At a certain high school, the Prom Committee is going to choose new members. There are 10 students from the Junior class and 3 students from the Senior
class who are willing to be new members. In how many ways can 7 new members be chosen if 2 or fewer must be from the Senior class?
The number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is; 705 ways
How to solve permutation and combination?The formula for probability combination is;
nCr = n!/(r! * (n – r)!)
where;
n is the total number of items.
r is the number of things that may be selected at one time.
The number of ways that 2 students can be selected from the senior class is;
N(2 students from the SR class) = 3C2 * 10C2 = 135 ways
Similarly;
N(1 student from the SR class) = 3C1 * 10C3 = 360
N(0 students from the SR class) = 3C0 * 10C4 = 210
Thus, number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is;
135 + 360 + 210 = 705 ways
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HELP PLEASE!
The answer choices are
A) 240
B) 270
C) 210
D) 120
If the rotation is clockwise the angle is 120°.
If the rotation is counterclockwise the angle is 240°
The correct options are A and D.
What is the angle of rotation that maps P to G?
We assume that the rotation is clockwise.
First, we can see that the rotation from P to F is just a rotation of 90°.
(point P as at 9 on a clock and point F is at 12 on a clock).
To go from point F to G, we need to move one of the sections defined by the dashed lines, and we know that each one of these measures 30°, then we need to add another 30° to the angle.
90° + 30° = 120°
Then the angle of rotation to map P to G is 120°.
The correct option is D.
Then if the rotation is counterclockwise, the rotation will be of 240°.
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Solve for x.
412≤1.2x
Responses
x≥334
x is greater than or equal to 3 and 3 over 4
x≤334
x is less than or equal to 3 and 3 over 4
x≥525
x is greater than or equal to 5 and 2 over 5
x≤525
The solution for x in the inequality is x ≥ 343
How to determine the solution for x?From the question, we have the following inequality expression that can be used in our computation:
412≤1.2x
Divide both sides of the inequality by 1.2
So, we have
412/1.2 ≤ 1.2x/1.2
Evaluate the quotients
343 ≤ x
Rewrite the expression as
x ≥ 343
Hence, the solution is x ≥ 343
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Find the average rate of change from x=4 to x=14
The average rate of change is given by -2/5. The correct option is (d).
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The given graph shows different values of y at x = 4 and x = 14 as follows,
At x = 4, y = 7
And at x = 14, y = 3.
Now, the average rate of change can be determined by taking the ratio of the difference of the values of y to that of x as follows,
(3 - 7)/(14 - 4)
= -4/10
= -2/5
Hence, the average rate of change x = 4 to x = 14 is given as -2/5.
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Determine the domain of the rational function ƒ(a) = 3/a+5
Answer:
domain { a ∈ R , a ≠ - 5 }
Step-by-step explanation:
the denominator of f(a) cannot equal zero as this would make f(a) undefined. Equating the denominator to zero and solving gives the value that a cannot be.
a + 5 = 0 ( subtract 5 from both sides )
a = - 5 ← excluded value
domain { a ∈ R, a ≠ - 5 }
Last month the price of one pound of carrot was $2 1/5 and joe sold 12 1/12
Answer:[tex]26\frac{7}{12}[/tex]
Step-by-step explanation:
2 1/5 * 12 1/2 = 319/12
319/12 = [tex]26\frac{7}{12}[/tex]
If 9 cows can fit in a field, how many fields are necessary to make sure 65 cows are all in a field?
fields
Answer: 8 fields are needed
Step-by-step explanation:
65 ÷ 9 = 7.222
You can't have a partial field, so you round up to find the number of fields for all 65 cows.
8 fields will fit 65 cows
Answer: 8
Step-by-step explanation:
you divide 65 by 9 but you cant have 7.222 cows so its 8
A carpenter states that it will take 21.5 hours
to build the deck. If the carpenter charges
$24.00 per hour, how much will the carpenter
be paid?
F
$45.50
G
$129.00
H
$504.00
J $516.00
Answer:
The carpenter will be paid $516.00
Step-by-step explanation:
1. Multiply
(Since the carpenter is being paid per hour, and the pay is $24.00, and the time it takes to work is 21.5, we can set up this equation):
21.5 x 24.00 = $516.00
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Kathryn invests $1000 in one account and $2200 in an account paying 3 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest?
