The value of n on the series 5 + 10 + 20 + ... = 5115 is 10
How to find the value of nThe given sequence is 5, 10, 20, ... is a geometric progression (GP) with
first term a = 5 and
common ratio r = 2
formula for the sum of the first n terms of a GP
Sn = a(rⁿ - 1) / (r - 1)
Substituting the values we have
5115 = 5(2ⁿ - 1) / (2 - 1)
Simplifying and multiplying both sides by 1
1023 = 2ⁿ - 1
2ⁿ = 1024
2ⁿ = 2¹⁰
Equation powers
n = 10
Therefore, the value of n is 10.
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Bob the builder is making 480kg of a concrete mix. Concrete is made by mixing cement , said and gravel in ratio 1:3:4.
How much sand does he need?
Answer:
x = the number of kg of cement
3x = number of kg of sand
4x = number of kg of gravel
x + 3x + 4x = 480
8x = 480, so x = 60
60 kg of cement
3(60) = 180 kg of sand
4(60) = 240 kg of gravel
Bob will need 180 kg of sand.
10 00
Taking the square root of a number technically results in two solutions.
For example, the square root of 16 is ____ or ___ because ___ = 16 and ____ = 16
Complete sentence is,
The square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16
We have to given that;
Taking the square root of a number technically results in two solutions.
Here, The number is,
⇒ 16
Take square root as;
⇒ √16
⇒ ± 4
Since, 4² = 16
And, (- 4)² = 16
Thus, We get;
the square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16.
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Express 0.01430 in Standard form
Answer:
1.430
Step-by-step explanation:
1.430 x 10^-2
Oak Street and Elm Street run parallel to each other. When Main Street
intersects them, it forms interior 24, measuring 50°. What is the measure of 27?
A. 130°
B. 45°
C. 35°
D. 145°
Answer:
130°
Step-by-step explanation:
<4=<8
180-50=130
Find the expected value of the winnings don a game that has the following payout probability distribution
The expected value of the winnings in this game is $1.23.
We have,
The expected value of a random variable is the sum of the products of each possible outcome and its probability.
In this case, the random variable is the winnings from the game and the payout probability distribution specifies the probabilities associated with each possible payout.
The expected value of the winnings is found by multiplying each payout by its probability and summing the products.
Expected value = (0)(0.50) + (1)(0.25) + (2)(0.13) + (4)(0.06) + (8)(0.06)
= 0 + 0.25 + 0.26 + 0.24 + 0.48
= 1.23
Therefore,
The expected value of the winnings in this game is $1.23.
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Determine the number of real solutions:
1. y=-3x^2+x+12
Answer:
2
Step-by-step explanation:
To determine the number of real solutions of the quadratic equation `y = -3x^2 + x + 12`, we can use the discriminant formula `b^2 - 4ac`.
First, we identify the values of a, b, and c:
a = -3
b = 1
c = 12
Next, we substitute these values into the discriminant formula:
b^2 - 4ac = (1)^2 - 4(-3)(12) = 145
Since the discriminant is positive (and not equal to zero), the quadratic equation has two distinct real roots. Therefore, the number of real solutions is 2.
The table gives the temperature (in "F) in five cities at 6 a.m. on the same day. Use the table to answer the questions.
Temperature
(°F)
-26
43
-14
City
Juneau
Springfield
Montreal
Milwaukee
Atlanta
-3
F lower
68
(a) How much lower was the 6 a.m, temperature in Juneau than in Atlanta?
(b) By noon, the temperature in Milwaukee had risen by 11 °F.
What was the temperature there at noon?
a) The temperature in Juneau was 23°F lower than in Atlanta.
b) The temperature in Milwaukee at noon would be -3°F.
(a) The temperature difference between Juneau and Atlanta is:
= -3 - (-26)
= 23°F lower in Juneau
Therefore, the 6 a.m. temperature in Juneau was 23°F lower than in Atlanta.
(b) Since the temperature in Milwaukee had risen by 11°F, its temperature at noon would be:
= -14 + 11
= -3°F
Therefore, the temperature in Milwaukee at noon would be -3°F.
