A student said that x = 4 was not a solution to the question 3(x -6) = -8
Here is their work:
3(x -6) = -8
3 (4 -6) = -8
12 -6 = -8
6≠ -8
so x = 4 is not a solution

Did the student substitute x=4 correctly? How do you know?

Did the student simplify with Order of Operations correctly? How do you know?

If you try the problem, what do you get when you substitute x=4 into the equation?

Answer:

Let us begin by simplifying the expression (-18x^3 + 17 +6) / (3x + 2):

- Combine the constants (17+6) to get 23.

- We now have (-18x^3 + 23) / (3x+2).

- Factor out -3 from the numerator to get -3(6x^3 -23)/ (3x+2).

- We can now cancel out the (3x+2) in both the numerator and denominator to get:

-3(6x^2 - 4x + 3)

Therefore, the answer is (C) -6x^2 + 4x - 3.

In this situation, Allison's insurance company will pay a total of $400,000.

First, we need to add up the total amount awarded to the people injured in the accident. This is $40,000 x 4 + $80,000 x 2 + $160,000 x 1 = $400,000.

Next, we need to look at Allison's insurance policy. She has 50/250 bodily injury insurance, which means that the insurance company will pay up to $50,000 per person and up to $250,000 per accident.

Since the total amount awarded is $400,000, the insurance company will only pay the maximum amount allowed per accident, which is $250,000.

Therefore, the insurance company will pay $250,000 and Allison will be responsible for the remaining $150,000.

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Answer:

$1,568.00

Step-by-step explanation:

I=700 x 0.28 x 8 =1568

The simple interest accumulated on a principle of $700 at a rate of 0.28% per year for 8 years is $1,568.00

The slope of a logarithmic graph depends on the type of logarithm used.

For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.

For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.

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Answer:

Did u find the answer for this

Step-by-step explanation:

The statement:

         a survey of 800 randomly selected adults in a certain country found that 82% believed that protecting the rights of those with unpopular views is a very important component of a strong democracy.

The statement is true

Explanation:

A survey of 800 randomly selected adults in a certain country found that 82% believed that protecting the rights of those with unpopular views is a very important component of a strong democracy.

In a strong democracy, people –citizens – govern themselves to the greatest extent possible rather than delegate their power and responsibility to representatives acting in their names. Strong democracy does not mean politics as a way of life, as an all-consuming job, game, and avocation, as it is for so many professional politicians. But it does mean politics (citizenship) as a way of living: an expected element of one’s life. It is a prominent and natural role, such as that of “parent” or “neighbor”

Therefore, the statement is true.

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Given:

Layla buys 3.6 pounds of dried fruit.

Cost of dried fruit is $4.55 per pound.

Cost per pound is multiplied to the number of pounds we buy.

Answer:

5x+35

Step-by-step explanation:

the parentheses means that you can multiply the outer number (5) with the inner numbers/variables

5*x=5x

5*7=35

5x+35

If the farmer plotted a straight line graph of how many goats he had left over time, the slope of the line would be -14.

To find the slope of the line representing the number of goats the farmer has over time, we need to use the formula:

Where y2 and y1 are the number of goats the farmer has at the end of two different months, and x2 and x1 are the number of months that have passed since he started selling the goats.

In this case:

So the slope of the line is:

The slope of the line is -14, which means that the number of goats the farmer has decreases by 14 goats per month.

It's important to note that when the value of the slope is negative, it means that the line is going down; this means that the farmer is selling goats at a constant rate.

This question is incomplete and should be written as:

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the x-coordinates of all local minima of the function g(x) are x = -√2.45.

To find the x-coordinates of all local minima of the function g(x), we need to find all the critical points and then determine which of them are local minima.

