Answer:
The common ratio is 2.
Write the fifteenth term of the binomial expansion of (a³+d) 24.
a^45d^9
To find the fifteenth term of the binomial expansion of (a³+d)24, we can use the binomial theorem, which states that the expansion of (a+b)n is given by the sum of the terms in the following formula:
(a+b)^n = a^n + na^(n-1)b + (n(n-1))/2a^(n-2)*b^2 + ... + b^n
Answer: 1,961,256a³⁰d¹⁴
Step-by-step explanation:
[tex]\displaystyle\\(x+y)^n \ is\ the\ binomial\ expansion \\\\The\ k\ term =C_n^{k-1}x^{n-k+1}y^{k-1}\\\\ n - the\ power \ of\ the \ binomial\\\\k - number\ of\ the\ term \ of\ the\ binomial[/tex]
[tex](a^3+d)^{24}[/tex]
[tex]The \ fifteenth\ term=C^{15-1}_ {24}(a^3)^{24-15+1}d^{15-1}\\\\The \ fifteenth\ term=C^{14}_{24}(a^3)^{10}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{(24-14)!14!} a^{30}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{10!14!}a^{30}d^{14} \\\\The \ fifteenth\ term=1,961,256 a^{30}d^{14}[/tex]
Which of the following is an example of rational function?
1.f(x)=3x²+1 over x-1
2.x over 3 = 8 over 3
3.1 over 3x-1 +3<0â
The example of rational function is option(1) which is f(x)=3x²+1 over x-1
What is Rational Function ?
A rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0.A rational function in the form of f(x) = p(x) / q(x) where, q(x) ≠ 0Hence, the example of rational function is option(1) which is f(x)=3x²+1 over x-1.
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Create 4 math problems where the solution is -60
-480 ÷ 8 = -60
2x = -120
-20 × 3 = -60
(2 × 3) × (-5 × 2) = -60
Given the following sequence, find the 77th term.
-8, -4, 0, 4, 8, ...
Answer:
Step-by-step explanation:
The given sequence is an arithmetic sequence with a common difference of 4. The 77th term of the sequence is the 77th term of the arithmetic sequence, which is given by the formula:
a_n = a_1 + (n - 1) * d
where a_n is the nth term of the sequence, a_1 is the first term of the sequence, and d is the common difference. Substituting the values for a_1, n, and d into this formula, we get:
a_77 = -8 + (77 - 1) * 4
= -8 + 76 * 4
= -8 + 304
= 296
Therefore, the 77th term of the sequence is 296.
Given 2 and one-eighth times negative 7 times five tenths, determine the product.
negative fourteen and five eightieths
negative 7 and seven sixteenths
fourteen and five fortieths
7 and one eighth
The product of the given numbers is, [tex]-7\frac{7}{16}[/tex].
What is product?
One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication. A product is the output of a multiplication operation.
The outcome of multiplying two or more numbers together in mathematics is called the product. With the help of examples, learn more about the product of fractions and decimals.
Given:
2 and one-eighth times negative 7 times five tenths.
We have to determine the product.
[tex]2\frac{1}{8} (-7)(\frac{5}{10} )[/tex]
Convert improper fraction into a fraction
[tex]2\frac{1}{8} = \frac{(2)(8)+1}{8} = \frac{17}{8}[/tex]
⇒
[tex](\frac{17}{8} )(-7)(\frac{1}{2}) \\-\frac{119}{16} \\-7\frac{7}{16}[/tex]
Hence, the product of the given numbers is, [tex]-7\frac{7}{16}[/tex].
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Please help me pass this assignment
What is the value of x?
The value of x is 27 in the given figure.
What is Angle?An angle is formed when two straight lines or rays meet at a common endpoint.
We need to find the value of x.
The given two angles are (4x+7) and 5(x-4).
The two angles are opposite angles so the two angles are equal.
Let us equate 4(x+7) and 5(x-4).
4x+7=5(x-4).
Apply distributive property on RHS
4x+7=5x-20
4x-5x=-20-7
-x=-27
Multiply both sides by minus
x=27.
Hence, the value of x is 27.
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a fair coin is tossed n times, and the number of heads, n, is counted. the coin is then tossed n more times. find the expected total number of heads generated by this process.
The anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.
Given that,
A fair coin is tossed n times, and the results are tallied by counting the heads. The coin is then thrown a further n times.
We have to calculate the anticipated total number of heads produced by this method.
We know that,
Either head or tail will appear when a coin is tossed.
The sample space of a random experiment is the collection of all feasible results. Therefore, if your random experiment involves flipping a coin, the sample space is "Head, Tail," or more tersely, "H, T."
So,
1/2n=N
Therefore, the anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.
