Which of the following equations uses the commutative property of addition to rewrite 1/3+2/5?

Select one:
a. 2/3+1/5=13/15
b. 1/3+2/5=5/15+6/15
c. 11/15−2/5=1/3
d. 2/5+1/3=11/15

Answer:

Step-by-step explanation:

Angles 1 and 3 are vertical angles, so are equal:

  m∠1 = m∠3 = 43°27'

Angles 2 and 3 are a linear pair, so are supplementary:

  m∠2 = 180° - m∠3 = 180° - 43°27' = 136°33'

Angles 2 and 4 are also vertical angles, so are equal:

  m∠4 = m∠2 = 136°33'

_____

There are 60 minutes in a degree, so 180° is the same as 179°60'. Subtraction can proceed in the usual way after this rewrite:

  180° - 43°27' = 179°60' -43°27'

  = (179 -43)° +(60 -27)' = 136°33'

Answer:

18 antelopes/km^2

Step-by-step explanation: Took the test ;)

Final answer:

The population density of antelopes near the watering hole is approximately 9 antelopes per km² when rounded to the nearest whole number.

Explanation:

The concept of population density is fundamental in ecology and refers to the number of individuals of a species per unit of area.

To calculate population density for the population of antelopes the biologist is studying, we first need to determine the area covered, which is a circle with a radius of 34 km.

Using the given value of pi (3.14), the area (A) is calculated with the formula A = πr², where r is the radius.

The area is therefore 3.14 × (34 km)² = 3.14 × 1,156 km² = 3,629.44 km².

Next, the population density (D) is determined by dividing the number of individuals (N) by the area (A), which in this case is D = N / A = 32 antelopes / 3,629.44 km² ≈ 0.00 88 antelopes per km².

Rounding the final value to the nearest whole number gives us a population density of 9 antelopes per km².

Answer:

The length of rectangular plot of land is 160 ft.

Step-by-step explanation:

L = 2 W (the length is twice the width)

P = 480 ft. (perimeter of rectangular plot of land)

L = ?

2. 2W + 2W= 480 ft  >>> (2 times twice width=L) + 2W=480 ft.

4W + 2W= 480 ft >>>> 6W= 480 ft.

W= 80 ft.

L = 2. 80 = 160 ft. (Length is twice the width)

P= 2L + 2W (formula for the perimeter)

2. 160 + 2. 80 = 480 ft.

Check the picture below.

For this case we have to define trigonometric relationships in rectangular triangles that the sine of an angle is given by the leg opposite the angle, on the hypotenuse of the triangle.

If we have to:

[tex]Sin A = \frac {3} {5}[/tex]

So:

Leg opposite angle A is: 3

The hypotenuse is: 5

If we apply the Pythagorean theorem, we find the value of the other leg:

[tex]x = \sqrt {5 ^ 2-3 ^ 2}\\x = \sqrt {25-9}\\x = \sqrt {16}\\x = 4[/tex]

So, the Sine of B is given by:

[tex]Sin B = \frac {4} {5}[/tex]

Answer:

[tex]SinB = \frac {4} {5}[/tex]

21

Step-by-step explanation:

Answer:

company A because its less money

Step-by-step explanation:

Answer:

A. X = 15 is the correct answer.

Step-by-step explanation:

It's the only one that really makes sense.

Hope this helped :)

The value of the variable x will be 15. Then the correct option is A.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.

The trapezoid is an isosceles trapezoid.

An isosceles trapezoid is the form of trapezoid on which the non-parallel sides are of equal length.

In the isosceles trapezoid, the sum of the opposite angles is 180 degrees.

Then the sum of the angle B and angle D will be 180°.

∠B + ∠D = 180°

 9x + 3x = 180

        12x = 180°

            x = 180°

            x = 15°

Thus, the value of the variable x will be 15.

Then the correct option is A.

The question was incomplete, but the complete question is attached below.