She invested $1000 at 2% and 2200 at 5% simple interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P₁ = 1000, P₂ = 2200, assuming r₁ = x% and r₂ = (x + 3)% and the sum of simple interest obtained from both these investments is $130.
∴ (1000×x×1)/100 + {(2200×(x + 3)×1}/100 = 130.
10x + 22x + 66 = 130.
32x = 64.
x = 2.
So, the rate of interest is 2% and 5%.
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Which statement best describes the functions represented in the graphs?
A.Both functions are continuous and linear.
B.Only function p is continuous and linear.
C.Both functions are discrete and exponential.
D.Only function a is discrete and exponential.
The statement that best describes the functions represented in the graphs is B. Only function p is continuous and linear.
What is a linear function?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
How to know continuous function?A function at a place can only be continuous if it is defined there, has a limit there, and its value at that point is equal to the value of the limit there.
The graph of function p is linear and continuous
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A student bikes 5000 m East to school in 30.0 min (1800 seconds), realizes he forgot his calculator for physics, spends 30.0 min (1800 seconds) going back going home, and then races back to school in 27.0 minutes (1620 seconds).
What is the student’s total distance traveled?
_______ meters
The number of seconds it took the student to travel back and forth is ________
seconds.
Determine the student’s average speed. ________
m/s
The total distance covered is 15000 m. The total time taken is 5220 seconds and the speed is 2.87 m/s.
What is the speed?We know that speed has to do with the ratio of the distance that has been covered to the time taken. The speed is a scalar quantity and as such we do not consider the direction hence we would not consider that going back in the opposite direction. The total distance can be obtained algebraically.
The total distance that the student travelled can be obtained from;
5000 m + 5000 m + 5000 m
= 15000 m
The total time taken in seconds = 1800 seconds + 1800 seconds + 1620 seconds
= 5220 second
Speed = Distance/ Time
= 15000 m/5220 second
= 2.87 m/s
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Suppose a mutual fund has total assets of $25,500,000 and liabilities of $2,100,000. Currently there are 10,200,000 shares outstanding. Determine the net asset value of the fund? Round to the nearest cent. Show your work
The net asset value of the given mutual fund will be 2.29.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
Multiplication = to multiply any two or more numbers or variables called multiplication.
As per the given,
Total assets = $25,500,000
Liabilities = $2,100,000
Total shares = 10,200,000
Net asset = (total assets - total liability)/total shares outstanding
Net assets = (25,500,000 - 2,100,000)/10,200,000
Net assets = 2.29
Hence "The net asset value of the given mutual fund will be 2.29".
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What is an equation of the line that passes through the points (4, 4) and (8, 5)?
Answer:
y=0.25x+3
Step-by-step explanation:
use desmos graphing calculator and put the coordinates into a table
Sydney owes her mother $5 and her brother owes her mother $7.Graph the integers that represents the amount they owe their mother as negative integer on a number line.How much more will her brother have to reap their than Sydney ?
Answer:
Sydney will have to pay -5, and her brother will have to pay -7. Her brother will have to pay $2 more than Sydney.
Step-by-step explanation:
Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 17 centimeters and a height of 13 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
3,203 cm2
2,295 cm2
1,020 cm2
731 cm2
Answer:
283 cm^2
Step-by-step explanation:
hi your welcome
Answer:
Step-by-step explanation:
radius = r = 17
height = h = 13
First calculate the total surface area =
2πr (r + h)
2 (3.14) 17 (17 + 13)
2 (3.14) 17 (30)
6.28 (17)(30)
106.76 (30)
3202.80 cm²
Then subtract the area of the bottom base of the cake:
Base of the cake is the area of the round base
π r² = 3.14 (17)²
3.14 (289) = 907.46 cm²
Subtract area of base from total surface area:
I am rounding:
3203 - 908 = 2295 cm²
Second option or B
Chris bought a guitar for $77.00 and sold it for $126.28. What percent profit did Chris make on the guitar
Answer:
ten is the fight one
Step-by-step explanation:
True
Answer:
39%
Step-by-step explanation:
126.28 minus 77 is 49.28.
