Alec can buy bottles of water in packages of 6 for $12.12 or in packages of 4 for $9.72. How much money does he save by buying 48 bottles of water at the better price?

Final answer:

To find the number of hours it takes for Robin to travel 320 miles using the equation y = 30x + 20, solve for x, yielding 10 hours.

Explanation:

The question asks about how many hours it will take for Robin to travel 320 miles, given the linear equation representing the distance traveled over time: y = 30x + 20. Here, 'y' represents the distance traveled in miles and 'x' represents the time in hours.

To find the number of hours required to travel 320 miles, we need to solve the equation for x when y is 320.

Let's set up the equation with y as 320:

320 = 30x + 20

To solve for x, subtract 20 from both sides:

300 = 30x

Now, dividing both sides by 30, we get:

x = 300 / 30

x = 10

So it will take Robin 10 hours to travel 320 miles.

The amount n = $ 400.72 as fraction is A = 10,018/25

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the amount be represented as n

Let the fraction be represented as A

Now , To write "four hundred dollars and seventy two cents" as a fraction, we can first write it as the sum of its parts:

$ 400.72 = $ 400 + $ 0.72

Next, we can convert the cents portion to a fraction by dividing by 100:

$ 0.72 = 72/100

Now we can combine the two parts by adding them as fractions:

$ 400.72 = $400 + $0.72 = $400 + 72/100

To convert this to a fraction, we need to find a common denominator, which is 100:

$ 400.72 = ($ 400 x 100 + 72) / 100

= 40,072 / 100

Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor of 4 gives:

$ 400.72 = 10,018/25

Hence , "four hundred dollars and seventy two cents" is equivalent to the fraction 10,018/25 in reduced form

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The given amount in fraction is [tex]\frac{40072}{100}[/tex] and its reduced fraction is [tex]\frac{10018}{25}[/tex].

1. Understanding the Total Amount in Cents:

Four hundred dollars and seventy-two cents' is equivalent to 400 dollars + 72 cents. First converting everything to cents. Since 1 dollar is equal to 100 cents:

[tex]four\ hunder\ dollars\ and\ seventy\ two\ cents = 400 \times 100\ \text{cents} + 72\ \text{cents}= 40072\ cents[/tex]

2. Since 1 dollar = 100 cents, dividing total amount in cents by 100:

[tex]Total\ amount= \frac{40072}{100}[/tex]

Reducing the fraction by dividing numerator and denominator by 4:
[tex]Reduced\ Fraction = \frac{10018}{25}[/tex]

Answer:

6

Step-by-step explanation:

22 - 4 = 18

18 / 3 = 6

Answer:

6

Step-by-step explanation:

22-4=18/3=6

start from what you get that use the inverse to get the the original answer

Answer:

2.5

Step-by-step explanation:

25 is the area so u have to divide it by 10. When u divide 25 by 10, you get 2.5. 2.5 inches represents the height

Answer:

the answer is A 2.5

Step-by-step explanation:

Answer:

a. The slope is incorrect

b. y = 3x, ( 0 , 0 )

c) y = 4 - x

Step-by-step explanation:

Given:-

The slope between two points (1, 3) and (6, -2) is 3.

a. Explain why the information Mary was given cannot be correct.

- The slope between two arbitrary points, ( x1 , y1 ) and  (x2 , y2) is given by the following relationship:

                         slope = ( y2 - y1 ) / ( x2 - x1)

- Use the given points (1, 3) and (6, -2) and determine the slope:

                        slope = ( -2 - 3 ) / ( 6 - 1 )

                        slope = ( -5 ) / ( 5 )

                        slope = -1

- Yes, the given slope is incorrect it should be = -1

b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the  coordinates of another point on the line

- We will assume the point (1,3) lies on line with a slope = 3.

- We will use the slope-intercept equation of line:

                              y = slope*x + c

Where,      m : Slope

                 c : y-intercept

                             y = 3x + c

Using the given correct point to evaluate the y-intercept (c):

                             3 = 3*1 + c

                             c = 0

- The equation of line is,

                            y = 3x

- The origin (0,0) lies on the line y = 3x.

c. If the given points are correct for the line, what is the slope? Write an equation for the line

- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.

- We will use the slope-intercept equation of line:

                              y = slope*x + c

Where,      m : Slope

                 c : y-intercept

                             y = -x + c

Using the given points to evaluate the y-intercept (c):

                             3 = -1 + c

                             c = 4

- The equation of line is,

                            y = -x + 4

Mary's information is incorrect because the slope of the line passing through the points (1, 3) and (6, -2) is -1, not 3. If the slope is actually 3, the line equation is y = 3x and an additional point on the line is (2, 6). If the given points are correct, the line equation is y = -x + 4.

