Find the nth term of this number sequence 1, 7, 13, 19, ...

How do i solve this?

Xelga [282]

Well this is considerably easy!

Create equivalent expressions in the equation that all have equal bases.

2^x=2^4

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

x=4

Verify each of the solutions by substituting them into 2^x=16

and solving.

x=4

3 0

3 years ago

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation o

Vikki [24]

Answer:

(a) The percent of her laps that are completed in less than 130 seconds is 55%.

(b) The fastest 3% of her laps are under 125.42 seconds.

(c) The middle 80% of her laps are from 126.80 seconds to 132.63 seconds.

Step-by-step explanation:

The random variable X is defined as the number of seconds for a randomly selected lap.

The random variable X is normally distributed with mean, μ = 129.71 seconds and standard deviation, σ = 2.28 seconds.

Thus, $X\sim N(129.71,\ 2.28^{2})$ .

(a)

Compute the probability that a lap is completes in less than 130 seconds as follows:

$P(X$

$=P(Z$

The percentage is, 0.55 × 100 = 55%.

Thus, the percent of her laps that are completed in less than 130 seconds is 55%.

(b)

Let x represents the 3rd percentile.

That is, P (X < x) = 0.03.

⇒ P (Z < z) = 0.03

The value of z for the above probability is:

z = -1.88

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\-1.88=\frac{x-129.71}{2.28}\\x=129.71-(1.88\times 2.28)\\x=125.4236\\x\approx 125.42$

Thus, the fastest 3% of her laps are under 125.42 seconds.

(c)

Let x₁ and x₂ be the values between which the middle 80% of the distribution lie.

That is,

$P(x_{1}$

The value of z for the above probability is:

z = 1.28

Compute the values of x₁ and x₂ as follows:

$-z=\frac{x_{1}-\mu}{\sigma}\\-1.28=\frac{x_{1}-129.71}{2.28}\\x_{1}=129.71-(1.28\times 2.28)\\x=126.7916\\x\approx 126.80$ $z=\frac{x_{2}-\mu}{\sigma}\\1.28=\frac{x_{2}-129.71}{2.28}\\x_{2}=129.71+(1.28\times 2.28)\\x=132.6284\\x\approx 132.63$

Thus, the middle 80% of her laps are from 126.80 seconds to 132.63 seconds.

5 0

4 years ago

WILL MARK BRAINLIEST ' IF YOU DONT KNOW DONT ANSWER

Soloha48 [4]

Answer: A) Alternate Exterior

Step-by-step explanation:

Let's find out the defenition of alternate exterior; "If a pair of parallel lines are cut by a transversal line, then the alternate exterior angles are congruent".

I hope this helps!

8 0

3 years ago

Expand each expression and collect like terms. a. -3(2p - 3q)

emmasim [6.3K]

Answer:

-6p+9q

Step-by-step explanation:

Multiply -3 with 2p and multiply -3 with 3q.

8 0

3 years ago

17 POINTS

notsponge [240]

This problem can be solved with a series of additions and subtractions.

The starting value is 500 and we first subtract 120 because on Monday they withdrew 120 dollars which leaves us with 380 dollars.

Next, we add 50 because on Wednesday they deposited 50 dollars which results in 430.

And, If I am not mistaken, we are done because when Braxton bought their basketball ticket, they used their debt card and did not withdrew from their checking account.

So, the answer is 430 dollars.

8 0

3 years ago