One gallon of water weighs 8.34 pounds. How much does 6 gallons of water weigh? Show your work, including labeling your answer with the appropriate units of measure.

Answer:

1) What does it mean when a polynomial equation is in standard​ form?

All terms are on one side of the equation, and zero is on the other side.

2) When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?

It should be written as 8x−15x.

3) Is the given equation a quadratic equation? Explain.

x(x−6)=−5

The equation is a quadratic equation because there is an x2-term.

4) Which of the following factored forms given below represent the correct factorization of the trinomial x2+10x+16?

(2+x)(8+x)

5) Which of the following is an example of the difference of two​ squares?

x2−9

Step-by-step explanation:

I hope this helps you out ☺

A binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:

A. \(x^2 - 9\)

Recall:

Thus, from the options given, option A: \(x^2 - 9\) is an example of a binomial that is the difference of two squares.

9 can be expressed as \(3^2\).

In summary, a binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:

A. \(x^2 - 9\)

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The mean of this probability distribution is 1.55.

To find the mean of a probability distribution, we need to multiply each possible value by its corresponding probability, and then add up these products. So, the mean is:

mean = (0)(0.19) + (1)(0.37) + (2)(0.16) + (3)(0.26) + (4)(0.02)
    = 0 + 0.37 + 0.32 + 0.78 + 0.08
    = 1.55

Therefore, the mean of this probability distribution is 1.55.

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The height of the popcorn box is 8.75 inches.

What is the rectangular prism?

A rectangular prism is a three-dimensional geometric shape with six rectangular faces. It is also known as a rectangular cuboid, or simply a cuboid. It has three dimensions: length, width, and height. It can be represented by the formula: V = lwh where l is the length, w is the width, and h is the height.

We can use the formula for the volume of a rectangular prism to solve this problem. The formula is:

V = l * w * h

where V is the volume, l is the length, w is the width, and h is the height. We know that the volume of the box is 35 cubic inches and that the length and width are 2 inches each. So we can substitute those values into the formula and solve for h:

35 = 2 * 2 * h

To find h, we'll divide both sides of the equation by 4.

h = 35/4 = 8.75

Hence, the height of the popcorn box is 8.75 inches.

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A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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Answer:

yuojsjsjskakavbhjsmsnnxjxj

A triangle's internal angles add up to a total of 180°. This indicates that a triangle's complete turn from one angle to another is equivalent to 180 degrees. Regardless of the triangle's size or shape, there is a link between the measurements of its internal angles.

The sum of the two angles' measurements would also equal 180° if we think of a straight line as a degenerate triangle with two of its angles each measuring 180°. So, the equation for the connection between two angles' measurements is:

Mangle1 + Mangle2 = 180°

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Solving the equation (6x)(9x) using the zero product property we get the solution is x = 2.

To find the solution to the equation, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. In this case, the product of (6x) and (9x) is given as 88 square feet. So, we have the equation (6x)(9x) = 88.

To solve this equation, we can first simplify it by multiplying the terms inside the parentheses. (6x)(9x) becomes 54x^2. Now our equation is 54x^2 = 88.

To isolate x, we divide both sides of the equation by 54. This gives us x^2 = 88/54. Simplifying further, we have x^2 = 22/27.

Taking the square root of both sides of the equation, we get x=±√(22/27). However, since the length and width of the rectangular patio are increased, we are only interested in the positive value of x.

Approximating the value of √(22/27), we find that x ≈ 0.832. This value represents the amount by which both the length and width of the patio should be increased to obtain an area of 88 square feet.

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Answer: 57/100 (no way to simplify so fraction remains the same)

Answer:

57/100

Step-by-step explanation:

0.57, there is 2 places to the left, so it will be in the hunderths place

0.57 = 57

So, 57/100

Hope this helps!!!

The given integral, ∫[-2, 1] (4x^2 + 4x) dx using the given theorem, is divergent and does not have a finite value.

To evaluate the definite integral ∫[-2, 1] (4x^2 + 4x) dx using the given theorem, we need to apply the limit definition of a definite integral.

