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
Read more about geometric series at:
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On a certain standardized test used for college entrance purposes, the mean score was 21 and the standard deviation was 5. The distribution was approximately normal. Carlos scored 31, two standard deviations above the mean. A total of 1.5 million people across the country took the test at the same time as Carlos. How many people had scores lower than Carlos?
a. 1,465,500 people
b. 977,000 people
c. 204,000 people
Answer:
A
Step-by-step explanation:
Carlos' score was 2 standard deviations from the mean, so his z-score was 2.0. You can either use the empirical 68-95-98.5 rule, or you can plug it into your calculator as normalcdf(-999, 2) = .977
So 97.7% of people had a score lower than Carlos!
.977 * 1.5 million = 1,465,500 people
A soup can have a volume of 54 π in³ and a height of 6 in.
What is the area for the label needed to wrap around the can with no overlaps? Express your answer in terms of π.
Answer:
The area of the label is 36*pi in²
Step-by-step explanation:
A can of soup has a shape of a cylinder, therefore it's volume is equal to:
Volume = pi*r²*h
We need to use the formula above to find the radius of the base, because we need to calculate the lateral area of the cylinder, which is given by:
Lateral area = 2*pi*r*h
Applying the data from the problem we have:
54*pi = pi*r²*6
pi*r²*6 = 54*pi
r² = 54*pi/(pi*6)
r² = 54/6 = 9
r = sqrt(9) = 3 in
Therefore the lateral area is:
lateral area = 2*pi*(3)*(6) = 36*pi in²
Answer:
18π in ²
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cylinder.
Given data
volume v = 54 π in³
Height h = 6 in
In this problem we are considering the surface area of the cylinder
(not the total though ) but the curved surface area
Let us solve for the radius of the shape
Volume = πr²h
54π= π*r²*6
54/6= r²
r²= 9
r= √ 9
r= 3in
Area of curved surface = 2πrh
Area = 2πrh
Area =2π*3*6
Area = 18π in ²
What's the x for
-2(x+3)=-10
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]-2(x+3)=-10\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x+3\right)}{-2}=\frac{-10}{-2}\\Simplify\\\frac{-2\left(x+3\right)}{-2}=\frac{-10}{-2}\\\frac{-2\left(x+3\right)}{-2}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{2\left(x+3\right)}{2}\\\mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1\\=x+3[/tex]
[tex]\mathrm{Simplify\:}\frac{-10}{-2}:\quad 5\\\frac{-10}{-2}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{10}{2}\\\mathrm{Divide\:the\:numbers:}\:\frac{10}{2}=5\\=5\\x+3=5\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\x+3-3=5-3\\\mathrm{Simplify}\\x=2[/tex]
Answer:
x+3=-10/-2=5
x=5-3=2
What’s the median of this set of data 71,37,22,81,65,54,52,41,48,71
Answer:
I'm glad you asked!
Step-by-step explanation:
Step 1:Order the numbers from least to greatest.
[tex]22,37,41,48,52,54,65,71,71,81[/tex]
Step 2:Now find the middle number.
[tex]22,37,41,48[/tex],52,54[tex],65,71,71,81[/tex]
Step 3:Since there are two numbers,we add them together then divide by 2.
[tex]52+54 =106[/tex]
[tex]106/2=53[/tex]
The median is 53.
Answer:
53
Step-by-step explanation:
PLEASE HELP THIS IS SUPER URGENT
Answer:
-1
Step-by-step explanation:
x+4/4 = 9/12
If you plug in -1, then 3/4=9/12.
This is a true proportion.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
PLEASE HELP MATH!!!!!! MULTIPLE CHOICE!!
Choose 1 answer:
(Choice A)
sin(30°)
(Choice B)
cos(30°)
(Choice C)
sin(300°)
(Choice D)
cos(300°)
(Choice E)
sin(330°)
(Choice F)
cos(330°)
Answer:
B should be the correct answer
Step-by-step explanation:
don't quote me on that
A flag pole broke in a storm it was originally 81 feet tall 28 feet are still sticking straight out of the ground where it snapped but the remaining piece has changed over and touches the ground some distance away how far away is the end of the pool from the base of the pool along the ground
Answer:
Step-by-step explanation:first u need to buy then break it into half with ur friend then ur friend will get all and u will only get one but u will be lonely if u don’t tell ur friend to give u
How to round three decimal places
Answer:
go FORWARD 3 places
Step-by-step explanation:
To measure the height of a mountain, a surveyor took two sightings, one 1000 feet farther from the mountain of the other. The first angle of elevation was 85° and the second was 83°.
