All categories

3 years ago

Find the value of x.

Mathematics

1 answer:

Sholpan [36]3 years ago

3 0

Answer:

x = √21.

Step-by-step explanation:

Triangles ADB and BCD are similar.

So their corresponding sides are in the same ratio:

x / 7 = 3 / x

x^2 = 21

x = √21.

You might be interested in

Christina must run around the rectangular soccer field during practice. The football field It measures 60 meters long by 45 mete

Reika [66]

Answer:

210 meters

Step-by-step explanation:

4 0

3 years ago

After 1 minute, a submarine had descended to −280 feet. After 9 minutes, the submarine had descended to −360 feet. Assuming a li

adelina 88 [10]

Answer:

the answer is 640

Step-by-step explanation:

-280-360 = 640

d(t)=-360

= 360*d*t

4 0

2 years ago

Marshall charges $22.00 per hour to cut yards in his neighborhood. Use the ratio of Marshall’s hours worked to the amount earned

Leni [432]

If there are $22 made per hour for 7 hours, you’d add 22 per hour in your table. 1 hour=$22, 2 hours=$44, 3 hours=$66, and so forth. make a table of these numbers up to 7 hours.

4 0

3 years ago

Read 2 more answers

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

I need help!!

netineya [11]

Answer:

2x +21

Step-by-step explanation:

$log_{5} {5}^{(2x - 9)} + log_{3} {729}^{5} \\ \\ = log_{5} {5}^{(2x - 9)} + log_{3} {( {3}^{6} )}^{5} \\ \\ = log_{5} {5}^{(2x - 9)} + log_{3} { {3}}^{6 \times 5} \\ \\ = log_{5} {5}^{(2x - 9)} + log_{3} { {3}}^{30} \\ \\ =(2x - 9) log_{5} {5} + 30 log_{3} { {3}} \\ \\ = (2x - 9).1 + 30(1 )\\ ( \because \: log_{a} { {a}} = 1) \\ \\ = 2x - 9 + 30 \\ \\ = 2x +21$

7 0

3 years ago