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3 years ago

Oscar is trying to incorporate more exercise into his busy schedule. He has several short

Mathematics

1 answer:

katovenus [111]3 years ago

7 0

Answer:

The arm routine lasts 10 minutes, and the abs routine lasts 15 minutes.

Step-by-step explanation:

Since Oscar is trying to incorporate more exercise into his busy schedule, and he has several short exercise routines he can complete at home, and last week, he worked out for a total of 35 minutes by doing 2 arm routines and 1 abdominal routine while That this week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 55 minutes exercising, to determine how long does each routine last the following calculation must be performed:

2ARM + 1ABS = 35

4ARM + 1ABS = 55

4ARM + 1ABS - 2ARM - 1ABS = 55 - 35

2ARM = 20

ARM = 20/2

ARM = 10

2 x 10 + ABS = 35

ABS = 15

Therefore, the arm routine lasts 10 minutes, and the abs routine lasts 15 minutes.

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The probability of rain on the last day of July is 95 % . If the probability remains constant for the first seven days of August

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The probability that it rains at most 2 days is 0.00005995233 and the variance is 0.516

<h3>The probability that it rains at most 2 days</h3>

The given parameters are:

Number of days, n = 7
Probability that it rains, p = 95%
Number of days it rains, x = 2 (at most)

The probability that it rains at most 2 days is represented as:

P(x ≤ 2) = P(0) + P(1) + P(2)

Each probability is calculated as:

$P(x) = ^nC_x * p^x * (1 - p)^{n - x}$

So, we have:

$P(0) = ^7C_0 * (92\%)^0 * (1 - 92\%)^{7 - 0} = 0.00000002097$

$P(1) = ^7C_1 * (92\%)^1 * (1 - 92\%)^{7 - 1} = 0.00000168821$

$P(2) = ^7C_2 * (92\%)^2 * (1 - 92\%)^{7 - 2} = 0.00005824315$

So, we have:

P(x ≤ 2) =0.00000002097 + 0.00000168821 + 0.00005824315

P(x ≤ 2) = 0.00005995233

Hence, the probability that it rains at most 2 days is 0.00005995233

This is calculated as:

Mean = np

So, we have:

Mean = 7 * 92%

Evaluate

Mean = 6.44

Hence, the mean is 6.44

<h3>The standard deviation</h3>

This is calculated as:

σ = √np(1 - p)

So, we have:

σ = √7 * 92%(1 - 92%)

Evaluate

σ = 0.718

Hence, the standard deviation is 0.718

<h3>The variance</h3>

We have:

σ = 0.718

Square both sides

σ² = 0.718²

Evaluate

σ² = 0.516

This represents the variance

Hence, the variance is 0.516

Read more about normal distribution at:

brainly.com/question/4079902

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A worldwide organization of academics claims that the mean IQ score of its members is 115, with a standard deviation of 17. A ra

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Answer: The probability of having a sample mean of 115.2 or less for a random sample of this size equal 0.508.

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3 years ago

Sassy Fashions buys dresses at wholesale and then marks them up for retail sale. They recently sold a dress at a 40% discount of

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3 years ago

Find side lengths C and H

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Answer:

$\displaystyle c=\frac{2\sqrt{3}}{3}\\\\\displaystyle h=7\sqrt{2}\\$

Step-by-step explanation:

<u>Right Triangles</u>

A right triangle can be identified by the fact it has an internal angle of 90°. In a right triangle, the trigonometric ratios stand.

Let's consider the triangle to the left. We need to calculate side c, one of the legs of the triangle. We can use the angle adjacent to it (60°) or the angle opposite to it (30°) with the appropriate trigonometric ratio.

We'll use the adjacent angle, and

$\displaystyle tan60^o=\frac{2}{c}$

Solving for c

$\displaystyle c=\frac{2}{tan60^o}=\frac{2}{\sqrt{3}}$

Rationalizing

$\displaystyle c=\frac{2}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}$

Now for the triangle to the right. The side h is the hypotenuse. Again, any of the two angles can be used (though they are equal, for it's an isosceles triangle). For any of them it is true that

$\displaystyle sin45^o=\frac{7}{h}$