I need help with 16-25 please
Simplify using only positive exponents

In this scenario, Evin's gas consumption is described by a slope of -1.25 gallons per mile. This means that for every mile Evin drives, he consumes 1.25 gallons of gas.

The given information states that the slope in this scenario is -1.25 gallons per mile. The slope represents the rate of change, indicating how the quantity of gas consumed changes with respect to the distance driven. In this case, for every mile Evin drives, he consumes 1.25 gallons of gas.

To calculate the gas consumption, you can multiply the distance driven by the slope. For example, if Evin drives 10 miles, the gas consumed would be 10 miles * (-1.25 gallons/mile) = -12.5 gallons. The negative sign indicates a decrease in gas, which implies consumption.

It's important to note that the given slope assumes a linear relationship between gas consumption and distance driven. In reality, gas consumption may vary depending on factors such as driving conditions, speed, and vehicle efficiency.

However, for the purposes of this scenario and based on the information provided, the gas consumption rate is assumed to be constant at -1.25 gallons per mile.

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Answer: 253/112

Step-by-step explanation:

\(N:2.75=5 \frac{3}{4}:7\\\\4N:11=23:28\\\\4N=\frac{23 \cdot 11}{28}\\\\N=\frac{(23 \cdot 11)/28}{4}\\\\N=253/112\)

Answer:

The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Step-by-step explanation:

hope this helps

correct me if this is wrong

Answer:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Given expression is:

Take 3 common from it:

So the factor are:

Answer:

$35

Step-by-step explanation:

25 x 1.4 = 35

Step-by-step explanation:

\(91.8 \div 12 = 7.65 \\ 19.35 \div 3 = 6.45\)

3 months

Answer:

y=-26.7x+14.1

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

y=−26.7x+14.1

Step-by-step explanation:

y=−17.5x+2.7x+14.1−11.9x

y=−26.7x+14.1

Solve for x:

Step 1: Flip the equation.

−26.7x+14.1=y

Step 2: Add -14.1 to both sides.

−26.7x+14.1+−14.1=y+−14.1

−26.7x=y−14.1

Step 3: Divide both sides by -26.7.

x=−0.037453y+0.52809

Solve for y:

y=−26.7x+14.1

The values of t that place 85% of the area in the middle of the distribution are between -3.379 and 3.379.

To find the values of t that place 85% of the area in the middle of the distribution, we need to find the t-scores that correspond to the 7.5th and 92.5th percentiles of the t-distribution with 46 degrees of freedom.

We can use a t-table or a statistical software to find these values. Using a t-table, we can look up the critical t-values for the two tails of the distribution that include 7.5% and 92.5% of the area.

For a two-tailed test at the 5% significance level with 46 degrees of freedom, the critical t-value is approximately 2.013.

To find the t-scores for the 7.5th and 92.5th percentiles, we need to multiply the critical t-value by the corresponding t-multiplier for the degrees of freedom. For 46 degrees of freedom, the t-multiplier is approximately 1.678.

Thus, the t-score that corresponds to the 7.5th percentile is -2.013 x 1.678 = -3.379, and the t-score that corresponds to the 92.5th percentile is 2.013 x 1.678 = 3.379.

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The given question is incomplete, the complete question is:

Consider a t distribution with 46 degrees of freedom. What values of t place 85% of the area in the middle of the distribution?

Answer:

8 weeks per painting

Step-by-step explanation:

1/4 of a painting in 2 weeks

Multiply everything x 4

4/4 or 1 painting in 8 weeks

The athlete sprints a distance of 403.4 meters in a time of 43.8 seconds. To calculate the average speed, we divide the distance traveled by the time taken. The average speed of the athlete is approximately 9.21 m/s.

Average speed is calculated by dividing the total distance traveled by the total time taken. In this case, the athlete covers a distance of 403.4 meters in a time of 43.8 seconds.

Average speed = Total distance / Total time

Substituting the given values:

Average speed = 403.4 m / 43.8 s

Calculating the result:

Average speed ≈ 9.21 m/s

Therefore, the athlete's average speed is approximately 9.21 m/s. Thus, the correct answer is A) 9.21 m/s.

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Answer:

Graph of exponential rising up to the right, through the point (0, 2).

Step-by-step explanation:

I think you mean  f(x) = 3^x + 1.

When x = 0, 3^x = 1, so the graph of f(x) = 3^x will rise up to the right and pass through point (0. 1)

The + 1 translates the graph up 1 unit so

The graph of f(x) = 3^x + 1 passes through the point (0, 2).

Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

By using substitution method, the equation is 10y²+56y-38.7=0

An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.

Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.