What is the mountain’s height?
Answer:
Height of the mountain was 28331.8 feet.
Step-by-step explanation:
An observer took the measurements from two sights C and D.
Point D was 1000 ft away from the earlier sight point C.
Angle of elevations from points C and D were 85° and 83° respectively.
From ΔABC,
tan85 = [tex]\frac{h}{x}[/tex]
x = [tex]\frac{h}{tan85}[/tex] -----(1)
Similarly, from ΔABD,
tan83 = [tex]\frac{h}{(x+1000)}[/tex]
x + 1000 = [tex]\frac{h}{tan83}[/tex]
x = [tex]\frac{h}{tan83}-1000[/tex] -----(2)
Now we substitute the value of x from equation (1) in the equation (2)
[tex]\frac{h}{tan85}=\frac{h}{tan83}-1000[/tex]
0.122785h - 0.087488h = 1000
0.035296h = 1000
h = 28331.822 ft
h ≈ 28331.8 ft
Therefore, height of the mountain was 28331.8 feet.
100 points. WILL MARK BRAINLIEST. EASY QUESTION
Topic: Fractions.
ONLY COMPLETE QUESTION 1
Answer:
1/4
Step-by-step explanation:
We have 3/4 of a tank
We will use 2/3 of the gas in the tank
That will leave us 1/4
Mathematically
3/4*2/3 = 2/4 =1/2 this is the amount that is used
Subtract this from the amount in the tank
3/4 -1/2
3/4 -2/4 = 1/4
This is the amount that is left in the tank
2) A player took 12 shots and
made 9. What percent did
he make?
Answer: 9/12 equals 0.75 so 75 percent is the answer.
Step-by-step explanation:
please help me with math
Answer:
592 sq. ft.
Step-by-step explanation
area of front and back=2[12×6]+2[1/2×12×8]=144+96=240 ft²
side area=2[(6+10)×11]=2×176=352 ft²
Total surface area=240+352=592 square feet.
Which inequality is represented by this graph?
A. 0 > X
B. X > 0
C. 0 >_ X
D. X >_ 0
Answer:
B. X > 0
Step-by-step explanation:
It is X > 0, because the circle is empty, which means that X cannot be 0, which allows s to eliminate C and D as an answer. The arrow shows that X is greater than 0. Therefore, you can eliminate A as an answer, leaving us with B. X > 0
The volume of this rectangular prism is 70 cubic units. If the area of the base is 28 square units, what is the height of the prism.
Answer:
height = 2.5 units
Step-by-step explanation:
The volume of a rectangular prism is given by the product of its base area and its height. If the area of the base is 28 square units and the volume is 70 cubic units, we can find the height as follows:
Volume = base area * height
70 = 28 * height
height = 70 / 28
height = 2.5 units
The height of the rectangular prism is 2.5 units.
Which is the expression 4×4×4×3×3×2×2×2×2 written using exponents?
Answer:
43 32 24
Step-by-step explanation:
4×4×4×3×3×2×2×2×2
I count 3 fours, 2 threes, 4 twos.
4×4×4×3×3×2×2×2×2
[tex]= 4^3 3^2 2^4[/tex]
That might be the answer; we don't see the choices.
Since 4 is 2² we can take another step.
[tex]= (2^2)^3 3^2 2^4[/tex]
[tex]= 2^6 3^2 2^4[/tex]
[tex]= 2^{10} 3^2[/tex]
That's the full prime factorization.
Answer: 2¹⁰ 3²
Use a net to find the surface area of the right triangular prism shown below (Please show how you worked it) :
104 square feet
412 square feet
468 square feet
504 square feet
Answer:
468 square feet; Option C
Step-by-step explanation:
We can see that the base of this triangular prism has dimensions 15 feet by 10 feet, so for starters let us compute the area of this base:
Area ⇒ 15 * 10 = 150 ft^2
Now the rectangular surface next to this base, has dimensions 9 feet by 10 feet, provided that 9 feet is a uniform height of the triangular prism:
Area ⇒ 9 * 10 = 90 ft^2
This third rectangle is provided with one dimensions, of 10 feet. If we were to imagine what part of the 3-d shape is is, it would in fact be the slanted top. To find the second dimension, you would imagine it to be 12 feet. Using that, the area of this rectangle is thus ⇒ 10 * 12 = 120 ft^2
Now the two triangles at the corners each have an area of ⇒ 1/2 * base * height = 1/2 * 12 * 9 = 6 * 9 = 54 ft^2, so they have a total area of ⇒ 108 ft^2
This means the surface area of the right, triangular prism is:
150 + 90 + 120 + 108 = Answer: 468 square feet
Bryan bought 10 daisies and 5 sunflowers. Each daisy cost $2 and each sunflower cost $5. Bryan had $12 left after he made his purchase.
