Six students from a statistics class reported the number of hours of television they watch per week. Here are their data: 8, 10, 5, 14, 3, 6. What is the standard deviation of the number of hours of television watched per week for this sample of six students?

Answer:

Mrs. Jackson worked 32 hours.

Step-by-step explanation:

Given:

Mrs.Jackson earned a $500 bonus for signing a 1 year contract to work as a nurse.

Her salary is $22 per hour.

If her first weeks check including the bonus is $1204.

Now, to find the hours Mrs. Jackson work.

Amount of bonus = $500.

Total salary = $1204.

So, we deduct the amount of bonus from the total salary:

[tex]1204-500=\$704.[/tex]

The remaining salary = $704.

As, given her salary is $22 per hour.

Now, to get the hours she work we divide the remaining salary $704 by $22:

[tex]704\div 22[/tex]

[tex]=32\ hours.[/tex]

Therefore, Mrs. Jackson worked 32 hours.

Answer:

Another way to decompose the number would be

43  taking the 4 of the left with tens like 40 ( 4*10) and 3 of the right as three separate ones ( 3*1= 3) .Adding 10s four times with  three one times would make 43

Final answer:

The student's question deals with decomposing numbers into tens and ones and relates to the concept of powers of ten in mathematics. Powers of ten notation is foundational in understanding place value, large, and small numbers. By breaking down numbers into tens and ones, students can grasp numerical values more effectively.

Explanation:

The question pertains to the mathematical concept of decomposing numbers into tens and ones using a ten-frame and involves powers of ten. In mathematics, numbers can be broken down into tens and ones to understand their value better. It's essential to note that each place in our numbering system is ten times greater than the place to the right of it. This is part of the reason we use powers-of-ten notation.

Decomposing Numbers

When decomposing a number like 24, for example, we can break it down into two tens (20) and four ones (4). If we used a ten-frame, we would fill in two full ten-frame grids to represent the tens and then add four individual marks to represent the ones.

Understanding Powers of Ten

When we discuss powers of ten, we're talking about how the counting system is structured, with each place value being ten times greater than the one before it. The digital numbering system got started because humans have ten fingers and counted with them, leading to an increase by tens.

A positive exponent, like 10³, tells us to multiply the base (10) by itself the number of times indicated by the exponent (3), which results in 1000. On the other hand, a negative number as the power indicates a division, so a power like 10⁻¹=0.1. If we have 10⁻⁴, it means 0.0001, which is ten times smaller than 0.001 (10⁻³).

When dividing by powers of ten, we move the decimal point to the left by the number of zeros indicated by the power. This process simplifies understanding large and small numbers by expressing them in terms of powers of ten or powers of one thousand for very large numbers.

Answer:

[tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex]

Step-by-step explanation:

We have been given that the desert temperature, H, oscillates daily between 40◦F at 5 am and 80◦F at 5 pm. We are asked to write a formula H in terms of t, measured in hours from 5 am.

We will use cosine function to write our required formula.

[tex]y=A\text{cos}[B(x-C)]+D[/tex], where,

A = Amplitude,

[tex]\text{Period}=\frac{2\pi}{|B|}[/tex]

C = Phase shift,

D = Vertical shift.

First of all, we will find amplitude using maximum and minimum values as:

[tex]A=\frac{\text{Maximum value}-\text{Minimum value}}{2}[/tex]

[tex]A=\frac{80-40}{2}[/tex]

[tex]A=\frac{40}{2}[/tex]

[tex]A=20[/tex]

Since period is 24 hours (5 am to 5 pm), so let us find B as:

[tex]24=\frac{2\pi}{|B|}[/tex]

[tex]B=\frac{2\pi}{24}[/tex]

[tex]B=\frac{\pi}{12}[/tex]

[tex]\text{Vertical shift}=\frac{\text{Maximum value}+\text{Minimum value}}{2}[/tex]

[tex]D=\frac{80+40}{2}=\frac{120}{2}=60[/tex]

There is no phase shift.

Since temperature is minimum when [tex]t=0[/tex], so we will use negative cosine as:

[tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex]

Therefore, our required function would be [tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex].

To model the desert temperature, use the sinusoidal function H(t) = 20 * cos(π/12 * t) + 60, which captures daily temperature changes between 40°F and 80°F, with parameters tuned to fit the given data.

