Suppose I'm trying to prove that 2 divides n2 - n for any natural number n If the end/goal of my induction step is 2 divides p2 Then my inductive hypothesis must have been Select one: a. n-n is true for n-0,1...,p-1 b.2 divides n2 - n for n-0,1,..,k-1 C. 2 divides n - n for n=0,1,...,p-1 d. 2 divides n-n for n=0,1,...,p e. 2 divides n -n for n=0,1,...,p+1

(a) The recursive formula for An is: An = (1.015)An-1 - 100.

(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].

(a) This formula says that to find the balance for month n, we take the balance for month n-1, multiply it by 1.015 (to account for the interest rate), and subtract 100 (to account for the withdrawal). This formula is consistent with the results for n=1,2,3 on the previous page.

(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].

This formula says that to find the balance for month n, we take the starting balance of 4000 multiplied by the interest rate raised to the power of n, and then subtract the sum of 100 multiplied by the geometric series (1 + r + r^2 + ... + r^(n-1)), where r = 1.015. This formula is consistent with the results for n=1,2,3 on the previous page.

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Answer:

10km

Step-by-step explanation:

Pythagoras

Formula=[tex]a^2+b^2=c^2[/tex]

[tex]6^{2} +8^{2} =c^2\\c^2=100\\c=\sqrt{100} \\c=10km[/tex]

a) Heating cost for a month with 25°F is $67.10

b) Heating cost for a month with 0°F is $98.60

c) Decrease in the monthly heating cost is $1.26

The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.

(a) To find the predicted heating cost for a month with an average temperature of 25°F, we can substitute x = 25 into the equation of the line of best fit:

y = -1.26x + 98.60

y = -1.26(25) + 98.60

y = 67.10

Hence, $67.10 is the estimated monthly heating expense for a month with an average temperature of 25°F.

(b) To find the predicted heating cost for a month with an average temperature of 0°F, we can substitute x = 0 into the equation of the line of best fit:

y = -1.26x + 98.60

y = -1.26(0) + 98.60

y = 98.60

Thus, $98.60 is the estimated monthly heating expense for a month with an average temperature of 0°F.

(c) The slope of the line of best fit is -1.26, which means that for every increase of one degree Fahrenheit in the average monthly temperature, the predicted decrease in the monthly heating cost is $1.26.

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Answer:

1) [tex]y\leq 2x-3[/tex]

2)See below photo, or graph it yourself using [tex]y < 2 - \frac{1}{2} x[/tex]. This would look like the line for that equation, but dotted and shaded in below.

3) I disagree with Oscar. Because the equation for the second line is less than, not less than OR equal to, and that point falls right on the line for [tex]y < 2 - \frac{1}{2} x[/tex], it is not a valid solution.

Step-by-step explanation:

1) First, I found the slope. It's rising 2 over 1, so the slope is 2/1 or 2. Then, the y-intercept, which is -3. From there I created the equation.

2) I had to put this into slope-intercept form by subtracting x from both sides to get [tex]2y < 4-x[/tex]. Then I divided both sides by two to get [tex]y < 2 - \frac{1}{2} x[/tex]. Then I put it into an online graphing program (I used desmos's).

3) Explains itself!

Let me know if this helped by hitting thanks or brainliest. If not, please comment and I'll get back to you ASAP!

The ratio of the deposit to the total of the 12 equal payments is 3 : 5.

The VAT on the van is calculated as follows:

VAT = 20% * £8500 = £1700

Total cost = £8500 + £1700 = £10200

Total amount paid in the 12 equal payments = 12 * £531.25 = £6375

Deposit = £10200 - £6375 = £3825

Deposit : Total of 12 equal payments = £3825 : £6375 = 3 : 5

Therefore, the ratio of the deposit Raya pays to the total of the 12 equal payments is 3 : 5.

