Farmer john’s tractor pulls a rope attached to a bale of hay through a pulley. At a certain moment, the tractor’s speed is 3 m/s and the bale is rising at 2 m/s. How far is the tractor from the bale at this moment?.

Answer:

a. Le salaire horaire de Gaspard peut être calculé en divisant la somme totale gagnée par le nombre d'heures travaillées :

salaire horaire = 213 € ÷ 20 h = 10,65 €/h

Donc, Gaspard est payé 10,65 € par heure de travail.

b. Pour la semaine prochaine, sachant que Gaspard travaille 17 heures, il peut calculer son salaire total en multipliant ses heures de travail par son salaire horaire :

salaire total = 17 h × 10,65 €/h = 180,45 €

Ainsi, Gaspard gagnera 180,45 € pour 17 heures de travail la semaine prochaine.

c. Pour la semaine dernière, sachant que Gaspard a gagné 138,45 € et son salaire horaire est de 10,65 €/h, on peut calculer le nombre d'heures de travail :

nombre d'heures de travail = 138,45 € ÷ 10,65 €/h ≈ 13 h

Donc, Gaspard a travaillé environ 13 heures la semaine dernière.

Answer:

Step-by-step:

1.The probability of picking a brown ball can be calculated as:

Probability of picking a brown ball = Number of brown balls / Total number of balls

Number of brown balls = 25

Total number of balls = 13 + 25 = 38

Probability of picking a brown ball = 25/38

Probability of picking a brown ball is approximately 0.658 or 65.8%

Therefore, the probability of Jaide picking a brown ball from the jar is approximately 0.658 or 65.8%.

2.There are four kings in a pack of 52 cards (one king for each suit). Therefore, the probability of drawing a king from a pack of 52 cards can be calculated as:

Probability of drawing a king = Number of kings / Total number of cards

Number of kings = 4

Total number of cards = 52

Probability of drawing a king = 4/52

Probability of drawing a king is approximately 0.077 or 7.7%

Therefore, the probability of getting a king when drawing a card at random from a pack of 52 cards is approximately 0.077 or 7.7%.

Answer:

6 workers

Step-by-step explanation:

Number workers to earnings is direct proportion.

8: 2400 :: x : 1800

Product of means = Product of extremes

2400 * x = 8*1800

           \(x = \frac{8*1800}{2400}\\\\x=6\)

Answer:

6 workers will earn Rs. 1800.

Step-by-step explanation:

Given :-

To find :-

Solution :-

Let

no. of workers will earn Rs. 1800 = x.

We need to write a ratio to solve.

using cross products

Divide each side by 2400

Hence, 6 workers will earn Rs. 1800.

Answer:

B

Using gradient of two points and equation of a straight line graph.

Problem 1

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Explanation:

It doesn't matter if the distribution is symmetric or not. The standard deviation is not affected by symmetry (or lack thereof). Instead, the standard deviation measures how spread out a data set is. If we had all points stacked on top of each other, forming a single tower of sorts, then the standard deviation would be zero. That doesn't happen with the Christchurch dot plot. Therefore, the standard deviation is some positive value. The more spread out the data is, the larger the standard deviation will be. The standard deviation is never negative.

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Problem 2

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

Explanation:

We have these two sets of data

S = {-1, 0,0,0,1,2,3,3,3,3,3,5,6,6,6,6,6,7,8}

C = {-4,-3,-3,-3,-2,-1,0,0,0,0,0,2,3,3,3,3,3,4,5}

where S and C represent St. Louis and Chicago respectively. We could calculate the standard deviation by hand; however, I find that to be tedious busy work. This is especially true if the data set is quite large. Instead, I recommend using a spreadsheet or calculator to compute the standard deviation. We want the sample standard deviation, since these data points are a representative sample of every day of the year.

You should find that the sample standard deviation of set S is roughly 2.716 while the sample standard deviation of set C is roughly 2.716

Therefore, the two standard deviations are equal.

Note that if we were to shift each dot of dot plot C exactly 3 units to the left, then they will line up perfectly with what dot plot S is showing. This shows that the data sets have the same level of spread.

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Problem 3

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

Explanation:

We could use a calculator like we did with problem 2. Simply enter the data values and crunch the numbers. However, I'll go with a visual approach.

Focus on the lower two dotplots. After looking closely at both, you should notice that they are almost identical graphs. The only difference is that the dot at "5" for Chicago has been moved to "8" for London. Every other dot is the same between data sets however.

