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
5•1000000 is how many times as large as 5•10000
Answer:
100 times
Step-by-step explanation:
5•1000000 has 2 more zeros than 5•10000 so that means the first number is 100 times larger than the second number! hope this helps and please mark as brainiest
please help real quick
Divide total km by the km in the scale:
112 / 16 = 7
The answer is A. 7 cm
Answer:
7 cm
Step-by-step explanation:
1 cm : 16 km :: x cm : 112 km
Product of mean = Product of extreme
16 * x = 1 * 112
x =[tex]\frac{112}{16}[/tex]
x = 7cm
A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi. A.21.2 B.24.7 C.7.9 D.31.8
Answer:
A = 56.5cm²
Step-by-step explanation:
r = 1.5cm
h = 4.5cm
A=2πrh+2πr2
A = 2πr(h+r)
A = 2 x 3.14 x 1.5 x ( 4.5 + 1.5 )
A = 56.62cm²
[tex] \large{ \underline{ \underline{ \bf{ \red{Given}}}}}[/tex]
Height of the cylinder = 4.5 cmDiameter of the cylinder = 1.5 cmConsider π = 3.14[tex] \large{ \underline{ \underline{ \bf{ \purple{To \: find}}}}}[/tex]
Surface area of the cylinder in cm²?[tex] \large{ \underline{ \underline{ \bf{ \green{Now, \: What \: to \: do?}}}}}[/tex]
For solving this question, we should know how to calculate the surface area of cylinder i.e Total surface are of cylinder = 2πr(r + h)
Where, r = radius of the cylinder and h is the height of the cylinder.
[tex] \large{ \bf{ \underline{ \underline{ \blue{Solution}}}}}[/tex]
We are provided with,
h = 4.5 cmd = 1.5 cmThen, Radius = 1.5 cm / 2
By using formula,
⇛ 2πr(r + h)
⇛ 2 × 3.14 × 1.5/2 (1.5/2 + 4.5) cm²
⇛ 2 × 3.14 × 3/4( 5.25) cm²
⇛ 24.7275 cm²
❇ Option B
✤ TSA of the cylinder = 24.7275 cm²
━━━━━━━━━━━━━━━━━━━━
Please help me on this question
Answer:
1st count the 1/2 circle with the formula
1/2 × phi × r²
=1/2 × 3,14 x 6²
=1/2 × 3,14 × 6²
=56,5
2st count the ractangle with the formhla
a × b
= 12 × 18
= 216
So we get 56,5+216= 272,5
Answer:
Hey there!
This problem will require a few steps to solve:
Step 1: Identify the "simple shapes" that make up the larger figure. Here, we see that there is a rectangle to the left, and a semicircle to the right.
Step 2: Find the area of the rectangle. This shouldn't be too hard, since we know that the formula for a rectangle's area is length times width. From the diagram, we have the length is 18cm, and the width is 12cm. 18 times 12=216.
Step 3: Find the area of the semicircle. This is slightly more difficult, but we know a semicircle is half of a circle, and the formula for circle area is [tex]\pi r^2[/tex]. Thus, the formula for a semicircle area is [tex]\frac{\pi r^2 }{2}[/tex]. We have d, or the diameter equal to 12, so the radius is 6, or half of the d. Plugging in the values, we find that the area for the semicircle is about 56.52.
Step 4: Add the areas of both simple shapes together: 216+56.52=272.52 cm^3.
Hope this helps :)
A 20% discount on pants, and its price became 48 after the sale, what was its price before
Answer:
$60
Step-by-step explanation:
Represent the original price by p. Then:
1.00 p = original price
0.20 p = discount
0.80p = price after discount = $48
Solving for p, we divide both sides by 0.80:
$48
p = ---------- = $60
0.80
How did the temperature change if: At first it increased by 25% and then decreased by 40%
Answer:
24.6 % decrease
Step-by-step explanation:
Let x be the original temperature
Increase by 25%
x + .25x
1.25x
Decrease by 40%
The amount decreased is
(1.25x) *.40
.496x
Subtract that from 1.25x
1.25x - .496x
.754x
We need to find the percent decrease
1 - .754 = .246
24.6 % decrease
Answer:
Temperature decreased by 25%
Step-by-step explanation:
Let initial temperature be t
Step 1
Increase by 25%:
t + 25% = t + 0.25 t = 1.25 tStep 2
Decrease by 40%:
1.25 t - 40% = 1.25 t - 0.4 * 1.25 t= 1.25 t - 0.5 t = 0.75 tTemperature changed from t to 0.75 t
The difference in %:
0.75 t - t = -0.25 t = 25% decreaseTemperature decreased by 25%
The segments shown below could form a triangle.
