All categories

2 years ago

Five hundred sixth-grade students

Mathematics

1 answer:

viktelen [127]2 years ago

6 0

<h3>The ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1</h3>

<em><u>Solution:</u></em>

Given that,

Five hundred sixth-grade students were surveyed

Which means,

sixth-grade students = 500

125 had traveled on an airplane

<em><u>What is the ratio of total sixth-grade students to the number of students who had traveled on an airplane?</u></em>

Therefore,

total sixth-grade students : students traveled on airplane = 500 : 125

<h3>Ratio = 500 : 125</h3>

Reduce to lowest terms,

Divide both sides by 5

<h3>Ratio = 100 : 25</h3>

Further reduce to simplest terms,

Divide both sides by 25

<h3>Ratio = 4 : 1</h3>

Thus the ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1

You might be interested in

Alissa has $360 for guitar lessons. She pays $25 for each lesson. How many lessons has she attended, if she still has $85 left?

bagirrra123 [75]

Answer:

11 lessons

Step-by-step explanation:

360-85=275

275/25=11

7 0

2 years ago

The graph represents the feasible region for the system:

morpeh [17]

We have been given a system of inequalities and an objective function.

The inequalities are given as:

$y\leq 2x\\
x+y\leq 45\\
x\leq 30\\$

And the objective function is given as:

$P=25x+20y$

In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.

The graph of the region is shown below:

From the graph, we can see that corner points of the feasible region are:

(x,y) = (15,30),(30,15) and (30,60).

Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.

$\text{At (15,30)}\Leftrightarrow P=25\cdot 15+20\cdot 30=975\\
\text{At (30,15)}\Leftrightarrow P=25\cdot 30+20\cdot 15=1050\\
\text{At (30,60)}\Leftrightarrow P=25\cdot 30+20\cdot 60=1950\\$

Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30

3 0

2 years ago

Read 2 more answers

Including Jose, there are eight people in his family.

SIZIF [17.4K]

Answer:

840

Step-by-step explanation:

Since the order matters, we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

In this question:

The first seat is Jose's.

The remaining four are organized among the other 7 members. So

$P_{(7,4)} = \frac{7!}{(7-4)!} = 840$

So the correct answer is:

840

7 0

2 years ago

Read 2 more answers

A turtle walks 7/8 of a mile in 50 minutes. What is the unit rate when the turtle’s speed is expressed in miles per hour?

yKpoI14uk [10]

Answer:

21/20

Step-by-step explanation:

a) One hour is equivalent to 60 minutes.

So we can multiply 50 minutes by the fraction $\frac{1 hour}{60 minutes}$ , so we could convert 50 minutes to hours.

It is:

$50 minutes * \frac{1 hour}{60 minutes}=\frac{50}{60}hours$

If we simplify the fraction, we have:

$50 minutes = \frac{5}{6}hours$

b) In order to express the turtle's speed in miles per hour, we have to divide

$\frac{7}{8}miles$ by $\frac{5}{6}hours$

So:

$\frac{\frac{7}{8}miles }{\frac{5}{6}hours }$

We simplify the expression by multiplying 7 mile by 6 and 8 by 5 hours:

$\frac{\frac{7}{8}miles }{\frac{5}{6}hours}=\frac{42 miles}{40 hours} =\frac{21 miles}{20 hours}$

4 0

2 years ago

Read 2 more answers

According to a Pew Research survey, about 27% of American adults are pessimistic about the future of marriage and the family. Th

IgorLugansk [536]

Answer:

P(X≤5)=0.5357

Step-by-step explanation:

Using the binomial model, the probability that x adults from the sample, are pessimistic about the future is calculated as:

$P(x)=\frac{n!}{x!(n-x)!} *p^{x}*(1-p)^{n-x}$

Where n is the size of the sample and p is the probability that an adult is pessimistic about the future of marriage and family. So, replacing n by 20 and p by 0.27, we get:

$P(x)=\frac{20!}{x!(20-x)!}*0.27^{x}*(1-0.27)^{20-x}$

Now, 25% of 20 people is equal to 5 people, so the probability that, in a sample of 20 American adults, 25% or fewer of the people are pessimistic about the future of marriage and family is equal to calculated the probability that in the sample of 20 adults, 5 people of fewer are pessimistic about the future of marriage and family.

Then, that probability is calculated as:

P(X≤5)= P(1) + P(2) + P(3) + P(4) + P(5)

Where:

$P(0)=\frac{20!}{0!(20-0)!}*0.27^{0}*(1-0.27)^{20-0}=0.0018$

$P(1)=\frac{20!}{1!(20-1)!}*0.27^{1}*(1-0.27)^{20-1}=0.0137$

$P(2)=\frac{20!}{2!(20-2)!}*0.27^{2}*(1-0.27)^{20-2}=0.0480\\P(3)=\frac{20!}{3!(20-3)!}*0.27^{3}*(1-0.27)^{20-3}=0.1065\\P(4)=\frac{20!}{4!(20-4)!}*0.27^{4}*(1-0.27)^{20-4}=0.1675\\P(5)=\frac{20!}{5!(20-5)!}*0.27^{5}*(1-0.27)^{20-5}=0.1982$

Finally, P(X≤5) is equal to:

P(X≤5) = 0.0018+0.0137 + 0.0480 + 0.1065 + 0.1675 + 0.1982

P(X≤5) = 0.5357

3 0

2 years ago