Jill lives miles away from her school, and Ben lives miles away from his school. Which statement is true?
A.
Ben travels farther than Jill to school.
B.
Jill travels farther than Ben to school.
C.
Ben and Jill travel exactly the same distance to school.
D.
Ben and Jill travel approximately the same distance to school.

Let x be the number of vitamins Cole takes in a day. Since he eats 3 bananas each day and they represent 0.3 mg of iron, the total ammount of iron the bananas represent is 0.9 mg.

This is going to be complemented by the vitamins he takes, since each vitamin has 1 mg of iron, the total ammount of iron he takes in a day is:

We know that he has to take at least 11 mg and at most 22 mg of iron each day, then, the total ammount of iron he takes and is permitted can be express as:

Solving for x, we have:

Therefore, Cole has to take at least 11 vitamins and at most 21 vitamins per day.

Answer:

A

Step-by-step explanation:

the graph of x'3 is B

the graph of x'(-1/3) is C

Answer:

-4/5

Step-by-step explanation:

When you divide -4 from 5 you get -0.80

The formula for finding revolution ​is

Revolutions = Distance traveled / Circumference of the object.

In physics and mechanics, revolutions refer to the number of times an object completes a full circular motion around an axis or a point.

A revolution is a complete turn around a fixed point or axis, and it is often measured in terms of rotations per minute (RPM) or cycles per second.

For example, a car tire completes one revolution when it turns once completely around its axis. Similarly, a planet completes one revolution when it completes one full orbit around its star.

The formula for finding revolution:  ​

The formula for finding the number of revolutions of a rotating object is:

Revolutions = Distance traveled / Circumference of the object

Where distance traveled is the linear distance that the object has covered, and circumference is the distance around the circular cross-section of the object.

Therefore,

The formula for finding revolution ​is

Revolutions = Distance traveled / Circumference of the object.

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Answer: 30%

Step-by-step explanation:

She spent $24 dollars out of the total money she had which was $80. The 24 represents the portion of the money that was spent on fruits. So therefore to find the percentage for put the portion used ($24) divided by the the total ($80) multiplied by a hundred to get the 30%.

The sample space for the two mornings at the stop light would be D. {red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}.

In probability theory, the sample space constitutes the collection of all potential results that could ensue from an experiment. Symbolized by S, it encompasses every plausible outcome that can arise when such a test is conducted.

The sample space would therefore be :
{red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}

This includes all the possible lights that could be seen on the two mornings by Julie.

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The missing marginal costs and benefits values are the following

Marginal benefit = $ 30

Marginal benefit = $25

See above we have a table with columns total cost, marginal cost , total benefits and marginal benefits. We have to determine the values in place of question mark (?) . Marginal benefit and marginal cost are two measures of how the price or value of a product changes.

Now, Marginal cost and benefits for row 2

change in total cost = 125- 100 = 25

change in units = 2 - 1 = 1

So, marginal cost = 25/1 = $25

Marginal benefit = change in total benefits/ change in units

= (150 - 120)/2-1 = 30/1 = $ 30

Change in total cost = 140 - 125 = 15

Change in units = 3 - 2 = 1

Change in total benefit = 175 - 150 = 25

So, marginal cost = 15/1 = $15

Marginal benefit = 25/1 = $25

Change in total cost = 160 - 140 = 20

Change in units = 4 - 3 = 1

Change in total benefit = 190 - 175= 15

So, marginal cost = 20/1 = $20

Marginal benefit = 15/1 = $15

Hence, we get all the values of question mark.

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Complete question:

Find Out the missing marginal costs and benefits in the above table. (see question marks) unit total cost marginal cost total benefit marginal benefit 1 100 100 120 120 2 125 ? 150 ? 3 140 ? 175 ? 4 160 ? 190 ?

Answer:

59

Step-by-step explanation:

2b^3+5 when b=3

Plug in the value of b

2*3^3+5 = 2*27+5 = 54+5 = 59

Answer:

1: Quotient

2: Difference

3: cos(x)cos(y)

Step-by-step explanation:

I just did it on Edge :)

Answer:

Step-by-step explanation:

it's right here lol

The expression shows the total amount in Diego's savings account after m months is 500 - 20m.

What is the total amount?

Two numbers are added together to form the sum. It is simple to figure out the sum of small integers. You can add two numbers using your fingertips. When two or more numbers are added together, a mathematical sum or maths sum is the outcome. It is the sum of the numbers when they are added up.

Here, we have

Given: Deigo has $500 in his saving account each month he takes out $20 to pay for karate class.

Let m be the number of months. Write an expression to show the total amount in Diego's savings account after m months.

The expression:

= 500 - 20m

Here m is the number of months

Hence, the expression shows the total amount in Diego's savings account after m months is 500 - 20m.

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Answer:

3

Step-by-step explanation:

6 divided by 2 is 3

Answer: 3

Step-by-step explanation:

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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Answer:

\((f+g)(x)=x^2-x-3\)

Step-by-step explanation:

We have \(f(x)=2x-1\) and \(g(x)=x^2-3x-2\)

Recall that \(f+g\) is defined by \((f+g)(x)=f(x)+g(x)\), therefore

\((f+g)(x)=f(x)+g(x)=2x-1+x^2-3x-2=x^2-x-3\)

a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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Answer:

For a given output value, there is, at most, one input value

Step-by-step explanation:

Given: the concept of function

To find: the statement that best describes the concept of a function

Solution:

A function is a relation in which every value of the domain has a unique image in the codomain.

Input value belongs to the domain and output value belongs to the codomain.

The statement ''For a given output value, there is, at most, one input value'' describes the concept of a function

The statement best describes the concept of a function is

For a given output value, there is, at most, one input value.

A relation is a function when each input has exactly only one output

Domain x is the input and range y is the output

In a function , each input x must have exactly only one output.

Input x cannot have two outputs.

The statement best describes the concept of a function is

For a given output value, there is, at most, one input value.

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In this case we can use the pythagorical theorem to find the distance so:

and we solve for x so:

so he is at 54.67 miles

Answer:

A = L × W A = L × W A=L×W.

A = L × W A = L × W A=L×W.

P = 2 L + 2 W P = 2L + 2W P=2L+2W.

The guests in the birthday party ate 33 cookies.

We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.

Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.

6 1/4 dozen = 25/4 dozen

3 1/2 dozen = 14/4 dozen

Now we can subtract the number of cookies that were left from the number of cookies that were made:

25/4 - 14/4 = 11/4 dozen

To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.

There are 12 cookies in one dozen, so:

11/4 x 12 = 33

Therefore, the guests ate 33 cookies.

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Step-by-step explanation:

given

\( \frac{7056}{x} = 42 \\ \\ 42x = 7056 \\ x = \frac{7056}{42} \\ = 168\)

also given

\( \frac{y}{112} = 8 \\ y = 8(112) \\ = 896\)

therefore

\( \frac{x}{y} = \frac{168}{896} \\ = \frac{3}{16} \)

Using the concept of domain and range of the functions, we have that:

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Hence we have that for the function graphed:

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Answer: $2000/yr

Step-by-step explanation:

$1/hour = $166.67/month

$1/hour = $40/week (50 weeks)

$1/hour = $38.46/week (52 weeks)

Answer:

Thus, the value of x is 1.

Step-by-step explanation:

4(2x+6)=32

8x+24 =32

8x =32-24

8x =8

x =8÷8

x =1

The definition of a quadratic spline is that;

A Quadratic Spline is the creation of a set of polynomial functions that are quadratic and follow the format f(x) = ax² + bx + c.

