a fair coin is tossed 2 times in succession. the set of equally likely outcomes is . find the probability of getting at least one tail.

The probability that Rosemary doesn't win the laptop in the NCRST competition is 1 - 0.715 = 0.285 and the probability is found to be 0.667, indicating that there is a 66.7% chance that Sylvester plays either the guitar or the clarinet.

In the given context, the probability that Sylvester plays the guitar is 1/4 (0.25), the probability that he plays the clarinet is 5/8 (0.625), and the probability that he plays both instruments is 5/24 (0.208). To find the probability that he plays the guitar or the clarinet, we can use the principle of inclusion-exclusion.

The probability of playing the guitar or the clarinet can be calculated as the sum of their individual probabilities minus the probability of playing both instruments. Therefore, the probability that Sylvester plays the guitar, or the clarinet is 0.25 + 0.625 - 0.208 = 0.667.

By adding the individual probabilities of playing the guitar and playing the clarinet and subtracting the probability of playing both instruments, we obtain the probability that Sylvester plays either the guitar or the clarinet. In this case, the probability is found to be 0.667, indicating that there is a 66.7% chance that Sylvester plays either the guitar or the clarinet.

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\({\qquad \qquad \huge \rm \underline { \underline{ Répondre}}}\)

Standard equation of an ellipse is :

\(\qquad \rm\dashrightarrow \: \dfrac{ {(x - h)}^{2} }{ {a}^{2} } + \dfrac{ {(y - k)}^{2} }{ {b}^{2} } = 1\)

If b is smaller than a, then it will be a horizontal ellipse, and if b is greater than a, it will be a vertical ellipse. and shifting depends upon coordinates of its centre.

Now, our given equation is :

\(\qquad \rm\dashrightarrow \: \dfrac{ {x}^{2} }{ 15 } + \dfrac{ {y }^{2} }{ {10} } = 1\)

\(\qquad \rm\dashrightarrow \: \dfrac{ {x}^{2} }{ {(\sqrt{15})}^{2} } + \dfrac{ {y}^{2} }{ {(\sqrt{10}) {}^{2} } } = 1\)

[ here, b = root 10 and a = root 15, hence a is greater than b here, which means : its a horizontal ellipse.

And since it is a horizontal ellipse with center at origin, it's major axis will lie on x - axis.

The angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\),\) which is approximately 1.107 radians or 63.43 degrees.

To determine the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\),\) we can follow these steps:

1. Express \(\(z_0\)\) in polar form: To find the polar form of \(\(z_0\)\), we need to calculate its magnitude \((\(r_0\))\) and argument \((\(\theta_0\))\). The magnitude can be obtained using the formula \(\(r_0 = |z_0| = \sqrt{\text{Re}(z_0)^2 + \text{Im}(z_0)^2}\)\):

\(\[r_0 = |2i + 1| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}\]\)

  The argument \(\(\theta_0\)\) can be found using the formula \(\(\theta_0 = \text{arg}(z_0) = \arctan\left(\frac{\text{Im}(z_0)}{\text{Re}(z_0)}\right)\)\):

\(\[\theta_0 = \text{arg}(2i + 1) = \arctan\left(\frac{2}{1}\right) = \arctan(2)\]\)

2. Find the polar form of \(\(w\)\): The polar form of \(w\) can be expressed as \(\(w = |w|e^{i\theta}\)\), where \(\(|w|\)\) is the magnitude of \(\(|w|\)\) and \(\(\theta\)\) is its argument. Since \((w = z^2\)\), we can substitute z with \(\(z_0\)\) and calculate the polar form of \(\(w_0\)\)using the values we obtained earlier for \(\(z_0\)\):

 \(\[w_0 = |z_0|^2e^{2i\theta_0} = \sqrt{5}^2e^{2i\arctan(2)} = 5e^{2i\arctan(2)}\]\)

3. Determine the argument of \(\(w_0\):\) To find the argument \(\(\theta_w\)\) of \(\(w_0\)\), we can simply multiply the exponent of \(e\) by 2:

  \(\[\theta_w = 2\theta_0 = 2\arctan(2)\]\)= 1.107 radians

Therefore, the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\).\)

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The complete question is:

"Determine the angle of rotation, in radians and degrees, at the point z0 = 2i + 1 when w = z^2."

There are 945 ways to form a committee of 4 members containing 2 men and 2 women from a group of 10 women and 7 men.

To find the number of ways to form a committee of 4 members containing 2 men and 2 women from a group of 10 women and 7 men, we can use the combination formula:

n C r = n! / (r! * (n - r)!)

where n is the total number of people (10 women + 7 men = 17), and r is the number of members in the committee (2 men + 2 women = 4).

First, we need to find the number of ways to choose 2 men from the group of 7 men:

7 C 2 = 7! / (2! * (7 - 2)!) = 21

Next, we need to find the number of ways to choose 2 women from the group of 10 women:

10 C 2 = 10! / (2! * (10 - 2)!) = 45

Finally, we can combine these choices by multiplying them together to get the total number of ways to form a committee of 4 members containing 2 men and 2 women:

21 * 45 = 945

Therefore, there are 945 ways to form a committee of 4 members containing 2 men and 2 women from a group of 10 women and 7 men.

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The expression of y - 4 = -2 ( x- (-4) ) in standard form is 2x + y = -4.

Standard form for the equation of a line is Ax + By =C where A is a positive integer and B and C are integers

A standard form is a method of writing mathematical concepts like an equation, expressions, or numbers in standard form. Example: 2.5 billion years is written as 2,500,000,000 years.

Given expression is,

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

y - 4 = -2 (x+4)

y - 4 = -2x - 8

Add 2x to each side

2x + y - 4 = 2x - 2x - 8

2x + y - 4 = - 8

Add 4 from each side

2x + y - 4 + 4  = - 8 + 4

2x + y = -4

Therefore,

The expression of y - 4 = -2 ( x- (-4) ) in standard form is 2x + y = -4.

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The slope of the equation is 34.95. The y - intercept is the value of c, that is y-intercept is 6.25. The value of C(8) is 285.85.

The y-intercept is the location on the graph where the y-axis meets. Finding the intercepts is crucial when graphing any function with the formula y = f(x). A function may have one of two different kinds of intercepts. Both the x-intercept and the y-intercept are involved. A function's intercept is the location on its graph when the axis is broken.

Given that, total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function c= 34.95u+ 6.25.

Comparing the equation with the standard equation of the line:

y = mx + c we see that,

m = 34.95

The slope of the equation is 34.95.

The y - intercept is the value of c, that is y-intercept is 6.25.

The value of C(8) is:

c= 34.95u+ 6.25

c = 34.95(8) + 6.25

c = 285.85

Hence, the value of c(8) is 285.85.

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By using proportions, 11 inches of wire can be bought for 33 cents.

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  "::" or "=".

Given the problem above, we need to find how many inches of wire can be bought for 33 cents

In order to solve this, we will use proportions.

So,

\(\begin{tabular}{c | l}Inches & Cents \\\cline{1-2}17 & 51 \\x & 33 \\\end{tabular}\implies\bold{\dfrac{17}{51} =\dfrac{x}{33} =51x=17\times33\implies x=\dfrac{17\times33}{51}}\)

\(\bold{x=\dfrac{17\times33}{51}\implies\dfrac{561}{51}\implies x=11 \ inches}\)

Therefore, 11 inches of wire can be bought for 33 cents.

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There are 277,200 ways to select a committee of four Republicans, three Democrats, and two Independents from the given group.

To select a committee of four Republicans, three Democrats, and two Independents from a group of 10 distinct Republicans, 12 distinct Democrats, and 4 distinct Independents, you can use combinations.

