Urgent!!!
lyra is canoeing with her scout troop. she needs to paddle north across the river to catch up to her troop where they
are having a picnic lunch on the opposite shore. the river's current travels east at 3 ft per second, and she can paddle
at 6ft per second.
by modeling this situation with vectors, a right triangle can be created.
1. lyra attempts to paddle directly across the river, perpendicular to
the current. what will lyra's speed be as she travels? answer in
feet per second
2. what direction does lyra travel? answer in degrees north of east.

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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Based on the given data, the professors' grading procedures have different variances. To determine if the difference is statistically significant at the 2% level of significance, we can use a two-sample F-test. The F-statistic is calculated by dividing the larger variance by the smaller variance. In this case, the F-statistic is 2.97. Using a critical value of 5.05, we can reject the null hypothesis that the variances are equal. Thus, the decision is that there is a statistically significant difference in the variance of the professors' grading procedures.

In statistics, variance is a measure of the spread of a distribution. When comparing two variances, we can use a two-sample F-test to determine if they are statistically different. The F-statistic is calculated by dividing the larger variance by the smaller variance. If the calculated F-value is greater than the critical value, we reject the null hypothesis that the variances are equal.

In this case, the professors' grading procedures have different variances, with Professor 1 having a larger variance than Professor 2. Using a two-sample F-test, we determined that the difference in variances is statistically significant at the 2% level of significance. This means that there is strong evidence to suggest that the professors' grading procedures differ in their spread of grades.

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Answer:

it equals .85 hope this helps!

Step-by-step explanation:

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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The legal description of a parcel in a subdivision that has been recorded with lot and block numbers on a plat of survey is the written description of the boundaries and location of the property, including the lot and block numbers as identified on the plat of survey. This legal description is used to define and identify the property for legal purposes such as real estate transactions, property taxes, and land use regulations.

The legal description of a parcel in a subdivision that has been recorded with lot and block numbers on a plat of survey is known as a "Lot and Block" description. This description typically includes the subdivision name, the specific lot number, and the block number within that subdivision. This information is used to accurately identify and locate the property within the larger plat of survey, ensuring proper documentation and reference for legal and real estate purposes.

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Answer:60 3/4

Step-by-step explanation: 4 1/2 times 2 1/4 = 10 1/8

4 1/2 times 3 = 13 1/2

3 times 2 1/4 6 3/4

Answer: 2π x radius

Step-by-step explanation:

The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line then the length of that line will be the circle's circumference.

The value of function f(x) for derivative f'(x) = (x + 1)/(1 + x²) by integrating is 22.541.

To find the function f(x), we need to integrate the given derivative f'(x).

∫(x + 1)/(1 + x²) dx = ½ ln(1 + x²) + arctan(x) + C

where C is the constant of integration.

Now we use the given initial condition f(1) = 0 to find the value of C.

0 = ½ ln(1 + 1²) + arctan(1) + C

C = -(π/4 + ½ ln 2)

Thus, the function f(x) is:

f(x) = ½ ln(1 + x²) + arctan(x) - π/4 - ½ ln 2

To find f(0), we substitute x = 0:

f(0) = ½ ln(1 + 0²) + arctan(0) - π/4 - ½ ln 2 = -π/4 - ½ ln 2 ≈ -1.459

Therefore, f(0) is approximately -1.459 + 1 + 22 = 22.541.

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Answer:

y=1x-5

Step-by-step explanation:

Answer:

The equation for line one is y = -2x - 5

Answer:

Brainliest this first then I will help you

Step-by-step explanation:

Answer:

ok

Step-by-step explanation:shheshh

Answer:

His car would be worth $15,502.24

Step-by-step explanation:

20% of 17,500 is 350. 350 x 6 = 2,100. 17,500 - 2,100 = 15,400. But that is not an answer choice so be go to  the closest number which is $15,502.24

90° counterclockwise rotation

Answer:

c

Step-by-step explanation:

The rate of speed of the slower bus is 68 km/h the faster bus travels 7 km/h faster when they meet in 2 hours, and the total distance traveled by each bus is 136 km.

Let's assume the rate of the slower bus is x km/h.

The rate of the faster bus is then (x + 7) km/h, as it is traveling 7 km/h faster.

When they travel toward each other, the total distance covered is the sum of their individual distances, which is 286 km.

We know that distance = rate × time.

For the slower bus, the distance it travels in 2 hours is 2x km.

For the faster bus, the distance it travels in 2 hours is 2(x + 7) km.

