Simplify the following distributive property 1.-3(4x-5) 2.4(2x+2) 3.-(6x-2)

Answer:

see the attachment of the answer!

Answer: 3(4a+3c)

Step-by-step explanation:

4 x 3a + 3c x 3c

= 3(4a+3c)

The angle between u and v , after rounding is approximately 121.2 degrees.

To find the angle between two vectors, you can use the dot product formula:
u · v = ||u|| ||v|| cos(theta)
where ||u|| and ||v|| are the magnitudes of the vectors u and v, and theta is the angle between them.
First, we need to calculate the magnitudes of u and v:
||u|| = sqrt((-3)^2 + 4^2) = 5
||v|| = sqrt(7^2 + 5^2) = sqrt(74)
Next, we can calculate the dot product of u and v:
u · v = (-3)(7) + (4)(5) = -1
Now we can use the dot product formula to solve for theta:
-1 = (5)(sqrt(74)) cos(theta)
cos(theta) = -1 / (5 sqrt(74))
theta = acos(-1 / (5 sqrt(74))) ≈ 121.2 degrees
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Answer:

Step-by-step explanation:

The volume of water in a pool can be calculated using the following formula:

Volume (in gallons) = Length (in feet) x Width (in feet) x Average Depth (in feet) x 7.5

For example, if your pool is 20 feet long, 15 feet wide, and has an average depth of 5 feet, the volume of water in your pool would be:

20 x 15 x 5 x 7.5 = 5625 gallons

Note: If you prefer metric units, the formula for volume in liters would be:

Volume (in liters) = Length (in meters) x Width (in meters) x Average Depth (in meters) x 1000

It's important to note that this formula assumes a standard rectangular or square pool shape. If your pool has a more complex shape, you may need to measure the volume in smaller sections and add the volumes together to get the total volume.

The carpenter has 8 boxes of screws, 0 2x4s, and 13 sheets of plywood left over after building 19 shelves and 24 tables.

Let's start by calculating the total amount of materials required to build 19 shelves and 24 tables:

For 19 shelves, we need:

19 boxes of screws

57 (3*19) 2x4s

38 (2*19) sheets of plywood

For 24 tables, we need:

48 (2*24) boxes of screws

96 (2242) 2x4s

24 sheets of plywood

So in total, we need:

19+48=67 boxes of screws

57+96=153 2x4s

38+24=62 sheets of plywood

However, we only have on hand:

75 boxes of screws

120 2x4s

75 sheets of plywood

Therefore, we can only use:

67 boxes of screws

120 2x4s

62 sheets of plywood

To find out how much of each material is leftover, we need to subtract the amount used from the amount on hand:

Screws: 75 - 67 = 8 boxes of screws left over

2x4s: 120 - 120 = 0 2x4s left over

Plywood: 75 - 62 = 13 sheets of plywood left over

Therefore, the carpenter has 8 boxes of screws, 0 2x4s, and 13 sheets of plywood left over after building 19 shelves and 24 tables.

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I would like to construct a 95% confidence interval with a 4% margin of error. We don't have an estimate for the percentage, so we use a conservative estimate.

This is the minimum sample size, so we need to round up to 601. The larger the sample, the more confident the responses truly represent the population.

This shows that for a given confidence level, the confidence interval gets smaller as the sample size increases. At least 1450 samples from each group are required.

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To determine the values of the missing entries in the table for the equation 8x - 4y = 12, we can choose various values for x or y and solve for the corresponding variable.

To find the missing entries in the table, let's consider a few examples by substituting values for either x or y into the equation 8x - 4y = 12:

For x = 0:

Substituting x = 0 into the equation gives 8(0) - 4y = 12, which simplifies to -4y = 12. Solving for y, we have y = -3. Therefore, the ordered pair is (0, -3).

For y = 0:

Substituting y = 0 into the equation gives 8x - 4(0) = 12, which simplifies to 8x = 12. Solving for x, we have x = 3/2. Thus, the ordered pair is (3/2, 0).

For x = 2:

Substituting x = 2 into the equation gives 8(2) - 4y = 12, which simplifies to 16 - 4y = 12. Solving for y, we have y = 1. Hence, the ordered pair is (2, 1).

By choosing different values for x or y, we can continue to find more ordered pairs that satisfy the equation 8x - 4y = 12. It is important to note that there are infinitely many possible solutions, as it is a linear equation with two variables.

