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3 years ago

Find the measure of each angle please?

Mathematics

1 answer:

melisa1 [442]3 years ago

3 0

The sum of interior angles of a hexagon is 720°.
.. x +150 +(2x -50) +(x +40) +80 +(x +20) = 720
.. 5x +240 = 720 . . . . . . . . simplify
.. 5x = 480 . . . . . . . . . . . . . subtract 240
.. x = 96 . . . . . . . . . . . . . . . .divide by 5

The angles (clockwise from lower left) are
.. 96°
.. 150°
.. 142°
.. 136°
.. 80°
.. 116°

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One and a half x + 3/4 x equals 5/8

USPshnik [31]

1 and 1/2x+3/4x=5/8
combine x's
1 and 1/2x=4/4x+2/4x=6/4x
6/4x+3/4x=5/8=9/4x
9/4x=5/8
multiply both sides by 8
18x=5
x=5/18

x=5/18 or aprox 0.277777777777

5 0

4 years ago

Read 2 more answers

What are the factors of 21

sweet-ann [11.9K]

Answer:

21: 3and 7 factors

54: 6and 9 factors

3 0

3 years ago

2. The National Safety Council routinely analyzes the benefit of seat belt use on driver safety. Their data showed that among 28

JulijaS [17]

Answer:

We conclude that there is difference in the proportion of deaths between the 2 groups.

Step-by-step explanation:

We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.

Let $p_1$ = proportion of deaths when drivers were not wearing seat belts.

$p_2$ = proportion of deaths when drivers were wearing seat belts.

So, Null Hypothesis, $H_0$ : $p_1=p_2$ {means that there is no difference in the proportion of deaths between the 2 groups}

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$ {means that there is difference in the proportion of deaths between the 2 groups}

The test statistics that would be used here Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of deaths when drivers were not wearing seat belts = $\frac{31}{2823}$ = 0.011

$\hat p_2$ = sample proportion of deaths when drivers were wearing seat belts = $\frac{16}{7765}$ = 0.002

$n_1$ = sample of drivers not wearing seat belts = 2823

$n_2$ = sample of drivers wearing seat belts = 7765

So, the test statistics = $\frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }$

= 4.438

The value of z test statistics is 4.438.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is difference in the proportion of deaths between the 2 groups.

Also, Margin of error (E) = $1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }$

= $1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }$

= 0.00397

5 0

3 years ago

The width and length of a rectangle (in feet)are consecutive odd integers. If the length is increased by 5 feet, the area of the

Tresset [83]

Original:
The width and length of a rectangle are consecutive odd integers
so W = x and L = x + 2

If the length is increased by 5 feet, then new L = x + 2 + 5 = x + 7

A = L x W
60 = (x + 7) x
60 = x^2 + 7x
x^2 + 7x - 60 = 0
(x - 5)(x + 12) = 0
x = 5 and x = -12

From here you have x = W = 5 ft and L = x + 2 = 5 + 2 = 7 feet

Area of original = 5 x 7 = 35

answer
the area of the original rectangle: 35 ft^2

4 0

3 years ago

What does it mean to say a data point has a residual of 0

slava [35]

The point lies directly on the regression line.

3 0

4 years ago