Since they meet, the sum of their distances should be equal to the total distance: 2x + 2(x + 7) = 286.

Simplifying the equation: 2x + 2x + 14 = 286.

Combining like terms: 4x + 14 = 286.

Subtracting 14 from both sides: 4x = 272.

Dividing both sides by 4: x = 68.

Therefore, the rate of the slower bus is 68 km/h.

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At the end of the analyzed period this plot of land will have the value as given by: Option D: 420,506.24

Deprecation, also called devaluation, is the decrement in price of an asset. Appreciation is opposite of deprecation. This indicates increment in the price of the considered thing.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

It is given that:

Now, consider appreciation of an amount A by P%.

Then, we have:

Increased price = Initial price + P% of initial price

Increased price = \(A + \dfrac{A}{100} \times P = A \times \left(1 + \dfrac{P}{100} \right)\)

Similarly, depreciated price by P% of an amount A is:

Decreased price = \(A - \dfrac{A}{100} \times P = A \times \left(1 - \dfrac{P}{100} \right)\)

We've got: A = 350,000

After 1st year, which had 12% appreciation, we get:

\(A_1 =A(1 + 12/100) = A(1.12)\\\)
After 2nd year, 10% appreciation we get:

\(A_2 =A_1(1 + 10/100) = A_1(1.1) = A(1.12)(1.1)\\\)

After 3rd year, which had 8% devaluation effect on the price, we get:

\(A_3 = A_2(1 - 8/100) = A_2(1-0.08) = A_2(0.92) = A(1.12)(1.1)(0.92)\)

After 4th year,  which had 6% appreciation effect on the price, we get:\(A_4 = A_3(1 + 6/100) = A_4(1+0.06) = A_3(1.06) = A(1.12)(1.1)(0.92)(1.06)\)

Thus, the final effect on A is:

\(A \rightarrow A(1.12)(1.1)(0.92)(1.06) = A(1.2014464)\\\$350,000 \rightarrow 350000(1.2014464) = 420506.24\: \rm dollars\)

Thus, at the end of the analyzed period this plot of land will have the value as given by: Option D: 420,506.24

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The projected misstatement of this sample would be $50,000, calculated as follows: ($4,000 / $5,000) x $10,000.

In a probability-proportional-to-size sample, each item's chance of being selected is proportional to its recorded amount, so larger accounts have a higher probability of being selected. In this case, the auditor selected an account with a recorded amount of $5,000, but found that it had an audited amount of $4,000.

To project the misstatement of this sample, the auditor needs to estimate the total misstatement in the population by multiplying the audited amount by the inverse of the sampling fraction, which is the sampling interval divided by the recorded amount of the selected item. So, the projected misstatement is ($4,000 / $5,000) x $10,000 = $8,000 x 6.25 = $50,000. This means that the auditor estimates the total misstatement in the population to be approximately $50,000 based on this sample.

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Coating the seed typically improves seed quality and germination rates, so the same seeding rate can be maintained even with coated seed.

To convert mass-based seeding rates to population-based establishment rates, we need to consider the area conversion factors provided:

a. Given a seeding rate of 60 lbs/acre for cereal rye, we can convert it to seeds per square foot by using the conversion factor of 1 acre = 43,560 square feet.

b. Given a seeding rate of 15 kg/ha for crimson clover, we can convert it to seeds per square meter using the conversion factor of 1 hectare = 10,000 square meters.

To convert population-based seeding rates to mass-based seeding rates, we can use the given area conversion factors:

a. Given a seeding rate of 30 plants/square foot for oats, we can convert it to pounds of seed per acre.

b. Given a seeding rate of 20 plants/square meter for hairy vetch, we can convert it to kilograms of seed per hectare.

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(a)To solve the system of equations, x^2 - y^2 = 16 and x^2 - y = 7, we can use substitution or elimination method to find the values of x and y.

(b) To graph the solution set of the system of inequalities, x^2 - y^2 > 7 and x^2 - y < 0, we need to plot the boundaries and shade the appropriate regions based on the given inequalities.

(a)Let's use the substitution method to solve the system of equations:

From the second equation, we can rewrite it as x^2 = y + 7.

Substituting this value of x^2 in the first equation, we get (y + 7) - y^2 = 16.

Rearranging the equation, we have -y^2 + y + 7 - 16 = 0.

Simplifying further, we get -y^2 + y - 9 = 0.

Now, we can solve this quadratic equation for y by factoring or using the quadratic formula.