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Answer:

Area of the composite figure = 42 in²

Step-by-step explanation:

Composite area of the given figure = Area of the rectangle + Area of the right triangle

Area of the rectangle = Length × Width

                                    = 6 × 5

                                    = 30 in²

Area of the right triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                         = \(\frac{1}{2}(4)(6)\)

                                         = 12 in²

Area of the composite figure = 30 + 12

                                                  = 42 in²

According to the above, the point s coincides with number -5, the point t coincides with number -8.24 and the point u coincides with number 6.28.

To identify the points that coincide with the expressions we must perform the mathematical operations shown. In this case, we must find the roots and multiply the 2 by the number pi as shown in the expressions column.

An important point is that we must do these operations in the positive form and then put the negative symbol because it is not possible to find the root of a negative number.

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Using it's concept, the scatter plot that accurately reflects the data given in the problem is scatter plot D.

A scatter plot is a graph that maps each input in the data-set to it's respective output, as points.

Considering this concept, an age of 12(x - axis) should be mapped to a time in minutes of 23(y-axis), and so on, until an age of 71 is mapped to a time of 33 minutes, which happens in option D.

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The answer of the calculation is 55 and -55 respectively.

Given that \(f(x)=7x−8 and g(x)=9−x²\), the following are the calculations:

(a) \(f(g(0))= >\)

To calculate\(f(g(0))\), we need to find the value of g(0) first.  

\(g(0) = 9 - 0² = 9\\f(g(0)) = f(9) = 7(9) - 8f(g(0)) \\= 63 - 8f(g(0))\\ = 55(b) g(f(0))= >\)

To calculate

\(f(0) = 7(0) - 8f(0) \\= -8g(f(0)) = 9 - f(0)²g(f(0)) \\= 9 - (-8)²g(f(0)) \\= 9 - 64g(f(0)) = -55\)

Therefore,

\((a) f(g(0)) = 55, \\(b) g(f(0)) = -55.\)

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Answer:

5(5x - 0.34

Step-by-step explanation:

Answer:

The correct answer is −10x+1.5

Step-by-step explanation:

−2(5x−0.75)

=(−2)(5x+−0.75)

=(−2)(5x)+(−2)(−0.75)

=−10x+1.5

The width of a poster with a total area of 500 cm² and margins of 6 cm at the top and 4 cm on the sides and bottom should be approximately 17.12 cm to have the largest printed area.

Let's start by finding the total area of the poster with the margins included.

At the top, the margin is 6cm, so the printed area is the width of the poster minus 2 times the margin:

Printed width at the top = (width - 2*6) = (width - 12)

Similarly, the printed width at the sides and bottom is:

Printed width at the sides and bottom = (width - 2*4) = (width - 8)

The printed height is:

Printed height = (total area / printed width) = (500 / width)

Therefore, the total area of the poster with margins is:

Total area = (Printed width at the top) * (Printed height) + 2 * (Printed width at the sides and bottom) * (Printed height)

Substituting the expressions we have derived for the printed height and widths, we get:

Total area = (width - 12) * (500 / width) + 2 * (width - 8) * (500 / width)

Simplifying this expression gives:

Total area = (500/w) * (3w - 40)

To maximize the printed area, we need to find the value of w that maximizes the total area. We can do this by taking the derivative of the total area with respect to w, setting it equal to zero, and solving for w:

d(Total area)/dw = -500/w^2 * (3w - 40) + 500/w * 3 = 0

Multiplying both sides by w^2 and simplifying gives:

3w^2 - 40w - 150 = 0

Solving for w using the quadratic formula gives:

w = (40 ± sqrt(40^2 - 43(-150))) / (2*3)

w ≈ 17.12 or w ≈ -2.79

Since the width of the poster cannot be negative, the only valid solution is w ≈ 17.12 cm.

Therefore, to have the largest printed area, the width of the poster should be approximately 17.12 cm.

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_____The given question is incomplete, the complete question is given below:

a poster is to have a total area of 500cm2 . there is a margin round the edges 6cm of at the top and 4cm at the sides and bottom where nothing is printed. what width should the poster be in order to have the largest printed area?

Answer:

The answer is option 2.

