Answers
The inverse functions and the domains and ranges of the inverse functions can be presented as follows;
A. The inverse function of f(x) is; [tex]f^{-1}(x) = \frac{3-x}{7\cdot x}[/tex]
B. f(g(x)) = [tex]\frac{3}{7\times \frac{(3-x)}{7\cdot x} + 1}[/tex] = x
C. The inverse function reverses the effect of the function. The inverse function is therefore;
x [tex]{}[/tex] y
10[tex]{}[/tex] 5
6[tex]{}[/tex] 8
5[tex]{}[/tex] 9
4[tex]{}[/tex] 13
2) Domain; 10, 6, 5, 4
Range; 5, 8, 9, 13
What is the inverse of a function?An inverse function maps the output, or y-value of a function to the input value or x-value of the function.
2. A. f(x) = 3/(7·x + 1)
The inverse function can be found as follows;
Let f(x) = y
y = 3/(7·x + 1)
(7·x + 1) = 3/y
7·x = (3/y) - 1 = (3 - y)/y
x = (3 - y)/(7·y)
Plugging in x = f⁻¹(x), and y = x, to get;
The inverse of the function; f⁻¹(x) = (3 - x)/(7·x)B. g(x) = (3 - x)/(7·x)
f(x) = 3/(7·x + 1)
f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = 3/(((3 - x)/(x)) + 1) = 3/(3/x - 1 + 1)
3/((3/x - 1 + 1) = 3/(3/x) = 3 × x/3 = x
Therefore; f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = x
C. The inverse of the function is the function that produces the input of the function from the function's output, therefore, the inverse of the function can be presented as follows;
x [tex]{}[/tex] y
10[tex]{}[/tex] 5
6[tex]{}[/tex] 8
5[tex]{}[/tex] 9
4[tex]{}[/tex] 13
2) The domain is the set of the possible inputs of the function, and the range is the set of the possible outputs of the function.
The domain of the inverse function is; 10, 6, 5, 4The range of the inverse function is; 5. 8. 9. 13Learn more on the inverse of a function here: https://brainly.com/question/9007328
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Related Questions
Find the area of a parallelogram, if its base is 25 cm and distance between two parallel side is 15 cm.
Answers
Answer:
Step-by-step explanation:
A=bh
[tex]=25\times15[/tex]
[tex]=375cm^2[/tex]
[tex]\sqrt[4]{567x^{9} y^{11} }[/tex]
Answers
Step-by-step explanation:
[tex]( \sqrt[4]{567} {x}^{9} {y}^{11} )^{4} [/tex]
[tex]567 {x}^{9} {y}^{11} [/tex]
The ratio of the student government budget for dances to its budget for charity events is 5 to 7. If $532.00 is budgeted for charity events, how much is budgeted for dances?
Answers
The amount budgeted for dances is approximately $380.00.
Assume that "x" is the budgeted sum for dances. The problem states that there is a 5:7 ratio between the budget for dances and the budget for charitable activities. Hence, we can write:
x/532 = 5/7
We can cross-multiply and simplify to find the answer for "x"
7x = 532 × 5
7x = 2660
x = 2660/7
x ≈ 380.00
The estimated $380.00 planned money for dances is the result.
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what to wright demo paragraph about Linear Equations pls help soon
Answers
A linear function is defined as y = mx + b, in which m is the slope and b is the y-intercept.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.More can be learned about linear functions at https://brainly.com/question/24808124
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A bakery sells chocolate cupcakes and mocha cupcakes. One day it sold 162 chocolate and 138 mocha. What percent of the cupcakes sold that day were chocolate?
Answers
Therefore, 54% of the cupcakes sold that day were chocolate.
What is fraction?A fraction is a way of expressing a quantity that represents a part of a whole. It consists of two numbers separated by a horizontal or diagonal line, where the number on the top is called the numerator and the number on the bottom is called the denominator.
Given by the question.
To find the percentage of cupcakes sold that were chocolate, we need to divide the number of chocolate cupcakes sold by the total number of cupcakes sold and then multiply by 100.