Given equations are:

2x+4y= -8.6

9x-5y=28

By using substitution method,

2x+4y= -8.6

⇒x+2y= -4.3

x= (-4.3/2y)

Substituting x value in the second equation, we get

9(-4.3/2y)-5y=28

-38.7-10y²=56y

10y²+56y-38.7=0

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We need to check if lines ℓ and k are parallel. For two lines to be parallel, they must have the same slope and different y-intercepts.Let's compare the given lines:Line ℓ: y = 34x + 6Slope of line ℓ = 34Line k: y = 34x - 7Slope of line k = 34We see that the slope of lines ℓ and k is the same (34), which means that they could be parallel.

However, we still need to check if they have different y-intercepts. Line ℓ: y = 34x + 6 has a y-intercept of 6.Line k: y = 34x - 7 has a y-intercept of -7.So, lines ℓ and k have different y-intercepts, which means they are not parallel. Therefore, the correct answer is b) No.In slope-intercept form, the equation of a line is y = mx + b, where m is the slope of the line and b is its y-intercept. In this case, both lines have the same slope of 34 (the coefficient of x). The y-intercepts are different (+6 for line l and -7 for line k). Thus, the lines are not parallel.

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The answer is option a) Yes. Lines ℓ and k are parallel to each other.

The two distinct lines defined by the following two equations in slope-intercept form are:

Line ℓ: y = 34x + 6

Line k: y = 34x - 7

To determine if the lines are parallel, we need to compare their slopes since two non-vertical lines are parallel if and only if their slopes are equal.

Both lines are in slope-intercept form, so we can immediately read off their slopes:

Line ℓ has a slope of 34, and line k has a slope of 34.

Both the lines ℓ and k have the same slope of 34.

Hence, the answer is option a) Yes. Lines ℓ and k are parallel to each other.

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Answer:

6x+9

(2x+3)3

you would distribute 3 into 3 and 2x to get...

6x+9

No, failing to reject the null hypothesis does not mean that we have proved it to be true beyond all doubt.

The null hypothesis is simply a statement that we assume to be true until we have sufficient evidence to reject it. Failing to reject the null hypothesis means that we do not have enough evidence to reject it, but it does not necessarily mean that the null hypothesis is true. There could be other factors or sources of variation that we have not accounted for in our analysis, which could affect our conclusion.

a. The null hypothesis is that the mean IQ for college students is 90, and the alternative hypothesis is that the mean IQ is less than 90.

b. The test statistic is:

\(t = ( \bar x -\mu) / (\sigma / \sqrt{n} )\)

where \(\bar x\) is the sample mean, \(\mu\) is the hypothesized population mean, σ is the population standard deviation, and n is the sample size. Plugging in the given values, we get:

t = (84 - 90) / (18 / √61) = -2.48

c. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-tailed (less than), we look for the area to the left of the observed t-value in the t-distribution with 60 degrees of freedom. Using a t-table or a calculator, we find the p-value to be 0.0082.

d. At the 0.05 level of significance, the p-value (0.0082) is less than the level of significance, so we reject the null hypothesis. This means that we have sufficient evidence to conclude that the mean IQ for college students is less than 90.

e. Based on the sample of 61 college students, we have sufficient evidence to conclude that the mean IQ for college students is less than 90. This suggests that the professor's initial claim of a mean IQ of 90 for college students may not be accurate.

The complete question is:

If we fail to reject the null hypothesis, does this mean that we have proved it to be true beyond all doubt? Explain your answer.

A professor claims that the mean IQ for college students is 90. He collects a random sample of 61 college students to test this claim and the mean IQ from the sample is 84.

a. What are the null and alternative hypotheses to test the initial claim?

b. Compute the test statistic. Assume the population standard deviation of IQ scores for college students is 18 points.

c. Find the p-value to test the claim at the 0.05 level of significance. Show/explain how you found these values.

d. Find a conclusion for the test (i.e., reject or fail to reject the null hypothesis). State your reasoning (i.e., why?).

e. Interpret your conclusion from part (d) by putting your results in context of the initial claim.

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Step-by-step explanation:

Wait Aw Minute ✌️ BRO I See

If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.

Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:

24 = (3/4) x

To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:

24 * (4/3) = x

Simplifying, we get:

32 = x

We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.

To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.

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Answer:

Frank is correct, because (see explanation below)

Step-by-step explanation:

Let's separate into two cases:

Case 1: Blue marble

\(\frac{6}{7}\) (There are 6 blues in the bag and 7 marbles in total in the bag, we put the 6 in the numerator because we want a blue marble first.)

Case 2: Green marble

\(\frac{1}{6}\) (There is only 1 green in the bag and 6 marbles remaining in the bag, because we already took 1 blue out in Case 1. We put 1 in the numerator because we want the green marbloe only.)

Multiply Case 1 with Case 2 because they are a combination:

\(\frac{6}{7} * \frac{1}{6} = \frac{1}{7}\)

Therefore Frank is correct.