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Mr. Saunder bought a 19 pound turkey for Thankgiving. The total cot of the turkey wa $25. 65. What wa the cot of turkey per pound? Write an equation to repreent the ituation
The equation used to represent the situation:
Cost per pound = Total Cost of Turkey / Number of Pounds
A formula known as an equation uses the equals sign to express how two expressions are equal. The meanings of the word equation and its translations into other languages might vary slightly; Finding the values of the variables that cause the equality to be true is the first step in solving an equation with variables.
Quantity = 19 pounds
Total Cost = $25.65
Now to calculate the cost of Turkey per pound, we can use the following equation:
Cost of Turkey per pound = Total Cost / Quantity of Pounds
Cost per pound = 25.65 / 19
Therefore, the cost of turkey per pound = $1.35
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The orientation factor is less important in because the reactants are blank and spherical (nondirectional); all collision orientations are equally effective
The orientation factor in a chemical reaction relates the frequency factor to the collision factor and depends on the extent of complexity of the reactants in a reaction.
Does the orientation factor depend on temperature?
The direction of the collision between the chlorine atoms and the ozone determines the pace of reaction; if the direction is incorrect, no reaction takes place. The right orientation will allow for response. The direction of collisions is independent of temperature.
According to the Collision Theory, molecules must collide with sufficient activation energy to break and re-form existing bonds, as well as with favorable spatial orientation, in order for a chemical reaction to occur.
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Select the true statements about the inequalities. -10 > -15, so -10 is located to the left of -15 on a horizontal number line. 8 > -13, so 8 is located to the left of -13 on a horizontal number line. 9 > -5, so 9 is located to the right of -5 on a horizontal number line. -6 < 1, so -6 is located below 1 on a vertical number line. -14 > 7, so -14 is located below 7 on a vertical number line. 11 < -13, so 11 is located to the right of -13 on a horizontal number line.
The statement which is true for the inequality will be equal to 9 > -5, so 9 is located to the right of -5 on a horizontal number line.
What is number line?A straight line of numbers is shown visually as a number line. This line is employed to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.
As per the given inequalities given in the question,
1.
-10 > -15, so -10 is located to the left of -15 on a horizontal number line.
The statement is wrong because -10 is located on the right side of -15
2.
8 > -13, so 8 is located to the left of -13 on a horizontal number line.
The statement is wrong because 8 is located on the right side of -13.
3.
9 > -5, so 9 is located to the right of -5 on a horizontal number line.
This statement is true, that 9 is located to the right of -5.
4.
-6 < 1, so -6 is located below 1 on a vertical number line.
This statement is true, that -6 is located to the below of -5.
5.
-14 > 7, so -14 is located below 7 on a vertical number line.
This statement is false.
6.
11 < -13, so 11 is located to the right of -13 on a horizontal number line.
This statement is also false.
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the 5th grade is having a picnic this Friday. There will be 182 students and 274 adults. Each table seats 12 people. How many tables are needed??
PLS I need the help
What is the vertex of the quadratic function?
(-6,1)
(6,-1)
(1,6)
(1.-6)
Answer:
(1,-6)
Step-by-step explanation:
Ordered pairs are (x,y)
The vertex of the quadratic formula is its lowest point if opening up, and its highest point if opening down
This one opens up so it is the lowest point
The x value of the vertex is x=1
the Y value of the vertex is y=-6
15. Gerald’ average core for nine tet wa 96. If the um of the core of two of hi tet wa 178, then what wa hi average for the other even tet
Let x is average for rest of seven test. Then average for remaining test is x= 2.27
What is average?The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Why is average called mean?The middle point of the set of values is the mean. It represents the mean of the data set's values. In statistics, the centre number, also known as the mean, is referred to as the average.
We want the TOTAL average to equal 94
4/9 of the 5 scores have an average of 178
Let x = average of the 5 remaining test, which is worth 5/9 of the total average.
We get: 94 = (4/9)(178) + (5/59)(x)
94=712/9+59x/9
846=712+59x
846-712=59x
134=59x
134/59=x
Solve: x = 2.27
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Gloria go shopping for school supplies she had a balance of $235.55 When she left home to school supplies total $52.50 she had a 10% off coupon what was the balance in your checking account after buying school supplies
189.55
...
.............
...
calculate the margin of error of a confidence interval for the difference between the two population means.
A 95% confidence interval with a 4% margin of error suggests that your statistic will be 95% of the time within 4 percentage points of the true population value.
A survey, may reveal that the 98% confidence interval is between 4.88 and 5.26. So, if the poll is repeated using the same methods, the true population parameter (parameter vs. statistic) will fall 98% of the time within the interval estimates (i.e. between 4.88 and 5.26).
The formal definition, on the other hand, includes a little more information. The margin of error in a confidence interval is defined as the range of values below and above the sample statistic. The confidence interval is a tool for demonstrating the level of uncertainty associated with a certain statistic (i.e. from a poll or survey).
