Each batch of lollipops contains 37.375 kilograms of sugar.
Here, we have to represent the given information using a tape diagram, we'll draw two rectangles, each representing a batch of lollipops.
The total amount of sugar used, which is 74.75 kilograms, will be divided equally between the two batches.
Now, draw the tape diagram:
Batch 1: [----] (to be determined)
Batch 2: [----] (to be determined)
Now, we know that the total amount of sugar used is 74.75 kilograms.
We need to divide this amount equally between the two batches.
Since there are two batches, we can divide the total sugar by 2 to find the amount of sugar in each batch:
74.75 kilograms / 2 = 37.375 kilograms
So, each batch of lollipops contains 37.375 kilograms of sugar.
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1. Write the ratio in the simplest form. 16:24 (1 point) 1:2 4:3 3:4 2:3
Any ratio can be simplified into its simplest form by dividing the numerator and denominator by the common factor.
The given ratio is 16:24. To bring the ratio in its simplest form we will look for the factors of 16 and 24 and look for the greatest number that divides both 16 and 24.
The greatest number that divides both 16 and 24 is 8.
16÷8=2
24÷8=3.
The ratio 16:24 in its simplest form is 2:3
The solution for the ratio in the simplest form is, 2 : 3
Given that,
16:24 is the specified ratio.
Now, By finding the largest integer that divides both 16 and 24 and the factors of 16 and 24, we may reduce the ratio to its most basic form.
Hence, 8 splits both 16 and 24 to the maximum possible extent.
So, we get;
16 / 8 = 2
24 / 8 = 3
Thus, the simplest form of the fraction is,
⇒ 16 : 24
⇒ 16 / 24
⇒ 2 / 3
It can be written as,
⇒ 2 : 3
So, the simplest form is,
⇒ 2 : 3
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There are 16 sixth graders and 20 seventh graders in the robotics club. For the first project the club sponsor wants to organize the club members into equal size groups. Each group will have only sixth graders or only seventh graders how may students will be in each group if each group has the greatest possible numbers of club members?
Answer:
There will be 4 students in each group and there will be 9 groups.
Step-by-step explanation:
There are 16 sixth graders and 20 seventh graders in the robotics club.
As we have to find the number of students that will be in each group if each group has the greatest possible numbers of club members, so we will find the HCF or highest common factor of 16 and 20.
16 = 2 x 2 x 2 x 2
20 = 2 x 2 x 5
HCF = 2 x 2 = 4
So, 16 sixth graders will be divided in [tex]\frac{16}{4}=4[/tex] groups
20 seventh graders will be in [tex]\frac{20}{4}=5[/tex] groups
total groups = [tex]4+5=9[/tex]
Hence, total there will be 9 groups with 4 students in each group.
Which of these graphs represents a function?
A)
B)
C)
D)
Someone please help me!
Erica's cell phone bill for July was $82. She sent a check for $50 and then made $37 worth of calls in August. How much did she owe on her cell phone bill?
Which two sets of angles are corresponding angles?
∠e and ∠h; ∠f and ∠g
∠e and ∠i; ∠f and ∠h
∠e and ∠g; ∠f and ∠h
∠e and ∠i; ∠f and ∠g
points A is 5,623m above sea level.points B is below sea level at -1,245m. what is the distance between the two points?
The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2)=
Answer:
The value of f(-2) is, -2
Step-by-step explanation:
The graph which is shown on the coordinate plane passes through the two points i.e, (2,0) and (0, -1).
First find the equation for this line:
Using Point-Slope form for the equation of line: [tex]y-y_{1}=m(x-x_{1})[/tex] ..[1]
where m is the slope given by ;
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
First find the slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-1-0}{0-2}[/tex]
⇒ [tex]m=\frac{-1}{-2} =\frac{1}{2}[/tex]
Now, substitute the value of m=[tex]\frac{1}{2}[/tex] , [tex]x_{1}[/tex]= 2and [tex]y_{1}[/tex]=0 in equation [1];
[tex]y-0=(\frac{1}{2})(x-2)[/tex] or
[tex]y=\frac{1}{2}\cdot (x-2)[/tex]
In this graph x represents the input of the process and Y the output of the process and f the function of the variable x i.e, y=f(x)
∴ [tex]y=f(x)=\frac{1}{2}(x-2)[/tex] ....[2]
now, we put the value of x=-2 inequation [2] to solve for f(-2).