More about the trapezoid link is given below.

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Answer:

median: 10.1

mean: 10.333

SD: 0.632

The median of the data set is 10.1 mph. The mean of the data set is 10.26 mph. The population standard deviation of the data set is approximately 0.5339 mph.

The median of a data set is the middle value when the data is arranged in ascending or descending order. To find the median of the given data set, we need to arrange the wind speeds in ascending order:

Since we have 12 values in the data set, the median will be the average of the 6th and 7th values, which are both 10.1. Therefore, the median of the data set is 10.1 mph.

The mean or average of a data set is found by summing all the values and dividing by the number of values. For the given data set, the sum of the wind speeds is 123.1 mph (9.6 + 9.7 + 9.9 + 9.9 + 10.0 + 10.1 + 10.1 + 10.3 + 10.7 + 10.8 + 11.0 + 11.9) and there are 12 values. Dividing the sum by 12, the mean of the data set is 10.26 mph.

The population standard deviation is a measure of the spread or dispersion of the data. To calculate it, we need to subtract the mean from each value, square the result, sum them all, divide by the number of values, and take the square root. Using the given wind speeds:

Summing these values gives us 3.4368. Dividing by 12, we get 0.2864. Finally, taking the square root, the population standard deviation of the data set is approximately 0.5339 mph.

Answer:

12

Step-by-step explanation:

Alright so we are asked to find the intersection of y=(x-8)^2 and y=36.

So plug second equation into first giving:  36=(x-8)^2.

36=(x-8)^2

Take square root of both sides:

[tex]\pm 6=x-8[/tex]

Add 8 on both sides:

[tex]8 \pm 6=x[/tex]

x=8+6=14 or x=8-6=2

So we have the two intersections (14,36) and (2,36).

We are asked to compute this length.

The distance formula is:

[tex]\sqrt{(14-2)^2+(36-36)^2}[/tex]

[tex]\sqrt{14-2)^2+(0)^2[/tex]

[tex]\sqrt{14-2)^2[/tex]

[tex]\sqrt{12^2}[/tex]

[tex]12[/tex].

I could have just found the distance from 14 and 2 because the y-coordinates were the same. Oh well. 14-2=12.

Answer:

∠ZYX = 58°

Step-by-step explanation:

The measure of an inscribed angle or a tangent- chord angle is one half the measure of the intercepted arc.

arc XY is the intercepted arc, hence

∠ZYX = 0.5 × 116° = 58°

Answer: [tex]ZYX=58\°[/tex]

Step-by-step explanation:

It is important to remember that, by definition:

[tex]Tangent\ chord\ Angle=\frac{1}{2}Intercepted\ Arc[/tex]

 In this case you know that for the circle shown in the figure, the arc XY measures 120 degrees, therefore you can find the measure of the angle ZYX. Then you get that the measure of the this angle is the following:

[tex]ZYX=\frac{1}{2}XY\\\\ZYX=\frac{1}{2}(116\°)\\\\ZYX=58\°[/tex]

Answer:

Jeff mows 9 yards of lawn in 30 minutes

Step-by-step explanation:

The equation that models the amount of time (t) in minutes it takes Jeff to mow an average sized yard is [tex]t=2n+12[/tex], where n is the number of yards he mows.

To find the number of yards Jeff mows in 30 minutes, we set the equation to 30 and solve for n.

[tex]\implies 2n+12=30[/tex]

Add -12 to both sides:

[tex]\implies 2n=30-12[/tex]

[tex]\implies 2n=18[/tex]

Divide both sides by 2

[tex]\implies \frac{2n}{2}=\frac{18}{2}[/tex]

[tex]\implies n=9[/tex]

Hence Jeff mows 9 yards of lawn in 30 minutes.

