Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?

(A) x/(x+y)
(B) y/(x+y)
(C) xy/(x+y)
(D) xy/(x-y)
(E) xy/(y-x)

Answer:

The probability that the student selected will be one who both walks to school and has been late to school at least once is = 0.15 or 15%

Step-by-step explanation:

From the question given, we find the probability that the student selected will be one who both walks to school and has been late to school at least once

Let,

B = Event that student walk to school

C = Event that student have been late to school at least once.

So,

P(B) = 0.40 , P(C) = 0.32

P(C | B) = 0.375

We apply the  multiplication rule,

P(B and C) = P(C | B) * P(B)

= 0.375 * 0.40

= 0.15 or 15%

Answer:

  -21 degrees

Step-by-step explanation:

Dropping 6 degrees per hour, the temperature drops 5×6 = 30 degrees in 5 hours. Starting at 9 degrees and dropping 30, the temperature becomes -21 degrees at 9 am.

Final answer:

The mass of the Earth's atmosphere from the surface up to an altitude of 5 km can be estimated by integrating the given density model over the surface area of a spherical shell between the radii corresponding to the Earth's surface and the 5 km altitude.

Explanation:

We will use the given model for the density of the Earth's atmosphere near the surface, δ = 619.09 - 0.000097p, to estimate the mass of the atmosphere up to an altitude of 5 km. The radius of the Earth is 6370 km, which is 6.370×106 meters. The altitude of 5 km is 5,000 meters, so we are considering the range of p from 6.370×106 meters to 6.370×106 meters + 5,000 meters.

To estimate the mass of the atmosphere between these two altitudes, we need to integrate the density function δ(p) over the surface area of the sphere at each value of p. For a thin spherical shell, the volume dV is given by the surface area 4πp2 times a small change in radius dp. Therefore, the mass dm contained in a shell is δ(p) * 4πp2 * dp.

To find the total mass, we integrate this expression between the two radii, resulting in:

M = ∫ 6.370×1066.375×106 δ(p) * 4πp2 * dp

Upon performing this integration, we would obtain the estimated total mass of the atmosphere between the ground level and 5 km of altitude.

integral_(6.37×10^6)^(6.375×10^6) (619.09 - 0.000097 p) 4 (π p)^2 dp = 767*10^18

Answer:

ticket owner loses an average of $0.95 per raffle ticket

Step-by-step explanation:

No profit organization plans to hold a raffle to raise funds for its operation .The expected value in this context is that ticket owner loses an average of $ 0.95

Answer:

B: The ticket owners lose an average of $0.95 per raffle ticket.

Step-by-step explanation:

Answer: 17.7

Step-by-step explanation:

212.4÷12 = 17.7

Answer: 17.7 miles per gallon

Step-by-step explanation:

Hi, to answer this question we have to divide the number of miles (212.4) by the number of gallons used (12).

Mathematically speaking:

212.4 /12 = 17.7 miles per gallon

17.7 is already rounded to the nearest tenth.

His truck gets  17.7 miles per gallon

Feel free to ask for more if needed or if you did not understand something.

Answer:

It is 44

Step-by-step explanation:

Answer: The area of one shaded square is 1 inch^2

The total area of all the shaded squares is 144/2 = 72 inches square

The total area of all the white squares is also 72 inches square

Step-by-step explanation:

If a total area of the chessboard is 144 square inches. The length of both sides are equal because it is a square. The formula for area is length ^2

The length of one side = √area

The length of one side = √144 = 12 inches

This means that both sides of the chessboard is 12 inches. Each side is divided into 12 partitions measuring 1 inch each. This forms a smaller square whose area is

1 inch by 1 inch. Therefore,

The area of one shaded square is

1 inch^2

The total area of the white squares and the shaded squares is 144. Therefore,

The total area of all the shaded squares is 144/2 = 72 inches square

The total area of all the white squares is also 72 inches square

Answer:

Option C.

Step-by-step explanation:

Given information

[tex]n_1=1563[/tex] and [tex]n_2=579[/tex]

[tex]x_1=61[/tex] and [tex]x_2=15[/tex]

Using the given information we get

[tex]p_1=\dfrac{x_1}{n_1}=\dfrac{61}{1563}\approx 0.039[/tex]

[tex]p_2=\dfrac{x_2}{n_2}=\dfrac{15}{579}\approx 0.026[/tex]

The formula for confidence interval for p_1 - p_2 is

[tex]C.I.=(p_1-p_2)\pm z*\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}[/tex]

From the standard normal table the value of z* at 95% confidence interval = 1.96.

