Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Thank you guys fir the help
Answer:
6x^3-2x^2+4x-8
Step-by-step explanation:
f(x) = 3x^2 +4x-6
g(x) = 6x^3 -5x^2 -2
f(x) + g(x) = 3x^2 +4x-6+ 6x^3 -5x^2 -2
Combine like terms
f(x) + g(x) = 6x^3+3x^2-5x^2+4x-6-2
=6x^3-2x^2+4x-8
Answer:
[tex]6 {x}^{3} - 2 {x}^{2} + 4x - 8[/tex]
Answer C is correct
Step-by-step explanation:
[tex]f(x) = 3 {x}^{2} + 4x - 6 \\ g(x) = 6 {x}^{3} - 5 {x}^{2} - 2 \\ (f + g)(x) =( 3 {x}^{2} + 4x - 6) + (6 {x}^{3} - 5 {x}^{2} - 2) \\ = 3 {x}^{2} + 4x - 6 +6 {x}^{3} - 5 {x}^{2} - 2 \\ = 6 {x}^{3} - 2 {x}^{2} + 4x - 8[/tex]
A simple random sample of 400 individuals provides 112 Yes responses. (a) What is the point estimate of the proportion of the population that would provide Yes responses
Answer:
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
Step-by-step explanation:
Point estimate of the proportion of the population that would provide Yes
The sample proportion of yes responses.
In the sample:
112 yes responses in the sample of 400, so:
[tex]p = \frac{112}{400} = 0.28[/tex]
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
An expression is shown below:
10n3 − 15n2 + 20xn2 − 30xn
Part A: Rewrite the expression so the GCF is factored completely. (4 points)
Part B: Rewrite the expression completely factored. Show the steps of your work.
Answer:
An expression is shown below:
10n³− 15n² + 20xn² − 30xn
Part A: Rewrite the expression so the GCF is factored completely. (4 points)
10n³− 15n² + 20xn² − 30xn
2*5*n*n*n-5*3*n*n+2*5*2*x*n*n-2*5*3*x*n
Greatest common factor=5*n=5n
Part B: Rewrite the expression completely factored. Show the steps of your work.
Solution given;
10n³− 15n² + 20xn² − 30xn
5n(2n²-3n+4xn-6x)
5n(2n²+4xn-3n-6x)
5n(2n(n+2x)-3(n+2x))
5n(n+2x)(2n-3)
Answer:
[tex]5n(2n-3)(n+2x)[/tex]
Step-by-step explanation:
Step 1: Rewrite the expression so the GCF is factored completely
[tex]10n^{3} - 15n^{2} + 20xn^{2} - 30xn[/tex]
The GCF is 5n so factor it out
[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]
Step 2: Rewrite the expression completely factored
[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]
[tex]5n(2n(n+2x)-3(n+2x))[/tex]
[tex]5n(2n-3)(n+2x)[/tex]
Answer: [tex]5n(2n-3)(n+2x)[/tex]
Farmer Dave harvested his corn. He stored 5/9 of his corn in one large silo and ¾ of the remaining corn in a small silo. The rest was taken to market to be sold.
a. What fraction of the corn was stored in the small silo?
b. If he harvested 18 tons of corn, how many tons did he take to market?
After storing 5/9 in the large silo there was 4/9 left ( 1-5/9 = 4/9)
A. Multiply 4/9 by 3/4:
4/9 x 3/4 = 12/36 = 1/3
1/3 of the corn was in the small silo.
B. 1-5/9 -1/3 = 4/9-1/3 = 4/9-3/9 = 1/9
1/9 of the corn went to market:
18 x 1/9 = 18/9 = 2
2 ton went to market.