The critical points of g(x) are the values of x where the derivative of g(x) is equal to zero or undefined. To find the derivative, we can use the power rule and the chain rule:

g'(x) = 11x^10 - 27x^8

Setting g'(x) = 0 to find the values of x where the derivative is equal to zero, we get:

11x^10 - 27x^8 = 0

11x^8(x^2 - 2.45) = 0

This equation has two solutions: x = 0 and x = ±√2.45.

To determine which of these critical points are local minima, we need to look at the sign of the second derivative of g(x) at each critical point. The second derivative is:

g''(x) = 110x^9 - 216x^7

For x = 0, we have:

g''(0) = 0 - 0 = 0

Therefore, we cannot determine whether x = 0 is a local minimum using the second derivative test.

For x = √2.45, we have:

g''(√2.45) = 110(√2.45)^9 - 216(√2.45)^7 ≈ -20.76

Since g''(√2.45) is negative, x = √2.45 is a local maximum.

For x = -√2.45, we have:

g''(-√2.45) = 110(-√2.45)^9 - 216(-√2.45)^7 ≈ 20.76

Since g''(-√2.45) is positive, x = -√2.45 is a local minimum.

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At a gas station, suppose that 54% of the customers purchase premium grade gas. assume that these customers decide independently. The probability that none of the next three customers purchase premium gas is 0.834

The likelihood that at least one of the following three customers will purchase premium gas is equal to the likelihood that none of the following three customers will do so. = 1 - (1-P(A))³ = 0.834

The likelihood that a customer would buy premium quality is 45%.

P(A) = 0.45 in this case.

P(B) = 0.55 is the likelihood that the consumer would buy a different grade.

Consequently, the likelihood that at least one of the following three clients will buy premium gas is

P(k=0) = (1 - P)ⁿ,

where the likelihood that at least one client will buy premium gas is complemented by the likelihood that the subsequent three customers will buy a different gas brand.

(1 - P(A))×(1 - P(A))×(1 - P(A)) = P(B)×P(B)×P(B) = 0.55³

and the complement is 1 - 0.55³  = 0.834

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Answer:

Step-by-step explanation:

4 hours and 30 minutes

Answer:

7.03 ft/s

Step-by-step explanation:

To obtain speed using the model :

Speed = sqrt(gL)

L = Length of leg, g = acceleration due to gravity

Length of leg of a giraffe = 6.03

g = 9.8 m/s or 32 ft/s²

Speed of giraffe in ft/s = sqrt(32 * 6.03) = 13.89 ft/ s

Speed of coyote ; L = 0.46 m

L in feets = 0.46 * 3.23 = 1.4858 feets

s = sqrt(1.4858 * 32) = 6.895 ft/s = 6.86 ft/s

Difference in speed :

13.89 - 6.86 = 7.03 ft/s

Giraffe has 7.03ft/s more speed Than a coyote

Answer:

Step-by-step explanation:

Let the total points be x

Mark earned 90% of x which is 108 points:

Total points were 120

The remaining sides are 11/2 and 11√3/4.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

In a 30-60-90 triangle,

The length of the side opposite the 30-degree angle = 1/2 x the length of the hypotenuse.

The length of the side opposite the 60-degree angle = √3/2 x the length of the hypotenuse.

The length of the hypotenuse = 2 x the length of the side opposite the 30-degree angle.

Now,

The length of the hypotenuse = 2x.

So,

2x = 11

x = 11/2

Now,

The lengths of the other two sides are:

= √3/2 x 11/2

= 11√3/4

And,

= 11/2

Thus,

The remaining sides are 11/2 and 11√3/4.

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Answer:

5x² - x + 3 = 0

Step-by-step explanation:

The standard form of a quadratic equation is

ax² + bx + c = 0 ( a ≠ 0 )

Given

5x² + 3 = x ( subtract x from both sides )

5x² - x + 3 = 0 ← in standard form

Answer:

Rounding to the nearest minute, the time it will take for Amanda and Hannah to be 16 kilometers apart on the river is 53 minutes.

