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3 years ago

∠A and ∠B are vertical angles. ∠A = 65x − 12 and ∠B = 43x + 10 How many degrees are in ∠A?

Mathematics

1 answer:

Margarita [4]3 years ago

7 0

Answer:

53 degrees

Step-by-step explanation:

Vertical angles are congruent so...

65x-12=43x+10

22x=22

x=1

Then add it into the equation of ∠A

m∠A= 65(1)-12

65-12

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Please help very urgent

Alik [6]

Answer:

32, 16, 8, 4, 2, 1

Explanation:

The geometric mean can be represented by $\sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}$ .

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

$a_{n} = a_{1} • r^{n-1}$

Where $a_{n}$ is the nth term, $a_{1}$ is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, $a_{1}$ will simply be 32.

Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

$\sqrt[5]{\frac{a_{6}}{a_{1}}}$ =

$\sqrt[5]{\frac{1}{32}}$ =

$\frac{1}{2}$ .

Therefore: $r = \frac{1}{2}$ .

Using all the information we have, we can find the explicit rule:

$a_{n} = a_{1} • r^{n-1}$

$a_{1}$ = 32
$r = \frac{1}{2}$

$a_{n} = a_{1} • r^{n-1}$ →

$\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}$

________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

$a_{1} = 32 • (\frac{1}{2})^{1-1}$

$a_{1} = 32 • (\frac{1}{2})^{0}$

$a_{1} = 32 • 1$

$a_{1} = 32$

$a_{6} = 32 • (\frac{1}{2})^{6-1}$

$a_{6} = 32 • (\frac{1}{2})^{5}$

$a_{6} = 32 • \frac{1}{32}$

$a_{6} = 1$

3 0

3 years ago

Read 2 more answers

There are 40 grams of sugar in a 12 oz can of Dr Pepper. If your max intake of sugar permitted for the day is 25 grams, how much

LenKa [72]

You would be able to drink 7.5oz of the can while you would only intake 25grams of sugar

7 0

3 years ago

Read 2 more answers

Is 2/3greater than 0.67

pickupchik [31]

Answer:

0.67>2/3

Step-by-step explanation:

If you divide 2 by 3, you will end up with 0.6.

Now, you can compare the two numbers 0.6 and 0.67.

3 0

3 years ago

A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 7 cm per second. Write a formula to exp

Alex Ar [27]

Answer:

r = 7t

or not mathematically,

r(t) = 7t

r(t) means, r, which is a function of t.

Step-by-step explanation:

Initial size of the radius = 0 cm, at t = 0 s

Rate of increase of the radius of the circle = 7 cm/s

dr/dt = 7

dr = 7 dt

∫ dr = 7 ∫ dt

r = 7t + C (C is the constant of integration)

At t = 0, r = 0,

0 = 0 + C

C = 0

r = 7t.

r(t) = 7t

3 0

3 years ago

Thirty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired

Varvara68 [4.7K]

Answer:

$X \sim Binom(n=10, p=0.3)$

And for this case we want to find this probability:

$P(X =2)$

And we can use the probability mass function and we got:

$P(X=2)=(10C2)(0.3)^2 (1-0.3)^{10-2}=0.233$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

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".

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:

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

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.3)$

And for this case we want to find this probability:

$P(X =2)$

And we can use the probability mass function and we got:

$P(X=2)=(10C2)(0.3)^2 (1-0.3)^{10-2}=0.233$

4 0

3 years ago