A. True
B. False
Answer:
A True
Step-by-step explanation:
B vertices would be the top of an isosceles
As any equal sides can form an isosceles, the measure of the base could be any size and isnt relevant to the triangle unless we are looking for a calculation for its height, which does not determine shape only equation.
Therefore with sides of triangles if they are equal we cna make the shape consist of any length base as long as it measures less than double than either side length.
Therefore a 1cm base does apply and can form a triangle of two equal sides 7cm and 7cm as the diagram asks.
Answer:
true
Step-by-step explanation:
THE reason it true is because on on the lines doesn't equal to the 2 other lines
Brian and Zach went to Village Grille for lunch. Brian‟s lunch cost $4 less than 3 times Zach‟s. The total cost for lunch was $25. How much did each boy spend on lunch? (Why did Brian eat so much?)
Answer:
no
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
help me i need help i want help
Answer:
two feet cubed
Step-by-step explanation:
Jill has two dimes she is going to use to perform a probability experiment. What will the sample space look like if she flips the two dimes simultaneously?
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 40 ft to 72 ft Thankyou!! please hurry tho lol
Answer:
5/9 is the simplest fraction for this ratio
The radius of a circle is 6. Using T, which equation expresses the ratio of the circumference of the circle to the circle's diameter?
Answer:
Option (B)
Step-by-step explanation:
The given question is incomplete; here is the complete question.
The radius of a circle is 6. Using π, which equation expresses the ratio of the circumference of the circle to the circle's diameter?
A) C/6 = π
B) C/12= π
C) C = 6πr
D) C = 12πr
Formula to get the circumference of the circle is,
C = 2πr = π × D
Where C = circumference of the circle
D = Diameter of the circle
By dividing with D on both the sides of the formula,
[tex]\frac{\text{C}}{\text{D}}=\pi[/tex]
Since, diameter 'D' = 2r,
[tex]\frac{\text{C}}{\text{2r}}=\pi[/tex]
[tex]\frac{\text{C}}{2\times 6}=\pi[/tex]
[tex]\frac{\text{C}}{12}=\pi[/tex]
Therefore, equation given in Option (B) will be the correct expression.
Two cities, A and B, are mapped on the coordinate plane. How far apart are they from each other? A. 145−−−√ units B. 97−−√ units C. 5 units D. 73−−√ units
Answer:
B
Step-by-step explanation:
From the graph we can notice that the coordinates of the cities are:
● A(2,3)
● B(6,-6)
There are many methods to figure out the distance between A and B. We will use the distance formula.
Let d be the distance between A and B.
● d = √[(2-6)^2 + (3-(-6))^2]
● d = √[(-4)^2 + (3+6)^2]
● d = √[ 4^2 + 9^2 ]
● d = √(16+81)
● d = √(97)
Answer:
The answer is B) 97 units
Step-by-step explanation:
From the graph we can notice that the coordinates of the cities are:
● A(2,3)
● B(6,-6)
There are many methods to figure out the distance between A and B. We will use the distance formula.
Let d be the distance between A and B.
● d = √[(2-6)^2 + (3-(-6))^2]
● d = √[(-4)^2 + (3+6)^2]
● d = √[ 4^2 + 9^2 ]
● d = √(16+81)
● d = √(97)
PLEASE HELP!!! Will give brainliest to quickest CORRECT answer. No explanation needed :) Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35 and an additional fee of $12 per class taken. Rebekah's goal is for each customer to spend at least $100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal. Let C represent the number of classes a customer takes. 1) Which inequality describes this scenario? A. 35+C≤100 B. 35+3≥100 C. 35+12C≤100 D. 35+12C≥100 2) What is the minimum number of classes a customer can take for Rebekah to meet her goal?
