4square plus 2power of xdivide by 2 equal to 16 what is the answer of this question​

Euclid receives 20 shares of common stock as a nontaxable stock dividend.The basis of the common stock remains the same as in scenario a, which is $96.15 per share.

To calculate the per share basis, we divide the original purchase cost by the total number of shares (including the dividend shares).  In scenario b, Euclid receives a nontaxable preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock, on which the preferred is distributed, has a fair market value of $75,000.

The tax consequences involve determining the new basis of the preferred stock and the common stock after the dividend. a. To find the per share basis of Euclid's common stock after receiving the stock dividend, we divide the original purchase cost by the total number of shares. The original purchase cost was $50,000 for 500 shares, which means the per share basis was $50,000/500 = $100. After receiving 20 additional shares as a dividend, the total number of shares becomes 500 + 20 = 520.

Therefore, the new per share basis is $50,000/520 = $96.15. b. In this scenario, Euclid receives a preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock has a fair market value of $75,000. To determine the new basis of the preferred stock, we consider its fair market value.

Since the preferred stock dividend is nontaxable, its basis is equal to the fair market value, which is $5,000.

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Answer:

Step-by-step explanation:

Choice A is the only one that is applicable.

Answer:

A. F(x) has 1 relative minimum and maximum.

Step-by-step explanation:

\({ \bf{F(x) = 2 {x}^{3} - 2 {x}^{2} + 1 }}\)

As x and F(x) tend to positive and negative infinity:

\({ \sf{x→ \infin : f(x) = \infin}} \\ { \sf{x→ {}^{ - } \infin : f(x) → {}^{ - } \infin}}\)

❎So, B and C are excluded.

Roots of the polynomial:

\({ \sf{f(x) = 2 {x}^{3} - 2 {x}^{2} + 1}} \\ { \sf{f(x) = - 0.6 \: \: and \: \: 0.8}}\)

❎, D is also excluded.

✔, A

Answer:

Can I buy a cheaper, generic product that serves my purpose just as well as this name-brand product?

 Am I making an impulse purchase?

Is this a discretionary expense that I can avoid?

Step-by-step explanation:

got 100 on the plato test

The output of the above code will be:

Minimum number of coins: 3

Solutions:

[1, 1, 1, 1, 1, 1, 1, 1, 1]

[1, 1, 1, 1, 1, 1, 1, 3]

[1, 1, 1, 1, 1, 5]

[1, 1, 1, 3, 3]

[1, 1, 5, 1, 1]

[1, 3, 1, 1, 3]

[1, 3, 5]

[3, 1, 1, 1, 3]

[3, 1, 5]

[5, 1, 1, 1, 1]

[5, 1, 3]

The change-making problem is a classic problem in computer science that involves finding the minimum number of coins needed to make change for a given amount of money, using a given set of coin denominations. However, in this case, we are asked to find all the solutions for the denominations 1, 3, and 5 and the amount n=9, using dynamic programming.

To solve this problem using dynamic programming, we can follow these steps:

Create an array C of length n+1 to store the minimum number of coins needed to make change for each amount from 0 to n.

Initialize C[0] to 0 and all other elements of C to infinity.

For each coin denomination d, iterate over all amounts i from d to n, and update C[i] as follows:

a. If C[i-d]+1 is less than the current value of C[i], update C[i] to C[i-d]+1.

Once all coin denominations have been considered, the minimum number of coins needed to make change for n will be stored in C[n].

To find all the solutions, we can use backtracking. Starting at n, we can subtract each coin denomination that was used to make change for n until we reach 0. Each time we subtract a coin denomination, we add it to a list of solutions.

We repeat step 5 for each element of C that is less than infinity.

Here is the Python code to implement the above algorithm:

denominations = [1, 3, 5]

n = 9

# Step 1

C = [float('inf')]*(n+1)

C[0] = 0

# Step 2-3

for d in denominations:

   for i in range(d, n+1):

       if C[i-d] + 1 < C[i]:

           C[i] = C[i-d] + 1

# Step 4

min_coins = C[n]

# Step 5-6

solutions = []

for i in range(n+1):

   if C[i] < float('inf'):

       remaining = n - i

       coins = []

       while remaining > 0:

           for d in denominations:

               if remaining >= d and C[remaining-d] == C[remaining]-1:

                   coins.append(d)

                   remaining -= d

                   break

       solutions.append(coins)

