a + bx.

Therefore, substitute the found values of a and b into the formula to write the linear regression equation for the given data set:

[tex]\boxed{y=34.27+7.79x}[/tex]

The correlation coefficient is the value of r, so r = 0.98 to the nearest hundredth.

The correlation coefficient, r, measures the strength of the linear correlation between two variables. |t is always between +1 and -1.

Values close to +1 mean a strong positive correlation.Values close to -1 mean a strong negative correlation.Values of r close to zero mean there is only a weak correlation.If r = 0, the variables aren't correlated.

As r = 0.98, there is a very strong positive correlation.

In context, this suggests that the more hours of studying for a test a student does, the higher their test score.

The following polygons are similar find the scale factor of the small figure to the large figure 1-2

Answers

Answer:

1.5 and 4

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original.

1

scale factor = [tex]\frac{DF}{AC}[/tex] = [tex]\frac{21}{14}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5

2

scale factor = [tex]\frac{8}{2}[/tex] = 4

Solve the equation -2x^2-13x+20=-3x^2 to the nearest tenth.

Answers

The solutions to the equation to the nearest tenth are x = 10.1 and x = 2.9.

We have,

-2x² - 13x + 20 = -3x²

Combining like terms

-2x² - 13x + 20 = -3x²

x² - 13x + 20 = 0 (adding 3x² to both sides)

Now we can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

In this case,

a = 1, b = -13, and c = 20.

Substituting these values into the quadratic formula:

x = (-(-13) ± √((-13)² - 4(1)(20))) / 2(1)

x = (13 ± √(169 - 80)) / 2

x = (13 ± √(89)) / 2

So the solutions are:

x = (13 + √(89)) / 2

x ≈ 10.1

and

x = (13 - √(89)) / 2

x ≈ 2.9

Therefore,

The solutions to the equation to the nearest tenth are x ≈ 10.1 and x ≈ 2.9.

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Andrew and Ruth Bacon would like to obtain an installment loan of 1850 to repaint their home. They can get the loan at an APR of a) 8% for 24 months or b) 11% for 18 months. Which loan has the lower finance charge?

Answers

8% for 24 months has the lower finance charge of $296, compared to option b) with a finance charge of $363.50.

To compare the two loans, we need to calculate the finance charge for each option.

For option a) at 8% APR for 24 months, we can use the following formula:

Finance charge = (loan amount x interest rate x time) / 12

Finance charge = (1850 x 0.08 x 24) / 12 = 296

So the finance charge for option a) is $296.

For option b) at 11% APR for 18 months, we can use the same formula:

Finance charge = (loan amount x interest rate x time) / 12

Finance charge = (1850 x 0.11 x 18) / 12 = 363.5

So the finance charge for option b) is $363.50.

Therefore, option a) has the lower finance charge of $296, compared to option b) with a finance charge of $363.50.

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Help WILL GIVE BRAINLIEST HEELLPPO

Answers

Answer:

B: 4.5

Step-by-step explanation:

(5 MARKS) Prove that F (c)(A + B) → (Vx) A (3.c)B. 4. (5 MARKS) All the sets in this problem are subsets of N. For any ACN, let us use the notation ADES N-A

Answers

To prove F(c)(A + B) → (Vx) A (3.c)B, we need to show that if the union of sets A and B is finite, then there exists an element x in A such that for all elements y in B, (x, y) is in the relation C.

Assume F(c)(A + B) is true. Then for any (x, y) in C, x belongs to A + B, which means x belongs to either A or B. If x belongs to A, then we have found an element x in A such that for all elements y in B, (x, y) is in C, and we are done. If x belongs to B, then we need to find another element in A such that the condition holds.

Since A and B are finite, their union A + B is also finite. Let n be the size of A + B. Then there are n distinct elements in A + B, say a1, a2, ..., an. Since there are more elements in A than in B (or equal if they have the same size), there must be at least one element of A among a1, a2, ..., an. Call this element x.

Now, consider any element y in B. Since x belongs to A + B and y belongs to B, their sum x + y belongs to A + B as well. But we know that x + y cannot be equal to x, since y is not in A. Therefore, x + y must be equal to one of the remaining n-1 elements of A + B, say ai. But then ai - x = y, so (x, y) is in C.

