Are the following statements true or false? Opposites are the same distance from zero on the number line in the opposite directions. Absolute value is the number's distance from zero.

Answer:

c

Step-by-step explanation:

9514 1404 393

Answer:

  -7

Step-by-step explanation:

It is helpful to recognize 128 = 2^7. Then you know ...

  \(\log_2\dfrac{1}{128}=\log_2{2^{-7}} =\boxed{-7}\)

__

If you don't know that, you can use the change of base formula:

  \(\log_2{\dfrac{1}{128}}=\dfrac{\log{\dfrac{1}{128}}}{\log{2}}=\dfrac{-2.1072}{0.30103}=\boxed{-7}\)

The dimensions of the deck will be 18 feet by 21 feet.

Let's denote the width of the deck as x feet. According to the problem, the length will be 3 feet greater than the width, so the length can be expressed as (x + 3) feet.

The perimeter of a rectangle is given by the formula: P = 2 * (length + width).

For the given problem, the perimeter is 78 feet, so we can set up the equation:

2 * ((x + 3) + x) = 78

Now, let's solve this equation to find the value of x, which represents the width of the deck.

2 * (2x + 3) = 78

4x + 6 = 78

4x = 78 - 6

4x = 72

x = 72 / 4

x = 18

So, the width of the deck is 18 feet. To find the length, we can substitute this value back into the expression for the length:

Length = x + 3 = 18 + 3 = 21 feet.

Therefore, the dimensions of the deck will be 18 feet by 21 feet.

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Answer:

FG

Step-by-step explanation:

Answer:

fg

Step-by-step explanation:

Answer:

30.4%

1000 at £1.10

1000 x 1.10 = £1100

35% of 1000 is given away

1000 - 35% = 1000 - 350 = 650 left

35% of £1100 = £385, subtract to get £715 pounds worth of pins left

650 are left, with 385 pounds lost

60% of 650 = 390 pins sold at £3 each

40% of 650 = 260 sold at £5 for 2

3 x 390 = £1170 made from the first lot

260/2 = 130 x 5 = £650 made from the second lot

£1170 + £650 = £1820 from sales

Sales - cost to make - losses (giveaways) = profit value

1820 - 1100 - 385 = 335 pounds of profit

To find the gross profit margin, we take the profit, and find what percentage of the production cost it is.

335 is about 30.45% of 1100

30.45%, which is 30.4% to 1 decimal place.

The user is not responsible for any errors and all care should be taken to validate answer by self before submission.

Answer:

x³ - 4x² + 6x - 24

Step-by-step explanation:

Given

(x² + 6)(x - 4)

Each term in the second factor is multiplied by each term in the first factor, that is

x²(x - 4) + 6(x - 4) ← distribute both parenthesis

= x³ - 4x² + 6x - 24

The dimensions of the largest field that can be enclosed with 136 ft of fencing are 72 ft by 64 ft. The area of the field is 4608 ft2.

The amount of fencing needed to enclose the field is equal to the sum of the lengths of all four sides. Since 136 ft of fencing is available, the sum of the lengths of all four sides must equal 136 ft.

Let x represent the length of one side and y represent the length of the other side. Then the equation for the amount of fencing needed can be written as follows:

x + x + y + y

= 136

Simplifying, we get:

2x + 2y = 136

To find the dimensions of the largest field that can be enclosed, we must maximize the area of the field. The area of the field is equal to the product of the lengths of the two sides:

A = xy

To maximize the area of the field, we must take the derivative of A with respect to x and set it equal to 0.

A' = y

Setting A' equal to 0, we get:

y = 0

Since y cannot be 0, this equation has no solution. To maximize the area of the field, we must instead take the derivative of A with respect to y and set it equal to 0.

A' = x

Setting A' equal to 0, we get:

x = 0

Since x cannot be 0, this equation has no solution. To maximize the area of the field, we must instead solve the equation 2x + 2y = 136 for x and y.

2x + 2y = 136

2x = 136 - 2y

x = 68 - y

Substituting x = 68 - y into A = xy, we get:

A = (68 - y)y

A = 68y - y2

Taking the derivative of A with respect to y and setting it equal to 0, we get:

A' = 68 - 2y

68 - 2y = 0

2y = 68

y = 34

Substituting y = 34 into x = 68 - y, we get:

x = 68 - 34

x = 34

Therefore, the dimensions of the largest field that can be enclosed with 136 ft of fencing are 34 ft by 34 ft. The area of the field is 4608 ft2.

