Donna opens a certificate of deposit (CD) with $2,000. The bank offers a 3% interest rate. If the account compounds quarterly, which of the following equations represents the future value of the account, after 1 year?

Answer:

6

Step-by-step explanation:

I took the k12 2.12 Quiz: Divide Fractions

Final answer:

To solve the quadratic word problem, we set up the equation x - 8/x = 2 and simplify it to x^2 - 2x - 8 = 0. Using the quadratic formula, we find two possible values for x: -2 and 4.

Explanation:

To solve this quadratic word problem, we set up the equation: x - 8/x = 2. To simplify the equation, we multiply both sides by x to eliminate the denominator: x^2 - 8 = 2x. Rearranging the equation, we get x^2 - 2x - 8 = 0. To find the solutions, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Substituting the values from our equation, we have x = (2 ± √(2^2 - 4(1)(-8))) / (2(1)). Solving the equation, we find two possible values for x: x = -2 or x = 4.

we know that

A unit rate is a ratio between two different units with a denominator of one

In this problem to find the unit rate divide the total distance by the total time

so

[tex]\frac{822.6}{18} \frac{Km}{hours}= 45.7\frac{Km}{hour}[/tex]

therefore

the answer is

The unit rate is equal to [tex] 45.7\frac{Km}{hour}[/tex]

The exact average speed when x = 56 seconds is approximately 30.86 mph.

To use linear approximation to approximate a person's average speed if they travel one mile in 56 seconds, we'll first find the derivative of the function [tex]\( s(x) = \frac{3600}{60 + x} \)[/tex] with respect to x.

[tex]\[ s'(x) = -\frac{3600}{(60 + x)^2} \][/tex]

Now, we'll evaluate the derivative at x = 0 to find the slope of the tangent line at that point, which will be our linear approximation.

[tex]\[ s'(0) = -\frac{3600}{(60 + 0)^2} = -\frac{3600}{3600} = -1 \][/tex]

So, the slope of the tangent line at x = 0 is -1.

Now, using the point-slope form of the equation of a line, we'll find the equation of the tangent line at x = 0:

y - s(0) = s'(0)(x - 0)

[tex]\[ y - s(0) = -1 \cdot x \][/tex]

y = -x + s(0)

We know that s(0) is the exact speed at x = 0, so we'll substitute x = 0 into the original function to find it:

[tex]\[ s(0) = \frac{3600}{60 + 0} = 60 \text{ mph} \][/tex]

So, the equation of the tangent line is:

y = -x + 60

Now, to approximate the average speed when x = 56, we'll substitute x = 56 into the equation of the tangent line:

y = -56 + 60 = 4

So, the approximate average speed when x = 56 seconds is 4 mph.

To find the exact speed, we'll substitute x = 56 into the original function s(x):

[tex]\[ s(56) = \frac{3600}{60 + 56} = \frac{3600}{116} \approx 30.86 \text{ mph} \][/tex]

So, the exact average speed when x = 56 seconds is approximately 30.86 mph.

Final answer:

To find the probability that the number of unspoiled eggs among the 6 selected is X, we can use the hypergeometric probability formula. This formula is used when the sample drawn is without replacement from a finite population.

Explanation:

To find the probability that the number of unspoiled eggs among the 6 selected is X, we can use the hypergeometric probability formula. This formula is used when the sample drawn is without replacement from a finite population. In this case, we have 18 total eggs in the carton, with 9 spoiled eggs. So the probability that X unspoiled eggs are selected out of the 6 can be calculated as:

P(X) = (C(X,6) * C(9,6)) / C(18,6)

Where C(n,r) represents the combination of n things taken r at a time.

Final answer:

The equation 20 x 1 = 20 demonstrates the Identity Property of Multiplication, which states that multiplying any number by one keeps its original value.

Explanation:

The property shown in the following equation 20 x 1 = 20 is the Identity Property of Multiplication. This property states that any number multiplied by one remains unchanged or that the number keeps its identity. The option B, Identify property of multiplication, is a typo, and it likely means to refer to the Identity Property of Multiplication. The options A, C, and D describe different properties that do not apply to this equation.

The Zero Property of Multiplication involves a multiplication where any number times zero is zero. The Negative One Property of Multiplication is not a standard mathematical property and seems to be a non-existent or misspelled option. The Identity Property of Division is not applicable as there is no division taking place in this equation.

divide the total spent by 5 to get what 1/5 is

37.60 / 5 = 7.52

 they spent $7.52 on other items

Answer:

58.3%  

Step-by-step explanation:

The percent decreased in the hours of television watched is 58.3%.

A percentage is a number or ratio that can be expressed as a fraction of 100. Also called per centum. one one-hundredth part; 1/100. percentage.

Given that, in 2002, the students watched an average of 12 hours of television per week. In 2012, the number of hours spent watching television decreased to 5 hours per week

We need to find the percent decrease in the hours of television watched,

Percent decreased = Difference in the initial and final quantity / initial quantity × 100

Percent decreased = 12-5 / 12 × 100 = 7/12 × 100

= 58.3%

Hence, the percent decreased in the hours of television watched is 58.3%

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5/2

Start by eliminating parentheses.

... 2n +4 +6 = -9 +8n +4

... 10 = -5 +6n . . . . subtract 2n

... 15 = 6n . . . . . . . add 5

... 15/6 = n = 5/2

_____

Check

(2·5/2 +4) +6 = -9 +4(2·5/2 +1)

5 +4 +6 = -9 +4(5 +1)

15 = -9 +24 . . . . . true, so the answer checks OK

Answer:

THE ANSWER IS 1

Step-by-step explanation:

A road trip with these parameters

The cost of gas is ...

... (2240 mi)/(28 mi/gal)·($3/gal) = $240

The cost of lodging is

... ($85/day)·floor(2240 mi/(650 mi/day)) = $85·3 = $255

Total cost of gas and lodging is $240 +255 = $495.

The cost for a 1/4 share is $495/4 = $123.75.

To calculate the second moment of area for a 4-inch diameter shaft about the x-x and yy axes, we use the formula I = π * d^4 / 64 and find that I = 4 * π in´ for both axes.

The student is asking for the calculation of the second moment of area, also known as the moment of inertia, for a shaft with a 4-inch diameter about both the x-x and yy axes.

The moment of inertia of a circular cross-section about its centroidal axis is calculated using the formula I = π * d^4 / 64, where d is the diameter of the shaft. In this case, the diameter d is given as 4 inches.

To calculate the second moment of area for the 4-inch diameter shaft, we substitute the diameter into the formula to get:

I = π * (4 in)^4 / 64 = π * 256 in´ / 64 = 4 * π in´.

So, the moment of inertia for both the x-x and yy axes would be the same and equal to 4 * π in´, since the shaft is symmetrical about these axes.

The post office sold 2000.

To find out how many 14-paisa stamps the post office sold to make Rs.280, we need to follow a step-by-step solution.

28000 paisas ÷ 14 paisas per stamp = 2000 stamps.