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2 years ago

What is the side length of a square with half the area of a square with area 198?

Mathematics

1 answer:

Murljashka [212]2 years ago

6 0

The square root of 198 is 14, so that is one side of that square. Divide by 2 to get 7 mm. B

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That you're positive that you should be trying out these difficult math questions, let’s get right to it! The answers to these q

Lemur [1.5K]

Answer:

that you're positive that you should be trying out these difficult math questions, let’s get right to it! The answers to these questions are in a separate section below, so you can go through them all at once without getting spoiled.

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Step-by-step explanation:

5 0

2 years ago

Ordered pair for the point

kupik [55]

Answer:

Step-by-step explanation:

(4, -3)

4 0

3 years ago

Read 2 more answers

When we toss a coin, there are two possible outcomes: a head or a tail. Suppose that we toss a coin 100 times. Estimate the appr

marin [14]

Answer:

96.42% probability that the number of tails is between 40 and 60.

Step-by-step explanation:

I am going to 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:

100 tosses, so $n = 100$

Two outcomes, both equally as likely. So $p = \frac{1}{2} = 0.5$

$E(X) = np = 100*0.5 = 50$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5$

Estimate the approximate probability that the number of tails is between 40 and 60.

Using continuity correction.

$P(40 - 0.5 \leq X \leq 60 + 0.5) = P(39.5 \leq X \leq 60.5)$

This is the pvalue of Z when X = 60.5 subtracted by the pvalue of Z when X = 39.5. So

X = 60.5

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

$Z = \frac{60.5 - 50}{5}$

$Z = 2.1$

$Z = 2.1$ has a pvalue of 0.9821

X = 39.5

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

$Z = \frac{39.5 - 50}{5}$

$Z = -2.1$

$Z = -2.1$ has a pvalue of 0.0179

0.9821 - 0.0179 = 0.9642

96.42% probability that the number of tails is between 40 and 60.

8 0

2 years ago

Find the values of the sine, cosine, and tangent for ZA C A 36ft B 24ft

Reptile [31]

<h2>Question:</h2>

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = $\frac{\sqrt{13} }{2}$ , cos A = $\frac{\sqrt{13} }{3}$ , tan A = $\frac{2 }{3}$

b. sin A = $3\frac{\sqrt{13} }{13}$ , cos A = $2\frac{\sqrt{13} }{13}$ , tan A = $\frac{3}{2}$

c. sin A = $\frac{\sqrt{13} }{3}$ , cos A = $\frac{\sqrt{13} }{2}$ , tan A = $\frac{3}{2}$

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Answer:</h2>

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Step-by-step explanation:</h2>

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

i. First calculate the value of the missing side AB.

Using Pythagoras' theorem;

⇒ (AB)² = (AC)² + (BC)²

Substitute the values of AC and BC

⇒ (AB)² = (36)² + (24)²

Solve for AB

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = $\sqrt{1872}$

⇒ AB = $12\sqrt{13}$ ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of $12\sqrt{13}$ ft (43.27ft).

ii. Calculate the sine of ∠A (i.e sin A)

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = $\frac{opposite}{hypotenuse}$ -------------(i)