Jenny spins a fair 4-sided spinner with the letters A B A and A on it

a) What is the probability that the spinner will land on A?

b) What is the probability that the spinner will land on A or B?​

The balance of the account after 4 years is approximately $818.17.

The formula for calculating the balance of a savings account with compound interest is:

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

where A is the balance after t years, P is the initial principal (deposit), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = $700, r = 0.02 (2% expressed as a decimal), n = 1 (compounded annually), and t = 4.

Plugging in these values, we get:

A = 700(1 + 0.02/1)^(1*4)

= 700(1.02)^4

= $818.17 (rounded to the nearest cent)

Therefore, the balance of the account after 4 years is approximately $818.17.

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The quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

The time taken by substance to reduce to its half of its initial concentration is called half life period.

We will use the half- life equation N(t)

N e^{(-0.693t) /t½}

Where,

N is the initial sample

t½ is the half life time period of the substance

t2 is the time in years.

N(t) is the reminder quantity after t years .

Given

N = 13g

t = 350 years

t½ = 1599 years

By substituting all the value, we get

N(t) = 13e^(0.693 × 50) / (1599)

= 13e^(- 0.368386)

= 13 × 0.691

= 8.98

Thus, we calculated that the quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

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The exact value of cscθ / csc(π - θ) is 1.

What is simplest radical form ?

The simplest radical form is the expression of a radical where the radicand (the number under the radical sign) has been simplified as much as possible.

First, we need to determine the hypotenuse of the right triangle formed by the terminal side of angle θ and the x-axis.

Using the Pythagorean theorem, we have:

\(h^{2}\) = 16+ 1*1

\(h^{2}\) = 16 + 1

\(h^{2}\) =17

h = \(\sqrt{17}\)

Now, we can find the value of sine and cosine of angle θ:

sinθ = opposite/hypotenuse = 1/ \(\sqrt{17}\)

cosθ = adjacent/hypotenuse = -4/\(\sqrt{17}\)

Therefore, cscθ = 1/sinθ = \(\sqrt{17}\)

Now, we can substitute these values into the expression cscθ / csc(π - θ):

cscθ / csc(π - θ) = \(\sqrt{17}\)) / csc(π - θ)

We know that csc(π - θ) = 1/sin(π - θ), and since sin(π - θ) = sinθ, we have:

csc(π - θ) = 1/sinθ = \(\sqrt{17}\)

Substituting this back into the expression, we have:

cscθ / csc(π - θ) = \(\sqrt{17}\)/ \(\sqrt{17}\)  = 1

Therefore, the exact value of cscθ / csc(π - θ) is 1.

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Answer:

20/27

Step-by-step explanation:

Answer:

Improper fraction: 13/10

Mixed number: 1 3/10

Decimal: 1.3

Step-by-step explanation:

Find common denominator: which is 30

Make each denominator equal 30, affecting the whole fraction:

6•2/15•2 + 3•3/10•3 + 3•6/5•6 =

12/30 + 9/30 + 18/30 = 39/30

Simplify: 39/30, divide both by 3: 13/10

And there is our answer!

Hope this helps, good luck! :D

Answer:

39/30

Step-by-step explanation:

Therefore, This equation will pass through the point (14,-28).y=-2x.

Explanation: Direct variation is a mathematical relationship between two variables that can be expressed as y=kx, where k is the constant of variation. To find the equation of direct variation that includes the point (14,-28), we need to first determine the value of k.To do this, we can plug in the x and y values from the point into the equation and solve for k.-28 = k(14) Divide both sides by 14 to isolate k.-28/14 = k Simplify.-2 = k Now that we know k is -2, we can write the equation of direct variation as y=-2x. This equation will pass through the point (14,-28).Answer:y=-2x

Therefore, This equation will pass through the point (14,-28).y=-2x.

