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Vesna [10]
2 years ago
10

How do i solve this ​

Mathematics
1 answer:
mylen [45]2 years ago
8 0

Answer:

T = 15

Step-by-step explanation:

<u>I = PRT </u>

I = $270 000

P = 150 000

R = 12% or 0.12

Put in the values for each variable.

270 000 = 150 000 × 0.12 × T

T = 270 000 ÷ 150 000 ÷ 0.12

  = 15

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If the value of a real number x satisfies -2x + 5= -1, then what is the value of 5x
Nitella [24]

-2x + 5 = -1

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divide each side by -2: x = 3

plug in 3: 5(3)

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At one point the average price of regular unleaded gasoline was ​$3.39 per gallon. Assume that the standard deviation price per
irinina [24]

This question was not written completely

Complete Question

At one point the average price of regular unleaded gasoline was ​$3.39 per gallon. Assume that the standard deviation price per gallon is ​$0.07 per gallon and use​ Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​?

Answer:

a) 88.89% lies with 3 standard deviations of the mean

b) i) 84% lies within 2.5 standard deviations of the mean

ii) the gasoline prices that are within 2.5 standard deviations of the​ mean is $3.215 and $3.565

c) 93.75%

Step-by-step explanation:

Chebyshev's theorem is shown below.

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.

3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.

4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.

​

(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

We solve using the first rule of the theorem

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

Hence, k = 3

1 - 1/k²

= 1 - 1/3²

= 1 - 1/9

= 9 - 1/ 9

= 8/9

Therefore, the percentage of gasoline stations had prices within 3 standard deviations of the​ mean is 88.89%

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean?

We solve using the first rule of the theorem

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

Hence, k = 3

1 - 1/k²

= 1 - 1/2.5²

= 1 - 1/6.25

= 6.25 - 1/ 6.25

= 5.25/6.25

We convert to percentage

= 5.25/6.25 × 100%

= 0.84 × 100%

= 84 %

Therefore, the percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean is 84%

What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

We have from the question, the mean =$3.39

Standard deviation = 0.07

μ - 2.5σ

$3.39 - 2.5 × 0.07

= $3.215

μ + 2.5σ

$3.39 + 2.5 × 0.07

= $3.565

Therefore, the gasoline prices that are within 2.5 standard deviations of the​ mean is $3.215 and $3.565

​(c) What is the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​?

the mean =$3.39

Standard deviation = 0.07

Applying the 2nd rule

2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.

the mean =$3.39

Standard deviation = 0.07

μ - 2σ and μ + 2σ.

$3.39 - 2 × 0.07 = $3.25

$3.39 + 2× 0.07 = $3.53

Applying the third rule

3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.

$3.39 - 3 × 0.07 = $3.18

$3.39 + 3 × 0.07 = $3.6

Applying the 4th rule

4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.

$3.39 - 4 × 0.07 = $3.11

$3.39 + 4 × 0.07 = $3.67

Therefore, from the above calculation we can see that the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​ corresponds to at least 93.75% of a data set because it lies within 4 standard deviations of the mean.

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3 years ago
a boat going upstream at 4 mph then travels downstream at 10 mph. what is the rate of the boat in still water​
elixir [45]

Answer:

7 mph

Step-by-step explanation:

If b is the rate of the boat, and s is the rate of the stream, then:

b − s = 4

b + s = 10

Solve the system of equations with substitution or elimination.  Using elimination, add the equations together:

2b = 14

b = 7

The boat's rate is 7 mph.

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3 years ago
A plastic ball is filled with gel to make a stress ball. If the ball has a radius of 4 cm, how much
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Answer:

267.947 cm^{3} of gel is required to fill the plastic ball.

Step-by-step explanation:

<em>The radius of the ball is given as 4 cm.</em>

<em>The gel is filled in the plastic ball, that means the gel occupies the volume of the radius.</em>

The volume of the sphere is given by the formula,

V = \frac{4}{3}(\pi)R^{3} , the R is the radius of sphere.

V = \frac{4}{3}(\pi)(4)^{3} = 267.947 cm^{3}

Thus, the volume of gel required to fill the plastic ball to make it stress ball is

267.947 cm^{3} of gel.

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