To write a formula for the desert temperature H in terms of t, measured in hours from 5 am, we can use a sinusoidal function that models the daily temperature oscillation.

We know:

The general form for the sinusoidal function is:

H(t) = A * sin(B*(t - C)) + D

Where:

From the given data:

Thus, the sinusoidal function becomes:

H(t) = 20 * cos(π/12 * t) + 60.

Answer:

64%

Step-by-step explanation:

pain

The answer is B) 64%.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Let X be the number of students out of 40 who like to hike. We know that P(X ≤ 15) = 0.36 and we want to find P(X ≥ 16).

Note that P(X ≥ 16) is the complement of P(X ≤ 15). That is,

P(X ≥ 16) = 1 - P(X ≤ 15) = 1 - 0.36 = 0.64

Therefore, the answer is B) 64%.

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Step-by-step explanation:

Let the number be n.

When ​one-fourth of a number is added to ​one-fifth of the​ number, the sum is 18

          [tex]\frac{n}{4}+\frac{n}{5}=18\\\\\frac{5n+4n}{4\times 5}=18\\\\9n=4\times 5\times 18\\\\n=20\times 2\\\\n=40[/tex]

The number is 40.

Answer:

unknown number is 40

Step-by-step explanation:

 Let x be the unknown number

one-fourth of a number is added to ​one-fifth of the​ number

[tex]\frac{1}{4}x+\frac{1}{5} x[/tex]

sum is 18

[tex]\frac{1}{4}x+\frac{1}{5} x=18[/tex]

To solve for x take LCD 20

[tex]\frac{5}{20}x+\frac{4}{20} x=18\\ \frac{9}{20} x=18\\[/tex]

multiply both sides by 20

[tex]9x= 360[/tex]

divide both sides by 9

x=40

Answer:

1 2/3

Step-by-step explanation:

Luis mixed all the trails thus:

4 2/3 + 1 1/4 + 1 1/3 + 3/4

= 15/3 + 5/4 + 4/3 + 3/4

= 60+15+16+9/12

Total trail mixed by Luis equals 100/12

He then divided 100/12 among his 5 friends thus:

100/12 ÷ 5

= 20/12

= 1 2/3 per friend.

Answer:

1  3/5

Step-by-step explanation:

the answer is 1.6 but you have to convert is to a fraction  because there are no  decimal numbers theres. if you convert it , it will be 1 3/5

The coordinates of the point on the graph when x=3 are C. (3, 5)

Step-by-step explanation:

Given piece-wise function is:

[tex]y = \left \{ {{4x+1\ \ \ x<3 } \atop {2x-1\ \ \ x\geq 3 }} \right.[/tex]

In order to determine the coordinates of the point on the graph where x=3 we will see which part of the function we have to consider as the function is in two pieces.

By observing we see that the second piece  of function will be used as it is for x≥ 3 so it includes 3.

Putting x = 3 in y = 2x-1

[tex]y = 2(3) -1\\y = 6-1\\y = 5[/tex]

Hence,

The coordinates of the point on the graph when x=3 are C. (3, 5)

Keywords: Functions, graph

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Answer:

-6, 8

Step-by-step explanation:

Let the numbers be represented by y

Square of y = y^2

Double y = 2 × y = 2y

Square of the number is 48 more than double the number is written mathematically as

y^2 = 2y +48

y^2 - 2y - 48 = 0

This is a quadratic equation and can be solved by method of factorisation

y^2 -2y - 48 = 0

y^2 + 6y - 8y - 48 = 0

(y^2 + 6y) - (8y - 48) = 0

y(y + 6) - 8(y + 6) = 0

(y + 6)(y - 8) = 0

y = -6, 8

The numbers are -6, 8

Answer:

8, -6

Step-by-step explanation:

Let the number be $n$, so we have $n^2 =48 + 2n$. Rearranging this equation gives $n^2 -2n-48=0$ and factoring gives $(n-8)(n+6)=0$. So, the numbers that fit the problem are $\boxed{n = -6~\text{and}~n = 8}$.

Answer:

(5/3, 41/3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = 10x - 3

y = 7x + 2

Step 2: Solve for x

Substitution

Step 3: Solve for y

Step 4: Check

Verify the solution set to the systems of equations by graphing the systems.

Where the 2 lines intersect is the solution set to the systems of equations.

We see graphically that point (1.666667, 13.66667), equivalent to (5/3, 41/3).