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Answer:

∠ BAC and ∠ CAD

Step-by-step explanation:

• Complementary angles sum to 90°

∠ BCA and ∠ ACD are a linear pair and sum to 180°

∠ BCA + 110° = 180° ( subtract 110° from both sides )

∠ BCA = 70°

the sum of the 3 angles in a triangle = 180°

in Δ ABC

∠ BAC + 55° + 70° = 180°

∠ BAC + 125° = 180° ( subtract 125° from both sides )

∠ BAC = 55°

in Δ ACD

∠ CAD + 110° + 35° = 180°

∠ CAD + 145° = 180° ( subtract 145° from both sides )

∠ CAD = 35°

then

∠ BAC + ∠ CAD = 55° + 35° = 90°

∠ BAC and ∠ CAD are complementary

Answer:

  (a)  ∠BAC and ∠CAD

Step-by-step explanation:

You want to know which angles in the figure are complementary.

Two angles are complementary when the total of their measures is 90°. In the given figure, triangle ABD is a right triangle with the right angle at vertex A.

The two acute angles at vertices B and D will be complementary:

  ∠ABC and ∠CDA . . . . . not on the list of choices

Ray AC divides the right angle into two complementary parts:

  ∠BAC and ∠CAD . . . . . first choice on the list

__

Additional comment

The two smaller triangles are isosceles. Angles CDA and CAD are both 35°, so have a sum of 70°. Likewise, angles ABC and BAC are both 55°, with a sum of 110°.

Angles BCA and ACD are a linear pair, so have a sum of 180°. They are supplementary, not complementary.

Answer:

-11

Step-by-step explanation:

48 ÷8=6-15=-9

99÷-9=-11

We need 144 men to build the house in 12 days working 13 hours a day.

Let M be the number of men needed to build the house in 12 days working 13 hours a day.

140 x 10 x 16 = M x 13 x 12

Simplifying the equation, we get:

22400 = 156M

Dividing both sides by 156, we get:

M = 144.1

An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.

Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.

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Barbara will get $7.20 back in change.

A sales tax that is typically added to the selling price by the seller.

Without tax, the total cost of the shirt and pants is:

$15.00 + $25.00 = $40.00

The sales tax is 7% of $40.00, which is as follows:

0.07 x $40.00 = $2.80

So, with tax, the total cost of the shirt and pants is:

$40.00 + $2.80 = $42.80

If Barbara pays with a $50 bill, she will receive the following change:

$50.00 - $42.80 = $7.20

As a result, Barbara will receive $7.20 in change.

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a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:

Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day

Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.

b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:

1 machine : 2.5 crates/day = 70 machines : x crates/day

Solving for x, we get:

x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day

Therefore, 70 of these machines would pack 175 crates of limes per day.

Step-by-step explanation:

a) The ratio of the number of machines to the number of crates packed per day can be written as:

60 : 150

To simplify this ratio, we can divide both sides by 10:

6 : 15

Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:

1 : 2.5

Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.

b) If 60 machines can pack 150 crates per day, then one machine can pack:

150/60 = 2.5 crates per day

So, 70 machines can pack:

70 × 2.5 = 175 crates per day

Therefore, 70 machines can pack 175 crates of limes per day.

a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.

b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.

a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.

Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.

Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.

b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.

Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.

Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.

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From the survey of 50 people 20 people like chocolate.

A survey was conducted with 50 people, out of which 30 liked chocolate, 20 liked vanilla, and 10 liked both. The question is asking how many people like chocolate.

To determine the number of people who like chocolate only, we subtract the number of people who like both flavors from the total number of people who like chocolate.

The number of people who like chocolate alone = total number of people who like chocolate - the number of people who like both

= 30 - 10= 20

This means that out of the 50 people surveyed, 20 individuals like chocolate, while 10 people enjoy both chocolate and vanilla.

Therefore, 20 people like chocolate.

