The process of solving a proportion is given below.
We are given that;
To show the process of solving a proportion
Now,
A proportion is an equation that states that two ratios are equal. For example, if we have 2 4 = 3 6[tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {3} {6}}}[/tex] , then we have a proportion.
To solve a proportion, we need to find the value of a missing term that makes the equation true. There are different methods to solve a proportion, but one common method is cross-multiplication. Here are the steps to solve a proportion by cross-multiplication:
Multiply the numerator of one ratio by the denominator of the other ratio.
For example, if we have 2 4 = x 6
[tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}[/tex] , then we multiply 2 by 6 and get 12.
Multiply the denominator of the first ratio by the numerator of the second ratio.
For example, if we have 2 4 = x 6
[tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}[/tex] , then we multiply 4 by x and get 4x.
Set the two products equal to each other. For example,
if we have [tex]2 4 = x 6 {\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}[/tex], then we set 12 = 4x.
Solve for the missing term. For example, if we have 12 = 4x, then we divide both sides by 4 and get x = 3.
Check your answer by plugging it back into the original proportion.
For example, if we have x = 3, then we plug it back into 2 4 = x 6 [tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}[/tex] and get 2 4 = 3 6
[tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {3} {6}}}[/tex] , which is true.
Therefore, by proportion answer will be given below.
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At Cascadia College, students need to take a 100 level Math and English courses plus an optional Philosophy course. In any quarter, the college needs to make available 4 less English sections than Math sections. In any quarter student demand for the optional Philosophy course is half as many sections as English sections. Available classrooms limit the total sections of all three courses to 44
Given these constraints how many sections of each course should the college make available each quarter to meet demand?
Math sections =
English sections =
Philosophy sections =
Answer:
Math sections = 20
English sections = 16
Philosophy sections = 8
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of Math sections.
y is the number of English sections.
z is the number of Philosophy sections.
Available classrooms limit the total sections of all three courses to 44.
This means that [tex]x + y + z = 44[/tex]
4 less English sections than Math sections.
This means that [tex]y = x - 4[/tex]
In any quarter student demand for the optional Philosophy course is half as many sections as English sections.
This means that [tex]z = \frac{y}{2} = \frac{x - 4}{2}[/tex]
Finding the number of Math sections:
We have both y and z as functions of x. So
[tex]x + y + z = 44[/tex]
[tex]x + x - 4 + \frac{x-4}{2} = 44[/tex]
[tex]2x + \frac{x-4}{2} = 48[/tex]
Multiplying everything by 2
[tex]4x + x - 4 = 96[/tex]
[tex]5x = 100[/tex]
[tex]x = \frac{100}{5}[/tex]
[tex]x = 20[/tex]
Then
[tex]y = x - 4 = 20 - 4 = 16[/tex]
[tex]z = \frac{y}{2} = \frac{16}{2} = 8[/tex]. So
Math sections = 20
English sections = 16
Philosophy sections = 8
A 4th grade class took a field trip to a science museum. There are 24 students in the class. Each students purchased $9 ticket for the museum and a box lunch, which was also $9.
Answer:
the nerd above me was wrong its 500 lol don tlisten to nerd ok
Step-by-step explanation:
big brain lol
What is the total length of all meteors that are 1 6/8 inches?
3 4/8
3 5/8
4 7/8
3 7/8
Anwser: Hitler was the first person to get a 100 bomb IRL
Explenation: Took me 900 years to figure this out
Help please this is urgent
Answer:
64 degrees
It says I have to have over twenty characters. this sentence does not have to be read
Answer:
it should be 64 if i am seeing it correctly
Step-by-step explanation:
its before 66 so the lowest one is 64
Find the distance between the points (5,-6), (-3,12)
Answer:
[tex]\displaystyle d = 2\sqrt{97}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (5, -6)
Point (-3, 12)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(-3-5)^2+(12+6)^2}[/tex][√Radical] (Parenthesis) Subtract/Add: [tex]\displaystyle d = \sqrt{(-8)^2+(18)^2}[/tex][√Radical] Evaluate Exponents: [tex]\displaystyle d = \sqrt{64+324}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{388}[/tex][√Radical] Simplify: [tex]\displaystyle d = 2\sqrt{97}[/tex]Taliyah plans to borrow $4500 from the bank to purchase a used vehicle. If she borrows the money at a rate of 4% simple interest for 2 years, what is the total amount she will have to pay back to the bank
Answer:
$4860
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year,
then, solving our equation
I = 4500 × 0.04 × 2 = 360
I = $ 360.00
The simple interest accumulated
on a principal of $ 4,500.00
at a rate of 4% per year
for 2 years is $ 360.00.