The inequality that describes the scenario will be; 35 + 12C ≥ 100.
The minimum number of classes a customer can take for Rebekah to meet her goal is 6
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
One-time initial fee = $35
Additional fee per class = $12
Minimum target = $100
Number of classes = C
One-time initial fee + (Additional fee per class) x (Number of classes) ≥ Minimum target
The inequality that describes the scenario will be;
35 + 12C ≥ 100
Then Solve for C to know the minimum number of classes a customer can take for Rebekah to meet her goal,
12C ≥ 100 - 35
12C ≥ 65
C ≥ 65 / 12
C ≥ 5.42
Thus, The minimum number of classes a customer can take for Rebekah to meet her goal is 6
Learn more about inequality ;
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click to see equation, show work pls!
Answer:
x = 6, 9
Step 1:
To solve this equation, we need to subtract 3 from both sides like this:
[tex]3\sqrt{x-5} +3(-3)=x(-3)\\3\sqrt{x-5} =x-3[/tex]
Step 2:
We square both sides (multiply using FOIL) to get rid of the radical.
[tex](3\sqrt{x-5} )^2 = (x-3)^2\\(3\sqrt{x-5} )^2: 9x-45\\ (x-3)^2: x^2+6x+9\\\\9x-45=x^2-6x+9[/tex]
If you did not understand how these were done, here is an example:
(x + 1)(x + 2)
First terms: x * x = x^2
Outer terms: x * 2 = 2x
Inner terms: 1 * x = x
2x - x = x
Last terms: 1 * 2 = 2
x^2 + x + 2
Step 3:
Solve for x:
9x - 45 = x^2 - 6x + 9
x^2 - 6x + 9 (+45) = 9x - 45 (+45)
x^2 - 6x + 54 (-9x) = 9x (-9x)
x^2 - 15x + 54 = 0
Factor:
(x^2 - 6x) + (- 9x + 54)
x(x - 6) - 9(x - 6)
Factor out (x - 6):
(x - 6)(x - 9) = 0
x - 6 = 0; 6 - 6 = 0
x - 9 = 0; 9 - 9 = 0
Our anwer: x = 6, 9
Order from least to greatest: 0.4 5/8 38% 0.52
Answer:
The correct ans is....
38%
0.4
0.52
5/8
Step-by-step explanation:
Order form least to greatest means " Ascending order "
38 % = 38/100
0.4 = 40/100
0.52 = 52/100
5/8 = 62.5/100
Hope this helps.....
Pls mark my ans as brainliest If u mark my ans as brainliest u will get 3 extra pointsAnswer:38% ,0.4 ,0.52 ,5/8
Step-by-step explanation:
becuase when you turn them into decimals you will get
38%=0.38
0.4=0.4
0.52=0.52
5/8=0.625
Hopes this helps
Someone pls help . Thank you sm !!
Answer:
28 = -3k + 728 - 7 = -3k
21 = -3k
21/-3 = k
k = -7
1/5 x - 17 = 3x/5 = 3 + 17
x/5 = 20
x = 5*20
x = 100
82 = 7/10 G + 1282 - 12 = 7G/10
70 = 7G/10
70*10 = 7G
700 = 7G
700/7 = G
G = 100
What is the measure of the acute angle formed by the lines 3x–5y=–15 and 4x+2y=7?
Answer:
85.6 degrees.
Step-by-step explanation:
The given equations of lines are
[tex]3x-5y=-15[/tex]
[tex]4x+2y=7[/tex]
We need to find the measure of the acute angle formed by these lines.