Final answer:

Jeff mows 9 lawns if it takes him 30 minutes, based on the equation t = 2n + 12

Explanation:

The question asks us to find out how many lawns Jeff mows if it takes him 30 minutes. The relationship between the amount of time (t) in minutes and the number of yards he mows (n) is given by the equation t = 2n + 12. Since we are given that t = 30 minutes, we can substitute the value of t into the equation to solve for n, the number of lawns.

30 = 2n + 12

By subtracting 12 from both sides of the equation we get:

18 = 2n

Next, we divide both sides of the equation by 2 to solve for n:

n = 9

Therefore, Jeff mows 9 lawns if it takes him 30 minutes.

Answer:

[tex]1.\ \ p(x)\geq0 & \text{ for all values of x.}\\\ 2.\ \sum\ p(x)=1[/tex]

Step-by-step explanation:

There are two requirements for a discrete probability​ distribution that must be satisfied as :-

1. Each probability must be greater than equals to zero.

2. Sum of all probabilities should be equals to 1.

The above conditions are also can be written as :

[tex]1.\ \ p(x)\geq0 & \text{ for all values of x.}\\\ 2.\ \sum\ p(x)=1[/tex]

A discrete probability distribution must satisfy two conditions: each individual outcome probability must be between 0 and 1, and the total of all outcome probabilities must equal to 1.

There are two key requirements that a set of data must meet to be considered a discrete probability distribution:

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Answer:

Conjugate radicals.

Step-by-step explanation:

The two roots a+sqrb and a-sqr b are called conjugate radicals.

Answer:

Step-by-step explanation:

Such questions generally arise in the context of measurement precision and/or accuracy. Apparently, we're to assume that these dimensions could be arrived at by rounding to the nearest km. In that case, they can be taken to have a possible error of ±0.5 km.

The minimum possible area is the product of the minimum possible dimensions: 1.5 km by 4.5 km = 6.75 km².

The maximum possible area is the product of the maximum possible dimensions: 2.5 km by 5.5 km = 13.75 km².

_____

Comment on combining measurement values

You will note that the nominal area is 2 km by 5 km = 10 km², and that the middle value between the minimum and maximum is slightly more than this, at 10.25 km².

It is typically the case that when measurements are combined by operations other than addition and subtraction, the nominal result is different from the middle result in the range of possibilities.

Answer:

  The ball bounces to 70% of its previous height with each bounce.

Step-by-step explanation:

In physics terminology, the number 0.7 is the coefficient of restitution. It is the ratio of the height of bounce (n+1) to the height of bounce (n).

The meaning of the number is that the ball bounces to 70% of the height of the previous bounce.

Answer:

The ball bounces to 70% of its previous height with each bounce.

Step-by-step explanation:

A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:

f(n) = 9(0.7)n

The number 0.7 represents that the ball bounces to 70% of its previous height with each bounce.

Answer:

AB= AC times AE/AD

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

In this problem

AB/AC=AE/AD

solve for AB

AB=(AC)(AE)/AD

Answer:

AB= AC times AE/AD

Step-by-step explanation:

AB is on the segment AC, therefore it is proportional to AC .

In order to fulfill the requirement that triangle ABE is a smaller scaled replica of triangle ACD, a scale factor must be applied to the sides of the original figure; in this case, the factor is AE/AD.

The correct answer from each drop-down menu is:

If cost 8 = 8 and tan20 = 17, then cos28 = -8/17.

To solve this problem, we can use the double angle formula for cosine:

cos2θ = 2cos²θ - 1

We know that cos20 = 17, so we can substitute this value into the formula:

cos2(20°) = 2(cos20°)² - 1

cos2(20°) = 2(17²)² - 1

cos2(20°) = -8/17

Therefore, the correct answer is cos28 = -8/17.

There were 26 fans at the game who were lucky enough to receive all three free items.

The Madd Batters minor league baseball team offered different incentives to its fans for the opening home game.

To determine how many fans were lucky enough to receive all three free items, we need to find the total number of fans that satisfy each condition.

The least common multiple of 75, 30, and 50 is 150.

