when the cake is cut into [tex]2[/tex] ounce pieces instead of [tex]3[/tex] pieces it yields [tex]180[/tex] pieces.
How to find large cake pieces ?
Given in the question when cake cuts into piece that each weight is [tex]3[/tex] ounce it yields [tex]120[/tex]
So original large cake weight is
[tex]w=120*3\\\\w=360[/tex]
So we can find cake pieces when cake cuts into weight [tex]2[/tex] each piece
[tex]pieces=\frac{360}{2}\\=180[/tex]
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NEED HELP ASAP PLEASE!
If a and b are positive integers such that [tex]a^{3b}[/tex] = x and [tex]a^{b}[/tex] = y, then [tex]\frac{x}{y^{2} }[/tex]= ?
If a and b are positive integers such that a^3b = x and a^b = y then x/y² is solved to be y
How to calculate for x/y²The problem is solved by simplifying and substitution
Simplifying the expression a^3b = x and a^b = y will result to
a^(b3) = x and a^b = y
y^3 = x
substituting y^3 = x into the equation x/y²
= x / y²
= y³ / y²
apply power rule
= y³ ⁻ ²
= y
hence the solution of the equation x/y² while considering that a^3b = x and a^b = y will result to a solution of y
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A tennis ball is dropped from a certain height. Its height in feet is given by h = -16t² + 19 where t represents the time in seconds after launch. What is the ball's initial height?please
The tennis ball's initial height is 19 feet.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
Given that, a tennis ball is dropped from a certain height.
Its height in feet is given by h = -16t²+19 where t represents the time in seconds after launch.
Initial height is 0
-16t²+19 =0
16t²=19
t²=19/16
t=√(19/16)
t=√1.1875
t=1.089 seconds
So, the initial height is 19
Therefore, the tennis ball's initial height is 19 feet.
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Write the number in scientific notation. 0.0805 8.05 × 10 8.05 × 10–2 0.805 × 10–1 80.5 × 100–3
how many pints are in 3 3/4 gal
Joshua Levine deposits $250 in an ordinary annuity at the end of each quarter in an account earning 6% interest compounded quarterly. According to the table below, what is the future value of the account in 2 years?
The future value of Joshua's account in 2 years, given the deposits and the interest, is $ 2, 108.21
How to find the future value of an annuity ?The fact that the amount that Joshua Levine deposits is a constant amount of $ 250, makes it an annuity. It is ordinary because it is deposited at the end of the period.
To find the value of this annuity, first find the periodic interest :
= 6 % / 4 quarters per year
= 1 . 5 %
Then find the number of periods :
= 2 years x 4
= 8 quarters
The future value is:
= Annuity x Future value interest factor, 8 periods, 1. 5%
= 250 x 8.4328391063537
= $ 2, 108.21
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The slope of the line represented by y = 5x is___
The slope of the line represented by y = 3 is ___
The slope of the line represented by x = 4 is___
Answer:
5, 0, Undefined.
Step-by-step explanation:
Answer:
1) 5
2) 0
3) Undefined
The SlopeSlope is a measure of steepness of a line. In Algebra 1, It is how much the y-value changes when the x-value increases by 1.
y-intercept is the y-value of the line when it intersects with the y-axis, or the y-value of the line when the x-value of the line is 0.
Slope-Intercept FormThis form is the most common form for expressing linear equations for graphing and is used when the slope and y-intercept is known.
Form
y = mx + b
Lets break it down. y and x stay as a variable when graphing is it only substituted for a constant when solving for x-intercept, etc.
m is the slope.
b is the y-intercept.
Q)Q1
y = mx + b
y = 5x
Because 5 is the m value, the slope is 5.
Q2
y = mx + b
y = 3
Think about it. What cancels out any real value? Multiplying it by 0. If there is no coefficient behind the x, it means the slope is 0.
y = 0x + 3 = y = 3
Because 0 is the m value, the slope is 0.
When y is equal to a constant after solving, it is a horizontal line with the y-intercept of the constant it is equal to (in this case 3).
Q3
y = mx + b
x = 5
The slope is undefined.
When x is equal to a constant after solving, it is a straight vertical line with the x-intercept of the constant it is equal to (in this case 5). The slope is always undefined.
