for every natural number n, n^5 + 4n is a multiple of 5 could begin with... what is the appropriate next step

Answer:

Susan payed $30 for her purchase

Step-by-step explanation:

Chicken: $12.36 per package (x2) = $24.72

Broccoli: $1.98 per pound (x1/2)   =   $0.99      +

Milk: $3.49 per gallon (x1)             =   $3.49

-and no added sales tax             ____________

                                                           $29.20

If Susan got $0.80 in return, then she must have payed $30 to begin with.

Answer:

The amount of money that Susan use to pay for the items = $30

Step-by-step explanation:

2×(12.36)+0.5×(1.98)+(3.49)+(0.8) = 30.

:)

Answer:

The graph of the inverse function is the same that the graph of the original function

Step-by-step explanation:

step 1

Find the equation of the function in the graph

Let

f(x) ---> the function in the graph

we know that

Is a linear function

take the points (0,6) and (6,0)

Find the slope of the linear function

[tex]m=(0-6)/(6-0)\\m=-1[/tex]

Find the the equation of the linear function in slope intercept form

[tex]f(x)=mx+b[/tex]

we have

[tex]m=-1[/tex]

[tex]b=6[/tex] ---> the y-intercept is given

substitute

[tex]f(x)=-x+6[/tex]

step 2

Find the inverse of the function f(x)

Let

y=f(x)

[tex]y=-x+6[/tex]

Exchange the variables (x for y and y for x)

[tex]x=-y+6[/tex]

Isolate the variable y

[tex]y=-x+6[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=-x+6[/tex]

[tex]f^{-1}(x)=f(x)[/tex]

In this problem the graph of the inverse function is the same that the graph of the original function

Graphing the inverse of a function is achieved by flipping the graph over the line y = x. In science, graphs of inversely proportional variables like P and V form a hyperbola, but these can be 'linearized' for clarity and accuracy. Often, a regression analysis is utilized to find the best fitting line within a set of data plots.

To graph the inverse of a function, you observe the function as a set of points in a 2D space (on a graph) and flip each point over the line y = x. This results in a new function, which is the inverse. When it comes to more specific functions like pressure and volume relationships, this is shown when plotting the inverse of the pressure (P^-1) versus the volume (V), or the inverse of volume (V^-1) versus the pressure (P).

Scientists often linearize data when graphs have curved lines because they're difficult to read accurately at low or high values. If you plot P (pressure) versus V (volume), you will get a hyperbola. This kind of function can be 'linearized' to make it easier to understand and interpret.

Finally, in many cases, such as plotting data points of inflation rate versus unemployment rate, the resulting graph can be analysed using a statistical process called regression. This helps to find the best fitting line for the set of data plots, which can often not perfectly fit the line.

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Answer:

[tex]z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5[/tex]  

[tex]p_v =2*P(Z>0.5)=0.617[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.  

Step-by-step explanation:

1) Data given and notation

n=400 represent the random sample taken

X=84 represent the number of items defective

[tex]\hat p=\frac{84}{400}=0.21[/tex] estimated proportion of defectives

[tex]p_o=0.2[/tex] is the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.2 or 20%:  

Null hypothesis:[tex]p=0.2[/tex]  

Alternative hypothesis:[tex]p \neq 0.2[/tex]  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.1[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(Z>0.5)=0.617[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.  

Answer: Comment: From the explanations below,

2x + y = 10

-6x = 3y + 7 had an infinite solution, while y = 14 -2x

6x + 3y = 42 has a fictitious solution, so also equation

2x + y = 17

-6x = 3y - 51.

Step-by-step explanation:

Answer:

(C) y = 14 - 2x

6x + 3y+ 42

(F) 2x + y = 17

-6x = 3y - 51

Step-by-step explanation:

Plato Correct answer.  Got them right.  Select the two boxes that have the equation written above.

Answer:

$119.32

Step-by-step explanation:

Leiff decides to buy his video game, with a price tag of $128, at this site

he will get the 15% discount when he checks out.

