fully expand the logarithm: log(x^3/z^5)

The true statement will be

1. ''L3 is perpendicular to L2''

What is Parallel lines?

Parallel lines are straight lines that do not intersect at any point.

Given that;

Line L1, L2 and L3 are in the same plane,

L1 is perpendicular to L2, and L3 is parallel to L1.

Now,

Line L1 is perpendicular to L2.

And, L3 is parallel to L1.

Then, Line L3 is perpendicular to line L2

Thus, The true statements will be

1. ''L3 is perpendicular to L2'' and

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The solution is: The starting term is -6

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Standard formula for arithmetic sequence:

an = a0 + d(n-1)

if we use the two terms given, setting a12 as starting term and a45 as the end term an.

170 = 38 + 33d 

170 - 38 = 33d

132 = 33d

132/33 = d

This is the common difference, use it to find the first term.

38 = a0 + (132/33)(12-1)

38 = a0 + (132/33)(11)

38 = a0 + 132/3

38 - 132/3 = a0

38 - 44 = a0

-6 = a0

The starting term is -6

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The dance committee could buy up to 75 helium balloons with their remaining budget of $60, after already spending $65 from their total budget of $125.

To determine the number of helium balloons that the dance committee could buy with their remaining budget, we first need to calculate how much money they have left after already spending $65. Since their total budget is $125, the remaining budget is calculated as $125 - $65 = $60.

Let's let b represent the number of balloons they can buy. The cost per balloon is $0.80, so the inequality representing the situation is 0.80b \<= 60. To solve for b, we divide both sides of the inequality by 0.80, which gives us b \<= 60 / 0.80, or b \<= 75.

Therefore, the dance committee could buy up to 75 helium balloons with their remaining budget, staying within their financial limitations.

Answer:

O.25

Step-by-step explanation:

Trust me on this one the answer was in the comments :/

The probability of a girl having black hair is determined by dividing the number of girls who have black hair by the total number of girls. Without actual numbers from the table, a specific probability cannot be calculated.

To find the probability that a girl has black hair, we have to first know the total number of girls, and then the number of girls who have black hair. Probability is determined by dividing the number of desired outcomes by the total number of outcomes. So in this case, if we let 'G' denote the total number of girls and 'B' be the number of girls with black hair, the formula for the probability would be P(B) = B / G. Without the actual numbers from the table, we cannot calculate the specific probability.

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y=-4/3x+300  i  hope this helps you

The question is about solving simultaneous equations. Two equations can be set up from the statements provided: x + y = 7 (sum of two numbers is 7) and 5x + 4y = 47 (five times the larger number plus four times the smaller number equals 47). After setting up these equations, solve for x and y.

The subject you are asking about falls under the area of Mathematics, specifically simultaneous equations. To solve this question, we need to set up two equations based on the problem's statement and then solve these two equations together.

Given the problem that the sum of two numbers is 7 and five times the larger number plus four times the smaller number is 47, we can set it up as follows:

Subtracting the first equation from the second gives 4x + 3y = 40 so y = (40 - 4x)/3. Substituting y into the first equation gives x = 7 - (40 - 4x)/3. Solve for x to find the larger number, then substitute x into the equation y = 7 - x to find the smaller number.

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The backpack will cost $13.64 during the 38% off sale at Toysrus, calculated by subtracting the discount ($8.36) from the original price ($22).

To calculate the discount amount, we multiply the original price by the discount percentage:

$22 * 0.38 = $8.36

Now, to get the sale price, we subtract the discount amount from the original price:

$22 - $8.36 = $13.64

Therefore, the backpack will cost $13.64 on sale.

Final answer:

To determine the sample size needed, use the formula for sample proportion: n = (z * sqrt(p * q)) / E. Plugging in the given values, the minimum sample size required is 178.

