In this exercise we have to explain the three possible methods of solving a proportion, as follows:
1) Vertical
2)Horizontal
3)Diagonal
What is proportion?It is the equality between two or more ratios derived from measurements extracted from quantities. When two ratios have the same result, we say they are proportional. If these ratios represent measures of some magnitude, we also say that they are proportional.
So we know that a proportion is given by the equality between two ratios and the resolution process consists of the following situation: “the product of the extremes is equal to the product of the means” or using the eventual cross multiplication.
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Shaun read 60 pages in 3/4 h. What is the unit rate that represents the number of pages Shaun can read in 1 h? Enter your answer in the box.
If Shaun read 60 pages in [tex]\frac{3}{4} $ h[/tex], the number of pages Shaun can read in 1 hour (unit rate) using proportion is: 80 pages (80 pages in 1 hour).
Given:
Number of pages Shaun read in 3/4 h = 60 pages
Thus, to find the unit rate that represents number of pages to be read by Shaun in 1 hour,
let x = number of pages read in 1 hour.
The following proportion would be created:
60 pages = 3/4 h
x pages = 1 h
Cross multiply[tex]\frac{3}{4} \times x = 1 \times 60\\\\\frac{3x}{4} = 60[/tex]
Multiply both sides by 4[tex]3x = 60 \times 4\\\\3x = 240\\\\[/tex]
Divide both sides by 3x = 80
Therefore, if Shaun read 60 pages in [tex]\frac{3}{4} $ h[/tex], the number of pages Shaun can read in 1 hour (unit rate) using proportion is: 80 pages (80 pages in 1 hour).
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How do you write 6.67 × 102 in standard form
Standard form refers to the regular way you write out a number, such as 4,300, as opposed to scientific notation, which is 4.3 x 10^3, or in expanded form, such as 4,000 + 300. You can convert numbers large and small to standard form in a few steps.
STANDARD FORM WITH LARGE NUMBERSTo convert a number from scientific notation to standard form, consider 1.5625 x 10^4. First, focus on the exponential number, which is 10^4. Multiply the base number, which is 10, by itself the number of times indicated by the exponent, which is four. You would do that like this:
10 x 10 x 10 x 10 = 10, 000
Plug the product -- which is 10,000 -- into the original equation to get this:
1.5625 x 10,000 = 15, 625
Therefore, the standard form of this number is 15,625.
For a number in expanded form, convert the number, using basic addition. For example, consider the expanded number 10,000 + 2000 + 100 + 10 + 9. Add up these numbers to get the standard form. Your equation would look like this:
10,000 + 2,000 + 100 + 10 + 9 = 12,119
Therefore, the standard form of the number is 12,119.
STANDARD FORM WITH SMALL NUMBERSSmall numbers, such as those less than one, can also be converted to standard form. For example, consider the scientific notation 5 x 10^-2. Start with 10^-2, and note that the exponent is negative, which in this case, is negative two. This indicates that the number will be a decimal, with the decimal point moving twice to the left of the base number, which in this case, is 10. This would give you 0.01. Your equation will look like this:
10^2-1 = 0.01
Plug in this value, which, in this case is 0.01, into your original equation to get this:
5 x 0.01 = 0.05
Therefore, the standard form of this number is 0.05.
Convert small numbers presented in expanded form, such as 0.0003 + 0.001 + 0.02 by adding like this:
0.0003 + 0.001 + 0.02 = 0.0213
In 2009, John paid $7,890 in federal income tax. In 2010, he paid 50% less. How much did John pay in 2010?
what is the perimetee of a square with the area of 121
Twelve more than three times a number equals two times the number. What is the number?
nasir has an annual salary of $64000, and his company pays him twice a month. What is the gross income per paycheck that Nasir receives
Answer:
2666.67 dollars.cents
simplify:
-4x^2(3x-7)
-7(k+9)=9(k-5)-14K
( Show work please )
What is the answer to a and b please and thank you
Arturo mixed together 1.24 pounds of pretzels, 0.78 pounds of nuts, 0.3 pounds of candy, and 2 pounds of popcorn. He then packaged it in bags that each contained 0.27 pounds. How many bags could he fill?
