150 miles 3/4 tank of gas 3 hours how far can you drive on one tank of gas?

The equation of the line of best fit is given as y = -11.2X + 1585

The slope indicates that the number of student would decrease by 11.2

To the nearest thousandth, The value of R is -0.9842. This shows that there is a strong negative correlation.

The x and the y values would be inputted . The output is as shown on the image. Then the negative value of the slope tells us that there is a decrease in the number of students

From the attached solution, the graph shows the slope is given as  y = -11.2X + 1585

The negative value shows that there is a decrease in the number of students. That is shown in the slope of -11.2

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Answer:

2 teaspoons

Step-by-step explanation:

24 tsp/12 cups = x tsp /1 cup

Cross multiplying, we have:

12x = 24

x = 2

The solution is 2 teaspoons of cocoa

Number of teaspoons of cocoa is given by the equation A = 2 teaspoons

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of teaspoons of cocoa be represented as A

Now , the equation will be

A batch of hot chocolate is made with 24 teaspoons of cocoa and 12 cups of milk

So , for 12 cups of milk = 24 teaspoons of cocoa is required

And , for 1 cup of milk A = 24 teaspoons of cocoa is required / 12

Substituting the values in the equation , we get

Number of teaspoons of cocoa A = 24 teaspoons / 12

Number of teaspoons of cocoa A = 2 teaspoons

Therefore , the value of A is 2 teaspoons

Hence , the number of teaspoons is 2

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Answer:

Answer(s):

1x4

2+2

2x2

Step-by-step explanation:

Hope this helps!

Answer:

≈20.56

Step-by-step explanation:

Since the total length of a side is 6 and the small bit is 2, the radius of the curve is 2. The curves are all 90° meaning they add up to one full circle, so you could just find the circumference of the circle with a radius of 2 plus the lengths between the curves.

Circumference = 2π(2) ≈ 12.57

Perimeter = 12.57 + 4(2) = 20.56

The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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The solution to the integral is (1/4) ln|x^4 - 5| + C, where C is the constant of integration.

To evaluate the integral ∫ (x³)/(x⁴ - 5) dx, we can use the substitution u = x⁴ - 5.

This will allow us to simplify the integral and express it in terms of u instead of x.

To make the substitution, we first find the derivative of u with respect to x:

du/dx = 4x^3

We can solve for dx in terms of du by dividing both sides by 4x³:

dx = du/(4x³)

Now we can substitute x⁴ - 5 for u and dx/(4x³) for dx in the integral:

∫ (x³)/(x⁴ - 5) dx = ∫ (1/(4(u + 5))) du

We can simplify this expression by factoring out the constant 1/4 and using the substitution v = u + 5:

∫ (x³)/(x⁴ - 5) dx = (1/4) ∫ 1/(v) dv

The integral of 1/v is ln|v|, so we can substitute back in for v and obtain:

(1/4) ln|x⁴ - 5| + C

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The price that maximizes revenue is p = 120.

The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.

Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:

R = p × q

R = p × (-5p + 1200)

To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.

dR/dp = -10p + 1200 = 0

Solving this equation for p:

-10p + 1200 = 0

-10p = -1200

p = -1200 / -10

p = 120

Therefore, the price that maximizes revenue is p = 120.

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Answer:

0 and -2

Step-by-step explanation:

\(5x^2+10x=0\\5x(x+2)=0\\\\Then\\5x=0\\\\x=\frac{0}{5}==>x_{1}=0 \\x+2=0==> x_{2}=-2\)

Answer:

x=5/3

Step-by-step explanation:

10-7=3x+2x

3=5x

x=5/3

Answer:

3/5

Step-by-step explanation:

rerange terms

10−2x=3x+7

−2+10=3+7

subtrace 10 on each side

−2+10−10=3+7−10

then simplify

The correct expression that represents the distance between the friends is 4 steps.

To calculate this

Joy walked 12 steps forward and Shaunte walked 8 steps backward. To find the distance between the two friends, we can add the number of steps they each took, so the expression would be:

12 + (-8) = 12 - 8 = 4

So the correct expression that represents the distance between the friends is 4 steps.

