Ming drove to the lake and back. On the trip there she drove 30 km/h and on the return trip she went 24 km/h. How long did the trip there take if the return trip took five hours?

Answers

Answer 1

The trip to the lake took  4 hours.

How long did the trip to the lake take?

The first step is to determine the distance of the trip.

Distance = average speed x time

24 km/h x 5 = 120 km

Time = distance / average speed

120 / 30 = 4 hours

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Related Questions

helppp im stuck :(
Hope you guys help me

Answers

Answer:

[tex]y=-\dfrac{1}{2}x+2[/tex]

Step-by-step explanation:

Define two points on the line:

  [tex]\textsf{let}\:(x_1,y_1)=(0,2)[/tex]

  [tex]\textsf{let}\:(x_2,y_2)=(4,0)[/tex]

Use the slope formula and the defined points to find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}=-\dfrac{1}{2}[/tex]

Substitute the found slope and one of the points into the point-slope form of a linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]

Simplify:

[tex]\implies y-2=-\dfrac{1}{2}x[/tex]

[tex]\implies y=-\dfrac{1}{2}x+2[/tex]

The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?

Answers

The number of cars that have passed through the intersection is 245.

How many cars passed through the intersection?

Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases.

The equation that represents direct variation is; c = wk

Where:

c = number of carsw = number of wrecks k = constant of proportionality

1085 = k31

k = 1085 / 31

k = 35

c = 7 x 35

c = 245

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Given that y is an integer, find all values of y such that y< 6

Answers

Answer:

Values: 3,4,5

Step-by-step explanation:

I hope this helps:)

As sample of 105 sanitation workers for the city of Euonymus, Texas, earns an average of $24,375 per year. The average salary for all Euonymus city workers is $24,230, with a standard deviation of $523. Are the sanitation workers overpaid? Conduct both one- and two-tailed tests.

Answers

The average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.

What are the null hypothesis and alternative hypothesis?

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

We have:

Average x = 24375

u = 24230

SD = 523

n = 105

Null hypothesis and alternative hypothesis for one-tail test:

H0: the average salary of sanitation workers in the city of Euonymus is not overpaid.

u = 24230

H1:  the average salary of sanitation workers in the city of Euonymus is overpaid.

u > 24230

Assume significance level = 0.05

From the Z-table:

Z(critical) = 1.645

Now,

Z = (x-u)/(SD/√n)

Z = (24375-24230)/(523/√105)

Z = 2.84

Z > Z(critical)

So, reject the null hypothesis.

The average salary of sanitation workers in the city of Euonymus is overpaid.

Now, from the two-tail test:

Null hypothesis and alternative hypothesis for one-tail test:

H0: the average salary of sanitation workers in the city of Euonymus is 24230

u = 24230

H1:  the average salary of sanitation workers in the city of Euonymus is not 24230

u ≠ 24230

Assume significance level = 0.05

From the Z-table for the two-tail test:

Z(critical) = ±1.96

Now,

Z = 2.84

Z > z(critical)

The average salary of sanitation workers in the city of Euonymus is not 24230.

Thus, the average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.

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Please answer all the questions txxxx

Answers

In the first image, the answer is the square root of 3,778 meters. In the second image, the answer is B, or 12 cm. In the third image, the answer is C, or 10^2 + 8^2 = x^2.

Explanations:

1st image: The longest side of the triangle is equal to the hypotenuse, which is c squared. Because a squared + b squared equals c squared, that would mean 23 squared + 57 squared equals c squared. 23 squared (23 x 23) equals 529, and 57 squared (57 x 57) equals 3,249. 3,249 + 529 = 3,778. This means that c squared equals 3,778. Now, to find c, we can find the square root of 3,778 which would be 61.5 meters rounded. That’s how I got my answer.

2nd image: 13 squared is the hypotenuse, which equals 169 because 13 x 13 is 169. Therefore, 5 squared (which equals 25) + b squared = 169. 169 - 25 = 144, and that means b squared equals 144. The square root of 144 is 12, so 12 cm is the length of the longer leg.