100-15= 85%

Discounted price=85% of 128 is [tex]0.85 \cdot 128=108.8[/tex]

Leiff pays 5.3% sales tax on the discounted price

5.3% is 0.053

sales tax amount=0.053 times 108.8=5.7664

So we add the sales tax amount and shipping fee

[tex]108.8+5.7664+4.75=119.32[/tex]

So $119.32 is the total amount

The total of Leiff’s online purchase is $119.31.

To calculate the total of Leiff's online purchase, we need to first calculate the discount on the video game.

The discount is calculated by multiplying the original price of the video game by the discount rate.

Discount = $128 * 15%

= $19.20

The discounted price of the video game is the original price minus the discount.

Discounted price = $128 - $19.20

= $108.80

The sales tax is calculated by multiplying the discounted price of the video game by the sales tax rate.

Sales tax = $108.80 * 5.3%

= $5.76

The total cost of the video game, including the discount and sales tax, is:

Total cost = $108.80 + $5.76

= $114.56

The total cost of Leiff's online purchase is the cost of the video game plus the shipping fee.

Total cost = $114.56 + $4.75

= $119.31

Therefore, the answer is $119.31.

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Answer:

c.Mean

Step-by-step explanation:

We have been given that the Sally is interested in taking a job in a city in which she's not familiar with the cost of living. She is especially concerned about the cost of housing and is interested in the average cost of a three bedroom home.

We know that in a normal distribution all central tendencies (mean, mode, median) are equal.

When a very large or very small valued data point is added to data set, mean is mostly affected by that outlier.

We know that mode of a data set is the point that appears at-most in the data set, so outliers doesn't affect mode.

Median of a data set is less affected by outliers.

The price of the three bedroom homes owned by millionaires will be greater than prices of houses owned by people in the neighborhood.

Therefore, mean will be most influenced by three bedroom homes owned by millionaires.

Answer:

On average the carnival gain on each play

= 0.04 dollars

Step-by-step explanation:

Given that a pond contains 100 fish: 78 purple, 21 blue, and 1 silver.

Fish            Purple     Blue          Silver    total

Frequency  78               21                 1    100

Prob          0.78      0.21             0.01      1

Revenue           0.4                0.8            13  

game fee 0.65        0.65            0.65  

Net revenue -0.25      0.15            12.35    

Net Rev*Prob -0.195      0.0315   0.1235   -0.04

Thus we get per player expected net revenue is -0.04

This would be gain for Carnival

Hence On average the carnival gain on each play

= 0.04 dollars

Final answer:

To calculate the carnival's average gain per play, determine the expected payoff for each fish type, subtract the cost to play, and sum these amounts. The carnival gains an average of $0.61 per play.

Explanation:

The student's question involves calculating the average gain for a carnival on each play of a carnival fishpond game. To find this, we need to determine what the carnival earns on average based on the probabilities of catching each type of fish (purple, blue, or silver) and the payoff for each.

Let's calculate the expected profit (gain) per play for the carnival. The probability and payoff for each type of fish are:

Purple fish: Probability = 78/100, Payoff = $0.40

Blue fish: Probability = 21/100, Payoff = $0.80

Silver fish: Probability = 1/100, Payoff = $13.00

The expected payoffs for the carnival from catching each type of fish are:

Purple: 78/100 * $0.40

Blue: 21/100 * $0.80

Silver: 1/100 * $13.00

Subtract the contestant's cost ($0.65) from each expected payoff to find the expected gain. Then, sum these expected gains to find the overall average gain for the carnival.

The carnival's expected gain is:

Expected Gain per Play = (78/100 * $0.40) + (21/100 * $0.80) + (1/100 * $13.00) - $0.65

Calculating:

Expected Gain per Play = ($0.3120) + ($0.1680) + ($0.1300) - $0.65

Expected Gain per Play = $0.61

This calculation shows that on average, the carnival gains $0.61 for each play of the fishpond game.

Answer:

He can take 5 Horses at max in his trailer at one time without going over the max weight his truck can tow. (Assuming the average weight of one horse to be equal to 1000 pounds)

Step-by-step explanation:

The no. of horses that can be carried by the truck can be found by simply dividing the maximum weight, that the truck can tow by the weight of a horse.