Therefore, we have shown that F(c)(A + B) → (Vx) A (3.c)B is true.

For the second part of the question, we need to show that for any set A in N, there exists a set B in N such that A is a subset of B and B is infinite.

Let B be the set of all natural numbers greater than the maximum element in A. Then A is clearly a subset of B, and B is infinite since it contains all natural numbers greater than a certain number.

Therefore, we have shown that for any set A in N, there exists a set B in N such that A is a subset of B and B is infinite.

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1(c) [3 pts] for the smokestack with the filter installed, find the probability that the amount of pollutant in a given sample will exceed 1/2.

Answers

To find the probability that the amount of pollutant in a given sample will exceed 1/2 for the smokestack with the filter installed, you need to determine the distribution of the pollutant levels and then calculate the probability based on that distribution.

To find the probability that the amount of pollutant in a given sample will exceed 1/2 when a filter is installed in the smokestack, we need to use the information provided in the question. However, we do not have any specific information on the distribution of the pollutant levels, so we cannot calculate the exact probability.
Instead, we can make some assumptions based on the purpose of the filter. Filters are typically installed to reduce the amount of pollutants emitted into the air, so it is reasonable to assume that the filter will decrease the amount of pollutant in each sample. Therefore, we can expect the probability of the pollutant level exceeding 1/2 to decrease when a filter is installed.
Without more information, we cannot give an exact probability, but we can say that it is likely lower than the probability without a filter. We would need to know more about the specific characteristics of the filter and the pollutant to make a more accurate estimate.

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Asemi annual coupon bond has a par value of $1,000 and matures in 10years. Today it sells for $887 and has a YTM of 10.9%. Solve forcoupon rate

Answers

The coupon rate for the semi-annual bond is approximately 11.96%.

Given the information provided, we have the following details:

- Par value: $1,000
- Maturity: 10 years
- Current price: $887
- YTM (Yield to Maturity): 10.9%

To solve for the coupon rate, we can use the bond pricing formula:

Bond Price = (C * (1 - (1 + r/2)^(-2n))) / (r/2) + (Par Value / (1 + r/2)^(2n))

Where:
- Bond Price = $887
- C = Coupon payment per period (which we need to find)
- r = YTM / 100 = 0.109
- n = Maturity in years = 10

Plugging in the given values:

$887 = (C * (1 - (1 + 0.109/2)^(-2*10))) / (0.109/2) + ($1,000 / (1 + 0.109/2)^(2*10))

Now, we can solve for the coupon payment, C:

C = (($887 * 0.109/2) - ($1,000 / (1 + 0.109/2)^(2*10))) / (1 - (1 + 0.109/2)^(-2*10))

C ≈ $59.80

Since this is a semi-annual bond, the annual coupon payment would be:

Annual Coupon Payment = C * 2 = $59.80 * 2 = $119.60

Finally, to find the coupon rate, we can divide the annual coupon payment by the par value:

Coupon Rate
= (Annual Coupon Payment / Par Value) * 100 = ($119.60 / $1,000) * 100 = 11.96%

So, the coupon rate for the semi-annual bond is approximately 11.96%.

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In a survey, 200 college students were asked whether they live on campus and if they own a car. Their responses are summarized in the following table below.

Answers

If in a survey, 200 college students were asked whether they live on campus and if they own a car, 55% of college students in the survey don't own a car.

To find the percent of college students who don't own a car, we need to add up the number of students who don't own a car and divide it by the total number of students in the survey. In this case, the total number of students in the survey is 200.

From the table, we can see that there are 88 students who live on campus and don't own a car, and 22 students who don't live on campus and don't own a car. So the total number of students who don't own a car is 88 + 22 = 110.

To find the percentage, we divide the number of students who don't own a car by the total number of students in the survey and then multiply by 100 to get the percentage:

Percentage of students who don't own a car = (110/200) x 100% = 55%

When working with percentages, we need to divide the number we are interested in by the total and then multiply by 100 to get the percentage.

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A continuous random variable X has a pdf of the form: f(x) = (265/652) x^3, for 0.90 < X < 1.80. Calculate the standard deviation (sigma) of X. Your answer: 0.138 0.715 O 0.340 0.828 O 0.417 O 0.232 O 0.172 O 0.532 O 0.258

Answers

The answer is not provided in the options given. The closest option is 0.172, but the correct answer is 0.155 (rounded to three decimal places).

