Please need help on this

A transformation translates the point S (-1,1) down 2 units and right 3 units. What rule describes this translation. A. (x,y)=(x

Fittoniya [83]

Down = -y
right= +x

Hence rule D. is correct

3 0

3 years ago

A Government company claims that an average light bulb lasts 270 days. A researcher randomly selects 18 bulbs for testing. The s

Fofino [41]

Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

In this question, we have that:

$\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2$

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when $X = 260$ . So

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

By the Central Limit Theorem

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

$Z = \frac{260 - 270}{21.2}$

$Z = -0.47$

$Z = -0.47$ has a pvalue of 0.3192.

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

5 0

3 years ago

A quadrilateral with vertices (-3,2),(-5,-4), (4,6), and (7,0) is dilated by a scale factor of 0.5.

Ksenya-84 [330]

Original vertices:
1 (-3, 2)
2 (-5,-4)
3 ( 4, 6)
4 ( 7, 0)

dilated by a scale factor of 0.50

1) -3*0.50 = -1.5 ; 2 * 0.50 = 1 ⇒ (-1.5,1)
2) -5*0.50 = -2.5 ; -4*0.50 = -2 ⇒(-2.5,-2)
3) 4*0.50 = 2; 6*0.50 = 3 ⇒ (2,3)
4) 7*0.50 = 3.5; 0*0.50 = 0 ⇒ (3.5,0)

B.)
-1.5 -2.5 2 3.5
<span> 1 -2 3 0 </span>

6 0

3 years ago

A shop sells stuffed animals. The sales team calculated that today's bear sales were 5 more than 5/4ths the number of all

slega [8]

Answer:

25

Step-by-step explanation:

25-5=20, 5/4*20=25

3 0

3 years ago

(A-6) to the power of 2 turned into equation

weeeeeb [17]

1) acknowledge the rule that anything that’s outside of the bracket applies to EVERYTHING inside of the bracket
2)apply the rule: (A-6)^2

3 0

3 years ago