Joshua watched 1 3 of a movie in the morning, and he watched some more at night. By the end of the day, he still had 1 5 of the movie left to watch. How much of the movie did Joshua watch at night
We can start solving the problem by using algebra. Let x be the total length of the movie in minutes. Then we know that:
1/3 of the movie is x/3 minutes.
1/5 of the movie is x/5 minutes.
We are told that Joshua watched 1/3 of the movie in the morning and had 1/5 of the movie left to watch at night. Therefore, we can set up the equation:
x/3 + y = x/5, where y is the length of the movie that Joshua watched at night.
We can then solve for y by isolating it on one side:
y = x/5 - x/3
We know that 1/3 + 1/5 = 8/15.
We can simplify by multiplying both sides of the equation by 15:
y = (8/15)*x = 8x/15
We can conclude that Joshua watched 8/15 or approximately 53.33% of the movie at night.
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
Slope and a point that is not an intercept is the information about the graph of the relationship is given.
The rate of painting is 8 m²/h.
28 square meters of the room are still left to paint after three hours. Let y represent the area in square meters that needs painting after x hours. We require a corresponding (x,y) pair in order to describe a point on a graph. In our situation, we require data on the rate of change in the correlation between the area still needing painting and the time after business hours. Hiro can paint eight square meters per hour. Thus, the equation Y = 8x, or the associated slope, is 8. (1)
By entering the number Y = 28 square meters into the previous formula 28 = 8X
=> X = 7/2
It is not an intercept but the point (7/2, 28).
Alternatively put, the location that is not the intersection with the slope
Your question is incomplete but most probably your full question was
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint. Let y represent the area (in square meters) left to paint after x hours.
Which of the following information about the graph of the relationship is given?
a)Slope and x-intercept
b) Slope and y-intercept
c)X-intercept and y-intercept
d) Y-intercept and a point that is not an intercept
e)Two points that are not intercepts
f)Slope and a point that is not an intercept
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2. Draw a number line diagram and write an expression to represent this situation: "On Tuesday at lunchtime, it was 29°C. By sunset, the temperature had dropped to 16°C.
314
X
1|2
Drag the expressions to the table to show whethe
than or equal to
Less than 1/
DRAG AND
DROP ITEMS
HERE
17
12
X
54
X
1|2
Equal to 1/2
DRAG AND
DROP ITEMS
HERE
12
CLEAR
More than
DRAG AND
DROP ITEMS
HERE
CHECK
The calculations 4(2/9) is 8/9 1, 2(2/5) is 4/5 1, and 8(2/5) is 16/5 > 1, 6×(1/5) is 6/5 > 1, 5×(1/4) is 5/4 > 1.
An example of a fraction?If q is less than 0, a fraction is expressed as p/q. A proper fraction is one that follows the rules, and an improper fraction is another. The numerator in proper fractions is less than the denominator, whereas in improper fractions, the opposite is true.
We are aware that when multiplying fractions, we can eliminate terms from the numerator and denominator of other fractions to make the problem simpler, and we can also multiply numerators and denominators together.
∴ 4×(1/4) = 1.
4×(2/9) = 8/9 < 1.
2×(2/5) = 4/5 < 1.
8×(2/5) = 16/5 > 1.
6×(1/5) = 6/5 > 1.
5×(1/4) = 5/4 > 1.
The calculations 4(2/9) = 8/9 1, 2(2/5) = 4/5 1, and 8(2/5) = 16/5 > 1, 6×(1/5) = 6/5 > 1, 5×(1/4) = 5/4 > 1.
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Fraction 4(2/9) is 8/9 < 1> 1, 6×(1/5) is 6/5 > 1, 5×(1/4) is 5/4 > 1.
What is fraction?If q is less than 0, the fraction is expressed as p/q. Fractions that follow the rules are good fractions and fractions that follow the rules are bad. For proper fractions, the numerator is less than the denominator, and vice versa for improper fractions. When multiplying fractions, you can remove terms from the numerator and denominator of other fractions to simplify the problem. We can multiply the numerator and denominator to each other. ∴ 4×(1/4) = 1.4×(2/9) = 8/9 <1> 1.6×(1/5) = 6/5 > 1.5×(1/4) = 5/4 > 1. Calculation 4(2/9) = 8/9 1, 2(2/5) = 4/5 1 and 8(2/5) = 16/5 > 1, 6×(1/5) = 6/ 5 > 1.5*(1/4) = 5/4 > 1.To learn more about fraction from the given link:
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Find the value of both expressions below when x = 5.
