(x^-4)^5
please simplify the expression

Answer:

On average the children on the camp made 7 new friends in the week.

Step-by-step explanation:

Given:

Average number of new friends camp made in 6 days = 5

Number of new friends made on the last day = 2

We need to find the number of new friends on average did the children make during the one week summer camp.

Solution:

Now we can say that;

to find the number of new friends on average did the children make during the one week summer camp is equal to sum of Average number of new friends camp made in 6 days and Number of new friends made on the last day.

framing in equation form we get;

the number of new friends on average made in 1 week =

Hence On average the children on the camp made 7 new friends in the week.

Final answer:

On average, each child made 30 friends in the first six days of camp and another 2 on the last day, totaling an average of 32 friends made during the one week summer camp.

Explanation:

The children participating at the summer camp made an average of five new friends each for the first six days. This means they made a total of 5 friends/day * 6 days = 30 friends on average in the first six days. On the last day of camp, each child made two more friends. So, for the week as a whole, each child made an average of 30 friends from the first six days + 2 friends from the last day = 32 friends on average during the week-long summer camp.

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Answer:

c. 52 rad/s

Step-by-step explanation:

Final question does not correspond with available option. The real question is: What is the angular speed in radians per second?

At first we assume that spin balance rotates at constant rate and convert given angular speed, measured in revolutions per minute, into radians per second:

Which corresponds to option C.

The wheel rotates at an angular speed of 52 rad/s and the equivalent road speed is about 39 mph.

To solve this, we need to consider the given spin speed which is 500 revolutions per minute and convert this to rev per second by dividing by 60.

This is because a minute has 60 seconds.

Hence, the wheel rotates at 500/60 = 8.33 rev/s.

Furthermore, we need to know that in physics, one full revolution equals 2π radians (this is the equivalent of going around a circle once).

So, to convert from revolution to radian, we multiply by 2π, so the wheels is spinning at 8.33 * 2π ≈ 52.36 rad/s, which most closely matches option c. 52 rad/s.

Lastly, the linear (or road) speed can be calculated by multiplying the Angular momentum by the radius of the wheel (which is half the diameter), so v = (52.36 rad/s) * (13 in) = 680.68 in/s.

To convert it to mph, note that 1 inch/s = 0.057 mph, hence the wheel is spinning at about 39 mph.

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Answer:

150 vouchers to wash trucks were sold

250 vouchers to wash compact cars were sold

Step-by-step explanation:

Here, we are interested in calculating the number of each type of vouchers sold.

Let the number of vouchers to wash trucks be x while the number of vouchers to wash compact trucks be y.

Firstly, we know that both sums up to be 400.

Mathematically;

x + y = 400 •••••••••(i)

Secondly,

since a voucher to wash trucks sell $4, and we sold a total of x, the amount generated from selling is 4 * x = $4x

Same way for the vouchers to wash compact cars, we have a total of $3 * y = $3y

The sum of both gives $1350, which is the total sales.

Mathematically;

4x + 3y = 1350 ••••••(ii)

So we have two equations to solve simultaneously;

x + y = 400

4x + 3y = 1350

Multiply equation i by 4 , we have;

4x + 4y = 1600

4x + 3y = 1350

Subtract equation ii from i, we have 4y-3y = 1600-1350

y = 250

From equation 1, we know that

x + y = 400

This means that;

x = 400 -y

x = 400 -250

x = 150