Answer:
floor seats=35
and the balcony seats =72
Step-by-step explanation:
Step one
given data
let the floor seats be x
and the balcony seats be y
so
45x+25y=3375-------1
x+y= 107----------------2
from 2, x= 107-y
put x= 107-y in 1
45(107-y)+25y=3375
4815-45y+25y=3375
collect like terms
-45y+25y= 3375-4815
-20y=-1440
divide both sides by -20
y=72
put y= 72 in eqn 2
x+72=107
x=107-72
x=35
When Colby was born, his parents invested $1,000 in a fund that paid an
annual interest of 8%. How old will Colby be when the investment is worth
at least $4,000?
Given :
When Colby was born, his parents invested $1,000 in a fund that paid an
annual interest of 8%.
To Find :
How old will Colby be when the investment is worth at least $4,000 .
Solution :
Let, time taken is x years.
So, the formula is :
[tex]P = A_o + \dfrac{A_o \times r\times t}{100}\\\\4000 = 1000 + \dfrac{1000\times 8\times t}{100} \\\\80t = 3000\\\\t = \dfrac{3000}{80} \ years\\\\t = 37.5\ years[/tex]
Therefore, Colby will be 37.5 years old.
The age of Colby will be [tex]37.5[/tex] years.
Simple interest :The amount after t years is given by,
[tex]A=P+(\frac{P*r*t}{100} )[/tex]
Where P is principal, r is rate and t is time in years.
Given that, [tex]A=4000,P=1000,r=8\%[/tex]
Substitute values in above equations.
[tex]4000=1000+\frac{1000*8*t}{100} \\\\\frac{1000*8*t}{100}=3000\\\\t=37.5years[/tex]
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What are the answers to the last two questions?
Answer:
1. (-1)(x^2+x-6)
2. (-1)(x+3)(x-2)
Step-by-step explanation:
Factoring
It's given the trinomial
[tex]-x^2-x+6[/tex]
1. There is no common factor (given).
2. Factor out -1:
Each term is divided by -1:
[tex]\mathbf{(-1)(x^2+x-6)}[/tex]
3. Now we factor the remaining trinomial. We find two numbers whose sum is 1 and the product is -6. These are 3 and -2, thus the trinomial is:
(-1)(x+3)(x-2)
what is an equation of the line that passes through the point (-6,-1) and is perpendicular to the line 6x-y=7? (has to be in y=mx+b form)
Answer:
y = [tex]-\frac{1}{6}[/tex] x - 2
Step-by-step explanation:
Slopes of perpendicular lines are opposite reciprocals.
If AB ⊥ CD , then [tex]m_{AB}[/tex] [tex]m_{CD}[/tex] = - 1
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
~~~~~~~~~~~
6x - y = 7 ⇔ y = 6x - 7
Slope of given line is 6
Slope of a perpendicular line is [tex]-\frac{1}{6}[/tex]
( - 6, - 1 )
y + 1 = [tex]-\frac{1}{6}[/tex] (x + 6)
y = [tex]-\frac{1}{6}[/tex] x - 2
NEED HELP WITH THIS
Answer:
Step-by-step explanation:
think of this as a system of equations where the colors just represent a variable like x or y
I'll just arbitrarily set colors to some variable letter so we have
purple = x
green =y
blue =z
red = a
yellow = b
so we can now rewrite the 4 known equations of the system :)
Eq. 1) x+y = 13
Eq. 2) 2y+2z=18
Eq. 3) 2x+3y=31
Eq. 4) z + 4a = 12
Eq. 5) a * y = b
so solve the 1st eq for y => y =13-x then plug that into the 3rd eq and slove for x => 2x + 3(13-x) =31
2x + 39 -3x = 31
2x-3x = 31 - 39
-x = -8
x=8
plug 8 into Eq. 1 for x and solve for y
8+y = 13
y=5
plug y into Eq 1 and solve for z
2(5) +2z = 18
10 +2z = 18
2z = 8
z = 4
plug z into E1 4 and solve for a
4 + 4a = 12
4a = 8
a = 2
plug a and y into Eq 5 and solve b
2 * 5 = b
10=b
go to the drawing and plug in each of the color values that we put as variable letters above and get an A+ on your homework.. :)
A recent poll found that 76% of a random sample of 100 American movie goers thought the popcorn sold at the movie theatre was overpriced.
If the sample size was increased to 10,000 American movie-goers, what effect would this have on the estimated percentage of American movie-goers who
think the popcorn is overpriced?