4x
Answer:
The expression below, 4x=20 when x=5.
Step-by-step explanation:
4(5)=20
What are 10 examples of substitutes?
The 10 examples of substitutes good and services are :
Butter and margarinePhysical books and e-booksSandals and flip-flopsTuna and salmonSteel-toe boots and composite-toe bootsMinivans and sport utility vehiclesEarrings and necklacesEyeglasses and contact lensesRed Delicious apples and Gala applesCappuccinos and lattesSimilar products that a client may employ for the same purpose are substitute goods. If the product they prefer is offered, your customers might buy it, but they might also look at alternatives if the price, the product's availability, or its quality changes. The demand for an item is frequently affected by these changes as well.
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math.....................................
Based on the box plot concept and the available options, the box plot that correctly represents the data is option A.
What is Box Plot?Box plot is a term that is used to describe the box and whisker plot which shows the five-number summary of a set of data.
Generally, this five-number summary is the minimum, first quartile, median, third quartile, and maximum.
Therefore, to get the right box plot we have the following steps.Make a box plot of the data.
Step 1: Order the data from smallest to largest. We have 52, 54, 56, 58, 60, 62, and 64Step 2: Find the median. The median is the middle number: 58Step 3: Find the quartiles. The first quartile is the median of the data points to the left of the median: 54. The third quartile is the median of the data points to the right of the median: 62Step 4: Complete the five-number summary by finding the min and the max. The min is the smallest data point, which is 52. The max is the largest data point, which is 64The five-number summary is: 52, 54, 58, 62, 64.Let's make a box plot for the same dataset from above.
Step 1: Scale and label an axis that fits the five-number summary.
Recall that Q1 = 54, the median is 58, and Q3 = 62
Also, the min is 52 and the max is 64.
Therefore, when we draw the box from Q1 to Q3 and from Q1 to the min, and from Q3 to the max, we have option A as the answer.
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What is the area of a triangle with the base of 7 cm and the height of 12 cm?
The area of a triangle with the base of 7 cm and the height of 12 cm is 42 square cm.
In the given question we have to find the area of a triangle with the base of 7 cm and the height of 12 cm.
The entire area bounded by a triangle's three sides is referred to as the triangle's area. In essence, it equals half of the base times height, or A = 1/2bh. So, in order to calculate the area of a triangular polygon, we need to know its base (b) and height (h).
Area of Triangle = 1/2 ×b×h
Area of Triangle = 1/2 ×7×12
Area of Triangle = 7×6
Area of Triangle = 42 square cm
Hence, the area of a triangle with the base of 7 cm and the height of 12 cm is 42 square cm.
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Is 7x 2x² a quadratic equation?
The equation [tex]7x-2x^{2} =0[/tex] is said to be a quadratic equation as the highest degree is 2.
The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no other term which is raised to a higher power than 2.
The given equation is [tex]7x-2x^{2} =0[/tex].
As we know that, a quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.
On comparing equation [tex]7x-2x^{2} =0[/tex] with standard form of quadratic equation [tex]ax^{2} +bx+c=0[/tex], we get, a = -2, b = 7,c = 0.
Thus, the equation [tex]7x-2x^{2} =0[/tex] is a quadratic equation.
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Which of the following are in proportion?
a)21, 35, 24, 40 b) 75, 21, 18, 6
The solution is Option A.
The proportion is given by 21 : 35 : : 24 : 40
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the equation will be
a)
The four set of numbers are = { 21 , 35 , 24 , 40 }
Now , the ratio of 21/35 = 3/5
The ratio of 24 / 40 = 3/5
Therefore, the proportion is expressed as
A = 3 : 5
And , the proportion equation is
21 : 35 : : 24 : 40
Hence , the proportion is 21 : 35 : : 24 : 40
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5. Some chickens and pigs are in a field. How many of each animal are
there if there are 32 heads and 80 legs in total?
Becuase a pig and a chicken each have one head each and we know there are 80 heads, we know that: C + P = 80. When you combine these equations, we find that there are 32 Pigs and 48 Chickens.