[tex]f(-2)=\frac{1}{2}(-2-2) =\frac{1}{2} \cdot (-4)[/tex]
Simplify we get;
[tex]f(-2)=-2[/tex]
Add the two expressions. 8k + 4 and 3k + 8
Enter your answer in the box.
THE ANSWER IS 11K + 12
Is 22/15 less than 14/31?
Is 19/35 greater than 27/19
Is 15/25 greater than 22/44
Is 30/25 less than 29/30
Of video game that originally cost $25.99 is on sale for 50% off if you have $14 would you have enough money to buy the video game explain (estimate)
Final answer:
After calculating 50% of $25.99, which is approximately $13, we find that the estimated sale price of the video game is $13. Therefore, if the student has $14, they will have enough money to buy the discounted video game.
Explanation:
The student is asking whether $14 would be enough to purchase a video game that is on a 50% off sale from its original price of $25.99. To find the sale price, we can take 50% of the original price and subtract it from the original price itself.
First, calculate 50% of $25.99: (0.50) imes $25.99 = $12.995. Since we are estimating, round the 50% value to $13. Now, subtract that from the original price to get the sale price: $25.99 - $13 = $12.99 (rounded to $13 for easier calculation).
In this estimate, the sale price is $13, which means that if the student has $14, they would have enough money to buy the video game on sale because $14 is greater than $13. Therefore, they will have $1 left after the purchase.
The formula f=n/4+37 estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute. Use the formula to estimate the temperature when n = 18 chirps/min. Round to the nearest whole number, if necessary. 41 42 37 46
[tex]f=\dfrac{n}{4}+37\\\\\text{substitute the value of n = 18 to the expression}\\\\f=\dfrac{18}{4}+37=4.5+37=41.5\approx42[/tex]
Answer: f = 42.
By using substitution of value n, temperature F in degree Fahrenheit is 42.
What is substitution method?"The substitution method is a simple way to solve a system of linear equations algebraically and find the solutions of the variables."
Given
Formula to estimate the temperature F in degree Fahrenheit
f = [tex]\frac{n}{4} +37[/tex]
n = 18 chirps/min
Substituting n in the formula
f = [tex]\frac{n}{4} +37[/tex]
⇒ f = [tex]\frac{18}{4}+37[/tex]
⇒ f = 4.5 + 37
⇒ f = 41.5 ≅ 42 (nearest whole number)
Thus, temperature F in degree Fahrenheit is 42.
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In science class Krissy labeled 26 vertebrae bones on a diagram of an adult human Doug labeled 1 bone in the throat and 6 bones of the inner ear for both ears. Most adult humans have 206 bones. Write an equation to solve for the number of bones left in the diagram that need to be labeled
Determine the independent variable (__________,y). what word goes in the blank space??
Ogden and Sylvio are both running backs for their respective football teams. Sylvio ran for a total of 82 yards while Ogden ran for a total of -21 yards. What is the difference in the number of yards they ran?
1/3(9−6m)+1/4(12m−8)
Answer:
M+1
Step-by-step explanation:
Use the distributive property to express 16+48
Final answer:
The sum of 16 and 48 can be expressed using the distributive property by factoring out the common factor of 16, yielding 16 + 48 = 16(1 + 3).
Explanation:
The question involves using the distributive property, a concept in mathematics, to express the sum of two numbers, specifically the numbers 16 and 48. To apply the distributive property, we look for a common factor that can be factored out. In this case, the common factor of both 16 and 48 is 16. Therefore, we can express the sum as:
16 + 48 = 16(1 + 3)Here, we've factored out the number 16 that is common to both terms in the sum. The distributive property allows us to then multiply 16 by each term inside the parentheses to get back the original expression.
This is an example of how the distributive property can simplify expressions and aid in mental calculations, such as understanding that 48 can be divided evenly by 16, resulting in 3.
