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3 years ago

1. Justin’s car can travel 77.5 miles using 3.1 gallons of gas.

2 answers:

Nadusha1986 [10]3 years ago

5 0

Distance/fuel=ratio 77.5/3.1 is proportional to xdistance/8.2 77.5/3.1=x/8.2 multiply both sides by (3.1*8.2) 635.5=3.1x divide both sides by 3.1 205=x 205 miles 2. easy peasy one way is boys+15=girls boys+girls=85 boys+boys+15=85 minus 15 2boys=70 divide 2 boys=35

lisabon 2012 [21]3 years ago

4 0

1) Write this as a ratio...

77.5 miles / 3.1 gallons = x miles / 8.2 gallons

Solve for x... multiply by 8.2 gallons on both sides (that cancels it on the right) side of the equation.

8.2 gallons * 77.5 miles / 3.1 gallons = x
635.5/ 3.1 = x
211.83 miles = x

Justin travels 211.83 miles on 8.2 gallons of gas

2) If we let boys = b, then girls has to be b + 15 (since there are 15 more girls than boys). Now together there are 85 members of the band so... boys + girls = 85 and since girls is b + 15, then...

b + b+15 = 85

Now solve for b. First combine like terms...

2b + 15 = 85

Now subtract 15 from each side (cancels the 15 on the left)

2b + 15 - 15 = 85 - 15
2b = 70

Now divide each side by 2 (cancels 2 on the left)

2b / 2 = 70 / 2
b = 35

So there are 35 boys in the band.

Just FYI, that also means there are 35+15 = 50 girls. Just so happens that 50 + 35 = 85 so our work checks!

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The diagram shows a logo

Charra [1.4K]

Answer/Step-by-step explanation:

✔️Find EC using Cosine Rule:

EC² = DC² + DE² - 2*DC*DE*cos(D)

EC² = 27² + 14² - 2*27*14*cos(32)

EC² = 925 - 756*cos(32)

EC² = 283.875639

EC = √283.875639

EC = 16.85 cm

✔️Find the area of ∆DCE:

Area = ½*14*27*sin(32)

Area of ∆DCE = 100.15 cm²

✔️Since ∆DCE and ∆ABE are congruent, therefore,

Area of ∆ABE = 100.15 cm²

✔️Find the area of the sector:

Area of sector = 105/360*π*16.85²

Area = 260.16 cm² (nearest tenth)

✔️Therefore,

Area of the logo = 100.15 + 100.15 + 260.16 = 460.46 ≈ 460 cm² (to 2 S.F)

5 0

3 years ago

With a height of 68 in, Nelson was the shortest president of a particular club in the past century. The club presidents of the

Ivahew [28]

Answer:

a. The positive difference between Nelson's height and the population mean is: $\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in$ .

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: $\\ z = -1.1739 \approx -1.174$ (Nelson's height is below the population's mean 1.174 standard deviations units).

d. Nelson's height is usual since $\\ -2 < -1.174 < 2$ .

Step-by-step explanation:

The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

$\\ z$ is the z-score.

$\\ \mu$ is the population mean.

$\\ \sigma$ is the population standard deviation.

From the question, we have that:

Nelson's height is 68 in. In this case, the raw score is 68 in $\\ x = 68$ in.
$\\ \mu = 70.7$ in.
$\\ \sigma = 2.3$ in.

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson's height and the mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

$\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in$ .

That is, the positive difference is 2.7 in.

b. How many standard deviations is that [the difference found in part (a)]?

To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:

$\\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174$

In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.

c. Convert Nelson's height to a z score.

Using formula [1], we have

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{68\;in - 70.7\;in}{2.3\;in}$

$\\ z = \frac{-2.7\;in}{2.3\;in}$

$\\ z = -1.1739 \approx -1.174$

This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

$\\ -2 < z_{Nelson} < 2$

$\\ -2 < -1.174 < 2$

Then, Nelson's height is usual according to that statement.

7 0

3 years ago

Megan and Suzanne each have a plant. They track the growth of their plants for four weeks. Whose plant grew at a faster rate, an

CaHeK987 [17]

In science, rate is a quantity measured with respect to another measured quantity. For the data given, we get the rate of each by calculating the slope. We do as follows:

Megan's rate = 12 - 4.5 / 4 -1 = 2.5 inches per week
Suzanne's rate = 11 - 5 / 4-1 = 0.5 inches per week

Therefore, the plant that grew at a faster rate would be Megan’s at 2.5 inches per week.

4 0

3 years ago

Read 2 more answers

5x-18<-8 I need help step by step

drek231 [11]

Answer:

x < 2

Step-by-step explanation:

$5x - 18 < - 8 \\ 5x - 18 + 18 < - 8 + 18 \\ 5x < 10 \\ \frac{5x}{5} < \frac{10}{5} \\ x < 2$