If a1 = 2 and an = -2an-1 + 3 then find the value of a5.

The solution is, the required cost of the used game X= 19.

An equation which can be expressed as a mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

So he bought the $120 game with $82

and 2 equally priced game.

This can be changed to an equation: 120= 82+2X.

The X represents the cost of the used game.

120= 82+2X

-82 -82

——————-

38= 2X

38= 2X

Divide by 2 on both sides

X= 19

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The value of k is,

The probability distribution as a table:

r   1     2          3

P(X)   0    1/15  2/15

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

To find the value of k, we can use the fact that the sum of the probabilities for all possible values of X must equal 1.

Therefore, we have:

P(X = 1) + P(X = 2) + P(X = 3) = k(4(1)(1²) + 4(2)(2²) + 4(3)(3²))

                                              = 24k

Since we also know that P(X = 1) = 0, we have:

P(X = 1) + P(X = 2) + P(X = 3) = P(X = 2) + P(X = 3) = 0.8

Substituting this into the equation above, we get:

0.8 = 24k

k = 0.8/24 = 1/30

Therefore, the probability distribution can be written as:

r 1 2 3

P(X) 0 1/15 2/15

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The fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

If the probability that the red team wins is 0.55, then the probability that they lose is 1-0.55 = 0.45.

Similarly, if the probability that the blue team wins is 0.60, then the probability that they lose is 1-0.60 = 0.40.

If we assume that the outcomes of each game are independent of each other and that there are no ties, then the expected number of games that the red team will win in a season of 160 games is:

Expected number of wins for the red team = (probability of winning) x (number of games)

= 0.55 x 160

= 88

Similarly, the expected number of wins for the blue team is:

Expected number of wins for the blue team = (probability of winning) x (number of games)

= 0.60 x 160

= 96

Therefore, the fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games (96 - 88 = 8).

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Answer:

YOU L HAHA

Step-by-step explanation:

LOS ER

Answer:

The surface area of a cylinder can be calculated using the formula:

Surface area = 2πr^2 + 2πrh

Where r is the radius and h is the height of the cylinder.

Plugging in the values we have:

Surface area = 2π(8^2) + 2π(8)(8) = 2π(64) + 2π(64) = 128π

Rounding to the nearest thousandth, we have:

Surface area = 128π = 403.23 in^2 (rounded to the nearest thousandth)

So the surface area of the cylinder with height 8 in and radius 8 in is 403.23 in^2.

Step-by-step explanation:

A division problem that would lead to a division remainder of 400 is 2, 400 ÷ 500.

You need to find a division problem where the quotient would be such that there would be a remainder of 400.

In that case, the first thing to do is to ensure that the divisor is greater than 400. If it is less, then the remainder cannot be 400.

We can the pick the next hundred after 400 which would be 500. Then, we need to find a number that when divided by 500, would result in 400 as a remainder.

This can be 900, 1, 400, 1, 900, 2, 400 etcetera.

The trick is to ensure that the number is 400 more than a multiple of 500.

Picking 2, 400, the division is therefore:

= 2, 400 ÷ 500

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The value for the Inequality 13x ≤ 200 is x ≤ 15.384.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

13 times a number x is less than or equal to 200.

Now, Writing the Inequality Mathematically

13x ≤ 200

x ≤ 200 / 13

x ≤ 15.384

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The permutation formula is used when the order matters as it does not remove the combinations with the same elements and different order from the equation.

For the combination formula, the term x! is removed, as it removes all the combinations with the same elements but different order.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

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Answer:

y = 2

Step-by-step explanation:

If x = -2, what is y = ?

When x = -2 the line crosses the y axis at 2, so y = 2

Answer: The final balance is $11,015.84.

The total compound interest is $3,845.84.

Answer:

Step-by-step explanation:

The two numbers are 42 and 49.

Let us suppose the numbers are x and y.

From the above question,

=> x + y = 91 ------(1)

Also,

=> x:y = 6:7

If we express y in terms of x,

Then, x/y = 6/7

It can also be written as,

=> y = 7x/6 ------(2)

On substitution of value from (2) into (1),

We get,

=> x + 7x/6 = 91

=> 13x/6 = 91

=> x = 6*7

=> x = 42

Now, Substituting the value of x in (1),

We get,

=> 42 + y = 91

=> y = 91 - 42

=> y = 49

Therefore, The values of the two numbers are 42 and 49.

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Answer:

D.666 cubic centimeters

Step-by-step explanation:

Volume of cylinder is 3 time the volume of cone of the same radius.

Volume of cylinder= πr²h

Volume of cone = 1/3 x πr²h

Answer:

It would be C.

Step-by-step explanation:

It would be C.

JKP, the smaller triangle, needs to be turned into J'K'P' to show proof the the triangles are similar. So the first thing you would have to do, because J'K'P' is exactly 2 times bigger than JKP, is multiply the x and the y by 2. However, this shifts the triangle, and we need the triangles to overlap to prove they are also the same size. So comparing the x and y values after we increase the sides of JKP, we would see we need to subtract the x value by 3, and the y value by 2.

