NUMBER 4 PLEASE THIS IS URGENT

The amount in the account after 20 years is $49530.32.

What is continuous compounding?

There is no cap on how frequently interest can compound thanks to continuous compounding. A balance can compound continuously an infinite number of times, which means interest is earned on it constantly.

Given:

Lira will not make any further investments in the withdrawals from the account until it is worth $10000.

Suppose that the interest rate for the account is 8.0% , compounded continuously.

We have to find the amount in the account after 20 years.

Consider, the compounded continuously formula

\(P(t)= P_0e^r^t\)

Where

P(t) = Value at time t.

\(P_0\) = Original principle sum = $10,000

r = Interest rate = 8.0% = 0.08

t = time in years = 20

Plug the values in the above formula

\(P(t) = 10000e^0^.^0^8^*^2^0\\P(t) = 49530.32\)

Hence, the amount in the account after 20 years is $49530.32.

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There is no value of (m,n) such that f(m,n) = k, which implies that k is not in the range of f. We have shown that f is not surjective.

To prove that the function f(m,n) = 2^m * 3^n is injective, we need to show that if f(m1,n1) = f(m2,n2), then (m1,n1) = (m2,n2).

Suppose that f(m1,n1) = f(m2,n2). Then we have:

2^m1 * 3^n1 = 2^m2 * 3^n2

Dividing both sides by 2^m1 * 3^n1 (which is nonzero), we get:

(2^m2 / 2^m1) * (3^n2 / 3^n1) = 1

Simplifying, we get:

2^(m2-m1) * 3^(n2-n1) = 1

Since 2 and 3 are both prime numbers, this implies that m2-m1 = 0 and n2-n1 = 0, which in turn implies that m1 = m2 and n1 = n2. Therefore, we have shown that f is injective.

To prove that f is not surjective, we need to find a natural number k that is not in the range of f. Let's suppose that k is in the range of f, so there exist m and n such that:

k = 2^m * 3^n

Without loss of generality, we can assume that m <= n (otherwise, we can just swap m and n). Then, we have:

2^m * 3^n >= 2^m * 3^m = (2/3)^m * 3^(2m)

We know that (2/3)^m approaches 0 as m approaches infinity, so for any large enough value of m, we have:

2^m * 3^n > k

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Answer:

$0.3

Step-by-step explanation:

$1.11 divided by 4 notebooks. Each notebook costs $0.3.

Answer:

119

Step-by-step explanation:

First find c. It is a straight line so 180. 180-112=68. 68+51=119. 180-119=61. 180-61=119.

Bonnie bought approximately 4 bags of chips and 14 cans of pop for a total cost of $17.50.

Let's assume the number of bags of chips Bonnie bought is x.

According to the given information, Bonnie bought ten more cans of pop than bags of chips. Therefore, the number of cans of pop Bonnie bought is x + 10.

We are also given that Bonnie spent $17.50 on these purchases.

Now, let's calculate the total cost of the bags of chips and cans of pop:

Cost of x bags of chips = x dollars

Cost of (x + 10) cans of pop = (x + 10) dollars

The total cost is the sum of the cost of bags of chips and cans of pop:

Total cost = x + (x + 10) = 2x + 10

According to the given information, the total cost is $17.50:

2x + 10 = 17.50

Subtracting 10 from both sides of the equation:

2x = 17.50 - 10

2x = 7.50

Dividing both sides by 2:

x = 7.50 / 2

x = 3.75

Therefore, Bonnie bought 3.75 bags of chips (which we'll assume is 4 bags since we can't have a fraction of a bag) and (3.75 + 10) = 13.75 (which we'll assume is 14 cans since we can't have a fraction of a can) cans of pop.

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The 2 decimal places for beta, 4 decimal places for firm-specific

variance, and 3 decimal places for covariance.

To calculate the beta of your portfolio, you need to determine the

weighted average beta of the individual assets in your portfolio.

The beta of a security measures its sensitivity to changes in the market.

By multiplying the weight of each asset by its beta and summing these

values, you can calculate the portfolio beta.

The formula for portfolio beta is:

Portfolio Beta = (Weight of Asset A * Beta of Asset A) + (Weight of Asset B

* Beta of Asset B) + ...

To calculate the firm-specific variance of your portfolio, you need to

subtract the market variance from the portfolio variance.

Firm-specific variance represents the risk that is specific to the individual

assets in your portfolio.

The formula for firm-specific variance is:

Firm-specific variance = Portfolio variance - Market variance

Lastly, to calculate the covariance between the portfolio and the market

index, you need to multiply the weight of each asset by its beta and sum

these products.

