How many possible ways are there to pick 5 basketball players out of a 25 player team?

Wonderful quote, have a nice day!

Answer:

nicee

Step-by-step explanation:

the equation of the horizontal line passing through (-3, 4) is y = 4.

The equation of a horizontal line is of the form y = c, where c represents the y-coordinate of any point on the line. In this case, we are given that the line passes through the point (-3, 4). Since the line is horizontal, the y-coordinate remains constant for all points on the line.

Therefore, the equation of the horizontal line passing through (-3, 4) is y = 4. This means that no matter what x-value we choose, the y-value will always be 4.

In other words, all the points on this line will have a y-coordinate of 4.

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Complete question is below

Write the equation of the horizontal line that passes through (-3, 4).

The equation for the horizontal line that passes through a given point is y = b.

A horizontal line is a straight line that is parallel to the x-axis. The equation of a horizontal line is of the form y = c, where c is a constant. Since the line is horizontal, the value of y remains constant for all values of x. Therefore, the equation of a horizontal line passing through a given point (a, b) is y = b.

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The solution that can be eliminated is (a) the solution –0.2 s can be eliminated because time cannot be a negative value.

The equation is given as:

h(t)) = -16t^2 + 40t + 7

From the question

When h(t) = 0, the values of t are

t = -0.2 and t = 2.7

The t in the function h(t) represents time

As a general rule, time cannot be negative.

This means that the solution t = -0.2 can be eliminated

Hence, the solution that can be eliminated is (a) the solution –0.2 s can be eliminated because time cannot be a negative value.

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\(Ainsley \: walked \: in \: \frac{1}{3} \: \: of \: a \: day \ \: = \frac{3}{5} mile\)

\( = \frac{1}{3} \times 24 = \frac{3}{5} \)

\(8 \: hours = \frac{3}{5} \: miles\)

\(Sarah \: walked \: in \: \frac{2}{6} of \: a \: day \: = \frac{5}{8} miles\)

\( \frac{2}{6} \times 24 = \frac{5}{8} \)

\(8 \: hours \: = \frac{5}{8} \: miles\)

Let us see who walked more :

\(Ainsley \: walked \: = \frac{3 \times 8}{40} \)

\( = \frac{24}{40} \: miles\)

\(Sarah \: walked \: = \frac{5 \times 5}{40} \)

\( = \frac{25}{40} \: miles\)

\( \frac{24}{40} < \frac{25}{40} \)

Sarah walked farther than Ainsley .

\( \frac{25}{40} - \frac{24}{40} = \frac{1}{40} \: miles\)

∴ Sarah walked farther than Ainsley by 1/40 miles .

A minutes to decimal chart is a table that shows the equivalent decimal representation of minutes. It is commonly used in various fields, such as finance and payroll, to calculate the number of hours worked or the amount of pay earned.

Here's a sample minutes to decimal chart:

Minutes   Decimal

0        0.0

15         0.25

30          0.5

45           0.75

60             1.0

To use the chart, simply find the number of minutes you want to convert, and look up its equivalent decimal representation. For example, if you have worked 30 minutes, you would look up 0.5 on the chart.

It's important to understand the concept of minutes to decimal chart and how to use it, as it is a useful tool in various industries and applications.

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The distance between the checkpoint and the front of the train is constantly receding linearly.

To calculate the distance between the front of the train and the checkpoint, we must take into account the constant speed of the train to know how many it travels in a given time.

In this case the train has a constant speed of 44 ft/s, so it can be inferred that the distance through time is linear because it does not change speed.

According to this, to know the distance between the front of the train and the checkpoint, it is necessary to multiply the speed by the number of seconds that have passed. For example 3 seconds.

Below is the complete table of the distance between the front of the train and the checkpoint at different times.

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Answer:

Step-by-step explanation:

If you're looking to find what b= Subtract a from both sides

-b=-a-8

Then divide negative 1 from both sides to equal

b=a+8

If you're looking to find what a= Add b to both sides

a=b+8

Answer:

(6x + 2)

Step-by-step explanation:

\(4(x+ 1 ) + 2(x - 1 ) \\\\4x + 4 + 2x - 2 \\\\4x + 2x + 4 - 2 \\\\6x + 2\)

the lower class limit represents the smallest data value that can be included in the classThe statement is true.