The total number of cupcakes sold is:
162 (chocolate) + 138 (mocha) = 300
The number of chocolate cupcakes sold as a fraction of the total number of cupcakes sold is:
162 / 300 = 0.54
To convert this fraction to a percentage, we multiply by 100:
0.54 x 100 = 54%
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Raymond was riding a zip-cable from the top of a viewing post. The cable is 55 yards long. The viewing post is 44 yards high and forms a right angle with the ground, as shown in the picture below.
Answers
Raymοnd will travel a hοrizοntal distance οf 33 yards.
What is Pythagοras theοrem ?The Pythagοrean theοrem, sοmetimes knοwn as Pythagοras' theοrem, is a basic Euclidean geοmetry relatiοnship between a right triangle's three sides. Accοrding tο this rule, the area οf the square with the hypοtenuse (the side acrοss frοm the right angle) is equal tο the sum οf the areas οf the squares with the οther twο sides.
The Pythagοrean equatiοn—οften referred tο as this theοrem's fοrm—can be used tο express the relatiοnship between the lengths οf the sides a, b, and the hypοtenuse c: a²+b² = c²
In οrder tο figure οut the hοrizοntal distance Raymοnd travels using his zip cable, we may simply apply Pythagοras theοrem which is, fοr a right triangle:
hypοtenuse² = base² + height²
base = √(hypοtenuse² - height²)
base = √(55² - 44²)
base = 33yards
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Statistics Card Question!
You are dealt a hand of 8 cards from a standard deck of 52 cards. Find the probability of being dealt five clubs and three cards with one card of each other remaining suit.
Answers
Therefore , the solution of the given problem of probability comes out to be 0.00439, or about 0.44%.
Probability : What is it?The main goal of the mathematical field known as model parameters is to determine the probability that a statement is accurate or that a particular event will occur. It is possible to symbolise chance by using any ranging between range 0 and 1, where 1 typically denotes certainty and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
To calculate the likelihood of receiving a hand of five clubs, three cards, and one card from each remaining deck,
Five clubs can be obtained in the following ways:
=> C(13,5) = 1,287
where C(n,r) indicates how many different ways r things were combined from a total of n options.
After selecting the five clubs, we must select three cards, one from each of the remaining three decks.
=> C(13,2) * C(3,2) = 702
As a result, there are three cards from each of the other two decks and five clubs, giving rise to the following combinations:
=> C(13,5) * [C(39,3) - C(13,2) * C(3,2)] = 328,664
Finally, there are C(52,8) = 74,837,381 potential hands with 8 cards.
The likelihood of receiving five clubs and three cards, along with one card from each of the other three decks, is as follows:
=> P = 328,664 / 74,837,381
=> P ≈ 0.00439, or about 0.44%.
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I need help on this question?
Answers
The tensions in the string are approximately 37.5 lb and 57.39 lb for T1 and T2, respectively.
Describe Tension?Tension is the force that is transmitted through a string, rope, cable, or any other object that is pulled taut by a force. It is a pulling force that is exerted on an object by the string or cable that is attached to it. Tension is a scalar quantity, meaning that it has a magnitude but no direction.
The tension in a string or cable depends on several factors, including the strength and stiffness of the material, the angle at which the string is attached to the object, and the amount of force applied to the string. In general, the tension in a string is equal to the force applied to the string, divided by the cross-sectional area of the string.
To find the tensions T1 and T2 in the string, we can use trigonometry and the fact that the weight is in equilibrium (i.e., not moving).
First, we can use the fact that the weight is in the middle of the string to split the weight into two equal components, one pulling on each end of the string.
