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4 years ago

Solve the inequality 5y+16<_56

Mathematics

1 answer:

bearhunter [10]4 years ago

3 0

Answer:

y=8

Step-by-step explanation:

5y+16<56 collect like terms

5y<56-16 subtract

5y<40. Divide both sides by 5

y=8

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It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is actually a normally dis

AlexFokin [52]

Answer:

a) 0.18% of cold sufferers experience fewer than 4 days of symptoms

b) 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

Step-by-step explanation:

Problems of normally distributed samples are 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:

$\mu = 7.5, \sigma = 1.2$

a. What proportion of cold sufferers experience fewer than 4 days of symptoms?

This is the pvalue of Z when X = 4. So

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

$Z = \frac{4 - 7.5}{1.2}$

$Z = -2.92$

$Z = -2.92$ has a pvalue of 0.0018.

So 0.18% of cold sufferers experience fewer than 4 days of symptoms.

b. What proportion of cold sufferers experience symptoms for between 7 and 10 days?

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 7. So

X = 10

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

$Z = \frac{10 - 7.5}{1.2}$

$Z = 2.08$

$Z = 2.08$ has a pvalue of 0.9812.

X = 7

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

$Z = \frac{7 - 7.5}{1.2}$

$Z = -0.42$

$Z = -0.42$ has a pvalue of 0.3372.

So 0.9812 - 0.3372 = 0.644 = 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

8 0

4 years ago

A certain radioactive material decays in such a way that the mass in kilograms remaining after t years is given by the function

Angelina_Jolie [31]

The mass of radioactive material remaining after 50 years would be 48.79 kilograms

<h3>How to determine the amount</h3>

It is important to note that half - life is the time it takes for the amount of a substance to reduce by half its original size.

Given the radioactive decay formula as

m(t)=120e−0.018t

Where

t= 50 years

m(t) is the remaining amount

Substitute the value of t

$m(t) = 120e^-^0^.^0^1^8^(^5^0^)$

$m(t) = 120e^-^0^.^9$

Find the exponential value

m(t) = 48.788399

m(t) = 48.79 kilograms to 2 decimal places

Thus, the mass of radioactive material remaining after 50 years would be 48.79 kilograms

Learn more about half-life here:

brainly.com/question/26148784

#SPJ1

7 0

2 years ago

Show your work for factoring or quadratic formula:

lutik1710 [3]

First, I'd simplify this problem by dividing every term by 2:

x^4 - 4x^3 + 5x^2 - 4x + 4 = 0

Then I'd think of the possible factors of that constant term, 4: They would be plus or minus 1, plus or minus 2, or plus or minus 4.

Let's try x = -4 as a possible root. Setting up and using synthetic division:

____________________
-4 / 1 -4 5 -4 4
-4 32
----------------------------
1 -8 37

This result is not helpful. So, try the possible root +4 instead:
________________
+4 / 1 -4 5 -4 4
   4 0 20 64
   ----------------------------
1 0 5 16 68 4 is not a root because the remainder
(68) is not zero.

Try x = 2:

________________
+2 / 1 -4 5 -4 4
   2 -4 2 -40
     ----------------------------
1 -2 1 -2 0

2 is a root because the remainder is zero.

Continue this process until you've found the other 3 roots.

Hint: Try the possible root x = -2 with the following coefficients:

____________
-2 / 1 -2 1 -2

---------------------

5 0

3 years ago

A chef at a restaurant cooks 90 meals in one day. 35% of the 90 meals were vegetarian. How many meals were vegetarian?

serg [7]

Answer is 31.5% vegetarian. Here is the my work. Hope this helps!