The lower class limit is the smallest value that can be included in a class interval.

Therefore, the statement is correct.

The lower class limit represents the smallest data value that can be included in a particular class. In a frequency distribution table, data values are grouped into classes, and each class has a lower and upper class limit. The lower class limit denotes the lowest value within that class, and any data value equal to or greater than the lower limit but less than the upper limit falls into that class.

The statement is true, as the lower-class limit indeed represents the smallest data value that can be included in the class.

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A group contains n men and n women. 2n! number of ways are there to arrange these people in a row if the men and women alternate. Arrangement is known as permutation.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

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The general solution to the differential equation u" + 17u = 0 is given by u(x) = C1cos(√17x) + C2sin(√17x), where C1 and C2 are arbitrary constants.

To find the general solution to the given differential equation, we assume a solution of the form u(x) = e^(rx), where r is a constant to be determined. Taking the second derivative of u(x), we have u''(x) = r^2e^(rx).

Substituting u(x) and u''(x) into the differential equation, we get r^2e^(rx) + 17e^(rx) = 0. Factoring out e^(rx), we have (r^2 + 17)e^(rx) = 0.

For a nontrivial solution, we set the expression in parentheses equal to zero, giving us r^2 + 17 = 0. Solving this quadratic equation, we find two complex roots: r = ±i√17.

Since the roots are complex, we can rewrite them as r = 0 ± √17i. Applying Euler's formula, e^(ix) = cos(x) + isin(x), we obtain e^(√17ix) = cos(√17x) + i sin(√17x).

The general solution is then given by taking the linear combination of the real and imaginary parts of e^(√17ix). Therefore, the general solution is u(x) = C1cos(√17x) + C2sin(√17x), where C1 and C2 are arbitrary constants representing the amplitudes of the cosine and sine functions, respectively.

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After 5 years, Richard will have a total of $220 in his savings account.

To calculate the total amount Richard will have in his savings account after 5 years with a 2% annual interest rate that is not compounded, we can use the formula:

Total amount = Principal + (Principal * Interest Rate * Time)

Where:

Principal = $200 (initial amount)

Interest Rate = 2% = 0.02 (converted to decimal)

Time = 5 years

Plugging in these values into the formula, we get:

Total amount = $200 + ($200 * 0.02 * 5)

Total amount = $200 + ($200 * 0.1)

Total amount = $200 + $20

Total amount = $220

Therefore, after 5 years, Richard will have a total of $220 in his savings account.

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We want to complete the steps to convert the given quadratic equation into vertex form.

Eventually we will get:

y = (x + 1)^2 - 2

For a quadratic equation with the vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

Here we start with:

y = x^2 + 2x - 1

1) First, we complete the perfect-square trinomial, we need to add and subtract 1 to get that:

y = x^2 + 2x - 1 + 1 - 1

2) Now we rewrite the equation to be able of completing squares:

y = (x^2 + 2x + 1) - 1 - 1

y = (x^2 + 2x + 1) - 2

3) Now we complete squares

y = (x + 1)^2 - 2

And this is the equation in vertex form, where you can see that the vertex is the point (-1, - 2)

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Answer:

x = 90

Squares add up to 360 degrees 90 + 90 + 90 + 90 = 360 Hope that helps!

Answer:

45 degrees

Step-by-step explanation:

The process you are referring to is called "simple random sampling."

Simple random sampling is a statistical method of selecting a sample from a population in which every possible sample of a given size has an equal chance of being selected. This means that each member of the population has an equal probability of being chosen for the sample, and every possible combination of individuals has an equal chance of being selected. This method of sampling is often used in scientific research and surveys to obtain a representative sample of the population.