49.28 divided by 126.28 is 0.39 and a bunch of other numbers but round it up and its 0.39. move the decimal to the right two places and youve got 39%
hope this helped!
5. Find the volumes of the following sugar containers. Round to
Domino 1 decimal place.
SUGAR
a. Domino granulated sugar in canister: radius-1.56 inches;
height-6.93 inches
in³
b. Domino sugar cubes in box: length-15.5 cm; width-8.6 cm;
height-3.8 cm.
Domino
SUGAR CUBES
cm³
The volume of the canister is 36.7 in³. The volume of box is 482.6 cm³
To find the volume of a canister, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, the canister has a radius of 1.56 inches and a height of 6.93 inches,
volume of canister = π × (1.56 inches)² × 6.93 inches
volume of canister = 36.7 in³
To find the volume of a box, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
In this case, the box has a length of 15.5 cm, a width of 8.6 cm, and a height of 3.8 cm
volume of box = 15.5 cm × 8.6 cm × 3.8 cm
volume of box = 482.6 cm³
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please help with this
Answer: There are multiple answers.
Step-by-step explanation: To find x...simply ad together what you have (The numbers given) and subtract from 180.
(I did this a while ago, don't take my word for it)
A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 10 hours. The company has only 1000 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day.
(a) Write the inequalities that describe the constraints on the number of each type of hedge trimmer produced. (Let x represent the number of cord-type models, and let y represent the number of cordless models.)
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
The inequalities that describe the constraints on the number of each type of hedge trimmer produced are:
x + y ≤ 200
2x + 10y ≤ 1000
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Total number of hours = 1000
Total number of trimmers = 200
Let x represent the number of cord-type models,
Let y represent the number of cordless models.
Now,
x + y ≤ 200
2x + 10y ≤ 1000
Thus,
The inequalities that describe the constraints on the number of each type of hedge trimmer produced are:
x + y ≤ 200
2x + 10y ≤ 1000
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Find X and RDB
X= ______
RDB=______
Using the secant-secant theorem,
[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]
The measure of the angle ∠RDB will be 45°.
What is the angle of the chord?In geometry, a chord of a circle is a straight line segment whose endpoints both lie on the circle. A diameter of a circle is the longest chord, and it passes through the centre of the circle.
Calculate the value of x as below,
( 13x + 7 - 60 ) / 2 = 5x - 10
13x - 53 = 10x - 20
3x - 53 = -20
3x = 33
x = 11
The measure of the angle ∠RDB is,
∠RDB = 5x - 10
∠RDB = ( 5 x 11 ) - 10
∠RDB = 45°
Therefore, the value of an angle ∠RDB will be 45°.
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Having difficulty with this
For the function y = 4x⁵, the value of d⁴y/dx⁴ = 320x.
What is a expression? What is a mathematical equation? What is Equation Modelling? What is differentiation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. We can write -
y = f(x)
y' = dy/dx = (d/dx)[f(x)]
We have the following function -
y = 4x⁵
The given function is -
y = 4x⁵
dy/dx = 20x⁴ {y = xⁿ, then y' = nxⁿ ⁻ ¹}
d²y/dx² = 80x³
d³y/dx³ = 160x²
d⁴y/dx⁴ = 320x
Therefore, for the function y = 4x⁵, the value of d⁴y/dx⁴ = 320x.
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help meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeee
Answer: 23.1, 13.35718336 years or 14 rounded
Step-by-step explanation:
[tex]Given:A= 23.1e^{0.0152t}[/tex]
when A = end amount, and t = years after 2000
Part A).
What was the population of the state in 2000. According to our function, this would be when t = 0
[tex]23.1e^{0.0152(0)}\\\\=23.1(1)\\\\=\boxed{23.1}[/tex]
Part B).
When will the population of the state reach 28.3 million?
