All categories

3 years ago

12.5% of what number is 24? Please help and show work

1 answer:

3 0

$12,5\%*x=24 \\ 0,125x=24 \ \ \ /:0,125\\ x=192$
As we all know:
$1\%= \frac{1}{100} \ \ \ therefore \ \ 12,5\%= \frac{125}{1000}$

You might be interested in

Verify the identity 6cos^2(x) -3 = 3 - 6sin^2(x)

Lorico [155]

Answer:

It is proved that $6\cos ^{2}x -3 = 3 - 6\sin ^{2} x$ .

Step-by-step explanation:

We already have the identity of x as $\sin ^{2}x + \cos ^{2}x = 1$ .......... (1) .

So, from equation (1) we can write that

$\cos ^{2} x = 1 - \sin ^{2} x$

⇒ $6\cos ^{2} x = 6 - 6 \sin ^{2} x$

⇒ $6\cos ^{2} x -3 = 6 - 6 \sin ^{2}x -3$

⇒ $6\cos ^{2}x -3 = 3 - 6\sin ^{2} x$

Hence, it is proved that $6\cos ^{2}x -3 = 3 - 6\sin ^{2} x$ . (Answer)

5 0

3 years ago

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use of one particular cust

Fiesta28 [93]

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given set of values

$321,397,559,454,475,324,482,558,369,513,385,360,459,403,498,477,361,366,372,320$

STEP 2: Write the formula for calculating the Standard deviation of a set of numbers

$\begin{gathered} S\tan dard\text{ deviation=}\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}} \\ where\text{ }x_i\text{ are data points,} \\ \bar{x}\text{ is the mean} \\ \text{n is the number of values in the data set} \end{gathered}$

STEP 3: Calculate the mean

$\begin{gathered} \bar{x}=\frac{\sum ^{}_{}x_i}{n} \\ \bar{x}=\frac{\sum ^{}_{}(321,397,559,454,475,324,482,558,369,513,385,360,459,403,498,477,361,366,372,320)}{20} \\ \bar{x}=\frac{8453}{20}=422.65 \end{gathered}$

STEP 4: Calculate the Standard deviation

$\begin{gathered} S\tan dard\text{ deviation=}\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}} \\ \sum ^{}_{}(x_i-\bar{x})^2\Rightarrow\text{Sum of squares of differences} \\ \Rightarrow10332.7225+657.9225+18591.3225+982.8225+2740.52251+9731.8225+3522.4225+18319.6225+2878.3225 \\ +8163.1225+1417.5225+3925.0225+1321.3225+386.1225+5677.6225+2953.9225+3800.7225 \\ +3209.2225+2565.4225+10537.0225 \\ \text{Sum}\Rightarrow108974.0275 \\ \\ S\tan dard\text{ deviation}=\sqrt[]{\frac{111714.55}{20-1}}=\sqrt[]{\frac{111714.55}{19}} \\ \Rightarrow\sqrt[]{5879.713158}=76.67928767 \\ \\ S\tan dard\text{ deviation}\approx76.68 \end{gathered}$

Hence, the standard deviation of the given set of numbers is approximately 76.68 to 2 decimal places.

STEP 5: Calculate the First and third quartile

$\begin{gathered} \text{IQR}=Q_3-Q_1 \\ \\ To\text{ get }Q_1 \\ We\text{ first arrange the data in ascending order} \\ \mathrm{Arrange\: the\: terms\: in\: ascending\: order} \\ 320,\: 321,\: 324,\: 360,\: 361,\: 366,\: 369,\: 372,\: 385,\: 397,\: 403,\: 454,\: 459,\: 475,\: 477,\: 482,\: 498,\: 513,\: 558,\: 559 \\ Q_1=(\frac{n+1}{4})th \\ Q_1=(\frac{20+1}{4})th=\frac{21}{4}th=5.25th\Rightarrow\frac{361+366}{2}=\frac{727}{2}=363.5 \\ \\ To\text{ get }Q_3 \\ Q_3=(\frac{3(n+1)}{4})th=\frac{3\times21}{4}=\frac{63}{4}=15.75th\Rightarrow\frac{477+482}{2}=\frac{959}{2}=479.5 \end{gathered}$

STEP 6: Find the Interquartile Range

$\begin{gathered} IQR=Q_3-Q_1 \\ \text{IQR}=479.5-363.5 \\ \text{IQR}=116 \end{gathered}$

Hence, the interquartile range of the data is 116

3 0

1 year ago

Suppose $1000 is invested at 8%, compounded quarterly. How much is in the account at the end of 4 years?

guajiro [1.7K]

The correct answer is $320

3 0

2 years ago

Which facts could be applied to simplify this expression? Check all that apply.

kykrilka [37]

The answer is B, C, and D. Like terms are terms with all the same variable, so 5x and -x are like terms.

C is correct. If we add -x to 5x, we get 4x. The other numbers remain unchanged because they have no like terms.

D is correct. Applying the rule of like terms, which is that like terms are numbers with the same variable, only add together numbers with the same variable.

Hope this helps!

3 0

3 years ago

Read 2 more answers

Use the grouping method to factor the polynomial below completely.

RSB [31]

The correct answer is D

5 0

3 years ago