For Republicans: C(10,4) = 10! / (4!(10-4)!) = 210 ways
For Democrats: C(12,3) = 12! / (3!(12-3)!) = 220 ways
For Independents: C(4,2) = 4! / (2!(4-2)!) = 6 ways

Now, multiply the combinations together to get the total ways:
210 (Republicans) × 220 (Democrats) × 6 (Independents) = 277,200 ways

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A                                                because that's the only one  that makes sence

Given an arithmetic sequence with the first term -6 and the common difference -7, the first five terms are: -6, -13, -20, -27, -34.

The formula for the n-th term of an arithmetic sequence is given by:

a(n) = a(1) + (n - 1) d

Where:

a(1): the first term

d = common difference

The consecutive terms of an arithmetic sequence can be obtained as:

a(n) = a(n - 1) + d

Information available in the problem:

first term = a(1) = -6

common difference = d = -7

Hence,

a(1) = -6

a(2) = -6 - 7 = -13

a(3) = -13 - 7 = -20

a(4) = -20 - 7 = -27

a(5) = -27 - 7 = -34

Therefore the first five terms are: -6, -13, -20, -27, -34

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You are more likely to win by playing regular defense.

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.

Assume out of 100 reviewed games, there were 50 regular defense games and 50 prevent defense games. And out of 50 regular defense games, 38 were won, 12 were lost.

And out of 50 prevent defense game, 29 were won, 21 were lost.

Probability to win the game by playing regular defense is:

P(win | regular) = 38/50 = 0.76

Probability to win the game by playing prevent defense is:

P(win | prevent) = 29/50 = 0.58

Since the probability of winning by regular defense game is more than prevent defense game (0.76 > 0.58),

Hence, you are more likely to win by playing regular defense.

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This question is incomplete

Complete Question

A baker uses 5.5 Ibs of flour daily

The baker's recipe for a loaf of bread calls for 12 oz of flour. If he uses all of his flour to make loaves of bread, how many loaves can he bake in seven days?

Answer:

51.3 loaves of bread

Step-by-step explanation:

Converting 5.5 Ibs to oz (ounces)

1 Ibs =>12 oz

5.5 Ibs => x

Cross Multiply

12 × 5.5 => 88 oz

1 loaf of bread =>12 oz

Hence, in 1 day

12 oz =>1 loaf of bread

88 oz => x

x =>88 oz/ 12 oz

x => 7.3333333333 loaves of bread

Hence, he can make 7.3333333333 loaves of bread in 1 day

Hence, in 7 days

1 day => 7.3333333333 loaves

7 days => x

x => 7 × 7.3333333333 loaves

x => 51.333333333 loaves of bread

Approximately => 51.3 loaves of bread

The number of "same" types of 2x3 matrices in reduced row echelon form, option (c) 4.

To determine the number of "same" types of 2x3 matrices in reduced row echelon form, we need to consider the possible configurations of the leading entries (pivot positions) in the matrix.

Since we have a 2x3 matrix, there can be at most two leading entries, one in each row. The possible configurations of the leading entries are as follows:

No leading entries (both rows contain only zeros): This is a valid configuration and counts as one type.

Considering the valid configurations, there are a total of 4 "same" types of 2x3 matrices in reduced row echelon form.

Therefore, the answer is c. 4.

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\( \sqrt{81 \: + \: 18 \sqrt{7} \: + \: 7} \)

\( \sqrt{(9 \: + \: \sqrt{7} ) ^{2} } \)

\( \boxed{ \bold{9 \: + \: \sqrt{7} }}\)

Answer:

As

so option D is correct.                    

