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VladimirAG [237]
2 years ago
6

Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.

Mathematics
1 answer:
MrRa [10]2 years ago
3 0

Answer:

180- 110= 70

70+x+90=180

160+x=180

180-160=x

20=x

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h a
Elodia [21]

We have been given that a sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. We are asked to find the volume of the sphere.  

We know that height of sphere is equal to its radius. This means that r=h.

\text{Volume of sphere}=\frac{4}{3}\pi r^3  

\text{Volume of cylinder}=\pi r^2 h

Using r=h, we will get:

\text{Volume of cylinder}=\pi r^2\cdot r

\text{Volume of cylinder}=\pi r^3

Upon comparing volume of sphere and volume of cylinder, we can see that volume of sphere is \frac{4}{3} times volume of cylinder.

\pi r^3=21

\frac{4}{3}\pi r^3=\frac{4}{3}\cdot 21

\frac{4}{3}\pi r^3=4\cdot 7

\frac{4}{3}\pi r^3=28

Therefore, the volume of the sphere would be 28 cubic meters.

4 0
3 years ago
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A number was subtracted from 15. After which, that result was multiplied by 5. This result was then divided by 5 for a result of
likoan [24]

Answer:

14

Step-by-step explanation:

15-14 = 1

1*5=5

5/1=1

6 0
2 years ago
What is the simplified form of 2/x^2-x - 1/x?
Pachacha [2.7K]

Answer:  \bold{(C)\ \dfrac{3 - x}{x(x-1)}}

<u>Step-by-step explanation:</u>

   \dfrac{2}{x^2-x}-\dfrac{1}{x}

=\dfrac{2}{x(x-1)}+\dfrac{-1}{x}

=\dfrac{2}{x(x-1)}+\dfrac{-1}{x}\bigg(\dfrac{x-1}{x-1}\bigg)

=\dfrac{2}{x(x-1)}+\dfrac{-x+1}{x(x-1)}

=\dfrac{2-x+1}{x(x-1)}

=\dfrac{3-x}{x(x-1)}

8 0
3 years ago
One stats class consists of 52 women and 28 men. Assume the average exam score on Exam 1 was 74 (σ = 10.43; assume the whole cla
Svetllana [295]

Answer:

(A) What is the z- score of the sample mean?

The z- score of the sample mean is 0.0959

(B) Is this sample significantly different from the population?

No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.

Step -by- step explanation:

(A) To find the z- score of the sample mean,

X = 75 which is the raw score

¶ = 74 which is the population mean

S. D. = 10.43 which is the population standard deviation of/from the mean

Z = [X-¶] ÷ S. D.

Z = [75-74] ÷ 10.43 = 0.0959

Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].

(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.

The estimated standard error of the mean is s/√n

S. E. = 16/√80 = 16/8.94 = 1.789

The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559

Setting up the hypotheses,

Null hypothesis: Sample is not significantly different from population

Alternative hypothesis: Sample is significantly different from population

Having gotten T- cal, T- tab is found thus:

The Critical (Table) t value is found using

- a specific alpha or confidence level

- (n - 1) degrees of freedom; where n is the total number of observations or items in the population

- the standard t- distribution table

Alpha level = 0.05

1 - (0.05 ÷ 2) = 0.975

Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;

The critical t value is 1.990

Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.

Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.

6 0
3 years ago
How do you subtract 1 integer by another
nikdorinn [45]
Use absolute value. If both signs are negative you will get a negative number. if both are positive you get positive. if the signs are different, subtract the smaller absolute value from the larger absolute value.
8 0
3 years ago
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