[tex]Slope=\dfrac{-\text{Coefficient of }x}{\text{Coefficient of }y}[/tex]
Slope of given lines are
[tex]m_1=\dfrac{-3}{-5}=\dfrac{3}{5}[/tex]
[tex]m_2=\dfrac{-4}{2}=-2[/tex]
Angle between two lines is
[tex]\tan \theta = \left|\dfrac{m_1-m_2}{1+m_1m_2}\right|[/tex]
[tex]\tan \theta = \left|\dfrac{\dfrac{3}{5}-(-2)}{1+\dfrac{3}{5}(-2)}\right|[/tex]
[tex]\tan \theta = \left|\dfrac{\dfrac{3+10}{5}}{\dfrac{5-6}{5}}\right|[/tex]
[tex]\tan \theta = \left|\dfrac{13}{1}\right|[/tex]
[tex]\tan \theta = 13[/tex]
[tex]\theta = \tan^{-1}(13)[/tex]
[tex]\theta \approx 85.6^{\circ}<90^{\circ}[/tex]
Therefore, the acute angle between given lines is 85.6 degrees.
Suppose a function f has an inverse. If f(2)=6 and f(3)=7, find: f−1(6)
Answer:
[tex]f^{-1}(6) = 2[/tex]
Step-by-step explanation:
Given
[tex]f(2) = 6[/tex]
[tex]f(3) = 7[/tex]
Required
[tex]f^{-1}(6)[/tex]
First, we need to determine the slope of the function using;
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
From the given parameters;
In [tex]f(2) = 6[/tex]
x = 2; y =6 --- Take this as x1 and y1
In [tex]f(3) = 7[/tex]
x = 3; y = 7 --- Take this as x2 and y2
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex] becomes
[tex]m = \frac{6 - 7}{2 - 3}[/tex]
[tex]m = \frac{- 1}{ - 1}[/tex]
[tex]m = 1[/tex]
Next, we determine the equation of the function using
[tex]y - y_1 = m(x - x_1)[/tex]
Substitute the values of x1,y1 and m
[tex]y - 6 = 1(x - 2)[/tex]
Open bracket
[tex]y - 6 = x - 2[/tex]
Add 6 to both sides
[tex]y - 6 + 6 = x -2 +6[/tex]
[tex]y = x + 4[/tex]
Next is to determine the inverse function by swapping the positions of x and y
[tex]x = y + 4[/tex]
Make y the subject of formula;
[tex]y = x - 4[/tex]
Replace y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = x - 4[/tex]
Now, we can solve for [tex]f^{-1}(6)[/tex]
Substitute 6 for x
[tex]f^{-1}(6) = 6 - 4[/tex]
[tex]f^{-1}(6) = 2[/tex]
Please help me on this question
Answer:
DE = 13.4 cm (to 1 decimal place)
Step-by-step explanation:
Given: ABCD is a square
BC = AC = 12 cm (opposite sides of a square are congruent)
E is midpoint of BC (given)
BE = EC = 12/2 = 6 cm
CD = AB = 12 cm (opposite sides of a square are congruent)
angle ECD is a right angle (interior angles of a square are 90 deg.)
Consider right triangle ECD
DE = sqrt(EC^2+CD^2) ............. pythagorean theorem
= sqrt(6^2+12^2)
= sqrt ( 36+144 )
= sqrt (180)
= 2 sqrt(45)
= 13.416 (to three dec. places)
How does 4D Shape look like? and, do (4 < n)D are possible?
ANSWER:
4d shape LOOKS LIKE THIS
Solve the following system. y = (1/2)x^2 + 2x - 1 and 3x - y = 1 The solutions are (____)and (______ ) (remember to include the commas)
Answer:
x=0, 2. y=-1, 5.
