Write a recursive formula for an, the nth term of the sequence 50, -10, 2, ....
a1
an
11

Answer: no exact answer

Step-by-step explanation:

Answer:

Step-by-step explanation: We can start the problem by using the principle of Proportional Equivalents. We can write two equations based on the given information:

Let's say that the rate of filling the pool with one large pump is x and the rate of filling the pool with one small pump is y.

Then, we can write the following two equations:

2x + 1y = 1/4 (because two large and one small pump can fill the pool in 4 hours)

1x + 3y = 1/4 (because one large and three small pumps can fill the pool in 4 hours)

Now we have two equations with two unknowns, x and y. We can solve for x and y using either substitution or elimination method. Let's use substitution method.

Solving for x:

From equation (1), we have 2x = 1/4 - 1y

Substituting this value of x in equation (2), we get:

1 (1/4 - 1y) + 3y = 1/4

Expanding and simplifying, we get:

1/4 - 1 + 3y = 1/4

3y = 1/2

y = 1/6

So, the rate of filling the pool with one small pump is 1/6.

Now that we have found the value of y, we can find the value of x.

x = 1/4 - 1y = 1/4 - 1 * 1/6 = 1/4 - 1/6 = 1/12

So, the rate of filling the pool with one large pump is 1/12.

Now that we have found the rate of filling the pool with each large and small pump, we can find the time it will take 4 large and 4 small pumps to fill the pool.

Let's call the rate of filling the pool with 4 large and 4 small pumps as R.

Then, R = 4 * 1/12 + 4 * 1/6 = 1/3

So, it will take 1/R = 3 hours to fill the pool with 4 large and 4 small pumps.

Answer:

340 CDs

Step-by-step explanation:

To answer this question, we're dealing with three functions for one problem, namely the revenue function, the cost function, and the profit function.

The revenue function is R(q) = pq, where p is the price of a certain good and q is the quantity sold.

The cost function is C(q) = variable cost + fixed cost, where variable costs changes depending on the quantity of goods produced and fixed cost is a one-time cost for the producer (e.g., an investment, rent, etc.).

The profit function is P(q) = R(q) - C(q) and is simply the cost function subtracted from the revenue function.

The "break-even point" is the point at which profit = $0 and the point at which cost = revenue.

From the problem, we see that Jason invested $3349 (once) for his CDs and each disk requires $3.65 for the materials so our cost function is C(q)  = 3.65q + 3349

Furthermore, we see that each disks sells for $13.50, so our revenue function is R(q) = 13.5q

Our profit function then is P(q) = 13.5q - (3.65q + 3349) = 13.5q - 3.65q - 3349 = 9.85q - 3349.

Thus, to find the break-even point, we set profit = 0 and solve for q:

[tex]0=9.85q-3349\\3349=9.85q\\340=q[/tex]

I think this is it

252-(193×n) =131

The cost of one pound of potato is 0.73 pounds.

The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Now in the given question , we have to find the cost of one pound of potato.

here we have to find the cost of one pound of potato mia bought.

she total spent $3.65 for them and bought five pounds of potatoes.

cost of one pound of potato

= [tex]\frac{total spent}{total bought} = \frac{3.65}{5} =0.73 pounds[/tex]

 hence, cost of one pound of potato is 0.73 pounds.

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The total value of $6800 compounded quarterly at 6% for 3 years is $8,123

From the question, we have

A = final amount

P = principal amount (initial investment) = $6800

r = annual interest rate = 0.06 ie. 6%

n = number of times interest is compounded per year = 4

t = time (in years) = 3

The total value is calculated as:

A = P(1 + r/n)^(nt)

substitute the known values in the above equation, so, we have the following representation

A = 6800(1 + 0.06/4)^(4*3)

Evaluate

A = 8130.2

Hence,, the value is $8130.2

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The amount of water used for each month and rounded off to the nearest 1000 is;

Amount of water used in May = 12567 litres

Amount of water used in June = 452 litres

Amount of water used in July = 15623 liters

Approximate amount of water used in May to the nearest 1000 = 13,000 liters

Approximate amount of water used in June to the nearest 1000 = 0 liters

Approximate amount of water used in July to the nearest 1000 = 16,000 liters

Therefore, the amount of water used each month rounded to the nearest 1000 are 13,000, 0, and 16,000 respectively.