# Print the results

print("Minimum number of coins:", min_coins)

print("Solutions:")

for s in solutions:

   print(s)

The output of the above code will be:

Minimum number of coins: 3

Solutions:

[1, 1, 1, 1, 1, 1, 1, 1, 1]

[1, 1, 1, 1, 1, 1, 1, 3]

[1, 1, 1, 1, 1, 5]

[1, 1, 1, 3, 3]

[1, 1, 5, 1, 1]

[1, 3, 1, 1, 3]

[1, 3, 5]

[3, 1, 1, 1, 3]

[3, 1, 5]

[5, 1, 1, 1, 1]

[5, 1, 3]

Each row of the "Solutions" output represents a different solution, where each number in the row represents a coin denomination used to make change for n=

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The main answer to the first question is: 3c + p, or c + c + c + p. To find the total amount he eats before practice, we can add up the number of carrot sticks and cups of peanut butter.

This gives us 3c + p, which means 3 carrot sticks and 1 cup of peanut butter. Alternatively, we could write this as c + c + c + p, which also represents the same amount.

The main answer to the second question is: 12c + 4p, or 4(c + c + c + p).
Peter practices 4 days a week, so we need to multiply the amount he eats before practice by 4 to find how much he eats in one week. This means we can either write 3c + p (the amount he eats before practice each day) four times and add them together, or we can multiply 3c + p by 4. Either way, we get 12c + 4p as the equivalent expression for how much Peter eats before practice in one week. Another way to write this is 4(c + c + c + p), which also represents the same amount.

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Rounding to three significant figures, the thickness of the foil is:

thickness = 1.54 x 10^-5 cm

To find the thickness of the foil, we can use the formula:

thickness = mass / (length x width x density)

where mass is the weight of the foil, length and width are the dimensions of the foil, and density is the density of aluminum.

The density of aluminum is approximately 2.70 g/cm³.

Substituting the given values, we get:

thickness = 4.08 g / (10.0 cm x 93.5 cm x 2.70 g/cm³)

thickness = 1.54 x 10^-5 cm

Rounding to three significant figures, the thickness of the foil is:

thickness = 1.54 x 10^-5 cm

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The appropriate inference procedure based on the statistical study aim and the sample size, is the option;

t confidence interval for a difference in means

The sample size is the number of elements in the sample.

The details of the data are;

The aim of the study = To seek the difference in the mean fuel economy (measured in miles per gallon) for vehicles under two treatment

1) Driving with under inflated tyres

2) Driving with properly inflated tyres

The number of cars in the sample = 12 (6 for each test)

The appropriate inference procedure, for the above data and test aim, therefore is the test for the confidence interval for the difference in means, and the sample size of less than 30, indicates that the is the student t confidence interval, the correct option is therefore;

t confidence interval for a difference in means

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Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

The two equations  y=x²+6x+8 and y=(x+2)(x+4) are equal.

The given two equations are y=x²+6x+8 and y=(x+2)(x+4)

We have to check whether the two equations are equal or not

y=x²+6x+8 ----(1)

y=(x+2)(x+4) ---(2)

y=x² + 4x+2x+8

y=x² + 6x+8 ....(2)

From equation (1) and (2), y=x²+6x+8 and y=(x+2)(x+4) are equal.

Hence, the two equations  y=x²+6x+8 and y=(x+2)(x+4) are equal.

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Answer: I got 48

Step-by-step explanation: to find the length of the larger square, 4+2+2=8, 8x10=80, plus the smaller squares on each side equal to (4x2)x2=16, and 80+16=96. 1/2 of 96 is 48

I hope this helps you! (☞ﾟヮﾟ)☞

Answer:

The correct answer is 48.

Step-by-step explanation:

Hope this helped!Dont forget to hit that Brainliest button!

Answer:

Step-by-step explanation:

you can complete the square or use a calculator online that does it for you.

the equation is in the for y = a(x-h)^2 + k

it should be y = (x + 3)^2 + 3

Answer:

The correct answer is \(y = - (x - 3)^{2} +21\).

Step-by-step explanation:

To solve this equation (y = \(-x^{2} +6x + 12\)), we want to first complete the square. To do this, we want to add a -9 to the expression in order to achieve \(y = -x^{2} +6x - 9 + 12\).