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HI PLEASE HELPP REFER TO PICTURE STATISTICS
We are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.
This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.
Hence, Using a t-distribution with 86 degrees of freedom (n-1), and a 95% confidence level (α=0.05), the critical value for the two-tailed test is 1.992.
The standard error can be calculated as:
SE = SD / √n = 15.6 / √100 ≈ 1.56
The margin of error (ME) can be calculated as:
ME = t x SE = 1.992 x 1.56 ≈ 3.11
The 95% confidence interval (CI) is then:
CI = mean ± ME = 5.9 ± 3.11 = (2.79, 9.01)
Therefore, we are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.
This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.
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9 se the given rules to complete the following tables. Classwork x y=-2r-8 y=-2x+8 HoNetwork =-5g-4 -3 -1 -2 -2 -2 -1 -3 -1 0 -4 0 1 -5 10 -6 2 100
The complete table for the linear function y = -2x + 8 is:
x y
1 6
2 4
3 2
4 0
5 -2
The given function is y = -2x + 8, which represents a linear equation in the slope-intercept form. In this form, the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
Comparing the given equation with the slope-intercept form, we can see that the slope of the line is -2, which means that the line goes down by 2 units for every 1 unit it moves to the right. The y-intercept of the line is 8, which means that the line intersects the y-axis at the point (0, 8).
The complete table:
x y
1 6
2 4
3 2
4 0
5 -2
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The complete question:
Complete the following table as per the function y = -2x + 8.
x y
1
2
3
4
5
Determine sin (A) and sin (B)
The values of sin (A) and sin (B) are sin(A) = 7/25 and sin(B) = 24/25
Determining the values of sin (A) and sin (B)From the question, we have the following parameters that can be used in our computation:
The right triangle
The values of sin (A) and sin (B) can be calculated using
sin = opposite/hypotenuse
Using the above as a guide, we have the following:
sin(A) = 14/50
sin(B) = 48/50
Simplify the equations
sin(A) = 7/25
sin(B) = 24/25
Hence, the values of sin (A) and sin (B) are sin(A) = 7/25 and sin(B) = 24/25
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For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
ASAP ASAP ASAP ASAP.
The equations has 8 a solution are
x/2 = 16
x/8 = 1
x/2 = 8
x/8 = 1
To check whether 8 is a solution for an equation, we substitute x = 8 into the equation and see if it satisfies the equation. If it does, then 8 is a solution; otherwise, it is not.
Substituting x = 8 into each equation, we get:
1. x + 6 = 8 + 6 = 14 (8 is not a solution)
2. 2x + 2 = 2(8) + 2 = 18 (8 is not a solution)
3. 4x - 2 = 4(8) - 2 = 30 (8 is not a solution)
4. 10 = 10 (8 is not a solution)
5. 2x = 4 (8 is not a solution)
6. 3x = 24 (8 is not a solution)
7. 8/2 = 4 (8 is a solution)
83 8/8 = 1 (8 is a solution)
Therefore, the correct answers are:
x/2 = 16
x/8 = 1
x/2 = 8
x/8 = 1
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You are considering a new project whose data are shown below. The required equipment has a 3-year tax life, after which it will be worthless, and it will be depreciated by the straight-line method over 3 years. Revenues and other operating costs are expected to be constant over the project's 3-year life. What is the project's Year 1 cash flow? Equipment cost (depreciable basis) $65,000 Sales revenues, each year $60,000 Operating costs (excl. depreciation) $25,000 Tax rate 35.0%
Find the area of the triangle with the given description. A triangle with sides of length 5 and 8 and include angle 79°.
The area of the triangle is 18.6 units²
Given data ,
Let the triangle be represented as ΔABC
Now , the sides of the triangle are
We can use the law of cosines to find the length of the third side of the triangle:
c² = a² + b² - 2ab cos(C)
c² = 5² + 8² - 2(5)(8)cos(79°)
c ≈ 9.05
Now, we can use Heron's formula to find the area of the triangle:
s = (5 + 8 + 9.05)/2 = 11.525
A = √(s(s-a)(s-b)(s-c))
A = √(11.525(11.525-5)(11.525-8)(11.525-9.05))
A ≈ 18.6
Hence , the area of the triangle is approximately 18.6 square units
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All points of the step function f(x) are graphed. What is the domain of f(x)?