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Answer:

Step-by-step explanation:

Given expression is,

\(\lim_{m \to \infty} \frac{4m^2-6m+1}{3m^2+5m+7}\)

By dividing denominator and numerator of the given fraction by m²,

\(\lim_{m \to \infty} \frac{\frac{4m^2-6m+1}{m^2} }{\frac{3m^2+5m+7}{m^2} }\)

= \(\lim_{m \to \infty} \frac{4-\frac{6}{m} +\frac{1}{m^2} }{3+\frac{5}{m} +\frac{7}{m^2} }\)

We know that \(\lim_{n \to \infty} \frac{1}{n}=0\)

\(\lim_{m \to \infty} \frac{4-\frac{6}{m} +\frac{1}{m^2} }{3+\frac{5}{m} +\frac{7}{m^2} }=\frac{4-0+0}{3+0+0}\)

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

Therefore, We can evaluate the limit of the expression by substituting ∞ in for m.

Answer:

Brad drank 1/8 bottle more water.

Step-by-step explanation:

Answer:y=x

Step-by-step explanation:

Easy as that because im smart

The Laplace transform of the given IVP yields the expression Y(s) = E(s) / (s-k) * 1 / (s^2 + k^2), which can be further simplified using partial fraction decomposition. The inverse Laplace transform of this expression gives us the final solution for y(t), which is a combination of cosine and sine functions with exponential decay.

Taking the Laplace transform of the given IVP, we get:
s^2Y(s) - sy(0) - y'(0) + k^2Y(s) = E(s) / (s-k)
Substituting y(0) and y'(0) as 0, we get:
s^2Y(s) + k^2Y(s) = E(s) / (s-k)
Y(s) = E(s) / (s-k) * 1 / (s^2 + k^2)
Using partial fraction decomposition, we can express Y(s) as:
Y(s) = 1 / (s^2 + k^2) - (s+10) / ((s-10)*(s^2 + k^2))
Taking the inverse Laplace transform, we get:
y(t) = cos(kt) - e^10t * cos(kt) / k + sin(kt) / k
In summary, the Laplace transform of the given IVP yields the expression Y(s) = E(s) / (s-k) * 1 / (s^2 + k^2), which can be further simplified using partial fraction decomposition. The inverse Laplace transform of this expression gives us the final solution for y(t), which is a combination of cosine and sine functions with exponential decay.

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The test statistic for this test is 3.09.

To calculate the test statistic for this test, we need to use the formula:

t = \((\bar x - \mu) / (s /\sqrt n)\)

where:

\(\bar x\) = the sample mean difference (after - before)

\(\mu\) = the population mean difference (assumed to be 0 if the test preparation course has no effect)

s = the standard deviation of the differences

n = the sample size (in this case, 30)

Plugging in the values given in the problem, we get:

t = \((6 - 0) / (10 / \sqrt 30)\) = 3.09

To determine whether a test preparation course improves scores on the ACT test, we can use a paired samples t-test.

This test compares the mean difference between two related groups (in this case, the pre- and post-test scores of the same students) to the expected difference under the null hypothesis that there is no change in scores.

The test statistic for a paired samples t-test is given by:

t = (mean difference - hypothesized difference) / (standard error of the difference)

The mean difference is the average difference between the two groups, the hypothesized difference is the expected difference under the null hypothesis (which is 0 in this case), and the standard error of the difference is the standard deviation of the differences divided by the square root of the sample size.

The mean difference is 6 points, the hypothesized difference is 0, and the standard deviation of the differences is 10 points.

Since there are 30 students in the sample, the standard error of the difference is:

SE =\(10 / \sqrt{(30)\)

= 1.83

Substituting these values into the formula for the test statistic, we get:

t = (6 - 0) / 1.83 = 3.28

The test statistic for this test is therefore 3.28.

To determine whether this test statistic is statistically significant, we would need to compare it to the critical value of t for 29 degrees of freedom (since there are 30 students in the sample and we are estimating one parameter, the mean difference).

The critical value for a two-tailed test at a significance level of 0.05 is approximately 2.045.

The test statistic (3.28) is greater than the critical value (2.045), we can conclude that the difference in scores between the pre- and post-test is statistically significant at a significance level of 0.05.