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To evaluate the Wronskian W(y1, y2)(x0) and show that y1 and y2 form a fundamental set of solutions, we consider the given functions y1(x) and y2(x) and compute their Wronskian at x0 = 1. The Wronskian is a determinant that helps determine linear independence and forms the basis for proving the fundamental set of solutions.

The Wronskian of two functions y1(x) and y2(x) is given by the determinant:

W(y1, y2)(x) = |y1  y2 |

                |y1' y2'|

where y1' and y2' denote the derivatives of y1 and y2 with respect to x.

For the first function y1(x) = Σn=0 to ∞ \(x^{(2n)}/(2^n * n!)\), we can find its derivative y1'(x) by differentiating each term of the series. Similarly, for the second function y2(x) = Σn=0 to ∞ \((2^n * n!) * x^{(2n+1)}/(2n+1)!\), we differentiate each term to find y2'(x).

Once we have y1'(x) and y2'(x), we can evaluate their values at x = 1 to compute y1'(1) and y2'(1).

Finally, substituting all the obtained values into the Wronskian formula, we calculate W(y1, y2)(1). If the Wronskian evaluates to a non-zero value, it implies that y1 and y2 are linearly independent and form a fundamental set of solutions.

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The correct answer is option (c) 2.06.  For every dollar of debt, Blaine and Lindsay have approximately $2.06 in assets

The asset-to-debt ratio for Blaine and Lindsay McDonald can be calculated by dividing their total assets by their total debt. Using the given values, the calculation would be as follows:

Asset-to-debt ratio = Total assets / Total debt

                   = $346,000 / $168,000

The asset-to-debt ratio is a financial metric that provides insight into the financial health and leverage of an individual, company, or entity. It measures the proportion of assets to debt and is used to assess the ability to meet financial obligations and the level of risk associated with the amount of debt.

In this case, Blaine and Lindsay McDonald have total assets valued at $346,000 and total debt of $168,000. By dividing the total assets by the total debt, we obtain the asset-to-debt ratio of approximately 2.06. This means that for every dollar of debt, Blaine and Lindsay have approximately $2.06 in assets. A higher asset-to-debt ratio generally indicates a stronger financial position and lower risk, as there are more assets available to cover the debt obligations.

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True, a probability/impact matrix or chart lists the relative probability of a risk occurring on one side of a matrix or axis on a chart and the relative impact of the risk occurring on the other.

A probability/impact matrix or chart is a useful tool in risk management and analysis.

It helps organizations evaluate and prioritize risks by considering their probability of occurrence and potential impact if they do occur.

The matrix/chart typically presents a grid or axis with different levels of probability and impact.

The probability of a risk refers to how likely it is to happen, while the impact represents the potential consequences or severity of the risk.

By plotting risks on the matrix/chart, organizations can visually assess and compare the risks based on their probability and impact.

This helps in identifying high-priority risks that require immediate attention and mitigation efforts.

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The probability that the entire batch of 6500 write-rewrite CDs will be accepted, given that 170 are defective and 6 are randomly selected for testing, is approximately 0.859 or 85.9%.

To find the probability that the entire batch of 6500 write-rewrite CDs will be accepted using acceptance sampling, we need to consider the number of defective CDs in the batch and the number of CDs selected for testing.

Given that the batch consists of 6500 CDs and 170 of them are defective, we know that the remaining 6500 - 170 = 6330 CDs are non-defective.

Now, if we randomly select 6 CDs for testing, we want to determine the probability that all 6 CDs are non-defective. To calculate this probability, we need to use the hypergeometric distribution.

The hypergeometric distribution calculates the probability of obtaining a specific number of successes (in this case, non-defective CDs) from a finite population (the entire batch) without replacement.

Using the hypergeometric distribution formula, the probability of selecting 6 non-defective CDs can be calculated as follows:

P(X = 6) = (C(6330, 6) * C(170, 0)) / C(6500, 6)

where C(n, r) represents the number of combinations of selecting r items from a set of n items.

Evaluating this expression, we find:

P(X = 6) = (C(6330, 6) * C(170, 0)) / C(6500, 6) ≈ 0.859

Therefore, the probability that the entire batch of CDs will be accepted is approximately 0.859, or 85.9%.

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The value of rate per toppings is, A = $ 0.50

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that;

The cost of 2 toppings = $ 3.99

The cost of 4 toppings = $ 4.99

Let the cost of the toppings be represented as A

Now , The equation will be;

The cost of 2 toppings = $ 3.99

So , 2A = 3.99  ..(1)

And, The cost of 4 toppings = $ 4.99

⇒ 4A = 4.99   .. (2)

Subtracting equation (1) from equation (2) , we get;

4A - 2A = 4.99 - 3.99

On simplifying the equation , we get

2A = 1.00

Divide by 2 on both sides of the equation , we get

A = $ 0.50

Therefore , The value of rate is, $0.50

Hence , The cost of one toppings = $ 0.50

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Answer:

Step-by-step explanation:

a) Number = x

Multiply it by 3 = 3*x = 3x

Now add 4 to it: 3x + 4

Equation:  

3x +4 = 22

b)

3x + 4 = 22

Subtract 4 from both sides

3x + 4 -4 = 22 - 4

        3x = 18

Divide both sides by 3

3x/3 = 18/3

x = 6

Answer:

Below in bold.

Step-by-step explanation:

The equation is

3x + 4 = 22

3x = 22 - 4 = 18

x = 18/3

x = 6.

Answer:

144

Step-by-step explanation:

do 5 into 600 and u get 12 have a good day!!!

Answer:

$144

Step-by-step explanation:

first, we need to divide 600 by 50, to get them organized for the best packages. 600/50 = 12.

then, we multiply that (the 12) by the cost ($12/ea) so 12*12 which is $144 if they use the bundling.

Given:

A graph that contains image and preimage.

To find:

Which figure is the preimage and which figure is the image.

Solution:

Initial figure is known as preimage and translated figure is known as image.

It is given that a triangle was translated 4 units down. It means, the upper triangle is preimage and the lower triangle is the image.

So, ΔFGH is the pre-image and ΔABC is the image.

Therefore, the correct option is B.

the answer is B :0

i got it right on my assignment !!!!

Answer:

24 is right

Step-by-step explanation:

f(x) = 2x + 1

Replace f(x) with y

y = 2x + 1

Switch x with y and y with x.

x = 2y + 1

Now solve for y. Subtract 1 from both sides.

x - 1 = 2y

Divide both sides by 2

(x - 1) / 2 = y

Replace y with f^-1(x)

f^-1(x) = (x - 1) / 2 is the inverse

Answer:

Step-by-step explanation:

y = 2x + 1

x = 2y + 1

2y + 1 = x

2y = x - 1

y = x/2 - 1/2

f^-1(x) = x/2 - 1/2

The definite integral ∫[a to b] f(x) dx can be expressed as the limit of a Riemann sum. In this case, we use the variables a and b to represent the limits of integration and f(x) to represent the integrand.

To find the definite integral of a function f(x) over the interval [a, b], we can approximate it using a Riemann sum. The Riemann sum divides the interval [a, b] into subintervals and evaluates the function at sample points within each subinterval.

Let's consider a partition of the interval [a, b] with n subintervals, denoted as Δx = (b - a) / n. We choose sample points within each subinterval, denoted as x₁, x₂, ..., xₙ. The Riemann sum is then given by:

R_n = ∑[i=1 to n] f(xᵢ) Δx.

To express the definite integral, we take the limit as the number of subintervals approaches infinity, which gives us:

∫[a to b] f(x) dx = lim(n→∞) ∑[i=1 to n] f(xᵢ) Δx.

In this expression, f(x) represents the integrand, dx represents the differential of x, and the limit as n approaches infinity ensures a more accurate approximation of the definite integral.

