180 students voted for blue and 60 students voted for green
Solution:
Let "x" be the total number of votes
From given,
[tex]\frac{5}{8}[/tex] of the votes were for blue
[tex]Blue\ votes = \frac{5}{8}x[/tex]
Therefore,
[tex]Remaining = 1 - \frac{5}{8}x = \frac{8x-5x}{8} = \frac{3x}{8}[/tex]
Given that,
5/9 of the remaining students voted for green
So we get,
[tex]Green\ votes = \frac{3x}{8} \times \frac{5}{9} = \frac{5x}{24}[/tex]
[tex]Green\ votes = \frac{5x}{24}[/tex]
So we have now accounted for 5/8 (blue) + 5/24 (green) of the votes
Therefore,
[tex]Remaining = 1-(\frac{5x}{8} + \frac{5x}{24}) = 1 -(\frac{15x+5x}{24})= 1 -\frac{20x}{24} = \frac{24x-20x}{24}\\\\Remaining = \frac{4x}{24}\\\\Remaining = \frac{1x}{6}[/tex]
48 students voted for red
Therefore, remaining 1/6 votes for 48
Let "x" be the total number of votes
Then we can say,
1/6 of "x" is equal to 48
[tex]\frac{1}{6} \times x = 48\\\\x = 48 \times 6\\\\x = 288[/tex]
Number of votes for Blue:
[tex]Blue\ votes = \frac{5}{8} \times x = \frac{5}{8} \times 288\\\\Blue\ votes = 180[/tex]
Number of Green votes:
[tex]Green\ votes = \frac{5}{24} \times x = \frac{5}{24} \times 288\\\\Green\ votes = 60[/tex]
Thus 180 students voted for blue and 60 students voted for green
How to write 2.751 in word from
Answer: Two and Seven hundred fifty one thousanths
Step-by-step explanation:
Find the sum of the complex numbers
(2 + 4i) + (9 +61)
A. 7+ 101
B. 11 + 21
C. 7+21
D. 11 + 101
Answer:
11+10i
Step-by-step explanation: (a+ib) + ( x+ iy) = ( a+ x) +i( b+ y)
so, (,2+4i) + (9+6i) = (2+9) + (4+6)i
= 11 + 10i
A 17 minute telephone call from Boston to Chicago costs 2.38 what is the cost per minute?
Answer:
0.14
Step-by-step explanation:
As for 17-minute call = 2.38 cost
Thus per minute call which is 1 minute call is = 2.38/17 min
Therefore the answer is 0.14
Alan, Brady and Matt shared 740 marbles. Alan has 20 fewer marbles than Brady and 120 fewer marbles than Matt. How many marbles did Alan have?
Answer:
[tex]200 \ marbles[/tex]
Step-by-step explanation:
[tex]Let\ Alan\ have\ =x\ marbles\\Brady\ have = (x+20)\ marbles\\Matt\ have = . (x+120)\ marbles\\\\Total\ marbles = 740\\x+(x+20)+(x+120)=740\\x+x+20+x+120=740\\3x+140=740\\3x=740-140\\3x=600[/tex]
Dividing [tex]3[/tex] both sides.
[tex]\frac{3x}{3}=\frac{600}{3}\\\\x=200[/tex]
We solve the problem by setting up a linear equation based on the information given. We solve it to find that Brady has 260 marbles and then deduct or add from this number to find the number of marbles for Alan and Matt. Our answer is that Alan has 240 marbles.
Explanation:This problem involves solving linear equations in order to find the number of marbles each person has. Firstly, we need to represent each person's marbles in terms of the other person's marbles as given in the question.
Let's say Brady has 'b' marbles. From the problem, we deduce that Alan has 'b-20' marbles (20 less than Brady). We can also deduce that Matt has 'b-20+120' marbles (120 more than Alan).
Given that the total number of marbles is 740, we can set up the equation b + (b - 20) + (b - 20 + 120) = 740. Solving this linear equation, we get b = 260. Then, substituting b in the expressions for Alan and Matt will give us the number of marbles for each person, implying Alan has 260 - 20 = 240 marbles.
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Find the missing side length of m.
Answer:
m=4
Step-by-step explanation:
Since we know that quadrilateral ABCD is similar to QRST, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of m.