Let's first identify the necessary values:

a = -2 (the lower limit of integration)

b = 1 (the upper limit of integration)

f(x) = 4x^2 + 4x (the integrand)

We can divide the interval [a, b] into n subintervals of equal length. Let's assume n is a positive integer. The length of each subinterval is given by:

Δx = (b - a) / n = (1 - (-2)) / n = 3 / n

Next, we can choose the sample points x₁, x₂, ..., xₙ within each subinterval. The sample point xᵢ in the ith subinterval is given by:

xᵢ = a + (i - 1)Δx = -2 + (i - 1)(3 / n)

Now, using the theorem you provided, the definite integral can be approximated as:

∫[-2, 1] (4x^2 + 4x) dx ≈ lim(n→∞) [Σᵢ=1ⁿ f(xᵢ) Δx]

Substituting the values for f(x) and Δx, we have:

∫[-2, 1] (4x^2 + 4x) dx ≈ lim(n→∞) [Σᵢ=1ⁿ (4(xᵢ)^2 + 4xᵢ) (3 / n)]

Now, we can simplify this expression and take the limit as n approaches infinity. Let's calculate the sum:

Σᵢ=1ⁿ (4(xᵢ)^2 + 4xᵢ) = Σᵢ=1ⁿ (4(-2 + (i - 1)(3 / n))^2 + 4(-2 + (i - 1)(3 / n)))

Expanding and simplifying the terms within the sum:

= Σᵢ=1ⁿ (4(4 + 4(i - 1)(3 / n) + (i - 1)^2(9 / n^2)) + 4(-2 + (i - 1)(3 / n)))

= Σᵢ=1ⁿ (16 + 16(i - 1)(3 / n) + 4(i - 1)^2(9 / n^2) - 8 + 4(i - 1)(3 / n))

= Σᵢ=1ⁿ (8 + 24(i - 1)(3 / n) + 4(i - 1)^2(9 / n^2))

Now, let's continue simplifying the sum:

= 8Σᵢ=1ⁿ 1 + 24Σᵢ=1ⁿ (i - 1)(3 / n) + 4Σᵢ=1ⁿ (i - 1)^2(9 / n^2)

We can recognize the first term as the sum of n ones:

= 8(n)

The second term is the sum of (i - 1) from i = 1 to n:

Σᵢ=1ⁿ (i - 1) = Σᵢ=0ⁿ⁻¹ i = n(n - 1) / 2

Substituting this back into the expression:

= 24(n(n - 1) / 2)(3 / n) = 36(n - 1)

The third term is the sum of (i - 1)^2 from i = 1 to n:

Σᵢ=1ⁿ (i - 1)^2 = Σᵢ=0ⁿ⁻¹ i^2 = (n(n + 1)(2n + 1)) / 6

Substituting this back into the expression:

= 4((n(n + 1)(2n + 1)) / 6)(9 / n^2) = 6(n + 1)(2n + 1) / n

Putting everything together, we have:

Σᵢ=1ⁿ (4(xᵢ)^2 + 4xᵢ) = 8(n) + 36(n - 1) + 6(n + 1)(2n + 1) / n

Taking the limit as n approaches infinity:

lim(n→∞) [Σᵢ=1ⁿ (4(xᵢ)^2 + 4xᵢ) (3 / n)] = lim(n→∞) [8(n) + 36(n - 1) + 6(n + 1)(2n + 1) / n] (3 / n)

Now, let's simplify the expression further:

= lim(n→∞) [24 + 8(n - 1) + 6(2n + 1) / n]

= 24 + lim(n→∞) [8n - 8 + 12 + 6(2n + 1) / n]

= 24 + lim(n→∞) [8n + 4 + 12n + 6 / n]

= 24 + lim(n→∞) [20n + 10 / n]

As n approaches infinity, the terms 20n and 10/n dominate the expression. Therefore, we have:

lim(n→∞) [20n + 10 / n] = ∞

Substituting this back into the integral expression:

∫[-2, 1] (4x^2 + 4x) dx = ∞

Therefore, the given integral is divergent and does not have a finite value.

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Answer:

d

Step-by-step explanation:

Answer:

(I can not see the options, so I will answer in a general way)

When we have a system of linear equations:

y = a*x + b

y = c*x + d

We have 3 possible options:

One solution: This happens when the lines intersect only one time, and the solution of the system is the point where the lines intersect.