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A frequency distribution in which high scores are most frequent is said to be positively skewed or right-skewed.

In statistics, skewness refers to the asymmetry of a probability distribution. A frequency distribution is said to be positively skewed or right-skewed if the majority of the data is concentrated on the right side of the distribution, while a few high values are outliers on the right tail. The frequency distribution will look like a graph that is shifted to the right with a longer tail on the right side.

Positive skewness means that the mean (average) of the data will be higher than the median (middle value). The median is a more robust measure of central tendency than the mean in a positively skewed distribution, because it is not influenced by the outliers on the right tail.

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The probability that the committee contains at least one man is 1 - (probability of selecting only women).

To find the probability, we need to determine the total number of possible committee combinations and the number of combinations with at least one man. There are 9 people (6 women + 3 men) to choose from, and we want to choose a committee of 4.

Total combinations = C(9,4) = 9! / (4!(9-4)!) = 126
Combinations of only women = C(6,4) = 6! / (4!(6-4)!) = 15

To find the probability of at least one man, we'll subtract the probability of selecting only women from 1:

P(at least one man) = 1 - (15/126) = 1 - 0.119 = 0.881

The probability that the committee contains at least one man is approximately 0.881, or 88.1%.

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Answer:

i think its none of the answers are correct but.

Step-by-step explanation:

Answer:

Mean of data set 28,44,20,20 = (28+44+20+20)/4 = 112/4=28.

Step-by-step explanation:

Answer:

B. 45 is the correct answer

100

Answer:

(-6,0) and (3,0)

Step-by-step explanation:

This function has two x intercepts: (-6,0) and (3,0)

Answer:

(- 6, 0) and (3, 0)

Step-by-step explanation:

Whenever a question mentions the x-intercept, the y intercept is 0 and vice versa.

Now, putting the equation equal to 0, we get:

= x + 6 = 0 and x - 3 = 0

= x = - 6 and x = 3

So the point is (- 6, 0) and (3, 0)

Hope this helps, and please mark me brainliest if it does!

Answer:

A

Step-by-step explanation:

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\(y = 4mx - 5\)

Add sides 5

\(y + 5 = 4mx - 5 + 5\)

\(y + 5 = 4mx\)

\(y + 5 = m \times (4x)\)

Divide sides 4x

\( \frac{y + 5}{4x} = \frac{m \times 4x}{4x} \\ \)

\( \frac{y + 5}{4x} = m \\ \)

\(m = \frac{y + 5}{4x} \\ \)

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Given

Procedure

Now for y

The answer would be x = 2.75 and y = 1.25

Answer:

The equation of the hyperbola can be presented as follows;

\(\dfrac{\left x \right ^{2}}{12} - \dfrac{\left y \right ^{2}}{24} = 1\)

Step-by-step explanation:

We have the equation of an hyperbola given as follows;

\(\dfrac{\left (x - h \right )^{2}}{a^{2}} - \dfrac{\left (y - k \right )^{2}}{b^{2}} = 1\)

The foal length = a² + b² = c²

c = focal length

The directrix = a²/c

The focal point are (h + c, k) and (h - c, k)

Therefore, by comparison with the given focal points, (6, 0) and (-6, 0), we have;

k = 0 and h + c = 6, h - c = -6

Therefore;

6 - c - c = -6

-2·c = -12

c = 6

h = 0

a²/c = 2

a² = 2 × 6 = 12

a = 2·√3

12 + b² = 6²

b² = 6² - 12 = 24

b² = 24

b = 2·√6

The equation of the hyper bola can then be written as follows;

\(\dfrac{\left (x - 0 \right )^{2}}{12} - \dfrac{\left (y - 0 \right )^{2}}{24} = 1\)

Which gives

\(\dfrac{\left x \right ^{2}}{12} - \dfrac{\left y \right ^{2}}{24} = 1\)

x² - y² = 12

y² = x² - 12.

Answer:

7.83333333 ≈ 7.80

Step-by-step explanation:

All we have to do is divide the amount of money by the amount of hours.

235 ÷ 30 = 7.83333333 ≈ 7.80

Answer:35 you are welcome

Step-by-step explanation:

Answer:

3/ax-4=20

first add 4 to both sides

3/ax=20+4

multiply by a/3

24a/3

so x=8a

Answer: 1/8a

Step-by-step explanation: add 4 to both sides first, which will give you 3/ax = 24. Now multiply both sides by ax/3 to get rid of the 3/ax, which will then give you 1 = 24 * ax/3, which equals to 1 = 24ax/3. This can be simplified further and you'll get 1 = 8ax. now divide both sides by 8a to isolate x, you will end up with 1/8a = x.

