12. Graph one period of the function.<br> y= - |6 sin 2πx|<br> Choose the correct graph.

lapo4ka [179]

Answer:

4) distributive property of multiplication over subtraction

8 0

3 years ago

For his phone service, David pays a monthly fee of $23, and he pays an additional $0.07 per minute of use. The least he has been

Sergeu [11.5K]

Answer:

1019/minutes

Step-by-step explanation:

$94.33 - $23 = $71.33

$71.33 ÷ 0.07 = 1019/mins

I hope this helps...

4 0

3 years ago

Need please help with the answer

Sladkaya [172]

Step-by-step explanation:

the volume of a rotating solid out of an xy area in a certain interval is pi times the integral of that area squared (because we are emulating adding the volumes of cylinder slices) in that interval along the given axis.

if that area is defined as the difference between 2 curves, then that difference (of the squares) has to be integrated.

the "outer" curve is y = x² + 3 = R, because it has always the larger y values compared to y = 2x + 1 = r.

the volume of an outer cylinder slice is

pi × R² × dx

and of an internal cylinder slice is

pi × r² × dx

therefore, the volume of the difference "washer" cylinder is

pi×R²×dx - pi×r²×dx = pi×(R² - r²)×dx

and now integrating the infinitely thin washers across the interval [0, 2].

R² = (x²+3)² = x⁴ +6x² + 9

r² = (2x+1)² = 4x² + 4x + 1

R² - r² = x⁴ + 2x² - 4x + 8

the integral of (R² - r²)dx :

1/5 x⁵ + 2/3 x³ - 4/2 x² + 8x = 1/5 x⁵ + 2/3 x³ - 2x² + 8x

in the interval of [0, 2] that gives us

1/5 2⁵ + 2/3 2³ - 2×2² + 8×2 - 0 = 32/5 + 16/3 - 8 + 16 =

= 32/5 + 16/3 + 8 = 96/15 + 80/15 + 120/15 = 296/15

and as final step multiplying this by pi :

296pi/15 = 61.99409503... units³ ≈ 62 units³

3 0

3 years ago

A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during

True [87]

Hello there!

The correct answer is D. 8.

Hope This Helps You!
Good Luck :)

4 0

3 years ago

Researchers obtained a sample of n = 10 children who attended daycare before starting school. The children are given a standardi

attashe74 [19]

Answer:

$t=\frac{55.5-50}{\frac{4.249}{\sqrt{10}}}=4.093$

$p_v =2*P(t_{9}>4.093)=0.00084$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

We can say that at 5% of significance the true mean is significantly different from 50.

Step-by-step explanation:

Data given and notation

53, 57, 61, 49, 52, 56, 58, 62, 51, 56

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X))^2}{n-1}}$

And we got:

$\bar X=55.5$ represent the sample mean

$s=4.249$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =50/tex] represent the value that we want to test [tex]\alpha=0.05$ represent the significance level for the hypothesis test (ASSUMED).

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is equal or not to 50 :

Null hypothesis: $\mu = 50$

Alternative hypothesis: $\mu \neq 50$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{55.5-50}{\frac{4.249}{\sqrt{10}}}=4.093$

P-value

We need to calculate the degrees of freedom first given by:

$df=n-1=10-1=9$

Since is a two-sided tailed test the p value would given by:

$p_v =2*P(t_{9}>4.093)=0.00084$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

We can say that at 5% of significance the true mean is significantly different from 50.

6 0

4 years ago

12. Graph one period of the function. y= - |6 sin 2πx| Choose the correct graph.