Write 87 tens and 2 ones as a base ten number

Express f(x) = |x-2| +|x+2| in the non-modulus form. Hence, sketch the graph of f.

alexgriva [62]

Recall that

$|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x$

There are three cases to consider:

(1) When $x+2$ , we have $|x+2|=-(x+2)$ and $|x-2|=-(x-2)$ , so

$|x-2|+|x+2|=-(x-2)-(x+2)=-2x-4$

(2) When $x+2\ge0$ and $x-2$ , we get $|x+2|=x+2$ and $|x-2|=-(x-2)$ , so

$|x-2|+|x+2|=-(x-2)+(x+2)=4$

(3) When $x-2\ge0$ , we have $|x+2|=x+2$ and $|x-2|=x-2$ , so

$|x-2|+|x+2|=(x-2)+(x+2)=2x$

So

$|x-2|+|x+2|=\begin{cases}-2x-4&\text{if }x$

4 0

1 year ago

A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the given angular veloci

Gemiola [76]

Answer:

t = 1.57 sec

distance, d = 98.65 mm

Step-by-step explanation:

Given an angle of 540°

At 6 revolutions per second, which is the angular velocity.

Radius, r = 10 mm

We are asked to find the time and the distance.

To find the time, let's use the formula:

$\theta = a*t$

Where $\theta$ = angle in radians.

Converting 540° to radians, we have:

$\theta = 540 * \frac{\pi}{180} = 9.42 rad$

Therefore, from the formula, let's find t.

$\theta = a*t$

$9.42 = 6 * t$

$t = \frac{9.42}{6} = 1.57$

time = 1.57

To find the distance, we have:

$\frac{1.57 * 360}{360} = \frac{d}{2 \pi r}$

$\frac{1.57 * 360}{360} = \frac{d}{2\pi 10}$

$1.57 = \frac{d}{20\pi}$

$d = 20 \pi *1.57$

d = 98.65 mm

Therefore, the time is 1.57 seconds and the distance is 98.65 mm

8 0

2 years ago

A small amphitheater has 8 rows that have 42 seats in each row. If an act needs to keep the first row empty but has all the rest

jok3333 [9.3K]

Answer:

i dont know sorry

Step-by-step explanation:

4 0

2 years ago

A hospital finds that 22% of its accounts are at least 1 month in arrears. A random sample of 425 accounts was taken. What is th

GenaCL600 [577]

Answer:

8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears

Step-by-step explanation:

For each account, there are only two possible outcomes. Either they are at least 1 month in arrears, or they are not. The probability of an account being at least 1 month in arrears is independent from other accounts. So the binomial probability distribution is used to solve this question.

However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .