How much more light does one collect with a 10-meter diameter telescope in 10 minutes than with a 1-meter diameter telescope in 100 minutes?.

Answer:

thxs

Step-by-step explanation:

Each year the account earns 5% interest, and you deposit 8% of your annual income with an annual income of $30000 which is growing at a continuous rate of 3% per year. The given differential equation models this situation dy/dt= 0.05y+2400e^(0.03*t)

First, let's break down the information given in the problem:
- y(t) represents your retirement account balance in dollars after t years.
- The account earns 5% interest each year, which means that the balance increases by 5% of the previous year's balance.
- You deposit 8% of your annual income into the account each year. Your current annual income is $30,000, but it is growing at a continuous rate of 3% per year.
Now, let's write the differential equation to model this situation. We know that the rate of change of y(t) is equal to the sum of the interest earned and the deposits made each year. In other words:
dy/dt = rate of interest + rate of deposits
The rate of interest is simply 5% of the current balance, or 0.05y. The rate of deposits is 8% of your current annual income, which is $30,000 plus 3% of your current annual income for each additional year. We can express this as \(0.08(30000)(1.03)^t\). Putting it all together, we get:
dy/dt = 0.05y + \(0.08(30000)(1.03)^t\)
But this isn't quite in the form of our desired answer yet. We can simplify the right-hand side by factoring out 0.05y, which gives us:
dy/dt = \(0.05y(1 + 1.6(1.03)^t)\)
Now we have our differential equation in the form of y' = ky, where k = \(0.05(1 + 1.6(1.03)^t)\). To solve this equation, we can use the separation of variables:
dy/y = k dt
Integrating both sides gives us:
ln|y| = kt + C
where C is the constant of integration. Exponentiating both sides gives us:
|y| = \(e^{(kt+C)}\) = \(Ce^{(kt)}\)
where C is a constant that depends on the initial conditions (i.e. the value of y when t=0). We can solve for C using the fact that y(0) = some initial value, say $10,000:
|10000| = \(Ce^{(0)}\)
C = 10000
So our final solution is:
y(t) = \(10000e^{(kt)}\)
where k is still equal to 0.05(1 + 1.6(1.03)^t). If we substitute this expression for k and simplify, we get:
y(t) = \(10000e^{(0.05t + 2400(e^{(0.03t)-1)/0.03)}}\)
which is equivalent to the answer given: dy/dt = 0.05y + \(2400e^{(0.03t)}\)

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The probability of getting exactly 1 three, to the nearest thousandth is 0.347.

We have,

Binomial distribution is the distribution of a random variable X for which there are only two possibilities. The probability p for the success and the probability of 1-p for the failure, which consist of n trials.

The binomial distribution has the formula,

P(x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

where x : number of times for a specific outcome within n trials

p : probability of success in each trial

n : number of trials

Given that a fair die is rolled 3 times.

Here, n = 3, x = 1

p = probability of getting three for 1 trial = 1/6

1 - p = 1 - 1/6 = 5/6

P(1) = ³C₁ (1/6)¹ (5/6)³⁻¹

    = 0.347

Hence the probability of getting exactly 1 three is 0.347.

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complete question:

If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 1 three?

The balance at the end of the of 3 years is $5,229.26.

The APY of the account is 15.06%

When an amount earns annual interest that is compounded semi-annually, it means that both the amount that is invested and the interest that has already been earned increases in value twice a year.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Balance = 5000 x (1 + 0.0075)^(2 x 3)

5000 x 1.0075^6 = $5,229.26

The annual percentage yield is the actual interest that is earned on an investment after accounting for the number of compounding.

APY = (1 + r/n)^n - 1

APY = (1 + 0.015/2)^2 - 1

APY = 1.0075^2 - 1 = 0.01506 = 15.06%

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To find the equation of the tangent plane to the given equation 2(x-2)^2 (y-1)^2 (z-3)^2=10, we need to find the gradient of the function and use the point-slope form of a plane.

First, we find the gradient of the function by taking the partial derivatives with respect to x, y, and z:

∂f/∂x = 4(x-2)(y-1)^2(z-3)^2

∂f/∂y = 4(x-2)^2(y-1)(z-3)^2

∂f/∂z = 4(x-2)^2(y-1)^2(z-3)

Next, we find the point on the surface where we want to find the tangent plane. For simplicity, let's choose the point (2,1,3), which is on the surface because 2(2-2)^2(1-1)^2(3-3)^2=0=10.

