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Alex787 [66]
3 years ago
9

1/3(x-1/3)-1/2(2/3x-1/2)

Mathematics
1 answer:
kenny6666 [7]3 years ago
4 0

For this case we must simplify the following expression:

\frac {1} {3} (x- \frac {1} {3}) - \frac {1} {2} (\frac {2} {3} x- \frac {1} {2})

So, if we apply distributive property to the terms within parentheses we have:

\frac {1} {3} x- \frac {1} {9} - \frac {2} {6} x + \frac {1} {4} =\\\frac {1} {3} x- \frac {1} {9} - \frac {1} {3} x + \frac {1} {4} =

We simplify taking into account that:

  • Equal signs are added and the same sign is placed.
  • Different signs are subtracted and the major sign is placed.

- \frac {1} {9} + \frac {1} {4} =\\- \frac {4} {36} + \frac {9} {36} =\\\frac {-4 + 9} {36} =\\\frac {5} {36}

Answer:

\frac {5} {36}

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Solve the equation 4x^2 – 32x + 64 = 0.
AlexFokin [52]

Answer: x = 4

Step-by-step explanation:  4x^2−32x+64=0

4(x−4)(x−4)=0

x−4=0 x−4=0

x=4

8 0
2 years ago
In Triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ.
Roman55 [17]

The perimeter of triangle ABC is 24 units

Step-by-step explanation:

If a segment joining the mid points of two sides of a triangle, then

this segment is:

  • Parallel to the third side
  • Its length is half the length of the third side

In The triangle XYZ

∵ A is the mid point of XY

∵ B is the mid point of YZ

∴ AB = \frac{1}{2} XZ

∵ XZ = 18 units

- Substitute the value of XZ in AB

∴ AB = \frac{1}{2} × 18 = 9 units

∵ B is the mid point of YZ

∵ C is the mid point of XZ

∴ BC = \frac{1}{2} XY

∵ AY = 7 units

∵ AY = \frac{1}{2} XY

∴ XY = 2 × AY

∴ XY = 2 × 7

∴ XY = 14 units

∴ BC = \frac{1}{2} × 14 = 7 units

∵ A is the mid point of XY

∵ C is the mid point of XZ

∴ AC = \frac{1}{2} YZ

∵ BZ = 8 units

∵ BZ = \frac{1}{2} YZ

∴ YZ = 2 × BZ

∴ YZ = 2 × 8

∴ YZ = 16 units

∴ AC = \frac{1}{2} × 16 = 8 units

∵ The perimeter of a triangle = the sum of the lengths of its sides

∴ Perimeter Δ ABC = AB + BC + AC

∴ Perimeter Δ ABC = 9 + 7 + 8 = 24 units

The perimeter of triangle ABC is 24 units

Learn more:

You can learn more about triangles in brainly.com/question/5924921

#LearnwithBrainly

5 0
3 years ago
Suppose the coffee industry claimed that the average U.S. adult drinks 1.7 cups of coffee per day. To test this claim, a random
kvv77 [185]

Answer:

a) This t-value obtained (2.92) is in the rejection region (t > 1.69), hence, the sample does not support the cofdee industry's claim.

b) p-value for this test = 0.006266

c) The p-value obtained for this test is lesser than the significance level at which the test was performed, hence, we can reject the nuĺl hypothesis and say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Step-by-step explanation:

a) Degree of freedom = n - 1 = 34 - 1 = 33

The critical value of t for a significance level of 0.10 and degree of freedom of 33 = 1.69

Since we are testing in both directions whether the the average U.S. adult drinks 1.7 cups of coffee per day using our sample,

The rejection region is t < -1.69 and t > 1.69

So, we compute the t-statistic for this sample data to test the claim.

t = (x - μ)/σₓ

x = sample mean = 1.95 cups of coffee per day

μ₀ = The standard we are comparing against = 1.7 cups of coffee per day

σₓ = standard error = (σ/√n)

σ = standard deviation = 0.5 cups

n = Sample size = 34

σₓ = (0.5/√34) = 0.0857492926 = 0.08575

t = (1.95 - 1.70) ÷ 0.08575

t = 2.9154759464 = 2.92

This t-value obtained is in the rejection region, hence, the sample does not support the cofdee industry's claim.

b) Checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 34 - 1 = 33

Significance level = 0.10

The hypothesis test uses a two-tailed condition because we're testing in both directions.

p-value (for t = 2.92, at 0.10 significance level, df = 33, with a two tailed condition) = 0.006266

c) To use PHStat, the claim that the average U.S. adult drinks 1.7 cups of coffee per day is the null hypothesis.

The alternative hypothesis is that the real number of cups of coffee that the average U.S. adult drinks as obtained from the sample data, is significantly different from the 1.7 in the coffee industry's claim.

The p-value obtained from PHstat = 0.0063

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.10

p-value = 0.0063

0.0063 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Hope this Helps!!!

5 0
2 years ago
Charlie mows lawns in his neighborhood. He charges $15 per hour. Write an equation to model this situation. Then find out how
Ede4ka [16]

Answer:

He will earn $180 equation: M= money h = hours m = h15

Step-by-step explanation:

15 dollars times however many hours is equal to the money he earns, in this case 15 x 12 = 180

6 0
3 years ago
Simplify the expression<br> 8s - 11s + 6
raketka [301]
8 s -11 s + 6= - 3 s + 6=
= 3( - s +2)
6 0
3 years ago
Read 2 more answers
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