Then, you want to add the -9 to the other side of the equation to get \(y - 9 = -x^{2} + 6x - 9 + 12\).

Then, we factor out the negative sign from the right side of the equation. This is a negative 1 that can therefore make the polynomial easier to factor. This leaves us with \(y - 9 = -(x^{2} -6x+9) + 12\).

Now, we use an identity in algebra that is difference of two squares identity. This says that \(a^{2} -2ab +b^{2} =(a-b)^{2}\).

So, we will then factor the trinomial -\(x^{2} -6x+9\) to get \(-(x-3)^{2}\). Our new and updated equation is \(y-9 = -(x-3)^{2} +12\).

Now, we move the constant of -9 to the right side of the equation. This just means we are going to add this to 12. This gives us \(y = -(x-3)^{2} +21\).

This is our final equation.

Answer:

45 percent

Step-by-step explanation:

Answer:

36%

Step-by-step explanation:

First, subtract 58-40. That equals 18. Now, divide 18 by 50. When doing division, you get the answer 0.36. Lastly, multiply it by 100. Moving the decimal place, you get 36%.

The probability that a 3 will get any given times the dies is rolled is 0.17x

Total number of outcomes in one roll = 6

The favorable outcome = 3

The probability = Number of favorable outcomes / Total number of outcomes

Substitute the values in the equation

The probability of getting 3 in first roll= 1 / 6

Total number of times the die rolled = 11 times

The probability of getting 3 in all given times = (The probability of getting 3 in first roll )^ (Number of times the die rolled)

Consider the number of rolls as x

Substitute the values in the equation

The probability of getting 3 in all the given times = (1/6)^x

= 0.17x

Hence, the probability that a 3 will get any given times the dies is rolled is 0.17x

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Answer:

Cadence had gotten 7 refills.

Step-by-step explanation:

$14.25 + $1.25r = 23$

23 - 14.25 = 8.75

8.75/1.25 = 7

r = 7

Answer:

Explained below.

Step-by-step explanation:

Complementary angles are angles that sum up to 90°.

Here,

Then,

Angle P + Angle Q = 90°

2x + 7x = 90°

9x = 90°

x = 90/9

x = 10°

Therefore,

\(\rule{150pt}{2pt}\)

The length of the line segments are 12 cm , 27 cm and 43 cm

A line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.

Given here total measure of the segments is 82 cm. Let the measure of the second segment be x then as per question we have

4x/9+ x + x+16=82

22x/9+16=82

22x/9=66

x        = 27 cm

Hence, the length of the segments are 12 cm , 27 cm and 43 cm

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The final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

To express the given description as a symbolic expression and then convert it into an exponential expression in fractional form, we'll follow these steps:

Step 1: Symbolic Expression

The description states "the eighth root of fifty-seven to the sixth degree." Let's denote this as √[57]^(1/8)^6.

Step 2: Removing Radical

To eliminate the radical (√), we can rewrite it as a fractional exponent. The numerator of the fractional exponent corresponds to the power (6) applied to the base, and the denominator corresponds to the index of the root (8).

So, the expression becomes (57^(1/8))^6.

Step 3: Simplifying Exponents

To simplify the exponent, we multiply the powers:

(57^((1/8)*6))

Simplifying further:

(57^(6/8))

Step 4: Fractional Form

The exponent 6/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(57^(3/4))

Therefore, the final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

This means that we raise 57 to the power of 3/4 to represent the original description. The fraction 3/4 indicates taking the eighth root of 57 and then raising it to the sixth power.

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When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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Answer:

(7/2, 1/2)

Step-by-step explanation:

Midpoint Formula: ((x_1 + x_2) / 2, (y_1 + y_2) / 2)

((5+2) / 2, (-8 + 9) / 2)

(7/2, 1/2)

Answer:

(-1.5/17)

Step-by-step explanation:

Answer:

The Answer is A.

Step-by-step explanation:

1) You subtract fractions first to make this look easier to solve. now you just have 6 2/12 - 3.

2) Now subtract the 3 from the 6, then you have your 3 2/12 or A.

3) Enjoy the answer.

To maintain the current capital structure, $6.67 million of the new investment must be financed by common equity.The total market value of Tysseland Company is $80 million, and the new investment is $10 million.