Answer:
2250
Step-by-step explanation:
you times 4500 with 2 and get 9000. Then, you take the 9000 and divide it by 4 and get 2250.
what is the distance between -14 and 36 feet
Answer:
Your awnser is 50
Step-by-step explanation:
Have a great day! :D
Answer:
50
Step-by-step explanation:
because if you look on a line graph -14 then it takes 14 feet to get it to 0 then 36 more to get it even with 36 then add 14 and 36 and u get 50
Tengo 618 galletas que repartí , puse 3 galletas en cada bolsa , cuantas bolsas utilize ?
Please find this answer!
Answer:
52
Step-by-step explanation:
what does 4/6 + 2/5 equal
Answer:
= 16 /15 (Decimal: 1.066667)
Step-by-step explanation:
4 /6 + 2 /5
= 4 /6 + 2 /5
= 2 /3 + 2 /5
= 10 /15 + 6 /15
= 10+6 /15
= 16 /15 (Decimal: 1.066667)
Answer:
16/15 or 1 1/15 as a mixed number
Step-by-step explanation:
Which number line best represents the solution to the inequality
3.3 w - 9 > -22.2?
Answer:
Step-by-step explanation:
3.3w - 9 > -22.2
3.3w > -13.2
w > -4
The number line w + 4 = 0 best represents the solution to the inequality
3.3 w - 9 > -22.2
What is a linear inequality?A linear inequality represents all the possible values of a linear variable.
Given,
3.3 w - 9 > -22.2
or 3.3 w > -22.2 + 9
3.3 w > -13.2
w > -13.2/3.3
w > -4
Hence, the required line is w + 4 = 0 .
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WILL GIVE BRAINIEST
Hank has read 25 percent of his book. If Hank has read 150 pages, which equation can be used to find the total number of pages in the book?
Answer:
Multiplication (150x4=600 25x4=100%)
Answer:
\frac{25}{100} \times x = 150
So,
x = \frac{150 \times 100}{25} = 600
Hank will use this equation.
Ans: A total of 600 pages are in the book.
Step-by-step explanation:
Factor the expression below.
4x2 - 1
If $2000 is invested at 4% interest compounded monthly, the value of the investment after t
years is given by the expression below. What is the value of the investment after 3.5 years?
2000(4)
. Simplify: (-4a+ b–2c) –(3a+ 2b–c)
Answer:
(-4a + b – 2c) – (3a + 2b –c)
-4a+b-2c-3a-2b+c
-7a-b-c
Step-by-step explanation:
The measure of angle STV is 160. The measure of angle STW is 105. The measure of angle WTV is x. Find the value of x
if someone could explain to me how to do this
You are the forecaster responsible for hurricane warnings on the southeast corner of the United States in September. Anyone that has lived in North Carolina for a while knows what is it is like at that time of the year, for example. The cost of issuing a warning like a hurricane involves people taking shelter, business stopping, the areas's economy paused - a moderate cost of C dollars. You also know the preventable loss should a hurricane come and the area be unprepared: property damage, lives lost -an extremely high loss of L dollars. Your weather forecast indicates hurricane with a probability of p.
(a) Should you issue a warning? Use expectations to create a decision rule for whether issuing or not a warning. Explain your rule.
(b) For what kind of extreme weather warnings is the decision more likely to be "do not warn" than "warn"? Explain.