∴ (5/3, 41/3) or x = 5/3 and y = 41/3 is the solution to the systems of equations.

Final answer:

The solution to the system of equations y = 10x - 3 and y = 7x + 2 is x = 5/3 and y = 19/3.

Explanation:

The solution of the system of equations given by y = 10x - 3 and y = 7x + 2 can be found by setting the two expressions for y equal to each other since they both equal y. This yields the equation 10x - 3 = 7x + 2. Solving for x, we first subtract 7x from both sides to get 3x - 3 = 2. Then we add 3 to both sides to get 3x = 5. Finally, dividing both sides by 3 gives us x = 5/3. Substituting x back into either original equation, we get y = 10(5/3) - 3 or y = 7(5/3) + 2, both of which simplify to y = 19/3. Therefore, the solution to the system is x = 5/3 and y = 19/3.

Answer: the probability that the first toss wins is:

P = 1/6 or 0.1667

Step-by-step explanation:

A die has six sides (that is 6 outcome per die)

For a pair of dice:

The Total number of possible outcomes = 6 × 6 = 36

The possible outcomes of 7 is:

(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

= 6

The probability P of getting 7 is:

P = number of possible outcomes of 7/total number of possible outcomes

P = 6/36 = 1/6

The probability that the first toss wins

P = 1/6 or 0.1667

Answer:the fraction of Mary's garden that has tulips is 2/3

Step-by-step explanation:

Let x represent the full area if Mary's garden.

Mary plants roses in 1/4 of her garden. This means that the portion of the garden on which she planted roses would be 1/4 × x = x/4

She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. This means that the portion if the garden that she has left to plant more flowers would be 1/12 × x = x/12

The portion of the garden on which she planted tulips would be

x - (x/4 + x/12) = x - (3x + x)/12 = x - 4x/12

x - x/3 = (3x - x)/3 = 2x/3

Therefore, the fraction of Mary's garden that has tulips would be

(2x/3) /x = 2/3

Final answer:

Mary has 2/3 of her garden planted with tulips.

Explanation:

To find the fraction of Mary's garden that has tulips, we need to first determine the fraction of her garden that she has planted with roses. We are given that Mary plants roses in 1/4 of her garden, so the fraction of her garden that she has planted with roses is 1/4. Since she has 1/12 of her garden left to plant more flowers, the fraction of her garden that she has planted with tulips is the remaining fraction, which is 1 - 1/4 - 1/12.

Let's simplify this expression. First, find a common denominator for 1/4 and 1/12, which is 12. Rewrite 1/4 with the denominator 12 as 3/12, and rewrite 1/12 with the denominator 12 as 1/12. Now we can subtract these fractions:

1 - 3/12 - 1/12 = 12/12 - 3/12 - 1/12 = 8/12 = 2/3

Therefore, 2/3 of Mary's garden has tulips.

Answer:

[tex]2\sqrt {10}[/tex]

Step-by-step explanation:

Given:

[tex]x=3\sqrt 5[/tex]

[tex]y=\sqrt 5[/tex]

As seen from the triangle, the triangle is a right angled triangle. Two sides of the triangle are given and we are asked to find the third side.

'x' is the hypotenuse as this side is opposite side to the right angled.

'y' and 'z' are the two legs of the triangle.

Now, using pythagoras theorem,

[tex]x^2=y^2+z^2\\\\(3\sqrt 5)^2=(\sqrt 5)^2+z^2\\\\9\times 5=5+z^2\\\\45-5=z^2\\\\40=z^2\\\\z=\sqrt {40}\\\\z=2\sqrt {10}[/tex]

Therefore, the measure of the side 'z' is [tex]2\sqrt {10}[/tex].

Hence, the third option is correct.

Answer:

  see below

Step-by-step explanation:

The leading minus sign tells you the graph opens downward. (x-3) in the squared term tells you the x-coordinate of the vertex is x=3. The graph that matches these characteristics is shown below.

Answer:

There are 7 dimes, 3 nickels, and 4 quarters.

Answer:

B. A continuous continuous data set because there are infinitely many possible values and those there are infinitely many possible values and those values cannot be counted values cannot be counted

Step-by-step explanation:

Given that the  volume of cola in a can is 12.1 oz

We have to find out whether discrete or continuous.

We can say a random variable is discrete if it takes values which have one to one correspondence with the set of natural numbers.

continuous if a one to one correspondence with set of natural numbers cannot be established.

