The maximum index of refraction of the fluid that will still cause total internal reflection within the prism is nf = n/sinΘc.
Total internal reflection is a phenomenon in which light passes through a medium with a higher index of refraction and bounces back into the same medium instead of exiting it. This is possible when the angle of incidence is greater than the critical angle of the material.
In the case of a prism surrounded by a fluid, the maximum index of refraction of the fluid that will still cause total internal reflection within the prism can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two materials.
The critical angle of the prism can be calculated as the angle at which the sine of the angle of refraction becomes equal to 1. The critical angle can be calculated using the equation:
sinΘc = 1/n
where n is the index of refraction of the prism.
The maximum index of refraction of the fluid can then be found by rearranging Snell's law and substituting the critical angle into the equation:
nf = n/sinΘc
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The question is in the picture.
Answer:
x = 3 , y = 8
Step-by-step explanation:
Consider the figure to be a parallelogram.
• opposite sides of a parallelogram are congruent
then
8x = 5x + 9 ( subtract 5x from both sides )
3x = 9 ( divide both sides by 3 )
x = 3
and
7y - 16 = 5y ( subtract 5y from both sides )
2y - 16 = 0 ( add 16 to both sides )
2y = 16 ( divide both sides by 2 )
y = 8
Question
Andre calculated the volume of a cylinder. Andre said, “I found the area of a circular cross section and multiplied it by the cylinder’s height.”
Do you agree with Andre's strategy? Explain your reasoning.
Yes, I agree with Andre's strategy for calculating the volume of a cylinder.
The volume of a cylinder is equal to the area of the base (which is a circle) multiplied by the cylinder's height. This formula is expressed as follows:
Volume = r2h, where r is the radius of the circular base and h is the cylinder's height.
We can use the following formula to calculate the area of the circular base:
Area = r2
So, if we multiply the area of the circular base by the cylinder's height, we get:
Volume = r2h is the formula for calculating the volume of a cylinder.
As a result, Andre's strategy of calculating the volume of a cylinder by finding the area of a circular cross section and multiplying it by the height of the cylinder is valid and correct.
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Every morning, a deli offers a “commuter special” in which customers can select a pastry, beverage, and a copy of one of the local papers and pay $1.00. Their options are listed in the table.
Commuter Special
Pastry
Beverage
Paper
Donut
Coffee
The Times
Brownie
Milk
The Herald
Muffin
Tea
Scone
Orange Juice
Croissant
Last Tuesday, the deli did not have any muffins. How did that affect the number of possible combinations?
It decreased the number of combinations by 1.
It decreased the number of combinations by 4.
It decreased the number of combinations by 8.
It decreased the number of combinations by 10.
When a number is increased by ten, the result is
three times the number. What is the number?
Answer:
used to works by in BBC FDA's in BBC FDA's keep that u now u now u now how to be successful so do it.
Step-by-step explanation:
no exception
Kingsley knows that 1 inch is about 2.54 centimeters.He wants to write an equation he can use to convert any given length in inche (I) to centimeters (c)
The equation of conversion between the length y inches to centimeters is y inches = 2.54y centimeters.
What is the relation between inches and centimeters?Both the inches and centimeters are units of length, where the inch is an ES unit and the centimeter is a CGS unit. They are connected by the relation, 1 inch equals 2.54 centimeters.
Let, the length is y inches.
It is known that 1 inch = 2.54 centimeters. So, convert the y inches to centimeters.
y inches = y×1 inch
= y×2.54 centimeters
= 2.54y centimeters
Therefore, the obtained answer is y inches = 2.54y centimeters, where y is the length of an object.
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the measure of the larger angle is 12 less than 3 times the measure of the smaller angle
Answer:
Let x be the measure of the smaller angle. Then the measure of the larger angle is 3x - 12.
We can write this as an equation:
larger angle = 3 * smaller angle - 12 or 3x - 12 = larger angle.
Alternatively, we can write it as:
smaller angle + larger angle = 180 (since they form a straight line)
Substituting larger angle with 3x - 12, we get:
x + 3x - 12 = 180
Simplifying:
4x - 12 = 180
4x = 192
x = 48
Therefore, the measure of the smaller angle is 48 degrees, and the measure of the larger angle is 3(48) - 12 = 132 degrees.