Answer:
A)
C ≤ LP issue warning
C > LP do not issue warning
B )
For ' do not warm ' the condition will be that C is moderate while L is extremely high
Step-by-step explanation:
Assuming Y is an indicator that represents if a warning is issued or not
probability of occurrence of Hurricane = p
where; C = cost of issuing a warning
L = cost incurred for not issuing warning
A) Determine if you should issue a warning or not
In this scenario there are about four possible cases
'do not warn' , ' Hurricane did not occur ' : ( 1-y) ( 1-p)' do not warn ' , ' Hurricane occurred ' : ( 1-y ) p ' warn' , ' Hurricane did not occur' : y ( 1-p)' warn', ' Hurricane occurred' : y (p)hence the expected cost ( E ) = L ( 1 - Y )p + Cy
when warning is issued = Y ( 1 )
expected cost ( E ) = C
assuming warning is not issued then Y = 0
hence expected cost ( E ) = LP
Hence the decision rule will be :
C ≤ LP issue warning
C > LP do not issue warning
B) For ' do not warm ' the condition will be that C is moderate while L is extremely high ( as seen in the question ) because this will make C/L to be very small. from the condition C > LP and this simply means that the probability of the Hurricane occurring is very small
What is 2/9 + 7/9 + 6/9 equal to
Answer:
15/9
Step-by-step explanation:
2/9+7/9+6/9
2×1, 7×1,6×1
2/9,7/9,6/9=15/9
If u want u can devide it
To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
First equation: 6x-5y=17
Second equation: 7x+3y=11
The first equation should be multiplied by 3 and the second equation by -5.
The first equation should be multiplied by 3 and the second equation by 5.
The first equation should be multiplied by 7 and the second equation by -6.
The first equation should be multiplied by 7 and the second equation by 6.
Answer:
C. The first equation should be multiplied by 7 and the second equation by -6.
Step-by-step explanation:
have a great day peeps :)
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The correct option is C.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
In the two of the given equation, to eliminate x we need to make the coefficients of x in both the terms equal, therefore, if we take the LCM of the two terms then it will be 42.
Thus, to make the coefficient of x equal to 42, we need to multiply the first equation should be multiplied by 7 and the second equation by -6.
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At a toy story,Colton can buy a passage of 8 mini footballs for 10.40. The price per mini football is $ ?
Answer:
The 8-pack is a better value
Step-by-step explanation:
Suppose you make hot chocolate. It's too hot to drink, so you put it in the freezer to cool it off. If the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit, what will the temperature of the hot chocolate be after 3 minutes? (k = 0.12)
A 132.56 degrees
B 272.33 degrees
C 149.46degrees
D 241.54 degrees
Need help please ..
Answer:
x = -11
Step-by-step explanation:
I'm assuming it's an isosceles triangle so 32 + 2x = 10;
subtract 32 from both sides;
2x = -22
x = -11
SOMEBODY HELP ME PLS? Anyone? :D
Answer:
Angle B is congruent to angle C
I need help factoring something
Answer:
x^4
Step-by-step explanation:
Hope this is right ! :)
This is very important and I need HELP!
Answer:
A
Step-by-step explanation:
1/144
.......... .......
Answer:
A
Step-by-step explanation:
What is 8/9 times 1/2
Answer:
4/9
Step-by-step explanation:
8*1/9*2 = 8/18=4/9
Answer:
0.4444444444444(repeating)
Step-by-step explanation:
good luck on your homework/test!
ASAP
What is the multiplicity of the root (x^3-1)?
What is the equation of a line, in general form, with a slope of -2 and a y-intercept of 8?
x + 2y - 8 = 0
2x + y - 8 = 0
2x - y + 8 = 0
[tex]2x+y-8=0[/tex].
Find cosX and cosZ. Write each answer as a fraction and as a decimal. Round to four decimals places, if necessary. Fractions to reduce and use /.
Answer/Step-by-step explanation:
Recall the acronym, SOHCAHTOA.
✔️Cos X = adj/hyp (CAH)
Adj = 10
Hyp = 26
Cos X = 10/26
Simplify
Cos X = 5/13 (as a fraction)
Cos X = 0.3846 (as a decimal to 4 d.p)
✔️Cos Z = adj/hyp (CAH)
Adj = 24
Hyp = 26
Cos Z = 24/26
Cos Z = 12/13 (as a fraction)
Cos Z = 0.9231 (as a decimal to 4 d.p)