In 2012, a Gallup poll (incorrectly) predicted that Romney would win the election, with Romney polling at 49% and Obama polling at 48%. The declared level of confidence was 95%, with a margin of error of 2. We can conclude that the results were computed to be 95% accurate within 2 percentage points.
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PLEASE HELP!!! Make sure to show your work.
1)How many triangles can be constructed
with angles measuring 16˚, 38˚ and 126˚?
Circle one answer:
A) None
B) One
C) Infinite (More than one)
A triangle has three angles that measure 16˚, 38˚ and 126˚ will lead to
C) Infinite (More than one)How to know when infinite number of triangles are formedThere are an infinite number of triangles produced when no side is specified.
The three angles produce an unlimited number of distinct triangles if side lengths are not provided.
The option that offered just angles—namely, angles of 16˚, 38˚ and 126˚—and no sides—meets the requirement for the production of an infinite number of triangle sides.
When there are options have sides or a side is provided, but not in accordance with that, to form an infinite number of triangles.
This condition forms infinite number of triangles
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Answer:
C) Infinite (More than one)
Step-by-step explanation:
Avery invested $4,700 in an account paying an interest rate of 5 1/8% compounded
continuously. Jayden invested $4,700 in an account paying an interest rate of 5 1/2%
compounded quarterly. After 12 years, how much more money would Jayden have in
his account than Avery, to the nearest dollar?
Answer:
20090089$
Step-by-step explanation:
Answer: $359
Step-by-step explanation:
I got the same problem on DeltaMath- You use the formula A = P ( 1 + r/n ) ^nt
P = 4700
R = 0.055
T = 12
N = 4
You plug it in to get 9052.7283 and then subtract 8693.386 to get 359.3423 which rounds to 359
The worldwide population is estimated to be around _______ by the year 2050.
a. 9 million
b. 9 trillion
c. 9 billion
d. 9.9 trillion
please select the best answer from the choices provided a b c d
Answer:
option c
Step-by-step explanation:
c. 9 billion people
Answer:
B. 9 Billion people
Step-by-step explanation:
Coefficient of x^5 in expansion of (2x-1)^6
The coefficient x⁵ in expansion of (2x - 1)⁶ is; -192
How to solve Binomial expansion?We are given the expression;
(2x - 1)⁶
Using Pascals triangle, the coefficient of the terms here are;
1 6 15 20 15 6 1
The general formula for binomial expansion is;
(x + y)ⁿ = ⁿC₀xⁿy⁰ + ⁿC₁xⁿ⁻¹y¹ + ⁿC₂xⁿ⁻²y²+......+ ⁿCₙx⁰yⁿ
Thus, we can find the expansion of (2x - 1)⁶ as;
1[(2x)⁶ * (-1)⁰] + 6[(2x)⁵ * (-1)¹] + 15[(2x)⁴ * (-1)²] + 20[(2x)³ * (-1)³] + [15(2x)² * (-1)⁴] + [6(2x)¹ * (-1)⁵] + [1(2x)⁰ * (-1)⁶]
= 64x⁶ - 192x⁵ + 240x⁴ - 160x³ + 60x² - 12x + 1
The coefficient we are looking for is -192
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Janie's goal is to spend no more than
$13 each week on coffee. The graph
shows the amount she has spent on
coffee over the last several weeks.
The unit rate of the graph that represents the proportional relationship is $12.5, which is below $13 per week. Therefore, Louis made the correct statement.
How to Interpret the Graph of a Proportional Relationship?The graph of a proportional relationship is typically a straight line that runs through the point of origin (0, 0).
The slope of the graph gives the unit rate, which is calculated as m = y/x.
Given the graph that shows the proportional relationship between the number of weeks and the amount spent on coffee, we can use one point on the line, (4, 50) to find the unit rate, which will given us how much is spent per week.
Therefore:
Slope/unit rate or amount spent per week = y/x = 50/4 = $12.5.
Based on this, we can state that Louis is correct by saying Janie has not met her goal, because $12.5 per week is below the target of $13 each week.
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find two numbers whose difference is 88 and whose product is a minimum. (smaller number) (larger number)
Two two numbers whose difference is 88 and whose product is a minimum are -44 and 44.
How to solve?Let the numbers be x and y where x is larger value and y is smaller number.
According to ques,
x - y =88
and we need to make product of numbers i.e 'xy' minimum.
So we can take x = 88 + y ------(2)
substituting value of x in xy, we get
(88 + y) (y) = y² + 88y ------(1) to make it minimum we need to equate its derivative equal to zero.
derivative of (1) is 2y + 88
Equating it to zero, we get
2y + 88 = 0
subtracting 88 from both sides, we get
2y = -88
Dividing 2 from both sides, we get
y = -44 ------(3)
Substituting value of y from (3) in (2), we get
x = 88 - 44
x = 44
So, we get value of x as 44 and y as -44 to get their product as minimum.