So, we divide 4000 by 150 to find the number of fans that satisfy the conditions for all three items.

Therefore, 26 fans at the game were lucky enough to receive all three free items.

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we know that θ is in the III Quadrant, and let's recall that on the III Quadrant sine and cosine are both negative, and since tangent = sine/cosine, that means that tangent is positive.  Let's also keep in mind that tan(π) = sin(π)/cos(π) = 0/-1 = 0.

well, the hypotenuse is just a radius unit, so is never negative, since we know sin(θ) = -(5/13), well, the negative number must be the 5, so is really (-5)/13.

[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a\implies \stackrel{III~Quadrant}{-12=a} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(\theta )\implies \cfrac{sin(\theta )}{cos(\theta )}\implies \cfrac{~~-\frac{5}{13}~~}{-\frac{12}{13}}\implies -\cfrac{5}{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\times -\cfrac{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{12}\implies \cfrac{5}{12} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(\pi +\theta )=\cfrac{tan(\pi )+tan(\theta )}{1-tan(\pi )tan(\theta )}\implies tan(\pi +\theta )=\cfrac{0+\frac{5}{12}}{1-0\left( \frac{5}{12} \right)} \\\\\\ tan(\pi +\theta )=\cfrac{~~\frac{5}{12}~~}{1}\implies tan(\pi +\theta )=\cfrac{5}{12}[/tex]

The value is 5/12.

To find the value of tan(π + θ) given that θ terminates in Quadrant III and sinθ = -5/13, we need to first note that in the third quadrant, both sine and tangent are negative. Since we already have the value for sine, we can use the Pythagorean identity to find the value for cosine. The identity is sin^2θ + cos^2θ = 1.

Starting with sinθ = -5/13, we square both sides to get sin^2θ = 25/169. Then, we use the Pythagorean identity to solve for cos^2θ which gives us cos^2θ = 1 - 25/169 = 144/169. Taking the positive and negative square root, since cosine is also negative in the third quadrant, we choose the negative root, cosθ = -12/13.

Now, tanθ is the ratio of sine to cosine, which is tanθ = sinθ/cosθ = (-5/13) / (-12/13). This simplifies to tanθ = 5/12. However, the question asks for tan(π + θ), not tanθ. The tangent function has a period of π, so tan(π + θ) = tanθ. Therefore, the answer is 5/12.

Answer:

E[X] is larger than  E[Y]

E[X]  = 39.283784  and E[Y] = 37

Step-by-step explanation:

Given data

total students = 148

bus 1 students = 40

bus 2 students = 33

bus 3 students = 25

bus 4 students = 50

to find out

E[X] and E[Y]

solution

we know bus have total 148 students and 4 bus

so E[X] is larger than  E[Y] because maximum no of students are likely to chosen to bus and probability of bus is 1/4  as chosen students

and probability  of 40 i.e. P(40)  students = 40/148

P(33) = 33/148

P(25) = 25 / 148

P(50) = 50 / 148

first we find out i.e

E[X]  = 40 P(40) + 33 P(33)+  25 P(25)+  50 P(50)

E[X]  = 40  (40/148) + 33 (33/148)+  25 (25/148)+  50 (50/148)

E[X]  = 39.283784

and

y is bus chosen

E[Y] = 1/4 (40+ 33 + 25 + 50)

so E[Y] = 1/4 (40+ 33 + 25 + 50)

E[Y] = 1/4 (148)

E[Y] = 37

so E[X]  = 39.283784  and E[Y] = 37

The values of E[X] and E[Y] can be calculated by finding the sum of the product of each bus's student count and their respective probabilities. E[X] is expected to be less than E[Y] because students are chosen from each bus inversely proportional to the bus's total students, while for Y, each bus has equal probability of being chosen.

The problem describes an expectation value calculation in the context of probability for two random variables X and Y. X represents a randomly selected student from 148 students who arrived at a stadium in 4 different buses and Y represents a randomly selected bus from the 4 buses and its number of students.

