The average person in North Carolina will eat about 12,300 pounds of sugar in a 70 or one lifespan about how many pounds of sugar does the average person in North Carolina eat a year

Barbarino's Rentals offers the better deal for a 432-mile trip at $117.30 compared to Mr. Kotters Rentals at $135.52. To spend the same amount at either company, Glenna would have to drive 600 additional miles over the free miles provided by the rentals.

To determine which car rental company offers the better deal for Glenna's trip to Key West, we need to calculate the total cost from both companies for a 432-mile trip. Let's start with Mr. Kotters Rentals. The cost for one week is a flat $99, plus $0.11 per mile for each mile over 100.

Therefore, Glenna would pay for 332 extra miles at a rate of $0.11 per mile. This calculation is (432 miles - 100 miles) * $0.11/mile = 332 * $0.11 = $36.52 in additional mileage charges. The total cost from Mr. Kotters Rentals would be $99 + $36.52 = $135.52.

Next, we calculate the cost with Barbarino's Rentals. They charge $75 for the week plus $0.15 per mile over 150 miles. The calculation for mileage is (432 miles - 150 miles) * $0.15/mile = 282 * $0.15 = $42.30. The total cost from Barbarino's Rentals would come out to $75 + $42.30 = $117.30.

Comparing the two totals, Barbarino's Rentals is the better deal at $117.30 compared to Mr. Kotters Rentals, which would cost $135.52.

Now, to find out how many miles Glenna would have to drive for the costs to be the same at either company, we set up the equation:
99 + 0.11x = 75 + 0.15x, where x represents the additional miles driven over the respective free miles. Solving this equation:

0.04x = 24
x = 600 miles
So, Glenna would need to drive 600 additional miles for the total costs from both rental companies to be equal.

Answer:

The customer's total cost for the DVD is $19.26

Step-by-step explanation:

Store buy the dvd for $12.00.

The store price is $12.00+50% more

The store price= $12.00 *(1+0.5)= $18.00

Final price (tax added)= $18.00 + 7%

Final price= $18.00 * (1 + 0.07)= $19.26

Answer:

The total cost of the DVD for the consumer was 19.26 $

Step-by-step explanation:

The sales price for the DVD was the price paid by the store plus 50%. To discover this value we will transform the percentage in a real number, by dividing it by 100, like following:

50/100 = 0.5

We then multiply this value by the price paid by the store (12) to find out how much is 50% of that. Then we add this value to the price paid by the store and we obtain the price of the DVD before taxes. So we do as following:

Price before taxes = price paid by the store + (price paid by the store)*0.5

Price before taxes = 12 + 12*0.5 = 18 $

On top of that there was 7% of tax for the consumer. We must repeat the same steps as before but using 7 instead of 50. So we have:

Final price = Price before taxes + (Price before taxes)*(7/100)

Final price = 18 + 18*0.07 = 19.26 $

The total cost of the DVD for the consumer was 19.26 $

Answer:

$50 is the value of interest earned in the first installment on a single bond

Step-by-step explanation:

Applying Interest earned in the first installment on a single bond ;

= PRT/100

P = $1.000

R = 5%

T = 1

Plugging the values in the equation ;

Interest = 1000 x 5 x 1 /100

= $50, hence option A is the correct one.

The recursive formula for the geometric sequence is [tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]

Explanation:

The given sequence is [tex]\{-16,4,-1,........\}[/tex]

We need to determine the recursive formula for the given geometric sequence.

To determine the recursive formula, first we shall find the common difference.

