The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient?
Answers
There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex]. Statement A best interprets the quotient.
What is the definition of a fraction number?A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.
The shaded part in step 1 is;
[tex]\rm 4 + \frac{1}{6} = 4 \frac{1}{6}[/tex]
Divide the shaded part with the unshaded part as ;
[tex]\rm \frac{4 \frac{1}{6} }{\frac{2}{3}}\\\\ \frac{25}{6} \times \frac{3}{2} \\\\\ \frac{25}{4} \\\\ 6 \frac{1}{4}[/tex]
There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex].
Hence, statement A best interprets the quotient.
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Answer: A
Step-by-step explanation:
Related Questions
At age 45, an elephant grows teeth, each weighing 4 kg. About how many pounds do these teeth weigh? Use the conversion factor 1 kg = 2.2046 lbs. Round to the nearest tenth where necessary.
Answers
4*2.2046
8.8184 lb.
Hope this helped!
4*2.2046
Is dividing 4/5 the same as multiplying by 5 then dividing by 4?
Answers
Two bags had 100 kilograms of sugar each. After taking out 3 times as much sugar from bag one than bag two, bag one had half as much sugar left as bag two. How much sugar is left in each bag?
Answers
bag two-80
The relationship 1/sin(θ) is equivalent to which of the following trigonometric functions?
A. cot(θ)
B. csc(θ)
C. arcsin(θ)
D. sec(θ)
Answers
Answer:
Option B is the correct answer.
Step-by-step explanation:
We have the following trigonometric relations
[tex]cosec\theta =\frac{1}{sin\theta }\\\\sec\theta =\frac{1}{cos\theta }\\\\cot\theta =\frac{1}{tan\theta }\\\\cot\theta =\frac{cos\theta}{sin\theta }\\\\tan\theta =\frac{sin\theta}{cos\theta }[/tex]
Here cosec θ is the correct answer.
Option B is the correct answer.
An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?
A. C(t) = 95 for 1 < x ≤ 2
B. C(t) = 95 for 2 < x ≤ 3
C. C(t) = 120 for 2 < x ≤ 3
D. C(t) = 120 for 4 < x ≤ 5
Answers
0-1 h= $45
1-2h= $70 ($45 +1*$25)
2-3h= $95 ($45 +2*$25)
3-4h= $120 ($45 +3*$25)
Looking at the list, the answer should be
B. C(t) = 95 for 2 < x ≤ 3
Solumedrol 1.5 mg/kg is ordered for a child weighing 50 lb. Solumedrol is available as 75 mg / 1 mL is available. How many mL must the nurse administer?
Answers
y = 5x – 1
–15x – 3y = 3
How many solutions does this linear system have?
one solution: (0, –1)
one solution: (1, 4)
no solution
infinite number of solutions
Answers
-15x - 3y = 3
-15x - 3(5x - 1) = 3
-15x - 15x + 3 = 3
-30x = 3 - 3
-30x = 0
x = 0
y = 5x - 1
y = 5(0) - 1
y = -1
it has one solution (0,-1) <=
y = 5x - 1...so we sub 5x - 1 in for y in the other equation
-15x - 3y = 3
-15x - 3(5x - 1) = 3
-15x - 15x + 3 = 3
-30x = 3 - 3
-30x = 0
x = 0
y = 5x - 1
y = 5(0) - 1
y = -1
it has one solution (0,-1) <=
What is the simplified expression for –3cd – d(2c – 4) – 4d?
A:–5cd
B:cd – 8d
C:5cd – 8d
D:–5cd – 8d
Answers
= –3cd – 2cd + 4d – 4d
= -5cd
answer
A:–5cd
find the solution of
2x - 2y = -20 and -2x + 4y = 14
Answers
Given 2x - 2y = -20 and -2x + 4y = 14, add the second equation to the first:
2x - 2y = -20
-2x + 4y = 14
----------------------------------------------
2y = -6. Solving for y: y = -3.
Find x by subst. y=-3 into either of the given equations.