To calculate the standard deviation of X, we first need to find the mean or expected value of X. We can do this by integrating the given pdf over the range 0.90 to 1.80:

E(X) = ∫[0.90,1.80] x*f(x) dx

= ∫[0.90,1.80] x*(265/652)*x^3 dx

= (265/652) * ∫[0.90,1.80] x^4 dx

= (265/652) * [x^5/5] from x=0.90 to x=1.80

≈ 1.315

Next, we can calculate the variance of X using the formula:

Var(X) = E(X^2) - [E(X)]^2

To find E(X^2), we integrate the pdf squared over the same range:

E(X^2) = ∫[0.90,1.80] x^2*f(x) dx

= ∫[0.90,1.80] x^2*(265/652)*x^3 dx

= (265/652) * ∫[0.90,1.80] x^5 dx

= (265/652) * [x^6/6] from x=0.90 to x=1.80

≈ 1.464

Var(X) = E(X^2) - [E(X)]^2

≈ 1.464 - 1.315^2

≈ 0.024

Finally, we take the square root of the variance to obtain the standard deviation:

sigma = sqrt(Var(X))

≈ sqrt(0.024)

≈ 0.155

Therefore, the answer is not provided in the options given. The closest option is 0.172, but the correct answer is 0.155 (rounded to three decimal places).

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if sales are expressed as a function of the amount spent on advertising, then the dollar amount at which , the rate of change of sales, goes from increasing to decreasing is call the [ select ] . if is that dollar amount, then is

Answers

If sales are expressed as a function of the amount spent on advertising, then the dollar amount at which the rate of change of sales goes from increasing to decreasing is called the point of diminishing returns or diminishers returns to scale.

It sounds like you want to know about the relationship between sales, advertising, and the rate of change. Here's an answer incorporating the terms you've mentioned:

If sales are expressed as a function of the amount spent on advertising, the dollar amount at which the rate of change of sales goes from increasing to decreasing is called the inflection point. If 'x' is that dollar amount, then 'x' represents the advertising budget at which the sales growth rate starts to decline.

This point indicates that increasing the amount spent on advertising beyond this dollar amount will result in a decrease in the rate of change of sales. This is known as the diminishers' scale to return.

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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.

Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.

Determine the theoretical probability of the spinner not landing on blue, P(not blue).

0.375
0.625
0.750
0.875

Answers

The theoretical probability of the spinner not landing on blue would be = 0.625. That is option B.

How to calculate the theoretical probability of the given event?

To calculate the theoretical probability of the given event, the formula that should be used is given as follows:

Probability = possible outcome/sample space

The possible outcome for other colours apart from blue = 5

The sample space = 8

Therefore probability = 5/8 = 0.625

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Solve the given differential equation.
t dQ/dt + Q = t^4 In(t)
-t^4/25 + t^4/5In(t) + c/t

Answers

the solution to the given differential equation is: Q(t) = -t^4/25 + t^4/5 ln(t) + C/t

To solve the given differential equation t dQ/dt + Q = t^4 ln(t), we'll first find the integrating factor, solve for Q(t), and then substitute the given terms.

Step 1: Find the integrating factor.
The integrating factor is e^(∫P(t)dt), where P(t) = 1/t in this case. So,

∫(1/t)dt = ln(t)

The integrating factor is e^(ln(t)) = t.

Step 2: Multiply the equation by the integrating factor.
t (t dQ/dt) + t(Q) = t^2 dQ/dt + tQ = t^5 ln(t)

Step 3: Integrate both sides of the equation.
∫(t^2 dQ/dt + tQ)dt = ∫(t^5 ln(t))dt

Using integration by parts on the right side (u = ln(t), dv = t^5 dt):

∫(t^5 ln(t))dt = (t^5 ln(t) / 5) - ∫(t^4 dt) = (t^5 ln(t) / 5) - (t^5 / 25) + C

Step 4: Solve for Q(t).
Since ∫(t^2 dQ/dt + tQ)dt = tQ, we have:

tQ = (t^5 ln(t) / 5) - (t^5 / 25) + C
Q(t) = -t^4/25 + t^4/5 ln(t) + C/t

So, the solution to the given differential equation is:

Q(t) = -t^4/25 + t^4/5 ln(t) + C/t

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A twelve-sided die has sides numbered 1 through 12. The die is rolled once. Find each probability.: P(odd or a multiple of 4)

Answers

The probability of getting an odd number or a multiple of 4 is 3/4.