The weight component pulling on T1 can be found by multiplying the weight by the sine of the angle between T1 and the horizontal:
W1 = (75 lb) * sin(50°)
W1 ≈ 57.39 lb
Similarly, the weight component pulling on T2 can be found by multiplying the weight by the sine of the angle between T2 and the horizontal:
W2 = (75 lb) * sin(30°)
W2 ≈ 37.5 lb
Since the weight is in equilibrium, the tensions in the string must be equal and opposite to these weight components:
T1 = W2 ≈ 37.5 lb
T2 = W1 ≈ 57.39 lb
Therefore, the tensions in the string are approximately 37.5 lb and 57.39 lb for T1 and T2, respectively.
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If you invest $1773 in an account that pays simple interest of 6 % How much Interest will you have
earned after 7 years?
Answers
Answer:
the interest earned will be $106.38.
The ratio of the age of a father to that of his son is 9:2 if the son is now 8 years old, the ratio of their ages in 4 years time will be
Answers
Answer: 72:16
Explanation:
Written as a simplified polynomial in standard form, what is the result when
(x + 5)2 is subtracted from 6x² + 3?
Answers
Expanding the square of the binomial (x + 5)^2, we get:
(x + 5)^2 = (x + 5)(x + 5) = x^2 + 10x + 25
Now, let's subtract (x + 5)^2 from 6x^2 + 3:
(6x^2 + 3) - (x^2 + 10x + 25)
Simplifying, we get:
6x^2 + 3 - x^2 - 10x - 25
Combining like terms, we get:
5x^2 - 10x - 22
Therefore, the result of subtracting (x + 5)^2 from 6x^2 + 3 is 5x^2 - 10x - 22, written in standard form.
If f=(x) is an exponential function where f(1)=8 and f(10.5)=72 then find the value of f(3.5)
Answers
Answer: We know that the function f(x) is an exponential function. An exponential function can be written in the form:
f(x) = a * b^x
where:
a = the initial value (when x = 0)
b = the base of the exponential function
x = the independent variable
To find the values of a and b, we can use the given information:
f(1) = 8, so:
8 = a * b^1
8 = a * b
f(10.5) = 72, so:
72 = a * b^10.5
We can now use the first equation to solve for a:
a = 8/b
Substituting this value into the second equation, we get:
72 = (8/b) * b^10.5
Simplifying:
72 = 8 * b^9.5
9 = b^9.5
b = 9^(1/9.5)
b = 1.4608 (approx.)
Substituting the values of a and b into the exponential function, we get:
f(x) = 8 * 1.4608^x
Now we can find f(3.5):
f(3.5) = 8 * 1.4608^3.5
f(3.5) = 8 * 6.2797
f(3.5) = 50.2376 (approx.)
Therefore, f(3.5) is approximately equal to 50.24.
Step-by-step explanation:
A sheet of cardboard 10 inches by 12 inches will be made into a box cutting equal-sized squares from each corner and folding up four edges. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?
Answers
Using the area formula for the measure for side of square cut out is obtained as 1 inch.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The length of the cardboard is 12 inch.
The breadth of the cardboard is 10 inch.
Let x inches square be cut from the 4 corners.
Then the length of the base = 12 - 2x.
Then the breadth of the base = 10 - 2x.
The area of the base is given is 80 inch².
The equation for the carboard will be -
l × b = area
Substitute the values into the equation -
(12 - 2x) × (10 - 2x) = 80
Simplify the equation -
120 - 24x - 20x + 4x² = 80
4x² - 44x + 40 = 0
x² - 11x + 10 = 0
Use the factorization method -
x² - 10x - x + 10 = 0
x(x - 10) - 1(x - 10) = 0
(x - 10)(x - 1) = 0
x = 10 or x = 1
Since, the breadth of the cardboard is 10 inches so x cannot be 10.
Therefore, the value of x is obtained as 1 inch.
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At a restaurant you only have $30 to spend on dinner. In addition to the cost of the meal you must pay a 8% sales tax and leave a 20% tip. What is the most expensive item you can order?
Answers
Answer: Let's break down the total cost of dinner into three components: the cost of the meal itself (M), the sales tax (T), and the tip (P).