In our case, we have volume of cola as 12.1 oz.  Between two readings say,12.1 oz and 12.15 oz. there may be infinite other values which the volume can take

i.e. this is a continuous data.

B. A continuous continuous data set because there are infinitely many possible values and those here are infinitely many possible values and those values cannot be counted values cannot be counted

is right answer

The volume of cola in a can, measured as 12.1 oz, is an example of continuous data because it could theoretically take any value in a certain range, unlike discrete data which can only have certain distinct values.

The volume of cola in a can being 12.1 oz represents continuous data. This is because continuous data can take on any value within a certain range or interval. In this case, the volume of the cola in the can could theoretically have been any number between certain limits, for example, 0 to 12.2 oz. This differs from discrete data, which can only take certain distinct or separate values, such as the number of cans of cola you might buy (1,2,3, etc.).

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Answer:

the answer would be C. The mean would increase.

Step-by-step explanation:

The mean has increased, the correct option is C.

Average is the mean of the data set obtained by summing all the values of the data set and then dividing it by the number of data in the set.

The total number of students is 19.

The outlier is 81

An outlier is a number that is different from the other set of numbers, it is obtained due to variability in the observation or due to experimental error.

The mean including the outlier of 81 equals 94.

For the mean including the outlier, it can be observed that the outlier is the left outlier or the smallest number.

Let x represent the sum of all the test scores

x / 19 = 94

x = 94 * 19

x = 1786

The sum without the outlier is 1786 - 81 = 1705

The mean without the outlier is

= 1705 / 18

= 94  13 /18

This is greater than 94.

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Answer:

Step-by-step explanation:

If angle 1 and angle 2 are supplementary, then

∠1 + ∠2 = 180°

If angle 2 and angle 3 are complementary, then

∠2 + ∠3 = 90°

We are given the values for angles 1 and 2, so:

(8x + 3) + ( 5x - 18) = 180 so

13x - 15 = 180 and

13x = 195 so

x = 15

Sub 15 in for x in angle 2 to find the measure of angle 2:

∠2 = 5(15) - 18 so

∠2 = 57°

That means that to find angle 3,

57° + ∠3 = 90 so

∠3 = 33°

The measure of angle 3 is found to be 33 degrees, using the relationships that angle 1 is supplementary to angle 2 and angle 2 is complementary to angle 3, along with their given expressions in terms of x.

To find the measure of angle 3, we must use the relationships between the angles given: angle 1 is supplementary to angle 2 and angle 2 is complementary to angle 3.

Since angle 1 and angle 2 are supplementary, their sum is 180 degrees. The equation is therefore:

(8x + 3) + (5x - 18) = 180

Solving for x gives:

13x - 15 = 180

x = 195 / 13

x = 15

Substitute x back into the expression for angle 2:

(5x - 18) = (5(15) - 18) = 57 degrees

Since angle 2 and angle 3 are complementary, they add up to 90 degrees:

angle 2 + angle 3 = 90

57 + angle 3 = 90

Subtract 57 from both sides to find angle 3:

angle 3 = 90 - 57

angle 3 = 33 degrees

Therefore, the measure of angle 3 is 33 degrees.

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Final answer:

Greg bought 12 books online. To find the number of books, set up the equation 6n + 3 = 75, subtract the shipping fee, and divide by the price per book.

Explanation:

Greg ordered books online for $6 each and paid a total of $75, which includes a $3 shipping fee. To determine the number of books Greg bought, you need to set up an equation that represents the total cost.

The cost of the books alone can be represented by 6 times the number of books (6n), and when you add the shipping cost of $3, it equals the total cost of $75. So the equation would be:

6n + 3 = 75

To solve for n, which is the number of books Greg purchased, follow these steps:

Subtract the shipping fee from the total cost: 75 - 3 = 72.

Divide the result by the cost per book: 72 ÷ 6 = 12.

Therefore, Greg bought 12 books.

Answer:

C.

is the right answer

Step-by-step explanation:

The value of the 4 in 64.723 is 100 times the value of the 4 in 9.048. The correct option is B

A system of writing numbers is known as a number system. It is the mathematical notation for consistently using digits or other symbols to represent the numbers in a given set.

