Find the area.<br> Don't need explanation

Draw algebra tile models to prove that 4+8x and 4(2x+1) are equivalent

irina [24]

4*(2x+1)=(2x+1)+(2x+1)+(2x+1)+(2x+1)=
2x+2x+2x+2x+1+1+1+1=
=8x+4
I hope this is ok !

4 0

4 years ago

The distribution of the baggage weights for passengers using a particular airline has a mean of 19.4 lbs and a standard deviatio

cupoosta [38]

We are to find the probability that the weight of total luggage for a sample of 100 passengers is less than 2100.

The mean weight of the luggage of passengers will be 2100/100 = 21.

So we have to find the probability of the mean weight to be less than 21.

Average weight = u = 19.4
Standard deviation = 5.3

Since we are dealing with a sample of 100. We will use the standard error.

Standard error = $\frac{s}{ \sqrt{n} }= \frac{5.3}{ \sqrt{100} }=0.53$

Now we have to convert the weight to z-score

$z= \frac{x-u}{ \frac{s}{ \sqrt{n} } }$

$z= \frac{21-19.4}{0.53}=3.018$

From z table we can find the probability of z being less than 3.018 is 99.87%.

Therefore, the probability that for (a random sample of) 100 passengers, the total luggage weight is less than 2,100 lbs is 99.87%

8 0

4 years ago

Read 2 more answers

A college theater charges $5 handling fee. tickets cost $58. what would the slope be

schepotkina [342]

The slope would be 58.

Slope = (change in y) / (change in x)

That relationship is established by the fixed cost of each ticket ($58). The handling fee is a constant that would shift the curve upward by $5, but would have no effect on the slope of the line since it is completely independent from the number of tickets being purchased (x).

6 0

4 years ago

A patio was to be laid in a design with one tile in the

Vlada [557]

Answer:

10

Step-by-step explanation:

The number of tiles in the design is 1 + 2 + 3 + ...

We can model this as an arithmetic series, where the first term is 1 and the common difference is 1. The sum of the first n terms of an arithmetic series is:

S = n/2 (2a₁ + d (n − 1))

Given that a₁ = 1 and d = 1:

S = n/2 (2(1) + n − 1)

S = n/2 (n + 1)

Since S ≤ 60:

n/2 (n + 1) ≤ 60

n (n + 1) ≤ 120

n must be an integer, so from trial and error:

n ≤ 10

Mr. Tong should use 10 tiles in the final row to use the most tiles possible.

7 0

3 years ago

A school authority claims that the average height of students is 178 cm. A researcher has taken a well-designed survey and his s

Hunter-Best [27]

Answer:

d) The difference exists due to chance since the test statistic is small

Step-by-step explanation:

From the given information:

Population mean = 178 cm

the sample mean = 177.5 cm

the standard deviation = 2

the sample size = 25

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis:

$H_o: \mu = 178$

Alternative hypothesis:

$H_1: \mu \neq 178$

The t-test statistics is determined by using the formula:

$t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t = \dfrac{177.5 - 178}{\dfrac{2}{\sqrt{25}}}$

$t = \dfrac{-0.5}{\dfrac{2}{5}}}$

$\mathbf{t= -1.25}$

Degree of freedom df = n- 1

Degree of freedom df = 25 - 1

Degree of freedom df = 24

At the level of significance ∝ = 0.05, the critical value = 2.064

Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance

Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small

5 0

3 years ago

Find the area. Don't need explanation