3rd image: x is equal to the hypotenuse, or c squared. Because the Pythagorean Theorem equation is a squared + b squared = c squared, your equation is 10 squared + 8 squared = x squared. That would make the only relevant answer C.

There are the answers and explanations for all of the problems. If you need further explanation on Pythagorean Theorem, let me know and I will explain!

Help me with this question please!! :)

Answers

Answer: 4.2%

Step-by-step explanation:

The probability the first response is correct is 1/6.The probability the second response is correct is 1/4.

Multiplying these, we get (1/6)(1/4), which is about 4.2%

4/3 - 1/2 What is the answer

Answers

Answer:

5/6

Step-by-step explanation:

4/3-1/2

1) make the denominators the same on both fractions

8/6-3/6=?

2) subtract numerators

5/6

3) simplify

cannot simplify

Answer:

5/6

Step-by-step explanation:

4/3  -1/2

The first step is to get a common denominator of 6

4/3 *2/2 = 8/6

1/2 * 3/3 = 3/6

8/6  -3/6

5/6

what is the domain of the ordered pair shown in the graph?

Answers

Answer:

D.

Step-by-step explanation:

It is the only one that contains all the x-values of the points. (Domain is the set of x-values).

The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.

Answers

y intercept is 2, which shows while changing the jobs employees bring two customers.

What is linear equation?

A linear equation is in the form, y = mx + b where m is the rate of change (slope) and b is the y intercept (initial value of y).

The complete question is:

The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.

Time Employed (Month)

If the equation for the line of best fit is y = 4.5x + 2, which of the following can be used to interpret the y-intercept in context?

Employee training takes 2 months.

Employee training takes 4.5 months.

Employees are likely to bring 2 customers with them when changing jobs.

Employees are likely to bring 4.5 customers with them when changing jobs.

As, linear equation is

y = mx + b

Let y be the number of customers and x be the length of time.

Then, y = 4.5x + 2

As, y intercept is 2, which shows while changing the jobs employees bring two customers.

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A shopkeeper buys 72 articles for $82.80. How much will he have to pay if he buys 150 such articles.​

Answers

Answer: He have to pay $172.5 if he buys 150 such articles.

72 articles for --> $82.80
1 article for - - - > 82.80/72

150 articles for --> (82.80/72)*150
                           = $172.5

Answer:

$172.5

Step-by-step explanation:

Given:

Shopkeeper buys = 72 articles

Price = $ 82.8

To Find:

The amount he'll need to pay If he buys 150 articles.

Solution:

Amount if he buys 150 articles

[tex] \boxed{\rm \: No. \: of \: articles \: he \:will \: buy × \cfrac{Cost \: of \: that \: article \: he \: has}{Number \: of \: articles \: he \: has}} [/tex]

[tex] = \$ \bigg(\rm150 * \cfrac{82.80}{72}\bigg) [/tex]

[tex]= \$ (150* 1.15)[/tex]

[tex] = \$172.5[/tex]

So we can conclude that:

$172.5 he will have to pay if he buys 150 such articles.

Which products result in a difference of squares? Select three options. a (x minus y)(y minus x) b (6 minus y)(6 minus y) c (3 + x z)(negative 3 + x z) d (y squared minus x y)(y squared + x y) e (64 y squared + x squared)(negative x squared + 64 y squared)

Answers

Answer:

By comparing all the expressions with the formula (a - b)(a + b) = (a² - b²), we find that c, d and e options are correct.

Step-by-step explanation:

Concept: The condition is that, the product should result in a difference of squares. In mathematics, we have such a formula which is (a - b)(a + b) = (a² - b²). So, we need to compare all the options with this relation.

(x - y)(y - x) = -(x² - 2xy + y²)

(6 - y)(6 - y) = 36 - 12y + y²

(3 + xz)(-3 + xz) = (xz + 3)(xz - 3) = x²z² - 9 . This expression is correct

(y² - xy)(y² + xy) = [tex]y^{4} - x^{2} y^{2}[/tex]. This expression is correct

(64y² + x²)(-x² + 64y²) = (64y² + x²)(64y² - x²) = [tex]4096y^{4} -x^{4}[/tex]. This expression is correct.