What is equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables. A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. A mathematical statement called an equation demonstrates the equality of two mathematical expressions.To learn more about algebraic refer to:
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Who found the formula for area?
Hippocrates of Chios was the first to show that the area of a disk
Who discovered area formula?
In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk (the region enclosed by a circle) is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality.
A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.
Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).
A model is, for example, the method for the area of a circle, πr2.
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.
Α= pi r^2
Divide each side by pi
A / pi = r^2
Take the square root of each side
sqrt( A / pi ) = sqrt(r^2)
sqrt( A / pi ) =r
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Which have 7 sides is called?
A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven")
Polygon Formula
The important polygon formulas are: The sum of interior angles of a polygon with “n” sides =180°(n-2) Number of diagonals of a “n-sided” polygon = [n(n-3)]/2. The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n.
with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended
This polygon has 7 sides
heptagon is a seven sided polygon
decagon is a ten sided polygon
dodecagon is a 12 sided polygon
hexagon is a six sided polygon
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Help pls
A three-column table is given.
Part A C D
Part 14 28 63
Whole B 40 90
What is the value of B in the table?
20
25
28
30
In the three column table the value of B is 20, and option I is the correct answer.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
From the information given, it's important to calculate the constant of proportionality. In this case, for C, we have 28 part and 40 whole, the constant will be:
Constant = Whole / Part
= 40/28
= 1.428
Therefore, the value of B will be:
Whole = Part × Constant
Whole = 14 × 1.428
B = 20
Hence in the three column table the value of B is 20, and option I is the correct answer.
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Answer:B=20
Step-by-step explanation:
i did the math
what is the equation of a line in point-slope form with a slope if 1/2 and the point (5,-2) is on the line?
The equation of the line in slope intercept form is y = 1 / 2x - 9 / 2.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the slope of the line is 1 / 2 and the line passes through (5, -2).
Hence,
y = 1 / 2 x + b
let's find the y-intercept using (5, -2)
Therefore,
-2 = 1 / 2 (5) + b
b = -2 - 5 / 2
b = -4 - 5/ 2
b = -9 / 2
Therefore, the equation of the line is y = 1 / 2x - 9 / 2
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Which of the following rational functions is graphed below?
Answer:A
Step-by-step explanation:
How do you find the predicted Y value?
The formula for calculating the anticipated value of y, known as the "fitted value," is y I = b 0 + b 1 x i.
What is Y value?Determine the graph's slope and a point first. Write a linear equation in slope-intercept form (y = mx + b) once this is finished.
Rewrite the equation using the supplied point (x, y) and slope (m), inserting the correct values for x, y, and m.
To find the y-intercept using this information, calculate the equation for b.
Find the two points in a graph or table that are displayed.
Take note of each point's coordinates (x, y) first. Find the rise and run to determine the slope using this information.
Y-coordinate difference divided by the.
Hence, The formula for calculating the anticipated value of y, known as the "fitted value," is y I = b 0 + b 1 x i.
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Gary wants to build a shed shaped like a rectangular prism in his backyard. He goes to the store and looks at several different options. The table shows the dimensions and volumes of four different sheds.
Use the formula V = l × w × h to complete the table.
Length (ft) Width (ft) Height (ft) Volume (ft3)Shed 1 15 9 2,160
Shed 2 10 10 1,300
Shed 3 12 9 864
Shed 4 15 12 12
Answer: Shed 1: 291,600 units^3. Shed 2: 130,000 units^3. Shed 3: 93,312 units^3. Shed 4: 2,160 units^3
Step-by-step explanation:
15 times 9 times 2,160 = 291,600
10 times 10 times 1300 = 130,000
12 times 9 times 864 = 93,312
15 times 12 times 12 =2,160
How do you do 3 step equations?
Answer: To solve a 3-step equation, you can follow these steps:
Simplify both sides of the equation, if necessary, by combining like terms.
Isolate the variable on one side of the equation.
Use inverse operations to solve for the variable.
Check your solution by substituting it back into the original equation.
Example:
Solve for x: 2x + 5 = 11
Subtract 5 from both sides of the equation: 2x = 6
Divide both sides of the equation by 2: x = 3
Check your solution by substituting x = 3 back into the original equation: 2(3) + 5 = 11
The solution is x = 3.