To understand these questions, it's important to know how the slope of a line is defined and how to write the equation of a line.

Given two points (x1, y1) and (x2, y2), the slope of the line is calculated as (y2 - y1) / (x2 - x1). For the points given, (1, 3) and (6, -2), the slope would be (-2 - 3) / (6 - 1) = -5/5 = -1. So, the slope of the line passing through these two points is not 3, which contradicts the information given. Therefore, the information Mary was given cannot be correct.

If the point (1, 3) and the slope 3 are correct, the equation of the line is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Substituting these values we get y - 3 = 3(x - 1). This simplifies to y = 3x. A point on this line can be (2, 6).

If the points (1, 3) and (6, -2) are correct, we've already calculated the slope as -1. To find the equation of the line we use the same formula, y - y1 = m(x - x1). Substituting these values we get y - 3 = -1(x - 1), simplifying to y = -x + 4.

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Answer: there were not a lot of safe places kids could play

Step-by-step explanation:

i got it right.

The problem led to playgrounds becoming more common in America cities is: Due to unsafe places.

Playgrounds is a safe place that is specifically set aside for children to play.

Playgrounds can tend to contribute to a child social growth when the child plays among is age group or peer group.

Playgrounds is common in America in order to prevent danger and injury because there were not safe places for children to play.

Therefore the problem led to playgrounds becoming more common in America cities is: Due to unsafe places.

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Answer:

The equation that can be used to determine the maximum height is given as h = 15tan4.76°

Step-by-step explanation:

The question given is lacking an information. Here is the correct question.

"By law, a wheelchair service ramp may be inclined no more than 4.76 degrees. If the base of the ramp begins 15 feet from the base of a public building, which equation could be used to determine the maximum height, h, of the ramp where it reaches the building's entrance"

The whole set up will give us a right angled triangle with the base of the building serving as the adjacent side of the triangle and the height h serving as the opposite side since it is facing the angle 4.76°

The side of the wheelchair service ramp is the hypotenuse.

Given theta = 4.76°

And the base of the building = adjacent = 15feet

We can get the height of the building using the trigonometry identity SOH CAH TOA.

Using TOA

Tan(theta) = opposite/Adjacent

Tan 4.76° = h/15

h = 15tan4.76°

The equation that can be used to determine the maximum height is given as h = 15tan4.76°

Answer:

hello we need to see the charts

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total number of kindergarten children in that region that were tested is 160

It is generally believed that nearsightedness affects about 12% of children in a certain region. Therefore,

The expected number of kindergarten children expected to be​ nearsighted is

12/100 × 160 = 19

Probability of success, p = 0.12

Probability of failure, q = 1 - p = 1 - 0.12 = 0.88

Standard deviation = √npq = √(160 × 0.12 × 0.88) = 4.11

Answer: 1,453

Step-by-step explanation:

Ed 2020

Answer:

1453 cm squared

Step-by-step explanation:

Answer:

(x/3) - 5.

Step-by-step explanation:

Let the number be x.

The quotient of the number and 3 is x/3.

So the expression is:

(x/3) - 5.

Answer:

Riko is wrong

Step-by-step explanation:

To find the distance of two point, we use the following formula:

A (x1, y1)

B (x1, y2)

AB = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]

In this situation, we have:

A (-2,-3)

B  (2,-5)

So the distance is: [tex]\sqrt{(2 - (-2))^{2} + (-5 - (-3))^{2} }[/tex] = [tex]\sqrt{4^{2} + 8^{2} }[/tex] = [tex]\sqrt{80} = 4\sqrt{5}[/tex]

Hope it will find you well.

Sample Response: No, Riko is not correct. The points do not have the same x-coordinates. If you connect the points, they do not form a horizontal or vertical line, so you cannot count spaces or use absolute value to find the distance.

Answer: continuous objective.

Step-by-step explanation:

Continuous objective-based control for self-optimizing systems with changing operation modes. Self-optimization enables technical systems to adapt their behavior to varying environmental conditions and changing operation modes. Objective functions serve as evaluation criteria for the system behavior.