The domain of the step function f(x) is given as follows:
{x | -4 < x ≤ 4}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.For the function graphed at the end of the answer, we have that:
The lowest value of x is the open circle at x = -4.The highest value of x is the closed circle at x = 4.Hence the domain of the step function f(x) is given as follows:
{x | -4 < x ≤ 4}.
Missing InformationThe function is given by the image presented at the end of the answer.
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A special safe lets you choose from 5 symbols for a 3-symbol-long pass code. You may enter a symbol any number of times. How many potential pass codes are there? 10 35 60 125
There are 35 potential pass codes. The Option B.
How many potential pass codes can be created?A pass code means string of characters used as a password to gain access to a computer or smartphone.
To get number of potential pass codes, we will combinations formula with repetition [tex](n + r - 1)[/tex] choose r.
n = number of options
r = length of the pass code.
The number of potential pass codes is:
= (5 + 3 - 1) Choose 3
= 7 Choose 3
= (7 x 6 x 5) / (3 x 2 x 1)
= 210 / 6
= 35.
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Janet Foster bought a computer and printer at Computerland. The printer had a $860 list price with a $100 trade discount and 2/10, n/30 terms. The computer had a $4,020 list price with a 25% trade discount but no cash discount. On the computer, Computerland offered Janet the choice of (1) paying $150 per month for 17 months with the 18th payment paying the remainder of the balance or (2) paying 6% interest for 18 months in equal payments.
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10
points
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Challenge Problem 10-37 (Algo) [LU 10-1 (2)]
Janet Foster bought a computer and printer at Computerland. The printer had a $860 list price with a $100 trade discount and 2/10, n/30 terms. The computer had a $4,020 list price with a 25% trade discount but no cash discount. On the computer, Computerland offered Janet the choice of (1) paying $150 per month for 17 months with the 18th payment paying the remainder of the balance or (2) paying 6% interest for 18 months in equal payments.
a. Assume Janet could borrow the money for the printer at 6% to take advantage of the cash discount. How much would Janet save? (Use 360 days a year. Round your answer to the nearest cent.)
b. On the computer, what is the difference in the final payment between choices 1 and 2? (Round your answer to the nearest cent.)
a) Janet would save $17.20 - $5.60733 = $11.59 by borrowing the money for the printer at 6% to take advantage of the cash discount. b) , the difference in the final payment between choices 1 and 2 is $1,107.60.
How to answer the aforementioned questionsa. The cash discount on the printer is calculated as 2% of the list price:
Cash discount = 2% * $860 = $17.20
Using the formula:
Interest = Principal * Rate * Time
Principal = Amount borrowed = List price - Cash discount = $860 - $17.20 = $842.80
Rate = 6% per year = 6%/100 = 0.06
Time = 30 days (since the terms are 2/10, n/30)
To convert the interest to a 360-day basis, we use the formula:
Interest = Principal * Rate * (Time/360)
Interest = $842.80 * 0.06 * (30/360) = $5.60733
Therefore, Janet would save $17.20 - $5.60733 = $11.59 by borrowing the money for the printer at 6% to take advantage of the cash discount.
b. Choice 1 for the computer involves paying $150 per month for 17 months, with the 18th payment paying the remainder of the balance. Choice 2 involves paying 6% interest for 18 months in equal payments.
For choice 1:
Remaining balance = List price - (17 * Monthly payment)
Remaining balance = $4,020 - (17 * $150) = $4,020 - $2,550 = $1,470
For choice 2:
Interest = Principal * Rate * Time
Principal = Amount borrowed = List price = $4,020
Rate = 6% per year = 6%/100 = 0.06
Time = 18 months
To convert the interest to a 12-month basis, we use the formula:
Interest = Principal * Rate * (Time/12)
Interest = $4,020 * 0.06 * (18/12) = $362.40
The final payment difference between choices 1 and 2 is:
Final payment difference = Remaining balance - Interest
Final payment difference = $1,470 - $362.40 = $1,107.60
Therefore, the difference in the final payment between choices 1 and 2 is $1,107.60.
