Answer: 32
Step-by-step explanation:
There are 18 boys and 14 girls (4 more boys than girls. 32 students total.
If the ratio of boys to girls is 9 : 7, there are 32 students in this Year 9 group altogether.
Let's denote the number of boys as "9x" and the number of girls as "7x" since the ratio of boys to girls is 9:7. We are also given that there are 4 more boys than girls, so we can set up an equation:
Number of boys = Number of girls + 4
9x = 7x + 4
Now, we can solve for "x":
9x - 7x = 4
2x = 4
x = 2
Now that we have the value of "x," we can find the number of boys and girls:
Number of boys = 9x = 9 * 2 = 18
Number of girls = 7x = 7 * 2 = 14
Finally, to find the total number of students in the group, we add the number of boys and girls:
Total number of students = 18 (boys) + 14 (girls) = 32.
The ratio of boys to girls is 9:7, and there are 4 more boys than girls.
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plz hurryA 3-column table with 6 rows. Column 1 is labeled Number Rolled with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Observed Frequency with entries 10, 12, 10, 10, 8, 10. Column 3 is labeled Relative frequency with entries StartFraction 1 over 6 EndFraction, A, StartFraction 1 over 6 EndFraction, StartFraction 1 over 6 EndFraction, B, StartFraction 1 over 6 EndFraction. A number cube is rolled 60 times. The results of those 60 trials are recorded in the table. Complete the table. A = B =
Answer:
The complete table is shown below.
Step-by-step explanation:
The data provided is:
Number Rolled Observed Frequency Relative frequency
1 10 [tex]\frac{10}{60}=\frac{1}{6}[/tex]
2 12 [tex]\frac{12}{60}=\frac{1}{5}[/tex]
3 10 [tex]\frac{10}{60}=\frac{1}{6}[/tex]
4 10 [tex]\frac{10}{60}=\frac{1}{6}[/tex]
5 8 [tex]\frac{8}{60}=\frac{2}{15}[/tex]
6 10 [tex]\frac{10}{60}=\frac{1}{6}[/tex]
TOTAL 60 1
The complete table is shown above.
Answer:
A= 1/5
B.2/15
Step-by-step explanation:
trust me i got it right on edg
I don’t know how to find this out
Answer:
C many solutions
Have a good day !What is the volume of a sphere with a radius of 9.9 ft, rounded to the nearest tenth of a cubic foot?
Answer:
the answer is attached to the picture
The volume of a sphere with a radius of 9.9 ft is 4062.3 cubic foot.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
The volume of the sphere is 4/3πr³
Radius is 9.9 ft.
Volume =4/3×3.14×(9.9)³
=4/3×3.14×970.3
=12187/3
=4062.3
Hence, the volume of a sphere with a radius of 9.9 ft is 4062.3 cubic foot.
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What is the definition of exponential growth?
A. A condition in which a quantity decreases at a steady rate
B. A condition in which a quantity increases at a steady rate
C. A condition in which a quantity increases at a rate that is
proportional to the current value of the quantity
D. A condition in which a quantity decreases at a rate that is
proportional to the current value of the quantity
Answer:
C. A condition in which a quantity increases at a rate that is
proportional to the current value of the quantity
Step-by-step explanation:
Exponential growth is increasing, but not at a steady rate. On a graph, it has a curve instead of being a straight line.
Which statement is true regarding the graphed functions?
f(4) = g(4)
f(4) = g(-2)
f2) = g(-2)
f(-2) = g(-2)
Answer ASAP
Answer: f(2) = g(-2)
Step-by-step explanation: f(x) line if u go to the x axis you see that it’s 2 the x intercept.....
The g(x) line you go to the x axis and see it is -2, that is the x intercept
3. An acute triangle with angles measuring 60 degrees,62°, and 58 degrees,
Possible or impossible
Answer:
Possible
Step-by-step explanation:
I need help ASAP! What is the value of x and what is the value of y?
Answer:
Step-by-step explanation:
4x and 5x are supplementary, so they add up to 180.
4x + 5x = 180 and
9x = 180 so
x = 20.
Because DE and BA are parallel, then 2y and 70 degrees are alternate interior and are equal to one another.
2y = 70 so
y = 35
Helpppp meee pleaseee!!!! Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with the dimensions shown below. Use the drop-down menus to explain how to determine the volume of the paperweight.