Answer:

3

Step-by-step explanation:

4x3 is 12

12-9 is 3

y = 3

Plug 3 in for x

y = 4(3) - 9

y = 12-9

y = 3

Answer:

100%

Step-by-step explanation:

Answer:

it takes 1st person 4 hour and second person is 8 hours

Step-by-step explanation:

Let t is the time (t >0)

We have:

<=> 1/3  = 1/t  + 1/t-8  

<=> [tex]t^{2} -14t = -24[/tex]

<=> [tex](t-7)^{2} =25[/tex]

<=> t  - 7 = 5

<=> t = 12

So it takes 1st person 4 hour and second person is 8 hours

Answer:

Person A complete the task in 1.125 hours

Person B complete the task in 9 hours

Step-by-step explanation:

Person A complete a task 8 hours sooner than person B

Working together they perform the task in 3 hours

Let call "x" hours person A  need to do the task alone

Then person B will take 8*x hours to do the job

In 1 hour person A do 1/x  part of the task

In 1 hour person B do 1/8*x  part of the task  

Then A + B in one hour of work will do

1/x + 1/8x   =  [ 8 + 1 ]/8*x    ⇒  9/8*x

And according to problem statement that time is 1/3 (one third of the time)

Then 3* (9/8*x) =  3

9 = 8*x

x = 9/8

x =  1.125 hours

And person B will take  8*1,125  = 9 hours

Answer:

x=4             x = -3/2

Step-by-step explanation:

4x^2 – 7x = 3x + 24

Subtract 3x from each side

4x^2 – 7x-3x = 3x-3x + 24

4x^2 – 10x =   24

Subtract 24 from each side

4x^2 – 10 -24 = 24- 24

4x^2 -10x-24=0

Divide each side by 2

4/2x^2 -10/2x-24/2=0

2x^2-5x-12=0

Factor

(x - 4) (2 x + 3) = 0

Using the zero product property

x-4 =0   2x+3 =0

x=4         2x = -3

x=4             x = -3/2

Answer:

answer is c and f for short answer

Step-by-step explanation:

i did the rating by accident

Answer: The measure of the central angle of the circle is 73°

Step-by-step explanation: Please see the attachments below

Answer: 287 degree

Step-by-step explanation:

Area of a sector = θ/360 x pi r^2

Where pi = 22/7

Given that the

area = 40.8 square inches

radius = 8 inches

40.8 = θ/360 × 3.143 × 8 × 8

θ = (360 × 40.8)/201.06

θ = 73 degree

The measure of the central angle of the circle = 360 - θ

= 360 - 73

= 287 degree

Answer:

990

Step-by-step explanation:

Out of 1,370 students, 990 are predicted to have a television in their bedroom

From the complete question, the probability that a student has a television in his bedroom is:

p = 72.23%

Given that the number of students is 1370

The expected number of students that have television is:

E(x) = p * n

This becomes

E(x) = 72.23% * 1370

Evaluate the product

E(x) = 989.5510

Approximate

E(x) = 990

Hence, out of 1,370 students, 990 are expected to have a television in their bedroom

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Answer:

8%

Step-by-step explanation:

Let's say the tax percent was x%. Then, we can write the equation:

4.75 + x% * 4.75 = 5.13

Notice that both terms on the left have 4.75 so factor that out:

4.75 * (1 + x%) = 5.13

Divide both sides by 4.75:

1 + x% = 5.13/4.75 = 1.08

Subtract 1 from both sides:

x% = 0.08

Remember that % simply means "out of 100", so x% = x/100:

x/100 = 0.08

Multiply both sides by 100:

x = 8

Thus, the tax rate is 8%.

Hope this helps!

Answer:

The right expression is Option A - 3/4 divided by 5

Step-by-step explanation:

The whole cheese is 1.

Since she ate 1/4 of it, thus, she has,

1 - 1/4 = 3/4 left.

Now she split this remaining cheese into 5 places. Thus, it is expressed as;

(3/4) ÷ 5

This corresponds with option A

The population of the town in 2007, according to the exponential growth function y = 8.5(1.1)x, would be approximately 16,630 people.

The function given is an exponential growth function, where y = 8.5(1.1)x. Here, the variable y represents the population in thousands and x represents the number of years after 2000. To find the town's population in 2007, we replace x with 7 (since 2007 is 7 years after 2000) and calculate y.

Using the formula, y = 8.5 * (1.1)7. When calculated, we find y to be approximately 16.63. This means that, according to the model, the town's population in 2007 would be approximately 16630 (because the model represents the population in thousands).

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Answer:

Longer: 17 ft and Shorter: 8 ft

Step-by-step explanation:

Here is what we know:

a = longer part

b = shorter part

a + b = 25

2b + 1 = a

Let's rearrange the equation

b = 25 - a

Now we can plug this into the other equation.