The measure of the larger angle is 12 less than 3 times the measure of the smaller angle x = 48
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’ meaning “corner.”
Angles can mean is an acute angle.
Let smaller angle = x
Larger angle = 3x - 12
x & (3x - 12) are supplementary
So, x + 3x - 12 = 180°
4x - 12 = 180
4x = 180 +12
4x = 192
x = 192/4
⇒ x = 48°
Hence, the measure of the larger angle is 12 less than 3 times the measure of the smaller angle x = 48
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Find the value of each variable using the properties of a parallelogram
The value of x is 10.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Parallelogram has the property that the consecutive or adjacent angles of a parallelogram are supplementary.
That is, they sum up to 180°.
Here, (6x)° and (12x)° are supplementary.
6x + 12x = 180
18x = 180
x = 10
Hence the value of x is 10.
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In theâ U.S., shoe sizes are defined differently for men andâ women, but inâ Europe, both genders use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female collegeâ students, converted from their reported U.S. shoe sizes.âa) Describe the shape.âb) How many modes does the histogramâ have? What might explainâ that?
a) The shape of the histogram appears to be roughly symmetric and bimodal.
b) The histogram appears to have two modes, explanation is given below.
c) D option is correct.
a) The shape of the histogram appears to be roughly symmetric and bimodal.
b) The histogram appears to have two modes, which may be due to the fact that the data includes both male and female students. The two modes may correspond to the average shoe sizes for men and women, respectively.
c) D option is correct. The distribution has two modes from 38 to 40 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.
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____ The given question is incomplete, the complete question is given below:
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both genders use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes.
a) Describe the shape.
view the histogram (The distribution is roughly symmetric and bimodal.)
b) How many modes does the histogram have? What might explain that?
c) Choose the correct answer below.
A. The distribution is multimodal, with modes from 38 to 40, from 44 to 46, and from 48 to 50. This may be due to having data for both men and women. The first two modes might be for women and the third for men.
B. The distribution has one mode from 44 to 46. This is due to the students having roughly the same mean shoe size.
C. The distribution has one mode from 38 to 40. This is due to the students having roughly the same mean shoe size.
D. The distribution has two modes from 38 to 40 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.
E. The distribution has two modes from 34 to 36 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.
F. The distribution is multimodal, with modes from 34 to 36, from 40 to 42, and from 43 to 50. This may be due to having data for both men and women. The first two modes might be for men and the third for women
G. The distribution does not have any modes, because it is uniform i Shoe Sizes Count.
Alice purchased a dress for $23.95, a necklace for $10.95, and a pair of
earrings for $6.79. What was the total amount of her purchase including 5%
tax?
Answer:
$43.77
Step-by-step explanation:
The total price without tax is $41.69. To add tax, we take 5% of this total (which ends up being $2.08) and add it to the total. This makes the final price $43.77.
The regular price on a pair of jeans is $54. The store advertises a back to school sale at 40% of the regular price of the jeans. Two weeks later, the store advertises a sale at an additional 20% off the sale price of the jeans. Two friends decided to purchase the jeans. Shannon says these jeans are now 60% of the regular price. Mary disagrees because she figures that the total discount is less than 60%. What is the cost of the jeans at the 40% off back-to-school sale. What is the cost of the jeans during the additional 20% off sale.
Answer:
See explanation
Step-by-step explanation:
40% of the original $54 is $21.60, therefore the pants are $21.60 off of their original price. This makes the pants $32.40.
20% of the new $32.40 is $6.48, therefore the pants are $6.48 off of the 40%-off price. This makes the pants $25.92 for their final price.
Reflect the triangle over the y-axis and find the coordinate of the image of point K.
K’(2, 1)
K’(–2, 1)
K’(–2, –1)
K’(2, –1)
K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.
Therefore, the coordinate of the image of point K is K’(-2, 1).
