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allochka39001 [22]

3 years ago

8

Tiwa spent 1 1/2 hours setting up her computer. It took her 3 times as long to install the software. How long did it take Tiwa t

o set up the computer and install the software

1 answer:

MrRissso [65]3 years ago

4 0

Answer:

Total time spent by Tiwa to set up the computer and install software = 6 hours

Step-by-step explanation:

Given:

Time spent by Tiwa to set up her computer = $1\frac{1}{2}\ hours$

Time spent to install the software is 3 times the time she took to set up the computer.

To find the total time Tiwa took to set up her computer and install the software.

Solution:

Time spent by Tiwa to install the software can be given as:

⇒ $3\times 1\frac{1}{2} \ hours$

<em>In order to multiply mixed numbers we first change them to fractions.</em>

We multiply the denominator to the whole number and add the numerator to it. Then we write the number as numerator of a fraction with the same denominator.

So, $1\frac{1}{2}=\frac{3}{2}$

So, we have:

⇒ $3\times \frac{3}{2}\ hours$

⇒ $\frac{9}{2}\ hours$

Total time spent by Tiwa to set up the computer and install software can be given as:

⇒ $\frac{3}{2}\ hours+\frac{9}{2}\ hours$

Since denominators are same, so we simply add the numerators.

⇒ $\frac{3+9}{2}\ hours$

⇒ $\frac{12}{2}\ hours$

⇒ $6\ hours$

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3 years ago

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard devi

Gelneren [198K]

Answer:

a) N(4, 1.6)

b) 4 days

c) $Z = 0.69$

d) There is a 30.85% probability of spending more than 4.8 days in recovery.

e) There is a 11.62% probability of spending between 3.2 and 3.7 days in recovery.

f) The 90th percentile for recovery times is 6.05 days.

Step-by-step explanation:

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.

In this problem, we have that:

Mean of 4 days and a standard deviation of 1.6 days. So $\mu = 4, \sigma = 1.6$ .

a. What is the distribution of X?

This is normal with mean 4 and standard deviation 1.6. So N(4, 1.6).

b. What is the median recovery time?

For the normal distribution, the median is the same as the mean. So the median recovery time is 4 days.

c. What is the Z-score for a patient that took 5.1 days to recover?

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

$Z = \frac{5.1 - 4}{1.6}$

$Z = 0.69$

d. What is the probability of spending more than 4.8 days in recovery?

This probability is 1 subtracted by the pvalue of Z when $X = 4.8$ . So

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

$Z = \frac{5.8 - 4}{1.6}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915.

This means that there is a 1-0.6915 = 0.3085 = 30.85% probability of spending more than 4.8 days in recovery.

e. What is the probability of spending between 3.2 and 3.7 days in recovery?

This probability is the pvalue of Z when X = 3.7 subtracted by the pvalue of Z when X = 3.2. So:

X = 3.7

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

$Z = \frac{3.7 - 4}{1.6}$

$Z = -0.19$

$Z = -0.19$ has a pvalue of 0.4247

X = 3.2

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

$Z = \frac{3.2 - 4}{1.6}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085

This means that there is a 0.4247 - 0.3085 = 0.1162 = 11.62% probability of spending between 3.2 and 3.7 days in recovery.

f. The 90th percentile for recovery times is

This probability is the value of X when Z has a pvalue of 0.90. So it is X when Z = 1.28.

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

$1.28 = \frac{X - 4}{1.6}$

$X = 4 = 1.28*1.6$

$X = 6.05$

The 90th percentile for recovery times is 6.05 days.

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3 years ago

WILL MARK BRAINLIEST consider the polynomial expression below x^3-3x^2+81x-243 rewrite the polynomial in the form (x-d)(x-e)(x+f

Natali [406]

Answer:

(x - 3)(x - 9i)(x + 9i)

Step-by-step explanation:

note that x = 3 gives

3³ - 3(3)² + 81(3) - 243 = 27 - 27 + 243 - 243 = 0, hence

x = 3 is a root and (x - 3) is a factor

x³ - 3x² + 81x - 243 ÷ (x - 3)

= (x - 3)(x² + 81)

solve x² + 81 = 0 ⇒ x² = - 81 ⇒ x = ± 9i, thus

x³ - 3x² + 81x - 243 = (x - 3)(x - 9i)(x + 9i) ← in factored form

3 0

3 years ago

Read 2 more answers