The formula for covariance is:

Covariance = (Weight of Asset A * Beta of Asset A) + (Weight of Asset B *

Beta of Asset B) + ...

Remember to not round your intermediate calculations, but round your

final answers to 2 decimal places for beta, 4 decimal places for firm

specific variance, and 3 decimal places for covariance.

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36,183.7 miles

To write in scientific notation, put the first digit and the decimal point after it.

Then multiply by 10 raised to the number of places that the decimal point was moved to the left.

3.61837 x 10^4

Answer:

3/4

Step-by-step explanation: i took test. pls give brainliest.

Answer:

Step 1, she reversed the values of x. It should have been 4 - (-2) not -2 - 4.

Step-by-step explanation:

Fern made a mistake in writing equation [1] where she wrote  {-2 - 4} in the denominator in place of {4 -(-2)}.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept

Given is Fern who is finding the slope of the line that passes through (-2, 8) and (4, 6).

In order to find the slope of the line, the following formula is used -

m = (y₂ - y₁)/(x₂ - x₁)

So, the slope of the line passing through the given points can be calculated using the following steps -

m = (6 - 8)/{4 -(-2)}                       ..[1]

m = -2/6                              

m = -1/3

Fern made mistake in writing equation [1]. She should have written

{4 -(-2)} in the denominator in place of {-2 - 4}

Therefore, fern made a mistake in writing equation [1] where she wrote  {-2 - 4} in the denominator in place of {4 -(-2)}.

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Answer:

432

Step-by-step explanation:

Answer:

432

Step-by-step explanation:

\(\frac{(14-3^{2}+1 )^{2} }{1/3.\frac{1}{4} }\)

Now, at first, we solve the numerator:

\((14-3^{2}+1 )^{2}\)

=\((14-9+1)^{2}\)

=\((15-9)^{2}\)

= \(6^{2}\)

= 36

Now let's solve the denominator:

1 ÷ 3 ×  \(\frac{1}{4}\)

=\(\frac{1}{3} . \frac{1}{4}\)

=\(\frac{1}{12}\)

Hence,

\(\frac{(14-3^{2}+1 )^{2} }{1/3.\frac{1}{4} }\)

=  \(\frac{36}{1/12}\)

= 36 x 12

= 432

Answer:

150°

Step-by-step explanation:

every line is equal to 180°. To find an angle, like this one, you have to subtract 30° from 180°. Therefor the answer is 150°.

If you need a further explanation just let me know

Given:

The equation of a circle is:

\((x-3)^2+y^2=32\)

To find:

Center and the circumference of the circle.

Solution:

The standard form of a circle is:

\((x-h)^2+(y-k)^2=r^2\)         ...(i)

Where, (h,k) is center and r is the radius.

We have,

\((x-3)^2+y^2=32\)           ...(ii)

On comparing (i) and (ii), we get

\(h=3,y=0,r=\sqrt{32}\)

So, the center of the circle is (3,0) and the radius of the circle is \(\sqrt{32}\).

Now, the circumference of the circle is:

\(C=2\pi r\)

\(C=2(3.14)(\sqrt{32})\)

\(C=35.525045\)

\(C\approx 35.5\)

Therefore, the circumference of the circle is about 35.5 units.

Answer:

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Answer:

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360, making a total of 24 divisors. 360 is a highly composite number.

Step-by-step explanation:

23 × 32 × 5

Answer:

What do you mean? I can help i just need nore info

The equation that she could use to determine x, the number of gigabytes of data Shaniece can use while staying within her budget is 48 + 3x = 61.20.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, Shaniece pays a flat cost of $48 per month and $3 per gigabyte and she wants to keep her bill at $61.20 per month.

Let the number of gigabytes be represented by x

This will be illustrated as:

48 + (3 × x) = 61.20

48 + 3x = 61.20

This represents the equation.

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Answer:

Length of fencing: 4, 6, 7, 9, 10

Cost: 36, 54, 63, 81, 90

Step-by-step explanation: I hope this gave you your answer!!

Therefore, it can be seen that the CIA profit/loss is $111,878.

Borrow $4 million in USD at the 4-month interest rate of 2.9%.

Convert the USD to CAD at the spot rate of 1.278 CAD/USD.

Invest the CAD in a 4-month Canadian deposit account at the 4.7% interest rate.

Sell the CAD forward at the 4-month forward rate of 1.2902 CAD/USD.

After 4 months, repay the USD loan and settle the forward contract.