Since, it is a geometric sequence, the common difference can be determined by

[tex]r=\frac{4}{-16} =-\frac{1}{4}[/tex]

[tex]r=-\frac{1}{4}[/tex]

Hence, the common difference of the given geometric sequence is [tex]r=-\frac{1}{4}[/tex]

The recursive equation for the geometric sequence can be determined using the formula,

[tex]a_n=r(a_{n-1})[/tex]

Substituting the value [tex]r=-\frac{1}{4}[/tex], we get,

[tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]

Thus, the recursive formula for the geometric sequence is [tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]

Answer:

Step-by-step explanation:

Given that,

Outcomes Heads= 4heads and

Outcomes Tails= 6tails

Total outcome of events n=10

Probability of head in is first throw is, the is the outcome of head divide by the total possible outcomes

P(Head in first throw)=4/10

P(H)=2/5

P(H) = 0.4

P(H) =40%

Answer:

0.4

Step-by-step explanation:

Answer:

The answer to your question is the letter B. x = 30

Step-by-step explanation:

Data

Find x

Process

To solve this problem use proportions. Compare the small triangle and the large triangle.

1) For the small triangle

                         x/ (24 - 4) = x/20

2) For the large triangle

                         (x + 6) / 24

3.- Equal both expressions

                         x/20 = (x + 6)/24

-Solve for x

                        24x = 20(x + 6)

-Expand

                        24x = 20x + 120

-Simplify like terms

                        24x - 20x = 120

                          4x = 120

-Result

                            x = 120/4

                            x = 30

Answer:

I) 8.760 * 10 ³ hours

II) 8.76582 * 10 ³ hours

Step-by-step explanation:

1) No. of hours in one year:

24 hours* 365 days= 8760 hours

Scientific Notation= 8.760 * 10 ³ hours

2) 1 year = 31556952 seconds

1 hour=3600

1 year = 31556952 seconds/3600  = 8765. 82 hours

Scientific Notation= 8.76582 * 10 ³ hours

3) The exact numbers of hours using 365 days is 8760 which is written as 8.760* 10 ³ in scientific notation. But using the given data we get =8.76582 * 10 ³ hours

Comparing these answers the first one  has only 3 significant figures

But the second answer has six significant figures if we round these we get 8.8  * 10 ³ hours which has two significant numbers

Aslo rounding the first gives 8.8 * 10 ³ hours which has two significant numbers  and is the same as the other answer rounded

Answer:

c= 0.10m+ 25

Step-by-step explanation:

using the format y=mx+b

25 is your flat cost that they charge every month, and 0.10 is what they charge per minute.

m is the number of minutes so that is the unknown variable.

c is your total cost.

you take the flat cost per month (25 dollars) and add it to however many minutes multiplied by 0.10 (.10m)

The equation for determining the total phone bill given a monthly fee of $25 and a rate of $0.10 per minute is, c = 25 + 0.10m. Here, c represents the total monthly cost and m represents the number of minutes of phone usage.

The subject of the question is linear algebra, and it requires forming an equation for a given scenario. In this case, the monthly cost of the cellular phone service is a function of the number of minutes of phone usage. The fixed monthly fee is $25, and there is an additional charge of $0.10 per minute.

So if m represents the number of minutes of phone usage, and c represents the total monthly cost, then the equation that can be used is: c = 25 + 0.10m

This is because for each minute used, an extra $0.10 is added to the total cost. If no minutes are used, the total cost is just the fixed $25. If 50 minutes are used, for example, the total cost is $25 + (0.10 * 50) = $30.

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Answer: the inequality that bests represents how many tickets she can buy is 1.5x ≤ 8

Step-by-step explanation:

Let x represent the number if tickets that she wants to buy at the school fair.

Each ticket cost one dollar and 50 Cent. This means that the total cost of x tickets would be

1.5 × x = $1.5x

Michaela has eight dollars to buy tickets at the school fair. Therefore, the inequality that bests represents how many tickets she can buy is

1.5x ≤ 8

Answer:

Answer in explanation

Step-by-step explanation:

In this question, we would be examining the validity of some statements on the number π(pi)

π Is a whole number?

This is wrong, π is a fraction of 22 to 7 parts I.e 22/7

π Is double the radius?

This is wrong. It is the diameter that is double the radius

π Is approximately 3.14?

This is correct to an extent. The actual value in decimal is around 3.142857142857143 which makes the 3.14 somehow correct

π represents the ratio of the circumference of the circle to the diameter?

This is correct.