Let's calculate the expected value for X (E[X]) and Y (E[Y]). The expected value of a random variable is computed as a weighted average of the possible outcomes, where each outcome is weighted by its probability. The formula is E(X) = µ = Σ xP(x). Therefore, we need to find the number of students on each bus and their respective probabilities.

For bus 1, we have 40 students, for bus 2, we have 33 students, for bus 3, we have 25 students, and for bus 4, we have 50 students. These numbers represent the possible outcomes for both random variables X and Y. Now, we need to find their respective probabilities, which are determined by the number of students in each bus divided by the total number of students (148).

For X or E[X], the probability of any student being chosen is inversely proportional to the number of students in each bus (since the student is being randomly chosen), while for Y or E[Y], the probability of any bus being chosen is the same (since the bus is being randomly chosen). Therefore, we can expect E[X] to be less than E[Y], as the probability distribution for Y is more weighted towards buses with more students.

To calculate E[Y] and E[X], we follow the expected value formula and multiply each outcome (each bus's number of students) by its probability for both X and Y. So, E[X] is summation over { 40 * ( 40 / 148), 33 * ( 33 / 148), 25 * ( 25 / 148), 50 * ( 50 / 148) } and E[Y] is summation over { 40 * ( 1 / 4), 33 * ( 1 / 4), 25 * ( 1 / 4), 50 * ( 1 / 4) } respectively.

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Answer:

The second, third and fourth are parallel to the given equation

Step-by-step explanation:

In order to determine if the slopes are the same, put all of the equations in slope-intercept form:  y = mx + b.  In order for lines in this form to be parallel, the m values of each have to be the exact same number, in our case, 4.  Equation 2 has a 4 in the m position, just like the given, so that one is easy.  Equation 2 is parallel.

Let's solve the third equation for y:

12x - 3y = 6 so

-3y = -12x + 6 and

y = 4x - 2.  Equation 3 is parallel since there is a 4 in the m position.

Let's solve the fourth equation for y:

-20x + 5y = 45 so

5y = 20x + 45 and

y = 4x + 9.  Equation 4 is also parallel since there is a 4 in the m position.

Answer:

The area is equal to [tex]8\ units^{2}[/tex]

Step-by-step explanation:

we have

A(0, 0), B(2, -2), C(0, -4), D(-2, -2)

Plot the figure

The figure is a square (remember that a regular polygon has equal sides and equal internal angles)

see the attached figure

The area of the square is

[tex]A=AB^{2}[/tex]

Find the distance AB

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the values

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

[tex]AB=\sqrt{(-2)^{2}+(2)^{2}}[/tex]

[tex]AB=\sqrt{8}[/tex]

[tex]AB=2\sqrt{2}\ units[/tex]

Find the area of the square

[tex]A=(2\sqrt{2})^{2}[/tex]

[tex]A=8\ units^{2}[/tex]

Answer:

so, I believe D and E, are Binomials.

Step-by-step explanation:

Bi- is 2

Mono- is 1

Hope my answer has helped you and if not i'm sorry.

Find the common ratio between each number given:

8/4 = 2

16/8 = 2

32/16 = 2

The common ratio is constant at 2, which means the next number would be 32 x 2.

A geometric series equation is written as an = a1r^n-1

Where a1 is the first term, r is the ratio and n is the term you want to find.

r was determined to be 2. The first term is given as 4 ( the first number in the series).

This means the equation becomes an = 4(2)^n-1

The answer would be B.

Answer:

The answer is B

Step-by-step explanation:

Answer:

  60 inches

Step-by-step explanation:

Put the given numbers in the formula and solve for the remaining unknown.

  P = 2L +2W

  18 ft = 2L +2×(4 ft)

  10 ft = 2L . . . . . . . . . subtract 8 ft

  5 ft = L . . . . . . . . . . . divide by 2

You want this in inches, so you make use of the fact that each foot is 12 inches.