Answer:
1. 1/2 * 5 * 5
2. 4
3. 7
4. 79
Step-by-step explanation:
IReady test
The volume of the paperweight will be 79.17 cubic inch
PrismA solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms is known as prism
What are steps to solve this problem?The steps are as follow:
Let volume of pyramid be [tex]V_{1}[/tex]Let volume of prism be [tex]V_{2}[/tex]Since the floor area is triangle∴ Area of floor = Area of triangle = ah/2
Where a=5 and h=5 from figure given
∴ Area of floor = (5*5)/2 = 12.5 sq.inch
Now, let us find the volume of pyramid and prism as follow:[tex]V_{1} = \frac{1}{3}sh \\V_{1} = \frac{1}{3}*7*\frac{1}{2}*5*5\\V_{1} = 29.17[/tex]
[tex]V_{2} = sh\\V_{2} = 4*\frac{1}{2}*5*5 \\V_{2} = 50[/tex]
Total Volume of paperweight will be [tex]V_{1}+V_{2}[/tex]∴ Total volume
[tex]=50+29.17\\=79.17[/tex]
Therefore the total volume of paperweight will be 79.17 cubic inch
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Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 6 miles from her home. The football field is 7 miles from the library.
a. How far is library from the park?
b. How far is the park from the football field?
Answer:
a. 6.48 miles b. 9.54 miles
Step-by-step explanation:
a. 7/x=x/6
x^2=42
x=6.48
b. 13/x=x/7
x^2=91
x=9.54
Answer:
A. 6.48 miles
B. 9.54 miles
Step-by-step explanation:
hope this helps :-)
HELPPPPPPP GIVING 100 POINTS FOR ANSWER.......Ivan bought a box of macadamia nuts to bring home from his trip. A rectangular prism with a length of 18 centimeters, width of 15 centimeters, and height of 3 centimeters. What volume of nuts could the container hold? 270 centimeters cubed 369 centimeters cubed 738 centimeters cubed 810 centimeters cubed
Answer:
18 x 15 x 3 is 810. The volume is 810.
Step-by-step explanation:
Volume of cuboid= Length*Width*Breadth
Volume of container= 18 cm X 15 cm X 3cm
Volume of container=810
Hope i helped
Answer:
[tex]810[/tex] centimeters cubed.
Step-by-step explanation:
The formula: [tex]Length * width * height[/tex]
[tex]18 *15*3 =810[/tex] centimeters cubed
When 18 is subtracted from six times a certain number, the result is − 42.
What is the number?
Answer:
18-6×10=-42
Step-by-step explanation:
all i did was put it in my calculator
A ball is dropped from 16 feet above a hard surface. After each time it hits the surface, it rebounds to a
height that is 3/4 of its previous maximum height. What is the total vertical distance, to the nearest foot, the ball has traveled when it strikes the ground for the 10th time? Write out the first five terms of this sum to help visualize.
Answer:
a) Total distance travelled to the nearest foot = 105ft
b) First 5 terms = 12, 9, 6.75, 5.0625, 3.796875
Step-by-step explanation:
From the question above, we can see that this is a geometric series or progression
Formula for geometric progression:
Tn = arⁿ-¹
Where
a = first term
r = common ration
n = number of terms
From the question, we are told that the ball dropped from 16 feet
Hence First term(a) = 16
We are told that the ball rebounds to 3/4 of it's previous height anytime it hits the surface.
Hence, common ratio(r) = 3/4
a) We are told to find total distance to the nearest foot that the ball travelled when it strikes the ground for the 10th time
This means we are to find the sum of the first 10 terms.
Because the ball rises and falls, we would use the rises form
Where the first term = 12 and the number of times is 9 because it rises 9 times
The formula we would use to find this sum is based on if the common ratio is less than or greater than 1
Our common ratio = 3/4, hence it is less than 1.
