Brainiest to whoever right

Simplify the radical expression (8+sqrt 11)(8-sqrt 11)

Elina [12.6K]

Foil, and should get 64-11 which equals 53.

3 0

3 years ago

A scatterplot consists of (1, 4.0), (2, 3.3), (3, 3.8), (4, 2.6), and (5, 2.7). The line of best fit used to model the data is y

zhenek [66]

Answer:

b

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The display provided from technology available below results from using data for a smartphone carrier's data speeds at airports

german

Answer:

The null and alternative hypothesis are:

$H_0: \mu=5\\\\H_a:\mu< 5$

Test statistic t=-0.256

P-value = 0.4

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that that smartphone carrier's data speeds at airports is less than 5 mbps.

Step-by-step explanation:

The question is incomplete:

Sample mean (M): 4.79

Sample STD (s): 5.8

Sample size (n): 50

This is a hypothesis test for the population mean.

The claim is that that smartphone carrier's data speeds at airports is less than 5 mbps.

Then, the null and alternative hypothesis are:

$H_0: \mu=5\\\\H_a:\mu< 5$

The significance level is 0.05.

The sample has a size n=50.

The sample mean is M=4.79.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=5.8.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.8}{\sqrt{50}}=0.82$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.79-5}{0.82}=\dfrac{-0.21}{0.82}=-0.256$

The degrees of freedom for this sample size are:

$df=n-1=50-1=49$

This test is a left-tailed test, with 49 degrees of freedom and t=-0.256, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.4) is bigger 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 that smartphone carrier's data speeds at airports is less than 5 mbps.

5 0

3 years ago

3.2 Simplify the following 3.2.1 -2+3(1 - 4) - 2

vovikov84 [41]

Answer:

$-13$

Step-by-step explanation:

$-2+3(1-4)-2$

Simplify:

$-2+3(1-4)-2\\-13$

-13 is your final answer!

5 0

3 years ago

Problem 0: Compute the inverse Laplace Transforms of:

kondaur [170]

Decompose each given F(s) into partial fractions.

$F(s) = \dfrac{s+1}{s(s-1)(s-3)}$

has partial fraction decomposition

$\dfrac{s+1}{s(s-1)(s-3)} = \dfrac as + \dfrac b{s-1} + \dfrac c{s-3}$

Combine the rational terms on the right and solve for the coefficients:

$\dfrac{s+1}{s(s-1)(s-3)} = \dfrac{a(s-1)(s-3) + b s(s-3) + c s(s-1)}{s (s-1) (s-3)}$

$1 = a(s-1)(s-3) + bs(s-3) + c s(s-1)$

$1 = 3 a + (-4 a - 3 b - c) s + (a + b + c) s^2$

$\begin{cases}3a=1 \\ -4a-3b-c = 0 \\ a+b+c=0 \end{cases} \implies a=\dfrac13, b=-\dfrac12, c=\dfrac16$

Then

$F(s) = \dfrac13 \times \dfrac1s - \dfrac12 \times \dfrac1{s-1} + \dfrac16 \times \dfrac1{s-3}$

Using the frequency-shifting property, the inverse transform is

$\boxed{f(t) = \dfrac13 - \dfrac{e^t}2 + \dfrac{e^{3t}}6}$

The other transform can be dealt with in the same manner.

$F(s) = \dfrac1{(s-1)(s-2)(s-3)} = \dfrac a{s-1} + \dfrac b{s-2} + \dfrac c{s-3}$

$\implies 1 = a(s-2)(s-3) + b(s-1)(s-3) + c(s-1)(s-2)$

$\implies 1 = 6 a + 3 b + 2 c + (-5 a - 4 b - 3 c) s + (a + b + c) s^2$

$\implies \begin{cases}6 a + 3 b + 2 c=1 \\ -5a-4b-3c = 0 \\ a+b+c=0\end{cases} \implies a=\dfrac12, b=-1, c=\dfrac12$

$\implies F(s) = \dfrac12 \times \dfrac1{s-1} - \dfrac1{s-2} + \dfrac12 \times \dfrac1{s-3}$

$\implies \boxed{f(t) = \dfrac{e^t}2 - e^{2t} + \dfrac{e^{3t}}2}$

5 0

2 years ago