It's important to note that a 3-step equation is not a specific term, it just means an equation that can be solved in 3 steps. It can be a linear equation or quadratic equation or any other type of equation.
Step-by-step explanation:
The accompanying table shows the value of a car over time that was purchased for 16100 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, determine the value of the car, to the nearest cent, after 16 years.
The value of car to the nearest cent, after 16 years will be $882.
Define the term exponential regression?It is a concept that describes processes that increase at a twice as fast rate. It is employed when the growth starts slowly but quickly accelerates without bounds or when the decay begins strongly but subsequently decelerates to zero.The preceding table displays the increase in value of a car that cost $16,100 over time, where x represents the number of years and y represents the car's cash value.
The formula for the exponential regression will be as follows:
y = A₀e∧(kx)
Where k is a constant and A₀ is the exponential regression coefficient.
So value of y would be $16,100 if x = 0. Next, we have
16,100 = A₀ e∧(k*0)
A₀ = 16,100
The equation will then be:
y = 16,100e∧(kx)
Hence value of y would be $13,431 if x = 1. Next, we have:
13,431 = 16,100e∧(k*1)
e∧(k) = 0.834
Considering all sides, we then have:
ln e∧(k) = ln 0.834
k = -0.181
The equation will then be:
y = 16,100e∧(-0.181*x)
For 16 years,
y = 16,100e∧(-0.181*16)
y = 16100*0.054
After that, a car's value will be:
y = 882
Thus, the value of the car to the nearest cent, after 16 years will be $882.
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Can you help me with this?:(
The formula for the given T-chart is f(x)=x-6. T-shaped graphic organiser used to divide information into two categories. A T chart can be used to contrast two ideas, list benefits and drawbacks, separate facts from opinions, and more.
What sort of T chart is that?T Charts are frequently used to compare facts and opinions, problems and solutions, and pros and cons.
What is a timeline with an example?A timeline is a diagram that shows the progression of the use of a group of resources. A timeline is frequently a sensible visualisation option if you're managing a software project and want to show who is doing what and when, or if you're planning a conference and need to schedule meeting rooms.
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The measures of two supplementary angles total 180 degrees. The measure of angle y is 65 degrees less than the measure of angle x. What are the measures of the angles?
The measure of angle x is 122.5 degrees. The measure of angle y is 57.5 degrees.
The measure of angle x is 115 degrees. The measure of angle y is 65 degrees.
The measure of angle x is 57.5 degrees. The measure of angle y is 122.5 degrees.
The measure of angle x is 65 degrees. The measure of angle y is 115 degrees.
The measure of angle x is 57.5 degrees. The measure of angle y is 122.5 degrees. The correct option is C.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
The measures of two supplementary angles total 180 degrees.
The measure of angle y is 65 degrees less than the measure of angle x.
Let the measure of angle y is m∠y.
And the angle measure of x is m∠x.
So,
m∠x + m∠y = 180° {equation 1}
And according to the question,
m∠y = m∠x - 65° {equation 2}
Substituting the value from equation 2 to equation 1,
2m∠x = 180 + 65
m∠x = 245/2
m∠x = 122.5°
And m∠y = 122.5 - 65
m∠y = 57.5°
Therefore, the angle measures are m∠x = 122.5° and m∠y = 57.5°.
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Use the point in the graph to find the equation of the line in point-slope form
A
y-3=5(x-1)
B
y+3=5(x+1)
C
y+3=5(x-1)
D
y-3=5(x+1)
Answer:
c
Step-by-step explanation:
welcome
Ofia and her brother combined to read a total of 40 book over the ummer ofia read a many book a her brother. How many book did each peron read?
The number of books Sophia and her brother read is 32 and 8 respectively.
Given that,
The total number of books = 40 books
The number of books Sophia read = 4[The number of books Sophia's brother read]
Assuming that the number of books Sophia's brother read = a
So, the number of books Sophia read = 4a
Thus,
a + 4a = 40
Solving the equation further, we get:
5a = 40
a = 8
The number of books Sophia's brother read = 8 books
Hence, the number of books Sophia read = 32 books
Therefore, The number of books Sophia and her brother read is 32 and 8 respectively.
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