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Please help with this question, if you can thank you
C. The slope of the graph is 1/3
Slope = (y2 - y1) ÷ ( x2- x1)
y2= 5, y1=2, x2=9, x1=0
y2-y1 = 5-2 = 3
x2-x1 = 9-0 = 9
Slope = 3/9 = 1/3
Point (25,125) means that the monthly home heating bill was $
for an average monthly temperature of
°F.
The point (25,125) means that the monthly home heating bill was $5 for an average monthly temperature of 1°F.
How to interpret the meaning of the point?From the question, we have the following parameters that can be used in our computation:
Point (25, 125)
This point can be expressed as
(x, y) = (25, 125)
The average monthly temperature bill is then calculated using the following equation
Average monthly temperature bill = y/x
Substitute the known values in the above equation, so, we have the following representation
Average monthly temperature bill = 125/25
Evaluate
Average monthly temperature bill = 5
Hence, the average monthly temperature = 5
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1. For each of the following, find 2 solutions and 2 non solutions.
a. 2x + 5y = 30
The following, find 2 solutions and 2 non solutions is [tex]x=\frac{30-5 y}{2}[/tex]
What is non solutions?
Ideal solutions are those that follow Raoult's law throughout the whole concentration range. A solution is said to as a non-ideal solution if it violates Raoult's law.
[tex]$$2 x+5 y=30$$[/tex]
[tex]Move $5 y$ to the right side[/tex]
[tex]$$2 x=30-5 y$$[/tex]
[tex]Divide both sides by 2[/tex]
[tex]$$\frac{2 x}{2}=\frac{30}{2}-\frac{5 y}{2}$$Simplify$$x=\frac{30-5 y}{2}$$[/tex]
Non solutions, in the plural, refer to anything that falls short of offering a fix for a problem. These batteries also lose their charge, rendering them useless for solving the more significant issue of storing and utilizing renewable energy.
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If a wire 1,325 feet long ha a reitance of 0. 65 ohm, what i the rei-tance to the nearet hundredth of one mile of the ame wire?
The resistance of wire to the nearest hundredth of one mile of the wire with mentioned details is 2.59 ohm.
Firstly we will convert length of wire to feet. As per the known information, 1 mile is 5280 feet. Moreover, as known resistance and length are directly proportional to each other.
Resistance 1/Resistance 2 = length 1/length 2
0.65/Resistance 2 = 1325/5280
Rewriting the equation according to length 2
Resistance 2 = (0.65×5280)/1325
Performing multiplication on Right Hand Side of the equation
Resistance 2 = 3432/1325
Performing division on Right Hand Side of the equation
Resistance 2 = 2.59 ohm
The resistance of wire is 2.59 ohm.
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A bag of dry pet food costs the pet store $18.66. A case of canned food costs $11.43. The owner puts in an order for 27 bags of dry food and 34 cases of canned food. The owner thinks he owes $1,835.49.
Answer: $892.44
Step-by-step explanation:
Take 27 times 18.66 = $503.82
Then take 34 times 11.43 = $388.62
Then add them to find total
503.82 + 388.62 = $892.44
The owner only owe $892.44
Points A, B, and C are colinear. A B C What is the slope of BC in simplest form?
Answer:
-1 /3
Step-by-step explanation:
To get from one point to the next, go DOWN1 and OVER3.
DOWN1 and OVER3 is the slope -1/3
From B to C it looks like DOWN2 and OVER6. That is -2/6. But that can be reduced to -1/3. So its the same.
Which bank would be best for Gerard to use, I need this today please
Answer:
Step-by-step explanation:
The best bank depends on the amount that Gerard will deposit. He can open an account with My bank and receive $100, or he can open with New bank and deposit lets say $5000 and he would receive an additional $250 because of the 5% bonus. It depends on the amount that Gerard is putting into the bank account when he opens it.
Thi month, Kami old 70 figurine in 2 ize. The large figurine old for $12 each, and the mall figurine old for $8 each. The amount of money he received from the ale of the large figurine wa equal to the amount of money he received from the ale of the mall figurine. How many large figurine did Kami ell thi month?
The large figurine old for $12 each, and the mall figurine old for $8 each. The amount of money he received from the ale of the large figurine wa equal to the 42
Let x represent the number of large figurines that Kami sold.
Let y represent the number of small figurines that Kami sold.
This month kami sold 70 figurines in 2 sizes. This means that
x + y = 70 - - - - - - - - - - 1
The large figurines sold for $12 each and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. This means that
12x = 8y
y = 12x/8
y = 1.5x
Substituting y = 1.5x into equation 1, it becomes
x + 1.5x = 70
2.5x = 70
x = 70/2.5 = 28
y = 1.5x = 1.5 × 28 = 42
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