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2 years ago

14. BUS TRIP A bus leaves at 10 A.M. to take students on a field trip to a

Mathematics

1 answer:

k0ka [10]2 years ago

6 0

The bus is 54.5 miles far from the site at the time of 11:30A.M as per the given information in the question.

<h3>What is the slope of a line?</h3>

The slope of a line indicates how steep it is. Slope is defined mathematically as "climb over run" (change in y divided by change in x).

It is assumed that a bus moving at a constant speed departs at 10 a.m. towards a historic location, is 100 miles away by 10:25 a.m., and is 65 miles away at 11:15 a.m.

We must create a point-slope equation that connects the distance from the place to the time in minutes after 10:00 a.m. Then, around 11:30 a.m., we need to figure out how far the bus is from the site.

A line's point-slope is y₂-y₁)=m(x₂-x₁)

Since x denotes the amount of minutes after 10:00 a.m., 10:25 a.m. is represented by x=25 and 11:15 a.m. by x=75.

At 10:25 a.m., a distance of 100 miles from the place is represented by 75.

The point represents a distance of 100 miles from the site at 10:25 a.m. The point represents a distance of 65 miles from the site at 11:15 a.m.

By substituting the points (25, 100) and (75, 65) into the slope formula and simplifying we get,

m=(y₂-y₁)/(x₂-x₁)

m=(65-100)/(75-25)

m=-35/50

m=-0.7

Now choose one of the points and substitute that point and the slope into the slope-point form

y₋y₁=m(x-x₁)

By choosing (x₁, y₁)=(25, 100)

By choosing (x₂, y₂)=(75, 65)

Since 11:30 A,M is 90 minutes after 10:00A.M

By substituting x=90 in the equation we get the value of y,

y-100= -0.7(90-25)

y-100= -0.7(65)

y-100 =-45.5

y= 54.5

Hence, the bus is 54.5 miles from the site at the time of 11:30 A.M

y-100= -0.7(x-25)

y-65= -0.7(x-75)

The bus is 54.5 miles from the site at 11:30A.M.

To know more about slope of a line, visit:

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Ksenya-84 [330]

Answer:

Width=10

Length=18

Step-by-step explanation:

The length is 2 feet less then twice the width

Let the width be x.

Then the length is 2x -2 based on the given information. Use this to make an equation since it is known that the area is 180feet squared.

x(2x-2)=180

2x^2 - 2x - 180 = 0

2( x^2 - x - 90) = 0

We now have a factorable quadratic.

2(x+9)(x-10)=0

So by zero product property, x=-9, x=10 Since a measure cannot be negative, -9 is an extraneous solution.

So x=10

Then the width is 10 and the length is 18

Hope this helps! Let me know if it is correct!

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4 years ago

Elise and her dad are planning to attend the state fair. An adult ticket is $21.00. The price of an adult ticket is $10.00 more

belka [17]

Answer:

C)two thirds x + 10 = 21

Step-by-step explanation:

The equation for determining how much it would be paid for the student tickets is shown below:

Given that

The ticket of an adult is $21

Now let us assume the price of the student ticket be x

So two third would be 2 ÷ 3x

And for adult it would be

2 ÷ 3x + 10

Now the equation is

2 ÷ 3x + 10 = 21

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3 years ago

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3 years ago

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It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell

Mademuasel [1]

Answer:

a) 75

b) 4.33

c) 0.75

d) $3.2 \times 10^{-13}$ probability that no one in a simple random sample of 100 young adults owns a landline

e) $6.2 \times 10^{-61}$ probability that everyone in a simple random sample of 100 young adults owns a landline.

f) Binomial, with $n = 100, p = 0.75$

g) $4.5 \times 10^{-8}$ probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.

This means that $p = 0.75$

(a) On average, how many young adults do not own a landline in a random sample of 100?

Sample of 100, so $n = 100$

$E(X) = np = 100(0.75) = 75$

(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33$

(c) What is the proportion of young adults who do not own a landline?

The estimation, of 75% = 0.75.

(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?

This is P(X = 100), that is, all do not own. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}$

$3.2 \times 10^{-13}$ probability that no one in a simple random sample of 100 young adults owns a landline.

(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?

This is P(X = 0), that is, all own. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}$

$6.2 \times 10^{-61}$ probability that everyone in a simple random sample of 100 young adults owns a landline.

(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?

Binomial, with $n = 100, p = 0.75$

(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?

This is P(X = 50). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}$

$4.5 \times 10^{-8}$ probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

8 0

3 years ago

4/5 ÷ 7/6 + 2/7 ∙2 1/5

Aleksandr [31]

<h2>The value of $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$ $=\dfrac{8}{7}$ </h2>

Step-by-step explanation:

We have,

$\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$

To find, the value of $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$ = ?

∴ $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$

$=\dfrac{4}{5}\times \dfrac{6}{7} +\dfrac{2}{7}.\dfrac{8}{5}$

$=\dfrac{24}{35} +\dfrac{16}{35}$

Taking LCM of denominator, we get

$=\dfrac{24+16}{35}$

$=\dfrac{40}{35}$

Dividing numerator and denominator by 5, we get

$=\dfrac{8}{7}$

∴ The value of $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$ $=\dfrac{8}{7}$

Hence, the value of $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$ is equal to $\dfrac{8}{7} .$

4 0

3 years ago