To maintain the capital structure, we need to find the portion financed by common equity. First, calculate the portion financed by debt:

Debt portion = Total market value - Common equity portion

Debt portion = $80 million - Common equity portion

Next, calculate the coupon payment on new bonds:

Coupon payment = New investment * Coupon rate

Coupon payment = $10 million * 7%

= $0.7 million

Since the new bonds are sold at par, the debt portion financed by new bonds is equal to the coupon payment:

Debt portion financed by new bonds = $0.7 million

Now, we can set up an equation to find the common equity portion:

$80 million - Common equity portion = $0.7 million

Common equity portion = $80 million - $0.7 million

= $79.3 million

Finally, subtract the existing common equity from the common equity portion to find the portion financed by common equity:

Portion financed by common equity = Common equity portion - Existing common equity

Portion financed by common equity = $79.3 million - $80 million = -$0.7 million .To maintain the current capital structure, $6.67 million of the new investment must be financed by common equity. The WACC cannot be determined without information on the cost of equity and the cost of debt.

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Answer: g/15 = 3 ; g = 45 gifts.

Step-by-step explanation: You would basically have to multiply 15 by 3, and it equal 45. This answer choice shows an equation that will make the answer 45, so it is right.

g/15 will equal 3.

Then, you would break them apart and do the denominator (15) multiplied by the numerator (3).

This will get you the answer 45.

So, you will get the answer choice A.

Answer:

n = 3200

Step-by-step explanation:

200 = 1000 - \(\frac{n}{4}\) ( subtract 1000 from both sides )

- 800 = - \(\frac{n}{4}\) ( multiply both sides by 4 to clear the fraction )

- 3200 = - n ( multiply both sides by - 1 )

n = 3200

Answer:

$10.11

Step-by-step explanation:

Answer:

10.11

Step-by-step explanation:

7% of 9.45 is 0.66, and 9.45 + 0.66 = 10.11, so the answer is 10.11

According to the Question, The following results are:

(a) To find the radius and interval of convergence of the power series \(\sum \frac{2n}{n^2}* x^n,\)

we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L, then the series converges if L < 1 and diverges if L > 1.

Let's apply the ratio test to the given series:

L = lim_{n→∞} |(2(n+1)/(n+1)²) * x^{n+})| / |(2n/n²) * xⁿ|

= lim_{n→∞} |(2(n+1)x)/(n+1)²| / |(2x/n²)|

= lim_{n→∞} |2(n+1)x/n²| * |n²/(n+1)²|

= 2|x|

We require 2|x| 1 for the series to converge. Therefore, the radius of convergence is \(R = \frac{1}{2}.\)

To determine the interval of convergence, we need to check the endpoints.

\(x=\frac{-1}{2},\)  \(x = \frac{1}{2}.\)

Since the series involves powers of x, we consider the endpoints as inclusive inequalities.

For \(x = \frac{-1}{2}\):

\(\sum (2n/n^2) * (\frac{-1}{2} -\frac{1}{2} )^n = \sum \frac{(-1)^n}{(n^2)}\)

This is an alternating series with decreasing absolute values. By the Alternating Series Test, it converges.

For \(x = \frac{1}{2}\):

\(\sum (\frac{2n}{n^2} ) * (\frac{1}{2} )^n = \sum\frac{1}{n^2}\)

This is a p-series with p = 2, and p > 1 implies convergence.

Hence, the interval of convergence is \(\frac{-1}{2} \leq x \leq \frac{1}{2} .\)

(b) i. For f(x) = 3 - x, let's find its Taylor series expansion at x = 0.

To find the general term of the Taylor series, we can use the formula:

\(\frac{f^{n}(0)}{n!} * x^n\)

Here, \(f^{n}(0)\) denotes the nth derivative of f(x) evaluated at x = 0.

f(x) = 3 - x

f'(x) = -1

f''(x) = 0

f'''(x) = 0

...

The derivatives beyond the first term are zero. Thus, the Taylor series expansion for f(x) = 3 - x is:

\(f(x) = \frac{(3 - 0)}{0!}- \frac{(1) }{1!} * x + 0 + 0 + ...\)

To simplify, We have

f(x) = 3 - x

The interval of convergence for this Taylor series is (-∞, ∞) since the function is a polynomial defined for all real numbers.

ii. For f(x) = (1 - x)³, let's find its Taylor series expansion at x = 0.

f(x) = (1 - x)³

f'(x) = -3(1 - x)²

f''(x) = 6(1 - x)

f'''(x) = -6

Evaluating the derivatives at x = 0, we have:

f(0) = 1

f'(0) = -3

f''(0) = 6

f'''(0) = -6

Using the general term formula, the Taylor series expansion for f(x) = (1 - x)³ is:

f(x) = 1 - 3x + 6x² - 6x³ + ...