After finding the values of y, we can substitute them back into the second equation to find the corresponding values of x.

(b)To graph the solution set, we first graph the boundaries of the inequalities. For x^2 - y^2 > 7, we draw the curve of the equation x^2 - y^2 = 7, which represents a hyperbola. For x^2 - y < 0, we graph the curve of the equation x^2 - y = 0, which represents a parabola opening upwards.

Next, we need to determine which regions satisfy the given inequalities. For x^2 - y^2 > 7, the shaded region lies outside the hyperbola. For x^2 - y < 0, the shaded region lies below the parabola.

By combining the shaded regions of both inequalities, we find the solution set of the system of inequalities. It includes the regions outside the hyperbola and below the parabola. We label the corners of the shaded region to indicate the solution set accurately.

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Answer:

Step-by-step explanation:

To solve this problem, we need to use exponential growth formula, which is:

P = P0 * e^(rt)

where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the time in years.

We can use the given data to find the annual growth rate r:

r = ln(P/P0) / t

where ln is the natural logarithm.

Using the population data from 1900 and 2000, we get:

r = ln(8.86/5.14) / 100 ≈ 0.0198

So the annual growth rate is approximately 0.0198, or 1.98%.

Now, we need to find the initial population P0 when King Karl XII died in 1718. Let's call this population X.

We know that the population has been growing exponentially since then, so we can use the formula above to relate the population in 1718 to the population in 1900:

X * e^(0.0198 * 182) = 5.14 million

where 182 is the number of years between 1718 and 1900.

Solving for X, we get:

X = 5.14 million / e^(0.0198 * 182) ≈ 0.14 million

Therefore, the population of Sweden when King Karl XII died in 1718 was approximately 0.14 million people.

Answer:

x - y = 4

Explanation:

I hope it's correct

answer:

x - y = 4

explanation:

\(\rightarrow \boxed{\frac{3^x}{3^y} = 81}\)

\(\rightarrow \boxed{3^{x-y} = 81}}\)

\(\rightarrow \boxed{3^{x-y} = 3^4}}\)

\(\rightarrow \boxed{x-y = 4}\)

Answer:

206.67 dollars

Step-by-step explanation:

Answer:

x= -5

Step-by-step explanation:

Answer:

1711568

Step-by-step explanation:

184*9302 = 1711568

Use a calculator to check your work

By solving some linear equations we can see that:

The first missing number is 5.

The second missing number is 9

Here we have a decomposition of the number 360, this means that if we define x as the missing number, then we must have that:

2*x*2*2*3*3 = 360

So we just need to solve this linear equation.

x*72 = 360

x = 360/72 = 5

x = 5

The missing number in the tree is 5.

Similarly, for the second tree if the missing number is y, we should have:

2*5*4*y = 360

40*y = 360

y = 360/40 = 9

The missing number is 9.

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Answer:

1) (x + 12)²+(y+6)²= 28

comparing above equation with(x-h)²+(y-k)²=r²

we get

r=√28

h=-12

k=-6

;.centre=(-12,-6)

radius =√28 units

2) x²+(y+7)²=15

comparing above equation with(x-h)²+(y-k)²=r²

we get

r=√15

h=0

k=-7

;.centre=(0,-7)

radius=√15 units

3) (x + 4)²+(y - 1)² = 4

comparing above equation with(x-h)²+(y-k)²=r²

we get

r=√4=2units

h=-4

k=1

;.centre=(-4,1)

radius=√2units

4) (x+3)²+(y-1)²= 8

comparing above equation with(x-h)²+(y-k)²=r²

we get

r=√8=2√2units

h=-3

k=1

;.centre=(-3,1)

radius=2√2units

Answer:  B. Acting as a lender of last resort.

A bank run occurs when a large number of depositors withdraw their funds from a bank, which can lead to a bank's insolvency.

A central bank like the Federal Reserve can help banks survive a bank run by acting as a lender of last resort.

This means that the central bank will provide funds to the bank in the form of loans or other financial assistance to ensure that it has enough cash on hand to meet the demands of depositors who are withdrawing their funds.

By doing so, the central bank can prevent the bank from going bankrupt and restore confidence in the banking system.

Other measures such as increasing the required reserve ratio or raising the discount rate may also be used to control the money supply and stabilize the economy, but they may not directly address the issue of a bank run.

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Answer:

I wish I've known, but try using Symbo-Lab or Math-Way. They help a lot.

Step-by-step explanation:

Answer:

229

Step-by-step explanation:

363 -892=229

229+363=892