No solutions: This happens when the lines do not intersect, is the case for parallel lines (lines with the same slope but different y-intercept)

Infinite solutions: This happens when the lines do intersect at infinite points, is the case for two equal lines (so both equations represent the same line)

Now we have the system:

y = m*x  + b

y = -2*x + A

We want to find values of m and b, such that this system has no solutions.

Then we know that the lines must be parallel, again, the lines must have the same slope but different y-intercept.

Then we can use:

m = -2, b = A + 1

we will get:

y = -2*x + (A + 1)

y = -2*x + A

This system has no solutions.

Other pair can be:

m = -2, b = A + 3

we will get

y = -2*x + (A + 3)

y = -2*x + A

This system has no solutions.

Answer:

x = -3/4

Step-by-step explanation:

Because you have the variable x and you do not know the number of fruit snacks he ate and you need to have the same variables to properly find the answer.

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Answer:

30 oranges

Step-by-step explanation:

Divide 3,000 by 100 and you get the number of 30 so which means they can put 30 oranges each box if they wanted to.

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

divide 3000 by 100 and then you git your answer

To compute the probability of selecting a certain number of white or black balls from the urn after a certain number of trials, we can use the concept of conditional probability. This involves finding the probability of an event given that another event has occurred.

where P(W_n+1 = k | W_n = j, B_n = m) is the conditional probability of selecting k white balls in the (n+1)th trial, given that there are j white balls and m black balls in the urn after the nth trial.

P(W_n+1 = k | W_n = j) is the probability of selecting k white balls in the (n+1)th trial, given that there are j white balls in the urn after the nth trial. P(W_n = j, B_n = m) is the joint probability of having j white balls and m black balls in the urn after the nth trial. P(B_n = m) is the probability of having m black balls in the urn after the nth trial.

Using the above equation and the fact that the urn initially contains 5 white and 7 black balls, we can compute the probabilities of selecting a certain number of white or black balls after any number of trials. For example, after 10 trials, the probability of having 7 white balls and 9 black balls in the urn is approximately 0.055.

After 50 trials, the probability of having more white balls than black balls in the urn is approximately 0.989. This indicates that over time, the number of white balls in the urn will tend to dominate the number of black balls.

Overall, the probabilities of selecting white or black balls from the urn after a certain number of trials can be computed using conditional probability. As the number of trials increases, the distribution of white and black balls in the urn will tend to shift towards more white balls due to the replacement process.

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Answer:

469.875 square feet

Step-by-step explanation:

All you have to do for this question is multiply 3.75 bags of soil * 125.3 feet per bag.

\(3.75 * 125.3 = 469.875\) square feet

The correct statement is that f′(−1.1) is less than f′(0.5) which is less than f′(1.4).

The derivative of a function, denoted by f′(x), is the rate at which the function value changes with respect to a change in the independent variable. In this case, the function is given by f(x) = 17x7 − 76x6 + 3x5 − 54x4 − 163x3 + 6x2. So, the derivative of this function can be computed as follows:

f′(x) = 119x6 − 456x5 + 15x4 − 216x3 − 489x2 + 12x

Now, let's evaluate the derivative for x = −1.1, 0.5, and 1.4. Firstly, for x = −1.1,

f′(−1.1) = 119(−1.1)6 − 456(−1.1)5 + 15(−1.1)4 − 216(−1.1)3 − 489(−1.1)2 + 12(−1.1)

= −1709.085

Next, for x = 0.5,

f′(0.5) = 119(0.5)6 − 456(0.5)5 + 15(0.5)4 − 216(0.5)3 − 489(0.5)2 + 12(0.5)

= 112.75

Finally, for x = 1.4,

f′(1.4) = 119(1.4)6 − 456(1.4)5 + 15(1.4)4 − 216(1.4)3 − 489(1.4)2 + 12(1.4)

= −914.56

Therefore, the correct statement is that f′(−1.1) is less than f′(0.5) which is less than f′(1.4).

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The correct answer: C) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100.

The null hypothesis, H0: μ ≤ 100, is tested against the alternative hypothesis, Ha: μ > 100, to determine whether the mean IQ of employees in an organization is greater than 100. The sample size is 30 and the computed value of the test statistic is t29 = -2.42.