We know that the sales tax is 8% of the meal cost, so we can write:
T = 0.08M
We also know that the tip is 20% of the total cost, which is the sum of the meal cost and the sales tax, so we can write:
P = 0.20(M + T) = 0.20(M + 0.08M) = 0.20(1.08M) = 0.216M
Finally, we know that the total cost of dinner must be no more than $30, so we can write:
M + T + P ≤ 30
Substituting the expressions for T and P that we derived earlier, we get:
M + 0.08M + 0.216M ≤ 30
Simplifying and solving for M, we get:
1.296M ≤ 30
M ≤ 23.15
Therefore, the most expensive item you can order is $23.15 or less (before tax and tip) to stay within your budget of $30.
Step-by-step explanation:
The cook has 22.5 gallons of spaghetti sauce and wants to pour it into 5 different containers.
If she pours the same amount of sauce in the each container, how many gallons of sauce would be in each of the 5 containers?
Answers
Answer:
22.5 Divided by 5 equals 4.5
Step-by-step explanation:
There is the answer
In her geology class, Nora learned that quartz is found naturally in a variety of colors. Nora's teacher has a giant box of colorful quartz pieces that he and his students have collected over the years. Nora picks a piece of quartz out of the box, records the color, and places it back in the box. She does this 18 times and gets 3 purple, 2 yellow, 5 white, and 8 pink quartz pieces.
Based on the data, what is the probability that the next piece of quartz Nora picks will be yellow?
Write your answer as a fraction or whole number.
Answers
The probability that Nora will pick a yellow quartz piece on the next selection is 1/9.
To calculate the probability of picking a yellow quartz piece on the next selection, we need to analyze the frequency of yellow quartz pieces relative to the total number of recorded quartz pieces.
Out of the 18 quartz pieces Nora picked, only 2 were yellow.
To find the probability, we divide the number of yellow quartz pieces by the total number of pieces recorded:
Probability = Number of yellow quartz pieces / Total number of recorded pieces
The number of yellow quartz pieces is 2, and the total number of recorded pieces is 18.
So the probability can be calculated as:
Probability = 2 / 18
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2 in this case:
Probability = 1 / 9
It's important to note that this probability assumes the picking process is random and that the distribution of colors in the giant box of quartz pieces remains constant over time.
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Need help on this multiple choice question
Answers
The answer is 12x³ - 14x² + 18x + 14.
What is the distributive property of multiplication?
The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
To multiply (4x + 2)(3x² - 5x + 7), we can use the distributive property of multiplication:
(4x + 2)(3x² - 5x + 7) = 4x(3x² - 5x + 7) + 2(3x² - 5x + 7)
Now we can simplify each term:
4x(3x² - 5x + 7) = 12x³ - 20x² + 28x
2(3x² - 5x + 7) = 6x² - 10x + 14
Putting the terms together, we get:
(4x + 2)(3x² - 5x + 7) = 12x³ - 20x² + 28x + 6x² - 10x + 14
Simplifying further:
(4x + 2)(3x² - 5x + 7) = 12x³ - 14x² + 18x + 14
Therefore, the answer is 12x³ - 14x² + 18x + 14.
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Help 100 plus brainiest
Answers
Answer:B.The constant of proportionality is 3. In the table the constant of proportionality is represented by the y-value when the x-value is 1. On a graph, the constant of proportionality represents the steepness of the line.
This is the answer because all of the Y's can be divided by X and equal three.
3 divided by 1 is 3, 15 divided by 5 is 3, 24 divided by 8 is 3, and 27 divided by 9 is 3.
This means that there is a constant rate, which is the proportionality,3. This is also represented by our first X and Y value. X is 1 and Y is 3, which means that the word length increases by 3.
I hope this helped & Good Luck <3!!!!
Correct answer is B.
Step-by-step explanation:So this table represents a set of values related by a constant of proportionality. This constant is just the value of the slope created when the values from the "x" and "y" axis are plotted into a two-dimensional graph.