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Answer: 15 pounds

Step-by-step explanation:

10.4(x)+4.3(10)=7.96(x+10)

10.4x+43=7.96x+79.6

2.44x=36.6

x=15 pounds

(check my work. I may have done something wrong, but the equation should be correct.)

Answer:

The triangle has an area of 192cm^2

Step-by-step explanation:

Given;

the formula to find the area of the triangle,

[tex]A=\frac{h_{b}b }{2}[/tex]

We can insert the values,

[tex]A=\frac{24*16}{2} \\\\\\A=\frac{384}{2} \\\\A=192cm^2[/tex]

The area of the triangle is 192cm^2.

Answer:

Step-by-step explanation:

The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).

The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).

The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:

1/36 * 1/36 = 1/1296

So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.

Step-by-step explanation:

The slashes through the lines indicate they're of the same length, which means this is an equilateral triangle. Therefore all three angles are 60 degrees.

The lines being parallel mean that angle x shares the same angle as the triangle in the bottom-right corner.

The parallel lines intersecting with the line segment that is consistent throughout the triangle makes the angle the same.

Step-by-step explanation:

We can see that the triangle in the picture is an equilateral triangle, because its sides are all marked with one dash, meaning they are equal lengths. We note that all the angles in an equilateral triangle are each 60°.

The little arrows on the top and bottom lines in the figure indicate that they are parallel, which means that the diagonal line between them creates a set of alternate angles (I've attached a pic of what alternate angles generally look like to make this clearer).

Alternate angles are equal, which means x is equal to the angle at the bottom right of the triangle, which is 60°.

Answer:

Step-by-step explanation:

In the compound interest formula: A = P(1 + r)^t

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

In the continuously compounded interest formula: A = Pe^(rt)

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

So the variables in the formulas and their descriptions are:

A: the amount of money in the account at the end of the term t, including interest

P: the initial principal, or the amount of money invested

r: the interest rate, usually expressed as a decimal

t: the number of time periods over which the interest is compounded.

On solving the provided question, we can say that By fraction, 3/4 times 5/7 is 15/28 and Action games are 15/28 of the apps.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

By fraction,

3/4 times 5/7 is 15/28.

Action games are 15/28 of the apps.

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Answer:

Step-by-step explanation:

we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base  (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.

6 * 8 + 4 * 5 =                     remember PEMDAS

48 + 20 =

68 m²

Answer:

11 bat and 8 helmets.

Step-by-step explanation:

Let x = the number of bats

Let y = the number of batting helmets

x + y = 19  Rewrite as y = 19 - x

18.25x + 24.50y = 369.75  Multiply by 100

1825x + 2450y = 36975  Substitute 19 - x for y

1825x + 2450(19 -x) = 39675   Distribute the 2450

1825x + 46550 - 2450x = 39675  combine like terms

-625x + 46550 = 39675  subtract 46550 from both sides

-625x = -6875  Divide both sides by -625

x = 11

He bought 11 bats

x + y = 19  Substitute 11 for x to solve for y

11 + y = 19  Subtract 11 from both sides

y = 8

He bought 8 helmets.

The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).

From the attached graph :

The area of the shaded region :

x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :

= [tex]\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy[/tex]

=  [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ][tex]| \limits^1_0[/tex]

Substitute the lower limit and upper limit we get,

= (5 /3 )( 1 )³ - 0  - ( 5 / 4 )( 1⁴) + 0

= ( 5 / 3 ) - ( 5 / 4 )

= ( 20 - 15 ) / 12

= 5 / 12

Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .

The given question is incomplete, I answer the question in general according to my knowledge:

Find the total area of the shaded region x = 5y³ , x = 5y² for the interval

( 5, 1 ).