It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

Given that there are two numbers 64.723 and 9.048. The value of the number 4 in one number is 100 times the other. As it is at one-hundredth place of another number

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Answer:

The distance that the conveyor belt moves the bottle is less than 90 meters

Step-by-step explanation:

Speed of the conveyor belt

120 cm/s

Time it takes to move the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.

But 60s = 1 minute

This gives

1.2 minutes = 1.2×60s seconds = 72 seconds

But speed = distance/time

so that distance = speed × time = 120cm/s ×(<72s)

From where distance = <8640cm<90m (90m×100=9000cm)

Time it takes to move the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.

Again 60s = 1 minute

This gives

1.1 minutes = 1.1×60s seconds = 66 seconds

Time it takes is more than 66s

But speed = distance/time

so that distance = speed × time = 120cm/s × (>66s)

From where distance >7920cm

However

7920cm < 90m (90m×100=9000cm)

So that

The distance that the conveyor belt moves the bottle is less than 90 meters

Answer:

The cubic polynomial is: x³ - x² - 6x.

Step-by-step explanation:

Given the degree and the roots of the polynomial we can find it.

An n - degree polynomial has n roots.

Here, given that the degree of the polynomial is 3 and three roots are given. Also, if (x - a) is a factor of a polynomial then x = a is a root of the polynomial. The converse is also true.

Since, the roots of the polynomial are given to -2, 0, 3 then it should have had the following factors.

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

Multiplying them we get:

⇒ [tex]$ (x^2 + 2x)(x - 3) $[/tex]

[tex]$ = x^3 - 3x^2 + 2x^2 - 6x $[/tex]

[tex]$ = x^3 - x^2 - 6x $[/tex] which is the required cubic polynomial.

Hence, the answer.

Answer:

B. Stratified sampling, because there are specific subgroups to investigate.

Step-by-step explanation:

Stratified Sampling is a sampling method and is used when the population has subgroups with different characteristics. Random sampling is applied in each of the sub-groups proportional to their size and then these samples combined together to create sample of the study.

Since there are three towns with people from different occupations ( retirees,business owners, office workers), it is better to use stratified sampling method.

The correct answer is option B). Stratified sampling, because there are specific subgroups to investigate.

To determine the most appropriate sampling method, one must consider the composition of the population and the goal of the study. In this scenario, the population consists of three distinct groups: retirees in town A, business owners in town B, and office workers in town C. Each group represents a different stratum within the overall population of the county.

Stratified sampling is a method that divides the population into subgroups, or strata, based on certain characteristics, such as age, occupation, or town of residence in this case. This method ensures that each subgroup is represented in the sample in proportion to its size in the overall population. Here's why stratified sampling is the most appropriate method for this situation:

1. Representation: Stratified sampling ensures that each town's unique demographic is represented in the sample. This is important because each group may have different voting patterns.

2. Precision: By sampling each stratum separately, the estimates of the average number of votes for each candidate can be more precise because the variance within each subgroup is likely to be lower than the variance across the entire population.

3. Comparability: Stratified sampling allows for direct comparison between the different strata, which in this case are the three towns.

4. Efficiency: If the strata are chosen such that the variance within each stratum is minimized, the overall variance of the estimate can be reduced, leading to a more efficient estimate.

Now, let's consider the other options:

A. Simple random sampling: While this method is unbiased, it may not provide representation from each of the three towns in proportion to their population sizes. This could lead to an inaccurate estimate if one group's voting behavior is significantly different from the others.

C. Systematic sampling: This method involves selecting elements from the population at regular intervals. It can be difficult to implement if there is no clear ordering of the population, and it may not ensure representation from each town.

D. Cluster sampling: This method would be appropriate if the population were spread across a wide area and could be divided into clusters that are more convenient to sample. However, since the population is already divided into distinct groups within specific towns, stratified sampling is a better choice.

E. All the above sampling methods: While each method has its own merits, not all are equally suitable for this particular scenario. Stratified sampling is the most appropriate because it specifically addresses the heterogeneity of the population across the three towns.

Answer: Christina's age is 13, Joanne's age is 42 and Devin's age is 21.

Step-by-step explanation: If Devin's age is represented by d, then Joanne's age will be 2d because Joanne is two times Devin's age. Also, if Devin is 8 years older than Christina, then Christina's age would be d - 8. If the sum of their ages is equal to 76, then;

2d + d + (d - 8) = 76

2d + d + d - 8 = 76

4d - 8 = 76

Add 8 to both sides of the equation

4d = 84

Divide both sides of the equation by 4

d = 21

Therefore, Devin is 21 years old

Joanne is 42 years old and

Christina is 13 years old.