11
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
O A. In 2 – In x
OB. 1 + In 2 - In x
Oc. In 2 + In x
OD. In 1 + In 2 - In
Reset
Next
Answer:
B. 1 + ln 2 - ln x
General Formulas and Concepts:
Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex] Logarithmic Property [Dividing]: [tex]\displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle ln(\frac{2e}{x})[/tex]
Step 2: Simplify
Expand [Logarithmic Property - Dividing]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2e) - ln(x)[/tex]Expand [Logarithmic Property - Multiplying]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + ln(e) - ln(x)[/tex]Simplify: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + 1 - ln(x)[/tex]Rewrite: [tex]\displaystyle ln(\frac{2e}{x}) = 1 + ln(2) - ln(x)[/tex]Write the expression as a trinomial: (y+7)(y-11). You want to make the expression into trynomial form, not simplified it
Answer:
y² - 4y - 77
Step-by-step explanation:
(y+7)(y-11)
y² - 11y + 7y - 77
y² - 4y - 77
What is the slope-intercept equation of the line below?
Answer:
y=-5/4x+3
Step-by-step explanation:
y=mx+c
m = (y1-y2)/(x1-x2) =(-2-3)/(4-0) =-5/4
sub the values y=3, x=0 to find c,
3 =-5/4(0) + c
c = 3
Solve forx.
(2x - 1) (5x+3) = 0
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{(2x - 1)(5x + 3) = 0}\\\rightarrow\large\textsf{10x}\mathsf{^2}\large\textsf{ + x - 3 = 0}[/tex]
[tex]\huge\text{FACTOR the LEFT SIDE of the equation}[/tex]
[tex]\large\textsf{(5x + 3)(2x - 1) = 0}[/tex]
[tex]\huge\text{SET the FACTORS to equal to 0}[/tex]
[tex]\large\textsf{5x + 3 = 0 or 2x - 1 = 0}[/tex]
[tex]\huge\text{SIMPLIFY \& YOU HAVE YOUR RESULT}\\\\\huge\text{to your question if you solved correctly.}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: \boxed{\mathsf{x = - \dfrac{3}{5}\ or \ x = \dfrac{1}{2}}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
5 less than three times a number is 37 what is the number
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
3x - 5 = 37
Step 2: Solve for x
[Addition Property of Equality] Add 5 on both sides: 3x = 42[Division Property of Equality] Divide 3 on both sides: x = 14Translate and solve: five less than z is 4
z -5 =4
neutralize the left -5 by adding 5 on both sides
z -5 (+5) = 4 (+5)
z = 9
Integrate the following. ∫[tex]84dx[/tex]
Answer:
[tex]\displaystyle \int {84} \, dx = 84x + C[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsDefinite/Indefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {84} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {84} \, dx = 84\int {} \, dx[/tex][Integral] Reverse Power Rule: [tex]\displaystyle \int {84} \, dx = 84x + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integrations
(1+y²)dx + (1+x²)dy = 0
This differential equation is separable:
(1 + y²) dx + (1 + x²) dy = 0
(1 + y²) dx = - (1 + x²) dy
dy/(1 + y²) = -dx/(1 + x²)
Integrating both sides gives
arctan(y) = -arctan(x) + C
and solving for y gives (over an appropriate domain)
y = tan(C - arctan(x))
(the domain being -1 ≤ y ≤ 1).
kofi earned 50 cedis mowing lawn. today, kofi earned 60% of what he earned yesterday mowing lawns. how much money did kojo earn mowing lawn today
Answer:
Kofi earned today = 30 cedis
Step-by-step explanation:
Given:
Kofi earned yesterday = 50 cedis
Kofi earned today = 60% of Kofi earned yesterday
Find:
Kofi earned today
Computation:
Kofi earned today = 60% of Kofi earned yesterday
Kofi earned today = 60% x 50
Kofi earned today = 0.60 x 50
Kofi earned today = 30
Kofi earned today = 30 cedis
Dr. Kingston predicted that swearing can help reduce pain. In the study, each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In one condition, the participants repeatedly yelled their favorite curse words while their hands were in the water. In the other condition the participants repeated a neutral word. The table below presents the amount of time that participants kept their hand in the ice in each condition.
Swear Words
Neutral Words
98
56
70
61
52
47
87
60
46
32
120
92
72
53
41
31
1. Calculate the mean for the Swear Words condition:_______________
Answer:
Step-by-step explanation:
First, we add them all up.
98+70+52+87+46+120+72+41 = 586
Now, we divide 586 by the number of things there are. 586 / 8 = 73.25.