Eric biked 1 km 125 m on Monday. On Tuesday, he biked 375 m less than on Monday. How far did he bike both days
what is 0.6144 divided by 1.6
-9x is greater than or equal to -3(x-4)
malcolm buys a 5/6 pound bag of black beans and a 3/4 pound bag of pinto beans. how many pond of beans does malcolm buy in all
5/6 + 3/4
5/6 = 10/12
3/4 = 9/12
10/12 + 9/12 = 19/12 = 1 7/12 pounds total
Answer: the answer is 1 7/12 pounds
Step-by-step explanation:
Because 5/6+3/4=1 7/12
Mark drew two lines that form a right angle. What word describes the lines mark drew
Answer:
Perpendicular Lines
Step-by-step explanation:
perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).
4. FH bisects ∠GFI, m∠EFG = 4y + 8 and m∠HFI = 2y + 6. Find m∠EFH.
please help me solve this
Answer:
m∠EFH=134
Step-by-step explanation:
FH bisects ∠GFI
So m<GFH=m<HFI
m∠EFG = 4y + 8 and m∠HFI = 2y + 6
m<GFH=2y+6
[tex]m<EFG+m<GF+m<HFI= 180[/tex] because its a linear pair
[tex]4y+8+2y+6+2y+6=180[/tex]
combine like terms and solve for y
[tex]8y+20=180[/tex]
Subtract 20 from both sides
[tex]8y=160[/tex]
Divide both sides by 8
y=20
m∠EFH=m<EFG+m<GFH
m∠EFH=[tex]4y+8+2y+6=6y+14=6(20)+14=134[/tex]
2a + 4b = d for b
I trying to solve for b.
I don't understand how to isolate the variable.
George is saving for a mortgage on a $125,000 house. He needs 20 percent for a down payment. He currently has $22,000. How long will it take George to save the rest of the money when he earns 5 percent interest per year?
(This is an economics question)
Will it be 2years, 1year, 3years or 5years?
Answer:
3 years
Step-by-step explanation:
Which expression would the model be most helpful in solving 5/6
5/6 divided 1/6, this is the correct answer
Which set of rational numbers is arranged from least to greatest?
−3.5, negative 1 over 4, 2, 1 over 3
−3.5, negative 1 over 4, 1 over 3, 2
2, 1 over 3, negative 1 over 4, −3.5
negative 1 over 4, 1 over 3, 2, −3.5
Cherries cost $5 for 2 pounds and $7.50 for 3 pounds.
Question:
a. What is the cost per pound?
b. Is it constant?
c. If you were to graph this situation, would you put weight or cost on the x-axis? Which one would you put on the y-axis?
d. Plot the two points described.
e. How much would 5 pounds of cherries cost? What did you do to solve this problem?
Draw your answer below:
A) 5/2 = 2.50, it costs $2.50 per pound
B) yes because 7.50 / 3 = 2.50 as well
C) weight would be on x-axis and cost on the Y axis
D) draw a graph and put the dots on (2,5) and (3,7.50) and draw a straight line
E) 2.50 *5 = $12.50, multiply cost per pound by pounds.
Given that the hypotenuse of this right triangle is 25 cm long and that tan(Θ) = 3 Find the values of x and y, accurate to the nearest tenth. A) x ≈ 7.9; y ≈ 23.7 B) x ≈ 23.7; y ≈ 7.9 C) x ≈ 7.9; y ≈ 26.4 D) x ≈ 26.4; y ≈ 79.1
Answer:
Step-by-step explanation:
The right triangle above you can use SOHCAHTOA and determine that tanθ =
y
x
. Replacing tanθ with 3 you get
3 =
y
x
3x = y
Then use the Pythagorean Theorem to
x2 + y2 = 252. Replace y with 3x
x2 + 9x2 = 625
10x2 = 625
x2 =
625
10
x =
25
10
= 7.9
Since,
y = 3x
y = 3(7.9) = 23.7
x ≈ 7.9; y ≈ 23.7
One carpet cleaning cost are shown in the table. The relationship is linear. Find and interpret the rate of change and the initial value for this situation.