Graph is attached.

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The demonstration of magnitude of power given by 80 kg monkey by climbing a 15 meter tree in half a minute is equal to option b.  392 J/S.

Weight 'm' of the monkey is equal to 80kilogram

Height 'h' of the tree is equal to 15 meter

Time 't' taken by monkey to climb a tree = half a minute

                                                                    = 30 minutes

g = 9.8 m/s²

Magnitude of power = ( m × g × h )/ t

⇒ Magnitude of power = ( 80 × 9.8 × 15 )/ 30

⇒ Magnitude of power = 784 / 2

⇒ Magnitude of power = 392 J/S

Therefore, the magnitude of the power for the given weight , displacement and time is equal to option b. 392 J/S.

The above question is incomplete, the complete question is:

A 80 Kg monkey climbs a 15 meter tree in half a minute. What is the magnitude of power the monkey demonstrated?

a. 13.1 J/S

b. 392 J/S

c. 784 J/s

d. 11760 J/s​

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Answer:

x = 80

Step-by-step explanation:

supplementary angles sum to 180°

sum the 2 angles and equate to 180

x + 40 + x - 20 = 180

2x + 20 = 180 ( subtract 20 from both sides )

2x = 160 ( divide both sides by 2 )

x = 80

Step-by-step explanation:

We can start by using an equation to represent the given information. Let's call the number p, and the number k, then:

k = (1/5)p + 6

So, "six more than one-fifth of a number p is equal to a number k" can be represented mathematically as k = (1/5)p + 6. To find the value of p, we can solve for p:

p = 5k - 30

So, p is equal to 5 times the value of k minus 30.

Answer:

Step-by-step explanation:

To calculate the compound interest on Mary's savings account, we can use the formula:

A = P * (1 + r/n)^(nt)

Where:

A is the amount after t years

P is the initial principal (£12000)

r is the interest rate (1.5%)

n is the number of times the interest is compounded in a year (let's assume it's compounded annually)

t is the number of years (2)

So, plugging in the values, we get:

A = £12000 * (1 + 0.015/1)^(1 * 2)

A = £12000 * (1.015)^2

A = £12000 * 1.0302

A = £12363.84

So, after 2 years, Mary's £12000 investment would be worth £12363.84, including the compound interest.

The amount that should be invested in order to have $2,290 in 16 years is $929.11.

What is compound interest?

The interest on a deposit calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compound interest is interest that is earned on interest.

Here, we have

Given: Xin will invest in an account paying an interest rate of 5.8% compounded annually.

Amount to invest = Future value / (1 + r)ᵗ

Where:

r = interest rate

t = time

X = $2,290 / (1 + 0.058)¹⁶

X = 2,290 / 2.46474

X = $929.11

Hence, the amount that should be invested in order to have $2,290 in 16 years is $929.11.

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Answer:  Weight of water in 1 cubic foot water (in pounds)

Weight of water in 1 cubic foot water (in ounces)=

Step-by-step explanation:

Given: One cubic foot holds 7.48 gallons of water.

One gallon of water weighs 8.33 pounds.

To find the weight of water in 1 cubic foot water in pounds we apply Unitary method.

Weight of water in 1 cubic foot water (in pounds)

⇒Weight of water in 1 cubic foot water (in pounds)

Since , 1 pound = 16 ounces .

Weight of water in 1 cubic foot water (in ounces)=

Step-by-step explanation:

Answer:

16.66667% increase

Step-by-step explanation:

100 x 350 - 300/ 300 = 50/3 = 16.66667% increase

Formula for percent increase is below↓

The required, each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

here,
To divide the 2 cakes equally among 7 people, we can use division. We can think of the total amount of cake as 2 whole cakes or 2/1 cakes. To find out how much cake each person can have, we can divide the total amount of cake by the number of people:

2/1 cakes ÷ 7 people = 2/1 × 1/7 = 2/7 cakes per person

So each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

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A. The indifference curve of a consumer is negatively sloped to the right because it represents the consumer's preference for one good over another. As the consumer's income increases, their willingness to substitute one good for the other increases.