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Find the domain and range of the function graphed below. Write your answers in interval notation.

Answers

Answer:

Domain: [tex][1, \infty)[/tex]Range: [tex](-\infty, -2][/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Solve this for me please

Answers

Answer:

30.5

Step-by-step explanation:

here :

n represents the number of trials

p represents the probability of success

 In a binomial distribution, The mean

 is equal to the product of those two values.

In other words,

The mean = n × p

                 = 122 × 0.25

                 = 30.5

Suppose there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates. Everything else equal, what is likely to happen to value of the MXN?

Answers

The value of MXN will increase.

The official currency of Mexico is The Mexican peso (MXN).

MXN is simply an abbreviation of the currency the Mexican peso, which is the official currency of the country of Mexico.

Similarly, the drop value in currency is defined as the expression that the currency is worth less as compared to all other countries.

When a currency's country interest rate drop, then the value of the currency increase. Here given in the question as there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates, the value of MXN will increase as the drop is more in Mexico which affects its currency MXN.

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Please help I’m confused

Answers

Answer:

Step-by-step explanation:

Describe the graph of a function g by observing the graph of the base function ƒ.
A. g(x) = 2ƒ(–x) g(x)
B. g(x)= -1/2f(x)
C. g(x)= 1/2f(-x)
D. g(x)= f(-1/2x)

Answers

The correct answer is option B which is g(x)= 1/2f(-x).

What is a graph?

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

As we can see in the graph that the value of the function g(x) will be calculated by the distance formula:-

[tex]g(x) = \dfrac{ 0 + 2}{2 - 0 }=\frac{2}{2}=1[/tex]

The value of the function f(x) will be:-

[tex]f(x) =\dfrac{2-0}{-4+0}=\dfrac{-1}{2}[/tex]

So g(x) = ( -1/2) f(x)

Therefore the correct answer is option B which is g(x)= 1/2f(-x).

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2) Sarah takes a small business loan for
$25,000. The term for repayment is 60
months and the interest rate is 5.75%.
formula,
Use the loan amortization
what is the estimated monthly
payment?

Answers

Using it's formula, it is found that the estimate monthly payment is of $480.42.

What is the monthly payment formula?

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

P is the initial amount.r is the interest rate.n is the number of payments.

The parameters are given as follows:

P = 25000, n = 60, r = 0.0575.

Hence:

r/12 = 0.0575/12 = 0.00479167.

Hence the payment will be of:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 25000(0.00479167)\frac{(1+0.00479167)^{60}}{(1+0.00479167)^{60}-1}[/tex]

A = 480.42.

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Write 31/8 as a mixed number.
Reward: Mark as brainlist.

Answers

Answer:

[tex]3 \frac{7}{8}[/tex]

Step-by-step explanation:

Line AB and line BC form a right angle at point B with points A(2,5) and B(8,3) . What is the equation of line BC ?

Answers

Answer: y = 3x - 21

Step-by-step explanation:

If the lines form a right angle, this means that they are perpendicular. Therefore, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other (in other words, their slopes multiply to -1).

The slope of AB is [tex]\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}[/tex]. This means that the slope of BC is 3.

Substituting into point-slope form,

[tex]y-3=3(x-8)\\\\y-3=3x-24\\\\\boxed{y=3x-21}[/tex]

I need help with this question

Answers

Which of the following smallest values

Need help with this geometry question

Answers

Answer: 10 inches

Step-by-step explanation:

Diagonals of a parallelogram bisect each other, so the top of the jack is 5(2)=10 inches off the ground.

Select the correct answer.
If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system?
OA. The lines in a system cannot be parallel.
There are infinitely many solutions.
B.
OC. There is exactly one solution.
D. There is no solution.
Reset
Next

Answers

Answer:

Look below!

Step-by-step explanation:

From the picture, the answer is A.

From the points, calculate the slope using y2-y1/x2-x1

you will find that the slope is -1

parallel lines have the same slope

so y = -x+1 is the correct answer

now,

parallel lines never intersect

therefore, they have no solution.