If we choose the first equation, then it becomes 2x - 2(-3) = -20
Solve this for x: 2x + 6 = -20, or 2x = -26, or x = -13.
The solution is (-13,-3).
To decrease an amount by 7%, what single multiplier should you use?
Answers
An ice cream company made a profit of $24,000 in 2011. The same company had a loss of $11,000 in 2012. What is the difference between the company's financial results for 2011 and 2012
Answers
The required difference in the financial result is $13000.
given that,
An ice cream company made a profit of $24,000 in 2011. The same company had a loss of $11,000 in 2012. What is the difference between the company's financial results for 2011 and 2012 is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
In the year 2011, an ice cream company made a profit of $24,000
in the year 2012, the same company had a loss of $11,000.
Difference in the result = 24000 - 11000 = $13,000
Thus, the required difference in the financial result is $13000.
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You own a house cleaning business. It takes you 2hours and 45 minutes to clean a house. You have 3 houses to clean tomorrow, how long would it take you to clean all three houses?
Answers
a grading machine can grade 48 tests in 1 minute. How
long will it take the machine to grade 300 tests?
Answers
i need help with 1 and 2
Answers
2) No, according to the commutative property of addition, it does not matter the order they are put in.
Hope this helps!
-40 + -110
-50 + -100
2: no the order does not matter because of the commutative property that says you can add in any order and it can be the same
A recursive arithmetic sequence is defined ad f(1)=6, f(n+1)=f(n)+5 for n>1. The first four terms of the sequence are shown in the table. Write an explicit formula that represents the sequence using function notation. Find the slope of the line that passes through the points given in the table. The slope is
Answers
f₁ = 6
f₂ = f₁ + 5 = 11
f₃ = f₂ + 5 = 16
f₄ = f₃ + 5 = 21
and so on
The sequence is
6, 11, 16, 21, ...,
This is an arithmetic sequence with a common difference of 5.
In function notation, the sequence is
[tex]f_{n+1} = 6 + 5n, \\ \, n=0,1,2, \, ...,[/tex]
This represents the equation of a straight line with n as the independent variable and f as the dependent variable.
The slope is 5.
A graph of the line is shown below.
Answer:
The sequence is [tex]f_{n+1} = 6 + 5n, \,\, n=0,1,2, \, ...,[/tex]
The slope is 5.
Answer:
Find the slope of the line that passes through the points given in the table. The slope is
✔ 5
.
Use one of the given points to find the y-intercept. Substitute values for x, y, and m into the equation y = mx + b and solve for b. The y-intercept is
✔ 1
.
Write the formula as a function of n in slope-intercept form. The function is
✔ f(n) = 5n+ 1
for n in the set of natural numbers.
Ryan runs 9 miles in 73 minutes. How many minutes does he take per mile?
Answers
So he takes 8 1/9 or 8 and around 7 minutes per mile.
The GCF of two different numbers is greater than the LCM of the numbers
Answers
Draw one card at random from a standard deck of cards. the sample space s is the collection of the 52 cards. assume that the probability set function assigns 1/52 to each of the 52 outcomes. let a = {x: x is a jack, queen, or king}, b = {x: x is a 9, 10, or jack and x is red}, c = {x: x is a club}, d = {x: x is a diamond, a heart, or a spade}.
Answers
Any face or number cards is 4/52, because there are 4 cards for each symbol. On the other hand, each symbol like heart, diamond, club or spade would each have a probability of 13/52 (counting numbers 2 to 10, Ace card, and the 3 face cards). Also, there are 26 each of red and black cards. Furthermore, the words 'or' and 'and' are hint words. When you see 'or', you have to add their individual probabilities. If you see the word 'and', you'll have to multiply them. With that said, the solution is as follows:
a.) P = 4/52 + 4/52 + 4/52 = 3/13
b.) P = (13/52 + 13/52 + 4/52)(26/52) = 15/52
c.) P = 13/52
d.) P = 13/52 + 13/52 + 13/52 = 3/4
We have P(A) = 3/13, P(A ∩ B) = 3/52, P(A ∪ B) = 17/52, P(C ∪ D) = 1, and P(C ∩ D) = 0.
