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4 years ago

SOLVE THIS PLEASE AND EXPLAIN FOR FULL POINTS:)))

Mathematics

1 answer:

blondinia [14]4 years ago

3 0

Answer:

x=30, y=90

Step-by-step explanation:

y+x and y-x are supplementary angles. They must add to 180 degrees

y+x+y-x = 180

Combine like terms

2y = 180

Divide by 2

2y/2 = 180/2

y= 90

y+x and 2x are supplementary angles. They must add to 180 degrees

y+x+2x = 180

y+3x =180

We know y =90

90+3x=180

Subtract 90 from each side

90-90 +3x = 180-90

3x= 90

Divide by 3

3x/3 = 90/3

x = 30

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g Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lesson

sergij07 [2.7K]

Answer:

[3.75 years, 5.45 years]

Step-by-step explanation:

The 90% confidence interval is given by the interval

$\large [\bar x-t^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}]$

where

$\large \bar x$ is the sample mean

s is the sample standard deviation

n is the sample size

$\large t^*$ is the 0.05 (5%) both-sided (**) critical value for the Student's t-distribution with 19 degrees of freedom (sample size -1), which is an approximation to the Normal distribution for small samples (n≤ 30).

Either by using a table or the computer, we find

$\large t^*= 1.729$

and our 90% confidence interval is

$\large [4.6-1.729*\frac{2.2}{\sqrt{20}}, 4.6+1.729*\frac{2.2}{\sqrt{20}}]=\boxed{[3.75,5.45]}$

(**) 5% of the area to the left of $\large -t^*$ and 5% to right of $\large t^*$ for a total of 90% inside the interval $\large [-t^*,+t^*]$

5 0

3 years ago

Jill invested $20,000 in an account that earned 5.5% annual interest, compounded annually. What is the value of this account aft

attashe74 [19]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad \begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\dotfill &\$20000\\
r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\dotfill &1\\
t=years\dotfill &10
\end{cases}$

$\bf A=20000\left(1+\frac{0.055}{1}\right)^{1\cdot 10}\implies A=20000(1.055)^{10}
\\\\\\
A\approx 34162.88916707\implies A\approx \stackrel{\textit{rounded up}}{34162.89}$

4 0

3 years ago

Use the linear combination method to solve.

Ronch [10]

Answer:

(1,0)

I hope this is good enough:

5 0

3 years ago

I REALKY NEED HELP WITH THISS WORTH 20 POINTS

exis [7]

Answer:

either (5,-8) or (5,12). Either answer would be applicable here.

Step-by-step explanation:

It's simple addition/subtraction. Either subtract 10 from 2 in order to get -8, or add 10 to two in order to get 12.

5 0

3 years ago

Write an equation for the linear function f with the given values Question number 8

ANEK [815]

Answer:

5. y = 2/3x + 1

8. y = 4/7x - 4

Step-by-step explanation:

5. (-6, -3) and (6, 5)

You can use the slope formula which is (y2-y1)/(x2-x1) to find the slope and plug it back into the slope-intercept form to find the y-intercept

(5-(-3)) / (6-(-6)) = 8 / 12 = 2/3

slope-intercept form: y=mx+b where m is the slope and b is the y-intercept

to find b you can plug in one of the coordinates and the slope

5 = 6(2/3) + b

5 = 4 + b

1 = b

y = 2/3x + 1

8. (-7, -8), (21, 8)

m = (8 - (-8)) / (21 - (-7)) = 16 / 28 = 4/7

plug in one of the coordinates and the slope to find b or the y-intercept

8 = 21(4/7) + b

8 = 12 + b

-4 = b

y = 4/7x - 4

6 0

2 years ago