Determine which of the following statements about the given triangles is true.​

Answers

Answer:

The answer be the 2 one

Step-by-step explanation:

I do it and it come right

12. Use the diagram to determine the value of x

Answers

Answer:

127 degrees = x

Step-by-step explanation:

A six sided polygon has interior angles that sum to

(n-2)(180) =  (6-2)(180 = 720

so all of the angles in the question add to 720

 98 + 133 + x + x + 155 + 80 = 720

  solve for x = 127 degrees

Answer:

x = 127

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6 , then

sum = 180° × 4 = 720°

sum the interior angles and equate to 720

x + x + 155 + 80 + 98 + 133 = 720 , that is

2x + 466 = 720 ( subtract 466 from both sides )

2x = 254 ( divide both sides by 2 )

x = 127

The table shows the heights of three different plants.

Answers

Answer:

7/4 meters

Step-by-step explanation:

the tallest plant is 19/8

since they have all the same denominaters we can just compare the top numbers

so

the smallestp lant is 5/8

19/8 - 5/8 = 14/8

7/4 is your final answer after simplifying

What is the distance between the given points?

Answers

Answer:

√85 which is approximately 9.2195

Step-by-step explanation:

Help me with this question please!! :)

Answers

Answer: 9516793/9765625

Step-by-step explanation:

We can subtract the probability none of them have been vaccinated from 1.

If 52% of people are vaccinated, then 48% of people are not vaccinated.

Thus, the probability is [tex]1-(0.48)^{5} =\frac{9516793}{9765625}[/tex]

Mr. Garret has a total of 20 students in his class. The number of female students is 4 less than twice the number of male students. How many female and how many male students does he have?​

Answers

Answer:

8 male, 12 female

Step-by-step explanation:

male = x

female = 2x - 4

2x - 4 + x = 20

3x - 4 = 20

3x = 24

x = 8

2(8) - 4 = 12

there are 8 male, 12 female

The drink you usually buy is on sale, the price has been reduced by $2 per can, this means you can get 28 cans for the same price that you usually pay for 20 cans, determine the original price

Answers

Answer:

The answer is $2.80.

Step-by-step explanation:

The price was reduced to two dollars and you buy 28 cans for the same price in which you got 20 cans at original price. So you need to take 28 cans times 2, which you will receive 56. Take 56 the price divided by 20 the original price cans and you will receive 2.8 or $2.80. To double check your work, take 2.80 times 20 and see if you get 56. #BallersKnowMath

from a survey involving 1000 University students market research company found that 780 students on laptops 460 on cars and 380 owned cars and laptops if a university student is selected at random what is each empirical probability. (A) the student owns either a car or laptop. (B) the student owns neither a car nor a laptop is.

Answers

Considering the definition of probability:

the probability that the student owns either a car or laptop is 86%.the probability that the student owns neither a car nor a laptop is 14%.

Definition of Probabitity

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The probability of any event A is defined as the quotient between the number of favorable cases (that is, the number of times that event A may or may not occur) and the total number of possible cases:

[tex]Probability=\frac{number of favorable cases}{total number of possible cases}[/tex]

Union of events

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

Complementary event

A complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

Events and probability in this case

In first place, let's define the following events:

A: The event that a student owned a laptop.

B: The event that a student owned a car.

Then you know:

P(A)= [tex]\frac{780}{1000}[/tex]= 0.78P(B)= [tex]\frac{460}{1000}[/tex]= 0.46P(F and R)= P(F∩R)= [tex]\frac{380}{1000}[/tex]= 0.38 [The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.]

In this case, considering the definition of union of events, the probability that the student owns either a car or laptop is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.78 + 0.46 -0.38

P(A∪B)= 0.86= 86%

Then, the probability that the student owns either a car or laptop is 86%.

On the other hand, considering the definition of the complementary event and its probability, the probability that the student owns neither a car nor a laptop is calculated as:

P [(A∪B)']= 1- P(A∪B)

P [(A∪B)']= 1 - 0.86

P [(A∪B)']= 0.14= 14%

Finally, the probability that the student owns neither a car nor a laptop is 14%.

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