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Answer:

5:3 = 5/3

Step-by-step explanation:

Given Sin∅ = 3/5

We know sin∅ = Perpendicular/Hypotenuse

And, By inverse relationship, we get

cosec∅ = Hypotenuse/Perpendicular = 1/sin∅

So, csc∅ = 5/3, 5:3

a block slides along a track that descends through distance h. The track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. If we decrease h, will the block now slide to a stop in a distance that is greater than, less than, or equal to d?As per the given information, when a block slides along a track that descends through a distance h, the track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. Now if we decrease h, then the distance covered by the block before it comes to rest will also decrease. So the block will slide to a stop in a distance that is less than d. Hence the answer is less than d.If we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?

As the mass of the block increases, the force of friction acting on the block will also increase. Hence the stopping distance will also increase. So the stopping distance now will be greater than d. Hence the answer is greater than d.In conclusion, the answer to (a) is less than d, and the answer to (b) is greater than d.

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The x-intercepts are (0, 0) and (4, 0), and the y-intercept is (0, 0).

By graphing linear equatiοns, yοu can explain the relatiοnship between twο variables visually. We can easily see what happens tο οne variable as the οther grοws by using a graph. The value οf the x variable rises as we mοve tο the right οn a graph.

[tex]y = (3/2)x^2 - 6x[/tex] is the given equatiοn.

We can use the fοrmula tο find the x-cοοrdinate(s) οf the vertex οf this parabοla:

x = -b/2a

where a and b are the cοefficients οf the equatiοn's x² and x terms, respectively.

In this case, a = 3/2 and b = -6, resulting in:

x = -(-6)/(2*3/2) = 4

As a result, the vertex's x-cοοrdinate is 4.

Tο find the y-cοοrdinate οf the vertex, enter this value οf x intο the fοllοwing equatiοn:

[tex]y = (3/2)(4)^2 - 6(4) = -12[/tex]

As a result, the parabοla's vertex is at the pοint (4, -12).

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The lower limit of a 90% confidence interval for the average difference in the number of days the temperature was above 90 degrees between 1948 and 2018 is -22.8 days and the upper limit is 28.6 days.

The margin of error for the 90% confidence interval is 25.4 days.

The 90% confidence interval does provide evidence that the number of 90-degree days increased globally comparing 1948 to 2018.

The 99% confidence interval also provides evidence that the number of 90-degree days increased globally comparing 1948 to 2018.

If the mean difference and standard deviation stay relatively constant, decreasing the degrees of freedom would make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.

Lowering the confidence level would also make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.

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Here are the solutions:

a) R4 = {(a, b, c, d) | a, b, c, d ∈ R}

b) P3 = {a0 + a1x + a2x^2 + a3x^3 | a0, a1, a2, a3 ∈ R}

c) M22 = {(aij) | i, j = 1, 2}

d) M23 = {(aij) | i = 1, 2, j = 1, 2, 3}

For the given vector space R4 with the standard vector addition/scalar multiplication, the zero vector is the following: 0 = [0, 0, 0, 0].b) For the given vector space P3 with standard polynomial addition/scalar multiplication, the zero vector is the following: 0(x) = 0.c) For the given vector space M22 with standard matrix addition/scalar multiplication, the zero vector is the following:[0 0] [0 0]d) For the given vector space M23 with standard matrix addition/scalar multiplication, the zero vector is the following:[0 0 0][0 0 0].

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Amina's percentage profit is 25%, as the percentage profit must be rounded down to the nearest whole number.

Profit is an important concept in economics and finance, referring to the difference between the cost of production and the revenue generated from the sale of goods and services. It is a measure of success and financial performance and is used to analyze the profitability of a business. Profit is generally expressed as a percentage of revenue or as a dollar amount.

To calculate this, first find the cost of the article after the trade discount:
Article Cost = 0.75p - (0.75p * 0.25) = 0.75p * 0.75 = 0.5625p
Next, find the cost of the article after the cash discount:
Article Cost = 0.5625p - (0.5625p * 0.05) = 0.5625p * 0.95 = 0.5343p
Finally, calculate the percentage profit:
Percentage Profit = (0.75p - 0.5343p) / 0.75p * 100 = 0.2167 / 0.75 * 100 = 28.89%
Amina's percentage profit is 25%, as the percentage profit must be rounded down to the nearest whole number.

