Answers
Problem 1
Answer: C) 132.6--------------------
Explanation:
a1 = 1.7 = amount of concrete for the first step
a4 = x = amount of concrete for the fourth step
Sn = sum of the first n terms of an arithmetic sequence
Sn = (n/2)*(a1 + an)
S4 = (4/2)*(a1 + a4)
S4 = 2(1.7+x)
S4 = 2x+3.4
S4 = 17
2x+3.4 = 17
2x = 17-3.4
2x = 13.6
x = (13.6)/2
x = 6.8
We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d
an = nth term of an arithmetic sequence
an = a1 + d(n-1)
a4 = a1 + d(4-1)
a4 = a1 + 3d
6.8 = 1.7 + 3d
6.8-1.7 = 3d
5.1 = 3d
(5.1)/3 = d
1.7 = d
d = 1.7
Coincidentally, the common difference is the same as the first term. This won't always happen.
Now we can compute the 12th term
an = a1 + d(n-1)
a12 = 1.7 + 1.7(12-1)
a12 = 20.4
which is then used to find the sum of the first 12 terms
Sn = (n/2)*(a1 + an)
S12 = (12/2)*(a1 + a12)
S12 = 6(1.7 + 20.4)
S12 = 132.6
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Problem 2
Answer: C) [tex]x^2 + (y-10)^2 = 225\\\\[/tex]--------------------
Explanation:
The center is (h,k) = (0,10) which is where the nozzle is located.
The distance from (0,10) to (0,25) is 15 units, so r = 15.
Also, the distance from (0,10) to (0,-5) is also 15 units.
Plug those values into the equation below.
[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-10)^2 = 15^2\\\\x^2 + (y-10)^2 = 225\\\\[/tex]
That equation represents the boundary of the circle, which is where the water can reach.
=============================================================
Problem 3
Answer: B) 2.336 ft--------------------
Explanation:
a1 = height 1st bounce = 6.7 fta2 = height 2nd bounce = 81% of a1 = 81% of 6.7 = 0.81*6.7 = 5.427a3 = height 3rd bounce = 81% of a2 = 81% of 5.427 = 0.81*5.427 = 4.39587Or note that,
a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 = 4.39587
which must mean,
a4 = a1*(0.81)^3a5 = a1*(0.81)^4a6 = a1*(0.81)^5This is based off the idea that [tex]a_n = a(r)^{n-1}[/tex]
So,
a6 = a1*(0.81)^5
a6 = 6.7*(0.81)^5
a6 = 2.33614554867
a6 = 2.336
Related Questions
which shape has 2 parallel sides ready
Answers
Answer:
You have two sets of parallel sides. A square has two sets of parallel sides, and it has the extra condition that all of the angles are right angles. So a square is definitely going to be a rhombus. Now, all rhombuses have four sides.
Step-by-step explanation:
Answer:
A Parallelogram
Step-by-step explanation:
Help help help help help help help math math
Answers
Answer:
Step-by-step explanation:
5x + 10 + 10x + 5 = 180
15x + 15 = 180
15x = 165
x = 11
please help i only have a few minutes left!!
Answers
Answer:
VI
Step-by-step explanation:
The letter "A" is a vowel and a capital letter, so this should be categorized in group VI, where the vowel circle and the capital letter circle overlap.
Answer:
F
Step-by-step explanation:
It is a capital letter and a vowel
x² – 2xy + y², x² + 2xy + y², 4x² – xy + y², x² – y²
Answers
Answer:
[tex]\left(4x^2-xy+y^2\right)\cdot \left(x+y\right)^2\cdot \left(x-y\right)^2\\[/tex]
Step-by-step explanation:
If A = -3n + 2, and B = 5n - 7, what is the value of A - B, in simplest form?
Answers
Answer:
2n-5
Step-by-step explanation:
So you would combine your like terms witch would be -3n+5n which would give you 2n then you would do 2-7 and get -5 then you get you answer 2n-5
The value of (A - B) in the simplest form is (A - B) = -8n + 9.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equations are A = -3n + 2 and B = 5n - 7.
The value of A - B is:
A - B
= -3n + 2 - (5n - 7)
= -3n + 2 - 5n + 7
= -8n + 9
Hence, the value of (A - B) in the simplest form is (A - B) = -8n + 9.
Learn more about equations here:
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The price of an item has risen to $152 today. Yesterday it was $95. Find the percentage increase.
Answers
Answer:
60% increase
Step-by-step explanation:
152 - 95 = -57
57 / 95 = 0.6
0.6 x 100 = 60
The football team has a total of 350 jerseys. There are 154 medium-sized jerseys. What percent of the jerseys are medium-sized jerseys?