Mathematically, circumference C = π * diameter D

Hence C/D = π

π Is approximately 22/7?

This is correct. This is the ratio used for π

Answer:

• Pi is approximately 3.14.

• Pi represents the ratio of the circumference to the diameter

• Pi is approximately 22/7

Step-by-step explanation:

From the options given:

A. Pi is a whole number:

Pi is equivalent to 3.141592654. Therefore, pi is not a whole number.

B. Pi is double the radius

Pi is not double the radius of a circle. Pi is a constant.

C. Pi is approximately 3.14.

In some cases, pi can be approximated as 3.14 instead of 3.141592654.

D. Pi represents the ratio of the circumference to the diameter.

Circumference of a circle, C = 2 × pi × radius

= 2 × pi × D/2 = pi × Diameter

Pi = circumference/Diameter

E. Pi is approximately 22/7

22/7 = 3.142857143

This is also a correct approximation.

Answer: D It is moving in a different direction as the kayak because it slowed Jaime down.

Step-by-step explanation:

Jaime can paddle her kayak at an average rate of 6 miles per hour in still water.

Distance = speed × time

After 2 hours of paddling north in a river, she traveled 8 miles. This distance covered was supposed to be

6 × 2 = 12 miles

Therefore, the following is true about the direction of the current in the river:

D It is moving in a different direction as the kayak because it slowed Jaime down.

Answer:

88

Step-by-step explanation:

Answer:

1) -8(v+4) = -8v - 32

2) -9(-8+3x) = 72 - 27x

Answer:

C. 139.7 minutes

Step-by-step explanation:

To find the answer we have to find the area of the floor and then divide it by how many feet George can clean in a minute.

To find the area, multiply the length by the width.

95 * 50 = 4,750

The floor is 4,750 sq ft. Divide this number by 34 to figure out how many minutes it will take for him to clean the entire floor.

4,750/34 = 139.7

It will take George approximately 139.7 minutes to mop the floor.

To determine the time it will take George to mop a 95 ft by 50 ft gym floor at a rate of 34 ft^2 per minute, we calculate the floor's area (4,750 ft^2) and divide it by the rate, resulting in approximately 139.7 minutes.

To find out how many minutes it will take George to mop the gym floor, we first need to calculate the total area of the floor that he will mop. The floor is a rectangle with dimensions 95 ft by 50 ft. Multiplying these dimensions gives us the area of the rectangle:

Area = Length x Width

Area = 95 ft x 50 ft

Area = 4,750 ft^2

Now we know that George can mop 34 ft^2 per minute. To determine how many minutes it will take him, we divide the total area by the area he can mop per minute:

Time = Total Area / Area per Minute

Time = 4,750 ft^2 / 34 ft^2/min

Time = 139.7 minutes

Therefore, it will take George approximately 139.7 minutes to mop the gym floor, which corresponds to option (c).

Answer:

4

Step-by-step explanation:

Answer:

line VX ; Converse of the Isosceles Triangle Theorem

Explanation:

Since the angle marks on the base of the triangle is same, they measure the same.

The Converse of the Isosceles Triangle Theorem states: If two angles of a triangle are congruent, then sides opposite those angles are congruent.

So line VT ≅ VX

Answer:

d. {(1,2),(2,2),(3,2),(4,2),(5,2),(6,2)}

Step-by-step explanation:

First one can be any of the six outcomes

Final answer:

The event that the second toss shows a two is represented as a subset of the sample space and includes all possible outcomes of the first toss with a two as the second element, written as {(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)} which is option d.

Explanation:

The question asks to represent a specific event from a probability experiment in set notation. The experiment involves tossing a die twice, and the event of interest is that the second toss results in a two. The sample space for two tosses of a six-sided die consists of all ordered pairs where the first element is the result of the first toss, and the second element is the result of the second toss. Since the die has six sides, the first element can be any number from 1 to 6, and the same applies to the second element.