The mean of the swear words condition is 73.25.
The triangles are similar. Find x.
Please help me!
GIVEN -> Triangles r similar
so sides r in ratio
[tex] \frac{2.4}{3} = \frac{2.8}{x} \\ 0.8 = \frac{2.8}{x} \\ x = \frac{2.8}{0.8} \\ x = \frac{28}{8} \\ x = 3.5 \: \: ans[/tex]
Answer:
3.5
Step-by-step explanation:
We can write a ratio to solve
2.4 2.8
----- = --------
3 x
Using cross products
2.4x = 3(2.8)
2.4x =8.4
Divide each side by 2.4
2.4x /2.4 = 8.4/2.4
x = 3.5
what represent the area of the rectangle in cm^2??
9514 1404 393
Answer:
d. 3x² +15x
Step-by-step explanation:
The area is the product of length and width.
A = LW
A = (3x)(x+5) = 3x(x) +3x(5) . . . . use the distributive property
A = 3x² +15x
Answer: D) 3x^2 + 15
==========================================================
Explanation:
Draw a horizontal line to divide the rectangle into two parts (they don't necessarily have to be equal parts). Refer to the diagram below. The upper rectangle is x by 3x. So its area is length*width = x*3x = 3x^2
The lower rectangle is 5 by 3x, so its area is 5*3x = 15x
Combine those two sub-areas back together to get the overall area of 3x^2 + 15x
You could also use the distribution rule
3x*(x+5) = 3x*(x) + 3x*(5) = 3x^2 + 15x
If you were asked to measure the success of a campaign to fight for human rights, what criteria would you use?
Step-by-step explanation:
Many factors would be used to assess the effectiveness of a human rights campaign, including the following:
Social Influence. Direct Interpersonal Reach. Participant Observation. Reputation. Volume of Search & Interest. Website Traffic.
National Research.
please can anyone help me with this question what is the probability of the spinner landing on an even number.
37. The trip between 2 towns is exactly 90 miles. You have gone 40% of this distance. How far have
you gone?
Answer:
36 miles
Step-by-step explanation:
We want to find 40% of 90 miles
40% * 90
.40 * 90
36 miles
We have to find travelled distance inorder to find this we have to find 40℅ of 90miles
[tex]\\ \Large\sf\longmapsto 90\times 40\℅[/tex]
[tex]\\ \Large\sf\longmapsto 90\times \dfrac{40}{100}[/tex]
[tex]\\ \Large\sf\longmapsto 9\times 4[/tex]
[tex]\\ \Large\sf\longmapsto 36miles [/tex]
A company producing a standard line and a deluxe line of dishwashers has the following time requirements (in minutes) in departments where either model can be processed.
STANDARD DELUXE
STAMPING 3 6
Motor installation 10 10
Wiring 10 15
The standard models contribute $20 each and the deluxe $30 each to profits. Because the Company produces other items that share resources used to make the dishwashers, the Stamping machine is available only 30 minutes per hour, on average. The motor installation Production line has 60 minutes available each hour. There are two lines for wiring, so the time Availability is 90 minutes per hour. Let x = number of standard dishwashers produced per hour y = number of deluxe dishwashers produced per hour.
Required:
a. Write the formulation for this linear program and then solve.
b. What is the value of the optimal profit ?
Complete Question
Complete Question is attached below
Answer:
[tex]M=160[/tex]
Step-by-step explanation:
From the question we are told that:
Standard models contribute $20
Deluxe models contribute $30
Availability Average :
Stamping machine S= 30 minutes per hour
Motor installation Production M=60 minutes
Wiring is W=90 minutes per hour
Generally the formulation of the linear program is given as
[tex]Maximium (M)=20x + 30 y[/tex]
Where
For Stamping machine
[tex]S= 3x + 6y \leq 30.....Equ 1[/tex]
For Motor installation Production
[tex]10x + 10y \leq 60....Equ 2[/tex]
For Wiring
[tex]10x + 15y \leq 90....Equ3[/tex]
Therefore
Solving Equ...(1,2,3) simultaneously we have
[tex]x=2\\\\y=4[/tex]
Therefore
[tex]Maximium\ (M)=20x + 30 y[/tex]
[tex]M=20(2)+30(4)[/tex]
[tex]M=160[/tex]
a. 8
b. 10
c. 3
d. 4
Answer:
4
Step-by-step explanation:
The number on the right squared in equal to the number on the left
5^2 =25
6^2 = 36
What squared = 16
4^2 = 16
The the missing number is 4
PLEASE HELP NO ONE IS ANSWERING ANY QUESTION I ASK!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 3x + 1
A) This is a polynomial.