Answer:

0.0000614

Step-by-step explanation:

Since it’s a -5 it’s 5 places back

Hope this helps! ;-)

Answer:

5 is c 6 is b

Step-by-step explanation:

Answer:

5) C 6) B

Step-by-step explanation:

Yw

Answer:

- 4x² + 6xy - y²

Step-by-step explanation:

8x² + 3xy + 4y² - 12x² + 3xy - 5y² ← collect like terms

= (8x² - 12x² ) + (3xy + 3xy) + (4y² - 5y²)

= - 4x² + 6xy - y²

Answer:

8x^2+6xy-5y^2+8y_1^2x^2

Step-by-step explanation:

Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set.

Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order.

Mode: The mode is the number that appears most frequently in a set of numbers.

Hi there! Yes, I can certainly show and explain the methods for calculating Mean, Median, and Mode. These are all measures of central tendency, which are used to describe the center of a data set.

Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set. For example, if you have the numbers 2, 4, 6, 8, and 10, the mean would be (2 + 4 + 6 + 8 + 10) / 5 = 6.

Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. For example, if you have the numbers 2, 4, 6, 8, and 10, the median would be 6. If you have the numbers 2, 4, 6, 8, 10, and 12, the median would be (4 + 6) / 2 = 5.

Mode: The mode is the number that appears most frequently in a set of numbers. If there is more than one number that appears the same number of times, there can be more than one mode. For example, if you have the numbers 2, 4, 6, 8, 10, and 10, the mode would be 10 because it appears twice and the other numbers only appear once.

I hope this helps! Let me know if you have any other questions.

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The values of the expressions for the given set of scores are:

a. εX = 0

b. εx^2 = 50

c. ε(x+3) = 15

To find the value of each expression for the given set of scores, let's calculate them one by one:

Set of scores: X = 6, -1, 0, -3, -2

a. εX (sum of scores):

εX = 6 + (-1) + 0 + (-3) + (-2) = 0

b. εx^2 (sum of squared scores):

εx^2 = 6^2 + (-1)^2 + 0^2 + (-3)^2 + (-2)^2 = 36 + 1 + 0 + 9 + 4 = 50

c. ε(x+3) (sum of scores plus 3):

ε(x+3) = (6+3) + (-1+3) + (0+3) + (-3+3) + (-2+3) = 9 + 2 + 3 + 0 + 1 = 15

Therefore, the values of the expressions are:

a. εX = 0

b. εx^2 = 50

c. ε(x+3) = 15

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The amount of energy the refrigerator uses per day is 3.6 kilowatt-hour (kWh)

The refrigerator energy usage per day in BTU is 12283.704 BTU

The BTU is an acronym for the British Thermal Unit, which is a measure of heat, which is specified in energy units.

The duration the refrigerator fan runs per hour = 30 minutes

The amount of energy the refrigerator uses every hour = 300 watts × 0.5 hour/hour = 150 watts

The amount of energy the refrigerator uses per hour = 150 watt-hour

1 kWh = 3412.14 BTU

Therefore;

The amount of energy in BTU the refrigerator uses per day = 12283.704 BTU

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Answer:it might be 46 if right please mark as brainliest

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

90 + x = 134 (exterior angle)

=> x = 134 - 90 = 44

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

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The forward Fourier Transform formula for a signal is X(jω) = F{x(t)}. The inverse Fourier Transform formula is x(t) = F^(-1){X(jω)}. The two formulas are related by the Fourier Transform property called duality or symmetry.

1. The forward Fourier Transform formula is given by:

  X(jω) = ∫[x(t) * e^(-jωt)] dt

  This formula calculates the complex spectrum X(jω) of a signal x(t) by integrating the product of the signal and a complex exponential function.

2. The inverse Fourier Transform formula is given by:

  x(t) = (1/2π) ∫[X(jω) * e^(jωt)] dω

  This formula reconstructs the original signal x(t) from its complex spectrum X(jω) by integrating the product of the spectrum and a complex exponential function.

  The similarity between these two formulas is known as the Fourier Transform property of duality or symmetry. It states that the Fourier Transform pair (X(jω), x(t)) has a symmetric relationship in the frequency and time domains. The forward transform calculates the spectrum, while the inverse transform recovers the original signal. The duality property indicates that if the spectrum is known, the inverse transform can reconstruct the original signal, and vice versa.

3. To determine the Fourier Transform of the given signal x(t) = [-1, 1, 0, -1], we apply the defining integral:

  X(jω) = ∫[-1 * e^(-jωt1) + 1 * e^(-jωt2) + 0 * e^(-jωt3) - 1 * e^(-jωt4)] dt

  Here, t1, t2, t3, t4 represent the respective time instants for each element of the signal.

  Substituting the time values and performing the integration, we can obtain the Fourier Transform of x(t).

Note: Please note that without specific values for t1, t2, t3, and t4, we cannot provide the numerical result of the Fourier Transform for the given signal. The final answer will depend on these time instants.

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