This would be when A = 28.3
[tex]28.3=23.1e^{0.0152t}\\\\\frac{28.3}{23.1} =\frac{23.1e^{0.0152t}}{23.1} \\\\\frac{28.3}{23.1} =e^{0.0152t}\\\\ln^{\frac{28.3}{23.1} }=ln^{e^{0.0152t}}\\\\ln^{\frac{28.3}{23.1} }=0.0152t\\\\t=\frac{ln^{\frac{28.3}{23.1} }}{0.0152} \\\\\boxed{t=13.35718336 \ \ years}[/tex]
Use the graph below to fill in the blank with the correct number:
f(2)=
Answer:
1
Step-by-step explanation:
[tex]f(2)[/tex] is equal to the [tex]y[/tex] coordinate of the point on the graph of the function with [tex]x[/tex] coordinate 2.
Graph stuff
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The quadratic equation y = x² - 8 · x + 18 represents the parabola shown in the figure.
How to derive the quadratic equation behind the graph of the parabola
In this problem we find a representation of a parabola, which is described algebraically by quadratic equations, that is, polynomials of the form:
y = a · x² + b · x + c
Where a, b, c are the coefficients of the polynomial.
We can determine the value of the coefficients from the knowledge of three points set on Cartesian plane. First, select the points from Cartesian plane:
(x₁, y₁) = (0, 18), (x₂, y₂) = (4, 2), (x₃, y₃) = (7, 11)
Second, create a system of linear equations with three variables and three equations by replacing the variables x and y on the quadratic equation:
c = 18
16 · a + 4 · b + c = 2
49 · a + 7 · b + c = 11
Third, solve the system by numerical methods:
(a, b, c) = (1, - 8, 18)
Fourth, write the resulting quadratic equation:
y = x² - 8 · x + 18
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isabel drove 335 miles in 5 hours at the same rate how any miles would she drive in 8 hours
Consider a political discussion group consisting of 9 Democrats, 9 Republicans, and 5 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting two Democrats.
Hence, the probability of selecting two Democrats is [tex]45[/tex].
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
The meaning of probability is basically the extent to which something is likely to happen.
Here given that,
Consider a political discussion group consisting of [tex]9[/tex] Democrats, [tex]9[/tex] Republicans, and [tex]5[/tex] Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention.
Let us assume ,
The discussion of the democratic is [tex]x_1=9[/tex].
The discussion of the democratic is [tex]x_2=9[/tex].
The discussion of the democratic is [tex]x_3=5[/tex]
So, the total number of candidates are
[tex]x_t=x_1+x_+x_3\\\\=9+9+5\\\\=23[/tex]
Probability of independate candidate from the group of candidates is
[tex]P_1=\frac{x_3}{x_t}\\\\P_1=\frac{5}{23}\\\\[/tex]
As, the remaining number of candidates after the selectio of the independent candidate is
[tex]x_r=x_t-1\\\\x_r=23-1\\\\x_r=22[/tex]
Now, the remaining number of candidates from the group of total remaining candidates is
[tex]P_2=\frac{x_1}{x_r}\\\\P_2=\frac{9}{22}[/tex]
So, the probability of an independent Democrat using the probability is
[tex]P=P_1[/tex] × [tex]P_2[/tex]
[tex]P=\frac{5}{23}[/tex] ×[tex]\frac{9}{22}[/tex]
[tex]P=\frac{110(207)}{506}\\\\P=\frac{22770}{506}\\\\P=45[/tex]
Hence, the probability of selecting two Democrats is [tex]45[/tex].
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select independent or not independent for each situation
Answer: the first one
Step-by-step explanation:
3F furniture dealer has always sold its merchandise through 4 company-operated
stores. Last year sales were birr 1million and net profit was 8% of sales. Fixed
costs were birr 170,000. As a result of shifting population and increased
competition, the four locations have become less desirable. 3F is considering
eliminating its retail stores in favor of door-to-door selling. It is estimated that
sales would increase by 25% and net profit by birr 30,000. Fixed costs would
increase by birr 30,000 because operations would be moved to a low-rent
warehouse. Required
a) What was the break-even point under the old situation?
b) What will be the break-even point under the proposed situation?
c) What birr sales volume must be obtained under the proposed plan to make as
much profit as last year?
The break-even point under the old situation is 680000, the break-even point under the proposed situation is 806451 and the birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.
Define breakeven point.In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even." Although opportunity costs have been paid and capital has obtained the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."