How much money did Bryan spend on the flowers? Which info isnt needed to answer this question?
Answer:
Bryan spent $45 on flowers. The last sentence isn't needed to answer this question.
Step-by-step explanation:
If you multiply 10 by 2, then 5 by 5, and add it at the end you get 45.
There are 25 students in a science class. Twenty percent of the students are randomly selected to participate in a teacher evaluation. How many combinations of students are possible?
Answer: 53,130 possible combinations
Step-by-step explanation:
First, we want to find how much is the 20% of 25.
This is:
N = (20%/100%)*25 = 5.
So 5 students out of 25 are selected.
When we want to calculate the number of combinations of N elements it a group of K elements, we have:
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here N = 25, and K = 5
[tex]C = \frac{25!}{20!*5!} = \frac{25*24*23*22*21}{5*4*3*2*1} = 53,130[/tex]
so we have 53,130 combinations.
Please help!
Eric has $4,610 in a savings account that earns 4% interest, compounded annually.
To the nearest cent, how much will he have in 2 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$ ___
Answer:
$ 4,986.18
Step-by-step explanation:
A = $ 4,986.18
A = P + I where
P (principal) = $ 4,610.00
I (interest) = $ 376.18
Sylvia read that the height of the Empire State Building is 443.2 m and wants to build a scale model of the building in her room. She knows that the height of the ceiling in her room is 8 ft. Write a scale that would allow a scale model of the Empire State Building in Sylvia's bedroom so that the top of the building would just touch her ceiling.
Answer:
Scale of 181: 1
Step-by-step explanation:
The first thing to do is to pass the feet by the meter, to work in the same units and thus create a consistent scale:
We know that one foot equals 0.3048 meters, therefore:
8 feet * 0.3048 meters / 1 foot = 2.4384 meters
So the scale would be:
443.2 / 2.4384 = 181.75
Which means that it is best to make a scale of 181: 1
Where 181 meters from the Empire State Building would equal 1 meter at home 0 181 inches would equal 1 inch at home
please answer quick!!
Answer: B
Step-by-step explanation:
[tex]\frac{2}{7k}(k-7)[/tex]
[tex]\frac{2k-14}{7k}[/tex]
[tex]\frac{2k}{7k}-\frac{14}{7k}[/tex]
[tex]\frac{2}{7}-\frac{2}{k}[/tex]
If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be true? On a coordinate plane, a straight line with negative slope represents (f + g) (x). It goes through points (negative 3, 4), (0, 1), and (1, 0).
Answer:
You did not write the options, but let's solve it in a general way.
f(x) and g(x) are quadratic functions, this means that:
f(x) = a*x^2 + b*x + c
g(x) = d*x^2 + e*x + f
now, (g + f)(x) is a linear function that goes trough the points (-3, 4), (0,1 ) and (1,0)
(g + f)(x) = s*x + k
We can find the slope of this linear function as:
S = (y2 - y1)/(x2 - x1)
i will use the first two points.
S = (1 - 4)/(0 - (-3) = -3/3 = -1
so we have: ( f + h)(x) = -1*x + k
and we can find k using one of the points, for example (0, 1)
1 = -1*0 + k
b = 1.
so we have: (f + g)(x) = -1*x + 1.
Now, (f+g)(x) = (a + d)*x^2 + (b + e)*x + (c + f) = -1*x + 1.
So we must have that:
a = -d
b + e = -1
c + f = 1.
Answer:
A. The leading coefficients of f(x) and g(x) are opposites.Step-by-step explanation:
Triangle CDE is translated down into the right forming triangle C’D’E’. Which congruency statement is correct?
Answer:
B: DCE=D'C'E'
I hoped this helped you!