[tex]\frac{ST}{CD}=\frac{RS}{BC}\\\\\frac{6}{15} =\frac{m}{10}\\[/tex]
[tex]\frac{6*10}{15} =m\\m=60/15=4[/tex]
m=4
What are the coordinates of its image, J'KL, if this
triangle is dilated by a factor of 5 with respect to the
origin?
Answer:
[tex]J'(-15,10)\\\\K'(15,10)\\\\L'(0,-20)[/tex]
Step-by-step explanation:
For this exercise you must remember that the original figure (before a transformation) is called "Pre-Image" and the one obtained after the transformation is called "Image".
Dilation is defined as a transformation in which the Image and the Pre-Image have the same shape, but different sizes.
If a figure is dilated by a scale factor "k" with respect to the origin, the rule is:
[tex](x,y)[/tex] → [tex](kx,ky)[/tex]
In this case, the vertices of the triangle JKL (the Pre-Image) are:
[tex]J(-3.2)\\\\K(3,2)\\\\L(0,-4)[/tex]
Knowing that the scale factor is:
[tex]k=5[/tex]
You get that the vertices of the triangle J'K'L' (Image), are:
[tex]J'=(5(-3),5(2))=(-15,10)\\\\K'=(5(3),5(2))=(15,10)\\\\L'=(5(0),5(-4))=(0,-20)[/tex]
Answer:
J'(–15, 10), K'(15, 10), and L'(0, –20)
Step-by-step explanation:Glad I could help
Simon makes 30 cakes he gives 1/5 of the cakes to Sali. He gives 10 percent of the 30 cakes to Jane what fraction of the 30 cakes does he have left?
Answer:
7/10
Step-by-step explanation:
0.1 = [tex]\frac{1}{10}[/tex]
1/5
30 × 1/10 = 3
30 × 1/5 = 6
6+3 = 9
30 - 9 = 21
21/30 simplified = 7/10
Answer:
7/10
Step-by-step explanation:
Total number of cakes made by Simon = 30 cakes.
Number of cakes gave to Sali =
1/5 Of total cakes = 1/5 x 30 = 6 cakes.
Number of the cakes gave to Jane = 10% of 30 cakes
10/100 as a decimal 0.10.
10% of 30 cakes = 0.10 times
30 = 3 cakes.
Total number of cakes left = Total cakes made - Cakes gave to Sali - Cakes gave to Jane
30-6-3 = 21
21 cakes left.
21/30 = 7/10
A flower pot’s base has six sides that are all the same length. Each side measures
x−6
units. The base’s perimeter is 78 units. what is the value of x?
Since we know there are 6 sides and each side has the length of x-6, we set up this equation and solve:
6(x-6)=78
x-6=13
x=19
So the value of x is 19, which means each side has a length of 13 units.
Hope this helped!
What does 4 1/4 subtracted by 1 2/3 equal
Answer:
2
Step-by-step explanation:
Answer:
2.58333333333
Step-by-step explanation:
calculator
What is the perimeter of the 9-inch by 12-inch photo?
9+9+12+12.
24+18.
Answer? 42 inches
Answer:
The perimeter is 42 inches
Step-by-step explanation:
The perimeter is the sum of each side. So 9 + 9 + 12 + 12 = 42
You can also use the formula, w*2 + l*2 = P
Hope this helped! :)
if the numerator and the denominator of a fraction are both odd numbers,can you write an equivalent fraction with a smaller numerator and denominator?give an example to explain
You can write an equivalent fraction with a smaller numerator and denominator
Fractions
This is the ratio of two integers:
Let the odd numerator be 5 Let the odd denominator be 15We are to determine if you can write an equivalent fraction with a smaller numerator and denominator.
Ratio = 5/15
Simplify
Ratio = (5*1)/(5*3)
Ratio = 1/3
This shows that you can write an equivalent fraction with a smaller numerator and denominator
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if a=10 and b=2,then a/b•b=
a=10 & b=2, according to this, 10/2=5, so now it's 5*2=10
Convert 13200 feet into miles
Answer:
2.5 miles
Step-by-step explanation:
to do this, you must know that there is 5280 feet in one mile.
then divide 5280 feet into 13200
13200 ÷ 5280 = 2.5
13200 feet can be converted to miles by dividing the length in feet by the conversion factor of 5280, which represents the number of feet in a mile.