The profit/loss from the CIA strategy is calculated as follows:

Profit/loss = (Interest earned on CAD deposit - Interest paid on USD loan) - (Forward rate - Spot rate)

In this case, the profit/loss is calculated as follows:

Profit/loss = (0.047 * 4,000,000 - 0.029 * 4,000,000) - (1.2902 - 1.278)

= $112,000 - $0.12

= $111,878

Therefore, the CIA profit/loss is $111,878.

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False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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a. The proportion of genetic abnormalities in recent years is greater than the proportion believed in the 1990s (p > 0.30). b. The number of successes (136) and the number of failures 265 should be at least 10. In this case, both criteria are satisfied. c. The z is 2.048. d. If the p-value is larger than the significance level, it would suggest that there is not enough evidence to reject the null hypothesis and conclude that the proportion has not significantly changed.

a. The hypotheses to test if the proportion of genetic abnormalities has increased in recent years can be stated as follows:

Null hypothesis (H₀): The proportion of genetic abnormalities in recent years is equal to or less than the proportion believed in the 1990s (p ≤ 0.30).

Alternative hypothesis (Ha): The proportion of genetic abnormalities in recent years is greater than the proportion believed in the 1990s (p > 0.30).

b. To conduct the hypothesis test, we need to verify if the conditions for performing the test are met. The conditions are as follows:

Random Sample: The study states that the 401 children were randomly selected, so this condition is met.

Independence: The sample should consist of independent observations. If the children were selected randomly and their genetic abnormalities are unrelated to each other, then the independence condition is likely satisfied.

Large Sample Size: For hypothesis tests involving proportions, it is recommended to have a large enough sample size to ensure the sampling distribution is approximately normal. There is no specific threshold, but as a guideline, both the number of successes (136) and the number of failures (401 - 136 = 265) should be at least 10. In this case, both criteria are satisfied.

c. To find the p-value, we need to perform a hypothesis test based on the given data. Since the sample size is large, we can use the normal approximation for the binomial distribution. We calculate the test statistic, which is the z-score for proportions, and then find the p-value.

The formula for the z-score for proportions is:

z = (\(\hat p\) - p₀) / √((p₀ * (1 - p₀)) / n)

where \(\hat p\) is the sample proportion, p₀ is the proportion under the null hypothesis, and n is the sample size.

In this case, \(\hat p\) (sample proportion) = 136 / 401 = 0.339, p₀ (proportion under the null hypothesis) = 0.30, and n (sample size) = 401.

Calculating the z-score:

z = (0.339 - 0.30) / √((0.30 * (1 - 0.30)) / 401)

z = 2.048

To find the p-value associated with this z-score, we look up the area to the right of the z-score in the standard normal distribution table or use statistical software.

d. The p-value represents the probability of observing a test statistic as extreme as the one calculated (or more extreme) assuming the null hypothesis is true. In this case, since we are testing if the proportion of genetic abnormalities has increased, the p-value is the probability of observing a sample proportion as large as or larger than 0.339, given that the true proportion is equal to or less than 0.30.

Without the actual p-value, it is not possible to provide a specific interpretation. However, if the p-value is smaller than the significance level (commonly chosen as 0.05), it would indicate that there is strong evidence to reject the null hypothesis and conclude that the proportion of genetic abnormalities has increased in recent years.

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15 friends pay £6 each for hall practice with inverse proportion

Friends  = 5

Each pays = £18

Total payments = 5*18

                          = 90

Friends = 15

Each pays = 90/15

                 = 6

Hence, 15 friends pay £6 each for hall practice with inverse proportion.

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(a) Probability that a randomly selected is 9.68%; (b) 29.12% will receive the tax break; (c) Minimum and the maximum starting salaries are 35,679.71 and 4,320.29. (d) 6.3% of the total number of students.

a) P(X>30,400) = P(Z>(30,400-20,000)/8,000)

                          = 1-P(Z<1.3)

                          = 0.0968

                         = 9.68%

b) P(X<15600) = P(Z<(15600-20000)/8000)

                        = 29.12%

c) Maximum of the starting salaries of the middle 95% is

                     (x - 20,000)/8,000 = 1,96

                                                  x  = 35,679.71

Minimum of the starting salaries of the middle 95% is

                      (x - 20,000)/8,000 = -1,96

                                                   x = 4,320.29

d) P(X>32,240) = 1-P(Z<(32,240-20,000)/8,000)

                         = 0.063

Therefore, the 189 represents 6.3% of the total number of students, means that the total number is 3,000.