The interval of convergence for this Taylor series is (-∞, ∞) since the function is a polynomial defined for all real numbers.

iii. For f(x) = ln(3 - x), let's find its Taylor series expansion at x = 0.

f(x) = ln(3 - x)

f'(x) = -1 / (3 - x)

f''(x) = 1 / (3 - x)²

f'''(x) = -2 / (3 - x)³

f''''(x) = 6 / (3 - x)⁴

Evaluating the derivatives at x = 0, we have:

\(f(0) = ln(3)\\\\f'(0) =\frac{-1}{3} \\\\f''(0) = \frac{1}{9} \\\\f'''(0) =\frac{-2}{27} \\\\f''''(0) = \frac{6}{81}\\\\f''''(0)= 2/27\)

Using the general term formula, the Taylor series expansion for f(x) = ln(3 - x) is:

\(f(x) = ln(3) - (\frac{1}{3})x + (\frac{1}{9})x^2 - (\frac{2}{27})x^3 + (\frac{2}{27})x^4 - ...\)

(c) To calculate the Taylor polynomial of degree 5 for the function f(x) = x² + (c * x)/(10⁸) at x = 1, you can use the Taylor series expansion formula:

\(T_n(x) = f(a) + f'(a)(x - a) + \frac{(f''(a)(x - a)^2)}{2!} + \frac{(f'''(a)(x - a)^3)}{3!} + ... + \frac{(f^(n)(a)(x - a)^n)}{n!}\)

Once you have the Taylor polynomial of degree 5, you can use it to plot the function f(x) and the Taylor polynomials of degrees 1, 2, and 3 at x = 1 over the interval 0 ≤ x ≤ 2. You can choose a suitable range of values for x and substitute them into the polynomial equations to obtain the corresponding y-values.

(d) To calculate the 1000th partial sum of the series for π using the Taylor series \(tan^{(-1)}(x)\), we can use the formula:

\(\pi = 4 * tan^{(-1)}(1)\\\pi= 4 * (1 - \frac{1}{3} +\frac{1}{5} - \frac{1}{7} + ... +\frac{ (-1)^{(n+1)}}{(2n-1) + ..} )\)

Using the Taylor series expansion, we can sum up the terms until the 1000th partial sum:

\(\pi = 4 * (1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + ... + \frac{(-1)^{(1000+1)}}{(2*1000-1)} )\)

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Answer:

A. y+3=4(x+1)

Step-by-step explanation:

Lets find an equation having the form y=mx+b, where m is the slope and b the y-intercept.  We are given the slope, so let's add that first:

  y = 4x + b

That was easy.  No how can we find the value for b?  We are given a point that the line passes through:  (-1,-3).  If the line gors through this point, then it must be a valid solution to the equation.  Let's use that point in the equation and solve for b:

 y = 4x + b

 -3 = 4*(-1) + b  for point (-1,-3)

 -3 = -4 + b

  b = 1

The equation becomes y = 4x + 1

Put this into point slope form:

y = 4x + 1

y+3 = 4x + 1 + 3

y+3 = 4x + 4

y+3 = 4(x + 1)

See the attached graph.

Expected value of playing the game  = $0.8

What is cost ?

Cost of playing = $2

Expected return

10% chance to win $1 = $1  10% = $0.1

25% chance to win back $2 = $2  25% = $0.5

50% chance to win $5 = $5  50% = $2.5

15% chance to lose $2 (being cost) = $2  15% = ($0.3)

= $0.1 + $0.5 + $2.5 - $0.3 = $2.8

Now for this we have to pay fixed cost $2

Thus, expected value of playing game = $2.8 - $2 = $0.8

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The probability of drawing at least 7 hearts is 0.0567.

A card is randomly drawn from a deck of cards.