(a) To find P(A), we first determine the number of outcomes in A, which consists of 12 cards (4 jacks, 4 queens, and 4 kings).
Since there are 52 cards in total, P(A) = 12/52 = 3/13.
(b) For P(A ∩ B), we look for the cards that are both in A and B.
There are 3 such cards (jack of hearts, jack of diamonds, and jack of hearts).
So, P(A ∩ B) = 3/52.
(c) To find P(A ∪ B), we combine the outcomes in sets A and B, but we avoid double-counting the jacks.
So, A ∪ B consists of 12 cards from A and 5 cards from B, totaling 17 cards.
Hence, P(A ∪ B) = 17/52.
(d) P(C ∪ D) includes all cards that are clubs, diamonds, hearts, or spades.
Since all cards fall into these categories, P(C ∪ D) = 1.
(e) P(C ∩ D) represents the probability of drawing a card that is both a club and either a diamond, heart, or spade.
Since clubs do not intersect with these suits, P(C ∩ D) = 0.
Complete Question:
Draw one card at random from a standard deck of cards. The sample space S is the collection of the 52 cards. Assume that the probability set function assigns 1/52 to each of the 52 outcomes.
Let
A = {x: x is a jack, queen, or king},
B = {x: x is a 9, 10, or jack and x is red},
C = {x: x is a club},
D = {x: x is a diamond, a heart, or a spade}.
Find (a) P(A), (b) P(A ∩ B), (c) P(A ∪ B), (d) P(C ∪ D), and (e) P(C ∩ D).
B. if lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6, how many of each would lucinda buy if she were rational? 0 kewpie dolls and 3 beanie babies 3 kewpie dolls and 0 beanie babies 2 kewpie dolls and 1 beanie baby 1 kewpie doll and 2 beanie babies
Answers
[tex]\begin{tabular} {|p {2cm}|p {2cm}|p {2cm}|p {2cm}|} \multicolumn {4} {|c|} {Lucinda's Kewpie Doll and Beanie Baby Marginal Benefits}\\[1ex] \multicolumn {2} {|c|} {Kewpie Dolls}&\multicolumn {2} {|c|} {Beanie Babies}\\[1ex] 1&\$15.00&1&\$12.00\\ 2&\$12.00&2&\$10.00\\ 3&\$9.00&3&\$8.00\\ 4&\$6.00&4&\$6.00\\ 5&\$3.00&5&\$4.00\\ 6&\$0.00&6&\$2.00\\ \end{tabular}[/tex]
If lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6,
Lucinda will buy the combination for which marginal benefit is the same.
Therefore, Lucinda will buy 2 kewpie dolls and 1 beanie baby, if she were rational.
Lucinda can rationally choose to buy 0 Kewpie dolls and 3 Beanie Babies, 3 Kewpie dolls and 0 Beanie Babies, 2 Kewpie dolls and 1 Beanie Baby, or 1 Kewpie doll and 2 Beanie Babies, as all combinations fit within her $18 budget. The prices for each are $6.
In order to determine how many Kewpie dolls and Beanie Babies Lucinda can buy, we need to explore her budget constraint. Lucinda has $18 to spend, and the prices of both Kewpie dolls and Beanie Babies are $6 each. We can calculate the maximum possible combinations of each that fit within her budget.
If Lucinda buys 0 Kewpie dolls and 3 Beanie Babies, she spends $0 + $18 = $18.If Lucinda buys 3 Kewpie dolls and 0 Beanie Babies, she spends $18 + $0 = $18.If Lucinda buys 2 Kewpie dolls and 1 Beanie Baby, she spends $12 + $6 = $18.If Lucinda buys 1 Kewpie doll and 2 Beanie Babies, she spends $6 + $12 = $18.All these combinations maximize her budget, so any of these options could be rational depending on her preference. Therefore, Lucinda could rationally choose to buy any of the following combinations: 0 Kewpie dolls and 3 Beanie Babies, 3 Kewpie dolls and 0 Beanie Babies, 2 Kewpie dolls and 1 Beanie Baby, or 1 Kewpie doll and 2 Beanie Babies.
