Answer:
90
Step-by-step explanation:
Let g and b represent the number of girls and boys attending, respectively.
After 15 girls left, the ratio of boys to girls was ...
b/(g -15) = 2/1
b = 2g -30 . . . . . multiply by (g-15)
__
After 45 boys left, the ratio of girls to boys was ...
(g -15)/(b -45) = 5/1
g -15 = 5b -225 . . . . . . multiply by (b-45)
g = 5b -210
Using the latter to substitute into the former, we have ...
b = 2(5b -210) -30
450 = 9b . . . . . add 450-b
50 = b . . . . . . 50 boys attended
g = 5(50) -210 = 40 . . . . . 40 girls attended
The number of students who attended the party was 50 +40 = 90.
_____
Check
After 15 girls left, the ratio of boys to girls was 50/25 = 2/1.
After 45 boys left, the ratio of girls to boys was 25/5 = 5/1.
Answer:
let b = original number of boys
let g = original number of girls
:
Of a group of boys and girls at Central Middle School's after-school party, 15 girls left early to play in a volleyball game.
The ratio of boys to girls then remaining was 2 to 1.
b%2F%28%28g-15%29%29 = 2%2F1
Cross multiply
b = 2(g-15)
b = 2g - 30
:
Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1.
%28%28g-15%29%29%2F%28%28b-45%29%29 = 5%2F1
cross multiply
g - 15 = 5(b-45)
g - 15 = 5b - 225
g = 5b - 225 + 15
g = 5b - 210
Replace b with (2g-30)
g = 5(2g-30) - 210
g = 10g - 150 - 210
g = 10g - 360
360 = 10g - g
360 = 9g
g = 360/9
g = 40 girls originally
find b
b = 2(40) - 30
b = 50 boys originally
" How many students attended the party?"
40 + 50 = 90 students
How many units away is 1 from -6 on a number line?
Answer:
7 units
Step-by-step explanation:
(number line:)
<- -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ->
←there are 7 units from 1 to -6 (you don't count the 0)
(I'm not sure if you understood my explanation, but I do am sure about the answer, so if there is something you didn't understand let me know, and which part are you confused about so I can help you out!)
Answer:
[tex]\huge\boxed{\sf 7\ units}[/tex]
Step-by-step explanation:
To find that how much far they are from each other, we can subtract both of them.
=> 1 - (-6)
=> 1 + 6
=> 7 units
So, they are 7 units apart from each other.
Three faucets fill a 100-gallon tub in 6 minutes. How long, in seconds, does it take six faucets to fill a 25-gallon tub? Assume that all faucets dispense water at the same rate.
Answer:
see below
Step-by-step explanation:
It would take 3 faucets 6/4 = 1.5 minutes to fill a 25-gallon tub since when the number of faucets stays the same, the volume of the tub and the time needed to fill the tub are directly proportional. However, when the volume of the tub stays the same, the number of faucets used and the time needed to fill the tub are inversely proportional, therefore, if I double the number of faucets used, it will half the time needed, so the answer is 1.5 / 2 = 0.75 minutes or 45 seconds.
Answer:
[tex]\large\boxed{45 seconds}[/tex]
Step-by-step explanation:
------------------------------------------------------------------------------------------------------------
Variable Key
Faucets = f
Minutes = m
Gallons = g
------------------------------------------------------------------------------------------------------------
Write an equation to display how long it takes for the 3 faucets to fill up a 100 gallon tub.
100g = 6m
Divide both sides of the equation by 6
m = 16.67g
This means that approximately 16.67 gallons are filled up per minute with 3 faucets. We found the measurement (gallons), which is based on the time (minutes). This is called the unit rate.
Now that we found the unit rate for 3 faucets, let's find the unit rate for 6 faucets by multiplying our unit rate by 2.
3f = 16.67g per minute
6f = (16.67g per minute)(2)
6f = 33.34 g per minute
We now know the unit rate for 6 faucets, so now all we have to do is divide that by 25 gallons, the second tub.
