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Find how long it takes $1500 to double if it is invested at 7% interest compound semiannually. Use the formula A=P (1+r/n)^nt to solve the compound interest problem.


It will take approximately how many Years ?

Round to the nearest tenth as needed.

The classmate's claim is incorrect, as a parabola cannot pass through two points with the same x-coordinate but different y-values, making it impossible for a single quadratic function to pass through points (3,4), (5,-2), and (3,0).

The error in your classmate's assertion that he can write the equation of a quadratic function that passes through the points (3,4), (5,-2), and (3,0) lies in the fact that a quadratic function is a parabola, and no parabola can pass through two points that have the same x-coordinate but different y-values. In other words, any vertical line (like x=3) can intersect a parabola at most once because a quadratic function has only one y value for each x value. Since (3,4) and (3,0) both have the x-coordinate of 3 but different y-coordinates, they cannot both lie on the same parabola. The equation of a quadratic function is typically written as [tex]y = ax^2 + bx + c[/tex], where a, b, and c are constants. To pass through specific points, these constants must be determined such that the function satisfies the coordinates of the points. However, due to the reason explained, no set of constants will satisfy the condition for the mentioned points.

Answer:

75% of the planets have moons

Step-by-step explanation:

In order to calculate this you just have to do a simple rule of three, in which you will use 888 as the 100 percent and you want to discover what percentage of that does 666 represents:

[tex]\frac{888}{100} \frac{666}{x} \\x=\frac{666*100}{888}\\ x=75\\[/tex]

So you have that 666 is the 75% of 888, that means that 75% of the planets have moons.

The probability of correctly guessing the combination will be 1/7140.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

A lock has a disk with 36 numbers written around its edge. The combination of the lock is made up of three numbers.

The total number of the events will be

Total event = ³⁶C₃

Total event = 36! / [(36 - 3)! x 3!]

Total event = 7140

The favorable number of the event will be one.

Then the probability of correctly guessing the combination will be

P = 1 / 7140

The probability of correctly guessing the combination will be 1/7140.

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Final answer:

To find how fast the distance between two ships is changing, we calculate the distance they have covered, form a right triangle, and use the Pythagorean theorem and related rates to find that the distance is changing at approximately 8.94 km/h at 4:00 PM.

Explanation:

To determine how quickly the distance between ship A and ship B is changing, we can use the concept of related rates from calculus. At noon, the ships are 170 km apart. Ship A travels east (towards ship B) at 30 km/h, and ship B travels north at 25 km/h. By 4:00 PM, four hours have passed.

First, let's calculate the distance each ship has traveled after 4 hours. Ship A would have covered 30 km/h * 4h = 120 km eastward. Ship B would have traveled 25 km/h * 4h = 100 km northward.

Next, we need to calculate the distance between the two ships at 4:00 PM. Since ship A is moving east and ship B is moving north, they are traveling at right angles to each other. The distance between the two ships forms the hypotenuse of a right triangle, with the sides being the distances traveled by each ship. Using the Pythagorean theorem, the distance between the two ships at 4:00 PM (D) is:

² = (170 km - 120 km)² + (100 km)²

² = (50 km)² + (100 km)²

² = 2500 km² + 10000 km²

= √12500 km²

= 111.80 km (approx)

Finally, we have to find the rate at which this distance is changing. Let x be the east-west distance from ship B to ship A, and y be the northward distance ship B has covered. Taking the derivative of the Pythagorean relation we have, x² + y² = ², with respect to time (t) gives us:

2x(/) + 2y(/) = 2(/)

Given that dx/dt = -30 km/h (since it's decreasing as ship A sails east) and dy/dt = 25 km/h, we can solve for d/dt:

2*50*(-30) + 2*100*(25) = 2*111.80*(d/dt)

-3000 + 5000 = 223.60*(d/dt)

2000 = 223.60*(d/dt)

d/dt = 2000 / 223.60

d/dt = 8.94 km/h (approx)

Therefore, the distance between the ships is changing at approximately 8.94 km/h at 4:00 PM.

Final answer:

At an interest rate of 2%, below the equilibrium rate of 5%, sellers of interest-bearing financial assets would need to raise interest rates to find willing buyers and reach the equilibrium.

Explanation:

If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2%, sellers of interest-bearing financial assets would need to raise interest rates to find willing buyers. This situation outlines how the market responds when the interest rate is below the equilibrium level. If the interest rate is below equilibrium, there is an excess demand for financial capital; too many borrowers and not enough lenders at this low rate. To attract more lenders (sellers of financial assets), the interest rate would need to be increased. Conversely, when the interest rate is above the equilibrium, there is an excess supply, meaning there are more suppliers of loans than there are borrowers. Sellers in this scenario lower interest rates to attract more borrowers, bringing the market back to equilibrium.

This concept is parallel to the example where, at an interest rate of 21%, the supplied funds increase greatly while the demand falls sharply, leading to excess supply. Suppliers of financial capital, such as credit card companies, will then reduce their rates to encourage more borrowing, pushing the interest rate back toward the equilibrium. In the case of a government borrowing increase, if it leads to a higher demand for financial capital, this would cause the demand curve to shift to the right and result in a higher interest rate, potentially crowding out private investment.

Answer:

45

Step-by-step explanation:

We know that,

If we have the numbers of the form xyz.

This gives that, x is placed at the hundredth place, y is placed at the tens place and z is located at ones place.

Since, we need a number between 20 and 50 having both tens and ones place.

We can take any number from 20 to 50.

For e.g. Let us take 45.

In 45, 4 is placed at the tens place and 5 is placed at the ones place.

Hence, 45 is the number between 20 to 50 having both tens and ones place.

The cost to print 1200 copies is $52.00.

The given data tells us that 320 copies cost $43.20. Each set of 40 copies costs $0.40, so 320 copies are 8 sets (320/40). The variable cost for 320 copies is 8 × $0.40 = $3.20.

We can then determine the fixed setup cost by subtracting the variable cost from the total cost for 320 copies: $43.20 - $3.20 = $40.00.

The total cost C for printing x copies can be expressed as:

C = fixed setup cost + variable cost per set × (x/40)

So the total cost for 1200 copies is:

C = $40.00 + $0.40 × (1200/40)

Calculating this, we get:

C = $40.00 + $0.40 × 30 = $40.00 + $12.00 = $52.00

Therefore, the cost to print 1200 copies is $52.00.

Using the Empirical Rule, it is determined that 95% of students are likely to get a GRE score between 350 and 650, and 50% of students will get a score above 500.

According to the Empirical Rule (also known as the 68-95-99.7 Rule), about 95% of the values in a data set with a normal distribution will fall within two standard deviations of the mean. In this case, the mean GRE score is 500 and the standard deviation is 75. Using this rule, we can determine that 95% of the students would likely score between 500 - (2 imes 75) and 500 + (2 imes 75), equating to scores between 350 and 650.

Regarding the percentage of students that will get a score above 500, the distribution is symmetric around the mean in a normal distribution. Since the mean is 500, 50% of the values will lie above the mean and 50% will lie below. Therefore, 50% of students are expected to score above 500.

Answer with explanation:

Number of Envelopes possessed by the person = 6

Probability of selecting an Envelope is equal to [tex]/frac{1}{6}[/tex].

It is given that,three envelopes contains $ 533 check and another 3 Envelope contain $ 1039 check.We can consider that any of three checks contain $ 533 and another three $ 1089.

Expectation

[tex]E(x)=x_{1}p_{1}+x_{2}p_{2}+x_{3}p_{3}+x_{4}p_{4}+x_{5}p_{5}+x_{6}p_{6}\\\\\frac{1}{6} \times [533+533+533+1039+1039+1039]\\\\=\frac{1}{6} \times [4716]\\\\=786[\tex]

E(x)=786          

The lengths of the three wire pieces are 20 cm for the first piece, 60 cm for the second piece, and 120 cm for the third piece.

A wire that is 200 cm long is cut into three pieces.

We are told that the second piece is 3 times as long as the first piece and the third piece is 2 times as long as the second piece.

Let's denote the first piece's length as x centimeters.

According to the problem, the second piece will then be 3x centimeters long, and the third piece will be 2 * 3x = 6x centimeters long.

To find the length of each piece, we need to set up the following equation based on the total length of the wire:

x + 3x + 6x = 200

Combining terms, we have:

10x = 200

Dividing both sides by 10, we find:

x = 20

Therefore, the first piece is 20 cm long, the second piece is 3 * 20 cm = 60 cm long, and the third piece is 6 * 20 cm = 120 cm long.

56.69 - 0.145(56.69)

= 56.69 - 8.22

= 48.47

the formula for discount price

Subtract the final price from the original price. Divide this number by the original price. Finally, multiply the result by 100. You've obtained a discount in percentages.

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The eighteenths of 2/3 is 12/18.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

let,

2/3 = n/18

What is the GCF of 3 and 18

3: 1,3

18: 1,2,3,6,9,18

GCF-3

Therefore, 2/3 = 12/18

because 3 × 6= 18

what you do to the denominator you have to do the numerator

so 2 × 6= 12.

hence, eighteenths of 2/3 is 12/18.

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The exponential equation that models the number of bacteria in hours is N = 8000 * (1 + 0.125)^t. The doubling time of the bacteria is 5.55 hours.

To find an exponential equation that models the number of bacteria in hours, we can use the formula: N = N0 * (1 + r)^t.

Where:

Plugging in the values, we have:

9000 = 8000 * (1 + r)^1

Dividing both sides by 8000, we get:

1.125 = 1 + r

Subtracting 1 from both sides, we find:

0.125 = r

Therefore, the exponential equation that models the number of bacteria in hours is: N = 8000 * (1 + 0.125)^t.

To find the doubling time of the bacteria, we can use the formula: t = log(2)/log(1 + r).

Plugging in the value of r (0.125), we have:

t = log(2)/log(1 + 0.125)

Using a calculator, we find that t is approximately 5.5452 hours. Rounded to the nearest 0.01 hours, the doubling time of the bacteria is 5.55 hours.

Answer:

f(x)=45x

Step-by-step explanation:

if the home is 495 miles away, 11 hours would take to drive home.

f(11)=45X11=495