The test preparation course did indeed improve scores on the ACT test. It's important to note that this is just a single study and that further research would be needed to confirm these results.

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Answer:

y = −5x − 19

Step-by-step explanation:

Find the equation using slope-intercept form.

y = −5x − 19

Answer:

Step-by-step explanation:

P (m) = a (m + 1) + b (m + 1) - c (m + 1)

P (m) = (a + b - c) (m + 1)

There are 2 prime factors

The advantages of the superposition theorem compared to other circuit theorems are its simplicity and modularity in circuit analysis, as well as its applicability to linear circuits.

Superposition theorem is a powerful tool in circuit analysis that allows us to simplify complex circuits and analyze them in a more systematic manner. When compared to other circuit theorems, such as Ohm's Law or Kirchhoff's laws, the superposition theorem offers several advantages. Here are two key advantages of the superposition theorem:

Simplicity and Modularity: One major advantage of the superposition theorem is its simplicity and modular approach to circuit analysis. The theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) across any component can be determined by considering each source individually while the other sources are turned off. This approach allows us to break down complex circuits into simpler sub-circuits and analyze them independently. By solving these individual sub-circuits and then superposing the results, we can determine the overall response of the circuit. This modular nature of the superposition theorem simplifies the analysis process, making it easier to understand and apply.

Applicability to Linear Circuits: Another advantage of the superposition theorem is its applicability to linear circuits. The theorem holds true for circuits that follow the principles of linearity, which means that the circuit components (resistors, capacitors, inductors, etc.) behave proportionally to the applied voltage or current. Linearity is a fundamental characteristic of many practical circuits, making the superposition theorem widely applicable in real-world scenarios. This advantage distinguishes the superposition theorem from other circuit theorems that may have limitations or restrictions on their application, depending on the circuit's characteristics.

It's important to note that the superposition theorem has its limitations as well. It assumes linearity and works only with independent sources, neglecting any nonlinear or dependent sources present in the circuit. Additionally, the superposition theorem can become time-consuming when dealing with a large number of sources. Despite these limitations, the advantages of simplicity and applicability to linear circuits make the superposition theorem a valuable tool in circuit analysis.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The equation for the amount left after t years if half life is

and initial amount is A is,

Determine the amount left after 450 years.

Thus amount of samarium left after 450 years is 11850 grams.

The length of the segment of the curve parameterized by r(t) = <2t, cos(πt²)> extending from (2, -1) to (4, 1) is approximately 4.61 units.

1. Determine the corresponding t values for the points (2, -1) and (4, 1).
  For (2, -1), we have 2t = 2 and cos(πt²) = -1, so t = 1.
  For (4, 1), we have 2t = 4 and cos(πt²) = 1, so t = 2.

2. Compute the derivative dr/dt:
  dr/dt =  = <2, -2πt * sin(πt²)>.

3. Calculate the magnitude of dr/dt:
  |dr/dt| = sqrt((2)² + (-2πt * sin(πt²))²) = sqrt(4 + 4π²t² * sin²(πt²)).

4. Integrate |dr/dt| from t = 1 to t = 2 to find the length of the curve segment:
  Length = ∫[1, 2] sqrt(4 + 4π²t² * sin²(πt²)) dt ≈ 4.61 units.

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Answer: 38% of the earnings are from the sale of bagels

Step-by-step explanation:

Bagels: $5.00 x 30 = $150

$150 is the bagel profits.

The total sales are $395.00

To find the percentage of earnings due to bagel sales simply divide.

$150 / $395 = 0.3797

convert the decimal to a percentage and round to the nearest whole.

0.3797 converts to 37.97%

37.97% rounds to 38%

To confirm this, multiply the percentage by the total

Answer:

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal amount (initial deposit)

r = interest rate per year (as a decimal)

t = time period in years

Plugging in the values:

P = £400

r = 0.05

t = 3

I = £400 * 0.05 * 3 = £60

Therefore, you would have earned £60 in interest after 3 years.