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Brilliant_brown [7]

3 years ago

10

Jim worked 40 hours last week, plus 8 overtime hours at the time-and-a-half rate. His gross pay was $884. A. What was his hourly

rate? B. What was his hourly overtime date?

1 answer:

marishachu [46]3 years ago

7 0

Answer:

Hourly rate: $17.

Hourly overtime rate: $25.5.

Step-by-step explanation:

Let x represent Jim's hourly pay.

We have been given that Jim worked 40 hours last week. So amount paid in 40 hours would be $40x$ .

We are also told that his over time pay is time-and-a-half rate that is $1.5x$ .

The amount earned for working 8 overtime hours would be $8\cdot 1.5x=12x$ .

Since Jim's gross pay was $884, so we will equate amount earned in 40 hours and 8 hours of overtime with 884 as:

$40x+12x=884$

$52x=884$

$\frac{52x}{52}=\frac{884}{52}$

$x=17$

Therefore, Jim's hourly rate is $17.

Overtime rate would be $1.5x\Rightarrow1.5(17)=25.5$

Therefore, Jim's hourly overtime rate is $25.5.

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Yesterday Jack drove 33 1/2 miles he used 1 1/4 gallons of gasoline what is the unit rate for miles per gallon

Ksivusya [100]

Answer: 26 4/5 miles pee gallon

Step-by-step explanation:

From the question, we are informed that Jack drove 33 1/2 miles and that he used 1 1/4 gallons of gasoline. The unit rate for miles per gallon will be calculated by dividing 33 1/2 by 1 1/4. This will be:

= 33 1/2 ÷ 1 1/4

= 26 4/5 miles per gallon

8 0

3 years ago

A rocket is launched straight up from the ground with an initial velocity of 192 feet per second. The equation for the height of

Ivenika [448]

The equation for the height of the rocket at time t given

$h= -16t^2+192t$

We have to find the time t, when the rocket reaches 560 feet.

That means we have to find t when h = 560 ft. we will place 560 in the place of h to find t now.

$h= -16t^2+192t$

$560 = -16t^2+192t$

In the right side, we can check -16 is the common factor. So we will take out -16 from the rigbht side.

$560 = -16(t^2 - 12t)$

To get rid of -16 from the right side and move it to left side, we will divide both sides by -16.

$560/-16 = -16(t^2-12t)/-16$

$-35 = t^2 -12t$

Now we will move -35 to the righ side by adding 35 to both sides.

$-35+35 = t^2-12t+35$

$0 = t^2 -12t+35$

$t^2-12t+35 = 0$

We will factorize thee left side to find the values of t now. We need to find a pair of factors of 35 that by adding them we will get -12.

The pair of factors of 35 are -5 and -7 and by adding -5-7 we will get -12.

$t^2-12t+35 =0$

$(t-5)(t-7) =0$

So by using zero product property we will get

$t-5 =0$

$t-5+5 = 0+5$

$t=5$

Also $t-7 =0$

$t-7+7 = 0+7$

$t=7$

So we have got the rocket reaches at 560ft when t = 5 seconds and also when t = 7 seconds.

Now part b.

When the rocket completes its trajectory and hits the ground then the height or h = 0. So we will place h = 0 there in the equation.

$h= -16t^2+192t$

$0= -16t^2 + 192 t$

$0 = -16(t^2-12t)$

$-16(t^2-12t) = 0$

We will move -16 to the other side by dividing it to both sides.

$-16(t^2-12t)/-16 = 0/-16$

$t^2-12t = 0$

We will take out the common factor t from the left side. By taking out t we will get,

$t(t-12) = 0$

We will use zero product property now. By using that we will get,

$t = 0$

ans also $t-12 = 0$

$t-12+12 = 0+12$

$t = 12$

When the rocket completes its trajectory and hits the ground the time t can not be 0. When t =0, the rocket starts the trajectory.

So when the rocket completes its trajectory and hits the ground ,

then t = 12seconds.

So we have got the required answers.

6 0

3 years ago

Select the choice that translates the following verbal phrase correctly to algebra:

likoan [24]

The answer is <span>one halfn − 16
</span>
Let the number be n.

<span>One half of a number is (1/2n)
</span><span>decreased by 16 is (-16)

</span><span>one half of a number decreased by 16 is
1/2n - 16

Or </span><span>one halfn − 16</span>

4 0

3 years ago

Round to the nearest tenth place it is repeating decimal 4/6

Scilla [17]

Answer:

0.7

Step-by-step explanation:

I divided 4 by 6

0.6666666666666...

Simplify to 0.7

8 0

3 years ago

The makers of a soft drink want to identify the average age of its consumers. A sample of 25 consumers was taken. The average ag

Lelu [443]

Answer:

a.1.90 years

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.005 = 0.995$ , so $z = 2.575$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this question:

$n = 25, \sigma = 3.8$

So

$M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90$

So the correct answer is:

a.1.90 years

8 0

3 years ago