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3 years ago

How many ways can 5 friends sit together at the movies in 5 seats?

Mathematics

1 answer:

ss7ja [257]3 years ago

3 0

Answer:

120

Step-by-step explanation:

The number of friends is 5 and there are 5 seats only. So , we can find it out with the help of permutations ,

$\implies ^n P_r = \dfrac{n! }{(n-r)!}$

⇒ 5! / (5-5)!

⇒ 5! / 1!

⇒ 5!

⇒ 5 × 4 × 3 × 2 × 1

⇒ 120

<h3>Hence there are 120 ways by which 5 friends sit together at the movies in 5 seats. </h3>

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A sofa is on sale for 27% off. The sale price is $657.

blondinia [14]

Answer:

If $657 is 27% off, then $657 = 100-27% or 73%.

So you want to know what's 100%. So you use a ratio. 100/73 * $657. Which equals $900.

Step-by-step explanation:

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3 years ago

A consumer advocate group selects a random sample of 205 snow foods in find 174 of them contain more what is indicated on the sn

Zinaida [17]

Answer: (0.809, 0.891)

Step-by-step explanation:

Let p = population proportion for a snack foods that contain more fat grams and was indicated on the snacks nutritional information .

As per given , we have

Sample size : n= 205

Sample proportion: $\hat{p}=\dfrac{174}{205}\approx0.85$

z-value for 90% confidence = 1.645

Confidence interval for p: $\hat{p}\pm z^* \sqrt{\dfrac{p(1-p)}{n}}$

$0.85\pm (1.645)\sqrt{\dfrac{(0.85)(1-0.85)}{205}}\\\\=0.85\pm (1.645)\sqrt{\dfrac{0.85\times0.15}{205}}\\\\= 0.85\pm (1.645)\sqrt{0.000621951219512}\\\\=0.85\pm0.041\\\\=(0.85-0.041,\ 0.85+0.041)\\\\= (0.809,\ 0.891)$

Hence, the required confidence interval = (0.809, 0.891)

5 0

3 years ago

Melissa wants to cover her square tabletop with a tablecloth. The area of the table is 144 in2. Which of the following tableclot

jenyasd209 [6]

Answer:

Step-by-step explanation:

just did the assignment

8 0

3 years ago

Read 2 more answers

A linear function has an x-intercept of 12 and a slope of StartFraction 3 Over 8 EndFraction. How does this function compare to

Nadya [2.5K]

Answer:

(B) It has the same slope and a different y-intercept

Step-by-step explanation:

The table is presented below:

$\left|\begin{array}{c|c}x&y\\----&---\\-\frac{2}{3} &-\frac{3}{4}\\\\-\frac{1}{6}&-\frac{9}{16}\\\\\frac{1}{3}&-\frac{3}{8}\\\\\frac{5}{6}&-\frac{3}{16}\end{array}\right|$

Gradient:

$m=\dfrac{-\frac{9}{16}-(-\frac{3}{4})}{-\frac{1}{6}-(-\frac{2}{3})}\\=\dfrac{-\frac{9}{16}+\frac{3}{4}}{-\frac{1}{6}+\frac{2}{3}}\\=\frac{3}{16}\div \frac{1}{2}\\m=\frac{3}{8}$

Next, we determine its y-intercept

Using the pair $(-\frac{2}{3},-\frac{3}{4})}$ in y=mx+c

$-\frac{3}{4}=(\frac{3}{8})(-\frac{2}{3})+c\\-\frac{3}{4}+\frac{1}{4}=c\\c=-\frac{1}{2}$

Comparing with the linear function has an x-intercept of 12 and a slope of $\frac{3}{8}$ , we find out that It has the same slope and a different y-intercept.

Option B is the correct option.

9 0

3 years ago

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One road crew can pave a section of highway in 15 h. a second crew can do the same job in 10h. how long would it take to pave th

irina1246 [14]

For this case what you can do is an average to calculate the number of hours it will take them to work together:
Let
t: average time.
hi: hours worked for each one.
n: number of teams.
The average will be given by:
t = (h1 + h2) / (n)
Substituting both values:
t = ((15) + (10)) / (2) = 12.5
answer
it would take 12.5 h to pave that same section of highway if both crews worked together

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3 years ago