Now we plug in the point into the gradient to find the normal vector to the plane:

∂f/∂x(2,1,3) = 4(2-2)(1-1)^2(3-3)^2 = 0

∂f/∂y(2,1,3) = 4(2-2)^2(1-1)(3-3)^2 = 0

∂f/∂z(2,1,3) = 4(2-2)^2(1-1)^2(3-3) = 0

So the normal vector is <0,0,0>.

Finally, we use the point-slope form of a plane to find the equation of the tangent plane:

0(x-2) + 0(y-1) + 0(z-3) = 0

Simplifying, we get:

0 = 0

This means that the tangent plane is the entire xyz-space, since any point satisfies this equation.

Therefore, the equation of the tangent plane to the given equation at the point (2,1,3) is 0 = 0.

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Answer:

1 is 1/9 2 is 1/9 3 is 5/9 4 is 8/9

Step-by-step explanation:

A(Ab AC AA) B(ba bb bc) C(ac bc cc)

Solution:

Note that:

This means...

Refer to table uploaded~

Answer:

1) 12 (option b)

2) 41, 9, 40 (option a)

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

1) Let the unknown leg be x cm long. Thus,

5² + x² = 13²

Simplify and solve.

25 + x² = 169

x² = 144

x = 12

2) Apply the Pythagorean Theorem.

9² + 40² = 41² = 81 + 1600 = 1681

1681 = 1681

a is true.

Just in case, let's check the other options.

5² + 8² = 9² = 25 + 64 = 81

89 = 81, false

b is false

10² + 11² = 12² = 100 + 121 = 144

221 = 144, false

c is false

3² + 4² = 6² = 9 + 16 = 36

25 = 36, false

d is false

Thus, a is the answer.

A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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Answer:

assuming that the equations are equal to zero the answers would be

3   ,   -3    ,  5

Step-by-step explanation:

Answer:

24.5

Step-by-step explanation:

Year 2000 would be 1, so year 2016 would be 17

Your equation is 1.5x - 1, and since we have x = 17, we simply plug it in:

1.5(17) - 1

25.5 - 1

24.5 is our estimated population using the line of best fit.

Answer:

23

Step-by-step explanation:

Note that the horizontal axis notes the years since 2000. This means that each increase in the x axis increases the year by 1. Thus, it means that at x=1, it is 2001, at x=2, it is 2002. In other words, in 2016, x=16.

We can just put this number into the equation:

y=1.5(16)-1

y=24-1

y=23

Answer: 7/12x

Step-by-step explanation:

Answer:

7x/12

Step-by-step explanation:

brainleist please

The maintenance cost expected to be incurred during July is $9,400. This corresponds to option C in the given choices.

To determine the maintenance cost expected to be incurred during July, we need to substitute the planned machine time of 9,000 hours into the cost formula Y = $5,800 + $0.40X.

Plugging in X = 9,000 into the formula, we get:

Y = $5,800 + $0.40(9,000)

Y = $5,800 + $3,600

Y = $9,400

Therefore, the maintenance cost expected to be incurred during July is $9,400. This corresponds to option C in the given choices.

The cost formula Y = $5,800 + $0.40X represents the fixed cost component of $5,800 plus the variable cost component of $0.40 per machine-hour. By multiplying the planned machine time (X) by the variable cost rate, we can determine the additional cost incurred based on the number of machine-hours. Adding the fixed cost component gives us the total maintenance cost expected for a given level of machine-time. In this case, with 9,000 hours of planned machine time, the expected maintenance cost is $9,400.

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Answer:

8-r/-2

8-12/-2

-4/-2

2

This is the answer

I think this will help you

Answer:

Here is the result:

(2, 3)      ↔      (2, 2)                     ∵ x = 2 is duplicated

(-5, 2)     ↔      (-5, 1)                     ∵ x = -5 is duplicated

(6, -5)     ↔      (6, 5)                     ∵ x = 6 is duplicated

(-1, 0)      ↔      (-1, 6)                     ∵ x = -1 is duplicated

Here, each matching pair has duplicated input values, so neither of them represents the function.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

We are given that we need to match the ordered pairs so that the relation defined by the set of ordered pairs does not represent a function.