[tex]C.I.=(0.039-0.026)\pm (1.96)\sqrt{\dfrac{0.039(1-0.039)}{1563}+\dfrac{0.026(1-0.026)}{579}}[/tex]

[tex]C.I.=0.013\pm (1.96)(0.008)[/tex]

[tex]C.I.=0.013\pm 0.016[/tex]

[tex]C.I.=(0.013-0.016,0.013+0.016)[/tex]

[tex]C.I.=(-0.003,0.029)[/tex]

The 95% confidence interval for p_1 - p_2. is (-0.003,0.029).

Therefore, the correct option is C.

Final answer:

The correct 95% confidence interval for the difference in proportions of dizziness between subjects taking Accupril and those not taking it, using the sample data provided, is (0.006, 0.092).

Explanation:

To create a 95% confidence interval for the difference in proportions (p_1 - p_2), where p_1 is the proportion of people who experience dizziness while taking Accupril, and p_2 is the proportion of people experiencing dizziness but not taking Accupril, we use the following formula:

Confidence Interval = (p_hat_1 - p_hat_2) ± Z*sqrt((p_hat_1*(1 - p_hat_1)/n_1) + (p_hat_2*(1 - p_hat_2)/n_2))

Where p_hat_1 and p_hat_2 are the sample proportions, n_1 and n_2 are the sample sizes, and Z is the Z-score corresponding to a 95% confidence level (1.96 for two-tailed tests).

After calculating these proportions and plugging the values into the formula, the confidence interval is (0.006, 0.092).

Hence, the correct answer is option a. (0.006, 0.092).

The plot of land forms right triangle.

Step-by-step explanation:

Let,

the three sides are a,b and c.

The sum of square of two sides equals to the square of third side. We will consider the larger side as c, therefore,

a= 2000 feet

b= 2100 feet

c= 2900 feet

Using Pythagoras theorem;

[tex]a^2+b^2=c^2\\(2000)^2+(2100)^2=(2900)^2\\4000000 + 4410000 = 8410000\\8410000 feet = 8410000 feet[/tex]

As the three sides satisfy pythagoras theorem, therefore, the plot of land form right triangle.

The plot of land forms right triangle.

Keywords: triangle, pythagoras theorem

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Explanation:

For the purpose of filling in the table, the BINOMPDF function is more appropriate. The table is asking for p(x)--not p(n≤x), which is what the CDF function gives you.

If you want to use the binomcdf function, the lower and upper limits should probably be the same: 0,0 or 1,1 or 2,2 and so on up to 5,5.

The binomcdf function on my TI-84 calculator only has the upper limit, so I would need to subtract the previous value to find the table entry for p(x).

Answer:

3/8 left

Step-by-step explanation:

I can't draw a model but I can still give an explanation.

1/2 required to memorize - 1/8 already memorized = 3/8 left

Maybe draw a rectangle with 8 divisions and label the situation.

Devon still needs to memorize 3/8 of his lines. This is determined by converting 1/2 to 4/8 and then subtracting the 1/8 he's already learned, leaving 3/8 of his lines remaining.

Devon aims to memorize 1/2 of his lines and has already memorized 1/8 of them. The task here is to find out how many more lines Devon has left to learn. In terms of fractions, this would involve subtracting the already learnt fraction (1/8) from the total goal (1/2).

Firstly, make sure both fractions have the same denominator, for easy calculation. In this case, you can convert 1/2 to 4/8. Now, subtract what you've already learnt. So 4/8 - 1/8 equals 3/8. That means Devon has 3/8 of his lines left to memorize.

To illustrate this visually, consider a pie representing all of Devon's lines. Cut it into 8 even slices. Four of these slices represent the half that Devon wants to learn. He has already learnt one slice (1/8 of the pie). So, he has three slices (3/8 of the pie) left to learn.

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Answer:

Step-by-step explanation:

a) Because you are only receiving $1500 and in exchange you would have to cover for this accident damage in the next year, which could be up to hundred of thousands of dollar. Sure there's a chance the your neighbor might drive safely, but the odds are far more in his favor than yours.

b) The insurance company collect payments from hundred of thousands buyers, making their cash flow up to tens of million dollar. Sure the expected value of accidents might be high but as a company they surely have capital to cover a handful of cases, if their calculation done right.

