Given the function defined in the table below, find the average rate of change, in

it takes someone 15 minutes to prepare 3 1/4 cups of juice how many hours would it take to prepare 32 1/2 cups of juice

wariber [46]

$\bf \begin{array}{ccll} minutes&\stackrel{juice}{cups}\\ \cline{1-2} 15&3\frac{1}{4}\\\\ x&32\frac{1}{2} \end{array}\implies \cfrac{15}{x}=\cfrac{3\frac{1}{4}}{32\frac{1}{2}}\implies \cfrac{15}{x}=\cfrac{\frac{3\cdot 4+1}{4}}{\frac{32\cdot 2+1}{2}}\implies \cfrac{15}{x}=\cfrac{\frac{13}{4}}{\frac{65}{2}}$

$\bf \cfrac{15}{x}=\cfrac{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{5}{~~\begin{matrix} 65 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{15}{x}=\cfrac{1}{10}\implies 150=x\leftarrow \begin{array}{llll} \textit{150 minutes or}\\\\ \textit{2 hours and a half} \end{array}$

4 0

3 years ago

sally's $1800 savings is in two accounts.Her total interest for the year was $93 from one account earning 6% interest and anothe

myrzilka [38]

Answer:

$500 invested at 3%

$1300 invested at 6%

Step-by-step explanation:

8 0

4 years ago

A cat gave birth to 3333 kittens who each had a different mass between 147147147147 and 159 g159\,\text{g}159g159, start text, g

harina [27]

Answer:

The correct option is (B).

Step-by-step explanation:

The median (m) is a measure of central tendency. To obtain the median, we assemble the data in arising order. If the data is odd, the median is the mid-value. If the data is even, the median is the arithmetic-mean of the two mid-values.

The mean of a data set is:

$\bar X=\frac{1}{n}\sum\limits^{n}_{x=0}{X}$

For the three kittens it is provided that the weights are in the range 147 g to 159 g.

So, the mean and median weight for the 3 kittens lies in the middle of this range.

Now a fourth kitten is born, with weight 57 g.

Now the range of the weight of 4 kittens is, 57 g to 159 g.

The mean is going to decrease as one more value is added to the data and the value is the least.

The median will also decrease because now the median will be mean of the 2nd and 3rd values.

But the mean would decrease more than the median because a smaller value is added to the data.

Thus, the correct option is (B).

5 0

3 years ago

Paola and her sister are eating lunch at a restaurant in Miami, Florida. They order two iced teas for $2.49 each, nachos for $15

slavikrds [6]

Answer:

1.82

Step-by-step explanation:

Add the prices to get the subtotal:

Sweet Tea:

2.49 * 2 = 4.98

4.98 + 15.99 + 4.99 = $25.96

The subtotal is $25.96

The sale's tax in Miami is 7% (the base 6% for FL, and the extra 1% for Miami).

$25.96 * 0.07 = 1.817 ≈ 1.82

The tax should be 1.82.

Hope this helps.

7 0

3 years ago

The sum of the first three terms in a GP is 38.Their product is 1728.Find the values of the three terms.

dusya [7]

Answer:

The value of the three terms is 8 and 18

Step-by-step explanation:

Let "a" be the first term and "r" be the common ratio.

Then from the condition, we have these two equations

a + ar + ar^2 = 38, (1)

a*(ar*)*(ar^2) = 1728. (2)

From equation (2), a^3*r^3 = 1728, or (ar)^3 = 1728, which implies

ar = root%283%2C1728%29 = 12; (3)

hence,

r = 12%2Fa. (4)

Now, in equation (1) replace the term ar by 12, based on (3). You will get

a + 12 + ar^2 = 38, which implies

a + ar^2 = 26. (5)

Next, substitute r = 12%2Fa into equation (5), replacing "r" there. You will get

a + a%2A%28144%2Fa%5E2%29 = 26, or

a + 144%2Fa = 26.

Multiply by "a" both sides and simplify

a^2 - 26a + 144 = 0,

%28a-13%29%5E2 - 169 + 144 = 0

%28a-13%29%5E2 = 25

a - 13 = +/- sqrt%2825%29 = +/- 5.

Thus two solutions for "a" are a = 13 + 5 = 18 or a = 13 - 5 = 8.

If a = 8, then from (4) r = 12%2F8 = 3%2F2.

If a = 18, then from (4) r = 12%2F18 = 2%2F3.

In the first case, if a = 8, then the three terms are 8, 8%2A%283%2F2%29 = 12 and 8%2A%283%2F2%29%5E2 = 18.

In this case, the sum of terms is 8 + 12 + 18 = 38, so this solution does work.

In the second case, if a = 18, then the three terms are 18, 18%2A%282%2F3%29 = 12 and 18%2A%282%2F3%29%5E2 = 8.

In this case, the sum of terms is 18 + 12 + 8 = 38, so this solution does work, too.

ANSWER. The problem has two solution:

a) first term is 18; the common difference is 2%2F3 and the progression is 18, 12, 8.

b) first term is 8; the common difference is 3%2F2 and the progression is 8, 12, 18.

4 0

3 years ago