B. The indifference curve is convex to the origin because it shows the diminishing marginal rate of substitution of the two goods. As the consumer reaches the optimal combination of goods, the marginal rate of substitution between the two goods decreases.

C. Using the Lagrange method, the optimum combination of goods can be determined as follows:

Let L(X,Y) be the Lagrangian of this problem:

L(X,Y) = √X² + Y² - λ(200 - 3X - 4Y)

Where λ is the Lagrange multiplier.

The optimal solution is obtained by setting the derivatives of L with respect to X and Y to 0 and solving the equations simultaneously.

∂L/∂X = 0 -> X = 11.85

∂L/∂Y = 0 -> Y = 8.57

Therefore, the optimum combination of goods is X = 11.85 and Y = 8.57.

D. The slope of the indifference curve is equal to the slope of the budget line. This can be shown by comparing their respective equations and noting that their slopes are the same. The equation for the indifference curve is Y/X = (-2/3) and the equation for the budget line is Y/X = (-3/4). Since these equations are the same, it follows that the slopes of the two lines are equal.

The y-coordinate for the solution to the system of equations is y = -3.

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be chosen over other algebraic methods for straightforward equations that don't require complicated calculations.

The system of equation is given as:

y = 1/2x - 4

y = -2x + 1

Substituting the value of y in equation 1 we have:

-2x + 1 = 1/2x - 4

-2x + 1 = x - 8 / 2

(-2x + 1)(2) = x - 8

-4x + 2 = x - 8

2 + 8 = x + 4x

10 = 5x

x = 2

Substituting the value of x in the second equation:

y = -2(2) + 1

y = -4 + 1

y = -3

Hence, the y-coordinate for the solution to the system of equations is y = -3.

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Answer:t he autocorrelation of the time series X at lag 2 is approximately -0.018.

Step-by-step explanation:

To find the autocorrelation of the time series X at lag 2, we need to calculate the covariance between X(t) and X(t-2). This can be done using the following formula:

r(2) = cov(X(t), X(t-2)) / var(X(t))

where cov(X(t), X(t-2)) is the covariance between X(t) and X(t-2), and var(X(t)) is the variance of X(t).

To calculate the covariance, we'll use the following formula:

cov(X(t), X(t-2)) = sum((X(t) - mean(X(t))) * (X(t-2) - mean(X(t-2)))) / (n - 1)

where n is the number of observations in the time series. To calculate the variance, we'll use the following formula:

var(X(t)) = sum((X(t) - mean(X(t)))^2) / (n - 1)

First, let's calculate the mean of X(t):

mean(X(t)) = (47 + 64 + 23 + 71 + 38 + 64 + 55 + 41 + 59 + 48) / 10 = 51

Next, let's calculate the covariance between X(t) and X(t-2):

cov(X(t), X(t-2)) = sum((X(t) - 51) * (X(t-2) - 49)) / (10 - 1) = -10.3

Finally, let's calculate the variance of X(t):

var(X(t)) = sum((X(t) - 51)^2) / (10 - 1) = 563.7

Plugging in these values, we can find the autocorrelation at lag 2:

r(2) = cov(X(t), X(t-2)) / var(X(t)) = -10.3 / 563.7 = -0.018

So the autocorrelation of the time series X at lag 2 is approximately -0.018.

Answer: 6.7

Step-by-step explanation: 7^2-2^2=45

square 45 =6.7

Answer: Scalene Right

Step-by-step explanation:

None of the side lengths are equal and there's a 90 degree angle

The value of f(3) is 2.

Option B is the correct answer.

A function has an input and an output with a relationship between them.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 1/4 x [tex]2^x[/tex]

Substitute x = 3.

f(3) = 1/4 x 2³

f(3) = 1/4 x 8

f(3) = 2

Thus,

The value of f(3) is 2.

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