Step-by-step explanation:

Let's call the time it takes for Amanda and Hannah to be 16 kilometers apart "t" (in hours). During this time, Amanda will have kayaked down the river a distance of 9t kilometers, and Hannah will have jet-skied up the river a distance of 42t kilometers. So, their total separation will be 9t + 42t = 51t kilometers. Setting this equal to 16, we get:

51t = 16

t = 16 / 51

To convert this to hours and minutes, we can multiply by 60 to convert the fraction to minutes:

t = 16 / 51 * 60 = approximately 53.33 minutes

The least squares estimate of the y-intercept is approximately 42.6. Option D is the correct answer.

To find the least squares estimate of the y-intercept, we need to perform linear regression on the given data points. The linear regression model is represented by the equation:

y = mx + b

where:

y is the dependent variable (in this case, "y")

x is the independent variable (in this case, "x")

m is the slope of the line

b is the y-intercept

To find the least squares estimate, we need to calculate the values of m and b that minimize the sum of squared differences between the observed y-values and the predicted y-values.

First, let's calculate the mean values of x and y:

mean(x) = (2 +5 + 4 + 3 + 6) / 5 = 20 / 5 = 4

mean(y) = (50 + 70 + 75 + 80 + 94) / 5 = 369 / 5 = 73.8

Next, we need to calculate the deviations from the means for each data point:

x deviations: 2 - 4 = -2, 5 - 4 = 1, 4 - 4 = 0, 3 - 4 = -1, 6 - 4 = 2

y deviations: 50 - 73.8 = -23.8, 70 - 73.8 = -3.8, 75 - 73.8 = 1.2, 80 - 73.8 = 6.2, 94 - 73.8 = 20.2

Now, we can calculate the sum of the products of the deviations:

Σ(x × y) = (-2 × -23.8) + (1 × -3.8) + (0 × 1.2) + (-1 × 6.2) + (2 × 20.2) = 47.6 - 3.8 + 0 - 6.2 + 40.4 = 78

Σ(x²) = (-2)² + 1² + 0² + (-1)² + 2² = 4 + 1 + 0 + 1 + 4 = 10

Finally, we can calculate the least squares estimate of the y-intercept (b):

b = mean(y) - m × mean(x)

To find m, we can use the formula:

m = Σ(x × y) / Σ(x²)

Substituting the values:

m = 78 / 10 = 7.8

Now we can calculate b:

b = 73.8 - 7.8 × 4 = 73.8 - 31.2 = 42.6

Therefore, the least squares estimate of the y-intercept is 42.6.

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Answer:

x = 30

Step-by-step explanation:

- 2x + 10 + 4x = 70, that is

2x + 10 = 70 ( subtract 10 from both sides )

2x = 60 ( divide both sides by 2 )

x = 30

Answer:

WAT DO U MEAN 30 POINTS UR ONLY GIVING 5

Step-by-step explanation:

ITS LITTERALLY RIGHT NEXT TO IT

The volume of the other solid (Solid B) is 3456 cubic feet.

Solid A has edges of 4 feet, and its volume is given as 16 cubic feet. Solid B has edges of 24 feet.

Since the solids are similar, they have the same shape, and their corresponding lengths are proportional. To find the ratio of their corresponding lengths, we can divide the length of an edge of Solid B by the length of an edge of Solid A:

Ratio = (length of edge of Solid B) / (length of edge of Solid A)

Ratio = 24 feet / 4 feet

Ratio = 6

Now that we have the ratio of their corresponding lengths, we can find the ratio of their volumes. The ratio of the volumes of similar solids is the cube of the ratio of their corresponding lengths:

Volume ratio = (length ratio)³

Volume ratio = 6³

Volume ratio = 216

Now we can use the volume ratio to find the volume of Solid B:

Volume of Solid B = (Volume of Solid A) × (Volume ratio)

Volume of Solid B = 16 ft³ × 216

Volume of Solid B = 3456 ft³

So, the volume of the other solid (Solid B) is 3456 cubic feet.