The required Triangle DCE is congruent to triangle D'C'E'. Option B is correct.
What is congruent geometry?In geometry, two figures are congruent if they have the same shape and size, and all their corresponding parts (sides, angles, and vertices) are congruent. Congruent figures can be moved, rotated, or reflected without changing their shape or size.
Here,
Triangle DCE is congruent to triangle D'C'E'.
This is because a translation is a type of transformation that preserves the shape and size of the original figure, so the two triangles are congruent with each other.
Thus, the required Triangle DCE is congruent to triangle D'C'E'. Option B is correct.
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Awaste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 19y * d ^ 3 of debris. Find the dimensions of the dumpster that will minimize its surface area.
Answer:
1.92 yd x 3.83 yd x 2.58 yd
Step-by-step explanation:
We have given a rectangular base, that its twice as long as it is wide.
It must hold 19 yd³ of debris.
Lets minimize the surface area, subject to the restriction of volume (19 yd³)
The surface is given by:
[tex]S=2(w*h+w*2w+2wh)=2(3wh+2w^2)[/tex]
The volume restriction is:
[tex]V=w*2w*h=2w^2h=19\\\\h=\frac{9.5}{w^2}[/tex]
replacing h in the surface equation, we have:
[tex]S=2(3wh+2w^2)=6w(\frac{9.5}{w^2})+4w^2=57w^{-1}+4w^2[/tex]
Derivate the above equation and set it to zero
[tex]dS/dw=57(-1)w^{-2} + 8w=0\\\\57w^{-2}=8w\\\\w^3=57/8=7.125\\\\w=\sqrt[3]{7.124} =1.92[/tex]
The height will be:
[tex]h=9.5/w^2=9.5/(1.92^2)=9.5/2.69=2.58[/tex]
Therefore,The dimensions that minimize the surface are:
Wide: 1.92 yd
Long: 3.83 yd
Height: 2.58 yd
Which represents the reflection of f(x) = StartRoot x EndRoot over the x-axis?
Step-by-step explanation: For edge2020 it is C graph.
Find a unit rate: Joel ran 1500 meters in 5 minutes, 5 seconds.
Answer:
minutes
Step-by-step explanation:
Simplify square root of five times the quantity six minus four square root of three.
6√5 - 4√3-
i took the test but sorry if its wrong
What are the solutions to the quadratic equation 4(x + 2)2 = 36
x = -11 and x = 7
x = -7 and x = 11
x = -5 and x = 1
x= -1 and x = 5
mentary
condary
s Notebo...
Spring
Previous Activity
Answer:
C) x = −5 and x = 1
Step-by-step explanation:
I took the test and I got it right
The solutions to the quadratic equation [tex]4(x + 2)^2 = 36[/tex] are as x = -5 and x = 1.
What is a solution for a quadratic equation?Suppose that we've a function y = f(x) such that f(x) is quadratic.
When y = 0, then the values of x for which f(x) = 0 is called solution of quadratic equation f(x) = 0
This solution gives values of x, and when we plot x and f(x), we'd see that the graph intersects the x-axis at its solution points.
We have the given quadratic equation
[tex]4(x + 2)^2 = 36[/tex]
solving for x
[tex]4(x + 2)^2 = 36\\\\(x + 2)^2 = 36/4\\\\(x + 2)^2 = 9\\\\(x + 2)^2 = 3^2\\\\(x + 2) = 3\\\\x = 1\\or \\\\x + 2 = -3\\\\x = -5[/tex]
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The following points for a function are graphed in the coordinate plane: (0, 4), (1, 5), (2, 6), and (3, 7).
What function is being graphed?
y = 4x
y = 2x + 3
y = x + 4
3x + 4
Answer:
y = x + 4
Step-by-step explanation:
I have attached the work to your problem below.
Please see the attachment.
I hope this helps.
Answer:
y = x + 4
Step-by-step explanation:
I took the lesson and got it correct
Cereal costs $3.00 for a 12 ounce box, $4.00 for a 16 ounce box, and $5.00 for a 20 ounce box. Which size cereal box has the lowest price per ounce?
Answer:
Step-by-step explanation:
For this problem, you have to find out how much each cereal costs per ounce. So you must divide each price by the amount of cereal you get and compare:
$4.08/16oz=$0.255/oz
Find the unit price ($/oz) of the remaining 2 then compare. The lowest value is the best buy!