Answer:
Step-by-step explanation:
Given that:
percentage of sample proportion = 76%
sample size = 100
Given that the sample proportion estimate is unbaised of the population proportion, then the percentage of all American movie-goers who think popcorn is overpriced is = 76%. Also, the mean of the sampling distribution appears to be independent of the sample size. Then, the estimate of the percentage will equally remain the same regardless it is even a sample of size 10000.
I don’t understand someone please help ! In the bottom it says follow the steps above to find the equation of these two trend line
1.(x2 , y2) =(3,12 ) ( x1 , y1) =(-6,-6)
2.(x 2 , y2 ) =(2,7 ) ( x1 ,y1) =(-2,-5)
Answer:
I really dont know
Step-by-step explanation:
Answer:
step below
Step-by-step explanation:
1. (0,9) (9,0) or (7,2) or (1,8)
2. m = rise/run = (0-9) / (9-0) = -1
3. y = mx + b for point (9,0)
y intercept ( b) = y - mx = 0 - (-1)*9 = 9
4. equation for trend line: y = -x + 9
check use (7,2): 2 = -7 + 9
PLS HELP MY HWS DUE IN 30 MINS AND PLS SHOW WORK TY
find each missing measure
m
m
Answer:
measure is the angle right- if so it's 76 each
180-28=152
152÷2=76
HELP ME!! I NEED SERIOUS HELP RN!
Answer:
hii, ok so (3, 2)
Step-by-step explanation:
Just imagine the dot at (3, -4). Now just go up 6 units. **i added a picture, its kinda junky, sorry**
#9 Can anyone please help me, this is Pythagoras Theorem Converse.
Answer:
(D).
Step-by-step explanation:
[tex]A_{b}[/tex] = A + [tex]A_{s}[/tex]
(A). 12 + 16 > 20
(B). 10 + 18 < 30
(C). 4 + 5 < 12
(D). 8 + 16 = 24
Suppose there is a game of chance that you would like to play. It costs $3 to play one time. There are 100 $1 bills, 20 $5 bills, 3 $20 bills, and 1 $100 bill in a box. You may reach into a box without looking and select one bill. Is this a fair game? Why or why not?
Answer:
1. It is not a fair game.
2. The game is not fair because the probability of winning and the probability of losing are not equal. In a fair game, the probability of winning is equal to the probability of losing. In this game, the probability of losing is 0.81 or 81%, while the probability of winning is 19% (100 - 81).
Step-by-step explanation:
Cost of playing the game one time = $3
Total number of bills in the box = 124 (100+20+3+1)
Chance of losing is represented by 100 of $1 bills = 100/124 = 0.81 or 81%
Chances of losing are represented by 20 of $5 bills, 3 of $20 bills, and 1 $100 bill = 0.19 or 19% (20/124 + 3/124 + 1/124).
PLS HELP NEED ANSWER ASAP PLSSSS
Eva left her home and drove for 4.3 hours due north at a rate of 60 miles per hour. After visiting a beach, she drove due south for 3.4 hours at 55 miles per hour.
How many miles is Eva from her home?
Answer:
166
Step-by-step explanation:
Jasmine sold half of her Barbie doll Collection
and then bought 9 dolls. She now has 13 dolls.
Barbie dolls did she begin with?
How many
Number 2 please , and if you can explain it too that would be helpful but if not it’s okay:)
Answer:
CI = 6,IA = 8
Step-by-step explanation:
I cant explain it no further
In the equation y=4 over 3 x +5 what is the slope and y-intercept
Answer:
Slope = [tex] \frac{4}{3} [/tex]
Y-intercept = 5
Does (3,4) satisfy the equation-5x + 2y = 23?
Answer:
[tex] - 5x + 2y = 23 \\ when \: \: x = 3 \: and \: y = 4 \\ = - 5(3) + 2(4) \\ = - 15 + 8 \\ = 7 \\ no \: it \: doesnot \\ \\ \\ if \: equation \: is \: 5x + 2y = 23 \\ = 15 + 8 \\ = 23 \\ hence \: it \: satisfies[/tex]
a carton of ice cream sold for $2.20 was on sale for 45% off. what was the original price of the ice cream?
Answer:
It was originally sold at roughly $4.887
Step-by-step explanation:
1) 2.20/.45 ≈ 4.8
2) 4.8 x .45 = 2.16
3) 4.88 x .45 = 2.196
4) 4.887 x .45 = 2.19915
The original price of the ice cream is $4.8
What is the discount price?Discounting a product means offering it at a lower price than the list price.
Given that, a carton of ice cream sold for $2.20 was on sale for 45% off.