To convert feet to miles,
divide the length in feet by the conversion factor of 5280, as there are 5280 feet in a mile. By dividing 13200 feet by 5280, the results in 2.5 miles. This means that 13200 feet is equal to 2.5 miles in length.To convert 13200 feet to miles, divide 13200 by 5280.
[tex]13200 / 5280 = 2.5[/tex] miles.
13200 feet is equivalent to 2.5 miles
Therefore, 13200 feet is equivalent to 2.5 miles by dividing the length in feet by the conversion factor of 5280, which represents the number of feet in a mile.
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Write an equation in point-slope form for the line through the given point that has the given slope.
(5, –8); m = –3
Answer:
y=mx+b is the formula. So -8=-3x+5 would be the answer..
since (x,y) just substitute these numbers you have it into the formulas... Take y from (5,-8) and place it into y=mx+b. Next take the slope which is -3. And then since its a postive number we add are x from (x,y). -8=-3x+5. We also add x next to the slope (-3) becuase we are trying to solve for x. And we always put it next to the slope. Hope this helps!
Answer:
Step-by-step explanation:
hello :
note :
Use the point-slope formula.
y - y_1 = m(x - x_1) you have : m=-3 and x_1 = 5 and y_1 = -8
an equation in the point-slope is : y +8 = m(x - 5)
Find the Highest Common Factor of 32 and 24
Answer:
the highest common factor of 32 and 24 is 8.
Step-by-step explanation:
Which expression is equivalent to 210d2 - 63d
Answer:
21d (10d - 3)
Step-by-step explanation:
Factor 21d out of 210d² - 63d
I don't know if this answered your question correctly, but that is how I would solve it.
The expression is equivalent to 210d² - 63d is 21d( 10d - 3).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 210d² - 63d
now, factorizing each term of expression
210d² = 2 x 3 x 5 x 7 x d x d
-63d = -3 x 3 x 3 x d
So, 210d² - 63d
= (2 x 3 x 5 x 7 x d x d) - (3 x 3 x 7 x d).
= 21d (2 x 5 x d - 3 )
= 21d( 10d - 3)
Hence, the equivalent expression is 21d( 10d - 3).
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Find the value of x in this polygon.
x =
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
PLATO
The solution to which inequality is shown in the number line below
Answer:
Could you provide a picture of said number line
PLEASE HELP ME WITH THIS QUICK 1. What is the measurement of PQ
Answer:
12.72 units
Step-by-step explanation:
Recall the mnemonics: SOHCAHTOA
We want to find PQ, which is opposite to the 58° angle.
So we use the sine ratio: SOH , which means Sine is Opposite/Hypotenuse
[tex] \sin(58 \degree) = \frac{PQ}{15} [/tex]
This implies that:
[tex]PQ = 15 \sin(58) [/tex]
We substitute the value for sin58° to get:
[tex]PQ = 15(0.848)[/tex]
PQ=12.72
.. Tanner collected 360 cans and bottles while fundraising for his baseball team. This was
40% of what Reggie collected. How many cans and bottles did Reggie collect?
Answer:
Reggie collected 900 cans and bottles.
Step-by-step explanation:
360 ÷ 40 = 9
9 x 100 = 900
900 - 40% = 540
900 - 540 = 360
So, Reggie collected 900 cans and bottles. And between him and Tanner, they collected 1,260 cans and bottles. It must have been VERY dirty where they were collecting the cans and bottles.
3.541 ( repeating 41) as a simplified fraction
[tex]\boxed{x=\frac{1753}{495}}[/tex]
Explanation:The steps are as follows:
Step 1. Let's create an equation such that x equals the decimal number
[tex]x=3.5414141...[/tex]
Step 2. Let's multiply x by 100
[tex]10x=35.414141... \ \ \ eq 1[/tex]
Step 3. Let's multiply x by 1000
[tex]1000x=3541.414141... \ \ \ eq2[/tex]
Step 4. Subtract equation (1) from (2)
[tex]1000x-10x=3541.414141... - 35.414141... \\ \\ 990x=3506 \\ \\ x=\frac{3506}{990} \\ \\ Dividing \ both \ numerator \ and \ denominator \ by \ 2: \\ \\ \boxed{x=\frac{1753}{495}}[/tex]
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The fraction that represent the given repeating decimal number is [tex]\frac{3506}{990}[/tex].
