All categories

3 years ago

What is the area of triangle ABC? Round to the nearest tenth of a square unit. square units

Mathematics

2 answers:

zysi [14]3 years ago

8 0

Answer: A = 61.8 square units

Step-by-step explanation:

Hi, we have to apply the Trigonometric area formula:

A = 1/2 ab sin (c)

Where a and b are the sides ( in this case we use the sides that are given to us, which are 10 and 13 ) and c is the included angle.

So, replacing the formula with the given values:

A = 1/2 (10) (13) sin 72°

A = 61.8 square units

Feel free to ask for more if it´s necessary or if you did not understand something.

Akimi4 [234]3 years ago

6 0

Use the formula.

Area = (1/2)*13*10*sin(72°) ≈ 61.8 units².

You might be interested in

Joshua ran 1.45 miles, and Jasmine ran 1.5 miles who Ran Farther?

Lilit [14]

Jasmine ran faster because 1.45 is less than 1.50 which can also be written as 1.5

7 0

3 years ago

Read 2 more answers

In the diagram, m∠COE = 55°. If m∠2 = 2x and m∠3 = x+10, what is the measure of angle 2?

hram777 [196]

So here is how we are going to get the measure of angle 2.
Since given that angle COE measures 55°, we will equate m∠2 = 2x and m∠3 = x+10 with 55. So, 55 = 2x + x + 10
55 = 3x + 10
55-10 = 3x
45 = 3x << divide both sides by 3 and the result is
15 = x
So now that we know x, we can now solve for angle 2.
m∠2 = 2x
m∠2 = 2(15)
m∠2 = 30°
I hope that this is the answer that you are looking for.

7 0

3 years ago

Read 2 more answers

Island A is 150 miles from Island B. A ship captain travels 310 miles from Island A and then finds that he is off course and 200

wolverine [178]

Answer:

156.37°

Step-by-step explanation:

We solve this above question, using Cosine rule which is given as:

Cos C = a² + b² - c²/2ab

Let the Angle be represented as: x

Cos x = 310² + 200² - 150²/2 × 310 × 200

x = arc cos [ 310² + 200² - 150²/2 × 310 × 200]

x = 23.63°

The angle, in degrees, that he must turn through to head straight for Island B is given as:

180° - 23.63°

= 156.37°

4 0

3 years ago

The age of the children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.8 years old. A fir

Kazeer [188]

Answer:

(1) (c) 5.30 years.

(2) (b) 0.289.

(3) (b) 0.80.

(4) (d) 0.50.

(5) (a) 5.25 years.

Step-by-step explanation:

Let X = age of the children in kindergarten on the first day of school.

The random variable X follows a continuous Uniform distribution with parameters a = 4.8 years and b = 5.8 years.

The probability density function function of X is:

$f_{X}(x)=\left \{ {{\frac{1}{b-a}} ;\ a$

(1)

The expected value of a Uniform random variable is:

$E(X)=\frac{1}{2}(a+b)$

Compute the mean of X as follows:

$E(X)=\frac{1}{2}(a+b)=\frac{1}{2}\times (4.8+5.8)=5.3$

Thus, the mean of the distribution is (c) 5.30 years.

(2)

The standard deviation of a Uniform random variable is:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}=\sqrt{\frac{1}{12}\times (5.8-4.8)^{2}}=0.289$

Thus, the standard deviation of the distribution is (b) 0.289.

(3)

Compute the probability that a randomly selected child is older than 5 years old as follows:

$P(X>5)=\int\limits^{5.8}_{5} {\frac{1}{5.8-4.8}}\, dx\\$

$=\int\limits^{5.8}_{5} {1}\, dx\\=[x]^{5.8}_{5}\\=(5.8-5)\\=0.8$

Thus, the probability that a randomly selected child is older than 5 years old is (b) 0.80.

(4)

Compute the probability that a randomly selected child is between 5.2 years and 5.7 years old as follows:

$P(5.2$

$=\int\limits^{5.7}_{5.2} {1}\, dx\\=[x]^{5.7}_{5.2}\\=(5.7-5.2)\\=0.5$

Thus, the probability that a randomly selected child is between 5.2 years and 5.7 years old is (d) 0.50.

(5)

It is provided that a randomly selected child is at the 45th percentile.

This implies that:

P (X < x) = 0.45

Compute the value of x as follows:

$P (X < x) = 0.45$

$\int\limits^{x}_{4.8} {\frac{1}{5.8-4.8}}\, dx=0.45$

$\int\limits^{x}_{4.8} {1}\, dx=0.45$

$[x]^{x}_{4.8}=0.45$

$x-4.8=0.45\\$

$x=0.45+4.8\\x=5.25$

Thus, the age of the child at the 45th percentile is (a) 5.25 years.

6 0

3 years ago

stan needs a mime.Mime a is offering his services for an intial 75 in addition to 25 per hour.Mime b is offering her services fo

AleksAgata [21]

75 + 25 x = 30 + 40 x
x = 3

If you rent them for 3 hours they have the same payment of 150

8 0

3 years ago