Final answer:

One should be reluctant to accept a $1500 payment to cover a neighbor's car accidents due to the potential for costs to exceed this amount. Insurance companies, with their risk-pooling model, accumulate enough in premiums to cover accidents across a large customer base and manage risk effectively.

Explanation:

You should be reluctant to accept a $1500 payment from your neighbor to cover his automobile accidents for the next year because the cost of a potential accident could far exceed the amount collected. If your neighbor is involved in an accident, the resulting expenses for vehicle repairs, medical bills, or other damages could be much greater than $1500, leaving you responsible for the remainder of the costs.

On the other hand, an insurance company can make such an offer because they operate on a system of pooled risk. If each of the 100 drivers pays a $1,860 premium each year, the insurance company will collect a total of $186,000. This amount is calculated to cover the expected costs of accidents across their entire customer base, using statistics and probability to spread the risk among many policyholders. While some drivers may have no accidents, others may have expensive claims, but the total premiums collected can cover the aggregate cost of the accidents that occur.

Additionally, insurance companies can classify people into risk groups and adjust the premiums accordingly. For example, drivers with a good driving record may pay less than those with a history of accidents. This allows the company to minimize their risk while ensuring that those who are less likely to file a claim aren't subsidizing those with higher risks.

Final answer:

An azimuth is a horizontal angle measured clockwise from a north base line, used in navigation and surveying to indicate direction. It measures angles from 0° to 360°, starting from the north and moving towards the east, which allows for precise direction determination on the earth's surface. The correct answer is A.

Explanation:

The question, "What is an Azimuth?" pertains to how angles, specifically bearings, are measured in relation to the earth's surface. The correct answer is: 'A. A horizontal angle measured clockwise from a north base line.' An azimuth is essentially a type of bearing used in navigation and surveying to indicate direction. It is a measure of rotation from the north direction towards the east, meaning the angle increases in a clockwise fashion. The concept originates from surveying practices and is crucial for determining directions accurately on the earth's surface.

The use of azimuth in surveying involves specifying angles in degrees from 0° to 360°, starting from north towards east, south, west, and back to north. This precise measurement allows geographers, surveyors, and navigators to determine directions and locations with respect to the north base line, which serves as a universal reference point.

Furthermore, azimuth measurements can distinguish between true north, which is the geographical north pole, and magnetic north, which is dictated by the earth's magnetic field. Despite this distinction, azimuths provide a consistent method for defining bearings across various contexts, making them indispensable in mapping and navigation.

The equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(3,-3) is y = x + 2

Given, two points are A(-5, 5) and B(3, -3)

We have to find the perpendicular bisector of segment AB.

Now, we know that perpendicular bisector passes through the midpoint of segment.

The formula for midpoint is:

[tex]\text { midpoint }=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

[tex]Here x_1 = -5 ; y_1 = 5 ; x_2 = 3 ; y_2 = -3[/tex]

[tex]\text { So, midpoint of } A B=\left(\frac{-5+3}{2}, \frac{5+(-3)}{2}\right)=\left(\frac{-2}{2}, \frac{2}{2}\right)=(-1,1)[/tex]

Finding slope of AB:

[tex]\text { Slope of } A B=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]\text { Slope } m=\frac{-3-5}{3-(-5)}=\frac{-8}{8}=-1[/tex]

We know that product of slopes of perpendicular lines = -1  

So, slope of AB [tex]\times[/tex] slope of perpendicular bisector = -1  

- 1 [tex]\times[/tex] slope of perpendicular bisector = -1  

Slope of perpendicular bisector = 1

We know its slope is 1 and it goes through the midpoint (-1, 1)

The slope intercept form is given as:

y = mx + c

where "m" is the slope of the line and "c" is the y-intercept

Plug in "m" = 1

y = x + c   ---- eqn 1

We can use the coordinates of the midpoint (-1, 1) in this equation to solve for "c" in eqn 1

1 = -1 + c

c = 2

Now substitute c = 2 in eqn 1

y = x + 2

Thus y = x + 2 is the required equation in slope intercept form

Answer:

13487 ft³

Step-by-step explanation:

Volume of a Cylinder: 2πr²*h

π = 3.14

r = 9 ft

h = 53 ft

Volume = 2(3.14)(9)²*53 = 13486.86 ft³

Rounded to nearest whole number

Volume of the Cylindrical Water tank is 13487 ft³

The volume of the cylindrical grain silo is found using the formula V = πr²h, where r is the radius and h is the height. Using the specifications of the silo (r=9 feet, h=53 feet), we find that the volume of the grain silo is about 13480 cubic feet.