The event that the second toss shows a two can be represented by the subset of the sample space where the second element of each ordered pair is a 2. Therefore, the correct set notation for this event would be {(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)} which corresponds to option d. This subset includes all possible outcomes of the first toss combined with the fixed outcome of the second toss being a two.

Answer:

The answer is A

Step-by-step explanation:

The cheapest route should be c) ABCDA, $960

Starting at A: Options are B = 220, C = 240, D = 310

Now

Choose B since it has the smallest value.

Now

From B: Options are C = 200, D = 210

Choose C since it has the smallest value.

From C: There is only one option i.e. D = 230 here we cannot choose A since it was our beginning point.

From D: We touched all of the vertices due to this,  return to the starting point, A = 310

So,

A → B → C → D → A --> 220 + 200 + 230 + 310 = 960

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Answer:

(10, 21)

Step-by-step explanation:

To get the point of intersection of the lines given ( it means we need to find at what value of x will correspond to the value of y)

y = 2x+1

y = x+11

insert equation i in equation ii

2x+1=x+11

2x-x = 11-1

x = 10

y = 2x+1 = 2(10)+1 = 20+1 = 21

(x,y) = (10, 21)

Answer: (10/3, 23/3)

Step-by-step explanation:

To determine the point of intersection of the two lines, we would solve both equations simultaneously. The given system of linear equations is expressed as

y = 2x + 1- - - - - - - - - - - - -1

y = - x + 11 - - - - - - - - - - - -2

We would eliminate y by

Subtracting equation 2 from equation 1, it becomes

0 = 3x - 10

Adding 10 to the left hand side and the right hand of the equation, it becomes

3x - 10 + 10 = 0 + 10

3x = 10

Dividing the left hand side and the right hand side of the equation by 3, it becomes

3x/3 = 10/3

x = 10/3

Substituting

x = 10/3 into equation 1, it becomes

y = 2 × 10/3 + 1

y = 20/3 + 1

y = 23/3

Answer:

517,262

Step-by-step explanation:

A population of butterflies grow in such a way that each generation is simply 1.5 times the previous generation. There were 350 butterflies in the first generation, how many will there be by the 19th generation?

----------------

Ans: (1.5)^18 * 350 = 517,262

Answer: there will be 517262 butterflies by the 19th generation.

Step-by-step explanation:

The population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. This means that the population is increasing in geometric progression. We would apply the formula for determining the nth term of a geometric progression which is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 350

r = 1.5

n = 19

Therefore, the 19th term or generation, T19 would be

T19 = 350 × 1.5^(19 - 1)

T19 = 350 × 1.5^18

T19 = 517262

Answer:

see the explanation

Step-by-step explanation:

The question in English is

On a ship, 1/7 of the crew members maintain the machinery, 2/7 the kitchen, 3/7 the bedrooms and corridors, and the remaining 18 are officers

Let

x ----> members that maintain the machinery

y ---->members that maintain the kitchen

z ----> members that maintain bedrooms and corridors

w ----> members that are officers

T ----> total number of members

we know that

The total sum of the fractions must be equal to 1

[tex]\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+w=1[/tex]

[tex]w=1-\frac{6}{7}[/tex]

[tex]w=\frac{1}{7}[/tex]

Remember that

The number of officers is 18

so

[tex]18=\frac{1}{7}T[/tex]

Find out the total number of members

solve for T

[tex]T=18(7)=126\ members[/tex]

Find out the number of members that maintain the machinery

[tex]x=\frac{1}{7}T[/tex]

[tex]x=\frac{1}{7}(126)=18\ members[/tex]

Find out the number of members that maintain the kitchen

[tex]y=\frac{2}{7}T[/tex]

[tex]y=\frac{2}{7}(126)=36\ members[/tex]

Find out the number of members that maintain bedrooms and corridors

[tex]z=\frac{3}{7}T[/tex]

[tex]z=\frac{3}{7}(126)=54\ members[/tex]

Answer:

The probability that at least one of the CD'S will be put back into the proper cases is 2/3

Step-by-step explanation:

The total amount of possibilities of putting back the CD's is equal to the total amount of ways of ordering a set of 3 elements, in other words, 3! = 6. In 4 of those 6 ways, at least one of the CD's is put back properly:

- All CD's are put back into the proper cases

- First disc is put back into its proper cases, Second disc is put back in third's position, and third  disc is put back in second's position.