  5 ft = 5×(12 in) = 60 in

The length of Sarah's fenced yard is 60 inches.

Answer:

60 IN

Step-by-step explanation:

DID THE QUIZ AND GOT IT CORRECT

Answer:

30°

Step-by-step explanation:

The measure of the arc is the same as the measure of the central angle that intercepts it, hence

m AC = ∠BAC = 30°

Answer:  The measure of arc BC is 30°

Step-by-step explanation:

It is important to remember that, by definition:

[tex]Central\ angle = Intercepted\ arc[/tex]

Therefore, in this case, knowing that the angle BAC (which is the central angle) in the circle provided measures 30 degrees, you can conclude that the measure of arc BC (which is the intercepted arc) is 30 degrees.

Then you get that the answer is:

[tex]BAC=BC[/tex]

[tex]BC=30\°[/tex]

Answer:

Ostrich can run in 5 second = 105 meter .

Step-by-step explanation:

Given  : The double number line shows that in 3 seconds an ostrich can run 63 meters .

To find : Based on the ratio shown in the double number line how far can the ostrich run in 5 seconds.

Solution : We have given

ostrich can run in 3 second = 63 meter .

Let ostrich can run in 5 second = x meter .

By the Ratio : 63 : 3 :: x : 5

[tex]\frac{63}{3} =\frac{x}{5}[/tex]

On cross multiplication

63 * 5 = 3 * x

315 = 3 x

On dividing both sides by 3

x = 105 meter .

Therefore, ostrich can run in 5 second = 105 meter .

[tex]\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_5&10\\ s_6&10r\\ s_7&10rr\\ s_8&10rrr\\ &10r^3 \end{array}\qquad \qquad \stackrel{s_8}{80}=10r^3\implies \cfrac{80}{10}=r^3\implies 8=r^3 \\\\\\ \sqrt[3]{8}=r\implies \boxed{2=r} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=8\\ s_8=80\\ r=2 \end{cases}\implies 80=s_1(2)^{8-1} \\\\\\ 80=s_1(2)^7\implies \cfrac{80}{2^7}=s_1\implies \cfrac{80}{128}=s_1\implies \boxed{\cfrac{5}{8}=s_1}[/tex]

Answer:

The probability that the sample will contain exactly three​ successes is 0.2668.

Step-by-step explanation:

Given information:

Sample size = 10

Probability of a success, p=0.30

Probability of a failure q=1-p = 1-0.30 = 0.70

The binomial formula to determine the probability is

[tex]P(X=r)=^nC_rp^rq^{n-r}[/tex]

where, n is the sample size, r is required number of success, p is probability of success and q is probability of failure.

We need to find the probability that the sample will contain exactly three​ successes.

[tex]P(X=3)=^{10}C_3(0.30)^3(0.70)^{10-3}[/tex]

[tex]P(X=3)=^{10}C_3(0.30)^3(0.70)^{7}[/tex]

[tex]P(X=3)=(120)(0.0022235661)[/tex]

[tex]P(X=3)=0.266827932[/tex]

[tex]P(X=3)\approx 0.2668[/tex]

Therefore the probability that the sample will contain exactly three​ successes is 0.2668.

Using the binomial distribution, it is found that there is a 0.2668 = 26.68% probability that the sample will contain exactly three​ successes.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that the sample will contain exactly three​ successes is P(X = 3), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = x) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.2668[/tex]

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Answer:

B: between 1 and 2

Step-by-step explanation:

Since you share 5 kg amongst 4 you need to divide it by 4.

5 / 4 = 1.25 kg

This is between 1 and 2 kg

Answer: B. Between 1 and 2 kilograms.

Step-by-step explanation: Divide the amount of coffee by the number of people.

5/4=1.25.

Each person will get 1.25 kilograms of coffee, which is between 1 and 2 kilograms.