Therefore, all we need is to match the ordered pairs which have the same input value as it would violate the relation to be function.

Here is the result:

(2, 3)      ↔      (2, 2)                     ∵ x = 2 is duplicated

(-5, 2)     ↔      (-5, 1)                     ∵ x = -5 is duplicated

(6, -5)     ↔      (6, 5)                     ∵ x = 6 is duplicated

(-1, 0)      ↔      (-1, 6)                     ∵ x = -1 is duplicated

Here, each matching pair has duplicated input values, so neither of them represents the function.

Answer:

(0, 2)

Step-by-step explanation:

The y-intercept on a graph represents the point where the graph intersects the y-axis. In the equation y = x + 2, the y-intercept can be found by setting x = 0 and solving for y.

When x = 0:

y = 0 + 2

y = 2

Therefore, the y-intercept on the graph of the function y = x + 2 is (0, 2).

The linear extension of l on s is {(1,3), (2,6), (5,), (1,5), (3,5)}.

The relation | on s = {1,2,3,5,6} means that two elements are related if they have the same parity (i.e., they are both even or both odd).
To find all linear extensions of | on s, we can first write down the pairs that are already related by |:
(1,3), (2,6), (5,)
We can then consider each remaining pair of elements and decide whether they should be related or not in a linear extension of |. For example, we could choose to relate 1 and 5, since they are both odd and do not currently have a relation.
One possible linear extension of | on s is:
{(1,3), (2,6), (5,), (1,5), (3,5)}

Note that there are several other possible linear extensions, depending on which pairs we choose to relate.

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The dimensions of the given rectangle is 2 1/2 meters (width) and 3 1/3 meters (length).

First, let's define the variables for the rectangle: let the width be w meters, and the length be (4/3)w meters since the length is 4/3 times the width. The area of a rectangle is calculated by multiplying its length and width. In this case, the given area is 8 1/3 square meters.

Now, we can write an equation using the area and dimensions:

Area = Length × Width
8 1/3 = (4/3)w × w

First, convert the mixed number 8 1/3 to an improper fraction, which is 25/3. Then, we can solve for w:

25/3 = (4/3)w²

To find w², multiply both sides by 3/4:

w² = (25/3) × (3/4)
w² = 25/4

Now, take the square root of both sides:

w = √(25/4)
w = 5/2

So, the width is 5/2 meters, or 2 1/2 meters. To find the length, multiply the width by 4/3:

Length = (4/3)(5/2) = 20/6 = 10/3

The length is 10/3 meters, or 3 1/3 meters. Therefore, the dimensions of the rectangle are 2 1/2 meters (width) and 3 1/3 meters (length).

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The CLV for transactors is $37.5, for revolvers it is $208.33, and for dormants, it is $2,000,000.

Customer Lifetime Value (CLV) is a financial analysis of the total revenue an organization can reasonably anticipate from a single customer over the course of their relationship. It is the net present value of the cash flows attributed to the relationship with a customer.

This metric is widely used in business to determine how valuable a customer is to the company.

The formula for CLV is:

CLV = (Average Value of a Sale) X (Number of Repeat Transactions) X (Average Retention Time in Months or Years)

There are three sub-segments of the credit card product: transactors, revolvers, and dormants.

The transactors are customers who pay off their credit card balance every month.

Revolvers are customers who carry a balance from month to month.

Dormants are customers who no longer use their credit card.

Each sub-segment will have a different CLV.

Here is how to calculate CLV for each sub-segment:

Transactors:

CLV = (Annual Fee) X (1/Churn Rate)

CLV = (450) X (1/12)

CLV = 37.5 dollars

Revolvers:

CLV = (Annual Interest Paid) X (Average Customer Lifespan)

CLV = (5000) X (1/24)

CLV = 208.33 dollars

Dormants:

CLV = (Number of Dormant Customers) X (Average Annual Spend per Customer) X (Profit Margin)

CLV = (10,000) X (1000) X (0.2)

CLV = 2,000,000 dollars

Therefore, the CLV for transactors is $37.5, for revolvers it is $208.33, and for dormants, it is $2,000,000.

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To find the number of days it will take for Juliana's investment to grow, we can use the formula for simple interest

I = P * r * t.

