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You are paid $82.50 for 71212 hours of work. What is your rate of pay?

yanalaym [24]

If you would like to know what is your rate of pay, you can calculate this using the following steps:

$82.50 ... 7.5 hours
$x = ? ... 1 hour

82.50 * 1 = 7.5 * x
82.50 = 7.5 * x /7.5
x = 82.50 / 7.5
x = $11

The correct result would be $11 per hour.

3 0

3 years ago

\tan \left(18\right)=\frac{x}{20}

noname [10]

Answer:

x ≈ 6.5

Step-by-step explanation:

We have the epresion $tan(18)=\frac{x}{20}$ and we want to find the value of $x$ .

Let's do it step-by-step

Step 1. Multiply both sides of the equation by 20

$tan(18)=\frac{x}{20}$

$20tan(18)=(\frac{x}{20} )(20)$

$20tan(18)=x$

Step 2. use the reflexive property of equality: if $a=b$ then $b=a$

$20tan(18)=x$

$x=20tan(18)$

Step 3. Using a calculator we get that $tan(18)=0.325$ . Replacing that value we get

$x=20(0.325)$

x ≈ 6.5

We can conclude that the value of x is approximately 6.5

4 0

3 years ago

Is the dilation from figure A to figure B an enlargement or a reduction? what is the scale factor?

iris [78.8K]

Reduction 1/3 I believe

3 0

3 years ago

X-2y+z=5 <br>3x+3y-2z=-6 <br>2x-y+3z=11 <br>find x+y+z

BartSMP [9]

x - 2y + z = 5 | *2
⇒ 2x - 4y+ 2z=10
3x + 3y - 2z = - 6 } I sum up these relations
--------------------------------
2x+3x - 4y+3y+2z-2z=10-6
5x - y = 4 (1)

3x + 3y - 2z = - 6 | *3 ⇒ 9x + 9y - 6z = - 18
2x - y + 3z = 11 | *2 ⇒ 4x - 2y + 6z= 22 I sum up these
----------------------------------
⇒ 9x+4x+9y-2y-6z+6z= 4
13x+ 7y= 4 (2)
I write (1) and (2)
5x - y = 4 | *7
35x - 7y= 28
13x+7y=4
48x = 32
x= 32/48=4/6 ( 32:8=4, 48:8=6)
x= 2/3
5x-y=4,
5*2/3-y=4
y=10/3 -4=10/3-12/3=-2/3
⇒ y= - 2/3
x - 2y + z = 5
2/3 - 2*(-2/3)+z=5
2/3+4/3+z=5
6/3+z=5
2+z=5
z=3
x+y+z=2/3-2/3+3=3

x+y+z=3

3 0

3 years ago

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that th

lisov135 [29]

Answer:

$z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074$

Now we can calculate the p value with this probability:

$p_v =P(z>2.074)=0.019$

If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.

Step-by-step explanation:

Information given

n=78 represent the random sample taken

X=36 represent the students with jobs

$\hat p=\frac{36}{78}=0.462$ estimated proportion of students with jobs

$p_o=0.35$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the proportion of students with jobs is higher than 0.35, the system of hypothesis are:

Null hypothesis: $p \leq 0.35$

Alternative hypothesis: $p > 0.35$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info we got:

$z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074$

Now we can calculate the p value with this probability:

$p_v =P(z>2.074)=0.019$

If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.

5 0

4 years ago