The given repeating of decimal number is [tex]3.5\bar{41}[/tex].
The decimal number can be written as [tex]3.5414141......[/tex]
Take [tex]x=3.5414141......[/tex]---------(i)
Multiply equation (i) by 10, we get
[tex]10x=35.414141......[/tex] ---------(ii)
Multiply equation (i) by 1000, we get
[tex]1000x=3541.4141......[/tex] ---------(iii)
Subtract equation (ii) from (iii), we get
[tex]1000x-10x=3541.4141......-35.4141......[/tex]
[tex]990x=3506[/tex]
[tex]x=\frac{3506}{990}[/tex]
Therefore, the fraction that represent the given repeating decimal number is [tex]\frac{3506}{990}[/tex].
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There are 6 blue socks, 7 white socks, and 8 gray socks in a drawer. If you pick sock without looking, what is the probability it will be blue?
Answer:
Pr(blue) = 2/7
Step-by-step explanation:
Blue = 6
White = 7
Gray = 8
Total socks = 6+7+8 =21
Probability of picking blue = number of blue ➗ total number of socks
Pr(blue) = 6/21
Divide both by 3 to make the fraction to the lowest term.
Pr(blue) = 2/7
I hope this was helpful, please mark as brainliest
Answer:
2/7
Step-by-step explanation:
6 blue socks
7 white socks and
8 gray socks
Total number of socks = 6 + 7 + 8
= 21
Probability of picking a blue sock without looking = no of blue socks / total number of socks
That’s 6/21
= 2/7
The probability of picking a blue sock is 2/7
Algebra identify the pattern. Then write the next three terms in each sequence. 63,58,53,48.....
Answer:43, 38, 33
Step-by-step explanation:
The pattern is subtracting 5
63 -5 = 58
58 - 5 = 53
53 - 5 = 48
48 - 5 = 43
43 - 5 = 38
38 - 5 = 33
If A and B are independent events, P(A and B) =
Answer:
If A and B are independent events, P(A and B) = P (A) * P (B)
Step-by-step explanation:
Let's recall that independent events means that when one event occurs, it has no impact or influence on the probability of another event occurring. Here’s an example. Let’s say that we have two events, A and B.
Event A : it rains in Seattle
Event B : the Super Bowl match is cancelled in Miami
The two events are independent; if it rains in Seattle, this will have no impact on the probability that the Super Bowl match is cancelled in Miami. Raining in Seattle and the cancellation of the Super Bowl are independent events, therefore:
P(A and B) = P (A) * P (B)
What is the simplest form for 28 out of 32
Answer:
Ans = 7/8
Step-by-step explanation:
28 out of 32
= 28/32
Dividing through by 4
= 28/4 / 32/4
= 7/8
What sort of answer do you expect for the problem below?
In a team bike race, each biker has to ride exactly 50 miles. If a team must
complete 560 miles, at least how many bikers are on each team?
A. a positive number
O
O
B. a negative number
Answer:
it would be a positive number
Step-by-step explanation:
this is because you cant have a negative number of bikers.
Petra must write a report with more than 1,000 words for her history class. So far, she has written 684 words. Write and solve an inequality to find how many more words Petra needs to write for her report.
Answer:
1684 words
Step-by-step explanation:
What is 10 2/6 minus 7 3/6
Answer:
2 5/6
Step-by-step explanation:
10 2/6 - 7 3/6
10 - 7 = 3
2/6 - 3/6 = -1/6
3-1/6 = 2 5/6
PLEASE HELP QUICK!!!!
Answer:
Step-by-step explanation:
ABC = 72 degrees
CBF = 108 degrees
DBE = 18 degrees
ADB = 90 degrees
120% of x is equal to 78.
Write an equation that shows the
relationship of 120%, x, and 78.
Use your equation to find x. Show
your reasoning.
Please help
Answer:
x = 65
Step-by-step explanation:
120% converts to the mixed decimal quantity 1.20.
Then 1.20x = 78, and this can be solved for x as follows:
Divide both sides by 1.20. We get: x = 78/1.20, or x = 65
Answer:
Step-by-step explanation: