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AlekseyPX
3 years ago
8

rac{2}{3} + 5x = 7 - 2x" alt="4 \frac{2}{3} + 5x = 7 - 2x" align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
liq [111]3 years ago
8 0
Convert the mixed number to a improper fraction 5x+2x=7-14/3, collect like terms 7x=7-14/3=7x=7/3, decide seven on both sides x= 1/3
Delicious77 [7]3 years ago
5 0

4 2/3+5x=7-2x

Add 2x to both sides.

4 2/3+7x=7

Subtract 4 2/3 on both sides.

7x=2 1/3

7x=7/3

Divide by 7 on both sides.

x=1/3

answer: x=1/3

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How do I write y=2x-7 in function notation?
mrs_skeptik [129]
Thus is how you write y=2x-7 in a function notation. ANSWER:F(x)=2x-7.
5 0
3 years ago
Read 2 more answers
Prove that sin20sin40sin60sin80=3/16
never [62]
We'll use the following properties of sine and cosine to prove this:

sin(a)\cdot sin(b) = \frac12(cos(a-b) - cos(a+b))

cos(a)\cdot cos(b) = \frac12(cos(a+b) + cos(a-b))

cos(180+a) = cos(180-a)

Then it's just a matter of filling it in...

sin20sin40 * sin60sin80 = 1/2(cos20 - cos60) * 1/2 (cos20 - cos140) =

1/8( cos40 + 1 - cos160 - cos120 - cos40 - cos80 + cos80 + cos200) =

1/8(1 -  cos160 - cos120 + cos200) =

1/8(1 -  cos160 - cos120 + cos160) =

1/8(1 - cos120 ) = 1/8( 1 + 1/2 ) = 3/16

5 0
3 years ago
A rectangular prism has the following dimensions. length: 18 inches width: 1 foot height: 14 inches If all the dimensions of thi
mojhsa [17]

Answer:

11,448 in²

Step-by-step explanation:

The area can be computed from ...

... A = 2(LW +H(L+W))

For the given prism, the area will be ...

... A = 2(18·12 +14(18+12)) = 2(216 +420) = 1272 . . . . in²

The area of a similar figure with dimensions 3 times as long will be 3² times as much. The area of the new figure is ...

... A = 3²×(1272 in²) = 11,448 in²

3 0
3 years ago
Read 2 more answers
The standard deviation for actuary salaries has a standard deviation of $36,730 . You collect a simple random sample of n=36 sal
Yanka [14]

Using the z-distribution, it is found that the lower limit of the 95% confidence interval is of $99,002.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm z\frac{\sigma}{\sqrt{n}}

In which:

  • \overline{x} is the sample mean.
  • z is the critical value.
  • n is the sample size.
  • \sigma is the standard deviation for the population.

In this problem, we have a 95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so the critical value is z = 1.96.

The other parameters are given as follows:

\overline{x} = 111000, \sigma = 36730, n = 36

Hence, the lower bound of the interval is:

\overline{x} - z\frac{\sigma}{\sqrt{n}} = 111000 - 1.96\frac{36730}{\sqrt{36}} = 99002

The lower limit of the 95% confidence interval is of $99,002.

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

8 0
2 years ago
1. If the area of a circle is 81pi square feet, find its circumference.
My name is Ann [436]

Answer:

the circumference is 18 pi feet.

Step-by-step explanation:

4 0
2 years ago
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