- Second Disc is put back correctly, and first and third not

- Thir disc is put back correctly and first and second got 'swapped'.

Thus, the probability that at least one of the CD'S will be put back into the proper cases is 4/6 = 2/3.

Answer:

Equation= X = 660÷22, Number of boxes is 30

Step-by-step explanation:

Since each box contains 22 cans, hence 22x is equivalent to 660 cans.

Equation = 22X = 660

Number of boxes X = 660÷22 = 30

Answer:

Step-by-step explanation:

Given:

Number of cans in a box, N = 22 cans

Total number of cans, Tc = 660 cans

Let the Number of boxes be x.

Therefore,

Tc = N × x

B.

660 = 22 × x

x = 660/22

= 30 boxes.

Answer:

Option D

86

Step-by-step explanation:

When your expectation is average of 81 for a total of 10 questions, your total score is 10*81=810

Currently, for 5 questions with an average of 76, your total score is 5*76=380

Difference between total expected score and current score is 810-380=430

Average of difference with 5 questions is 430/5= 86

Jake cannot achieve an average above 89 with the final exam alone.

The final exam counts twice as much as the midterm, so the weights are 2 for the final and 1 for the midterm. The average score A can be calculated using the formula:

[tex]\[ A = \frac{\text{weight of midterm} \times \text{midterm score} + \text{weight of final} \times \text{final score}}{\text{total weight}} \][/tex]

Given that Jake's midterm score is 67 and the weights are 1 for the midterm and 2 for the final, the total weight is  1 + 2 = 3 . We want Jake's average A to be between 81 and 92.

For the lower bound of the average (81), we have:

[tex]\[ 81 = \frac{1 \times 67 + 2 \times f}{3} \][/tex]

Solving for  f :

[tex]\[ 81 \times 3 = 67 + 2f \] \[ 243 = 67 + 2f \] \[ 2f = 243 - 67 \] \[ 2f = 176 \] \[ f = \frac{176}{2} \] \[ f = 88 \][/tex]

So, the minimum score Jake needs on the final exam to achieve an average of at least 81 is 88.

For the upper bound of the average (92), we have:

[tex]\[ 92 = \frac{1 \times 67 + 2 \times f}{3} \][/tex]

Solving for  f:

[tex]\[ 92 \times 3 = 67 + 2f \] \[ 276 = 67 + 2f \] \[ 2f = 276 - 67 \] \[ 2f = 209 \] \[ f = \frac{209}{2} \] \[ f = 104.5 \][/tex]

However, since the maximum score for the final exam is 100, the highest possible average Jake can achieve is 100 (since [tex]\( 67 + 2 \times 100 = 267 \)[/tex], and [tex]\( \frac{267}{3} = 89 \))[/tex].

In conclusion, Jake needs to score at least 88 on the final exam to achieve an average of at least 81, but he cannot achieve an average above 89 with the final exam alone. Thus, the range of scores on the final exam for Jake to get an average between 81 and 92 is from 88 to 100. However, the upper bound of Jake's average is actually 89, not 92, due to the maximum score constraint on the final exam.

Answer:

An experiment

Step-by-step explanation:

An observational study is a study in which the researchers collect data related to what is visible or heard. In this type of study the researchers do not have any control on the variables used for the research work .The researcher do not bring any changes in the behavior of the variables that is they are accepted the way they are.

An experiment is a method used in which the researchers pick up a sample from a group and test them to get a proof or knowledge about something.

Both Observational study as well as an experiment are used in statistics social sciences and psychology etc.

Thus the case given here is an experiment because there is no alterations done with the variables.

The scenario given is an experiment because it deliberately manipulates conditions (music or no music) to test its effect on students' ability to memorize words. By comparing outcomes, this study seeks to establish a causal relationship.