A Quadratic Spline is simply defined as the creation of a set of polynomial functions that are quadratic, or relatively simple to comprehend and must follow the quadratic function format which is;

f(x) = ax² + bx + c

where;

a, b and c are the values gotten in the process of doing the Splines to create the desired functions.

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If  the cost for using 35 HCF IS 61.83. . the cost for using 19 HCF of water is :$68.31.

Straight line: y=mx+b, m=slope, b=y-intercept

Let y=cost of using 19 HCF water

Let x =amount of water used

m=∆y/∆x =(61.83 - 32.13) / (35-19)

m=∆y/∆x =29.7 /16

m=∆y/∆x = 1.85625

m=∆y/∆x = 1.86  ($/HCF) (approximately)

equation: y=1.86x+b

Solving for b using point (19, 32.13)

32.13 =1.86×19+b

32.13=35.34+b

b=35.34 -32.13

b=3.21

equation:

f(x)=1.86x+3.21

f(25)=1.86×35+ 3.21

= 68.31

Cost of using 35 HCF water= $68.31

Therefore the cost price is $68.31.

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I got you, buddy!

Let x be the length of the shortest side. Then, the length of the second side is 2x, and the length of the third side is x + y, where y is the additional length.

The perimeter of the triangle is the sum of the three sides, so we have:

x + 2x + (x + y) = 60

Simplifying this equation, we get:

4x + y = 60

We also know that the area of a triangle is given by:

A = (1/2)bh

where b is the length of the base, and h is the height. Since the base of the flower bed is the shortest side of length x, we can choose the height to be y. Therefore, we have:

A = (1/2)xy

Now we need to solve for x and y. We can use the equation for the perimeter to solve for y:

y = 60 - 4x

Substituting this into the equation for the area, we have:

A = (1/2)x(60 - 4x)

Simplifying and expanding, we get:

A = 30x - 2x^2

To maximize the area, we can take the derivative of A with respect to x and set it equal to 0:

dA/dx = 30 - 4x = 0

Solving for x, we get:

x = 7.5

Substituting this back into the equation for y, we get:

y = 60 - 4x = 45

Therefore, the dimensions of the flower bed are:

shortest side = x = 7.5 feet second side = 2x = 15 feet third side = x + y = 52.5 feet

The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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Step-by-step explanation:

it is just 2.50 divided by 5 will give you 0.5

Answer:

its                                                                                                                                                

Step-by-step explanation:

Answer:

0.49926

Step-by-step explanation:

We solve for this using z score formula

z-score is

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation

The probability that defect length is at most 20 mm is calculated as:

x = 20mm, μ = 33 mm, σ = 7.9mm

z = 20 - 33/7.9

= -13/7.9

= -1.64557

Obtaining the Probability value from Z-Table:

Probability (At most 20mm) = P(x ≤ 20mm) P(z = -1.64557)

P(x ≤ 20) = 0.049926

Therefore, the probability that defect length is at most 20 mm is 0.049926

Answer:

The probability that defect length is at most 20 mm is 0.0495.

Step-by-step explanation:

We are given that the defect length of a corrosion defect in a pressurized steel pipe is normally distributed with a mean value of 33 mm and a standard deviation of 7.9 mm.

Let X = the defect length of a corrosion defect in a pressurized steel pipe

The z-score probability distribution for the normal distribution is given by;

                             Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = mean defect length = 33 mm

           \(\sigma\) = standard deviation = 7.9 mm

So, X ~ Normal(\(\mu=33 \text{ mm}, \sigma^{2} = 7.9^{2} \text{ mm}\))

Now, the probability that defect length is at most 20 mm is given by = P(X \(\leq\) 20 mm)

        P(X \(\leq\) 20 mm) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{20-33}{7.9}\) ) = P(Z \(\leq\) -1.65) = 1 - P(Z < 1.65)

                                                             = 1 - 0.9505 = 0.0495              

The above probability is calculated by looking at the value of x = 1.65 in the z table which has an area of 0.9505.