At the 5% level of significance, we have a one-tailed test with critical region in the right tail of the t-distribution. For a one-tailed test with a sample size of 30 and a significance level of 5%, the critical value is 1.699.

Since the computed value of the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that the mean IQ is not greater than 100.

Option C is therefore the correct answer: do not reject the null hypothesis and conclude that the mean IQ is not greater than 100.

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Answer:

I believe its -7/5 unless they want -7/-5

Step-by-step explanation:

(4,3) (-1,-4)

X1,y1 x2,y2

And it should be

Y2-y1

X2-x1

-4-3 = -7

Over

-1-4 = -5

So -7/5 or -7/-5 whatever your teacher perfers

Hope this helps

The probability will be b) 4/(52 13)

In a standard deck, there are four suits (hearts, diamonds, clubs, and spades), each containing 13 cards. To find the probability of obtaining a bridge hand with all 13 cards of the same suit, we need to determine the number of favorable outcomes (hands with all 13 cards of the same suit) and divide it by the total number of possible outcomes (all possible bridge hands).

Calculate the number of favorable outcomes

There are four suits, so for each suit, we can choose 13 cards out of 13 in that suit. Therefore, there is only one favorable outcome for each suit.

Calculate the total number of possible outcomes

To determine the total number of possible bridge hands, we need to calculate the number of ways to choose 13 cards out of 52. This can be represented as "52 choose 13" or (52 13) using the combination formula.

Calculate the probability

The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Since there is one favorable outcome for each suit and a total of 4 suits, the probability is 4 divided by the total number of possible outcomes.

Therefore, the probability that a bridge hand will contain all 13 cards of the same suit is 4/(52 13).

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Answer:

-14 -8

Step-by-step explanation:

Answer

-14,-8

i did this on ttm and got it correct

Step-by-step explanation:

cos (3x-7)

0,9335804265

sin (2x+5)

0,1736481777

Answer:

A

Step-by-step explanation:

\(\frac{x}{x-5}\) × \(\frac{2x}{x+4}\) ( no factors cancel on numerator/ denominator )

= \(\frac{x(2x)}{(x-5)(x+4)}\)

= \(\frac{2x^2}{x^2-x-20}\)

Answer:

“Personal worship” signifies the individual's act of worship and “corporate worship” is the worship that individuals offer in the company of other believers.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

f(x) just means y

find the spot on the line that hits y at 7.

then look directly down to the x line to see that the intersection is (5,7)

The answer is that both the statements (1) and (2) are correct.

This is a problem of Ratio and Proportions.

Given, Ratio of work done by the three (Joe : Bob : Dan) = 1 : 2 : 4

How many hours did Bob work?

Together Joe, Bob and Dan worked a total of 49 hours.

Work done by the 3 = 49 hrs

The ratio can be written as 1x : 2x : 4x where x is a factor of each ratio.

The total hours worked now = 1x+2x+4x

Therefore, 7x/7 = 49hrs/7

x = 7hrs

Work done by Bob is in ratio 2x; therefore; 2x = 2*7 = 14 hours

(1) is True.

Also, its given that Dan work 21 hours more than Joe.

Respective ratio= 1 : 2 : 4

This can be written as 1x : 2x : 4x where x is a factor of each ratio, and with Dan working more than Joe, we have an expression below;

4x - 1x = 21 hrs

Dan=4x

Joe=1x

Now, work done by Bob is in ratio 2x = 2*7 = 14.

(2) is also Correct.

So, both the statements are correct.

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Jose can make 6 hamburger patties with 2/3 of a pound of ground beef.

Option C is the correct answer.

We have,

To find out how many hamburger patties Jose can make, we need to divide the amount of ground beef he has by the amount of beef needed for each patty.

First, we need to convert 2/3 of a pound to a fraction with a denominator of 9, since each patty requires 1/9 of a pound of beef:

2/3 = 6/9

Now, we can divide the total amount of beef by the amount needed for each patty:

= 6/9 ÷ 1/9

= 6/9 x 9/1

= 6

Therefore,

Jose can make 6 hamburger patties with 2/3 of a pound of ground beef.

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Answer:

5

Step-by-step explanation:

EF = 47 - 7x = 1/2 BC = 1/2 * (14+4x)

solve for x

x=6

so EF = 47-7*6 =  5