Max. No of Horses = (Max weight truck can tow)/(Average weight of one    horse)

The weight of a horse is not given in the question .Thus, we assume the average weight of one horse, to be equal to 1000 pounds, we get:

Max. No of Horses = 5000 pounds/ 1000 pounds

Max. No of Horses = 5

Answer:

C. Darwin realized this also applied to plant and animal populations, and this struggle for existence resulted in an opportunity for natural selection to act on differences within populations.

Step-by-step explanation:

Thomas Malthus in his Malthusian theory of population concluded that since population increases geometrically and  resources only increase arithmetically, there will reach a point in time when the resources will be not be able to sufficiently cater for the population.

The Charles Darwin theory of Evolution is based on five key observations and conclusions drawn from them. These observations and inferences are summarized as:

Based off these observations, it is seen that there will be a struggle amongst the members of the specie for the limited resources.

From the last two observations, the species that survive then pass on their traits to their offspring and the cycle repeats itself with each subsequent generation being better evolved than the previous ones.

Thus, Darwin discovered that the Malthusian theory of population also applies to plant and animal populations where scarcity of resources gives room for natural selection to take place due to the variation within populations.

Answer:

B = 47°

Step-by-step explanation:

THe theorem to solve this is very simple. The angle created Angle B intercepts to arcs, one major, another minor.

The major arc is DE, 142 degrees.

The minor arc is AC, 48 degrees.

The two secants intersect outside the circle and creates a vertex angle, Angle B. The theorem tells us that the measure of that vertex angle would be ONE HALF of the difference of the two intercepted arcs. So, we have:

[tex]B=\frac{1}{2}(142-48)=47[/tex]

So, B = 47°

[I'm still thinking sorry]

I'm assuming 2x-12 is the angle measure of DAC in degrees.

Let p=AB=AD, q=AC

By the Law of Cosines,

22² = p² + q² - 2pq cos 48°

q² - 2pq cos 48° + p² - 22² = 0

We also require by the triangle inequality

CD+AD < AC

16 + p < q

Let's set them equal and see where we are.

q=p+16

(p+16)² - 2p(p+16) cos 48° + p² - 22² = 0

p≈12.2125,

q≈28.2125

16² = p² + q² - 2 pq cos DAC

16² = 12.2125² + 28.2125² - 2 (12.2125)(28.2125) cos DAC

cos DAC = (12.2125² + 28.2125²  - 16²)/(2 (12.2125)(28.2125) ) = 1

That's a surprise, DAC maxes out at a right angle

90 = 2x - 12

102 = 2x

x = 51

Answer: 6 < x < 51

Answer:

[tex]Jade's\,score=5*right\,answers[/tex]

Step-by-step explanation:

Because all the questions have the same point, we can find the weight (value) of each question dividing the total points by the total number of answers questions:

[tex]\frac{100}{20}= 5[/tex]

Now with the weight of each question the only thing we should to do is to multiply it by the number of the questions she got right:

[tex]Jade's\,score=5*right\,answers[/tex]

Let check if our equation works, if Jade got all the answers right, we expect she got a 100 score. Let verify on the equation

[tex]Jade's\,score=5*(20)=100[/tex], that's what we expected

If she got 10 right answers, we expect 50 score and if she got 0 right answers, we expect 0 score, let check again:

[tex]Jade's\,score=5*(10)=50[/tex]

[tex]Jade's\,score=5*(0)=0[/tex]

Again, we obtain the expected scores, so we can conclude our equation works.

To find Jade's score on the math test, calculate the points per question by dividing the total points (100) by the number of questions (20). Each question is worth 5 points. Jade's score is the number of questions she got right multiplied by 5 points.

To calculate Jade's score on a math test with 20 questions that is worth a total of 100 points, we can start by finding out how many points each correct answer is worth. Since the total points are evenly distributed among the questions, we divide the total points by the number of questions.

Each question is worth 5 points (100 points total ÷ 20 questions).

Let x represent the number of questions Jade got right. The equation to calculate Jade's score is then:

Score = 5 × x

To find Jade's score, we simply multiply the number of questions she got right by 5. For example, if Jade answered 16 questions correctly, her score would be 80 points (5 points/question × 16 questions).

