It says "A group buys 5 tickets and 4 popcorns and spends $82"

Tan12=22 over x. Find x

kondaur [170]

Answer:

x=-34.6

Step-by-step explanation:

(x)tan12= 22/x(x)

tan12\xtan12=22/tan12

x= -34.6

6 0

3 years ago

Use mathematical induction to prove that if L is a linear transformation from V to W, then L (α1v1 + α2v2 +· · ·+αnvn)= α1L (v1)

e-lub [12.9K]

Answer:

The proof is shown in the explanation below.

Step-by-step explanation:

Analysis:

The proof by induction focuses on n. In this case, let n = 1, and $L^{1}$ will be a linear operator since $L^{1} = L$

The exercise will show that $L^{n}$ is a linear operator on V and that $L^{n+1}$ is also a linear operator on V. This, follows that:

$L^{n+1} (av) = L(L^{m}(v_{1}+v_{2})\\ = L(L^{m} (v_{1} + L^{m}v_{2})\\ = L(L^{m}v_{1} + L(L^{m}v_{2})\\ = L^{m+1}(v_{1}) + L^{m+1}(v_{2})$

6 0

2 years ago

Read 2 more answers

In a survey of 2,800 people who owned a certain type of car, 560 said they would buy that type of car again. What percent of th

STALIN [3.7K]

20% people were satisfied with the car

Step-by-step explanation:

Percentage of a certain quanitity is calculated by using the following formula

$Percentage=\frac{Quantity}{Total}*100$

Given

Total people surveyed = 2800

People satisfied with the car = 560

So,

$Percentage= \frac{560}{2800}*100\\=0.2*100\\=20\%$

Hence,

20% people were satisfied with the car

Keywords: Percentage

Learn more about percentage at:

#LearnwithBrainly

3 0

3 years ago

The area (

stira [4]

Hello :
f(r) = πr².... r > 0
the domain is : ] 0; + ∞[

4 0

3 years ago

Elderly drivers. In January 2011, The Marist Poll published a report stating that 66% of adults nationally think licensed driver

katrin [286]

Answer:

(a) Hence, the margin of error reported by The Marist Poll was correct.

(b) Based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.

Step-by-step explanation:

We are given that the Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age.

It was also reported that interviews were conducted on 1,018 American adults, and that the margin of error was 3% using a 95% confidence level.

(a) Margin of error formula is given by;

Margin of Error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

where, $\alpha$ = level of significance = 1 - 0.95 = 0.05 or 5%

Standard of error = $\sqrt{\frac{\hat p(1-\hat p)}{n} }$

Also, $\hat p$ = sample proportion of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age = 66%

n = sample of American adults = 1.018

The critical value of z for level of significance of 2.5% is 1.96.

So, Margin of Error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

= $1.96 \times \sqrt{\frac{0.66(1-0.66)}{1,018} }$ = 0.03 or 3%

Hence, the margin of error reported by The Marist Poll was correct.

(b) Now, the pivotal quantity for 95% confidence interval for the population proportion who think that licensed drivers should be required to retake their road test once they turn 65 is given by;

P.Q. = $\frac{\hat p-p}{ \sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ~ N(0,1)

So, 95% confidence interval for p = $\hat p \pm \text{Margin of error}$

= $0.66 \pm 0.03$

= [0.66 - 0.03 , 0.66 + 0.03]

= [0.63 , 0.69]

Hence, based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65 because the interval does not include the value of 70% or more.

7 0

3 years ago