When r< 1, sum of n terms =
Sn = a(1 - rⁿ)/ 1 - r
It is important to
Where a = 12
r = 3/4
n = 9
Sn = 12( 1 - (3/4)^9) / 1- 3/4
Sn = 104.79ft
Approximately = 105ft
b) First five terms
Using the formula
Tn = arⁿ-¹
Where
a = first term = 12
r = common ration
n = number of terms
First term, n = 1 = 12 × 3/4^(1-1)
= 12 × 3/4 ^(0)
= 12× 1
= 12
Second term, n = 2 = 12 × 3/4^(2-1)
= 12 × 3/4 ^(1)
= 36/4
= 9
Third term, n = 3 = 12 × 3/4^(3-1)
= 12 × (3/4)²
= 6.75
Fourth term, n = 4= 12 × 3/4^(4-1)
= 12 × (3/4)³
= 5.0625
Fifth term, n = 5 = 12 × 3/4^(5-1)
= 12 × (3/4)⁴
= 3.796875
Therefore, the first 5 terms = 12, 9, 6.75, 5.0625, 3.796875
The rebound of the ball from the height is an illustration of a geometric series
The total vertical distance at the 10th rebound is 60.352 feetThe first five terms of the sum are 16, 12, 9, 6.75 and 5.0625(a) The total vertical distance
The given parameters are:
[tex]\mathbf{a = 16}[/tex] -- the first term
[tex]\mathbf{r = \frac 34}[/tex] -- the common ratio
[tex]\mathbf{n = 10}[/tex] -- number of terms
The total vertical distance when it strikes for the 10th time is the sum of nth terms of the geometric series.
So, we have:
[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1- r}}[/tex]
Substitute values for (a), (r) and n
[tex]\mathbf{S_{10} = \frac{16(1 - 3/4^{10)}}{1- 3/4}}[/tex]
Simplify
[tex]\mathbf{S_{10} = \frac{16(0.943)}{0.25}}[/tex]
[tex]\mathbf{S_{10} = 60.352}[/tex]
Hence, the total vertical distance at the 10th rebound is 60.352 feet
(b) The first five terms of this sum
The nth term of a geometric series is:
[tex]\mathbf{T_n = ar^{n-1}}[/tex]
So, we have:
[tex]\mathbf{T_1 = 16}[/tex]
[tex]\mathbf{T_2 = 16 * 3/4 = 12}[/tex]
[tex]\mathbf{T_3 = 12 * 3/4 = 9}[/tex]
[tex]\mathbf{T_4 = 9 * 3/4 = 6.75}[/tex]
[tex]\mathbf{T_5 = 6.75 * 3/4 = 5.0625}[/tex]
Hence, the first five terms of the sum are 16, 12, 9, 6.75 and 5.0625
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Mr. Hernandez combines 1 gallon of orange juice, 3 pints of pineapple juice, and 2 quarts of lemon‐lime soda to make punch for a party. He allows 2 cups of punch for each guest. Will there be enough punch to serve all 14 guests? How much, if any, punch will be left?
Answer:
In total there are 30 cups and there are 2 left over
Step-by-step explanation:
The first thing is to clarify the equivalences, we have to:
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
We will pass everything to cups,
1 gallon of orange juice = 16 cups
3 pints of pineapple juice = 6 cups
2 quarts of lemon ‐ lime soda = 8 cups
So in total they would be 16 + 6 + 8 = 30 cups
How to get 2 cups for 14 guests in total would be 28 cups, which means that if 2 cups are left and left over.
Someone please help me
Answer:
3/2
Step-by-step explanation:
Since the lines goes through the point (0,0)
We have a point (2,3)
The slope is y/x = 3/2
HELP GUYS PLEASE ANSWER FAST
Answer:
5/4
Step-by-step explanation:
Slope is y1-y2/x1-x2 so if you plug in the coordinates you get 4-(-1)/4-0 which you would get 5/4
MAKE AN EQUATION, solve it.
A man has $0.70 in dimes and nickels. He has 8 coins altogether. How many nickels does he have?
Answer:
Number of nickels: 2,
Number of dimes: 6
Step-by-step explanation:
Say d ⇒ number of dimes, n ⇒ number of nickels; from this we can formulate two equation knowing the cost per dime ⇒ $ 0.1, and the cost per nickel ⇒ $0.05
d + n = 8,
0.1 * d + 0.05 * n = 0.7 ⇒ Let us solve through substitution
d = 8 - n into 0.1 * d + 0.05 * n = 0.7,
0.1 * ( 8 - n ) + 0.05 * n = 0.7,
0.8 - 0.1 * n + 0.05 * n = 0.7,
0.8 - 0.1n + 0.05n = 0.7,
- 0.05n = - 0.1,
Number of nickels: 2 ⇒ Now let us substitute this value into the first equation as to solve for d, dimes
d = 8 - 2,
Number of dimes: 6
5+3 I’m just asking a dumb question so that u can get points so ya!