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CROWN PLEASE HELP ME (ALSO PLEASE SEPARATE IT)
Answer: WVZ=84 XVW=84 IFH= 14 EFG= 58
Step-by-step explanation:
9x-15=5x+29- do 9-5 to get 4x then 29+5 to get 44 then divide 44 by 4
6x+25=2x+3- do 6-2 to get 4x then 3-25 to get -22 then divide -22 by 4
10, 110, 210, 310, …
find a^30
The 30th term value is 2900.
What is an arithmetic sequence?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
A sequence,
10, 110, 210, 310, …
To find the common difference:
110 - 10 = 100
So, d = 100
Remember that,
aₙ= a₁ + (n-1)d
aₙ=a₁+(n−1)d
So,
aₙ = 10 +(n−1)100.
a₃₀ = 10 + (30 - 1)100
a₃₀ = 10 + 29(100)
a₃₀ = 10 + 2900
a₃₀ = 2910.
Therefore, a₃₀ = 2910.
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Function w is a nonlinear function. Which representation could represent function w?
A representation that could represent function w (nonlinear function) is: D. table D.
What is a linear function?In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
Therefore, table D represents a non-linear function because the slope is not constant and the common difference is not constant between successive data points.
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I really need the answer for this. My teacher about to grade it. Yall please help me out.
Answer: i think that its D
Step-by-step explanation:
im really sorry if its wrong
Answer:
Step-by-step explanation:
Take my answer with a grain of salt as this is an educated guess based on the problem.
The exponentiation rule for raising a power to another power (a^b)^c = a^{bc} therefore a power to a power is equal to the powers multiplied together. so if the base is equal to (32/5) and the power is -2x. some number raised to the x is equal to (32/5)^-2x therefore because -2^x is equal to -2x the answer is B which is the original base (32/5) with the exponent -2 when raised to the x will be equal to (32/5)^-2x.
Therefore, B is the answer
solve please i need help am failing class will give brainliest for the
correct answer
Answer:
9 a3 b8
Step-by-step explanation:
109 a11 b16 - 100 a8 b8
In the year 2002, a company made $6.5 million in profit. For each consecutive year after that, their profit increased by 5%. How much would the company's profit be in the year 2004, to the nearest tenth of a million dollars?
7.2 million is the company's profit be in the year 2004.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the company's profit in the year 2004
We have to first calculate its profit in the year 2003.
We know that its profit in 2002 was $6.5 million, so we can use the formula:
Profit in 2003 = profit in 2002 + (5% of profit in 2002)
= $6.5 + (0.05 x $6.5 )
= $6.825 million
Now, to find the profit in 2004, we use the same formula:
profit in 2004 = profit in 2003 + (5% of profit in 2003)
= $6.825 + (0.05 x $6.825 )
= $7.16625 million
profit in 2004=$7.2 million
Hence, 7.2 million is the company's profit be in the year 2004.
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the correlation coefficient will always take values
The correlation coefficient can take values between -1 and 1, inclusive. A correlation coefficient of -1 indicates negative correlation and 1 indicates positive correlation.
A correlation coefficient of -1 indicates a perfect negative correlation, meaning that as the values of one variable increase, the values of the other variable decrease. A correlation coefficient of 1 indicates a perfect positive correlation, meaning that as the values of one variable increase, the values of the other variable also increase.
A correlation coefficient of 0 indicates no correlation, meaning that there is no relationship between the two variables. Correlation coefficients can take any value between -1 and 1, inclusive, including fractional and decimal values.
Positive values indicate positive correlation, negative values indicate negative correlation, and values close to 0 indicate little or no correlation. The magnitude of the correlation coefficient indicates the strength of the relationship between the two variables.
The closer the coefficient is to 1 or -1, the stronger the relationship between the variables.
