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3 years ago

What is the value for x?

Mathematics

1 answer:

schepotkina [342]3 years ago

3 0

Right of the bat, I know the measure of angle C equals 73° because of the Isosceles Base Angle Theorem. Then, due to the Triangle Sum Theorem, I know that all of the measures in the triangle must add to 180°. To find this, just subtract 73 and 73 from 180. Finally, because angle B equals (6x + 4) and 34°, just set them equal to each other to find the value of x.

180 - 73 - 73 = measure of angle B
34° = measure of angle B

6x + 4 = 34
- 4 - 4
6x = 30
6x / 6 = 30 / 6
x = 5

Hope this helps!

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What is the equation for exponential growth in Biology?

SpyIntel [72]

The exponential growth in biology is A=Pert, where "A" is the ending amount of whatever you're dealing with , "P" is the beginning amount of that same "whatever", "r" is the growth or decay rate, and "t" is time. The formula is related to the compound-interest formula, and represents the case of the interest being "compounded continuously".

8 0

4 years ago

the sum of three numbers is 79. The second number is 5 times the first, while the third is 16 more than the first. Find the Numb

faust18 [17]

Let the 1st number be x; 2nd number be y; 3rd number be z.

x + y + z = 79

x = number we are looking for.
y = x * 5 ==> 5 times the first
z = x + 16 ==> 16 more than the first

Therefor,

x + (x * 5) + (x+16) = 79

1st step, multiply the 2nd number: x * 5 = 5x

x + 5x + x + 16 = 79

Add all like numbers:

7x + 16 = 79

To get x, transfer 16 to the other side and change its sign from positive to negative.

7x = 79 - 16
7x = 63

To get x, divide both sides by 7

7x/7 = 63/7
x = 9

To check. Substitute x by 9.

x + (x * 5) + (x+16) = 79

9 + (9 * 5) + (9 + 16) = 79
9 + 45 + 25 = 79
79 = 79 equal. value of x is correct.

4 0

4 years ago

Read 2 more answers

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

Cloud [144]

Answer:

$z=\frac{13-20}{4}=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu$

$p_v = P(Z$

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

We need to check the conditions in order to use the normal approximation.

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.2=20$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$

The z score is given by this formula:

$z=\frac{x-\mu}{\sigma}$

If we replace we got:

$z=\frac{13-20}{4}=-1.75$

Let's assume that we conduct the following test:

H0: $\mu \geq 20$

H1: $\mu$

We want to check is the score for the student is significantly less than the expected value using random guessing.

So on this case since we have the statistic we can calculate the p value on this way:

$p_v = P(Z$

5 0

3 years ago

Please help NO LINKS

inn [45]

Answer:

(5,-6)

Step-by-step explanation:

This is where the two lines meet. I hope this helps ◕ ◡ ◕

5 0

3 years ago

Read 2 more answers

Given right triangle ABC, what is the value of tan(A)?

Angelina_Jolie [31]

You didn't provide more information regarding triangle but from given options, it seems that triangle has ratio from shortest side to longest side would be 5 : 12 : 13

So 13 would be hypotenuse since it is longest.

Now A cannot be right angle because tangent is not defined at 90°.

Also tan(A) would be ratio of opponent side to adjacent side (think SOH CAH TOA)

So either opposite side would be 5 or 12, and adjacent side would be 12 or 5 respectively.

So the answer is either 5 / 12 or 12 / 5 but only option provided is 12/5 so that would be your answer.

Final answer: 12 / 5

7 0

4 years ago

Read 2 more answers