Pls help me
Answers
Answer:
Step-by-step explanation:
Given : The total number of jerseys = 350
The number of medium-sized jerseys = 154
Then, the percent of the jerseys are medium-sized jerseys will be :-
\begin{gathered}\dfrac{\text{Number of medium-sized jerseys }}{\text{Total jerseys}}\times100\\\\=\dfrac{154}{350}\times100\\\\=0.44\times100=44\%\end{gathered}
Total jerseys
Number of medium-sized jerseys
×100
=
350
154
×100
=0.44×100=44%
Therefore , the percent of the jerseys are medium-sized jerseys = 44%
3 3/4 divided by 1 1/3 in fraction answer
Answers
Answer: 4/3
Step-by-step explanation:
The dot product of u ∙ u = 45 what is the length of u?
Answers
Answer:
67 hah why you solve this
[tex]\textbf{u} \cdot \textbf{u} = 45\\\\\implies |\textbf{u}|^2 =45\\\\\implies |\textbf{u}| = 3\sqrt{5}[/tex]
A 15 kg ball is thrown into the air. It is going at 4m/s when thrown. How much potential energy will it have at the top?
Answers
Answer:
A ball is thrown vertically upward with a speed of 25.0 m/s
How much pure alcohol must a pharmacist add to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution? ASAP
Answers
20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.
Let x represent the volume of pure alcohol (100%) in cm³ needed to be added. Hence:
x * 100% + 10 cm³ * 10% = 70% * (x + 10 cm³)
x * 1 + 10 * 0.1 = 0.7 * (x + 10)
x + 1 = 0.7x + 7
x - 0.7x = 7 - 1
0.3x = 6
x = 20 cm³
Therefore 20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.
Find out more on equation at: https://brainly.com/question/13763238
Answer:
20 cm³
Step-by-step explanation:
What is the gradient of the graph shown?
Give your answer in its simplest form.
Answers
Answer:
[tex]\displaystyle m = \frac{-1}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Step-by-step explanation:
Step 1: Define
Identify points from given graph.
Point (0, -1)
Point (-3, 0)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m.
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{0 - -1}{-3 - 0}[/tex][Order of Operations] Evaluate: [tex]\displaystyle m = \frac{1}{-3}[/tex]Write the missing volues to make these equivalent fractions correct.
2/3 = 4/ = /12
Answers
Answer:
2/3 = 4/6 = 8/12
Step-by-step explanation:
Casey borrowed $4500 at a 5% interest rate for 4 years.
What was the total interest?
Enter your answer in the box.
Hint: Use the formula I=P*R*T where
I= Interest Earned/Owed
P= Principal
R= Rate
T= Time
PLEASE HURRYYYY!
Answers
I = $4500 x 5% x 4
5% = .5
4500 x .5 x 4 = 9,000
I think this should be correct .
rico wants to buy a battery operated toy car which caused 580 7.50 he has already save one 50.00 points his ninong give him 200 point zero zero if he saved 12.50 a day from his allowance how long will it take him to save the rest of money to buy the toy car
Answers
Answer:
19 days
Step-by-step explanation:
1 - Make an equation with the variables provided.
150 + 200 + 12.50x = 587.50
2 - Simplify both sides.
350 + 12.50x = 587.50
3 - Subtract 350 from both sides.
12.50x = 237.50
4 - Divide by 12.50 to find your x variable.
x = 19 days
Brainliest would be appreaciated! :-)
WILL GIVE BRAINLIEST THANK AND FIVE STAR!
Which equation is equivalent to 32x−4y+1=0?
y=4x−1y is equal to 4 x minus 1
y=−38x−14y is equal to negative 3 eighths x minus 1 fourth
y=38x+14y is equal to 3 eighths x plus 1 fourth
y=−4x+1
Answers
Answer:
y=−38x−14y is equal to negative 3 eighths x minus 1 fourth is the answer.
How many different five-letter
arrangements can be made from the
letters in the word "PLUTO"?
5
25
60
120
Answers
Answer:
my guess would probably be 5 but it could also be 25. (id like to say the answer but i cant cause this should be something for you to decide the answer not me.
Step-by-step explanation:
I hope this helps you!
Please help! photo is attached with the problem.
Answers
Sofia walks from her house to the park. She reaches the park at 5 5 : : 25 25 . If it is a 40 40 -minute walk, what time did she leave her house?