Answer:

63 degrees

Step-by-step explanation:

add 4x + 23 and 6x + 7, then equal that to 130. When you find x, plug it into 4x+23 and get 63.

Answer:

-2L² + 50L − 300 ≥ 0

Step-by-step explanation:

View Image

Perimeter is the sum of all the sides. She got 50 feet of fence work with. So our equation right now is:

y + y + x + x = 50

However, she used her house for one of the side, so we can remove one of the side. Our new equation is now:

y + y + x = 50

Solve for one of the side. I solved for x because it's easier to work with and substitute later. I got x = 50 - 2y.

Now I solve for area. Area of a rectangle is Length * Width.

A = LW

I used x and y for my sides so my area is this instead:

A = yx

Substitute in x.

A = y(50 - 2y)

A = 50y - 2y²

Area must be a minimum of 300ft², so

50y - 2y² ≥ 300

50y - 2y² - 300 ≥ 0

replace y with L because that's what they used in the answer choice

-2L² + 50L − 300 ≥ 0

Answer:

-2l^2+50l-300 ≥ 0

l(50 − 2l) ≥ 300

(l − 15)(l − 10) ≤ 0

Step-by-step explanation:

Answer:

The proper time sequence of the three political parties/movements, from earliest to latest is as follow:

Step-by-step explanation:

Answer:

  (3/4)(√3)r²

Step-by-step explanation:

The largest such triangle is an equilateral triangle. It will have a side length of r√3. The area can be found a number of ways, one of which is to use the formula for the area of an equilateral triangle of side length s:

  A = s²·(√3)/4

Using s=r√3, we get ...

  A = (3/4)(√3)r²

Answer:the number of sixth graders is 28

Step-by-step explanation:

Total number of students in the school band is 70. 40% are sixth graders. 20% are seventh graders and the rest are eighth graders. This means that the percentage of eighth graders is 100 - (40+20) = 100 - 60 = 40%

This means that the number of sixth graders would be 40% of the total number of students in the school band. It becomes

40/100 × 70 = 0.4×70 = 28

Answer:

[tex]2^{2005}[/tex]

Step-by-step explanation:

We are given [tex]f^{[2005]}(x) = \frac {1}{2}[/tex].

Hence, [tex]f(f^{[2004]}(x))=\frac{1}{2}[/tex].

Assume [tex]y=f^{[2004]}(x)[/tex].

Hence, [tex]f(y)=\frac{1}{2}[/tex] or [tex]y=\frac{1}{4}[/tex] or [tex]y=\frac{3}{4}[/tex].

So we can conclude that [tex]f^{[2004]}(x)=\frac{1}{4}[/tex] or [tex]f^{[2004]}(x)=\frac{3}{4}[/tex].

So we can find [tex]f(f^{[2003]}(x))=\frac{1}{4}[/tex] orf(f^{[2003]}(x))=\frac{3}{4}.

Assume [tex]z=f^{[2003]}(x)[/tex].

Hence, [tex]f(z)=\frac{1}{8}[/tex] or f(z)=\frac{7}{8} or f(z)=\frac{5}{8} or f(z)=\frac{3}{8}.

Therefore, we double the number of possible solutions for each iteration.

Thus, the number of solutions is [tex]2^{2005}[/tex].

Answer:

145

Step-by-step explanation:

To find the number of boxes to reach the goal, divide the goal amount by the box amount:

[tex]650 \div 4.50 \approx144.444444[/tex]

Since you can't sell .444444 of a box, you must sell 145 boxes.

1/2, or one half. since she cuts it into 2.

Answer:

Step-by-step explanation:

You just need the distance formula here.  It's very simple to follow:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }[/tex]

which, for us, looks like this:

[tex]d=\sqrt{(13-4)^2+(19-7)^2}[/tex] and

[tex]d=\sqrt{9^2+12^2}[/tex] and

[tex]d=\sqrt{81+144}[/tex] and

[tex]d=\sqrt{225}[/tex] so

d = 15

Answer:

(3) Jonah's graph has a steeper slope than Rowan's

Step-by-step explanation:

First we are going to write the equations for the amount of money that each one save

y = a+bx

 Where y: Amount of money in the jar

             a: Initial saving

             b: Money saved every week ( graph's slope )

             x: Number of week

Then, for Rowan

y = 50 + 5x

and for Jonah

y = 10 + 15x

Initially Rowan's graph lies above Jonah's graph but this situation change with time.