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The volume of a hexagonal pyramid in cubic feet with the same dimensions = 1220 ft³

A hexagοnal pyramid is a three-dimensiοnal geοmetric shape that cοnsists οf a base that is a regular hexagοn (a six-sided pοlygοn with all sides and angles equal) and six triangular faces that meet at a single pοint abοve the base, called the apex.  The six triangular faces fοrm a pyramid shape with the base, which is why it's called a hexagοnal pyramid.

This relatiοnship can be derived using the fοrmula fοr the vοlume οf a pyramid  V = (1/3)Bh, where B is  area οf  base and h is  height οf pyramid. Since the base οf the pyramid is a hexagοn inscribed within the hexagοnal base οf the prism, the area οf the base is (3√3/2)a², where a is the side length οf the hexagοn. The height οf the pyramid is the same as the height οf the prism, which we can call h.

Thus, the volume of pyramid is

[tex]\rm V_p[/tex] = (1/3)(3√3/2)a²h

= (√3/2)a²h, while the volume of prism is

[tex]\rm V_p[/tex]r = [tex]\rm B_p[/tex]r h = (3√3/2)a²h.

Dividing [tex]\rm V_p[/tex]r by 3 gives [tex]\rm V_p[/tex]

so we have [tex]\rm V_p[/tex] = [tex]\rm V_p[/tex]r/3, as claimed. so

[tex]\rm V_p[/tex] = 3360/3 ft³

[tex]\rm V_p[/tex] = 1220ft³

volume of a hexagonal pyramid in cubic feet 1220ft³

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The combined score on the 2022 SAT test ranges from 400 to 1600. If you were to randomly draw five numbers from a 400-1600 number set, the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers is approximately 0.004%

To find the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers, we need to find the probability of the following event: “the three other random numbers drawn lie between the highest and lowest values.

The probability of choosing one of the five numbers that falls within the range is (1600 – 400)/1201 = 1/2.25.

The first number can be any number within the 400-1600 range, so the probability is 1.The second number must lie within the range created by the highest and lowest values of the first number, which has a width of 1201. Thus, the probability is 1201/3201.

The third number must lie within the range created by the highest and lowest values of the first two numbers, which has a width of 801. Thus, the probability is 801/2401.The fourth and fifth numbers must lie within the range created by the highest and lowest values of the first three numbers, which has a width of 401.

Thus, the probability is 401/1601.Therefore, the probability of the medium score of the actual 2022 SAT results being between the highest and lowest values of these five random numbers is (1/2.25) * (1201/3201) * (801/2401) * (401/1601) * 1 = 0.000038 or approximately 0.004%.

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A principal gathered data about the distance in miles that his teachers and bus drivers live from the school. then, the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.

Interquartile Range:

In descriptive statistics, the interquartile range (IQR) is a measure of the statistical distribution, the distribution of data. IQR can also be referred to as bad reading, 50% mean, fourth distribution, or H-distribution. It is defined as the difference between the 75th and 25th percentile of the data. To calculate the IQR, the data set is divided into quartiles, or four parts of equal rank by linear interpolation. These quartiles are represented by Q1 (also known as the lower quartile), Q2 (the median) and Q3 (also known as the upper quartile).

The lower quartile is the 25th percentile and the upper quartile is the 75th percentile, so IQR = Q3 − Q1

Basically, the interquartile range represents the width or “spread” of the collection. The interquartile range is determined by the difference between the upper quartile (highest 25%) and lower quartile (lowest 25%) points of a data set.

From the figure, we can find:

The interquartile range of the bus driver is: 20 -10 = 10

The interquartile range of the teacher is: 30 -15 = 15

Therefore,

the interval interquartile distance is bus The driver's distance was 5 miles less than the interquartile range of the teacher's distance.

Complete Question:

A principal gathered data about the distance in miles that his teachers and bus drivers live from the school .The box plots below show these data.

(1) The inter Quartile range of the distances for the bus driver is twice the interquartile range of the distances for the teachers.