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Find the volume of this rectangular pyramid. Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. 8 m 9 m 8 m 0|0 E 08 m² G m3
The value of the volume of this rectangular pyramid is,
⇒ V = 192 m³
We have to given that;
In rectangular pyramid,
Lenght = 8 m
Width = 9 m
Height = 8 m
Hence, The volume of this rectangular pyramid is,
⇒ V = 1/3 x Length x width x height
⇒ V = 1/3 × 8 × 9 × 8
⇒ V = 192 m³
Thus, The value of the volume of this rectangular pyramid is,
⇒ V = 192 m³
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People are invited to compete to be a contestant in a television quiz show.
Here are some possible outcomes for the person who is chosen.
A: The contestant is a woman over 25 years old. B: The contestant is a man.
C: The contestant is 21 years old. D: The contestant is a 30-year-old man.
a List the possible pairs of mutually exclusive outcomes.
b List three of the outcomes that are all mutually exclusive.
c What can you say about the probabilities of B and D?
a) The possible pairs of mutually exclusive outcomes are given below:
A and B
A and C
A and D
B and C
B and D
C and D
b) The Three of the outcomes that are said to be all mutually exclusive are:
A (The contestant is a woman over 25)B ( The contestant is a man.)C (The contestant is 21 years old )c) The probability of having B and D is written as P(B or D) = P(B) + P(D)
What is the probability?Mutually exclusive events cannot happen at the same time, like rolling a kick the bucket and getting a 1 and a 2. In this case, there are four conceivable results: A, B, C, and D, a few of which we commonly select.
For example, If A is the outcome, C or D cannot be. To find mutually exclusive pairs, we check which outcomes cannot occur together. A and B are mutually exclusive because they cannot both be true.
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The area of the object nelow
[tex] {77.05 \: m}^{2} [/tex]
hope this is correct
how do you solve 3/(n-1) = 2n/(n+4)
Step-by-step explanation:
To solve the equation 3/(n-1) = 2n/(n+4), follow these steps:
Step 1: Cross-multiply to eliminate the fractions.
3 * (n + 4) = 2n * (n - 1)
Step 2: Distribute the terms on both sides.
3n + 12 = 2n^2 - 2n
Step 3: Move all terms to one side and set the equation to zero.
2n^2 - 5n - 12 = 0
Step 4: Factor the quadratic equation, if possible. In this case, we can factor by finding two numbers that multiply to -24 and add to -5.
(2n + 3)(n - 4) = 0
Step 5: Use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
2n + 3 = 0 or n - 4 = 0
Step 6: Solve for 'n' in each equation.
2n + 3 = 0 => n = -3/2
n - 4 = 0 => n = 4
So, there are two possible solutions for 'n': -3/2 and 4.
Answer: n= 4 , (-3/2)
Step-by-step explanation:
Your goal is to isolate n by getting it by itself
Multiply both sides by (n-1) to get 3 = ((2n)(n-1))/(n+4)
Use distributive property on the 2n * (n-1) to get 3 = (2n^2 - 2n)/(n+4)
Multiply both sides by (n+4) to get 3n + 12 = 2n^2 - 2n
Subtract 12 and 3n from both sides to get 2n^2 - 5n -12 = 0
Solve the quadratic using any method you like
Factoring would give you (n - 4)(2n + 3) = 0
So n= 4 and -3/2
The area of a circle is 81л m². What is the circumference, in meters? Express your
answer in terms of π.
Answer:
Step-by-step explanation:
Formulas:
A = (pi)(radius^2)
C = (pi)(Diameter)
Find the radius
81pi = pi * (r)^2
r^2 = 81
r = 9
Use radius to find diameter
D= 2r
D = 18
Use circumference formula
C = 18π
Solve using long division. 142/6 =
Answer: 23.666
(if you would like an explanation please let me know)
Geoff sold his handknit hats for
$15 each at the farmers' market. He
bought $45 of yarn to make the hats.
If x represents the number of hats
sold, which expression represents
Geoff's earnings?
If x represents the number of hats sold, the expression representing Geoff's earnings is 15x.