It is always true that Jonah's graph has a steeper slope than Rowan's, because for Rowan's graph the slope is 5 and for Jonah's graph the slope is 15

Then the answer is:  

(3) Jonah's graph has a steeper slope than Rowan's

3) Jonah's curve has a steeper slope than Rowan's is True, All others are false

Rowan Savings Equation = 50 + 5t , where t is weekly time

Rowan Savings = 10 + 15t , where t is weekly time

        1             50 + 5 (1) = 55           10 + 15 (1) = 25

        2            50 + 5 (2) = 60          10 + 15 (2) = 40

        3            50 + 5 (3) = 65          10 + 15 (3) =  55

        4            50 + 5 (4) = 70           10 + 15 (4) = 70

        5            50 + 5 (5) = 75           10 + 15 (5) = 85

At t weeks < 3 , Rowan savings > Jonah savings. At t weeks > 4, Jonah savings > Rowan savings. At t = 4 units, their savings are equal. So, none savings curve is above the other 'always'.

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Answer:

Dh/dt  = 0.082 ft/min

Step-by-step explanation:

As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of  1 feet and height     h = 2 feet.

The volume of a circular cone is:

V(c)  = 1/3 * π*r²*h

Then differentiating on both sides of the equation we get:

DV(c)/dt   = 1/3* π*r² * Dh/dt   (1)

We know that DV(c) / dt   is  1 ft³ / 5 min      or     1/5  ft³/min

and  we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment

By proportion we know

r/h  ( at the top of the cone  0,5/ 2)   is equal to  r/0.5  when water is 1/2 foot deep

Then      r/h   =   0,5/2   =  r/0.5

r  =  (0,5)*( 0.5) / 2        ⇒   r  =  0,125 ft

Then in equation (1) we got

(1/5) / 1/3* π*r² =  Dh/dt

Dh/dt  = 1/ 5*0.01635

Dh/dt  = 0.082 ft/min

Answer:

It would take 25 minutes for Patrick to complete the project alone.

Step-by-step explanation:

They did the project in 20 minutes, that is, 100% of the project, so:

[tex]x + y = 1[/tex]

In which x is the percentage that Patrick worked and y is the percentage that Stewart worked.

Patrick works four times as quickly as Stewart, so x = 4y.

So

[tex]x + y = 1[/tex]

[tex]4y + y = 1[/tex]

[tex]5y = 1[/tex]

[tex]y = 0.2[/tex]

-----------

[tex]x = 4y = 4*0.2 = 0.8[/tex]

Patrick did 80% of the project in 20 minutes. We can solve this problem by a simple rule of three, in which the time it would take for him to complete the project alone is 100%. So

20 minutes - 0.8

x minutes - 1

[tex]0.8x = 20[/tex]

[tex]x = 25[/tex]

It would take 25 minutes for Patrick to complete the project alone.

Patrick, who works four times as quickly as Stewart, would take 25 minutes to complete the project alone.

This question is about rates and can be solved using algebra. Let's denote the rate at which Stewart can do the work as S and the rate at which Patrick does the work as P. Since Patrick works four times as quickly as Stewart, P=4S. The rate at which they work together is S+P. According to the question, together they can complete the job in 20 minutes, so their combined rate is 1 job per 20 minutes or 1/20. Therefore, S + P = 1/20.

Substitute P=4S into the equation, we get S + 4S = 1/20, which simplifies to 5S = 1/20. Solve this equation, we find that S = 1/100. So Stewart alone would finish the job in 100 minutes. Since Patrick is four times faster, Patrick alone would complete it in 100/4 = 25 minutes.

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Answer:

C. y = -3

Step-by-step explanation:

Line L is perpendicular to the y-axis, so line L is just a straight horizontally line going from left to right.

This mean that the x-coordinate they gave us is irrelevant since our flat line is going to pass through all possible x-values. The only thing we need to focus on the the y-value.

