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3 years ago

Please answer this question now

Mathematics

1 answer:

artcher [175]3 years ago

7 0

Answer:

$Area = 538.5 m^2$

Step-by-step Explanation:

Given:

∆XVW

m < X = 50°

m < W = 63°

XV = w = 37 m

Required:

Area of ∆XVW

Solution:

<em>Find side length XW using Law of Sines</em>

$\frac{v}{sin(V)} = \frac{w}{sin(W)}$

W = 63°

w = XV = 37 m

V = 180 - (50+63) = 67°

v = XW = ?

$\frac{v}{sin(67)} = \frac{37}{sin(63)}$

Cross multiply

$v*sin(63) = 37*sin(67)$

Divide both sides by sin(63) to make v the subject of formula

$\frac{v*sin(63)}{sin(63)} = \frac{37*sin(67)}{sin(63)}$

$v = \frac{37*sin(67)}{sin(63)}$

$v = 38$ (approximated to nearest whole number)

$XW = v = 38 m$

<em>Find the area of ∆XVW</em>

$area = \frac{1}{2}*v*w*sin(X)$

$= \frac{1}{2}*38*37*sin(50)$

$= \frac{38*37*sin(50)}{2}$

$Area = 538.5 m^2$ (to nearest tenth).

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Given a point translated from A(1,2) to B(4,4). If a point C at (0,0) is translated in the same way, what will be its new endpoi

FinnZ [79.3K]

Answer:

B.(3,2)

Step-by-step explanation:

Point translated from A(1,2) to B(4,4).

This means that for x, we add 3 units(4 - 1 = 3), while for y, we add two units(4 - 2 = 2).

If a point C at (0,0) is translated in the same way, what will be its new endpoints?

0 + 3 = 3

0 + 2 = 2

B.(3,2)

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3 years ago

GRAVITY The height above the ground of a ball thrown up with a velocity of 96 feet per second from a height of 6 feet is 6+96t-1

Nata [24]

Here the time function is h(t) = [6 + 96t - 16t^2] feet.

The initial height of the ball is 6 feet. That's when t=0. h(0)=[6+0-0] ft = 6 ft.

At t=7 sec, h(t) = [6 + 96t - 16t^2] feet becomes
h(7 sec) = h(t) = [6 + 96(7) - 16(7)^2] feet This produces a large negative number (-106 ft), which in theory indicates that the ball has fallen to earth and burrowed 106 feet into the soil. Doesn't make sense.

Instead, let t=1 sec. Then h(1 sec) = h(t) = [6 + 96(1) - 16(1)^2] feet
=[6 + 96 -16] ft, or 86 ft.

One sec after the ball is thrown upward, it reaches a height of 86 feet. It continues to rise, slowing down, until it finally stops for an instant and then begins to fall towards earth.

6 0

4 years ago

(10 points)Assume IQs of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice

vesna_86 [32]

Answer:

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Step-by-step explanation:

To solve this question, we need to use the binomial and the normal probability distributions.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Probability the president will have an IQ of at least 107.5

IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that $\mu = 100, \sigma = 15$

This probability is 1 subtracted by the p-value of Z when X = 107.5. So

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

$Z = \frac{107.5 - 100}{15}$

$Z = 0.5$

$Z = 0.5$ has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 probability that the president will have an IQ of at least 107.5.

Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So

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

$Z = \frac{130 - 100}{15}$

$Z = 2$

$Z = 2$ has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549$

$P(X \geq 1) = 1 - P(X = 0) = 0.0451$

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?

0.3085 probability that the president will have an IQ of at least 107.5.

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Independent events, so we multiply the probabilities.

0.3082*0.0451 = 0.0139

8 0

3 years ago

11 is 10% more than ?

djyliett [7]

Answer: 21

Step-by-step explanation:

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3 years ago

Read 2 more answers

7 x 11 x 4.5 x 4.5 x 4.5 x 8.5

stepladder [879]

Answer:

59641.3125

Step-by-step explanation:

7 x 11 x 4.5 x 4.5 x 4.5 x 8.5

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346.5 x 4.5 x 4.5 x 8.5

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6 0

3 years ago