1. Choose 2 random ordered pairs (OP) from the table.Notation: (x, y)
OP 1: (1, 3)
OP 2: (5, 15)
2. Calculate the slope.Slope formula: [tex]m=\frac{y_{2} -y_{1}}{x_{2} -x_{1} }[/tex]
Substituting in the formula and calculating:
[tex]m=\frac{(15) -(3)}{(5) -(1)}\\ \\m=\frac{12}{4} \\ \\m=3[/tex]
3. Choose the correct answer.This value for the slope, or contant of proportionality, is enough to determine the correct answer. Correct answer is answer B.
4. Analyze.This constant represent the relation between the word length (x) and the score (y) is 3. Therefore, each time a word length increases one time, the score increases 3 times as much.
5. Graph of the function.Chech the attached image.
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AEFD - AEIH by the SSS similarity theorem. Which ratio is also equal to
EF
EI
- and ED/EH
Answers
For the given triangles, EF/EI=DF/HI and also ED/EH=DF/HI.
What is a triangle's definition?
A triangle is a closed two-dimensional shape with three straight sides, three angles, and three vertices (or corners). It is formed by connecting three non-collinear points in a plane with straight lines. The sum of the interior angles of a triangle is always 180 degrees, and each exterior angle is equal to the sum of its two adjacent interior angles. Triangles can be classified based on the length of their sides and the size of their angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.
Now,
As given triangle are similar by SSS.
that means ratio of respective sides will be equal.
Then, ED/EH=EF/EI=DF/HI
Hence,
we can see that EF/EI=DF/HI and also ED/EH=DF/HI.
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4) Range: 3, 3, 4, 5, 5, 8, 9,
5) Mode: 2, 3, 7, 7, 9,
6) Mode: 2, 6, 8, 8, 9,
7) Median: 2, 2, 3, 4, 8,
8) Median: 2, 4, 5, 5, 8, 8,
9) Range: 2, 5, 6, 7, 7, 8, 9,
10) Range: 2, 2, 3, 4, 7, 9, 9,
Answers
Range = 9-3 = 6
Mode = 7
Mode = 8
Median = 3
Median = (5+5)/2 = 5
Range = 9-2 = 7
Range = 9-2 = 7
Louise measured the perimeter of her rectangular scrapbook to be 138 cm. If the scrapbook is 39 cm wide, how long is the scrapbook?
Answers
2(+W)
P = 2(+W)
We know the perimeter is 154 and the width is 45
Substituting these values into the equation
154 = 2 (I+45)
Divide each side by 2
154/2 = 2/2 (I+45)
77=1+45
Subtract 45 from each side
77-45 = 1+45-45
32=1
The length is 32 cm
find the suffice area of a rectangular prism with l = 16m, w = 19m and h =2m
Answers
Answer: The surface area of the rectangular prism is 1356 square meters.
Step-by-step explanation:
The surface area of a rectangular prism is given by the formula:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Substituting the given values, we get:
SA = 2(16m)(19m) + 2(16m)(2m) + 2(19m)(2m)
SA = 1216m^2 + 64m^2 + 76m^2
SA = 1356m^2
Therefore, the surface area of the rectangular prism is 1356 square meters.
Which net matches the figure?
___________________________________
(Reporting any spams/wrong answers)
(giving brainliest to the correct answer)
____________________________________
Answers
Answer:
Figure D.
Step-by-step explanation:
The given Figure is a cube , which is a three-dimensional shape that has six square faces, twelve edges, and eight vertices. All of its faces are congruent and perpendicular to each other.
Figure D will turn into Square box when it is folded. Rest all are either Cuboid or Irregular Shaped objects when folded.
The students at Porterville Elementary sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with t tickets sold.
$800 = $16t
What is the unit rate in the equation above?
A.
$784 per raffle ticket
B.
$16 per raffle ticket
C.
$50 per raffle ticket
D.
$800 per raffle ticket
Answers
HURRY The projected worth (in millions of dollars) of a large company is modeled by the equation y=246(1.11)x. The variable x represents the number of years since 1997.
What is the projected annual percent growth, and what should the company be worth in 2005?