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l
Charlie is saving money to buy an everlasting gobstopper. He estimates that he will need $13.50. However, he forgot about the added
sales tax. The actual price of his gobstopper is $15.25. What is Charlie's percent error? (ROUND TO THE NEAREST TENTH)
The percentage error of Charlie is given by the equation A = 13 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage error of the gobstopper be A
Now , the initial price of the gobstopper = $ 13.50
The final price of the gobstopper = $ 15.25
Now , the equation will be
The percentage error A = ( final price - initial price / initial price ) x 100
The percentage error A = [ ( 15.25 - 13.50 ) / 13.50 ] x 100
The percentage error A = ( 1.75 / 13.50 ) x 100
The percentage error A = 0.1296 x 100
The percentage error A = 12.96 %
The percentage error A = 13 %
Hence , the percentage error is 13 %
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A rocket is launched from the top of an 88-foot cliff with an initial velocity of 100 ft/sec. a. Use the vertical motion formula h(t) = -16t2 + vt + c to write an equation that represents the height of the rocket with respect to time. b. Determine how long the rocket will take to hit the ground at the base of the cliff (h = 0) after it is launched. Round to the nearest hundredth of a second.
Answer:17
Step-by-step explanation:
i took the test
Ms. Hart wrote the expression s – 11.
Write a sentence about a real-life situation that matches this expression.
Answer:
Jack has a toy poodle names Lucy. He is supposed to feed Lucy 11 ounces of dog food a day. He has s ounces of food in the bag he bought for the month. The amount of dog food left in the bag after feeding Lucy today is represented by s-11.
The volume of a cylindrical concrete pillar is approximately 12,042 cubic centimeters. The diameter of the pillar is 10 centimeters.
What is the height of the pillar? Use π ≈3.14 .
The height of the cylindrical concrete pillar is approximately 153.2 centimeters.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as;
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
We are given that;
Diameter of pillar= 10cm
Volume = 12,042 cubic centimeters
Now,
First, we need to find the radius of the pillar. The diameter of the pillar is given as 10 centimeters, so the radius is half of that:
r = 10/2 = 5 centimeters
Now we can substitute the given volume and radius into the formula and solve for the height:
12,042 = π(5)^2h
Divide both sides by π(5)^2:
h = 12,042 / (π(5)^2)
h ≈ 153.2 centimeters (rounded to one decimal place)
Therefore, by the given volume the answer will be 153.2 centimeters.
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5.) Yesterday your friend made needs to make 3 more gallons of the same shade. She 1 gallon of dark pink paint using the information in the table. Today she
white tint to 3 gallons of base paint. Explain the error in her reasoning. says that she should add 9 parts red tint and 2 parts
Our friend's mistake when wanting to make a new mixture of pink paint is that she is only going to add 2 parts of white paint, the correct formula would be 3.
What is painting?Painting is the practice of applying paint, pigment, color or other medium to a solid surface.
To mix 3 gallons of pink paint we must take into account the following information:
1 gallon of pink paint is equal to 3 parts red paint and 1 part white paint.
To find out how many parts we need to prepare 3 gallons of pink paint we must multiply the mix values for a gallon by 3.
Red paint:
3 x 3 = 9
White paint:
1 x 3 = 3
Therefore, we need to use 3 parts white paint and 9 parts red paint to make 3 gallons of pink paint.
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The diagram shows a tennis ball, centre O, resting on a flat surface PQR. A ruler, PTS, rests on the ball at T. PT = 20 cm and ZTPQ = 30°. Calculate the radius of the tennis ball correct to the nearest millimetre. P 20 30°
The radius of the ball which is the each of the smaller balls is R = 2r.
What is volume of circle?The formula for the volume of a sphere is V = 4/3 π r³, where V = volume and r = radius. The radius of a sphere is half its diameter. So, to calculate the surface area of a sphere given the diameter of the sphere, you can first calculate the radius, then the volume.
We can use the following formula to get the volume of a sphere whose radius is "r": A sphere's volume is equal to 4/3r³.
here, we have,
Given,
A steel ball which is melted down to make eight smaller identical balls.
If the radius of the original steel ball was 20 cm:
Let the spherical ball's radius be R.
And with r being the radius of 8 similar balls,
According to the inquiry,
Volume of 8 similar balls = the volume of a larger sphere
3/4πR³ = 8 × 3/4πr³
R³ = 8r³
R = 2r
Hence, The radius of the ball which is the each of the smaller balls is R = 2r.
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Use the function to find the zeros. One factor is given.
f(x)=2x³ +x²-5x+2, the given factor is (x+2)
Answer: x = 0, 2 or 3/2 (look at the image for the solution)
Step-by-step explanation:
Number of terms: 8 - 4c
The Number of terms in the expression 8 - 4c is 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
We are given an expression as;
8 - 4c
Here c is the variable.
