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3 years ago

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A reporter determines a baseball player’s batting average, which is a ratio of the number of hits to number of times at bat. The

result is shown on a calculator as 0.212121....Write this repeating decimal as a fraction.

1 answer:

Tpy6a [65]3 years ago

6 0

Answer:

21/99 or 7/33

Step-by-step explanation:

x = 0.212121

Then we multiple the decimal and x by hundred.

100x = 21.212121

Then we subtract the 21.212121 by 0.212121.

100x = 21.212121 - 0.212121

But when you are subtracting 100x, you need to subtract 100x by x because in the first step it said x = 0.212121.

100x - x = 21.212121 - 0.212121

You will have at the end is

99x = 21

Divide 99 on both side and you left with

21/99 or 7/33 simplified version

You might be interested in

Suppose that the distance, in miles, that people are willing to commute to work is an exponential random variable with a decay p

garik1379 [7]

Answer:

<em>m</em> = $\frac{1}{20}$
<em>μ</em> = 20
<em>σ </em>= 20

The probability that a person is willing to commute more than 25 miles is 0.2865.

Step-by-step explanation:

Exponential probability distribution is used to define the probability distribution of the amount of time until some specific event takes place.

A random variable <em>X</em> follows an exponential distribution with parameter <em>m</em>.

The decay parameter is, <em>m</em>.

The probability distribution function of an Exponential distribution is:

$f(x)=me^{-mx}\ ;\ m>0, x>0$

<u>Given</u>: The decay parameter is, $\frac{1}{20}$

<em>X</em> is defined as the distance people are willing to commute in miles.

The decay parameter is <em>m</em> = $\frac{1}{20}$ .
The mean of the distribution is: $\mu=\frac{1}{m}=\frac{1}{\frac{1}{20}}=20$ .
The standard deviation is: $\sigma=\sqrt{variance}= \sqrt{\frac{1}{(m)^{2}} } =\frac{1}{m} =\frac{1}{\frac{1}{20}} =20$

Compute the probability that a person is willing to commute more than 25 miles as follows:

$P(X>25)=\int\limits^{\infty}_{25} {\frac{1}{20} e^{-\frac{1}{20}x}} \, dx \\=\frac{1}{20}|20e^{-\frac{1}{20}x}|^{\infty}_{25}\\=|e^{-\frac{1}{20}x}|^{\infty}_{25}\\=e^{-\frac{1}{20}\times25}\\=0.2865$

Thus, the probability that a person is willing to commute more than 25 miles is 0.2865.

7 0

3 years ago

Evaluate the Riemann sum for f(x) = 3 - 1/2 times x between 2 and 14 where the endpoints are included with six subintervals taki

Digiron [165]

Answer:

-6

Step-by-step explanation:

Given that :

we are to evaluate the Riemann sum for $f(x) = 3 - \dfrac{1}{2}x$ from 2 ≤ x ≤ 14

where the endpoints are included with six subintervals, taking the sample points to be the left endpoints.

The Riemann sum can be computed as follows:

$L_6 = \int ^{14}_{2}3- \dfrac{1}{2}x \dx = \lim_{n \to \infty} \sum \limits ^6 _{i=1} \ f (x_i -1) \Delta x$

where:

$\Delta x = \dfrac{b-a}{a}$

a = 2

b =14

n = 6

∴

$\Delta x = \dfrac{14-2}{6}$

$\Delta x = \dfrac{12}{6}$

$\Delta x =2$

Hence;

$x_0 = 2 \\ \\ x_1 = 2+2 =4\\ \\ x_2 = 2 + 2(2) \\ \\ x_i = 2 + 2i$

Here, we are using left end-points, then:

$x_i-1 = 2+ 2(i-1)$

Replacing it into Riemann equation;

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} \begin {pmatrix}3 - \dfrac{1}{2} \begin {pmatrix} 2+2 (i-1) \end {pmatrix} \end {pmatrix}2$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - (2+2(i-1))$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - (2+2i-2)$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 -2i$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 2i$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - 2 \lim_{n \to \infty} \sum \imits ^{6}_{i=1} i$

Estimating the integrals, we have :

$= 6n - 2 ( \dfrac{n(n-1)}{2})$

= 6n - n(n+1)

replacing thevalue of n = 6 (i.e the sub interval number), we have:

= 6(6) - 6(6+1)

= 36 - 36 -6

= -6

5 0

2 years ago

A pizza with a diameter of 8 inches costs $10 and a pizza

Rina8888 [55]

Answer:

8 inch is your best buy

Step-by-step explanation:

8inch diameter =10 dollars

5 inch radius = 12 dollars

so if we get each equal to the diameter it should be 10 inch and that would be 24 dollars vs . 8 in for 10 dollars. So best buy would be 8 inch

8 0

2 years ago

A car travels a distance of D km at 80 km/h and arrives 20 min late. If the car travels at

Leya [2.2K]

It’s would be 160 km since 160/80x60=120 min and 160/120x60=80min

4 0

1 year ago

On Tuesday kali by five CDs on Wednesday Half of all the CDs that she had were destroyed on Thursday there were 22 left how many

pshichka [43]

Answer:

39

Work:

(x+5)/2=22

We will reverse this equation.

We will start by moving the 2 through inverse operations.

22x2=44

Now we have the equation

x+5=44

We will subtract 5

44-5=39

x=39

the unknown variable equals 39

Kali had 39 CDs on Monday

4 0

3 years ago