Step-by-step explanation:

Given the expression

\(\sqrt[3]{\left(-0.05\right)^{24}}\)

\(\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\)

\(\sqrt[3]{\left(-0.05\right)^{24}}=\left(\left(-0.05\right)^{24}\right)^{\frac{1}{3}}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\)

                  \(=\left(-0.05\right)^{24\cdot \frac{1}{3}}\)

                  \(=\left(-0.05\right)^8\)  

\(\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}\)

                  \(=0.05^8\)

Hence, the simplification will be:

\(\sqrt[3]{\left(-0.05\right)^{24}}=0.05^8\)

Therefore, option D is correct.                                            

Answer:B.(-0.05)^8

Step-by-step explanation:

Solving a system of equations we can see that:

First, let's define the variables:

With the given information we can write 3 equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

Then we need to solve a system of equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

We can first replace the first equation into the third to get:

(3/4)*V + V + K = $386.4

And rewrite the second to get:

k = V + $18

And replace that in the other equation:

(3/4)*V + V + V + $18 = $386.4

Now we can solve this for V:

V*(1 + 1 + 3/4) = $386.4 - $18

V*(11/4) = $368.40

V = (4/11)*$368.40 = $133.96

Now that we know the value of V, we can replace it in:

K = V + $18 = $133.96 + $18 = $151.96

A = (3/4)*V = (3/4)*$133.96 = $100.47

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Answer:

A=254.34

Step-by-step explanation:

1. A=πr²

2. A=π(9)²

3. A=π(81)

4. A=3.14(81)

5. A=254.34

Answer:

a=254.34 in^2

Step-by-step explanation:

We need to figure out the are of the water well which is a circle with a radius of 9.

This can be represented by the equation

\(a=\pi (9)^2\)

Now just simplify.

\(a=\pi (81)\)

a=254.34

The formula for the number of cells after t days is: Number of cells = 300 + 240 * t. The number of cells present after 5 days is 1500.

In the given question, we are asked to find a formula for the number of cells after t days, given an initial number of 300 cells and a rate of increase of 240 cells per day.

To find the formula, we can use the concept of linear growth. Since the rate of increase is constant, we can express the number of cells after t days using the formula:

Number of cells = Initial number + Rate of increase * Number of days

Substituting the given values, we have:

Number of cells after t days = 300 + 240 * t

This formula represents the number of cells after t days based on the given rate of increase.

In part (b) of the question, we are asked to use the formula obtained in part (a) to find the number of cells present after 5 days. To do this, we substitute t = 5 into the formula:

Number of cells after 5 days = 300 + 240 * 5 = 300 + 1200 = 1500

Therefore, the number of cells present after 5 days is 1500.

The question may have some typos and unclear instructions, so it is important to verify the information provided and clarify any doubts to ensure accurate interpretation and calculation.

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The personal banker given lending arrangement, the APR for your cousin's buddies who borrowed $20 and repaid $40 at the end of the month would be 120%

The annual percentage rate (APR) for your cousin's lending arrangement,  to make a few assumptions. That each lending transaction occurs on the first day of the month and is repaid on the last day of the same month. Based on these assumptions, calculate the effective APR as follows:

Calculate the interest charged for a $20 loan over one month:

Interest = $40 (repaid amount) - $20 (loaned amount) = $20

Divide the interest by the loan amount and multiply by 100 to get the monthly interest rate:

Monthly Interest Rate = (Interest / Loan Amount) ×100 = ($20 / $20) ×100 = 100%

Multiply the monthly interest rate by 12 to obtain the annual interest rate:

APR = Monthly Interest Rate ×12 = 100% ×12 = 120%

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

There is a maximum value of 7/6 located at (x, y) = (5/6, 7).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 10.

Rearranging the constraint, we get:

6x + y = 10,

or, y = 10 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(10 - 6x) = 10x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 10 - 12x ... (i)

Equating to 0, we get:

10 - 12x = 0,

or, 12x = 10,

or, x = 5/6.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.

The value of y, when x = 5/6 is,

y = 12 - 6x,

or, y = 12 - 6*(5/6) = 7.

The value of f(x, y) when (x, y) = (5/6, 7) is,

f(x, y) = xy,

or, f(x, y) = (5/6)*7 = 7/6.

Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).

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The probability that X is greater than 145.28 is approximately 0.0465.

Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Answer:

x ≥ 110 - 65

x ≥ 45

Step-by-step explanation:

Answer:

Principal in account A = $200

Principal in account B = $600

Account B earned more interest in the first month.