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For the first question, we need to use the formula for average velocity, which is: average velocity = (change in distance)/(change in time)In this case, the distance is given by the function h(t), and the interval we are interested in is from t = 2 seconds to t = 5 seconds. So we need to calculate:

average velocity = (h(5) - h(2))/(5 - 2)

To find h(5) and h(2), we need to use the function that represents the height of the object. Let's call this function h(t). We don't have the actual function, but we know that it represents the height of the object (in feet) for time t seconds. So we can use any function that satisfies this condition. Let's use:

h(t) = 10t - 5t^2

Now we can find h(5) and h(2):

h(5) = 10(5) - 5(5^2) = -65

h(2) = 10(2) - 5(2^2) = 10

Substituting these values into the formula for average velocity, we get:

average velocity = (-65 - 10)/(5 - 2) = -25 ft/sec

So the average velocity over the interval (2,5) is -25 ft/sec (rounded to four decimal places).

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Answer:

I think it's A ,Forgive me if its wrong its not a 100%.

Step-by-step explanation:

But if it is correct, im glad to be of service

To determine the cost of the flip-flops before tax, we need to subtract the tax amount from the total cost including tax. The tax rate is given as 8%. The explanation below will provide the solution.

Let's assume the retail price of the flip-flops before tax is x.

We know that the tax rate is 8%, which means the tax amount is 8% of the retail price, or 0.08x.

The total cost including tax is given as $17.27. This can be expressed as:

x + 0.08x = $17.27

Combining like terms, we have:

1.08x = $17.27

To find the value of x, we divide both sides of the equation by 1.08:

x = $17.27 / 1.08 ≈ $16.01

Therefore, the cost of the flip-flops before tax (the retail price) is approximately $16.01.

In summary, the retail price of the flip-flops before tax is approximately $16.01.

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The range is the set between all of the possible output values, which always shown on y-axis by identify any given domain and then finding the range of any functions is by taking graphs into consideration.

To discover the area and variety, we without a doubt remedy the equation y = f(x) to decide the values of the unbiased variable x and gain the area. To calculate the variety of the feature, we without a doubt explicit x as x=g(y) after which discover the area of g(y).

Because the area refers back to the set of viable enter values, the area of a graph includes all of the enter values proven at the x-axis. The simplest approach of locating the variety of a feature, say y = f(x), is to explicit x as g(y) and pick out the area set for g(y). This might be the variety for the given feature f(x).

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1) If the couple must sit together, there are 240 ways that they can be seated.

2) If the couple must not be together, there are 720 ways that they can be seated.

1) If the couple must sit together, we can think of them as one unit. So, there are 5 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.

The couple can be arranged in two different ways within their unit. So, the total number of ways they can be seated is: 5! × 2 = 240.

2) If the couple must not sit together, we can think of them as separate units. So, there are 6 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.

The couple cannot be seated next to each other, so there are 3 possible units where they cannot be seated next to each other. Once we have chosen one of these units for the starting point, there are 2 ways to arrange the couple within their unit. Therefore, the total number of ways they can be seated is: 5! × 2 × 3 = 720.

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The value of arctan(-1) as a simplified fraction is -π/4.

The arctan function, or inverse tangent function, returns the angle whose tangent is a given number. In this case, we want to evaluate arctan(-1).

The tangent function represents the ratio of the length of the side opposite an angle to the length of the adjacent side in a right triangle. The tangent of an angle is negative when the angle is in the second or fourth quadrant of the unit circle.

For arctan(-1), we are looking for the angle whose tangent is -1. In the unit circle, the tangent of -π/4 (negative pi/4) is -1.

Therefore, the value of arctan(-1) can be expressed as -π/4, which represents an angle of -45 degrees or -π/4 radians.

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Parts (a) and (b) are functions since they pass the vertical line test.

Part (c) is not a function. It fails the vertical line test since it is possible to pass a single vertical line through more than one point on the curve. In other words, some x input leads to more than one y output. A function can only have one output for any given input.

--------------------

The domain of part (a) is the set of all real numbers. We can plug in any value for x. The domain in interval notation is (-infinity, infinity) as this describes the entire real number line. The domain is the set of all possible inputs.

The range for part (a) is the set of y values such that \(1 \le y \le 3\) because the lowest points are when y = 1 and the highest points are when y = 3. The range is the set of all possible outputs. The range in interval notation is [1, 3]. Note the use of square brackets to include the endpoint.

----------------------

The domain for part (b) is also the set of real numbers. The reasoning is the same as part (a).

The range of part (b) is \(y \ge 0\) since y = 0 is the lowest y possible output, and there is no largest output y value. The range in interval notation is [0, infinity).

----------------------

The domain of part (c) is different from the others. On this graph, the left-most point is when x = -2, so the domain is the set of real x values such that \(x \ge -2\) which translates to [-2, infinity) in interval notation.

The range of part (c) is the set of all real numbers. Any y value is a possible output because the parabola stretches upward and downward forever.