Step-by-step explanation:
y=(1/2)x^2+2x-1
3x-y=1
---------------------
3x-y=1
y=3x-1
-----------
(1/2)x^2+2x-1=3x-1
(1/2)x^2+2x-3x-1-(-1)=0
(1/2)x^2-x-1+1=0
(1/2)x^2-x=0
factor out the x
x[(1/2)x-1]=0
zero property,
x=0, (1/2)x-1=0
-------------------
(1/2)x-1=0
1/2x=0+1
1/2x=1
x=1/(1/2)=(1/1)(2/1)=2/1=2
-----------------------------------
x=0, x=2
-------------
y=(1/2)(0)^2+2(0)-1=0+0-1=-1
-------------
y=3(0)-1=0-1=-1
-----------------------
y=(1/2)(2)^2+2(2)-1=(1/2)(4)+4-1=4/2+4-1=2+4-1=6-1=5
----------------------
y=3(2)-1=6-1=5
Answer:
The solutions are (0, -1) and (2, 5)
Step-by-step explanation:
y = (1/2)x^2 + 2x - 1 ------ eqn(I)
3x - y = 1
y = 3x - 1 ------------- eqn(II)
Equate eqn(I) & (II)
(1/2)x^2 + 2x - 1 = 3x - 1
Multiply each term by 2
x^2 + 4x - 2 = 6x - 2
x^2 + 4x - 6x = -2 + 2
x^2 - 2x = 0
x(x - 2) = 0
x = 0, 2
Substitute the values of x in eqn(II)
y = 3x - 1
When x = 0
y = 3(0) - 1 = 0 - 1 = -1
y = 3x - 1
When x = 2
y = 3(2) - 1 = 6 - 1 = 5
The solutions are (0, -1) and (2, 5)
Plz help I’ll mark brainliest
Answer:
x = 22.62°Step-by-step explanation:
To find the measure of angle x we use cosine
[tex] \cos( \alpha ) = \frac{adjacent}{hypotenuse} [/tex]
From the question
PO is the hypotenuse = 13
The adjacent is 12
Substitute the values into the above formula
That's
[tex] \cos(x) = \frac{12}{13} [/tex]
[tex]x = \cos^{ - 1} ( \frac{12}{13} ) [/tex]
x = 22.6198
We have the final answer as
x = 22.62° to the nearest hundredthHope this helps you
Answer:
Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle. If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal.
Step-by-step explanation:
To make a project, you need a rectangular piece of fabric
3 ft wide and 4 ft long. How many square feet of fabric do
you need?
I
Answer:
12 ft²
Step-by-step explanation:
area = length * width
area = 4 ft * 3 ft
area = 12 ft²
help can somewon help me plzz
Answer:
I would say b
Step-by-step explanation:
3 x 10^-4
Use the formula
A = nr2 and find the area of a circle with
radius 5 cm. Use i = 3.14.
Answer:
A = 78.5 cm²
Step-by-step explanation:
A = πr²
A = (3.14)(5)²
A = (3.14)(25)
A = 78.5 cm²
The area of the circle with a radius of 5 cm will be 78.5 cm².
Hope that helps.
What’s the mass of a liquid if its density is 0.95 G/ml and its volume is 200 ml
Answer:
190 g
Step-by-step explanation:
Mass =Density
Volume
Let the mass be x.
x/200=0.95
x=200 x 0.95
x = 190 g
Thank you!
PLS HELP ME WITH THIS QUESTION I NEED IT QUICK! anything helps..
Answer:
Graph A
Step-by-step explanation:
if you look at the numbers on the top row they correspond with the left side of the graph and the bottom row of numbers correspond with the bottom of the Graph.
Answer:
Graph A)
Step-by-step explanation:
The first points 20,70 and 30,70 are both plotted correctly on this graph, same with the other points. :)
Matt measures 3 pieces of string. The first piece is 544 cm. The second piece is 144 cm, and the third piece is 112 cm. How many METERS of the string does he have altogether?
Answer:
8.10
Step-by-step explanation:
1metre =100 centmetres
1st piece is 5.44m
2nd piece is 1.44m
3rd piece is 1.12m
Total length= 8.10m
C) look at the scale factor for parts a and b. do they represent a reduction or enlargement of the empire state building? How do you know?
Answer:
Enlargement
Step-by-step explanation
It is enlargement, because it went up by three. Instead of reducing.
We cannot tell the result because the actual size of blocks used for modelling the Empire State Building is not known.
How are scale construction formed?For a particular scaled construct, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]
All feet measurements will then be multiplied by s/k to get the corresponding lengths in the constructed scaled structure.
For case a) or b), we used the scale factors as:
1 block : x feet, where x was either 2 or 5 feet.
But we are not specified what size is of the block which is used to model the building.
It may be that block is greater than x feet, or may be smaller. This will decide whether there is enlargement or reduction of the actual building, respectively.
Thus, we cannot tell the result because the actual size of blocks used for modelling the Empire State Building is not known.
Learn more about scale factors here :
https://brainly.com/question/8765466