25g / 33.34 g = 0.75 minutes
Convert to seconds
0.75 minutes = 3/4 of a minute
1 minute = 60 seconds
Substitute
3/4(60)
[tex]\large\boxed{45 seconds}[/tex]
Hope this helps :)
Please answer ASAP
Randomly pick 6 points from a square of side = 1. Show that you can always find 2 points from these 6 that their distance is less or equal to [tex]\frac{\sqrt{2} }{2} }[/tex]
Randomly pick 5 points from a sphere. Show that you can always find a closed semi-sphere ( half a sphere and boundary) that contains 4 points.
Problem 1.
My thinking is that the furthest you can get is have two points at each opposite corner, so the distance between them is sqrt(2). If we have two other points with this property, then all four corners are filled up. It is possible to pick two points where the distance is 1 unit.
Then a fifth point can be placed at the center such that the distance from it to any of the corners is sqrt(2)/2. We placed the fifth point at the center to try to get as far away as possible from the other four points.
Basically we're trying to find the worst case scenario (leading to the largest distance possible) and seeing how we can fill up the square. This establishes the upper bound. Any other kind of scenario will have a distance less than the upper bound.
===================================================
Problem 2.
For this one, I'm not sure what to make of it. The terminology is a bit strange so I'm not going to be fairly helpful here. Sorry about that.
If I had to guess, I'd assume it has something to do with the fact that a plane is uniquely defined by 3 points. That fourth point is not coplanar with the other three, which helps define the semi-spherical portion. The fifth point is just extra. The points can't be all collinear or else a plane won't form. Though to be honest, I'm still not sure about problem 2. I'd get a second opinion.
A shipping container in the shape of a rectangular prism is 60 feet long, 45 1/2 feet wide, and 14 feet tall. What is the volume of the shipping container? A. 2,400 ft.^3 B. 2,730 ft.^3 C. 38.220 ft.^3 D. 76,440 ft.^3 Please include work!!
Find all points having an x- coordinator of 5 whose distance from the point (-1,-3) is 10. (type an ordered pair. Use a comma to separate answers as needed.)
Answer:
(5,5) and (5,-11)
Step-by-step explanation:
You can find this out by plotting a circle with the diameter of 10 on the point "(-1,-3)". Then find all the times the circle is on the x axis of 5.
Answer:
so when the mughal emperor humayun had died akbar his son was put as kind of india he was 10 yearls old when his father died and then Bairam Khan was elected as a regent for Akbar.
Step-by-step explanation:
PLEASE HELP ME!! I WILL GIVE BRAINLIEST!!
Find the output, y, when the input, x, is -5.
Answer:
[tex]\boxed{y = -2}[/tex]
Step-by-step explanation:
Hey there!
To find y when x is -5 we go to -5 on the x-axis.
When at -5 find where the blue line is vertical to -5,
which is -2.
Hope this helps :)
(08.01) Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point
Answer:
the answer is D
Step-by-step explanation:
y=x-1
2=3-1
2=2
y=-3x+11
2=-3(3)+11
2=-9+11
2=2
Answer:
Step-by-step explanation:
If both lines pass through the point (3, 2), we automatically know that (3, 2) is the soution of the system of linear equations given here, AND that (3, 2) is a solution of equation A and equation B both.
The five-number summary for the number of touchdowns thrown by each quarterback in the British Football League is shown in the following table. About what per cent of quarterbacks in the British Football League threw more than 13 touchdowns?
Answer:
25%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
Which statement best compares the two functions?
The minimum of function A occurs 1 unit higher than the minimum of function B.
The minimum of function A occurs 3 units higher than the minimum of function B.
The minimum of function A occurs 5 units lower than the minimum of function B.
The minimum of function A occurs 7 units lower than the minimum of function B.
Answer:The minimum of function A occurs 1 unit higher than the minimum of function B.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Trust
plz help me i need help
Find the surface area and volume of the following figures.