The student is trying to find the volume of a cylinder. The volume V of a cylinder can be found using the formula: V = πr²h where r is the radius of the base, h is the height and π is about 3.14.

To find the volume V of the grain silo, first, square the radius r, which is 9 feet: 81 square feet. Then multiply the result by the height h, which is 53 feet: 4293 cubic feet. Lastly, multiply the result by π, which we should approximate as 3.14: 13480 cubic feet rounded to the nearest whole number.

So, the volume of the grain silo is about 13480 cubic feet.

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Answer:

[tex]\overline{BD}\ and\ \overline{AC}[/tex]  bisect each other is sufficient to Prove  Δ ABE ≅ Δ CDE

Step-by-step explanation:

Given: (if it is given)

[tex]\overline{BD}\ and\ \overline{AC}[/tex]  bisect each other, i.e

AE ≅ CE

BE ≅ DE

To Prove:

Δ ABE ≅ Δ CDE

Proof:

In  Δ ABE and Δ CDE

      AE ≅ CE     …………..{ BD and AC bisect each other at E}

∠ AEB ≅ ∠ CED      ………….{Vertically opposite angles are equal}

     BE  ≅ DE     ……….{ BD and AC bisect each other at E}  

Δ ABC ≅ Δ PQR ….{Side-Angle-Side test} ......PROVED

Answer:

ΔDBE≅ΔQAP  (by RHS criteria)

Step-by-step explanation:

Given that, [tex]PQ=DE[/tex], [tex]PB=AE[/tex], [tex]QA[/tex]⊥[tex]PE[/tex]

and [tex]DB[/tex]⊥[tex]PE[/tex]

⇒∠PAQ=90° and ∠EBD=90°(definition of perpendicular lines)

Its given that PB=AE,

subtracting AB on both sides,

we get: PB-AE=AB-AE

         ⇒PA=EB (equals subtracted from equals, the remainders are equals)

Therefore, ΔDBE≅ΔQAP (by RHS criteria)

conditions for congruence:

So, ∡D=∡Q(as congruent parts of congruent triangles are equal)

Answer:

y=1.25x+4

Step-by-step explanation:

Answer:

x = 1 and x = -3

Step-by-step explanation:

roots are points that y = 0

in two points we have this

x = 1 and x = -3

Answer:

standard deviation is 0.51

Step-by-step explanation:

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1065 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.62 hours with a standard deviation of 0.51

Answer: [tex]LSA=128\ cm^2[/tex]

Step-by-step explanation:

The formula for calcualte the Lateral surface area of a prism is:

[tex]LSA=Ph[/tex]

Where "P" is the perimeter of the base and "h" is the height of the prism.

Notice that the base is a triangle. Since the perimeter is the sum of its sides, you get that this is:

[tex]P=5\ cm+6\ cm+5\ cm\\\\P=16\ cm[/tex]

You can identify in the figure that the height is:

[tex]h=8\ cm[/tex]

Therefore, you can substitute these values into the formula in order to calculate the Lateral surface area of the given prism. This is:

[tex]LSA=(16\ cm)(8\ cm)\\\\LSA=128\ cm^2[/tex]

Answer:

128

Step-by-step explanation:

Answer:

The number of hours worked per week

Step-by-step explanation:

To study this issue, one administrator was assigned to examine the relationship between the number of hours worked per week in a semester and that semester's GPA for a random sample of students.

Here the explanatory variable is - the number of hours worked per week.

An explanatory variable or also called an independent variable, is the variable that is manipulated by the researcher based on the variations in the response variable of an experimental study.

Answer:

c) Sample parameters are usedto make inferences about population statistics

Step-by-step explanation:

In statistics we use samples to make inferences about population

That is the great advantage of the whole role of distribution. Once you know a particular situation or experiment, that you can associate to one specific distribution and compute parameters, you can obtain from a relative smaller quantity of dataand  with good approximation, inferences about the whole population (that can be conform by a very big numbers of elements)

Answer: D. Sample statistics are used to make inferences about population parameters.