The study described in the student's question is an experiment because it involves a deliberate manipulation of conditions to test a hypothesis. The manipulation in this case is the presence or absence of music while memorizing words. Since there are two groups and each group is subjected to different conditions (one with music and one without), this defines a controlled experiment. Experiments involve comparing the outcomes of different treatments, in this case, music or silence, which enables researchers to make causal inferences about the effect of the independent variable (music) on the dependent variable (ability to remember words).

Now, looking at the studies referenced, the effects of music on different cognitive tasks, like memorization and reading comprehension, have been explored in various ways. While some experiments, like the one comparing the memorization of words with and without music, show that silence may be more conducive for memorization, other studies have found positive effects of music on tasks such as reading comprehension or overall task behavior.

Answer:

Option C is Correct

Step-by-step explanation:

Given System is

3x + 5y =  1

2x + 4y  = −4

Multiply the first equation by −2, and multiply the second equation by 3

we get

-6x-10y = -2 ----------(i)

6x+12y = -12 ---------(ii)

then we add both equations we get

2y = -14

y = -7

now put y = -7 in euation one we get

-6x-10(-7) =14

-6x+70=14

subtracting 70 from both sides we get

-6x=-56

dividing (-6) both sides we get

x=56/6 or x =28/3

so here is our solution

(x,y)=(28/3 , -7)

answer.

Answer:

The Bureau of Consumer Protection stops unfair and fraudulent business practices and taking appropriate actions against them.

Step-by-step explanation:

The Bureau of Consumer Protection is a body who looks into safeguarding the financial interests of the consumers. It stops unfair and fraudulent business practices by taking necessary and appropriate actions against them. They take necessary reaction as of suing the person or business involved. The Bureau of Consumer Protection also develops rules and regulations to maintain a fair marketplace. They also educate consumers about their responsibilities and rights.

Answer:

The Bureau of Consumer Protection stops unfair and fraudulent business practices and taking appropriate actions against them. The Bureau of Consumer Protection is a body who looks into safeguarding the financial interests of the consumers. It stops unfair and fraudulent business practices by taking necessary and appropriate actions against them. They take necessary reaction as of suing the person or business involved. The Bureau of Consumer Protection also develops rules and regulations to maintain a fair marketplace. They also educate consumers about their responsibilities and rights.

Step-by-step explanation:

e d g e

Answer:

The answer to your question is Yes, the point P lies on the circle

Step-by-step explanation:

Data

P (2[tex]\sqrt{3}[/tex], 2)

Center (0, 0)

Q (0, -4)

Process

1.- Find the radius of the circle

dCQ = [tex]\sqrt{(0-0)^{2}+ (-4 + 0)^{2}}[/tex]

dCQ = [tex]\sqrt{0^{2} + (-4)^{2}}[/tex]

dCQ = [tex]\sqrt{16}[/tex]

dCQ = 4

2.- Find the equation of the circle

    (x - 0)² + (y - 0)² = 4²

-Simplification

           x² + y² = 16

3.- Substitute P in the equation of the circle

          (2[tex]\sqrt{3}[/tex])² + (2)² = 16

           4(3) + 4 = 16

               12 + 4 = 16

                     16 = 16

4.- Conclusion

The point (2[tex]\sqrt{3}[/tex], 2) lies on the circle because when we evaluate the equation of the circle with this point, we get the length of the radius.

Answer:

31

Step-by-step explanation:

Y = 6x+1

When x is 5

y = 6(5)+1 = 30 +1 =31

Answer:

A probability must be between zero and one

Step-by-step explanation:

We are to explain why −0.41 cannot be the probability of some event.

Probability is the chance of occurring a particular event out of total possible events.

If total possible events are n, and number of favourable outcomes for any event A is x then probability is x/n.

Here note that both x and n cannot be negative.

also x cannot exceed n.

Probability can never exceed 1 and also can never be an integer except 0 or 1 as special cases.

So the probability can never be negative and cannot exceed 1.

So correct answer is

A probability must be between zero and one