White figure Area = 128[tex]\pi[/tex]
White surface area = appro. 301
Yellow area = 320[tex]\pi[/tex]
Yellow Surface area = approx. 653
Area found with = 2πrh+2πr2
Surface Area found with = 2πrh+2πr2
You need to memorize them for tests
Hope that helped!!! k
helpyffhvjvjnvhdfuguig
Answer:
x = 0, x = 4
Step-by-step explanation:
12x - 21 = 5x + 7(x - 3)
First, foil out the right side --> 5x² - 15x + 7x - 21, which simplifies down to 5x² - 8x - 21.
Move the 12x - 21 to the right side by subtracting --> 0 = 5x² - 20x.
Factor out a 5x --> 0 = 5x(x - 4)
If you want to solve for x, set 5x = 0 and x - 4 = 0.
For 5x = 0, divide both sides by 5 to isolate the x --> x = 0/5, which simplifies down to x = 0.
For x - 4 = 0, add 4 to both sides to isolate the x --> x = 0 + 4, which simplifies down to x = 4.
Plug the values back into the original equation to check if it works
12(0) -21 = 5(0) + 7((0) - 3) --> -21 = -21
12(4) - 21 = 5(4) + 7((4) -3) --> 27 = 27
Hope this helps!
Solve the equation using the multiplication property of equality and the reciprocal of
1
4
.
1
4
( r −
5
2
) =
1
8
An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 70% more of the substance? (Round your answer to one decimal place.) hr
Step-by-step explanation:
half life time-50%-8.4hr
so for 10%- 8.4/5=1.68 hr
now for 70%
1.68 × 7 = 11.76 hrs
to one decimal place - 11.8hrs
11.8 hours ago, there were 70% more of the substance if an isotope of lead has a half-life of 8.4 hours.
What is half-life?Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay.
Half-life period - 50% -8.4hours
so for 10%- 8.4/5 = 1.68 hour
now for 70%
1.68 × 7 = 11.76 hours
To one decimal place - 11.8hours
Hence, 11.8hours is the answer.
To learn more about half-life here
https://brainly.com/question/17159063
#SPJ2
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = 6x − x2, y = 8; about x = 2
Answer:
[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]
Step-by-step explanation:
Given that:
y = 6x - x² , y = 8 about x = 2
To find the volume of the region bounded by the curves about x = 2; we have the radius of the cylindrical shell to be x - 1, the circumference to be 2 π (x -2 ) and the height to be 6x - x² - 8
6x - x² - 8
6x - x² - 8 = 0
-x² + 6x - 8 = 0
x² - 6x + 8 = 0
(x -4) (x - 2 ) = 0
So;
x = 2 , x = 4
Thus, the region bound of the integral are from a = 2 and b = 4
Therefore , the volume of the solid can be computed as :
[tex]V = \int \limits ^b _a \ 2x \times f(x) \ dx[/tex]
[tex]V = \int \limits ^4_2 2 \pi (x -2) (6x -x^2 -8) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 (6x^2 - x^3 -8x -12 x - 2x^2 +16) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 (8x^2 -x^3-20x +16) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 ( -x^3+8x^2-20x +16) \ dx[/tex]
[tex]V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2[/tex]
[tex]V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2[/tex]
[tex]V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ][/tex]
[tex]V = 2 \pi [\dfrac{ 4}{3}][/tex]
[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]
5. The cost of movie tickets at the
Cinema Verite is 9 dollars for adults
and five dollars for children under 12.
During the Saturday and Sunday
matinees, adults are charged 8 dollars
for admission and children under 12
are charged 4 dollars. At any time at
all, there is a group discount for groups
of 15 or more adults at a cost of 6
dollars per ticket. What is the cost for 2
adults and 3 children during the
Saturday matinee?
a. 27
b. 28
C. 14
d. 32
Answer:
its 28 dude, because it says that adults and children are played more on saturday.(adults on Saturday=$8 and children under 12 are $4
PLEASE HELP!!! ASAP!!!