Explanation:

To determine the sample size needed, we can use the formula for sample proportion:

n = (z * sqrt(p * q)) / E

Where:

n is the sample size

z is the z-value corresponding to the desired confidence level (in this case, 80%)

p is the population proportion (0.4)

q is 1 - p

E is the maximum allowable error (0.05)

Plugging in the values, we have:

n = (z * sqrt(p * q)) / E = (0.84 * sqrt(0.4 * (1 - 0.4))) / 0.05 ≈ 177.6

Since we cannot have a fractional number of individuals, we round up to the next whole number. Therefore, we would need a minimum sample size of 178 to be 80% confident that the population proportion is estimated to within 0.05.

The function [tex]\( f(x) \)[/tex] is: [tex]\[ f(x) = 2x^2 + x^3 + 3x^4 + 5x + 4 \][/tex]

Given:

[tex]\[ f''(x) = 4 + 6x + 36x^2 \][/tex]

[tex]\[ f(0) = 2 \][/tex]

[tex]\[ f(1) = 10 \][/tex]

1. Integrate [tex]\( f''(x) \)[/tex] to find [tex]\( f'(x) \)[/tex]:

[tex]\[ f'(x) = \int (4 + 6x + 36x^2) \, dx = 4x + 3x^2 + 12x^3 + C_1 \][/tex]

2. Integrate [tex]\( f'(x) \)[/tex] to find [tex]\( f(x) \)[/tex]:

[tex]\[ f(x) = \int (4x + 3x^2 + 12x^3 + C_1) \, dx = 2x^2 + x^3 + 3x^4 + C_1x + C_2 \][/tex]

3. Use the initial condition [tex]\( f(0) = 2 \)[/tex] to find [tex]\( C_2 \)[/tex]:

[tex]\[ 2x^2 + x^3 + 3x^4 + C_1x + C_2 \text{ at } x=0 \][/tex]

[tex]\[ 2 = C_2 \][/tex]

[tex]\[ C_2 = 2 \][/tex]

4. Use the initial condition [tex]\( f(1) = 10 \)[/tex] to find [tex]\( C_1 \)[/tex]:

[tex]\[ f(1) = 2(1)^2 + (1)^3 + 3(1)^4 + C_1(1) + 2 = 10 \][/tex]

[tex]\[ 2 + 1 + 3 + C_1 + 2 = 10 \][/tex]

[tex]\[ 8 + C_1 = 10 \][/tex]

[tex]\[ C_1 = 2 \][/tex]

Thus, the function [tex]\( f(x) \)[/tex] is:

[tex]\[ f(x) = 2x^2 + x^3 + 3x^4 + 5x + 4 \][/tex]

The complete question is:

Find f(x). f ''(x) = 4 + 6x + 36x2, f(0) = 2, f (1) = 10

Answer:

the answer is sequence (usa test prep)

Step-by-step explanation:

Answer:

2·x^3 + 5·x^2 - 8·x - 20 = 0

You see that the term will be 0 for x = 2

(2·x^3 + 5·x^2 - 8·x - 20) / (x - 2) = 2·x^2 + 9·x + 10 = 0

You can use the abc-formula to solve the quadratic equation.

x = -2.5 ∨ x = -2

So the factored form will be

2·x^3 + 5·x^2 - 8·x - 20 = 2·(x - 2)·(x + 2)·(x + 2.5)

Answer:

2·x^3 + 5·x^2 - 8·x - 20 = 0

You see that the term will be 0 for x = 2

(2·x^3 + 5·x^2 - 8·x - 20) / (x - 2) = 2·x^2 + 9·x + 10 = 0

You can use the abc-formula to solve the quadratic equation.

x = -2.5 ∨ x = -2

So the factored form will be

2·x^3 + 5·x^2 - 8·x - 20 = 2·(x - 2)·(x + 2)·(x + 2.5)

The correct answer is: $20

Explanation:

As we are interested in finding the cost for a barrel of gasoline, we need to read the percentage of gasoline from the pie-chart first—which is 34%.

Now number of barrels containing gasoline = 34% of 60 million barrels = [tex] \frac{34}{100} * 60 = 20.4 [/tex] million barrels

For all the barrels, the total income is $408 million; therefore, in order to find the per-barrel cost, we need to divide $408 by 20.4:

[tex] \frac{408}{20.4} = \$20 [/tex]

Hence the correct answer is $20.