Step-by-step explanation: got it right on edge 23  :)

Answer:16/15^2

Step-by-step explanation:

Answer: 250000 pounds

Step-by-step explanation:

The area of one field is 16 acres and the area of the second field is 1 1/4 times bigger. This means that the area of the second field is

1.25 × 16 = 20 acres.

A barn of wheat on the first field makes up 37 1/2 thousands of pounds per acre. This means that the total wheat on the first field will be the amount of wheat per acre × total number of acres. It becomes

37.5 × 16 = 600 000 pounds of wheat.

On the second, it is 1 2/15 times as much per acre. This means that an acre on the second field contains

17/15( converted 1 2/15 to improper fraction) times the number of wheat per acre on the first field.

Amount of wheat per acre for the second field = 17/15 × 37.5 = 42.5

This means that the total wheat on the second field will be the amount of wheat per acre × total number of acres. It becomes

42.5 × 20 = 850 000 pounds of wheat.

We will subtract the amount of wheat gathered from field 1 from the amount gathered from field 2. It becomes 850000 - 600000 = 250000 pounds of wheat. Therefore,

The amount of wheat gathered from the second field is 250000 pounds more than the amount from the first field

Answer:

$40,000

Step-by-step explanation:

Let x represent the selling price of the bull.

We have been given that a cattle rancher would like to make $36,400 after paying a 9% commission to the auctioneer.

The commission would be 9% of selling price, that is [tex]\frac{9}{100}x=0.09x[/tex].

The profit of the rancher can be counted after paying off the commission that would be [tex]x-0.09x[/tex].

Since rancher wants to make $36,400 after paying a 9% commission, so we can represent this information in an equation as:

[tex]x-0.09x=36,400[/tex]

[tex]0.91x=36,400[/tex]

[tex]\frac{0.91x}{0.91}=\frac{36,400}{0.91}[/tex]

[tex]x=40,000[/tex]

Therefore, for a selling price of $40,000 the rancher will make the required amount of money.

Number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days

Given that  

A team of seven workers started a job, which can be done in 11 days.

On the morning of the fourth day, several people left the team. The rest of team finished the job in 14 days.  

Need to determine how many people left the team.  

Let say complete work be represented by variable W.

=> work done by 7 workers in 11 days = W

[tex]\Rightarrow \text {work done by } 1 \text { worker in } 11 \text { days }=\frac{\mathrm{W}}{7}[/tex]

[tex]\Rightarrow \text {work done by } 1 \text { worker in } 1 \text { day }=\frac{W}{7} \div 11=\frac{W}{77}[/tex]

As its given that for three days all the seven workers worked.

Work done by 7 worker in 3 day is given as:

[tex]=7 \times 3 \times \text { work done by } 1 \text { worker in } 1 \text { day }[/tex]

[tex]=7 \times 3 \times \frac{W}{77}=\frac{3W}{11}[/tex]

Work remaining after 3 days = Complete Work - Work done by 7 worker in 3 day

[tex]=W-\frac{3 W}{11}=\frac{8 W}{11}[/tex]

It is also given that on fourth day some workers are left.

Let workers left on fourth day = x

So Remaining workers = 7 – x

And these 7 – x workers completed remaining work in 14 days

[tex]\begin{array}{l}{\text { As work done by } 1 \text { worker in } 1 \text { day }=\frac{W}{77}} \\\\ {\text { So work done by } 1 \text { worker in } 14 \text { days }=\frac{W}{77} \times 14=\frac{2 \mathrm{W}}{11}} \\\\ {\text { So work done by } 7-x \text { worker in } 14 \text { days }=\frac{2 \mathrm{W}}{11}(7-x)}\end{array}[/tex]

As Work remaining after 3 days = [tex]\frac{8W}{11}[/tex] and this is the same work done by 7- x worker in 14 days

[tex]\begin{array}{l}{\Rightarrow \frac{\mathrm{8W}}{11}=\frac{2 \mathrm{W}}{11}(7-x)} \\\\ {=>4=7-x} \\\\ {=>x=7-4=3}\end{array}[/tex]

Workers left on fourth day = x = 3

Hence number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days.

equation:

4=7-x

answer:

3 people left the team.