The value of the trigonometric equation sin D = 0.923

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔBCD

Now , the measure of BC = 24

The measure of side CD = 10

So , the measure of hypotenuse BD = √ ( BC )² + ( CD )²

Substituting the values in the equation , we get

The measure of BD = √ ( 576 ) + 100

The measure of BD = √ ( 676 )

The measure of BD = 26

Now , from the trigonometric relations ,

sin θ = opposite / hypotenuse

Substituting the values in the equation , we get

sin D = 24 / 26

On simplifying the equation , we get

sin D = 0.923

Hence , the equation is sin D = 0.923

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Answer:

Below

Step-by-step explanation:

5.2 * .83     second

(5.2 * .83) * .83   =    5.3 * .83^2     third

.

= 5.2 ( .83)^4        Fifth   = 2.468 ft

Answer:

3ab2+1 = -23

3a^2b-1 =-25

Step-by-step explanation:

The number of years the interest was compounded quarterly is given by the equation b = 9.098 years

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after b years be A = $ 26,725.00

The number of years be = b

The number of times the interest is applies n = 4 ( quarterly )

Let the principal amount be P = $ 7,000

A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

t = ln ( A/P ) / n [ ln ( 1 + r/n ) ]

t = b = n ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.15/4 ) ] )

On simplifying the equation , we get

b = ln ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.0375 ) ] )

b = ln ( 3.81785714 ) / 4 [ ln ( 1.0375 ) ]

On further simplification , we get

b = 9.098 years

Hence , the number of years the interest was applied is 9 years 1 months

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The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years

To solve this problem, we can use the formula for exponential growth:

V(t) = V₀ * (1 + r)^t

Given that the parameters are;

To determine time t when the value of the equipment will be less than $7500.

Let's set up an inequality;

V(t) < 7500

Substituting the formula for V(t), we get:

V₀ * (1 + r)^t < 7500

Substitute the values

(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

Hence, the value is 2.64 years.

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Answer:

Step-by-step explanation:

The tide over a 24-hour period can be modeled by a sinusoidal function of the form:

f(x) = A * sin(Bx) + C

where A is the amplitude, B is the frequency, and C is the vertical shift.

To determine the values of A, B, and C, we need three points. Let's use the following points:

(0, 5): This is the value of the tide at midnight, 5 ft.

(12, 9.5): This is the value of the tide at its high, 9.5 ft.

(6, 0.5): This is the value of the tide at its low, 0.5 ft.

Using the first point (0, 5), we can calculate the vertical shift, C:

C = 5

Using the second point (12, 9.5), we can calculate the amplitude, A:

A = (9.5 - 5) / 2 = 2.25

Using the third point (6, 0.5), we can calculate the frequency, B:

0.5 = 2.25 * sin(B * 6) + 5

4.5 = 2.25 * sin(B * 6)

2 = sin(B * 6)

B * 6 = sin^-1(2)

B * 6 = pi / 2

B = pi / (2 * 6) = pi / 12

So, the final equation is:

f(x) = 2.25 * sin(pi * x / 12) + 5

This represents one period of the sinusoidal function that models the tide over a 24-hour period, with time x measured in hours since midnight.

Answer:

Step-by-step explanation:

Rational numbers are numbers that can be written in the form pq, where p and q are integers and q≠0. The difference between rational numbers and fractions lies in the fact that fractions cannot have negative numerator or denominator.

so, yes.

Nicholas will earn a commission of

Nicholas will earn a commission of 4% on the total price of the two cars sold to Mr. Sherman.

The total price of the two cars is $33,500 per car, so for two cars, the total price would be

= $33,500 * 2

= $67,000.

Therefore, Nicholas will earn a commission of 4% of $67,000

= $67,000 * 0.04

= $2,680.

hence, Nicholas will earn $2,680 in commission for selling the two cars to Mr. Sherman.

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An area of a rectangle is 32x¹²y⁹ square inches and the length is 8x⁴y³ therefore the expression which represents the width of the rectangle in inches is 4x⁸y⁶.

This is referred to as a quadrilateral with four right angles.

Area of rectangle = Length × width

Width = Area/ Length

       =   32x¹²y⁹  /  8x⁴y³

        = 4x⁸y⁶

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Answer:3/a-6

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the height of the rocket, we can use the tangent function. We know the angle of elevation (75°), the height of Homer's eyes (1.8 meters), and the distance from Homer to the rocket (8 meters), so we can use the formula:

tan(angle) = height / distance

We'll solve for the height:

height = distance * tan(angle)

height = 8 * tan(75°)

However, we need to convert the angle from degrees to radians first, as the tangent function operates in radians. We can use the formula:

radians = degrees * (π / 180)

radians = 75° * (π / 180) = 1.309 radians

Now, we can substitute the value for the angle in radians back into the original equation:

height = 8 * tan(1.309)

Using a calculator, we can find that the height is approximately 15.57 meters.