Let the original price of the carton be x.
x*45% = 2.20
x = 2.20*100/45
x = 4.8
Hence, the original price of the ice cream is $4.8
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please someone help me
Answer:
-16
Step-by-step explanation:
-8(x+2)=24 x= -5
-8x + (-16) = 24 x= -5
-8*x = -8x
-8*2= -16
WRITE AN EQUATION THAT MODELS EACH STATEMENT :
John is five years more than twice as old as his sister :
Step-by-step explanation:
Take John's sister's age as "x"
So, so twice his sister's age means = 2x
And 5 years more, means = 2x + 5
So finally John's age = 2x + 5
Answer:
y=2x+5
Step-by-step explanation:
Cathy has n CDs Gerry has 3 more than twice the number of CDs that cathy has. in terms of n, how many CD does Gerry have?
Answer:
I think this would be 2n+3
Step-by-step explanation:
I learned this in class and I think that since you Gerry has twice the number of CDs (n) + 3, it would be 2n+3. I'm in middle school though, so I don't know if in highschool there's another step, but I hope this helps! :)
___________: next to or adjoining to something else.
Hey there!
The correct answer is adjacent.
The exact definition in the Oxford dictionary is "next to or adjoining something else."
Hope it helps and have a great day!
P.S. A picture of adjacent angles is below, you can see they are adjacent because they are connected.
Your receipt for your visit at a restaurant is
shown below. If you leave a 15% tip, what is the
new total amount? Explain your method.
pls hurry
Answer:
36.66
Step-by-step explanation:
Basically you just find the tip 4.782 and add it to 31.88 the total. 36.662 and then round to to get 36.66.
Answer:
36.66
Step-by-step explanation:
Basically you just find the tip 4.782 and add it to 31.88 the total. 36.662 and then round to to get 36.66.
Velma is analyzing spending habits of the gang. She find a mean monthly discretionary expense of $70 spent on having meals out with friends. The standard deviation of the distribution is 5. Give the range of amounts within 1 standard deviation of the mean and explain what percent of friends will have be within 1 standard deviation if it is a normal distribution.
Answer:
im here for the points
Step-by-step explanation:
Help me please I only have 5 mins left
Answer:
A.5
B.16
C.11
D.3
E.5
Step-by-step explanation:
1) 6.61; tenths
You have to round it to the 10ths place
Answer:
6.6
Step-by-step explanation:
under 5 round down, 5 and up round up
36. Write the triangle congruence criterion illustrated
by each pair of triangles.
Answer:
A - ASA
B - ASA
C - SAS
D - SSS
Step-by-step explanation:
I hope this helps you out!
jenny has 68 1/2 pages of her left to read. How many pages will she have left after she reads 26 1/6 pages?
Answer:
42 1/3
Step-by-step explanation:
We subtract 26 1/6 from 68 1/2. We do this by finding the LCM of 6 and 2. That is 6. We multiply 1/2 by 3/3 to get 3/6. Now, we subtract. 68 - 26 is 42, and 3/6 - 1/6 is 2/6. Our answer is 42 2/6. That can be simplified to 42 1/3.
Jenny will have 42 whole 1/2 pages left after she reads 26 whole 1/6 pages if Jenny has a total of 68 whole 1/2 pages.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Jenny has [tex]68\frac{1}{2}[/tex] pages.
She reads [tex]26\frac{1}{6}[/tex]
Let's suppose the remaining pages is x, then the value of x:
[tex]\rm x = 68\frac{1}{2}-26\frac{1}{6}\\\\\rm x = \frac{137}{2}-\frac{157}{6} \\\\\rm x = \frac{411-157}{6} \\\\\rm x = \frac{254}{6}[/tex]
[tex]\rm x = \frac{127}{3}[/tex] or
[tex]\rm x = 42\frac{1}{3}[/tex]
Thus, Jenny will have 42 whole 1/2 pages left after she reads 26 whole 1/6 pages if Jenny has a total of 68 whole 1/2 pages.
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Can someone help me?
Answer:
y =4(x-3)^2+2 => y=4x^2-24x+38
y=2(x-3)^2+4 => y=2x^2-12x+22
y=2(x+3)^2+4 => y= 2x^2+12x+22
Y= 4(x+3)^2+2 => y= 4x^2+24x+38
Step-by-step explanation:
PLEASE HELP, THIS IS A BENCHMARK. WILL GIVE BRAINLIEST!
Use the description of AABC below to solve Parts A and B.
m
Part A: Which of the following is the value of x?
A. x = 10
B. x= 5
B. x = 4
D. x = 2
Part B: Order the sides of ABC from shortest to longest. Drag and drop the displayed choices to order.
2(3x-2)=14 pls help
help hell help help gelp help