Note that the negative sign in front of Shaunte's steps indicates that she walked backward, and the positive sign in front of Joy's steps indicates that she walked forwards.

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Answer:

$ 4,425.69

Step-by-step explanation:

A = $ 4,425.69

A = P + I where

P (principal) = $ 4,253.00

I (interest) = $ 172.69

Answer:

There are nine female students, and twenty-two male students.

Step-by-step explanation:

We're told that the total number of male and female students is 31:

\(m + f = 31\)

We're also told that there are 13 more male than female students:

\(m = f + 13\)

So we can substitute the latter piece of information into the former, which will tell us how many female students there are:

\(m + f = 31\\(f + 13) + f = 31\\f + f = 31 - 13\\2f = 18\\f = 9\)

So there are nine female students.  We can now take either of the initial tow equations, and plug the resulting f value to find m:

\(m = f + 31\\m + 9 = 31\\m = 31 - 9\\m = 22\)

So there are nine female students, and twenty-two male students.

Answer:

Compound.

Step-by-step explanation:

A compound sentence consists of two independent clauses and one coordinating conjunction to join the two clauses together. "She fell to the floor" is the first independent clause and "She cried all afternoon" is the second independent clause while "and" is the coordinating conjunction.

she fell to the floor and cried all afternoon is a compound sentence.

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Using the graph of the system of equations we can see that the x-coordinates of the solutions are x = 0 and x = 2.

Here we have the graph of a system of equations, we can see that one is a line and the other is a quadratic equation.

To find the solutions on a graph, we need to find the points where the lines intercept. Here we can see that there are two points where the graphs intercept, these points are:

(0, 1) and (2, 5)

Then the x-coordinate of the solutions are x = 0 and x = 2.

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The correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.

The correct methods for "thinking out computation" (mental arithmetic) are a, b, and c.

a) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15. This method is correct because it breaks down the calculation into smaller, easier-to-manage parts.

b) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21. This method is also correct because it simplifies the calculation by subtracting 10 first, and then subtracting the remaining 7.

c) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997. This method is correct because it simplifies the calculation by multiplying 1000 by 3 first, and then subtracting 1 three to get the correct answer.

d) 150 ÷ 3 Think: what equals 150 x 3, that's 450. This method is incorrect because it is actually doing the opposite operation (multiplication instead of division) and therefore does not result in the correct answer. The correct method would be to think about how many times 3 can go into 150, which is 50.

In conclusion, the correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.

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The correct methods for "thinking out computation" (mental arithmetic) are:
A) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15
B) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21
C) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997
D) 150 ÷ 3 Think: what equals 150 x 3, that's 450

All four methods of "thinking out computation" provided in the question are correct and valid.

Method (a) is using the "doubles" method, which is a common mental arithmetic technique. By recognizing that 7+7 is 14, it is easy to add 1 more to get 15.

Method (b) is using the "subtracting by tens" method. By recognizing that 38 minus 10 is 28, it is easy to subtract 7 more to get 21.

Method (c) is using the distributive property of multiplication. By recognizing that 999 is very close to 1000, we can multiply 3 by 1000 and then subtract 3 to get 2997.

Method (d) is using the inverse operation of multiplication. By recognizing that 150 is a multiple of 3, we can think of 150 as 3 times some unknown number, and then determine that number by dividing 150 by 3. The answer is 50, which is the same as thinking of what equals 150 times 3 (450).

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Answer:

x=6

Step-by-step explanation:

Answer:

inversely proportional

Step-by-step explanation:

The personal banker given lending arrangement, the APR for your cousin's buddies who borrowed $20 and repaid $40 at the end of the month would be 120%

The annual percentage rate (APR) for your cousin's lending arrangement,  to make a few assumptions. That each lending transaction occurs on the first day of the month and is repaid on the last day of the same month. Based on these assumptions, calculate the effective APR as follows:

Calculate the interest charged for a $20 loan over one month:

Interest = $40 (repaid amount) - $20 (loaned amount) = $20

Divide the interest by the loan amount and multiply by 100 to get the monthly interest rate:

Monthly Interest Rate = (Interest / Loan Amount) ×100 = ($20 / $20) ×100 = 100%

Multiply the monthly interest rate by 12 to obtain the annual interest rate:

APR = Monthly Interest Rate ×12 = 100% ×12 = 120%

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a). We have proved all the given conditions.

b). It is true that condition 3 holds for all regular languages L1 and L2.

(a) Regular languages L1 and L2 can be suggested as follows:

Let \(L_1={0^{(n+1)} | n\geq 0}\)

and

\(L_2={1^{(n+1)} | n\geq 0}\)

We have to prove three conditions:1. L1 ⊈ L2:

The given languages L1 and L2 both are regular but L1 does not contain any string that starts with 1.

Therefore, L1 and L2 are distinct.2. L2  L1:

The given languages L1 and L2 both are regular but L2 does not contain any string that starts with 0.

Therefore, L2 and L1 are distinct.3. (L1 ∪ L2)* = L1* ∪ L2*:

For proving this condition, we need to prove two things:

First, we need to prove that (L1 ∪ L2)* ⊆ L1* ∪ L2*.

It is clear that every string in L1* or L2* belongs to (L1 ∪ L2)*.

Thus, we have L1* ⊆ (L1 ∪ L2)* and L2* ⊆ (L1 ∪ L2)*.

Therefore, L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Second, we need to prove that L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Every string that belongs to L1* or L2* also belongs to (L1 ∪ L2)*.

Thus, we have L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Therefore, (L1 ∪ L2)* = L1* ∪ L2*.

Therefore, we have proved all the given conditions.

(b)It is true that condition 3 holds for all regular languages L1 and L2.

This can be proved by using the fact that the union of regular languages is also a regular language and the Kleene star of a regular language is also a regular language.

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Answer:  Choice B.

No, because one x-value corresponds to two different y-values.

Specifically we have x = 3 map to both y = 5 and y = 6 at the same time. A function is only possible when each x value goes to one y value only.

A handy trick is to look at the list of x coordinates. If any x coordinates repeat themselves, then we likely won't have a function.

The y values can repeat, but the function won't be one-to-one.

Use of the vertical line test is a visual way to check if we have a function or not.

Answer:

1 3, and 4 ones are correct

Step-by-step explanation:

jk

To translate the given sentence into an inequality, we need to identify the key words and their mathematical symbols. The words "sum" and "is at most" indicate addition and less than or equal to, respectively.

Therefore, the inequality can be written as 9 + X ≤ 15. This means that the sum of nine and any number X cannot exceed 15, or in other words, X must be less than or equal to 6. To solve for X, we can subtract 9 from both sides of the inequality, giving us X ≤ 6. Therefore, any number less than or equal to 6 satisfies the given condition. This is an example of how to translate a sentence into an inequality and use it to find a solution for the variable.

To translate the given sentence into an inequality, we'll use the key terms provided. The sum of "nine" and "X" can be represented as 9 + X. The phrase "at most" signifies that the total is less than or equal to a certain value, in this case, 15. Now we can "translate" the sentence into an inequality:

9 + X ≤ 15

This inequality represents that the sum of nine and X is less than or equal to 15. To find the possible values of X, you can subtract 9 from both sides of the inequality:

X ≤ 15 - 9
X ≤ 6

So, X can be any value less than or equal to 6.

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Answer:

7 no =option B

8 no =option

9 no=option D

10 no=option c

Step-by-step explanation:

Answer:

6.7

Step-by-step explanation:

let n = the number

3n + 9 = 29

3n = 20

n = 20/3 or 6.67

The ratio of flour to butter in this scenario is 3:2.

(a)  a random variable coming from a normal distribution and p ( x < 5.3 ) = 0.79 , then p ( x > 5.3 ) = 0.21 .

(B) the posterior distribution will likely place more weight on values of 0 closer to 0.75, as the observed sequence is more likely to come from a biased coin than a fair coin.

In this problem, we are dealing with a population of novelty coins, where 80% of the coins are fair (with a 50% chance of landing heads) and the remaining 20% of the coins have a 75% chance of landing heads. We need to determine the prior distribution for the parameter 0, which represents the probability of heads for a randomly selected coin. The prior distribution can be expressed as a weighted combination of   a random variable coming from a normal distribution and p ( x < 5.3 ) = 0.79 , then p ( x > 5.3 ) = 0.21 .

Given the sequence of tosses HHHTH from a randomly selected coin, we can use this data to calculate the posterior distribution of 0. The posterior distribution represents the updated probabilities for the parameter 0 after taking into account the observed data. In this case, the posterior distribution will be a combination of the prior distribution and the likelihood of observing the given sequence of tosses. By applying Bayesian inference, we can calculate the updated probabilities for 0 based on the data and the prior distribution.

To summarize, the prior distribution for the parameter 0 is a weighted combination of the probabilities of heads for fair coins and biased coins in the population. The posterior distribution is obtained by updating the prior distribution with the observed data, reflecting the updated probabilities for 0 based on the sequence of tosses HHHTH.

Now, let's explain the process of determining the posterior distribution of 0. We start with the prior distribution, which is a combination of 0.8 for fair coins and 0.75 for biased coins. After observing the sequence HHHTH, we calculate the likelihood of obtaining this sequence for each possible value of 0, considering the probabilities associated with fair and biased coins. For example, for a fair coin (0.5), the likelihood of observing HHHTH is (0.5)^4 * (1-0.5) = 0.03125, while for a biased coin (0.75), the likelihood is (0.75)^4 * (1-0.75) = 0.0703125.

To obtain the posterior distribution, we multiply the prior distribution by the corresponding likelihoods for each value of 0 and normalize the result to ensure it sums to 1. The normalized values represent the updated probabilities for 0, given the observed data. In this case, the posterior distribution will likely place more weight on values of 0 closer to 0.75, as the observed sequence is more likely to come from a biased coin than a fair coin.

In conclusion, the process of determining the posterior distribution involves updating the prior distribution with the observed data, considering the likelihood of obtaining the sequence of tosses. By applying Bayesian inference, we can calculate the updated probabilities for the parameter 0, reflecting our updated beliefs about the probability of heads for the randomly selected coin.

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The predicted college GPA for a student with a high school GPA of 3.3 and an ACT score of 31 is approximately 2.747 on a four-point scale.

To compare the models based on goodness of fit, we need to look at the adjusted R-squared values. The adjusted R-squared adjusts for the number of predictors in the model and provides a measure of how well the model fits the data while considering the degrees of freedom.

Comparing the models:

Model A: Adjusted R-squared = 0.74

Model B: Adjusted R-squared = 0.73

Model C: Adjusted R-squared = 0.72

Model D: Adjusted R-squared = 0.75

Based on the adjusted R-squared values, we can see that Model D has the highest value (0.75), indicating the best goodness of fit among the four models. Model A has the second-highest value (0.74), followed by Model B (0.73), and Model C (0.72).

Therefore, the correct answer is:

d. D>A>B>C

Now, let's move on to the second part of your question regarding predicting the college GPA of a student.

The estimated model is:

colGPA = β1 + β2 hsGPA + β3 ACT + ω1

Given:

β1 = 0.6

β2 = 0.35

β3 = 0.032

hsGPA = 3.3

ACT = 31

To predict the college GPA of a student, we substitute the values into the equation:

colGPA = 0.6 + (0.35 * 3.3) + (0.032 * 31)

= 0.6 + 1.155 + 0.992

= 2.747

Therefore, the predicted college GPA for a student with a high school GPA of 3.3 and an ACT score of 31 is approximately 2.747 on a four-point scale.

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Connection between normal probabilities and empirical rule links to an external site probability is 0.95 probability is 0.02.

The parts from a supplier in an average  have a mean value  of 31.8 inches and a standard deviation value  of 2.4 inches. Probability is 0.02, which is inconsistent with the.

Probability is basically the chances of something happening . The theoretical probability is the form of probability that is  based on the reasoning behind probability. For example, if a coin is tossed than the theoretical probability of the chance or outcome of getting a head will be ½.

Probability is the branch of mathematics that basically deal for outcome of something or the chances of getting the favorable outcome four main types of probability exist: classical, empirical, subjective and axiomatic.

Probabilities always range between 0 and 1. The formula to find the  probability can be expressed as: Probability =Favorable number of Outcomes / Total Number of Outcomes. or. P(A) = f / N.

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