Step-by-step explanation:

Given that the TU and UF added up together to form a length of 32. In order to find TU, you have to subtract length of UF from 32 :

TU + UF = 32

TU + 20 = 32

TU = 32 - 20

TU = 12

Answer: C outside of the circle

Step-by-step explanation:

The answer is c because

point 4, -1 falls outside of the

circle.

Hope this helps :)

Answer:

Its on the circle

Step-by-step explanation:

Answer:

y=2x

Step-by-step explanation:

y= 2x

b is 0 because there is no y-intercept and it's going up 2 right 1 so the slope is 2

Answer:

Step-by-step explanation:

Chicken nugget

Answer:

6

3.5

Step-by-step explanation:

a=2b

a=2(3) = 6

7=2b = 7/2 = 3.5

I hope this helps.

Answer:

The test statistic or the z-score is -298.484.

Given data:

To compute the value of the test statistic, we need to calculate the z-score using the sample mean, the population mean under the null hypothesis, the standard deviation, and the sample size.

Sample mean (x) = 5.4 minutes

Population mean under the null hypothesis (μ) = 66 minutes

Standard deviation (σ) = 1.3 minutes

Sample size (n) = 41

The formula for the test statistic (z-score) in this case is:

z = (x- μ) / (σ / √n)

Plugging in the values:

z = (5.4 - 66) / (1.3 / √41)

Calculating the expression inside the parentheses:

z = -60.6 / (1.3 / √41)

Calculating the square root of 41:

z = -60.6 / (1.3 / 6.403)

Calculating the division inside the parentheses:

z = -60.6 / 0.202

Calculating the final value:

z ≈ -298.484

Null Hypothesis (H0): The mean installation time has not changed (μ = 66 minutes).

Alternative Hypothesis (H1): The mean installation time has changed (μ ≠ 66 minutes).

Level of significance (α) = 0.025 (this corresponds to a two-tailed test since we have "not equal to" in the alternative hypothesis).

For a two-tailed test at the 0.025 level of significance, the critical values are ±1.96.

Since the test statistic (-300.495) is much smaller (in absolute value) than the critical value (-1.96) for a two-tailed test at the 0.025 level of significance, we reject the null hypothesis.

Conclusion: At the 0.025 level of significance, there is enough evidence to suggest that the mean installation time has changed from 66 minutes for the most popular computer program made by RodeTech, based on the data from the sample.

Hence, the value of the test statistic is approximately -298.484.

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Answer:

its a commutative property becaus its just changing the order

Answer:

b = -1

Step-by-step explanation:

3 - 2(b - 2) = 2 - 7b (Use the distributive property)

3 - 2b + 4 = 2 - 7b (Add 3 and 4)

7 - 2b = 2 - 7b (Add 7b to both sides)

7 - 2b + 7b = 2 (Add -2b to 7b)

7 + 5b = 2 (Subtract 7 from both sides)

5b = 2 - 7 (Subtract 7 from 2)

5b = -5 (Divide both sides by 5)

b = -5/5 (Divide -5 by 5)

b = -1

Work Check: (Substituting b for -1)

3 - 2(b - 2) = 2 - 7b

3 - 2(-1 - 2) = 2 - 7(-1)

3 - 2(-3) = 2 - (-7)

3 - (-6) = 2 - (-7)

3 + 6 = 2 + 7

9 = 9

That is true, so b = -1

Answer:

A unit rate is ratio where the denominator is usually 1. We can calculate unit rate as a division of two quatities. For example, the price of 10 apples is $20, then the unit rate is the division of $20 by the number of apples

$20/10 = $2 per apple

So, the unit rate is the price per apple.

Answer:

-6x-4

Step-by-step explanation:

2(-3x)-4

-6x-4

r F(x) is your frame function since it is on the outside, when every you get to an x in the F function you plug in the G function then solve as normal.

Its A because i checked myself

Answer:

2.67

Step-by-step explanation:

n/a because I don't want to be a part of the way u passed out of the way and I will be there

Answer:

a 33 I think

Step-by-step explanation:

i am not really good at that

Answer:

B. 46

10% of 200 is 20 so 23% of 200 is 46

The cosine ratio for angle B in the right triangle is given as follows:

cos(B) = 15/17.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For angle B, the parameters are given as follows:

Hence the cosine is given as follows:

cos(B) = 15/17.

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