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tester [92]
3 years ago
7

A bag contains 5 red cubes and 7 white cubes. Celinda will select one cube, put it in her pocket, and then select a second cube.

Which expression gives the probability that she will select two red cubes?
Mathematics
1 answer:
GenaCL600 [577]3 years ago
4 0

Answer:

The expression which gives the probability that she will select two red cubes = 5/12 * 4/11 ....

Step-by-step explanation:

According to the statement there are 4 red cubes and 7 white cubes.

The total number of cubes are = 7+5 = 12

If she picks up one red cube then the number of ways of picking up red cubes out of 12 is = 5/12

If she picks up 2nd red cube then  the number of ways of picking up 2nd red cube = 4/11

Therefore the expression which gives the probability that she will select two red cubes = 5/12 * 4/11 ....

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A physician orders 140mg of a medication to give orally. You have 125mg/5mL on hand. What is the correct dose of medication to g
adelina 88 [10]
<h2>Hello!</h2>

The answer is: The correct dose of medication to give is 5.6 mL

<h2>Why?</h2>

To solve this problem we need to establish a relationship between the prescripted medication and the available solution.

Let's write the needed equations to establish the relantionship:

\frac{125mg}{5mL}=1\\\\125mg=5mL

The available solution means 125 mg each 5 mL of solution, so:

\frac{125mg}{5mL}=\frac{140mg}{x}\\\\x*\frac{125mg}{5mL}=140mg\\\\x=140mg*\frac{5ml}{125mg}=\frac{700mg*mL}{125mg}=5.6mL

Hence, the correct dose of medication to give is 5.6 mL of the 125 mg/5mL solution.

Have a nice day!

3 0
3 years ago
Jada solved the equation Negative StartFraction 4 over 9 EndFraction = StartFraction x over 108 EndFraction for x using the step
navik [9.2K]

Answer:

A

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed w
EastWind [94]

Answer:

The p-value obtained is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours

Step-by-step explanation:

Complete Question

fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed with a mean of 700 hours and a standard deviation of 45 hours. Test the hypothesis that mean is 700 hours against the alternative hypothesis that the mean is not equal to 700 hours, if a random sample of 30 bulbs has an average life of 688 hours. Use a P-value in your answer.

Solution

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the mean life of the fluorescent lights is 700 hours.

The alternative hypothesis will now be that the mean life of the fluorescent lights is significantly different from 700 hours.

Mathematically,

The null hypothesis is represented as

H₀: μ = 700

The alternative hypothesis is represented as

Hₐ: μ ≠ 700

To do this test, we will use the z-distribution because no information on the population standard deviation is known

So, we compute the z-test statistic

z = (x - μ₀)/σₓ

x = sample mean = 688 hours

μ₀ = 700 hours

σₓ = standard error = (σ/√n)

σ = standard deviation = 45 hours

n = Sample size = 30

σₓ = (45/√30) = 8.2158383626 = 8.216

z = (688 - 700) ÷ 8.216

z = 1.46

checking the tables for the p-value of this z-statistic

Significance level = 0.05 (This is used when significance level isn't given)

The hypothesis test uses a two-tailed condition because we're testing in two directions.

p-value (for z = 1.46, at 0.05 significance level, with a two tailed condition) = 0.14429

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.14429

0.14429 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours.

Hope this Helps!!

6 0
3 years ago
What number is 21% of 450?
Akimi4 [234]

Answer:

94.5

Step-by-step explanation:

450 / 100 = 4.5

4.5 * 21 = 94.5

HOPE THIS HELPS

PLZ MARK BRAINLIEST

3 0
2 years ago
Please solve 5 f <br> (Trigonometric Equations)<br> #salute u if u solved it
Zanzabum

Answer:

\beta=45\degree\:\:or\:\:\beta=135\degree

Step-by-step explanation:

We want to solve \tan \beta \sec \beta=\sqrt{2}, where 0\le \beta \le360\degree.

We rewrite in terms of sine and cosine.

\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}

\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}

Use the Pythagorean identity: \cos^2\beta=1-\sin^2\beta.

\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}

\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)

\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta

\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0

This is a quadratic equation in \sin \beta.

By the quadratic formula, we have:

\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }

\sin \beta=\frac{2}{2\cdot \sqrt{2} } or \sin \beta=\frac{-4}{2\cdot \sqrt{2} }

\sin \beta=\frac{1}{\sqrt{2} } or \sin \beta=-\frac{2}{\sqrt{2} }

\sin \beta=\frac{\sqrt{2}}{2} or \sin \beta=-\sqrt{2}

When \sin \beta=\frac{\sqrt{2}}{2} , \beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )

\implies \beta=45\degree\:\:or\:\:\beta=135\degree on the interval 0\le \beta \le360\degree.

When  \sin \beta=-\sqrt{2}, \beta is not defined because -1\le \sin \beta \le1

4 0
3 years ago
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