Step-by-step explanation:

Given two accounts:

Account A:

Time = 9 months = \(\frac{9}{12}\) years

Interest rate = 3.8%

Interest earned = $5.70

Account B:

Time = 27 months = \(\frac{27}{12}\) years

Interest rate = 2.4%

Interest earned = $32.40

To find:

Principal in each account.

Most interest earned in the first month?

Solution:

First of all, let us have a look at the formula for Simple Interest.

\(SI = \dfrac{P\times R\times T}{100}\)

Putting the values for Account A and finding the value of Principal:

\(5.70 = \dfrac{P_A \times 3.8\times 9}{100\times 12}\\\Rightarrow P_A = \dfrac{570\times 12}{3.8\times 9}\\\Rightarrow P_A=\$200\)

Now, Putting the values for Account B and finding the value of Principal:

\(32.40 = \dfrac{P_B \times 2.4\times 27}{100\times 12}\\\Rightarrow P_B = \dfrac{3240\times 12}{2.4\times 27}\\\Rightarrow P_B=\$600\)

Interest earned in one month i.e. \(\frac{1}{12}\) years:

Account A:

\(SI_A = \dfrac{200\times 3.8\times 1}{100\times 12}\\\Rightarrow SI_A = \$0.63\)

\(SI_B = \dfrac{600\times 2.4\times 1}{100\times 12}\\\Rightarrow SI_B = \$1.2\)

Account B earned more interest in the first month.

Therefore, the answers are:

Principal in account A = $200

Principal in account B = $600

Account B earned more interest in the first month.

Answer:

All angles on a triangle and stright line add up to 180°.  

So, A and C= 50° because the triangle is isosceles. Therefore, then B+A+C+= 180°.

B=°

C=130°

D= 25°

Answer:

Step-by-step explanation:

COPY PASTE I WROTE THE ANSWER ON THERE!!! :)))

Answer:

Step-by-step explanation:

If Mrs. Burdell​'s storage container is 3 feet​ long, 2 feet​ wide, and 8 feet tall, then the volume of the strorage container is expressed as shown;

Volume = Length *Breadth * Height

Volume of the container = 3*2*8 = 48ft³

If she each boxes she is to fit into the storage container has a volume of 1ft³, the total number of boxes she can fit into the container is expressed as:

Number of container = volume of the storage container/volume of a container

= 48ft³/1ft³

= 48 boxes

Since she can fit 48 boxes successfully in her storage tank, then she can fit 44 boxes as well into the storage tank since the total number of boxes the tank can take is greater tan the proposed amount of boxes in question.

So, yes she  fit 44 boxes if each has a volume of 1 cubic foot in her container

Step-by-step explanation:

Volume of a sphere is

\(v = \frac{4}{3} \times \pi \times {r}^{3} \)

We are given the volume, v, and asked to find the radius, r.

Substitute 4500 ft^3 for v, solve for r.

\(4500 = \frac{4}{3} \times \pi \times {r}^{3} \)

Multiply both sides by 3/4 to eliminate 4/3

\( \frac{3}{4} \times 4500 = \frac{4}{3} \times \pi \times {r}^{3} \times \frac{3}{4} \)

\( \frac{13500}{4} = \pi \times {r}^{3} \: \\ then \: divide \: by \: \pi\)

\( \frac{3375}{\pi} = {r}^{3 \: \: take \: the \: cubed \: root \: of \: both \: sides} \)

\( \frac{ \sqrt[3]{ {15}^{3} } }{ \sqrt[3]{\pi} } = \sqrt[3]{r} \)

\( \frac{15}{ \sqrt[3]{\pi} } = r \)

That approximates to 10.27 ft^3

Answer:

There are 29% chance that they will skip their breakfast

Step-by-step explanation:

40 / 14 x 10 = the percentage of the kid skipping his breakfast

40 / 14 x 10 = 28.5%

28.5 = (rounded off) = 29%

The kid has a 29% chance of skipping the breakfast