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3 years ago

What is the 6th value in the sequence with the explicit formula an=−2n−14?

Mathematics

1 answer:

Zinaida [17]3 years ago

4 0

The 6th value in a sequence is -26.

<u>Step-by-step explanation</u>:

The formula for nth term is a sequence ⇒ an = -2n-14
To find 6th value in a sequence, substitute n=6 in the formula.

an = -2n-14

⇒ a6 = -2(6)-14

⇒ a6 = -12-14

⇒ a6 = -26

∴ The 6th value in a sequence is -26.

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In a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the b

myrzilka [38]

Answer:

D) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/6.

Step-by-step explanation:

The Number of boxes = 6

Box containing a prize = 1

Probability of success, p = box containing a price / number of boxes = 1 /6

Number of trials = 5

Probability of success on exactly 2 trials, r = 2

Hence,

P(r = 2) = nCr * p^r * (1-p)^(n-r)

n = 5 ; r = 2 ; p = 1/6

Using a binomial probability calculator :

P(r = 2) = 0.1608

8 0

4 years ago

3. Angle 6 and Angle 7 are

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Angles 6 and 7 are vertical angles

6 0

3 years ago

A boat’s sail is a right triangle. The length of one side of the sail is 7 feet more than the other side. The hypotenuse is 13 f

Svetach [21]

Answer: the other two sides are 5 feet and 12 feet

Step-by-step explanation:

Length of one side be x , that means the other side is x + 7

by Pythagoras theorem:

$x^{2}$ + $(x+7)^{2}$ = $13^{2}$

expanding , we have:

$x^{2}$ + $x^{2}$ + 14x + 49 = 169

$2x^{2}$ + 14x + 49 - 169 = 0

$2x^{2}$ + 14x - 120 = 0

divide through by 2 , we have

$x^{2}$ + 7x - 60 = 0

By factorizing , we have

(x - 5)(x+12) = 0

Therefore:

x = 5 or x = -12

Since , the side can not be negative , so

x = 5

That means the other side will be 5+ 7 = 12

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4 years ago

A campaign strategist wants to determine whether demographic shifts have caused a drop in allegiance to the Uniformian Party in

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Answer:

d. There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that there is a significant drop in allegiance to the Uniformian Party in Bowie County.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.62\\\\H_a:\pi$

The significance level is 0.05.

The sample has a size n=196.

The sample proportion is p=0.57.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.62*0.38}{196}}\\\\\\ \sigma_p=\sqrt{0.001202}=0.035$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.57-0.62+0.5/196}{0.035}=\dfrac{-0.047}{0.035}=-1.369$

This test is a left-tailed test, so the P-value for this test is calculated as:

$\text{P-value}=P(z$

As the P-value (0.0855) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that there is a significant drop in allegiance to the Uniformian Party in Bowie County.

6 0

3 years ago

For Tran thank you appreciate it

Anestetic [448]

Step-by-step explanation:

Let alpha be the unknown angle. We can set up our sine law as follows:

$\frac{ \sin( \alpha ) }{5 \: m} = \frac{ \sin(42) }{3.6 \: m }$

$\sin( \alpha ) = \frac{5 \: m}{3.6 \: m} \times \sin(42) = 0.929$

Solving for alpha,

$\alpha = arcsin(0.929) = 68 \: degrees$

3 0

3 years ago