2(25 - a) + 1 = a

50 - 2a + 1 = a

51 - 2a = a

51 = 3a

a = 17 ft

To find b, plug a into one of the equations.

17 + b = 25

b = 8 ft

I hope this helped! :)

Answer:

a) 5180

Step-by-step explanation:

We must calculate with respect to each of the options:

a)  5180

We have that the mean (m) is equal to 5850, the standard deviation (sd) 1125 and the sample size (n) = 20

They ask us for P (x <5180)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (5180 - 5850) / (1125 / (20 ^ 1/2))

z = -2.66

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <-2.66) = 0.0039

Which means that the probability is 0.39%, which is a very low probability, which is not necessary to calculate the other options, we already know that this data is very unusual.

The mean expense of (a) 5180 is considered unusual because its z-score is approximately -2.67, which is beyond the usual ±2 range for a normal distribution.

To determine which of the given mean expenses would be considered unusual, we will use the concept of the Standard Error of the Mean (SEM) and the properties of a normal distribution.

The SEM can be calculated as:

[tex]SEM = \frac{\sigma}{\sqrt{n}}[/tex]

Where:

So,
[tex]SEM = \frac{1125}{\sqrt{20}} = 251.21[/tex]

We then determine the z-scores for the given mean expenses to see how many standard errors away from the population mean they are. The population mean is $5850.

A z-score beyond ±2 is generally considered unusual. Therefore, the mean expense of 5180 would be considered unusual as its z-score is approximately -2.67.

Answer:

n = 192

Step-by-step explanation:

The volume of a cube is given by the formula;

V = L³

where L = cube side

Given L as 1/4, the equation become;

V = (1/4)³

V = 1³/4³

V = 1/64

But volume of n cube = volume of rectangular prism

Therefore,

n * 1/64 = 3

n = 64 * 3

n = 192

Therefore, 192 units is needed.

Answer:

27/72

Step-by-step explanation:

27/72 is correct because it is not equal to the ration 3:8

A ratio shows us the number of times a number contains another number. The ratio that is not equivalent to gray square to total square is C, that is 21/60.

A ratio shows us the number of times a number contains another number.

As we can see that the total number of squares is 8, while the number of gray scales is 3. Therefore, the ratio of the gray scales to total square can be written as,

[tex]\rm \dfrac{Gray\ Square}{Total\ Square}= \dfrac{3}{8}[/tex]

Now, if the option is reduced then,

A.)

[tex]\dfrac{9}{24} = \dfrac{3 \times 3}{3 \times 8}=\dfrac38[/tex]

B.)

[tex]\dfrac{15}{40} = \dfrac{5 \times 3}{5 \times 8}=\dfrac38[/tex]

C.)

[tex]\dfrac{21}{60} = \dfrac{7 \times 3}{5 \times 3 \times 4}=\dfrac{7}{20}[/tex]

D.)

[tex]\dfrac{27}{72} = \dfrac{3 \times 3 \times 3}{3 \times 3 \times 8}=\dfrac38[/tex]

Thus, the ratio that is not equivalent to gray square to total square is C, that is 21/60.

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Answer:

median-7

minimum-1

lower quartile-2

maximum-12

upper quartile-11

Step-by-step explanation:hope this helps

Answer:

The upper quartile is 11.

the lower quartile is 2.

the maximum is 12.

the minimum is 1.

the median is 7.

Step-by-step explanation:

Answer:

Step-by-step explanation:

√20 can be rewritten as the product of two radicals:  √4√5,

and √4 = 2.

Thus, 5√20 = 5(2)√5 = 10√5.  Thus, B:  10 is correct; k = 10.

Answer:

[tex]x = \frac{1}{2}[/tex]

Step-by-step explanation:

The ratio of gallons used for one shower is obtained by dividing the total of gallons by the number of showers per day:

[tex]n = \frac{17\,galllons}{2\,\frac{showers}{day} }[/tex]

[tex]n = 8.5\,\frac{gallons}{shower}[/tex]

The ratio of gallons used for one shower to total gallons used is:

[tex]x =\frac{8.5\,gallons}{17\,gallons}[/tex]

[tex]x = \frac{1}{2}[/tex]

Answer:

1:2

Step-by-step explanation:

For the each shower 17gallons is used

Daily shower is twice = 17*2

= 34 gallons

The ratio of the shower to the daily shower will be:

Each shower / daily shower

17/34 = 1/2

1:2