Christina is 13 years old, Devin is 21 years old, and Joanne is 42 years old. This is found by defining Christina's age as x, then setting up and solving an equation based on the problem's provided relationships.

In this math problem, we have three individuals: Joanne, Devin, and Christina, and we know their ages in relation to each other's.

We know that Joanne's age is two times Devin's. We also know Devin is eight years older than Christina. Finally, we know the sum of all three ages is 76.

Let's denote Christina's age as x. Consequently, Devin's age would be x + 8 because he is 8 years older than Christina. As Joanne's age is two times Devin's age, Joanne's age would be 2*(x + 8).

The sum of their ages is 76, which gives us the following equation:
x (Christina's age) + x + 8 (Devin's age) + 2*(x + 8) (Joanne's age) = 76.

Solving this equation, we get:
4x + 24 = 76
Subtract 24 from both sides gives us 4x = 52, and dividing both sides by 4 gives x = 13.

So, Christina's age is 13, Devin's age is 13 + 8 = 21, and Joanne's age is 2*21 = 42.

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Answer:the cost of one child's ticket is $6

the cost of one adult ticket is $9

Step-by-step explanation:

Let x represent the cost of one child's ticket

Let y represent the cost of one adult ticket.

Tickets for a minor league baseball game for an adult and two children cost a total of $21. This means that

2x + y = 21 - - - - - - - - - - 1

The adult ticket is three dollars more than a child's ticket. This means that

y = x + 3

Substituting y = x + 3 into equation 1, it becomes

2x + x + 3 = 21

3x + 3 = 21

3x = 21 - 3 = 18

x = 18/3 = 6

y = x + 3 = 6 + 3

y = 9

the maximum number of boxes that will fit on the shelf is 21.

To find out the maximum number of boxes that will fit on the shelf, we need to calculate the area of the shelf and the area of each box, then divide the total area of the shelf by the area of each box.

Given:

- Shelf dimensions: 65 cm x 35 cm

- Box dimensions: 180 mm x 60 mm

First, let's convert all dimensions to the same unit. Let's choose millimeters for consistency:

Shelf dimensions:

- Length: [tex]\(65 \, \text{cm} \times 10 \, \text{mm/cm} = 650 \, \text{mm}\)[/tex]

- Width: [tex]\(35 \, \text{cm} \times 10 \, \text{mm/cm} = 350 \, \text{mm}\)[/tex]

Now, let's calculate the area of the shelf:

[tex]\[ \text{Shelf area} = \text{Shelf length} \times \text{Shelf width} \][/tex]

[tex]\[ \text{Shelf area} = 650 \, \text{mm} \times 350 \, \text{mm} \][/tex]

[tex]\[ \text{Shelf area} = 227,500 \, \text{mm}^2 \][/tex]

Now, let's calculate the area of each box:

[tex]\[ \text{Box area} = \text{Box length} \times \text{Box width} \][/tex]

[tex]\[ \text{Box area} = 180 \, \text{mm} \times 60 \, \text{mm} \][/tex]

[tex]\[ \text{Box area} = 10,800 \, \text{mm}^2 \][/tex]

Now, to find out the maximum number of boxes that will fit on the shelf, we divide the shelf area by the area of each box:

[tex]\[ \text{Maximum number of boxes} = \frac{\text{Shelf area}}{\text{Box area}} \][/tex]

[tex]\[ \text{Maximum number of boxes} = \frac{227,500 \, \text{mm}^2}{10,800 \, \text{mm}^2} \][/tex]

[tex]\[ \text{Maximum number of boxes} \approx 21.06 \][/tex]

Since we can't have a fraction of a box, the maximum number of boxes that will fit on the shelf is 21.

complete question given below:

The campsite shop sells boxes of Funshine Cereal.

The base of each box is a 180 mm x 60 mm rectangle.

The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle.

Work out the maximum number of boxes that will fit on the shelf.

the maximum number of boxes that will fit on the shelf is 21.

To find the maximum number of boxes that fit on the shelf, we divide the shelf area by the area of each box.