B) The base is x + 1.
C) The base is 3.
D) This is not an exponential function because the variable is in the exponent position.
Answer:
sorry in dont know the ans
A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey?
Attitude 1st Survey 2nd Survey
Optimistic 7% 6%
Slightly Optimistic 9% 6%
Slightly Pessimistic 31% 37%
Pessimistic 53% 51%
Step 4 of 10: Find the expected value for the number of respondents who are optimistic. Round your answer to two decimal places.
Answer:
Yes. the Psychologist can confirm his theory that the attitudes have changed over time, based on the first and second surveys.
The expected value for the number of respondents who are optimistic is:
= 16.25
Step-by-step explanation:
Attitude 1st Survey 2nd Survey
Optimistic 7% 6%
Slightly Optimistic 9% 6%
Slightly Pessimistic 31% 37%
Pessimistic 53% 51%
Expected value of optimistic respondents:
Attitude
Optimistic Expected Value
1st Survey 8.75 (250 * 7% * 50%)
2nd Survey 7.50 (250 * 6% * 50%)
Total EV 16.25
how many distinct permutations can be formed using the letters of the word robberies
Answer:
45360 arrangements
Step-by-step explanation:
Given the word 'robberies'
Number of letters = 9 letters in total
Repeated letters ; r = 2 ; b = 2 ; e = 2
Therefore, the number of distinct arrangement of letters is :
(total letters)! / repeated letters!
The number of distinct arrangement of letters is :
9! / (2! * 2! * 2!) = (9*8*7*6*5*4*3*2*1) / (2*2*2)
362880 / 8 = 45360 arrangements
My son is 31 years younger than me. In one years time my son's age will be one quarter my current age. How old am I?
Define business.Write the type of business
Answer:
A company or an entrepreneurial entity engaged in commercial, industrial, or professional activity is referred to as a business. A limited liability company (LLC), a sole proprietorship, a corporation, and a partnership are examples of different types of businesses.
A piece of iron wire can be made into a circle with a radius of three centimeters.If I make a square around this wire,what is the area of the square
Answer:
the area should be 3 centimeters around the square
Step-by-step explanation:
Amelia is calculating the density of soccer balls in a bag. She knows the number of balls in the bag and the volume of the bag. Which of the following formulas can be used to calculate the density of balls in the bag?
Density = volume of bag over number of balls
Volume of shelf = density over number of balls
Density = number of balls over volume of bag
Number of books = density over volume of bag
Answer:
Density = number of balls over volume of bag
The formula that can be used to calculate the density of the balls in the bag is Density = number of balls over volume of bag
What is the formula for density?"[tex]Density=\frac{Mass}{Volume}[/tex]"
What is mass?"It is the measure of the matter inside a body."
For given question,
Amelia knows the number of balls in the bag and the volume of the bag.
She wants to calculate the density of soccer balls in a bag.
Here, mass = the number of balls in the bag
By using the density formula,
[tex]Density=\frac{number~of~balls}{volume~of~the~bag}[/tex]
Therefore, the formula that can be used to calculate the density of the balls in the bag is Density = number of balls over volume of bag
Learn more about the density here:
https://brainly.com/question/16823734
#SPJ2
[tex]\sqrt{25}[/tex]=?
[tex]Hello[/tex] [tex]There[/tex]
The answer is...
[tex]5.[/tex]
[tex]HopeThisHelps!![/tex]
[tex]AnimeVines[/tex]
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
123456-6-&55674
Step-by-step explanation:
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