The compound average annual return over 4 years, with annual returns of 9.2%, 13.0%, and 6.6%, is approximately 8.73%.



To calculate the compound average annual return, you need to find the geometric mean of the annual returns over the given period. Here's how you can do that:

1. Convert the annual returns into decimal form by dividing them by 100:

  - 9.2% becomes 0.092

  - 13.0% becomes 0.13

  - 6.6% becomes 0.066

2. Add 1 to each decimal form of the annual returns to obtain the growth rates:

  - 0.092 + 1 = 1.092

  - 0.13 + 1 = 1.13

  - 0.066 + 1 = 1.066

3. Multiply the growth rates together:

  1.092 * 1.13 * 1.066 = 1.350036456

4. Take the fourth root of the product to find the compound average annual return over 4 years:

  ∛1.350036456 ≈ 1.0873

5. Subtract 1 from the result and multiply by 100 to express the compound average annual return as a percentage:

  (1.0873 - 1) * 100 ≈ 8.73%

Therefore, the compound average annual return over the 4-year period is approximately 8.73%.

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Answer:

Step-by-step explanation:

Answer:

PQ ≈ 4.24, QR ≈ 2.83, PR ≈ 5.1

m∠Q = 90°, m∠P ≈ 34°, m∠R ≈ 56°

Step-by-step explanation:

thats it

The direct answer to the equation of the tangent line to ƒ(x) at x = 0 is y = 71x + 4.

To find the equation of the tangent line, we need to determine the slope of the tangent line at x = 0, which is equal to the derivative of ƒ(x) evaluated at x = 0. Since ƒ(x) = 4 + 67, the derivative of ƒ(x) with respect to x is 0. Therefore, the slope of the tangent line is 0. The equation of a line with a slope of 0 passing through the point (0, ƒ(0)) = (0, 4) is y = 71x + 4.

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The slope of function f(x) is of -1, while the slope of function g(x) is of zero. Thus, the function g(x) has a greater slope.

Given a table of values, the slope of a linear function is given by the rate of change of the output variable y relative to the input variable x.

From the table of function f(x), we have that when x increases by 2, y decays by 2, hence the slope of the function is given as follows:

m = -2/2 = -1.

From the graph, the slope is also given by the change in y divided by the change in x.

The graph at the end of the answer shows a constant line, meaning that y remains constant even when x changes, thus the change in y is of zero, meaning that the slope of function g(x) is of zero.

The graph of function g(x) is given by the image shown at the end of the answer.

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Answer:

A linear function is written in slope-intercept form as:

y = a*x + b

Where a is the slope and b is the y-intercept.

So any function of this shape, is a linear function, such that when graphed it is a straight line.

In this case, the function you wrote is:

Q: y = 1/3x + 2

Now, if the function is exactly what you wrote, then x is in the denominator:

y = 1/(3*x) + 2

Clearly, this is different than the general linear equation you can see above (here the variable is in the denominator) then in this case Q is non-linear.

If instead, the actual function Q is:

Q: y = (1/3)*x + 2

Then this is a linear equation, where the slope is 1/3 and the y-intercept is 2.

Answer:

0.01235

Step-by-step explanation:

we can solve for probability by using the formula;

favourable outcome/total number of outcomes

in this question, the number of favorable outcome = 3

the total number of outcomes = 3⁵

=  3x3x3x3x3 = 243

probability = 3/243

= 0.012345678

this can be approximated to be 0.01235

0.01235 is therefore the probability that all 5 customers would pick the same soft drink as their favorite drink.

Mother of Mia is the mother of the daughter of the mother of Mia's daughter

The statement "BLANK is the mother of the daughter of the mother of Mia's daughter" can be a bit confusing, but it essentially refers to the maternal grandmother of Mia's daughter.

Let's break it down: Mia has a daughter, who we'll call "A." The phrase "the mother of Mia's daughter" refers to Mia herself.

So, "the mother of the daughter of the mother of Mia's daughter" means the mother of Mia, who we'll call "B."

Therefore, B is the maternal grandmother of A.

Without any additional information about who Mia or her family members are, we cannot determine the identity of B. It could be any woman who is Mia's mother.

In other words, the answer to this question is simply "the mother of Mia," without any specific name or description.

The statement is designed to test the reader's understanding of family relationships and their ability to parse complex phrasing, rather than to provide specific information about a person's identity.
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