What is an expression?An algebraic expression is a mathematical statement that combines variables, constants, values, numbers, and other quantities based on mathematical operands but without using equal symbols (=).
The selling price per handknit hat = $15
The total cost of materials (yarn) for making the hats = $45.
Let the number of hats sold = x
Expressions:Total earnings from the sales = 15x
Total cost = $45
Net earnings = 15x - 45
Thus, the expression that represents Goefft's earnings from the sale of handknit hats is 15x.
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What is the function equation for the graph below?
Answer:
f(x)= - [x] + 3
Step-by-step explanation:
because it describes a negative slope and 3 units up from the origin
what should be subtracted from -5/12 to get 1
Answer=
-17/12 should be subtracted from-5/12 to get the answer 1
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Advanced algebra please help!!
The time, t, required to drive a certain distance varies inversely with the speed r. if it takes 7 hours to drive the distance at 55 miles per hour, how long ill it take to drive the same distance at 65 miles per hour, how long will it take to drive the same distance.
A. about 6.25 hours
B. about 385.00 hours
C. about 5.92 hours
D. about 3.21 hours
Option C. It t will take approximately 5.923 hours to drive the same distance at 65 miles per hour.
How to solve for the time takent = k / r
where k is the constant of variation.
First, we need to find the constant of variation, k, using the given information:
t = 7 hours when r = 55 mph
7 = k / 55
To find k, multiply both sides by 55:
k = 7 * 55 = 385
Now that we have the constant of variation, we can find the time it will take to drive the same distance at 65 mph:
t = k / r
t = 385 / 65
t ≈ 5.923 hours
So, it will take approximately 5.923 hours to drive the same distance at 65 miles per hour.
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Graph these integers on a number line:0,-5,1,3
Answer:
-5,0,1,2,3
Step-by-step explanation:
in a number line the negative numbers are always on your left hand side and as you head to the right they increase thus becoming positive integers
A class is presented with the following problem.
In a bag of marbles, the ratio of white marbles to red marbles is 2:3 and the ratio of red to black marbles is 6:11. What is the ratio of white to black marbles?
Connor, who likes using fractions, writes 2/3 *6/11 = 4/11 announces, without explanation, that the ratio of white to black marbles is 4:11. Explain why he is right. (Hint: taking the number of black marbles to be the whole unit, what fraction are red, and then what fraction are white?)
Answer:
Therefore, Connor is correct in his explanation that the ratio of white to black marbles is 4:11.
Step-by-step explanation:
Connor is correct in his reasoning. Let's break down the problem step by step to understand why.
Given:
Ratio of white marbles to red marbles = 2:3
Ratio of red marbles to black marbles = 6:11
To find the ratio of white to black marbles, we can follow these steps:
Step 1: Consider the black marbles as the whole unit.
Let's assume there are 11 black marbles (since the ratio of red to black marbles is 6:11).
Step 2: Determine the number of red marbles.
Since the ratio of red marbles to black marbles is 6:11, out of the assumed 11 black marbles, there are (6/11) * 11 = 6 red marbles.
Step 3: Determine the number of white marbles.
Using the ratio of white marbles to red marbles (2:3), we can find the number of white marbles. Since the ratio is 2:3, the number of white marbles would be (2/3) * 6 = 4.
Step 4: Find the ratio of white to black marbles.
Now that we have determined there are 4 white marbles and 11 black marbles, the ratio of white to black marbles is indeed 4:11.
name the leading coefficient and degree of the polynomial 12+5x^y+4x
Answer:
The leading coefficient is 5, the degree is y+1
Step-by-step explanation:
The polynomial 12+5x^y+4x has two terms, 12 and 5x^y+4x. The leading coefficient of the polynomial is 5, which is the coefficient of the term with the highest degree. The degree of the polynomial is y+1, which is the highest power of x in any term of the polynomial after like terms have been combined. The degree is determined by adding the exponents of the variables in the term with the highest degree, which is 5x^y in this case. The exponent of x is 1 and the exponent of y is y, so the degree is y+1. Therefore, the leading coefficient is 5 and the degree is y+1.