I = interest earned
P = principal amount (initial investment)
r = interest rate per year (in decimal form)
t = time in years In this case,

Juliana's principal amount (P) is $3,300, the interest rate (r) is 6.25% or 0.0625, and she wants to reach $3,450. We need to solve for t. $3,450 = $3,300 * 0.0625 * t Divide both sides of the equation by ($3,300 * 0.0625) to isolate t:
t = $3,450 / ($3,300 * 0.0625)
t = 17 So it will take Juliana approximately 17 days for her investment to grow to $3,450.

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If you want to scale your ratio up, you need to multiply or increase the values of both the numerator and the denominator of the ratio by the same factor.

A ratio represents the relationship between two quantities and is expressed as the quotient of two numbers. Scaling up a ratio means increasing the values of both the numerator and the denominator while maintaining the same relative relationship between them.

To scale up a ratio, you can follow these steps:

Determine the scaling factor: The scaling factor is the value by which you want to increase the ratio. It can be any positive number greater than 1.

Multiply both the numerator and the denominator by the scaling factor: Multiply the original numerator and denominator of the ratio by the scaling factor. This ensures that both quantities are scaled up proportionally.

By multiplying both parts of the ratio by the same scaling factor, you maintain the same ratio relationship while increasing the absolute values of the quantities.

For example, let's consider the ratio 2:5. If we want to scale it up by a factor of 3, we would multiply both the numerator and the denominator by 3:

2 * 3 : 5 * 3

6 : 15

The scaled-up ratio becomes 6:15, which maintains the same ratio relationship as 2:5 but with larger absolute values.

Scaling up a ratio can be useful in various scenarios, such as when you want to increase the size or quantity of something while maintaining the same relative proportions. It allows you to expand the scale of the ratio without altering the underlying relationship between the quantities involved.

In summary, to scale up a ratio, you need to multiply both the numerator and the denominator of the ratio by the same factor. This ensures that the ratio maintains its relationship while increasing the absolute values of the quantities.

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Answer:

C. $20

Step-by-step explanation:

Lets make our equation. "x" will be our first journal, and "4/5x + 12" will be our second journal. So our equation is: x + 4/5x + 12 = 30

Subtract 12 from each side: x + 4/5x = 18

Combine like terms : 1 4/5 x = 18

Divide each side by 1 4/5 : x = 10

Plug in x for the journals-

1 = 10

2 = 4/5 of 10 = 8 + 12 = $20

I hope this helped, please mark Brainliest, thank you!

Answer:0.75

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

i like to turn them into improper fractions

4 and 1/2 is 9/2

6 is 6/1

to divide fractions, multiply by the reciprocal

6/1 flipped is 1/6

then multiply

9/2 x 1/6 = 9/12

simplify

3/4

The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

From the given expression ,

y = 2.5 x + 10

So, we have to find the length of line segment from x = 0 to x = 16.

so when x = 0 ,

y = 0+10

y = 10

and when x=1

y = 2.5*1+10

y=12.5

and similarly

when x = 2

y = 2.5* 2 + 10

y = 15

So, like this the sequence will be goin on y = 10 , 12.5 , 15 , 17.5 and etc .

Hence, The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.

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Answer:  Choice A.  \((\text{x}-5)^2\)

Work Shown:

\(G(\text{x}) = \text{x}^2\\\\G(F(\text{x})) = (F(\text{x}))^2\\\\G(F(\text{x})) = (\text{x}-5)^2\\\\\)

Answer:

it's like this the answer

Step-by-step explanation:

x⁴-8x²y²+16y²-256

(x²-8xy)²+(4y-16)²

Answer:

x⁴-8x²y²+16y²-256

(x²-8xy)²+(4y-16)²

Step-by-step explanation:

The outcome of the complex number given is 7i+8/10 in its most basic form. Option C

Complex numbers are referred to as the square root of negative numbers. For instance √-1 = i.

In this expression 'i" is a complex number.

Given the expression below;

-7+8i / 10i

Rationalise

-7+8i / 10i * 10i/10i

= 10i(-7+8i)/10(i²)

= -70i+18(-1)/10(-1)

= -70i - 18/-10

= 7i+1.8

Hence the result of the given complex number in its simplest form is 7i+8/10

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