Answers
Answer:
4:45
Step-by-step explanation:
hope this helps
Line f has a slope of -9/7. Line g is perpemdicular to f. What is thr slope of line g
Answers
Pls help I’ll brainlest ASAP
Answers
2 / 3 = 0.7 i think
/I could use some help i dont know this
Answers
Answer:
4.5+19.75=24.25
Step-by-step explanation:
what are the values? f(3)
Answers
Answer:
it's simply what we follow and respect like we value our culture
Step-by-step explanation:
hope this will help
Freddy’s savings account went from $520 to $321 after he purchased a new bike. What was the percent decrease? *
Answers
If my calculations are correct, the percentage decrease faced here is roughly 38.2%. Based on the calculations, the bicycle costs 199$ and when the cost is subtracted from 520, you would create the percentage of 38.2%.
Divide (x^3+2x-6x-9) by (x+3)
Answers
Answer:
x² - 3x + 5 - [24÷(x+3)]
Step-by-step explanation:
1. Expand (x³ + 2x - 6x - 9)
= x³ - 4x - 9
2. Divide [x³ - 4x - 9 by x+3]
= x² + [(-3x^2-4x-9) ÷ (x+3)]
3. Divide [(-3x^2-4x-9) by (x+3)]
= -3x + [(5x-9) ÷ (x+3)]
x² - 3x + [(5x-9) ÷ (x+3)]
4. Divide [(5x-9) ÷ (x+3)]
= 5 + [(-24) ÷ (x+3)]
x² - 3x + 5 + [(-24) ÷ (x+3)]
= x² - 3x + 5 - [24 ÷ (x+3)]
What is the prime factorization of 24?
1. 2x2x2x3
2. 2x2x3
3. 8x3
4. 6x4
Answers
Answer:
1. 2x2x2x3
Step-by-step explanation:
Let's do process of elimination.
2. 2x2x3
2x2=4 4x3=12
2 is false.
3. 8x3
8x3=24
3 is true, but 8 is not a prime number.
4. 6x4
6x4=24
4 is true, but 6 is not a prime number.
This leaves 1. 2x2x2x3.
1. 2x2x2x3
2x2=4 2x3=6 6x4=24
1 is true, and 2 and 3 are prime numbers. So, the answer is 1.
-hope it helps
Answer:
1. 2x2x2x3
Step-by-step explanation:
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.
[tex]24\:\mathrm{divides\:by}\:2\\\\\quad \:24=12\cdot \:2[/tex]
[tex]12\:\mathrm{divides\:by}\:2\\\\\quad \:12=6\cdot \:2[/tex]
[tex]6\:\mathrm{divides\:by}\:2\quad\\\\ \:6=3\cdot \:2[/tex]
[tex]2, 6\:\mathrm{divides\:by}\:2\quad \\\\\:6=3\cdot \:2[/tex]
Please solve i need help :,) tyy
Answers
Answer:
6. 47
7. –25
8. 15
9. –33
10. –9
Step-by-step explanation:
Substitute.
6. x=-7
y = -8x - 9
= -8(-7)-9
= 56-9
y=47
7. x=2
y= -8x-9
= -8(2)-9
= -16-9
y= -25
8. x=-3
y= -8x-9
= -8(-3)-9
=24-9
y= 15
9. x=3
y= -8x-9
= -8(3)-9
= -24-9
y= -33
10. x=0
y= -8x-9
= -8(0)-9
= 0-9
y= -9
Determine whether each sequence is arithmetic, geometric, or neither. Explain
-6, -3, 0, 3, ...
Answers
Answer:
Its arithmetic because it's being added 3 each time.
Answer:
Arithmetic
Step-by-step explanation:
Arithmetic refers to addition and subtraction. Geometric refers to multiplication and division.
In this instance, the sequence has a common difference of 3 (3 is added as the sequence continues).
please help ill mark brainliestO
Answers
Answer:
Yes triangles ACB and FGC are similar using AA.
(Please don't hate if it's wrong)
A self-storage center has many storage rooms that are 6 ft wide, 10 feet deep, and 12 ft high. What is the volume of the room?
Answers
The volume of the storage room is the amount of space in the storage room, and it is 720 cubic feet
The dimensions are given as:
[tex]Width = 6ft[/tex]
[tex]Depth = 10ft[/tex]
[tex]Height = 12ft[/tex]
The volume of the storage room is the product of the dimensions.
So, we have:
[tex]Volume= Width \times Depth \times Height[/tex]
Substitute values for Width, Depth and Height
[tex]Volume= 6ft \times 10ft \times 12ft[/tex]
Multiply the dimensions
[tex]Volume= 720ft^3[/tex]
Hence, the volume of the storage room is 720 cubic feet
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