Responses
a. 11%, $510.74 million
b.11%, $566.92 million
c.21%, $629.28 million
d.21%, $273.06 million
Answers
The projected annual percent growth is 11% and the worth in 2005 will be $566.92 million. The solution has been obtained by using linear equation.
What is a linear equation?
The degree of the linear equation is 1. It is clear that in linear equations with exponents greater than one, there are no variables. The equation for this graph produces a straight line.
We are given an equation as y = [tex]246(1.11)^{x}[/tex]
From this, we get the percentage of annual growth as
⇒ (1.11 - 1) * 100
⇒ 0.11 * 100
⇒ 11%
The worth of company in 2005 is given by
y = [tex]246(1.11)^{x}[/tex], where x = 8
On substituting, we get
⇒ y = [tex]246(1.11)^{8}[/tex]
⇒ y = $566.92 million
Hence, the projected annual percent growth is 11% and the worth in 2005 will be $566.92 million.
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how do i go about finding x° and ycm, please?
I've tried Sine Rule & Cosine Rule... I thought i had done it correctly until i worked out the angles added up to much higher than 180° so it cannot be correct... can anyone help?
Answers
From the solution;
x = 62.62°
y = 8.9 cm
What is the sine rule?The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.
By the use of the sine rule;
a/Sin A = c/Sin C
Sin C = cSin A/a
C = Sin-1(cSin A/a)
C = Sin-1(7.8 * sin 66.4/9.2)
C = 50.98°
B = 180 - (50.98° + 66.4)
B = 62.62°
Then;
a/Sin A = b/Sin B
9.2/Sin66.4 = b/Sin 62.62
b = 9.2 * Sin 62.62/Sin66.4
b = 9.2 * 0.89/0.92
b = 8.9 cm
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Union and intersection of intervals
B and C are sets of real numbers defined as follows.
B = {v|v>3}
C={v|v≤9}
Write BUC and B n C using interval notation.
If the set is empty, write Ø.
Answers
Answer:
CARDIAL NUMBERS = GEOGRAPHY NUMBER AND HAS BEEN A STRANGER I AM FINE BUT THEN ALSO SAYING THE SAME HERE
What is the value of x?
Numerical Value only pls.
Answers
Answer:
19
Step-by-step explanation:
The two values are equal to each other because they are vertically symmetrical (i forgot the term, havent dine this in a while) so 3x-3 = [6(x - 10)] so to simplify this, you could say 6x - 60 = 3x-3, which makes it a lot more understandable. To find x, add 60 to both sides and tou should come out with 6x = 3x + 57, we now subtract 3x from both sides to get 3x = + 57, divide by three then you get the balue of x, which is 19
1. Some students like their squash strong and use the ratio of 1:2 of squash to water How many litres of water are needed to mix with 1 litre of squash?
Answers
Answer:
If the ratio of squash to water is 1:2, it means that for every 1 unit of squash, we need 2 units of water.
So, to mix 1 liter of squash, we need 2 liters of water.
Therefore, the number of liters of water needed to mix with 1 liter of squash is 2 liters.
Step-by-step explanation:
37 students shared 5 pizzas equally? What fraction of the pizza did each student receive?
Answers
Answer:
Each student received 40/37 of a pizza slice.
Step-by-step explanation:
To find the fraction of the pizza each student received, we can start by finding the total number of pizza slices. Since each pizza was shared equally among 37 students, we can multiply the number of pizzas (5) by the number of slices in each pizza to get the total number of slices:
Total number of slices = 5 pizzas x 8 slices per pizza = 40 slices
Next, we can divide the total number of slices by the number of students to get the number of slices each student received:
Number of slices per student = 40 slices ÷ 37 students
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:
Number of slices per student = 40/37 slices
Therefore, each student received 40/37 of a pizza slice.
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To find the fraction of the pizza each student received, we need to divide the total number of pizzas by the total number of students:
5 pizzas ÷ 37 students = 5/37 pizzas per student
Therefore, each student received 5/37 of a pizza.