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3 years ago

6

1/4x plus 5 equals -4, what is x

1 answer:

morpeh [17]3 years ago

4 0

1/4x + 5 = =4
subtract 5 to both sides
1/4x = 4 - 5
1/4x = -1
multiply 4 to both sides
x = -1 x 4
x = -4

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3 years ago

Heights of Women. Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 8 c

Bogdan [553]

Answer:

a) 6.68% of heights less than 150 centimeters

b) 58.65% of heights between 160 centimeters and 180 centimeters

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 162, \sigma = 8$

a) The percentage of heights less than 150 centimeters

We have to find the pvalue of Z when X = 150. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{150 - 162}{8}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

6.68% of heights less than 150 centimeters

b) The percentage of heights between 160 centimeters and 180 centimeters

We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.

X = 180

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{180 - 162}{8}$

$Z = 2.25$

$Z = 2.25$ has a pvalue of 0.9878

X = 160

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{160 - 162}{8}$

$Z = -0.25$

$Z = -0.25$ has a pvalue of 0.4013

0.9878 - 0.4013 = 0.5865

58.65% of heights between 160 centimeters and 180 centimeters

7 0

3 years ago

Annie walks 15 feet away from her house and places a mirror on the ground. She backs 4 feet away from the mirror so that she can

Firdavs [7]

Answer:

18.75 ft

Step-by-step explanation:

The given scenario can be drawn as shown in the following attachment.

Given that,

$m\angle DCE=\angle ACB$ and $m\angle DEC=\angle ABC=90^{\circ}$

Therefore, $\Delta ABC\sim \Delta DEC$

$\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{EC}$

$\Rightarrow \dfrac{AB}{5}=\dfrac{15}{4}$

$\Rightarrow AB=\dfrac{15\times 5}{4}=18.75$ ft

AB is the height of the house.

7 0

3 years ago

Read 2 more answers

prohojiy [21]

Where is the other one?

4 0

3 years ago

Find the area of the regular pentagon. 4.1 cm 6 cm Area = [?] cm? Enter your answer to the nearest tenth.

Assoli18 [71]

Answer:

Area of the given regular pentagon is 61.5 cm².

Step-by-step explanation:

Area of a regular polygon is given by,

Area = $\frac{1}{2}aP$

Here, a = Apothem of the polygon

P = Perimeter of the polygon

Apothem of the regular pentagon given as 4.1 cm.

Side of the pentagon = 6 cm

Perimeter of the pentagon = 5(6)

= 30 cm

Substituting these values in the formula,

Area = $\frac{1}{2}(4.1)(30)$

= 61.5 cm²

Therefore, area of the given regular pentagon is 61.5 cm².

8 0

3 years ago