So because that dot has been moved out further from the group, the data set for London is more spread out. Therefore, the standard deviation is higher here. The statement that Chicago has a lower standard deviation is true.

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Problem 4

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Explanation:

Make a spreadsheet as you see in the diagram labeled "problem 4" (see attached image below). The x values are the midpoints of each interval. The column f represents the frequencies. We multiply the x values and frequencies to get the x*f column. Adding up everything in that column gets us the value 4590 (shown in gray). Divide that over n = 100 to get the sample mean xbar = 45.9

The f*(x-xbar)^2 column consists of multiplying each frequency (f) with the expression (x-xbar)^2. Adding up everything in that column leads to the value shown in yellow. Divide that over n-1 = 99 to get 50.9495 approximately. Then apply the square root to get roughly 7.1379 which is the standard deviation.

To recap, we found these values

So the mean salary is $45,900 and standard deviation is about $7,138. While these values don't perfectly match any of the given choices, we're fairly close to "social sciences", which is likely the answer.

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Problem 5

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

Explanation:

We use the same format and steps as problem 4. The difference of course is that we're dealing with a different data distribution. Refer to the table that says "problem 5" to see the spreadsheet.

The value in gray represents the sum of the x*f values. Divide that over n = 100 to get 5220/100 = 52.2

The value in yellow represents summing everything in the f*(x-xbar)^2 column (we don't sum in the yellow value itself or we'll have circular logic going on here). Divide that result in yellow over n-1 = 99 to get roughly 293.3434; then apply the square root to get roughly 17.1273 and this is the sample standard deviation.

To summarize so far, we have:

This then corresponds to

Like before, those last two values don't match up perfectly with any of the three given professions; however, we're fairly close to the mean and standard deviation of the business majors. This is likely the answer.

The correct answer is E. Both A and C are true.

Piecewise continuity refers to the continuity of a function that is defined by different formulas or rules on different intervals. To determine if a function is piecewise continuous on an interval [a, b], we need to consider certain conditions.

Option A states that the function is continuous at all but perhaps finitely many points of [a, b]. This means that the function may have a finite number of discontinuities, but it is continuous at all other points within the interval.

Option C states that the function has finite limits as t approaches a and as t approaches b from within the interval. This means that as t gets arbitrarily close to the endpoints a and b, the function approaches finite values.

Both of these conditions are necessary for a function to be considered piecewise continuous on [a, b]. If a function satisfies both conditions, it means that it is continuous almost everywhere within the interval, except possibly at finitely many points, and it has finite limits as t approaches the endpoints of the interval.

Therefore, the correct answer is E. Both A and C are true.

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Answer:

\(1\dfrac23\)

Answer:

This would be 1 2/3

Step-by-step explanation:

we do this by making the 5 the same denominator as 1/3

Answer:

AC = √105 ≈ 10 cm (nearest whole number)

Step-by-step explanation:

Use Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse of a right triangle)

Give one of the legs = 4cm and the hypotenuse = 11 cm:

⇒ 4² + AC² = 11²

⇒ 16 + AC² = 121

⇒ AC² = 121 - 16

⇒ AC² = 105

⇒ AC = ±√105

As distance is positive, length of AC = √105 ≈ 10 cm (nearest whole number)

Step-by-step explanation:

AB²=BC²+CA²

(11)²=(4)²+ CA²

121=16 + CA²

121-16= CA²

105=CA²

√105=CA

10.2=CA

hope this helps you

have a good day

Answer:

11

Step-by-step explanation:

If i am correct n= the days so with the days adding up day 10 juan would have 55 of the 100 candies, day 11 he would have 66. The statement said at least 64, so it would have to be 64 or the closet amount to 64 but it cannot be lower than 64. So there for 66 is the closest to the given amount, and in order for juan to get 64 he would need to take candies out for 11 days.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Yes, the other person is right.

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (1, 7)

The solution to the linear and quadratic equation is as follows:

For the linear, a solution is 1 and 7.

This is because when x = 1, f(x) = 7

For the quadratic equation, 1 and 7 also works.

2x² + x + 4

2(1)² + 1 + 4

2 + 1 + 4 = 7

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Answer:

37 + 42

Step-by-step explanation:

Like it and 5 stars ur welcome

Answer:

5.2491

Step-by-step explanation:

I'm sorry if this is incorrect

Answer:

52,491 = 5.2491 * 10 to the 4th power

Step-by-step explanation:

52,491

Move 4  times to the left

Here it is step by step

1. 5249.1 ( moved one place over)      

2. 524.91 ( moved over two places)

3. 52.491 ( moved over three places)

4. 5.2491 ( moved four places)

Answer:

m = -3/4

Step-by-step explanation:

Let's look at how much x and y change as we move from A to B:

x increases by 6, from -3 to 3, and y increases by 8, from 7 to 15.  Thus, the slope, m, is rise / run, or (change in y):  m = 8/6 = 4/3.