Given that, a twelve-sided die has sides numbered 1 through 12. we need to find the probability of getting a number odd or a multiple of 4.

Probability = favorable outcomes / total number of outcomes

For odd numbers =

Favorable outcomes = 1, 3, 5, 7, 9, 11 = 6

P(odd number) = 6/12 = 1/2

For multiple of 4 =

Favorable outcomes = 4, 8, 12 = 3

P(multiple of 4) = 3/12 = 1/4

P(odd or a multiple of 4) = 1/2 + 1/4 = 3/4

Hence, the probability of getting an odd number or a multiple of 4 is 3/4.

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Stevic delivers newspapers. He has already earned $36 delivering the Sunday paper and $12 delivering the Saturday paper. He earns $4 for each Sunday paper delivered and $2.50 for each Saturday paper delivered.


Part A

Enter numbers in the boxes to complete the rules for finding Stevic's earnings.

Sunday newspaper: Start at $ and add $

Saturday newspaper: Start at $ and add $

Part B

Stevic wants to compute his total earnings after delivering 15 papers on each day.

I'm actually in fifth grade

Answers

Answer:

Part A:

Sunday newspaper: Start at $36 and add $4 for each paper delivered.

Saturday newspaper: Start at $12 and add $2.50 for each paper delivered.

Part B:

To calculate Stevic's total earnings after delivering 15 papers on each day:

Earnings from Sunday papers = $36 + ($4 x 15) = $96

Earnings from Saturday papers = $12 + ($2.50 x 15) = $49.50

Total earnings = Earnings from Sunday papers + Earnings from Saturday papers

Total earnings = $96 + $49.50

Total earnings = $145.50

Therefore, Stevic's total earnings after delivering 15 papers on each day is $145.50.

Step-by-step explanation:

The height y (in feet) of a ball thrown by a child is
y=−1/16x^2+2x+5
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? feet
(b) What is the maximum height of the ball? feet
(c) How far from the child does the ball strike the ground? feet

Answers

(a) When the ball leaves the child's hand, x = 0, so we can substitute this into the equation:
y = -1/16(0)^2 + 2(0) + 5
y = 5
Therefore, the ball is 5 feet high when it leaves the child's hand.

(b) To find the maximum height of the ball, we need to determine the vertex of the parabola. The x-coordinate of the vertex is given by:
x = -b/2a
where a = -1/16 and b = 2. Substituting these values:
x = -2/(2(-1/16))
x = 16
To find the y-coordinate, we substitute x = 16 into the equation:
y = -1/16(16)^2 + 2(16) + 5
y = 21
Therefore, the maximum height of the ball is 21 feet.

(c) To find how far from the child the ball strikes the ground, we need to determine the value of x when y = 0. Substituting y = 0 into the equation:
0 = -1/16x^2 + 2x + 5
Multiplying both sides by -16 to eliminate the fraction:
0 = x^2 - 32x - 80
We can solve for x using the quadratic formula:
x = (32 ± sqrt(32^2 - 4(1)(-80))) / 2(1)
x = (32 ± sqrt(1472)) / 2
x = 16 ± 8sqrt(2)
Since the ball cannot land behind the child, we take the positive value:
x = 16 + 8sqrt(2)
Therefore, the ball strikes the ground approximately 29.1 feet from the child.

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the kyoto protocol was signed in 1997, and required countries to start reducing their carbon emissions. the protocol became enforceable in february 2005. in 2004, the mean carbon dioxide emission was 4.87 metric tons per capita. the table below contains the carbon dioxide emissions from a random sample of countries from a recent study. is there enough evidence to show that the mean carbon dioxide emission is now lower than it was in 2004? test at the 3% level.

Answers

There is enough evidence to show that the mean carbon dioxide emission is now lower than it was in 2004.