Answer:

Step-by-step explanation:

a) The probability that the hand contains exactly one ace

No of ways of selecting one ace and four non ace would be

=[tex]4C1 (48C4)\\\\= 778320[/tex]

i.e. α=778320

b) the probability that the hand is a flush

No of ways of getting a flush is either all 5 hearts or clubs of spades or dice

= [tex]4(13C5) = 5148[/tex]

ie. β=5148

c)  the probability that the hand is a straight flush

In each of the suit to get a straight flush we must have either A,2,3,4,5 or 2,3,4,5,6, or .... or 9,10, J, q, K

So total no of ways = [tex]=9(13C5) 4\\= 46332[/tex]

γ=46332

The probability of getting a hand with exactly one ace from a standard deck is 748,704/2,598,960. For a flush, the probability is 5,148/2,598,960. For a straight flush, the probability is 40/2,598,960.

The total number of possible five card hands from a standard deck is C(52,5)=2,598,960.

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Answer:

  [tex]\boxed{x=2}[/tex]

Step-by-step explanation:

The equation of a parabola with vertex (h, k) and directrix-to-vertex distance p is given by ...

  (y -k)^2 = 4p(x -h)

The directrix is the line x = (h -p)

Here, we have the vertex at x=5. The distance from the directrix satisfies ...

  12 = 4p

  12/4 = p = 3

So, the directrix is at x = 5 - 3, or x = 2.

_____

The graph shows the given parabola along with the focus and directrix. The dashed lines are intended to show that each of those is in the right place, as the distance from any point on the parabola is the same to the focus and the directrix.

Final answer:

The equation of the directrix of the parabola with the equation (y + 2)² = 12(x - 5) is x = 2.

Explanation:

To find the equation of the directrix of a parabola, we first need to identify the vertex form of the parabola's equation. The given equation of the parabola is (y + 2)² = 12(x - 5). This equation indicates that the parabola opens horizontally to the right since the squared term is (y + 2)² and the x is positive in the standard form of the equation. The vertex of the parabola is at the point (5, -2).

For a parabola in the form (y - k)² = 4p(x - h), where (h, k) is the vertex, the directrix is a vertical line if the parabola opens horizontally. The value of p determines the distance from the vertex to the focus and to the directrix. The given equation can be rewritten as (y + 2)² = 4(3)(x - 5), so here p is equal to 3. Since the parabola opens to the right, the directrix will be to the left of the vertex at a distance of 3 units.

The equation for the directrix is thus a vertical line x = h - p. Plugging the vertex coordinates and p into this formula, we get x = 5 - 3, which simplifies to x = 2. Therefore, the equation of the directrix of the given parabola is x = 2.

Ronna collected [tex]12\frac{3}{4}[/tex] bags of clothes

Step-by-step explanation:

Tristan and Ronna are collecting clothes for a clothing drive

We need to find how many bags of clothes  Ronna collected

∵ Ronna collected 3 times as many clothes as Tristan did

- That means Ronna collected 3 × the amount that Tristan did

∵ Tristan collected [tex]4\frac{1}{4}[/tex] bags

- Multiply the amount of Tristan by 3 to find the amount of Ronna

∴ Ronna collected = 3 × [tex]4\frac{1}{4}[/tex]

Change the mixed number to improper fraction

∵ [tex]4\frac{1}{4}[/tex] = [tex]\frac{(4*4)+1}{4}=\frac{17}{4}[/tex]

∴ Ronna collected = 3 × [tex]\frac{17}{4}[/tex]

∴ Ronna collected = [tex]\frac{51}{4}[/tex]

Change the improper fraction to mixed number by divide 51 by 4

∵ 51 ÷ 4 = 12 and reminder 3 (4 × 12 = 48 and 51 - 48 = 3)

∴ [tex]\frac{51}{3}=12\frac{3}{4}[/tex]

∴ Ronna collected = [tex]12\frac{3}{4}[/tex] bags of clothes

Ronna collected [tex]12\frac{3}{4}[/tex] bags of clothes

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Final answer:

Using Hooke's Law, the spring constant is calculated from the given force and stretch, which is then used to calculate the work done for a larger stretch. The work done in stretching the spring from its natural length to 0.7 feet is approximately 4.29 foot-pounds.

Explanation:

To solve this problem, we need to use Hooke's Law, which says that the force needed to stretch or compress a spring is directly proportional to the distance the spring is stretched or compressed from its natural length. The formula for the force on a spring is F = kx, where k is the spring constant and x is the stretch from the natural length.

First, we can find the spring constant using the information given: a force of 7 pounds to stretch the spring 0.4 feet beyond its natural length.

Therefore, the work done in stretching the spring from its natural length to 0.7 feet is approximately 4.29 foot-pounds.