Answer:
Number of bags Arturo can fill = 16
Step-by-step explanation:
Arturo mixed together 1.24 pounds of pretzels, 0.78 pounds of nuts, 0.3 pounds of candy, and 2 pounds of popcorn
Total pounds of mix = 1.24 + 0.78 + 0.3 + 2 = 4.32 pounds
He then packaged it in bags that each contained 0.27 pounds.
Capacity of each bag = 0.27 pounds
[tex]\texttt{Number of bags he can fill =}\frac{\texttt{Total pounds of mix}}{\texttt{Capacity of each bag}}\\\\\texttt{Number of bags he can fill =}\frac{4.32}{0.27}\\\\\texttt{Number of bags he can fill =}16[/tex]
Number of bags Arturo can fill = 16
A line contains the points (−26, −37) and (−32, −61) .
What is the slope of the line in simplified form?
Enter your answer in the box.
Answer:
The slope of the line containing the points (-26,-37) and (-32,-61) is 4
Step-by-step explanation:
Given:
Two points of the line (-26,-37) and (-32,-61)
To find:
Slope(m) of the line =?
Solution:
The Equation of slope of two points is
[tex]Slope m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Let (-26,-37) be[tex](x_1,y_1)[/tex]
and (-32,-61) be [tex](x_2,y_2)[/tex]
Now substituting the values ,
[tex]m=\frac{(-61+37)}{(-32+26)}[/tex]
[tex]m=\frac{-24}{-6}[/tex]
m=4
Thus the slope of the line is 4
A gym holds one 60-minute exercise class on Saturdays and several 45-minute classes during the week. Last week all of the classes lasted a total of 285 minutes. Write an equation you can use to find the number of weekday classes.
Jon and Lexi are playing a marble game. According to their rules, 6 points are awarded for each red marble collected and 2 points are awarded for each blue marble collected. Which expression represents Jon's total score if he has r red marbles and b blue marbles? 6r − 2b 6r + 2b 6r − 4b 8rb
1. 6 points are awarded for each red marble collected, then for r red marbles collected are awarded 6r points.
2. 2 points are awarded for each blue marble collected, then for b blue marbles collected are awarded 2b points.
3. If he has r red marbles and b blue marbles collected, then in total Jon has score 6r+2b.
Answer: correct choice is B.
What is the equation of a line, in point-slope form, that passes through (−2, −6) and has a slope of 13 ?
y+2=13(x+6)
y−6=13(x−2)
y+6=13(x+2)
y−2=13(x−6)
30 pts
plz help need to get an a or i die by my mom :P
The equation of the line in point-slope form that passes through (-2, -6) and has a slope of 13 is y + 6 = 13(x + 2).
Explanation:The equation of a line in point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
To find the equation of the line that passes through (-2, -6) and has a slope of 13, we can substitute the values into the formula:
y - (-6) = 13(x - (-2))
Simplifying this equation, we get y + 6 = 13(x + 2). Therefore, the correct equation of the line in point-slope form is y + 6 = 13(x + 2).
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Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3).
The rate of change is −1/3, and the y -intercept is 7 1/3
The rate of change is –3, and the y -intercept is 18.
The rate of change is 3, and the y -intercept is –6.
The rate of change is 1/3, and the y -intercept is 4 2/3
the line parallel to x-3y=-12 that passes through (-3,4)
The equation of the line parallel to x-3y=-12 that passes through (-3,4) is y=x/3+5.
What is the standard equation of a line?The standard equation of a line is given by
y = mx+c
Here m is the slope and c is the y intercept
The slope can be determined by
m = (y₂ -y₁)/(x₂ -x₁)
The line function equation is
x - 3y = -12
y = (1/3)x +4
When a line is parallel to another line, the slope of the lines is same.
So, the slope of the line parallel to the line x - 3y = -12 is 1/3
y = (1/3)x +c
As the line passes through the point (-3,4)
4 = (1/3) * (-3) +c
4 = -1 +c
c = 5
The equation is
y=x/3+5
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(4 - 1)[(1 + 6) + 2]
the sum of two integers is 6 create a list of the possible two integers
John has a bag of marbles that contains 12 red marbles, 20 green marbles, and 17 blue marbles. Homework Help ✎ If John pulls one marble out of the bag, what is the probability that it will not be red? That is, P(not red)?