To test whether the mean carbon dioxide emission is now lower than it was in 2004, we need to conduct a one-sample t-test.

We are given a random sample of carbon dioxide emissions from a recent study. Let's assume that this sample is representative of the population of interest. The null hypothesis is that the true population mean of carbon dioxide emissions is equal to or greater than the mean in 2004 (4.87 metric tons per capita). The alternative hypothesis is that the true population mean is less than the mean in 2004.

We can set up the hypotheses as follows:

H0: μ >= 4.87

Ha: μ < 4.87

where μ is the true population mean of carbon dioxide emissions.

We are given the sample data in a table, but we don't know the population standard deviation, so we will use the sample standard deviation to estimate it. The sample mean is calculated as:

x = (4.28 + 3.94 + 3.27 + 3.81 + 3.43 + 3.09 + 2.52 + 2.98 + 3.23 + 3.36) / 10 = 3.43

The sample standard deviation is calculated as:

s = √(((4.28 -x)² + (3.94 - x)² + ... + (3.36 - x)²) / 9) = 0.659

The sample size is n = 10.

We can calculate the t-statistic as:

t = (x- μ) / (s / √(n)) = (3.43 - 4.87) / (0.659 / √(10)) = -4.26

The degrees of freedom for this test are df = n - 1 = 9. We can use a t-distribution table or a calculator to find the p-value associated with this t-statistic and degrees of freedom.

Using a t-distribution table with df = 9, we find that the p-value for a one-tailed test at the 3% level is less than 0.001. This means that the probability of observing a t-statistic as extreme as -4.26, assuming the null hypothesis is true, is less than 0.001.

Since the p-value is less than the significance level of 0.03, we reject the null hypothesis and conclude that there is enough evidence to show that the mean carbon dioxide emission is now lower than it was in 2004 at the 3% level.

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If PQ = 12, find the measure of the dilation image of P'Q' with a scale factor of 3/4

Answers

The measure of the dilation image P'Q' with a scale factor of 3/4 is given as follows:

P'Q' = 9 units.

What is a dilation?

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor for the dilation in this problem is given as follows:

k = 3/4.

The length of the original segment is of 12 units, hence the length of the dilated segment is given as follows:

P'Q' = 3/4 x 12 = 36/4 = 9 units.

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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.


Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3

Determine the probability that a student studied for 5 hours.
23.0
0.70
0.23
0.16

Answers

The probability that a student studied for 5 hours is given as follows:

0.23.

How to calculate a probability?

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of students in this problem is given as follows:

1 + 3 + 2 + 5 + 9 + 7 + 3 = 30.

Out of those 30 students, 7 studied five hours, hence the probability is given as follows:

p = 7/30 = 0.23.

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Determine the circumference of the circle. Use 3.14 as an approximation for π.
The radius of the circle is 7 cm.

Please help me out. Thank you.

Answers

Answer:

43.96 cm

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = 2πr

where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.

Given that the radius of the circle is 7 cm, we can substitute this value into the formula and simplify:

C = 2πr

C = 2 × 3.14 × 7

C = 43.96

Therefore, the circumference of the circle is approximately 43.96 cm.

if p=-6 and q = 4 what is the smallest subset containing the value of the expression below? p^2 +q/ -|p|-q

Answers

The value of the given expression is -4, which is integer. Therefore, option B is the correct answer.

The given expression is (p²+q)/(-|p|-q).

Here, p=-6 and q=4.

Substitute p=-6 and q=4 in the given expression we get

((-6)²+4)/(-|-6|-4)

= 40/(-10)

= -4

Therefore, option B is the correct answer.

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Solve 1/3x- 1 = 5.

A. x = 12
B. x = 18
C. x = 1
D. x=2

Answers

Answer:

option B: x= 18

Step-by-step explanation:

To solve 1/3x - 1 = 5, we can start by adding 1 to both sides of the equation:

1/3x - 1 + 1 = 5 + 1

Simplifying:

1/3x = 6

Multiplying both sides by 3:

3(1/3x) = 3(6)

Simplifying:

x = 18

Therefore, the solution is x = 18, which is option B.

Which of the following represent direct variation?

Answers

Answer:

all yes

Step-by-step explanation:

what is the surface area of 8yd by 3yd by 1 yd?