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The appropriate statistical technique to compare money spent at the store between two groups in a marketing research study is the independent-samples t-test.

The independent-samples t-test is used to compare the means of two independent groups. In this case, the groups are the ones who received the coupon and the ones who did not, and they are independent because the participants were randomly assigned to each group.

The null hypothesis for the independent-samples t-test is that there is no difference between the means of the two groups. The alternative hypothesis is that there is a significant difference between the means of the two groups.

By conducting an independent-samples t-test on the data, the researcher can determine whether the difference in money spent at the store between the two groups is statistically significant or simply due to chance. If the p-value is less than the significance level (usually 0.05), the researcher can reject the null hypothesis and conclude that there is a significant difference between the two groups in terms of the money spent at the store.

Therefore, the independent-samples t-test is an appropriate statistical technique to compare the means of two independent groups and test for significant differences between them.

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You can replace the symbol x with the given value in the given equation and then calculate the value of y. Know that coefficients are in multiplication with the variables.

The value of y in the given equation when x = 0.3 is given by

Option C: 9.25

If you have got a variable's value in the given expression, you can replace that variable with the value that you got.

Suppose that the given expression is \(3x + 4\) and you know that x = 5, then you can put that value in place of x as:
\(3x + 4|_{x=5} \: \: = \: \:3 \times (5) + 4 = 15 + 4 = 20\)

It is because \(3x\) means \(3 \times x\) and is written in short as \(3x\)

Putting the value x = 0.3 in the given equation, we get;

\(5x + 2y = 20\\5 \times 0.3 + 2y = 20\\1.5 + 2y = 20\\\\\text{Subtracting 1.5 from both sides}\\\\1.5 - 1.5 + 2y = 20 - 1.5\\2y = 18.5\\\\\text{Dividing both sides by 2}\\\\\dfrac{2y}{2} = \dfrac{18.5}{2}\\\\\dfrac{2 \times y}{2} = y = 9.25\)

Thus,

The value of y in the given equation when x = 0.3 is given by

Option C: 9.25

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Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

3*15 = 45

45-9 = 36, so he has enough money

9514 1404 393

Answer:

Step-by-step explanation:

The function puts a minus sign on 3 times the magnitude of the input.

1. y = -|3×17| = -51

2. y = -|3×10| = -30

3. y = -|3×20| = -60

4. -6 = -|3x|

  2 = |x| . . . . divide by -3

  x = ±2 . . . . two possibilities

Answer:

Step-by-step explanation:

One that has the next least in common with the rest.

Answer:

4/11 is already simplified as much as it can be in fraction form. as a percent its 36.3636%

Step-by-step explanation:

The simplified expression of 4/11 is 4/11

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

4/11

This means that we divide 4 by 11

So, we have the following representation

4/11

In the above, we have

The numerator 4 is less than the denominator 11

This means that the expression is already simplified

Hence, the simplified expression is 4/11

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To start with, we know that the school allots £1500 for the trip to the theater. Also, we know that the theater tickets have a regular cost of £35, and there's a 1/5 discount. So the actual cost of the ticket is: £35 - (1/5 * £35) = £28.So, the amount of money left for train tickets and other expenses is:£1500 - (3 * £28) = £1416.Now,

we know that a train ticket for the day will cost £12. And since there are 3 teachers, we will deduct £36 from the amount left for students' train tickets and other expenses. Hence, the amount left for students will be: £1416 - £36 = £1380.To find the maximum number of students, we need to find out how many students can go to the theater with the amount we have. We can do this by dividing the amount by the total cost of taking one student to the theater (which includes the theater ticket and the train ticket):£1380 / (£28 + £12) = £1380 / £40 = 34.5.So, the maximum number of students who can go to the theater is 34 (since we can't have half a student!). Therefore, 34 students and 3 teachers can go on the trip. In total, there will be 37 people on the trip.

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