Answer:
8
Step-by-step explanation:
thank u god!
Answer:
5+3 = 8!!!! :D
Step-by-step explanation:
Five plus three, is going to equal to eight total.
There are 10 students in a class: 6 boys and 4 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?
Answer:
1/ 6
Step-by-step explanation:
Therefore, the required probability is 1/6.
Answer:
1/6
Step-by-step explanation:
Think of drawing 1 student at a time without replacement.
First drawing:
p(boy) = 6/10
Second drawing:
p(boy) = 5/9
Third drawing:
p(boy) = 4/8
p(3 boys) = 6/10 * 5/9 * 4/8 = 3/5 * 5/9 * 1/2 = 3/18 = 1/6
Answer: 1/6
what is the slope of the line passing through (13,-2) and (3,-2)
Answer:
Slope (m) =0
Slope (m) =
ΔY
ΔX
= 0
θ =
arctan( ΔY )
ΔX
= 0°
ΔX = 3 – 13 = -10
ΔY = -2 – -2 = 0
Distance (d) = √ΔX2 + ΔY2 = √100 = 10
Evaluate l-a21, given a = 5, b=-3, and c= -2.
-10
10
-25
25
Answer:
10
Step-by-step explanation:
assuming those are meant to be absolute value brackets you have -5 x 2 which is -10 but because it is in the absolute value lines all answers become positive =10
What is the purpose of a regression line
Answer:
B. to show the general tendency of the points in a scatterplot
Step-by-step explanation:
Find the value of x in the figure below:
a. 20
b. 60
c. 180
d. 40
Answer:
d. 40
Step-by-step explanation:
2x + x +( x + 20) have to all equal 180 degrees in a triangle.
2x + x + x + 20 = 180
2x + 2x + 20 = 180
4x + 20 = 180
4x = 180 - 20
x = (180-20) / 4
x = 160 / 4
x = 40
Answer:
D. 40Step-by-step explanation:
This is the answer that was right for me, I just did this question :) Hope this helps! :D
y=sin 20 find the period
Answer:
In most cases u are either given the value of "t" or the question would be written this way: y=sin20t where as, when comparing we would get the exact value of T(period) at the end
a basket contains 20 green apples and 30 red apples if a piece of fruit is selected at random from the basket what is the probability that it will not be a red apple
Answer:
because
most people like green apples
833 ÷ 64 showing remainders
Answer:
13.015625
Step-by-step explanation:
Answer:
13 remainder 1.
I have attached the work to your question.
Please see the attachment below.
I hope this helps!
PLEASE HELP!!! Due very soon!! - The graph below represents the height of a football pass, in feet, x seconds after it is thrown. Which of the following best describes the interpretation of f(2) ?
I think it is either b or c. Please tell me which is correct!!! Pls!!!
Answer:
The answer is D.
Step-by-step explanation:
By the time 4 seconds has passed, the line is at the bottom of the graph, which represents the time the ball has landed. I hope this helps.
Find the volume of the triangular prism.
Answer:
225/4 sqrt(3) in ^3
Step-by-step explanation:
The volume is found by
V = Bh
The B is the triangle
B = s^2 sqrt(3)/4
= 5^2 sqrt(3)/4
25/4 sqrt(3)
We know the height is 9
V = 25/4 sqrt(3) *9
V = 225/4 sqrt(3)
this is approximately 97.42785793 in^3
A total of 511 tickets were sold for the school play. They were either adult tickets or student tickets. There were 61 more student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
255
Step-by-step explanation:
EXPLANATION We are looking for the number of adult tickets sold. number of adult tickets sold =x We are given that there were 61 more student tickets sold than adult tickets. number of student tickets sold =+x61 The total number of tickets sold was 511.
An investor invested a total of $900 in two mutual funds. One fund earned a 7% profit while the other earned a 4% profit. If the investor's total profit was $51, how much was invested in each mutual fund? The amount invested in the mutual fund that earned 7% was?
Answer:
y = 400 (amt invested at 4%)
x = 500 (amt invested at 7%)
Step-by-step explanation:
Kindly check attached picture for detailed explanation
Is 8/6 equivalent to 16/12 as a ratio
Answer:
they are equivalent
Step-by-step explanation:
8/6
Divide the top and bottom by 2
4/3
16/12
Divide the top and bottom by 4
4/3
They are the same so they are equivalent