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Ad libitum [116K]

2 years ago

8

The monthly utility bills in a city at e normally distributed, with a mean $100 and a standard deviation of $13. find the probab

ility that a randomly selected utility bill is (a) a less than $70, (b) between $85 and $120, and(c) more than $140.

1 answer:

dmitriy555 [2]2 years ago

5 0

Answer:

how's your day

Step-by-step explanation:

how's your day

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satela [25.4K]

Answer:

$\large\boxed{2a+14}$

Step-by-step explanation:

$4(a + 2 ) - 2 (a - 3)\qquad\text{use distributive property:}\ a(b+c)=ab+ac\\\\=4a+8-2a-(-6)\qquad\text{combine like terms}\\\\=(4a-2a)+(8+6)\\\\=2a+14$

5 0

3 years ago

There are 37 paper clips in a box. Carmen places more paper clips in the box. Which equation models the total number of paper cl

Anon25 [30]

37+n=p because all your doing is putting the numbers into a problem with the correct signs.

7 0

3 years ago

Read 2 more answers

If x = 5, then which inequality is true?

barxatty [35]

Answer:

B

Step-by-step explanation:

cause when we substitute 5 in the equation we get 3<7which is true.

7 0

3 years ago

Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

<h3>16</h3>

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

<h3>17</h3>

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

<h3>18</h3>

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

<h3>15</h3>

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

3 years ago

Which is the most accurate way to estimate 25% of 53?

Alex Ar [27]

You can calculate them out and check which one is the most accurate

so if one of the choices was 1/3 of 50, then you would do:
1/3 in the calculator (should be 0.333...) times 50

And you can compare it with the EXACT number, which is:
0.25*53=13.25

This way you can test all the options

8 0

3 years ago