In the given question, last year sales= birr 100000
net profit= 8% of sales
Fixed costs= birr 170000
Estimated sales increase= 25%
Estimated net profit= birr 30000
Increase in fixed cost due to moving to low-rent warehouse= birr 30000
(a) The break-even point under the old situation (X):
= 100,000 * a - 170,000
=1,000,000 * 8%
a= 25% (net profit)
X*a= 1170,000
X=680,000
That is, the break-even point under the old situation is 680000.
(b) The break-even point under the proposed situation is:
= 1,250,000 x b - 170,000- 30,000
= 80,000 + 30,000
b= 24.8%
X*b=200,00
X=806451
The break-even point under the proposed situation is 806451 and
(c) The birr sales volume must be obtained under the proposed plan to make as much profit as last year is:
X*b -200,000= 80,000
X*b = 280,00
X= 1,129,032
The birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.
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Find the sum of the arithmetic sequence 1, 3, 5, 7, … , 99.
The sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given sequence is 1, 3, 5, 7, … , 99.
It is a arithmetic sequence, the difference between two consecutive terms will be same
d=3-1=2
first term a=1
l=last term =99
We need to find 99 is which term in the sequence
Aₙ = a + ( n - 1 ) d
99=1+(n-1)2
99=1+2n-2
99=2n-1
100=2n
Divide both sides by 2
50=n
Now we need to find the sum of 50 terms
Sₙ=n/2(l+d)
=50/2(99+2)
=25(101)
=2525
Hence, the sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525
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C. Solve the following;
1. Elisse has 20 meters of ribbon. How many 15 cm of ribbon can be cut from it?
2. Mr. JB has a rectangular lot that measures 550 meters by 0.75 km. What is the area of the land in square meter. He is selling the whole lot for 206, 250,000 pesos, how much is the price per square meter?
3. Drinking 8 glasses of water a day is good for your health. If each glass of water is equivalent to 148 mL, how many liters of water you need to consume everyday.
4. Your baby brother has a body temperature of 100°F. What is his body temperature in °C ? Does he has a normal body temperature?
5. Your mother asked you to buy 2.5kg of sugar. Each pack of sugar in the store weighs 250 grams. How many packs of sugar will you buy?
6. The 120 grams powdered milk make 12 cups of milk. How many kilograms of powdered milk can produce 60 cups of milk. How many liters is 60 cups of milk?
7. You have 8 modules to study in a day. Your teacher gave you this schedule for 5 days from Monday to Friday.
Answer:
133, 412500, 500, 1.184, 37.8, 10, 0.6
Step-by-step explanation:
If we think about how many centimeters are in a meter, we know that
1m = 100cm
Using this, we can see that
20m = 2000cm
Now divide by 15:
2000 ÷ 15 ≈ 133
She can make roughly about 133 ribbons.
To solve the next question, we need to know how many kilometers are in a meter
1km = 0.001m
Let's covert 0.75 into m:
0.75 × 1000 = 750
Now solve for the area:
750 × 550 = 412500
The area of the rectangle is 412500
If he is selling the home for 206,250,000 pesos,
206,250,000 divided by 412500
206,250,000 ÷ 412500 = 500
The price per square meter is 500
If each glass is 148 milliliters, and we need to convert that into liters, we can use the equation:
1L = 1000mL
So converting 148 into liters,
148mL = 0.148L
Now, multiply by 8.
0.148 × 8 = 1.184L
We need to convert 100 Fahrenheit to Celsius.
100 F ≈ 37.8
This is definitely not a normal body temperature.
We can convert grams to kilograms using the equation:
1kg = 1000 g
Converting 2.5kg to g would look like this:
2.5kg = 2500g
250g × 10 = 2500g
We need to buy 10 packs of sugar.
If 120 grams of powdered milk can produce 60 cups of milk, and we need to figure out how many kg can produce the same amount, we use the equation:
1kg = 1000g
Converting 120g to kg would look like this:
120 ÷ 1000 = 0.120
Now, we need to figure out how many times 12 goes into 60.
12 × 5 = 60
Now we multiply 0.120 by 5
0.120 × 5 = 0.6
I hope this helps!