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2 years ago

PLEASE HELP URGENT!! DONT LINK FILES!!! HELP!!

Mathematics

1 answer:

Tomtit [17]2 years ago

4 0

Answer:

Base = 8

Step-by-step explanation:

Area of a triangle can be calculated as:

Area = 0.5 x Base x Height

The values of the area and the height are given in order to find the length.

A= 52 in^2

Height= 13

First we have to find the base or the length. Using the values above we can set up the equation as:

1. 52= (0.5)(13)(b)

2. 52/0.5(13)

3. b=8

Answer: The length of the guitar or the base would be 8 inches.

I hope this helps and for future problems regarding this topic use the formula above!!

Formula: 0.5 x Base x Height

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2 years ago

A manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective

andriy [413]

Answer:

(a) P(X $\leq$ 20) = 0.9319

(b) Expected number of defective light bulbs = 15

(c) Standard deviation of defective light bulbs = 3.67

Step-by-step explanation:

We are given that a manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random.

Firstly, the above situation can be represented through binomial distribution, i.e.;

$P(X=r) = \binom{n}{r} p^{r} (1-p)^{2} ;x=0,1,2,3,....$

where, n = number of samples taken = 150

r = number of success

p = probability of success which in our question is % of bulbs that

are defective, i.e. 10%

Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.

So, Let X = No. of defective bulbs in a box

Mean of X, $\mu$ = $n \times p$ = $150 \times 0.10$ = 15

Standard deviation of X, $\sigma$ = $\sqrt{np(1-p)}$ = $\sqrt{150 \times 0.10 \times (1-0.10)}$ = 3.7

So, X ~ N( $\mu = 15, \sigma^{2} = 3.7^{2})$

Now, the z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) Probability that this box will contain at most 20 defective light bulbs is given by = P(X $\leq$ 20) = P(X < 20.5) ---- using continuity correction

P(X < 20.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{20.5-15}{3.7}$ ) = P(Z < 1.49) = 0.9319

(b) Expected number of defective light bulbs found in such boxes, on average is given by = E(X) = $n \times p$ = $150 \times 0.10$ = 15.

Standard deviation of defective light bulbs is given by = S.D. = $\sqrt{np(1-p)}$ = $\sqrt{150 \times 0.10 \times (1-0.10)}$ = 3.67

8 0

3 years ago

Using place value how to increase 2384598 by six million

Leno4ka [110]

6 million = 6,000,000

2,384,598 + 6,000,000 = 8,384,598

your answer is 8,384,598

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3 years ago

Y- (z + x - 2); use x = 4, y = 5, and z = 2 Please evaluate using the values given

frez [133]

It's gonna be 5 - (2 + 4 -2)
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therefore, it will be
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Next, distribute the negative to the four and add normally.

= 5 - 4
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3 years ago

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Which is a true statement about an exterior angle of a triangle?

svlad2 [7]

Answer:

B. It forms a linear pair with one of the interior angles of the triangle.

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3 years ago