a) Z = ( × - μ ) ÷ σ Where μ mean of population σ standard deviation Z is the abscissa to give the area or probability we are looking for associated to the value 10 ounces ( × )

So: Z = ( 10 - 9 ) ÷ 1.2 ⇒ Z = 1/1.2 ⇒ Z = 0.83 it has to be below this value

From Z tables we get P [ Z ≤ 0.82 ] = 0.7910 0r 79.10 %

b) Following the same procedure: We look for

P [ Z > ( x - μ ) ÷ σ ] ⇒ Z = ( 12 -10 ) ÷ 1.2 = 2.5

From Z table we get the area under the curve from the left tail up to the point Z < 2.5 ( 2.5 not included) but we were asked for the area out of that previous so 1- 0.9930 = 0.007 is the area we are looking for

So P (b) = 0.007 or 7 %

Finally between the two points above mentioned ( 10 ≤ Z ≤ 12 ) we use the previous values (taking in consideration the limits, according to the problem statement )

Z ≤ 10 Z ⇒( 10-9 ) ÷ 1.2 Z = 0.7967

Z ≥ 12 Z ⇒ ( 12 - 9 ) ÷ 1.2 Z = 0.9952

The interval is between these two points

0.9952 - 0.7967 = 0.1985 ⇒ or 19.85 %

The attached help in the understanding of the solution

5 0

3 years ago

Monica sells lemonade over the summer and uses conical paper cups to serve

Alina [70]

Answer: She would need 206 paper cups.

Step-by-step explanation: First of all, Monica has a 10-gallon container full of lemonade and this translates into 37850 cubic centimetres volume of lemonade. The conversion rate has been provided as one gallon equals 3785 cubic centimetres, therefore ten gallons would be 3785 times ten which gives you 37,850 cubic centimetres of lemonade.

Each cone shaped paper cup has a diameter measuring 8 centimetres and 11 centimetres in height. The radius of the cone shaped cup therefore is 4 centimetres (radius equals diameter divided by two). The volume of each cup therefore is given as;

Volume of a cone = (πr²h)/3

Volume of a cone = (3.14 * 4² * 11)/3

Volume of a cone = 552.64/3

Volume of a cone = 184.2

If each cone could hold 184 cubic centimetres of lemonade, then the entire ten gallons would require the following number of cone shaped cups;

Number of cups = Total volume/Volume of a cup

Number of cups = 37850/184.2

Number of cups = 205.48

Rounded to the nearest whole number, this becomes

Number of cups ≈ 206

Therefore Monica would need 206 cone shaped paper cups to empty the entire 10 gallons of lemonade.

4 0

3 years ago

What is a true statement about negative exponents?

Nadya [2.5K]

Answer:

Raising something to a negative exponent is just taking the reciprocal of the amount.

Step-by-step explanation:

Let's assume that you wanted to know what $x^{-2}$ is.

To find it, you would take the reciprocal of the x amount. So $x^{-2}$ becomes $\frac{1}{x^{2}}$ .

This works because of the nature of exponents. Exponents represent the number of times you are multiplying a value by itself. So $a^{3}$ would be equal to a · a · a. To increase the exponent, you increase the number of times the value is multiplied by itself: To increase $a^{3}$ to $a^{5}$ , you would have to multiply a with $a^{3}$ two more times (a · a · a · a · a). To decrease the exponent, you must divide the value by itself. So to decrease $a^{5}$ to $a^{2}$ , you would have to divide $a^{5}$ by a 3 times.

If the exponent is 0, the value is equal to 1. But you can still decrease the exponent into negative numbers. You just divide 1 by a the desired amount of times: $\frac{1}{a^{3}}$ means that you are dividing 1 by a 3 times.

Hope this helps.

3 0

2 years ago