A. 6 units <br> B. 12 units <br> C. 21 units <br> D. 25 units <br> Pls help :(

Please help :( Algebra 2 Question

satela [25.4K]

Answer:

number of action figures = 3 + 6(n-1)

at n = 9: number of action figures = 51

Step-by-step explanation:

first row: 3

second row: 6 more than the row before it (3) = 6 + 3 = 9

third row: 6 + 9 = 15

arithmetic series: $a_n = a_1 + (n-1)d$ , where

$a_n$ is the nth term in the output

$a_1$ is the first output

n is the input

d is the difference between terms

here, we are given the row, and we want to figure out the number of action figures. thus, row = input and number of action figures = output.

the first output, in the first row, is 3

the difference between the number of action figures in each row is 6

thus, our formula is

$a_n = 3 + (n-1)6 = 3 + 6(n-1)$

when the row is 9, the number of action figures is equal to

3 + 6(9-1) = 3 + 6 * 8 = 51

8 0

2 years ago

Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of

maria [59]

Answer:

305 °F

Step-by-step explanation:

The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.

<h3>Cooling Model</h3>

The solution to the differential equation described by Newton's law of cooling is the exponential equation ...

y = ab^t +c

where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.

For this problem, the ambient temperature is c=80, and the differences of interest are ...

a = 1200 -80 = 1120

b = (830 -80)/1120 = 75/112

Using these values in the model gives ...

y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t

Note that units of time are hours.

<h3>Application</h3>

We want y when t=4.

y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212

The core temperature after 4 hours is about 305 °F.

__

<em>Additional comment</em>

The differential equation will have a solution of the form ...

$T-T_R=(T_0-T_R)e^{kt}$

where k = ln(75/112) ≈ -0.40101

In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.

5 0

1 year ago

Translate the phrase into an algebraic expression the product of c and 8

MAVERICK [17]

Product is multiplying. when you multiply a letter with a number you don't put any symbols so it would be 8c

6 0

3 years ago

A. -5<br> B. 4<br> C. -4<br> D. 5

Nostrana [21]

The answer is D. In the function $y=4/(x-5)$ , A value of 5 would make the denominator 0. This is undefined, so 5 is excluded.

4 0

3 years ago

Suppose a large shipment of microwave ovens contained 12% defectives. If a sample of size 474 is selected, what is the probabili

melisa1 [442]

Answer:

$P(\hat p>0.14)$

And using the z score given by:

$z = \frac{\hat p -\mu_p}{\sigma_p}$

Where:

$\mu_{\hat p} = 0.12$

$\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149$

If we find the z score for $\hat p =0.14$ we got:

$z = \frac{0.14-0.12}{0.0149}= 1.340$

So we want to find this probability:

$P(z>1.340)$

And using the complement rule and the normal standard distribution and excel we got:

$P(Z>1.340) = 1-P(Z$

Step-by-step explanation:

For this case we have the proportion of interest given $p =0.12$ . And we have a sample size selected n = 474

The distribution of $\hat p$ is given by:

$\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}})$

We want to find this probability:

$P(\hat p>0.14)$

And using the z score given by:

$z = \frac{\hat p -\mu_p}{\sigma_p}$

Where:

$\mu_{\hat p} = 0.12$

$\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149$

If we find the z score for $\hat p =0.14$ we got:

$z = \frac{0.14-0.12}{0.0149}= 1.340$

So we want to find this probability:

$P(z>1.340)$

And using the complement rule and the normal standard distribution and excel we got:

$P(Z>1.340) = 1-P(Z$

4 0

3 years ago

A. 6 units B. 12 units C. 21 units D. 25 units Pls help :(