So we know that the line passes through (__, -3)

the equation y = -3 gives us a horizontal line that passes through (__, -3).

Therefore answer is C.

Answer A and B are wrong because they gave us vertical lines, we want horizontal lines. D and E are wrong because those are diagonal lines, we want flat horizontal lines.

Answer:

  C

Step-by-step explanation:

The elements of the matrix need to match the coefficients in the equations.

Answer:

c.

Step-by-step explanation:

h

Answer:

[tex]\frac{5}{9}\approx0.556[/tex]

Step-by-step explanation:

A pair of dice is rolled so the outcome space will be.

[tex]S= \{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]

Total number of elements [tex]=36[/tex]

Possible outcomes in which sum is less than [tex]6[/tex] or greater than [tex]8[/tex]

[tex]S_{1} = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(3,6),\\(4,1),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\}[/tex]

Number of element in this space [tex]=20[/tex]

P(sum is less than [tex]6[/tex] or greater than [tex]8[/tex])

[tex]=\frac{Favourable\ outcomes}{total\ outcomes} \\=\frac{20}{36}\\ =\frac{5}{9}[/tex]

Answer:

Size C can is the best buy.

Step-by-step explanation:

The given question is incomplete; here is the complete question.

One brand of canned salmon is sold in four different sizes.

Size A The 7 1/5 -ounce can costs $3.49.

Size B The 16 1/2 -ounce can costs $6.49.

Size C The 24 3/4 -ounce can costs $8.49.

Size D The 30 2/3 -ounce can costs $10.99. What is the unit rate for each size to the nearest cent? If the cost is less than a dollar, put a zero to the left of the decimal point.

Size Unit rate

A (Blank)

B (Blank)

C (Blank)

D (Blank)

What size is best to buy? explain how you know.

For Size A - [tex]7\frac{1}{5}[/tex] ounce or [tex]\frac{36}{5}[/tex] ounce can costs $3.49

Therefore, per ounce cost = [tex]\frac{\text{Total cost}}{\text{Size of can}}[/tex]

= [tex]\frac{3.49}{\frac{36}{5}}[/tex]

= [tex]\frac{3.49\times 5}{36}[/tex]

= $0.48

For Size B - [tex]16\frac{1}{2}[/tex] or [tex]\frac{33}{2}[/tex] ounce can costs $6.49

Per ounce cost = [tex]\frac{6.49}{\frac{33}{2}}[/tex]

= [tex]\frac{6.49\times 2}{33}[/tex]

= 0.39

For size C - [tex]24\frac{3}{4}[/tex] ounce or [tex]\frac{99}{4}[/tex] ounce can costs $8.49

Per ounce cost = [tex]\frac{8.49}{\frac{99}{4}}[/tex]

                         = [tex]\frac{8.49\times 4}{99}[/tex]

                         = $0.34

For size D - [tex]30\frac{2}{3}[/tex] or [tex]\frac{92}{3}[/tex] ounce can for $10.99                                                              

Per ounce cost = [tex]\frac{10.99}{\frac{92}{3} }[/tex]

                         = [tex]\frac{10.99\times 3}{92}[/tex]

                         = $0.36

For size C, per ounce cost of the can is the least. Therefore, size C can is the best buy.

Answer:

c

Step-by-step explanation:

In the experimental design we are choosing a random rats from both sets either male and female.

each set contains 2 elements (A,B), where A is a  Female i.e F1, F2,F3,F4

and B is a male i.e M1,M2,M3,M4.

none of the sets can have 2 male or 2 female.

Only option 'C' has sets which contains B (F3, F2) and D (M3, M4) which is impossible.

Hence c is the answer.

The  assignment of treatments that is impossible is given as

c.) A (F1, M1), B (F3, F2), C (F4, M1), D (M3, M4)

Treatment, the way by which someone acts towards someone else.

Generally, from the parameters, we see that

A is a  Female i.e F1, F2,F3,F4

B is a male i.e M1,M2,M3,M4.

In conclusion, the sets can't have 2 male or 2 female.

Therefore, we have

c.) A (F1, M1), B (F3, F2), C (F4, M1), D (M3, M4)

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