Now any line perpendicular to AB has a slope which is the negative reciprocal of this 4/3:  m = -3/4

Answer: x = 0 represents the price of the drink

Step-by-step explanation:

A circle is a curve sketched out by a point moving in a plane. The area of the sector PQR is 41.346 units².

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given the radius of the circle is 8 units, while the angle of the sector is 74°. Therefore, the area of the sector is,

Area of the sector = π×R²×(74/360)

                              = π × 8² × 0.20556

                              = 41.346 units²

Hence, the area of the sector PQR is 41.346 units².

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The equation in percentage given by, $2.21 + 8% tax = $2.3868 rounds to $2.4 to the nearest tenth.

Given an equation,

$2.21 + 8% tax = $2.3868

This is an equation which relates the cost including the percentage of tax.

When 2.21 is added to the tax amount, we get $2.3868.

2.21 + (0.08 × 2.21) = 2.3868

Here it is not mentioned up to what decimal we have to round the figure.

If 2.3868 is rounded to the nearest whole number, it becomes 2.

If 2.3868 is rounded to the tenth, it becomes 2.4.

If 2.3868 is rounded to the hundredth, it becomes 2.39.

Hence the rounded amount to the nearest tenth is $2.4.

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Answer:

From top to bottom

9

27/2

108/6

135/3

Step-by-step explanation:

Find how much is in 1 hour (unit rate)

Do 9/2 x 3=27/2

27/2 x 2/3=54/6=9

4/3 x 27/2= 108/6

Notice how all are solved with the unit rate

In a 12-hour period of digital clock, there are 2 instances.

The 12-hour clock runs from 1am to noon and then from 1pm to midnight. The 24-hour clock runs from 00:00 (midnight) to 23:59.

In a 12-hour period on a digital clock, there are a few instances when each succeeding digit is one more than the preceding digit. Let's break it down hour by hour,

1. 01:23 (only in the 1st hour)
2. 12:34 (only in the 12th hour)

In a 12-hour period, there are only 2 instances when each succeeding digit is one more than the preceding digit on a digital clock.

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Based on the cost of the property to Julie in 2007 and the various costs incurred since then, the amount of gain would be $166,350.

First find cost Julie has incurred in total:
= 236,500 + 5,250 + 25,000 - 4,100

= $262,650

The gain is therefore:

= Selling price - Total cost incurred

= 429,000 - 262,650

= $166,350

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Answer:

Well, the full question needs to be explained first. It very well is 7.4 miles back to the grocery store.

Step-by-step explanation"

First you have to take the time from home to school, x2 then divided 1.2 because the grocery store is a different coordinate than school, and multiply by your needing.

The amount of grams of carbohydrates in each cereal is 87.5 grams

From the question, we have the following parameters that can be used in our computation:

Carbohydrate = 700% of protein.

This means that

Carbohydrate = 7 of protein

Solving further, we make use of the following notations

The amount of protein = x

So, we have

Carbohydrate = 7x

The proportion of both must be 100%

i.e.

proteins + carbs = 100%

So, we have

x + 7x = 100

Evaluate the like terms

8x = 100                

Divide both sides by 8

8x/8 = 100/8

Evaluate

x = 12.5

Recall that

Carbohydrate = 7x

So, we have

Carbohydrate = 7*12.5

Carbohydrate  = 87.5 grams

Hence, the amount of grams of carbohydrate is 87.5

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Area of rectangle = length×breadth

Answer:

there equal

Step-by-step explanation:

the absolute value of 3 is 3

and the absolute value of -3 is 3

hope this helps

let me know if you need help with anymore

Have a great day!

Answer:

20(5+1) is equivalent to 100 + 20

Answer: 20 (5 + 1)

Step-by-step explanation: 20 x 5 = 100

                                             20 x 1 = 20

hopefully that helped :)

Answer:

Pretty sure DC is also 7.

Step-by-step explanation:

The triangle seems equal on both sides so if AC = 7, then DC = 7.

Answer:

DC= 7

Step-by-step explanation:

ΔABC≅ΔDBC

AB=DB

BC=BC and

CA=CD

given AB= 10

AC= 7

DC= AC =7

so DC will be 7

hope it helps

have a great day!!

Answer:

less than < the first option