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4 years ago

NEED HELP NOW 100 POINTS 2 PICTURES BELOW PLEASE ANSWER ALL 100 POINTS!!!

Mathematics

2 answers:

saw5 [17]4 years ago

8 0

Answer:

<u>Problem 1 :</u> Option B, x = 9

<u>Problem 2:</u> Option A, r = 45

<u>Problem 3:</u> Option D, m = 7

<u>Problem 4:</u> Option B, b/2 - 4 = 9; Total Bill was $26

<u>Problem 5:</u> Option C, 3h + 5 = 11; h = 2

Step-by-step explanation:

Problem 1

<u>Step 1: Add 3 to both sides </u>

2x - 3 + 3 = 15 + 3

2x = 18

<u>Step 2: Divide both sides by 2 </u>

2x / 2 = 18 / 2

x = 9

Answer: Option B, x = 9

Problem 2

<u>Step 1: Add 4 to both sides </u>

r/3 - 4 + 4 = 11 + 4

r/3 = 15

<u>Step 2: Multiply both sides by 3 </u>

r/3 * 3 = 15 * 3

r = 45

Answer: Option A, r = 45

Problem 3

<u>Step 1: Subtract 7 from both sides </u>

7 + 3m - 7 = 28 - 7

3m = 21

<u>Step 2: Divide both sides by 3 </u>

3m / 3 = 21 / 3

m = 7

Answer: Option D, m = 7

Problem 4

<u>Step 1: Make an expression </u>

b/2 -> You and your friend

-4 -> You owe to your friend

9 -> Total your friend gives you

<u>Equation:</u> b/2 - 4 = 9

<u>Step 2: Add 4 to both sides </u>

b/2 - 4 + 4 = 9 + 4

b/2 = 13

<u>Step 3: Multiply both sides by 2 </u>

b/2 * 2 = 13 * 2

b = $26

Answer: Option B, b/2 - 4 = 9; Total Bill was $26

Problem 5

<u>Step 1: Make an expression </u>

3h -> 3 dollars an hour

+5 -> Initial cost

11 -> Total Cost

<u>Equation:</u> 3h + 5 = 11

<u>Step 2: Subtract 5 from both sides </u>

3h + 5 - 5 = 11 - 5

3h = 6

<u>Step 3: Divide both sides by 3 </u>

3h / 3 = 6 / 3

h = 2

Answer: Option C, 3h + 5 = 11; h = 2

lbvjy [14]4 years ago

6 0

Answer:

Step-by-step explanation:

2x - 3 = 15

2x - 3 + 3 = 15 + 3

2x = 18

x = 18/2

x = 9

2 . r/3 - 4 = 11

r/3 - 4 + 4 = 11 + 4

r/3 = 15

r = 15 * 3

r = 45

3 . 7 + 3m = 28

7 + 3m - 7 = 28 - 7

3m = 21

m = 21/3

m = 7

4 . b/2 - 4 = 9

let b/2 You and your friend

-4 You owe to your friend

9 Total your friend gives you

b/2 - 4 + 4 = 9 + 4

b/2 = 13

b = 13 * 2

b = $26

5 . 3h + 5 = 11

let

3h = 3 dollars per hour

+5 Initial cost

11 Total Cost

3h + 5 - 5 = 11 - 5

3h = 6

h = 6 / 3

h = 2

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Answer:

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Step-by-step explanation:

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let X the random variable who represents the test score of a student taking his final examination. We know from the problem that the distribution for the random variable X is given by:

$X\sim N(\mu =73,\sigma =10.5)$

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

Solution to the problem

We want to find the value of n that satisfy this condition:

$P(71.5 < \bar X$

And we can use the z score formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

And we have this:

$P(\frac{71.5-73}{\frac{10.5}{\sqrt{n}}} < Z$

And we can express this like this:

$P(-0.14286 \sqrt{n} < Z< 0.14286 \sqrt{n} )=0.94$

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$P(-0.14286 \sqrt{n} < Z< 0.14286 \sqrt{n} )=1-2P(Z$

If we solve for $P(Z$ we got:

$P(Z$

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And using this we have this equality:

$-1.881 = -0.14286 \sqrt{n}$

If we solve for $\sqrt{n}$ we got:

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4 years ago

Determine whether the relation is a function: {(6, 1), (8, –3), (6, 7)}.

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Hello there! The answer would be the first one, or No. At least one output results in two inputs.

When dealing with functions: you must remember that x does not repeat. So, lets look at the relation given, {(6, 1), (8, –3), (6, 7)}. You can see that x does repeat, so this is not a function. This eliminates second and fourth option choices. Out of the options A and C, A would be your choice since x is the input value and y is the output value, and there are two input values.

Hope his helps and have a great day!

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4 years ago

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Answer:

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b) 0.9663

c) 0.237

d) 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.5 million tons of cargo per week

Standard Deviation, σ = 0 .82 million tons

We are given that the distribution of number of tons of cargo handled per week is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( port handles less than 5 million tons of cargo per week)

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$P( x < 5) = P( z < \displaystyle\frac{5 - 4.5}{0.82}) = P(z < 0.609)$

Calculation the value from standard normal z table, we have,

$P(x < 5) =0.7287= 72.87\%$

b) P( port handles 3 or more million tons of cargo per week)

$P(x \geq 3) = P(z \geq \displaystyle\frac{3-4.5}{0.82}) = P(z \geq −1.82926)\\\\P( z \geq −1.82926) = 1 - P(z < -1.829)$

Calculating the value from the standard normal table we have,

$1 - 0.0337 = 0.9663 = 96.63\%\\P( x \geq 3) = 96.63\%$

c)P( port handles between 3 million and 4 million tons of cargo per week)

$P(3 \leq x \leq 4) = P(\displaystyle\frac{3 - 4.5}{0.82} \leq z \leq \displaystyle\frac{4-4.5}{0.82}) = P(-1.829 \leq z \leq -0.609)\\\\= P(z \leq -0.609) - P(z < -1.829)\\= 0.271-0.034 = 0.237= 23.7\%$

$P(3 \leq x \leq 4) = 23.7\%$

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We have to find the value of x such that the probability is 0.85.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 4.5}{0.82})=0.85$

$= 1 -P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.85$

$=P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.15$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.036) = 0.15$

$\displaystyle\frac{x - 4.5}{0.82} = -1.036\\x = 3.65$

Thus, 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

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