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3 years ago

Find the length of the third angle of a triangle given that the first two angles are 35 and 70.

1 answer:

7 0

Hi,

the interior angles of a triangle always add up to 180 degrees. Therefore 35 + 70 + ? = 180.
so, 35+70 = 105. 180-105= 75 degrees.

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Explain how to model the division of –24 by –4 on a number line.

lianna [129]

Answer:

Here's one way to do it.

Step-by-step explanation:

-24 ÷ (-4)

-24 is the final number on the number line

-4 means you count by 4s on the number line moving backwards.

Start at 0 facing forward.
Move backwards in steps of four units from 0 to -24.
Count the number of steps you took (six).

Answer: +6 (The sign is + because you are still facing forward).

8 0

3 years ago

Estimate √97.5 / 1.96

evablogger [386]

Answer: 5

Step-by-step explanation:

1. You have the following expression given in the problem above:

$\frac{\sqrt{97.5}}{1.96}$

2. You can estimate the result by rounding the numerator and the denominator.

3. As you can see, you can round up 97.5 to 100.

4. Then, you can round up 1.96 to 2.

5. Therefore, you have:

$\frac{\sqrt{100}}{2}$

$\frac{10}{2}=5$

6. Therefore, the result is 5.

3 0

3 years ago

The distance between bases on a baseball field is 27.43 meters.

Mkey [24]

27.43 * 4.5 = 123.435

Joe jogged 123.435 meters

8 0

3 years ago

f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

Perform the operation given that a = {−3, −2, −1, 0, 1, 2, 3}, b = {−4, −2, 0, 2, 4}, and c = {0, 1, 2, 3, 4}. (enter your answe

Ludmilka [50]

A ∩ c={0,1,2,3}

b ∪ (a ∩ c)={-4,-2,0,1,2,3,4}

7 0

3 years ago