So, the height of the rocket is approximately 15.57 meters.

Answer:

Yes

Step-by-step explanation:

To find this out. If you divide the denominators by each other, they would need to be the same value as if you divide the numerators by each other

[tex]45 \div 9 = 5[/tex]

^ 45 and 9 were the denominators, we divide and get 5

Now for the numerators

[tex]10 \div 2 = 5[/tex]

^ 10 and 2 we're the numerators, dividing also gave 5

Answer:

yes.

Step-by-step explanation:

let us check. to be a proportion they must be equivalent

however, what do we multiply to get there? let us check..

[tex]\frac{2x}{9x} =\frac{10}{45}[/tex]

cross multiply...

2x * 45 = 9x * 10

90x = 90x

yes, they will be proportional!

you can even do it without the X, i just put x in to make it clearer.

From the table which represents the  exponential function , the multiplicative rate of change of function is (a) 1/5 .

The exponential function is expressed mathematically as : y = a(b)ˣ ;

where "a" is = initial value of function , and "b" is = multiplicative rate of change  ;

We first substitute , the first two values from the exponential table ;

we get ;

⇒ 2 = a(b)¹  

⇒ 2 = ab    ,...,,....equation(1) ;

Now substituting the second value ,

we get ;

⇒ 2/5 = a(b)²    ,....equation(2) ;

On dividing equation(2) by equation(1) ,

we get;

⇒ 2/(2/5) = ab/ab²  ;

⇒ 5 = 1/b ;

⇒ b = 1/5 .

Therefore , the multiplicative rate of change is b = 1/5 .

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The given  question is incomplete , the complete question is

The table represents an exponential function.

What is the multiplicative rate of change of the function ?

(a) 1/5

(b) 2/5

(c) 2

(d) 5

There were a total of 95,082 students from country C.

A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviatiοns "pct.," "pct," and "pc" are alsο occasionally used. It is frequently denοted using the percent symbol "%," though. The amοunt of percentages has no dimensions. With a denominatοr of 100, percentages are basically fractiοns.

To shοw that a number is a percentage, place a percent symbol (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questiοns on a test (75/100), you receive a 75%. Tο compute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.

x represents the number οf students from cοuntry C.

then 122percent  of x = 116,000

122/100 * x = 116000

x = 116000 * 100/122 = 95,082 students

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Answer:

Step-by-step explanation:

a) The number of people showing up at the bar during any given minute is a Poisson process with an average rate of 1 person per minute. Let X be the number of people who show up during a random minute. Then X follows a Poisson distribution with parameter λ = 1. The probability of at least 3 people showing up in a random minute is:

P(X >= 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:

P(X = k) = (e^-λ) * (λ^k) / k!

Plugging in λ = 1, we get:

P(X = 0) = e^-1 / 0! = 1/e

P(X = 1) = e^-1 * 1^1 / 1! = 1/e

P(X = 2) = e^-1 * 1^2 / 2! = 1/2e

So, the probability of at least 3 people showing up in a random minute is:

P(X >= 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2)) = 1 - (1/e + 1/e + 1/2e) = 1 - (2/e + 1/2e) = 1 - (5/2e)

b) The probability of having to wait at least 3 minutes for the next person to show up is equal to the probability of having 0, 1, or 2 people show up during the first three minutes. Using the same calculation as above, we find:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = (1/e) + (1/e) + (1/2e) = (2/e + 1/2e) = (5/2e)

So, the probability of having to wait at least 3 minutes for the next person to show up is 1 - (5/2e) = 1 - P(X <= 2).

c) If he has already waited for 1 minute, the probability of having to wait at least 3 more minutes for the next person to show up is equal to the probability of having 0 or 1 people show up during the next 2 minutes. Using the same calculation as above, we find:

P(X <= 1) = P(X = 0) + P(X = 1) = (1/e) + (1/e) = 2/e

So, the probability of having to wait at least 3 more minutes for the next person to show up is 1 - (2/e) = 1 - P(X <= 1).

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The area of the wall is 275 ft square

The number of gallon to cover the wall approximately is 3

the price of the paint is $73.5

1. The area of the wall is given as l * w

this is the value that is used to solve for the area of a rectangle

the length is given as 10 ft

the width is given as 22 ft

the area would be 10 * 22

= 220 ft square

find the area of the triangle = rectangular part is given as height = 15 ft - 10 ft = 5 ft

base = 22 ft

area = 1/2 b h

= 0.5 * 22 * 5

= 55

total area = 220 + 55 = 275 ft square

2. If 1 gallon of paint covers 105 ft

the amount that would cover 275 ft would be gotten when we cross multiply

1 = 105 ft

x  = 275 ft

275 ft = 105 x

x = 275 / 105

x = 2.619

x ~ 3 gallons of paint

3. If one gallon is 24.5 dollars, the total amount that you would purchase is 3 * 24.5

= $73.5

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