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3 years ago

An angle measures 124 more than the measure of its supplementary angle. What is the measure of each angle?

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

6 0

Answer:

Step-by-step explanation:

Suplementary angles add to 180°

If one of angles is 124° more than the other then if we subtract 124° from the larger angle we get two equal angles which sum is also 124° less

180° - 124° = 56°

56° - sum of two equal angles

56° ÷ 2 = 28° - the measure of smaller angle

28° + 124° = 152° - the measure of larger angle

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How do you factor #8x^3+4x^2-18x-9#?

kvasek [131]

This expression is a good candidate for "factoring by grouping." I note that the first 2 terms and the last 2 terms share a common factor, 2x+1:

8x^3 + 4x^2 - 18x - 9
4x^2 *(2x + 1) -9 (2x+1)

This can be re-written as (2x+1)(4x2-9)

The latter factor is also easily factorable:

(2x+1)(2x-3)(2x+3) (answer)

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4 years ago

Given two dependent random samples with the following results:

skad [1K]

Answer:

We Fail to reject Null Hypothesis.

Step-by-step explanation:

We are given two dependent random samples;

Population 1 Population 2 d = Population 1 entry-Population 2 entry $d^{2}$

52 61 52 - 61 = -9 81

81 71 81 - 71 = 10 100

72 82 72 - 82 = -10 100

67 62 67 - 62 = 5 25

73 79 73 - 79 = -6 36

73 77 73 - 77 = -4 16

76 71 76 - 71 = 5 25

83 85 83 - 85 = -2 4

∑ $d^{2}$ = 387

Now, Null Hypothesis, $H_0$ : $\mu_1 = \mu_2$ or $\mu_d = 0$

Alternate Hypothesis, $H_1$ : $\mu_1 \neq \mu_2$ or $\mu_d \neq 0$

The test statistics for paired data is given by;

$\frac{dbar - \mu_d}{\frac{s_d}{\sqrt{n} } }$ follows $t_n_-_1$

where, $dbar$ = Mean of Population 2 data - Mean of Population 1 data

Mean of Population 1 data = $\frac{52+81+72+67+73+73+76+83}{8}$ = 72.125

Mean of Population 2 data = $\frac{61+71+82+62+79+77+71+85}{8}$ = 73.5

Hence, $dbar$ = 73.5 - 72.125 = 1.375

$s_d$ = Standard Deviation of paired data = $\sqrt{\frac{\sum d^{2} - n*(dbar)^{2} }{n-1} }$ = $\sqrt{\frac{387 - 8*(1.375)^{2} }{8-1} }$

= 7.3

n = no. of observations = 8

So, Test Statistics = $\frac{1.375 - 0}{\frac{7.3}{\sqrt{8} } }$ follows $t_7$

= 0.533

Now, if the critical value of t at 7 degree of freedom is less than the test statistics then we will reject null hypothesis.

At 0.01 level of significance, the t table gives a critical value of 3.499. Since our test statistics is less than the critical value we will not reject null hypothesis and conclude that there is no significant difference between the two population means.

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4 years ago

If you know the radius, r, of a circle, what do you multiply rby to get the circle's CIRCUMFERENCE?

KengaRu [80]

Answer:

C=2 x pi x radius

Step-by-step explanation:

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3 years ago

-2(x+1)-x+5 what do you think it is

Archy [21]

Answer:

The answer is -3x + 3

4 0

3 years ago

Delaney bought a crate for her puppy when it was 3 months old. The crate is in the shape of a rectangular prism. Since the puppy

Alika [10]

Answer:

The volume of the new crate is exactly 174.4% of the old crate.

Step-by-step explanation:

Volume of a rectangular prism:

The volume of a rectangular prism of dimensions x, y and z is given by:

$V = xyz$

She decided that the dimensions of the new crate needs to be increased by 40% of the original length.

Each dimension is increased by 40%, which means that each is multiplied by 1 + 0.4 = 1.4. So

$V = 1.4x(1.4y)(1.4z) = (1.4)^3(xyz) = 2.744(xyz)$

Percentage:

The new volume is 2.744 the original volume. Considering the original volume is 100% = 1, it increased by 2.744 - 1 = 1.744 = 1.744*100% = 174.4%.

The volume of the new crate is exactly 174.4% of the old crate.

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3 years ago