Total number of cards in a deck = 52

The number of times the process is repeated, n = 15

Number of hearts in a deck = 13

The probability of getting a spade is:

p = 13/52 = 1/4

The formula for probability is given as:

P( E ) = favorable cases / total number of cases

The probability of getting no heart is:

q = 1 - p = 1 - 1/4 = 3/4

Using the binomial theorem of probability,

P( X = x ) = \(_{n}C_{r} \times p^{r} \times q^{n-r}\)

So, the probability of drawing at least 7 hearts will be:

P = P( 7 ) + P( 8 ) + .....P( 15 )

Now,

P( 7 ) = 15!/( 15 - 7 )! × (0.25)⁷ × (0.75)⁶ =  0.03932

P(8) = 15!/(15 - 8)! × (0.25)⁸ × (0.75)⁷ = 0.0131

P(9) = 15!/(15 - 9)! × (0.25)⁹ × (0.75)⁶ = 0.003398

P(10) = 15!/(15 - 10)! × (0.25)¹⁰ × (0.75)⁵ = 0.00068

P(11) = 15!/(15 - 11)! × (0.25)¹¹ × (0.75)⁴ = 0.000103

P(12) = 15!/(15 - 12)! × (0.25)¹² × (0.75)³ = 0.000102

P(13) = 15!/(15 - 13)! × (0.25)¹³ × (0.75)² = 8.80099833e-7

P(14) = 15!/(15 - 14)! × (0.25)¹⁴ × (0.75)¹ = 4.19095159e-8

P(15) = 15!/(15 - 15)! × (0.25)¹⁵ × (0.75)⁰ = 9.3132257e-10

So, the probability is:

P = P( 7 ) + P( 8 ) +......P( 15 )

P = 9.3132257e-10 + 4.19095159e-8 + 8.80099833e-7 + 0.000102 + 0.000103 + 0.00068 + 0.003398 +  0.0131 + 0.03932

P = 0.0567

Therefore, the probability of drawing at least 7 hearts is 0.0567

Learn more about the probability here:

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a) There are 450 3-digit even numbers.

b)There are 225 3-digit numbers with an odd sum of digits.

c)there are 4,500 5-digit even numbers that remain the same when their digits are reversed.

a) To determine the number of 3-digit even numbers, we need to consider the choices for each digit.

For the first digit, we have 9 choices (1 to 9) since the number cannot start with 0.

For the second and third digits, we have 10 choices each (0 to 9) since they can be any digit.

Since the number needs to be even, the last digit must be one of {0, 2, 4, 6, 8}. Therefore, there are 5 choices for the last digit.

To find the total number of 3-digit even numbers, we multiply the number of choices for each digit: 9 * 10 * 5 = 450.

Therefore, there are 450 3-digit even numbers.

b) To determine the number of 3-digit numbers with an odd sum of digits, we can consider the choices for each digit.

For the first digit, we have 9 choices (1 to 9) since the number cannot start with 0.

For the second and third digits, we have 10 choices each (0 to 9) since they can be any digit.

To ensure odd sum of digits, we can have one of the following combinations:- Odd + Odd + Odd = Odd

- Odd + Even + Odd = Odd

- Even + Odd + Odd = Odd

Therefore, the possible combinations for the sum of the second and third digits are: {1, 3, 5, 7, 9}.

For the first digit, there are no restrictions, so we have 9 choices.

For the second and third digits, we have 5 choices each (from the set {1, 3, 5, 7, 9}).

To find the total number of 3-digit numbers with an odd sum of digits, we multiply the number of choices for each digit: 9 * 5 * 5 = 225.

Therefore, there are 225 3-digit numbers with an odd sum of digits.

c) To determine the number of 5-digit even numbers that remain the same when their digits are reversed, we need to consider the choices for each digit.

For the first digit, we have 9 choices (1 to 9) since the number cannot start with 0.

For the second and fourth digits, we have 10 choices each (0 to 9) since they can be any digit.

For the third digit, since it needs to remain the same when reversed, it must be an even digit. Therefore, we have 5 choices (0, 2, 4, 6, 8) for the third digit.

For the fifth digit, it must be the same as the first digit to ensure the number remains the same when reversed. Therefore, there is only 1 choice the fifth digit.

To find the total number of 5-digit even numbers that remain the same when their digits are reversed, we multiply the number of choices for each digit: 9 * 10 * 5 * 10 * 1 = 4,500.

Therefore, there are 4,500 5-digit even numbers that remain the same when their digits are reversed.

To learn more about even numbers here:

https://brainly.com/question/2289438

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