Answer:
28 units²
Step-by-step explanation:
→ Work out the size of the triangle if it was a full rectangle
Height = 4 and Base = 2
→ Work out area of triangle
0.5 × Height × Base ⇒ 0.5 × 4 × 2 ⇒ 2 × 2 ⇒ 4
→ Minus the area of the triangle from the "imaginary full' rectangle
Area of rectangle = Length × Width ⇒ 8 × 4 ⇒ 32
32 - 4 = 28
Answer:
[tex]\huge\boxed{28\ units^2}[/tex]
Step-by-step explanation:
The figure consists of a triangle, a square and a rectangle.
Area of Triangle:
[tex]\sf \frac{1}{2} (Base)(Height)\\Where \ Base = 2 , Height = 4 \\=> \frac{1}{2} (2)(4)\\=> 4\ units^2[/tex]
Area of Square:
[tex]\sf (Length)(Length)\\(4)(4)\\=> 16\ units^2[/tex]
Area of rectangle:
[tex]\sf (Length)(Width)\\Where \ Length = 4 , Width = 2\\=> (4)(2)\\=> 8 \ units^2[/tex]
Area of the whole figure:
=> 4 + 16 + 8
=> 28 units²
Find the value of m∠ACD. A. 30º B. 15º C. 60º D. 90º
Answer:
A. 30 degrees
Step-by-step explanation:
Set the two angles equal to each other:
3x-15 = 45-x
Solve for x:
4x -15 = 45
4x = 60
x = 15
Finally, plug in the x to one of the equations (preferably 45 - x since it's easier to solve) and solve for x.
45 - 15 = 30
Answer:
A 30 degrees
Step-by-step explanation:
a 20-foot flagpole casts a 6-foot Shadow how tall is a nearby building that casts a 30-foot shadow
The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.
Answer :
The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.
Drag each object to show whether distance is proportional to time in the situation represented.
Answer: please find the answer in the explanation.
Step-by-step explanation:
1.) The distance is not proportional to time. Because the distance was constant from time = 3 seconds to 10 seconds.
2.) A person running down a field to score a touchdown. Not enough information.
3. A dog jogging at a constant speed for 20 minute. The distance is proportional to time because of the constant speed.
4.) The distance is proportional to time because their is increase in distance covered and increase in time taken.
5.) A truck passing through the 4 cities at a constant speed. The distance is proportional to time because the speed is constant.
6.) A horse running around a race track. Distance is not proportional to time because this is not a linear motion.
Evaluate 9x*2 y*−2 for x = –3 and y = 2. Answers:
Answer:
20 and 1/4.
Step-by-step explanation:
9x^2 * y^(-2), for x = -3 and y = 2.
9(-3)^2 * 2^(-2)
= 9 * 9 * (1/4)
= 81 * 1/4
= 81 / 4
= 20.25
= 20 and 1/4.
Hope this helps!
Answer:
Step-by-step explanation:
Let's fill the values in.
9(-3)*2(2)*-2
Using PEMDAS, we would first multiply the two numbers where x and y used to be.
-27 * 4 * -2
Now we would finish multiplying this.
216.
Hope this helps!! <3
Plzz help I’ll mark brainliest
Answer:
6cot 50
Step-by-step explanation:
Tan 50=6/x
x= 6/(tan 50)
x= 6cot 50°
Answer:
? = 6 cot 50
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 50 = 6 /?
? tan 50 = 6
? = 6 / tan 50
We know that 1 / tan 50 = cot 50
? = 6 cot 50
Please help! Dad will murder me if I don't have this done by the time he gets home! 100 points for whoever solves this!
