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andriy [413]
2 years ago
9

What is the area of △ABC ? Enter your answer, as a decimal, in the box. Round only your final answer to the nearest tenth. units

² Triangle A B C has leg A C labeled 10 and leg B C labeled 17. Angle A C B is labeled 25.1 degrees.
Mathematics
1 answer:
fiasKO [112]2 years ago
5 0

Answer: 36.1\ units^2

Step-by-step explanation:

You need to use the SAS area formula. This is:

A=\frac{a*b*sin(\alpha)}{2}

Given the triangle ABC, you know that:

a=AC=10\ units\\b=BC=17\ units\\\alpha=\angle ABC=25.1\°

 Therefore, substituting these values into the formula, you get that the area of the triangle ABC is:

A=\frac{(10\ units)(17\ units)*sin(25.1\°)}{2}\\\\A=36.1\ units^2

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An article written for a magazine claims that 78% of the magazine's subscribers report eating healthily the previous day. Suppos
Schach [20]

Answer:

89.44% probability that less than 80% of the sample would report eating healthily the previous day

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.78, n = 675

So

\mu = E(X) = np = 675*0.78 = 526.5

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{675*0.78*0.22} = 10.76

What is the approximate probability that less than 80% of the sample would report eating healthily the previous day?

This is the pvalue of Z when X = 0.8*675 = 540. So

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

Z = \frac{540 - 526.5}{10.76}

Z = 1.25

Z = 1.25 has a pvalue of 0.8944

89.44% probability that less than 80% of the sample would report eating healthily the previous day

8 0
3 years ago
A rePrism measures 6.7 cm by 3.2 cm by 9 cm what is the volume of the rectangle prism
Blizzard [7]

Answer:

The volume is 192.96

Step-by-step explanation:

You multiply length x width x height to find the volume.

6 0
3 years ago
Help!!! Choose the product . - 6p ^ 3 * (3p ^ 2 + 5p - 1)
Lunna [17]

Answer:

-18p^{5} -30p^{4} +6p^{3}

Step-by-step explanation:

(-6p^{3} )(3p^2+5p-1)

(-6p^3)(3p^2)+(-6p^3)(5p)+(-6p^3)(-1)

-18p^{5} -30p^{4} +6p^{3}

<em>hope this helps.....</em>

8 0
2 years ago
If the area of the rectangle is 130 square inches then what is the rectangles height, h
fomenos

Answer:

130/l in where l is the length of the rectangle

Step-by-step explanation:

The formula for area of a rectangle is length by width where the width is the height of the rectangle

Given that area=130 in²

Lets assume the length of this rectangle is =l inches

Then ;

A=l*w

130 =l*w

130/l = w

130/l in = height

5 0
3 years ago
Factor x^2+6x-16 into the form (x+a)(x-b), what is a and b?
vfiekz [6]

Answer:

a=-8 b=2

Step-by-step explanation:

x^2+6x-16

x^2+(8-2)x-16=0

x^2+8x-2x-16=0

X(X+8)-2(X+8)=0

(X+8)(x-2)=0

Compare with (X+a)(X+b)

Where we get a=-8 b=2

8 0
2 years ago
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