Therefore, The definite integral of a function f(x) over the interval [a, b] can be represented as the limit of a Riemann sum. Here, a and b denote the integration limits, and f(x) represents the function being integrated.

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Answer:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70...

Step-by-step explanation:

Answer: y= -1/20x + 38/5

or

y= -1/20x + 7.6

Step-by-step explanation:

y-y1 = m(x-x1)

m = 8-7 / -8 - 12 = 1/-20 = -1/20

y-8 = -1/20(x+8)

y=-1/20x - 8/20 + 160/20

y= -1/20x + 38/5

or

y= -1/20x + 7.6

z_1 and z_2 are complex number;

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

To calculate z₁z₂ and z₁/z₂, we need to perform the complex number operations on z₁ and z₂. Let's break down the calculations step by step:

i) To find z₁z₂, we multiply the magnitudes and add the angles:

z₁z₂ = 4cos(cos(π/4) + isin(π/4)) * 2cos(2π/3) + isin(2π/3))

= 8cos((cos(π/4) + 2π/3) + isin((π/4) + 2π/3))

= 8cos(7π/12) + isin(7π/12)

ii) To find z₁/z₂, we divide the magnitudes and subtract the angles:

z₁/z₂ = (4cos(cos(π/4) + isin(π/4))) / (2cos(2π/3) + isin(2π/3))

= (4cos((cos(π/4) - 2π/3) + isin((π/4) - 2π/3))) / 2

= 2cos(π/12) + isin(π/12)

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

Please note that the given calculations are based on the provided complex numbers and their angles.

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Answer:

Step-by-step explanation:

adam 7.5 to 634

Answer: To find out what Kelly's next score must be in order to obtain an average that is more than 88, we first need to find the current average of her scores. To do this, we add up her current scores and divide by the number of scores:

(79 + 89 + 86 + 93) / 4 = 337 / 4 = 84.25

Since the current average is 84.25, which is less than 88, Kelly must score higher than 88 on her next quiz to bring the average up to more than 88. To be specific, Kelly must score at least 89 on her next quiz.

Step-by-step explanation:

Answer:C

Step-by-step explanation:

The rate of change of f'(x) at (1, 15) is -27.

The notation f'(x) represents the derivative of the function f(x). Therefore, f'(x) = 2x - 3 can be obtained by differentiating the given function f(x) = x² - 3x + 6. To find the rate of change of f'(x) at (1, 15), we need to evaluate f''(x) at x = 1.

Taking the derivative of f'(x), we get f''(x) = 2. Therefore, f''(1) = 2. The rate of change of f'(x) at (1, 15) is equal to f''(1) times the rate of change of x, which is 0.

Hence, the rate of change of f'(x) at (1, 15) is f''(1) * 0 = 0.

Alternatively, we can also find the rate of change of f'(x) at (1, 15) by evaluating f'(x) at x = 1, which gives f'(1) = -1. Therefore, the rate of change of f'(x) at (1, 15) is -1 * 2 = -2.

However, this is the rate of change of f'(x) with respect to x. To find the rate of change of f'(x) at (1, 15) with respect to f(x), we need to use the chain rule.

Let u = x² - 3x + 6. Then f'(x) = u', where u' = 2x - 3.

Differentiating u with respect to x, we get du/dx = 2x - 3.

At (1, 15), we have u = 4 and du/dx = -1.

Using the chain rule, we get:

f''(x) = (d/dx)(2x - 3) = 2

Therefore, the rate of change of f'(x) at (1, 15) with respect to f(x) is -1 * 2 = -2.

Finally, to convert the rate of change of f'(x) with respect to f(x) to the rate of change of f'(x) with respect to x, we need to multiply by du/dx at (1, 15), which is -1.

Hence, the rate of change of f'(x) at (1, 15) with respect to x is (-2) * (-1) = 2.

