Please Help :( Due tomorrow 5/21

A right triangle has the hypotenuse c = 12 cm and an angle A = 30°. Find the length of side a, which is opposite angle A. A. 7.4

vagabundo [1.1K]

On the one hand we know that sin(30) = 1/2. On the other hand we know that sin(A) = a/c. From these two relations we obtain that 1/2 = a/c <=> 1/2 = a/12 <=> a = 12*1/2 <=> a = 6. So the answer is D. 6cm.

5 0

3 years ago

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If

djyliett [7]

Answer:

Option a. 0.9811

Step-by-step explanation:

First, you need to use a normal distribution table to solve this. If you don't have it, then see the attached table so you can guide yourself.

Now, we want to know the probability of randomly select 75 women whose height have a mean between 63 and 65 inches, knowing that in general, the mean is 63.5 and standard deviation of 2.5

To do this, you should calculate first the Z score value for both heights, one for 63 inches and the other with 65 inches. Then, with those values, we'll look the table to get the area under the curve, and thus, the probability. To calculate Z use the following expression:

Z = x - μ / (σ/√n)

Where:

μ: mean height

σ: standard deviation

x: height required

n: sample population

We have all the data so let's calculate both values of Z:

Z1 = 63 - 63.6 / (2.5/√75) = -2.08

Z2 = 65 - 63.6 / (2-5/√75) = 4.85

With these Z score, let's watch the table, and see which area belongs to,

In the case of Z1, the area is 0.0188, while Z2 is 1.

To know the probability, all we need to do is substract those values:

P = 1 - 0.0188 = 0.9812

Option a) is the most accurate and closest result to this.

5 0

4 years ago

(3 points)

Snezhnost [94]

Answer:

The exponential Function is $20+12h=200$ .

Farmer will have 200 sheep after 15 years.

Step-by-step explanation:

Given:

Number of sheep bought = 20

Annual Rate of increase in sheep = 60%

We need to find that after how many years the farmer will have 200 sheep.

Let the number of years be 'h'

First we will find the Number of sheep increase in 1 year.

Number of sheep increase in 1 year is equal to Annual Rate of increase in sheep multiplied by Number of sheep bought and then divide by 100.

framing in equation form we get;

Number of sheep increase in 1 year = $\frac{60}{100}\times20 = 12$

Now we know that the number of years farmer will have 200 sheep can be calculated by Number of sheep bought plus Number of sheep increase in 1 year multiplied by number of years is equal to 200.

Framing in equation form we get;

$20+12h=200$

The exponential Function is $20+12h=200$ .

Subtracting both side by 20 using subtraction property we get;

$20+12h-20=200-20\\\\12h=180$

Now Dividing both side by 12 using Division property we get;

$\frac{12h}{12} = \frac{180}{12}\\\\h =15$

Hence Farmer will have 200 sheep after 15 years.

6 0

3 years ago

(-3c+6) + (-c+8) simplify with a step by step please

mel-nik [20]

Step-by-step explanation:

$= ( - 3c + 6) + ( - c + 8)$

$= - 3c + 6 - c + 8$

$= - 3c - c + 6 + 8$

= -4c + 14

hence -4c + 14 is the answer ...

hope it helped !!

6 0

2 years ago

Simplify . 16x3y2/36xy2z3

dezoksy [38]

$\frac{16 {x}^{3} {y}^{2} }{36x {y}^{2} {z}^{3} } = \frac{4 {x}^{2} }{9 {z}^{3} } \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ - a} = \frac{1}{ {x}^{a} }$

3 0

3 years ago