Answer:
3(4)to the 3
Step-by-step explanation:
4x = 2x + 2x + 5(x-x) does this have one solution, no solution or infinite solutions
Answer:
infinite solutions
Step-by-step explanation:
4x = 2x + 2x + 5(x-x)
Simplify
4x = 2x + 2x + 5*0
4x = 2x + 2x
4x = 4x
Divide by x
4 =4
This is always true so this has infinite solutions
d) Use your knowledge of scale drawings and image sizes to fill in the missing
information in the table. (3 points)
Empire State Building
Original
Image
Actual Height
(in feet)
1,450
1,450
1,450
Reduced
Image
Model Height
(in blocks)
145
1
1
Scale Factor
25
50
Answer:
Your table is filled in below.
Step-by-step explanation:
The scale factor is the ratio of image size to original size. In part (d), the image height is "blocks" while the original height is "feet". So, the units of the scale factor are "blocks/ft".
Sometimes a scale factor has units, like this, and sometimes it is expressed as a pure number. A map scale factor might be the pure number ratio 1 : 62500, or it could also be expressed with units as 1 in : 1 mile.*
__
* actually, these are slightly different scales. 1:62500 is about 0.98643 inches per mile.
Answer: Image
Step-by-step explanation:
took the test
need help with these questions!!! please explain bc I don't really get it!
Answer:
1. b. 2. a. 3. a.
Step-by-step explanation:
1. (f + g)x = f(x) + g(x)
= x^2 + 2x + 4
(f + g)(-1) = (f + g)(x) where x = 1 so it is
(-1)^2 + 2(-1) + 4
= 1 - 2 + 4
= 3.
2. We find (f o g)(x) by replacing the x in f(x) by g(x):
= √(x + 1) and
(f o g)(3) = √(3 + 1)
= √4
= 2.
3. (f/g) c = f(x) / g(x)
= (x - 3)/(x + 1)
The domain is the values of x which give real values of (f/g).
x cannot be - 1 because the denominator x + 1 = -1+1 = 0 and dividing by zero is undefined. So x can be all real values of x except x = -1.
The domain is (-∞, -1) U (-1, ∞)
Please Help ;-;" :Mr. Gordon’s science class is studying blood types. The table below shows the probability that a person living in the US has a particular blood type. ( Type 0=9/20) (Type A=41/100) (Type B=1/10) (Type AB=1/25) What is the probability that three students selected randomly from the class will have A, B, and AB blood, respectively? Explain how you would solve this problem.
Answer:
A = 6.9%
B = 0.1%
AB = 1.6%
Step-by-step explanation:
A=0.41=41/100
B=0.1=1/10
AB=0.25=1/25
41/100³ = 0.41³ = 0.069 = 6.9%
1/10³ = 0.1³ = 0.001 = 0.1%
1/25³= 0.25³ =0.016 = 1.6%
I did to the power of 3 because the equation just looks like this
41/100 x 41/100 x 4/100
this is because you are multiplying each number by the amount of students selected.
Use a number line to approximate the value of root 33
Let's think about the square root of 33 here for a second.
What two perfect squares surround 33?
The answer is 25 and 36.
Then, let's take the square root of both 25 and 36, which are 5 and 6. Therefore, since the square root of 25 and 36 are both nearest to the square root of 33, then the square root of 3 must be between 5 and 6.
The correct answer is A (or option 1): 5 < root 33 < 6
Hope this helps! :)
Answer:
a (the first choice)
Step-by-step explanation:
To start, you should think of square root values near 33 that you know the answer to. For example, the square root of 25 is 5, and the square root of 36 is 6. Therefore, you know that the square root of 33 is 5.something because it is in between 25 and 36.
What is the value of f(1)?
Answer:
A function normally tells you what y is if you know what x is.
what is the first step to solving this problem: 3x-10=2(x+3)
Answer:
x = 16
Step-by-step explanation:
3x - 10 = 2(x+3)
First step is solve this:
2(x+3) = 2*x + 2*3 = 2x + 6
then:
3x - 10 = 2x + 6
3x - 2x = 6 + 10
x = 16
Check:
3*16 - 10 = 2(16+3)
48 - 10 = 2*19 = 38
Answer:
x = 16
Step-by-step explanation:
you start off by isolating the variable