Answers

Answer:

The surface area is 70 yards

Step-by-step explanation:

The formula for surface area is (SA)=2lw+2lh+2hw. Meaning it would be 2 times (8 times 3 + 8 times 1 + 3 times 1) which equals 70 yards.

Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select
three options.
6 feet by 2 feet by 3 feet
6 feet by 5 feet by 4 feet
7 feet by 6 feet by 4 feet
8 feet by 3 feet by 7 feet
8 feet by 4 feet by 3 feet
Mark this and return
Save and Exit
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Answers

The three options with dimensions resulting in a surface area greater than 140 square feet are:

6 feet by 5 feet by 4 feet7 feet by 6 feet by 4 feet8 feet by 3 feet by 7 feet  

To determine whether the dimensions of a rectangular prism result in a surface area greater than 140 square feet, we can use the formula for the surface area of a rectangular prism:

Surface Area = 2lw + 2lh + 2wh

    where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Option 1: 6 feet by 2 feet by 3 feet

Surface Area = 2(6)(2) + 2(6)(3) + 2(2)(3) = 24 + 36 + 12 = 72 square feet

This option does not have a surface area greater than 140 square feet.

Option 2: 6 feet by 5 feet by 4 feet

Surface Area = 2(6)(5) + 2(6)(4) + 2(5)(4) = 60 + 48 + 40 = 148 square feet

This option has a surface area greater than 140 square feet.

Option 3: 7 feet by 6 feet by 4 feet

Surface Area = 2(7)(6) + 2(7)(4) + 2(6)(4) = 84 + 56 + 48 = 188 square feet

This option has a surface area greater than 140 square feet.

Option 4: 8 feet by 3 feet by 7 feet

Surface Area = 2(8)(3) + 2(8)(7) + 2(3)(7) = 48 + 112 + 42 = 202 square feet

This option has a surface area greater than 140 square feet.

Option 5: 8 feet by 4 feet by 3 feet

Surface Area = 2(8)(4) + 2(8)(3) + 2(4)(3) = 64 + 48 + 24 = 136 square feet

This option does not have a surface area greater than 140 square feet.

Therefore, the three options with dimensions resulting in a surface area greater than 140 square feet are:

6 feet by 5 feet by 4 feet7 feet by 6 feet by 4 feet8 feet by 3 feet by 7 feet

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When Landon moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 24 inches tall and Tree B was 40 inches tall. Each year thereafter, Tree A grew by 9 inches per year and Tree B grew by 5 inches per year. Let

A represent the height of Tree A

t years after being planted and let

B represent the height of Tree B

t years after being planted. Write an equation for each situation, in terms of

,
t, and determine the height of both trees at the time when they have an equal height.

Answers

The equations are;

H = 24 + 9x

H = 40 + 5x

How do you convert word equations to mathematical equations?

In a word problem, there are usually one or more unknown quantities that you need to find. Identify these unknowns and assign them a variable.

We have to know that Tree A was 24 inches tall and Tree B was 40 inches tall. Each year thereafter, Tree A grew by 9 inches per year and Tree B grew by 5 inches per year.

Then for tree A;

H = 24 + 9x

For tree B

H = 40 + 5x

Where x is the number of years that the trees stay.

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(1) For z = 1+ i evaluate the expressions. (a) zz (b) Re(z) + Im(z) Z 2 + 2

Answers

To evaluate the expressions for z = 1 + i, we'll consider each part:

(a) zz (the product of z and its complex conjugate):
First, find the complex conjugate of z, which is the same as z but with the imaginary part negated: z* = 1 - i. Now, multiply z and z*:
z * z* = (1 + i)(1 - i) = 1 - i + i - i^2 = 1 - i^2 = 1 - (-1) = 1 + 1 = 2.

(b) Re(z) + Im(z) Z^2 + 2:
Re(z) is the real part of z, which is 1. Im(z) is the imaginary part of z, which is 1. Now, square z:
Z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i.
Finally, calculate Re(z) + Im(z) Z^2 + 2:
1 + 1(2i) + 2 = 1 + 2i + 2 = 3 + 2i.

So, the expressions evaluated are (a) zz = 2 and (b) Re(z) + Im(z) Z^2 + 2 = 3 + 2i.


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