(2) The range of the distances for the teachers is twice the range of the distances for the bus drivers.

(3) the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.

(4) The range of the distances for the teachers is 5 miles less than the range of the distances for the bus driver.

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Answer: C. The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.

Answer:

what

Step-by-step explanation:

what

The ribbon cost $0.60 per foot.

[tex]\text{Total number of ribbon used} = (5.75 + 11.75) = 17.50 \ \text{feet}[/tex]

[tex]\text{17.50 feet of ribbon cost} = \$10.50[/tex]

[tex]\text{1 foot of ribbon cost = x}[/tex]

[tex]17.50 \times x = 1 \ foot \times \$10.50[/tex]

[tex]x = 1 \ foot \times 10.50\div17.50[/tex]

[tex]x = \$0.60[/tex]

Therefore, The ribbon cost per foot $0.60 per foot.

Answer:

Step-by-step explanation:

How does Priestley present the theme of social class in Act 1? 3 paragraphs 80 POINTS!!!

INTRODUCTION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?

PARAGRAPH 1 -

PARAGRAPH 2-

PARAGRAPH 3-

CONCLUSION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?

The average productivity of the workforce, A(x), is given by

A(x) = p(x)/x,

where p(x) is the total value of the production when there are x workers in the plant.

A'(x) is the derivative of A(x) with respect to x.

A'(x) = (p(x)/x)' = (p'(x)x - p(x))/x^2.

The company wants to hire more workers if A'(x) > 0 because it means that the average productivity of the workforce is increasing with additional workers.

A'(x) > 0 if p'(x) is greater than the average productivity, which is p(x)/x.

Therefore, A'(x) > 0 if p'(x) > p(x)/x.
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Answer:

m = -9/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4, -6) (2, 3)

We see the y increase by 9, and the x decrease by 2, so the slope is

m = -9/2

Answer:

You didn't give any options, but I'm guessing one of them has a 3 in the tens digits, which should be the right answer

Step-by-step explanation:

300?

The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.

To estimate y(2.5) with step size 0.1 using Euler's Method, we need 5 iterations. The iterative formula is Yn = Yn-1 + hF(xn-1, Yn-1), where F(x, y) = 4y + 3xy. Using this formula and the initial condition Y(2) = 1, the 5 iterations are:

Therefore, the approximation of y(2.5) using Euler's method with step size 0.1 is

.

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In order to make the additionaI 100 toy cars required to meet demand, the company wiII need to run the machine for 8 hours.

To answer mathematics issues invoIving proportionaI reIationships, utiIize the unitary method. It entaiIs determining the vaIue of a singIe unit or item and using that data to determine the vaIue of a specified number of units or items. When tackIing chaIIenges in business, finance, and science that require rates, ratios, and proportions, the unitary technique is very heIpfuI. The unitary technique, for instance, can be used to caIcuIate a singIe item's price given the price of aII the other products combined.

given

The formuIa beIow can be used to determine how Iong it wiII take to generate the requisite number of toy cars if we know the rate at which the machine produces them:

Time is caIcuIated as (Number of toy cars required - Number of toy cars in stock) / Production Rate.

For instance, if the machine can produce 10 toy cars per hour and the business needs to make an additionaI 100 to compIete the order, but they aIready have 20 toy cars on hand, the time needed to make the extra toy cars wiII be:

Time = (100-20) / 10 = 8 hours.

In order to make the additionaI 100 toy cars required to meet demand, the company wiII need to run the machine for 8 hours.

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Complete question:

1. A machine at a cοmpany makes toy cars at a constant rate. The company received an order for toy cars that exceeded the number of toy cars that the company had in stock.

Which three pieces of information are needed to determine the amount of time it will take the machine to make enough additional toy cars to fill the order?

Select the three pieces of information that are needed.

A. the cost to make each toy car

B. the rate that the machine makes toy cars

C. the number of toy cars requested in the order

D. the number of people needed to run the machine

E. the number of toy cars available when the order was received