The first one is 8 and the second one is 4c
Therefore, number of terms are 2
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pls helppppp its math and its pretty hard
A maintenance worker needs to wax a restaurant floor shaped like the image shown. A six-sided figure. There is a horizontal base of 35 feet then another horizontal base below it of 20 feet. The longest side is to the right and is 40 feet. The top is 30 feet. There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet. If the wax cost $1.38 a square foot, how much will the wax cost to cover the floor? $1,224.75 $1,569.75 $2,104.50 $2,449.50
If the wax cost $1.38 a square foot, the cost of wax to cover the area of the floor is $1,569.75.
The correct option is B.
What is the total area of the floor?The total area of the floor is calculated from the shape of the floor.
The floor is made up of a trapezoid and a rectangle.
The area of a trapezoid can be calculated as:
A = (a + b)/2 * h
where
a and b are the lengths of the bases and h is the height.
The trapezoid has a height of 15 feet and bases of 35 feet and (20 - 20) or 10 feet. So its area is:
A = (35 + 10)/2 * 15
A = 337.5 square feet
The rectangle has a base of 20 feet and a height of 40 feet. So its area is:
A =20 * 40
A = 800 square feet
The total area of the figure is the sum of the areas of the trapezoid and triangle:
A = 337.5 + 800
A = 1137.5 square feet
Finally, to find the cost of the wax, we multiply the area by the cost per square foot:
Cost = 1137.5 * $1.38
Cost = $1569.75
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A line passes through the coordinates (0,1) and 4,3). What is the y-intercept for the line in slope-intercept form
The equation of the line is y = ( 1/2 )x + 1 and the y intercept is b = 1
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 1 )
Let the second point be Q ( 4 , 3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 3 - 1 ) / ( 4 - 0 )
Slope m = 2/4
Slope m = 1/2
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 1 = ( 1/2 ) ( x - 0 )
y - 1 = ( 1/2 )x
Adding 1 on both sides , we get
y = ( 1/2 )x + 1
Hence , the equation of line is y = ( 1/2 )x + 1
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Follow the given steps to subtract mixed numbers with different denominators: Step 1– Convert the mixed numbers into improper fractions. Step 2– Find the common multiple of both the denominators. Step 3– Convert the fractions as common denominators.
The steps for subtracting mixed numbers are the transformation of improper fractions, subtraction of denominator, then subtracting numerator, making it the smallest term, and reverse.
Finding the difference between two mixed numbers is required when subtracting mixed numbers. The steps for subtracting mixed numbers are as follows:
Step 1: Transform the mixed values into improper fractions in step 1. To achieve this, divide the total by the denominator, then add the numerator. The new numerator is the outcome, and it is positioned above the denominator.
Step 2: Identify a common denominator in step two. You must identify a common denominator to subtract fractions with various numerators.
Step 3: Subtract the fractions in step three. Subtract the numerators from the fractions while maintaining the same denominator.
Step 4: Make the outcome simpler. Simplify the outcome if you can by breaking the fraction down into its smallest terms. 13/4 in this instance may be expressed as 3 1/4.
Step 5: Reverse the incorrect fraction to a mixed number in step 5. Divide the numerator by the denominator to return the improper fraction to a mixed number. The full number serves as the numerator, and the remainder serves as the quotient.
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The question is -
How to Subtract mixed numbers?
eric reads an article that says 15 out of 25 adults use their computer everyday. He collects data from a random sample of adults. Out of 1,270 adults, estimate the number of adults who use their computer every day. Please show your work!
The number of people that read their computer everyday out of 1270 surveyed adults using the given fraction is; 762 people
How to solve fraction problems?Wea re told that eric reads an article that says 15 out of 25 adults use their computer everyday. Thus, fraction of those that read their computer everyday = 15/25
Now, to find the number of people that read their computer everyday out of 1270 surveyed adults using the article fraction is;
15/25 * 1270 = 762 people
This represents the number of people that read their computer everyday
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Answer:
Step-by-step explanation:(:;44(()6)!