Therefore, the rate of change of f'(x) at (1, 15) is -27, which is equal to 2 times the rate of change of f(x) at (1, 15), which is -13.5.

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Simplification form of 1/5 raised to the power minus 1 is 5.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

If a fraction's top and bottom share only one additional common factor, it is said to be in its simplest form. In other words, the top and bottom cannot be divided further and remain full numbers. Simplest form is also referred to as "lowest words."

The reduced form of a fraction is another name for its most basic form. For instance, the simplest representation of a fraction with a common component of 1 is 34 The simplest form, however, is not 2/4 because 12 is a further simplification of 2/4 that can be written.

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Answer: 21

Step-by-step explanation:

Answer:

√97

Step-by-step explanation:

Answer:

Your answer is 2,600.019

Step-by-step explanation:

Very simply to answer it with or without a calculator.

2.6 * 10^3 + 0.19 * 10^-2

Without calculator
First move the decimal points before adding.

2.6 * 10^3 = 2,600.

0.19 * 10^-2 = 0.0019

This equation 2.6 * 10^3 + 0.19 * 10^-2 becomes

2,600 + 0.0019

Then add.

2,600.0019

Based on the calculations, the sum of the areas of the rectangles is equal to: A. 0.25 square unit.

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

By critically observing the figure (see attachment), we can logically deduce the following information:

Width of rectangle A = 2 units

Width of rectangle B = 2 units.

Width of rectangle C = 4 units.

Next, we would determine the length and area of each of the rectangle.

The length of the first rectangle is given by:

Length of rectangle, y = 3^-x

Length of rectangle, y(0) = 3⁻⁰ = 1 units.

Length of rectangle, y = 3^-x

Length of rectangle, y(2) = 3⁻² = 0.11 unit.

Area of first rectangle = 2(0.11)

Area of first rectangle = 0.22 square unit.

For the second rectangle, we have:

Length of second rectangle, y = 3^-x

Length of second rectangle, y(4) = 3⁻⁴ = 0.012 unit.

Area of second rectangle = 2(0.012)

Area of second rectangle = 0.025 square unit.

For the third rectangle, we have:

Length of third rectangle, y = 3^-x

Length of third rectangle, y(8) = 3⁻⁸ = 0.00015 unit.

Area of third rectangle = 4(0.00015)

Area of third rectangle = 0.0006 square unit.

Now, we can calculate the sum of the areas of the rectangles:

Total area = 0.22 square unit + 0.025 square unit + 0.0006 square unit.

Total area = 0.246 ≈ 0.25 square unit.

Total area of rectangle = 0.25 square unit.

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Complete Question:

Figure 3 shows the graph of y = 3^−x and three inscribed rectangles. What is the sum of the areas of the rectangles?

[a] 0.25

[b] 0.50

[c] 2.45

[d] 6.26

[e] 12.68

Assuming that Douglas had no other purchases on his credit card, he paid a total of $855.00 for the sofa.

To begin with, we must determine the sofa's final cost, including sales tax:

Total cost = Cost of sofa + Sales tax

Total cost = $670 + (7.94% of $670)

Total cost = $670 + $\((670*\frac{7.94}{100} )\)

Total cost = $723.20

Then, we must figure out the interest rate per month:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 11.05% / 12

Monthly interest rate = 0.9208%

The following is the calculation for a loan with constant payments and its monthly payment:

Monthly payment = (Loan amount x Monthly interest rate) ÷ (1 - (1 + Monthly interest rate)^(-Number of months))

The loan amount is the total cost of the sofa, which is $723.20. The number of months is 3 years x 12 months/year = 36 months.

Monthly payment \(=\frac{723.20*0.9208}{(1 - (1 + 0.9208)^{-36})}\)

Monthly payment = $23.75 (to the closest cent)

Douglas made 36 monthly payments of $23.75, so the total amount he paid for the sofa is:

Total paid = Monthly payment × Number of payments

Total paid = $23.75 × 36

Total paid = $855.00

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