Given:

- Shelf dimensions: 65 cm x 35 cm

- Box dimensions: 180 mm x 60 mm

First, let's convert the shelf dimensions to millimeters for consistency:

Shelf dimensions:

- Length: [tex]\(65 \, \text{cm} \times 10 \, \text{mm/cm} = 650 \, \text{mm}\)[/tex]

- Width: [tex]\(35 \, \text{cm} \times 10 \, \text{mm/cm} = 350 \, \text{mm}\)[/tex]

Now, calculate the area of the shelf:

[tex]\[ \text{Shelf area} = \text{Shelf length} \times \text{Shelf width} \]\[ \text{Shelf area} = 650 \, \text{mm} \times 350 \, \text{mm} \]\[ \text{Shelf area} = 227,500 \, \text{mm}^2 \][/tex]

Next, calculate the area of each box:

[tex]\[ \text{Box area} = \text{Box length} \times \text{Box width} \]\[ \text{Box area} = 180 \, \text{mm} \times 60 \, \text{mm} \]\[ \text{Box area} = 10,800 \, \text{mm}^2 \][/tex]

Now, find the maximum number of boxes that fit on the shelf:

[tex]\[ \text{Maximum number of boxes} = \frac{\text{Shelf area}}{\text{Box area}} \]\[ \text{Maximum number of boxes} = \frac{227,500 \, \text{mm}^2}{10,800 \, \text{mm}^2} \]\[ \text{Maximum number of boxes} \approx 21.06 \][/tex]

Since we can't have a fraction of a box, the maximum number of boxes that will fit on the shelf is 21.

The probable question maybe:

The campsite shop sells boxes of Funshine Cereal.

The base of each box is a 180 mm x 60 mm rectangle.

The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle.

Work out the maximum number of boxes that will fit on the shelf.

Answer:

Available information is not sufficient to solve the questions

Step-by-step explanation:

Let Cm = Computers Ordered by Company M

Let Cn = Computers Ordered by Company N

Let Pm = Printers Ordered by Company M

Let Pn = Printers Ordered by Company N

Cm + Pm = 50 --- Equation 1

Cn + Pn = 60 ----- Equation 2

1. Company M and N ordered the same number of computers

Here,

Cm = Cn

Substitute Cm for Cn in equation 2

Cm + Pm = 50

Cm + Pn = 60

Subtract Equation 2 from 1

Pm - Pn = 50 - 60

Pm - Pn = -10

Pm = Pn - 10

Substitute Pn-10 for Pm in equation 1

Cm + Pn - 10 = 50

Make Pn the subject of formula

Cm = 50+10-Pn

Cm = 60 - Pn

Hence, the number of computers ordered by Company M is 60 minus the number of printers ordered by Company n

2. Company N ordered 10 more printers than Company M.

Here,

Pn = 10 + Pm

Make Pm the subject of formula

Pm = Pn - 10

Substitute Pn-10 for Pm in equation 1

Cm + Pn - 10 = 50

Make Cm the Subject of formula

Cm = 50 + 10 - Pn

Cm = 60 - Pn

Hence, the number of computers ordered by Company M is 60 minus the number of printers ordered by Company n

Condition 1 and 2 points to the same result

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m = 1/7 is the slope

(x,y) = (0,0) is the origin the line goes through

y = mx+b

0 = (1/7)*0 + b

0 = 0+b

b = 0 is the y intercept

y = mx+b

y = (1/7)x+0

y = (1/7)x is the equation of the line

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To plot the equation of this line, mark the point (0,0) first.

Then move up 1 unit and to the right 7 units to arrive at (7,1) as the second point.

Draw a straight line through (0,0) and (7,1) as shown in the diagram below.

Point P is (0,0) and point Q is (7,1)

Points A through E in the same diagram represent the answer choices A through E.

Of the answer choices, only point D is on this line, so point D is the answer.

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A non-visual way to find the answer is to plug each (x,y) coordinate from each answer choice into the equation we found above.

So for choice A we plug in x = 0 and y = 7

y = (1/7)*x

7 = (1/7)*0

7 = 0

we end up with a false equation, so choice A is ruled out. Similar stories happen with B, C, and E as well.

With choice D however, we plug in x = 14 and y = 2, and we get...

y = (1/7)*x

2 = (1/7)*14

2 = 14/7

2 = 2

Since we get a true equation, this confirms that (14,2) is on the graph of y = (1/7)x.

Defining the wrong choice:

Therefore, "Choice D" is the correct choice.

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