All categories

4 years ago

explain step by step how to solve. please point out any similarities in the steps used for each question

Mathematics

1 answer:

Mamont248 [21]4 years ago

6 0

#1
m∠A=180 - 115 - 24 = 41°

By the law of sines:

b/sinB = a/sinA ⇒
b = (a*sinB)/sinA = (21*sin24°)/sin41° = (21*0.4067)/0.656 ≈ 13

c/sinC = a/sinA ⇒
c = (a*sinC)/sinA = (21*sin115°)/sin41° = (21*0.9063)/0.656 ≈ 29

#2
m∠C=180 - 119 - 27 = 34°

By the law of sines:

b/sinB = a/sinA ⇒
b = (a*sinB)/sinA = (13*sin119°)/sin27° = (13*0.8746)/0.454 ≈ 25

c/sinC = a/sinA ⇒
c = (a*sinC)/sinA = (13*sin34°)/sin27° = (13*0.5592)/0.454 ≈ 16

#3
m∠C=180 - 57 - 37 = 86°

By the law of sines:

c/sinC = a/sinA ⇒
c = (a*sinC)/sinA = (11*sin86°)/sin57° = (11*0.9976)/0.8387 ≈ 13.1

You might be interested in

What is the area of the circle?

dmitriy555 [2]

We know that the area of a circle has the formula A=πr²

We are given the diameter, and as we know that the diameter is twice the radius, we can divide the given diameter by 2.

27 ÷ 2= 13.5

Now, plug-in the number into the formula.

A=πr²

A=π×13.5²

A=π×182.25

(Assume π=3.14)

A=3.14 × 182.25

A=572.265

A=572.3 square meters.

Therefore, the area of the circle is 572.3 square meters.

8 0

3 years ago

Evaluate each expression if A=Z, B=5, X=4, and N=10. what is the answer for [a+8 (b-2)]^2÷4

nalin [4]

Hi!

<h3>Put in the values. </h3>

[z+8(5-2)]^2/4

<h3>Now use PEMDAS to solve. </h3>

Parentheses - Subtraction

[z+8*3]^2/4

Parentheses - Multiplication

[z+24]^2/4

Exponents

z+576/4

Division

<h2>When you evaluate [a+8 (b-2)]^2÷4, you get z + 144</h2>

Hope this helps! :)

-Peredhel

8 0

3 years ago

You have drawn a simple random sample of 36 college students, asking each student how much rent they pay per month. You obtain a

Karo-lina-s [1.5K]

Answer:

$573-1.690\frac{22}{\sqrt{36}}=566.8033$

$573+1.690\frac{22}{\sqrt{36}}=579.1967$

And the 90% confidence interval would be between [566.80 and 579.20]

Step-by-step explanation:

Information given

$\bar X=573$ represent the sample mean

$\mu$ population mean (variable of interest)

s=22 represent the sample standard deviation

n=36 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are given by:

$df=n-1=36-1=35$

The Confidence level is 0.90 or 90%, the significance would be $\alpha=0.1$ and $\alpha/2 =0.05$ , and the critical value for this case would be $t_{\alpha/2}=1.690$

And replacing we got:

$573-1.690\frac{22}{\sqrt{36}}=566.8033$

$573+1.690\frac{22}{\sqrt{36}}=579.1967$

And the 90% confidence interval would be between [566.8033 and 579.1967]

6 0

4 years ago

: A theater sells tickets for a concert. Adult tickets sell for $6.50 each, and children's tickets sell for $3.50 each. The thea

BARSIC [14]

Answer: 321 adult tickets and 227 children tickets were sold.

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of children tickets that were sold.

The total number of tickets that the theatre sold is 548. This means that

x + y = 548

Adult tickets sell for $6.50 each, and children's tickets sell for $3.50 each. The total ticket sales was $2881. This means that

6.5x + 3.5y = 2881 - - - - - - - - - - -1

Substituting x = 548 - y into equation 1, it becomes

6.5(548 - y) + 3.5y = 2881

3562 - 6.5y + 3.5y = 2881

- 6.5y + 3.5y = 2881 - 3562

- 3y = - 681

y = - 681/ -3

y = 227

x = 548 - y = 548 - 227

x = 321

5 0

3 years ago

What is the slope of the line that passes through the points (-3,2) and (-1,-5)

Oduvanchick [21]

Answer:

m = -7/2

Step-by-step explanation:

(y2-y1) / (x2-x1)

(-5 - 2) / ( -1 -3)

= -7/2

hope that helps :D

7 0

3 years ago