Write the value of the digit of 281'480'100
please help , I have no idea of how to do this
if the length and width of a rectangle quadruple what happens to the area
The area of the rectangle becomes 16 times the previous one.
Given that,
The length and width of a rectangle quadruple what happens to the area is to be determined.
the rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
What is surface area?Surface area is defined as the area of the surface that is uncovered.
Here,
The length(L) = 4 L
The width (W) = 4W
area of the rectangle = length * width = LW
The new area of the rectangle = 4L * 4W
= 16 LW
= 16 * area of the rectangle.
Thus, the area of the rectangle becomes 16 times the previous one.
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How are ratios, rates, and unit rates used to solve problems?
Who ever helps will get 15 points and a thanks what are some ways you could break apart 7✖️9 using distributive property Tks and u will win your reward
The x-intercept is the x-coordinate of the point where a graph crosses the x-axis.What is the slope of a line that has a y-intercept but no x-intercept?Explain.
Answer:
slope = 0
Step-by-step explanation:
Given that the line has no x intercept. This means that the line does not intersect the x-axis at all. This can happen only if the line is parallel to the x axis. The line does have a y intercept. Si the line does intersect the y axis.
When a line is parallel to the x axis, its slope is 0.
Expressing the equation of the line in intercept format :
y = mx + c , where m is the slope and c is the intercept
In this case, the slope m is 0 .
So the equation becomes y = c.
add two fractions to determine the fraction equal to 0.1545454
To add two fractions, convert the decimal fraction to a proper fraction by placing the decimal part over an appropriate power of 10. Then, find a common denominator and add the fractions together. Finally, simplify the resulting fraction if possible.
Explanation:Addition of FractionsTo add two fractions, you need a common denominator. Since the given fraction is a decimal, you can convert it into a fraction by placing the decimal part over the appropriate power of 10. In this case, 0.1545454 can be written as 1545454/10000000. Now, find a common denominator between the two fractions and add them together.
For example:
Convert the given fraction to 1545454/10000000.Find a common denominator, such as 100.Convert both fractions so they have the same denominator, in this case 100, by multiplying the numerator and denominator of each fraction by appropriate factors.Add the numerators together and write the sum over the common denominator.Simplify the fraction if possible.By following these steps, you can determine the fraction equal to 0.1545454.
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what is the greatest common factor of x2y and xy2 ?
BTW, the twos are supposed to be small and in the top right corner of the number before it, but it won't let me put it there.
One hundred employees of a company are asked how they get to work and whether they work full time or part time. The table below shows the results. If one of the 100 employees is randomly selected, find the probability that the person drives alone or bicycles to work.
public transportation: fulltime-9 parttime-8
bicycle: fulltime-3 parttime-4
drive alone:fulltime-32 parttime-28
carpool:fulltime-9 parttime-7
Answer:
0.67
Step-by-step explanation:
There are 3+4 = 7 people who bicycle to work. There are 32+28 = 60 people who drive alone to work. This makes 7+60 = 67 people.
This makes the probability 67/100 = 0.67.
The probability that the person drives alone or bicycles to work is 0.67
What is probability?Probability is a measure of the likelihood of a statement or a theoretical expectation is correct.
Given that, 100 employees of a company are asked how they get to work and whether they work full time or part-time,
People who drive bicycle to work = 3 + 4 = 7
People who drive alone to work = 32 + 28 = 60
People who drive alone or with bicycle = 7 + 60 = 67
The probability that the person drives alone or bicycles to work = 67/100 = 0.67.
Hence, The probability that the person drives alone or bicycles to work is 0.67
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A number cube will be rolled 100 times as part of an experiment. Which calculation would you use to predict the number of times a 4 will be rolled?
Answer:
(100) (1/6)
A cube has six sides the odds of rolling a four is 1 in 6 and you rolled a 100 times
∠A
and
∠B
are vertical angles with
m∠A=x
and
m∠B=4x−30
.
What is
m∠A
?
Answer:
m∠A=10°
Step-by-step explanation:
we know that
Vertical angles are the angles opposite each other when two lines cross. The angles are congruent.
so
In this problem we have
m∠A=m∠B
substitute the given values
[tex]x=4x-30[/tex]
Solve for x
[tex]4x-x=30\\3x=30\\x=10[/tex]
Find the measure of angle A
m∠A=x
substitute the value of x
m∠A=10°