I have 7 hundreds blocks, 5 tens blocks, and 8 ones blocks. I use my blocks to model two 3-digit numbers. What could my two numbers be?
Answers
5 tens blocks = 50
8 ones blocks = 8
---------------------------------------- add them
700 + 50 + 8 = 758
f(x) = 3x + 10x and g(x) = 4x – 2, find (f – g)(x)
Answers
1meter =1x10^9 in sicentific notation
Answers
What is 3/8 written as a decimal
Answers
Which set of ordered pairs could be generated by an exponential function?
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
Answers
Answer:
THE ANSWER IS D
Step-by-step explanation:
THE ANSWER IS D because if you square 3 you get 9, if you cube 3, you get 27
Answer: (0, 1), (1, 3), (2, 9), (3, 27)
Step-by-step explanation:
walt is mixing fruit punch for the party. he combines 1 gallon 2 quarts 3 pints of orange juice , 1 gallon 3 quarts 7 pints of pineapple juice, and 1 gallon 3 quarts 3 pints of ginger ale. what is the total liquid measure of the punch ?
Answers
3 gallon 8 quarts 13 pints or
6 gallon 2 quarts 1 pints
In this question, there are orange juice, pineapple juice, and ginger ale mixed to make the fruit punch. All the juice is using gallon, quarts and pints unit for their volume. Since the unit is already same, you just need to add them first then convert it into the bigger unit. The first calculation would be:
1 gallon 2 quarts 3 pints +
1 gallon 3 quarts 7 pints +
1 gallon 3 quarts 3 pints =
3 gallon 8 quarts 13 pints
If you need to change the volume unit into the biggest unit(gallon) then we need to start from changing pints into quarts. A quarts equal 2 pints, then the calculation would be: 3 gallons + 8 quarts + (13 pints / 2 quarts/pints)= 3 gallon + 14 quarts + 1 pints
Next, change the quarts to the gallon with ratio 4 quarts are equal to 1 gallon. The result would be: 3 gallons + (14 quarts / 4 quarts/gallon) + 1 pints = 6 gallon 2 quarts 1 pints
The governor of state a earns $50,935 more than the governor of state b. If the total salaries is $287,225. Find the salaries for both
Answers
a = b + 50,935
b + 50,935 + b = 287,225
2b + 50,935 = 287,225
2b = 287,225 - 50,935
2b = 236,290
b = 236,290/2
b = 118,145 <=== what governor b earns
a = b + 50,935
a = 118,145 + 50,935
a = 169,080 <=== what governor a earns
the some of two consecutive even integers is 170. find the two integers.
Answers
x + x + 2 = 170
2x + 2 = 170
2x = 170 - 2
2x = 168
x = 168/2
x = 84
x + 2 = 84 + 2 = 86
so ur 2 numbers are 84 and 86
The required value of integers are 84 and 86 respectively.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
Suppose the first even integer be x.
Then, the second even integer is x + 2.
Since the sum is given as 170, the following equation can be formed as,
x + x + 2 = 170
⇒ 2x + 2 = 170
⇒ 2x = 168
⇒ x = 84
Then, the other integer is 84 + 2 = 86.
Hence, the two integers for the given case are 84 and 86 respectively.
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Each second for 20 seconds, an elevator descends 6 feet. Find the total change in elevation.
Answers
Simplify the expression
- 3/6 - 5/7
can you show me how?
Answers
-21/42 - 30/42
-51/42
- 51/42 = - 1 9/42
hope this help
how do you evaluate the expression |4/13|
Answers
First, you need to find the quotient of 4 and 13, obviously.
4/13 is equal to roughly 0.308.
Those grouping symbols around it tell you that you need to find the absolute value.
Absolute value is how far away a number is from 0 on a number line. 3, for example has a absolute value of 3, and -6 has an absolute value of 6.
So, the absolute value of 4/13 is about 0.308.
Hope this helps. :)
-Spagoot