find the theoretical probability.​

Answer:

B) Mia Hamm helped her soccer team at the University of North Carolina at Chapel Hill win four NCAA titels.

Step-by-step explanation:

The first option is an opinion, not a fact.

Answer:76

Step-by-step explanation:

):!/

The amount donated by the person follows a geometric progression, which is given by an exponential function.

First part:

Second part;

An exponential function is one in which the input variable is an index of a constant

A constant rate relationship is one in which at all points of the function, the ratio of the output to input stays the same or is a constant.

The given parameters are;

The Pennies a person plans to donate to the library on each day of the month, is given by the following table;

Day. Amount Donated

1. 1

2 2

3 4

4 8

First part

Required;

If the relationship between the day and the amount donated is a constant rate relationship

Solution;

Given that we have;

1/1 = 2/2 ≠ 4/3 ≠ 8/4, the relationship between the day of the month and the amount donated is not a constant rate relationship

Second part;

The shape of the graph of Day to the Amount Donated

Solution;

The sequence of the day has a constant difference of one day, which is given by the equation;

U = 1 × n

Where;

U = The day of the month

n = The number of days

The sequence for the amount donated is given by the exponential function;

S = a•r^n

Where;

a = The first term = 1

r = The common ratio = 2

U = The number of days

The graph of Amount Donated to the Days is therefore the graph of an exponential function, please see the attached graph of Amount Donated to the Day of the month

The possible questions obtained from a similar question are;

First part; If the amount donated and the days have a constant rate relationship

Second part; The shape of the graph of the Amount Donated to the Day of the month

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Answer:

6.5 yards of cord were bought

Step-by-step explanation:

234/36=6.5

Answer:

\(g'(x) = \frac{x^2}{100} +2\)

Step-by-step explanation:

Given

\(g(x) = 10\sqrt{x - 2\)

Required

Determine the inverse function

\(g(x) = 10\sqrt{x - 2\)

Replace g(x) with y

\(y = 10\sqrt{x -2\)

Swap the positions of x and y

\(x = 10\sqrt{y -2\)

Divide through by 10

\(\frac{x}{10} = \sqrt{y - 2\)

Square of both sides

\(\frac{x^2}{100} = y - 2\)

Make y the subject

\(y = \frac{x^2}{100} +2\)

Replace y with g'(x)

\(g'(x) = \frac{x^2}{100} +2\)

Hence, the inverse function is: \(g'(x) = \frac{x^2}{100} +2\)

Answer:

C

Step-by-step explanation:

Answer:

The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt.

This means that \(n = 352, \pi = \frac{92}{352} = 0.2614\)

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a p-value of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 - 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.2011\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 + 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.3217\)

As percent:

0.2011*100% = 20.11%

0.3217*100% = 32.17%.

The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).

Answer:

The answer is D

Step-by-step explanation:

The measure of the height of the pole (h) will be;

⇒ h = 24 ft.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

We have to given that;

The length of the wire which connects the top of a utility pole to a point on the ground = 25 foot

And, A point on the ground located 7 feet away from the base of the pole.

Now,

Let the height of the pole = h

So, We can apply the Pythagoras theorem as;

⇒ 25² = h² + 7²

⇒ 625 = h² + 49

⇒ h² = 625 - 49

⇒ h² = 576

⇒ h = √576

⇒ h = 24 ft.

Thus, The height of the pole = 24 ft.

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0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.

Given that,

Standard deviation (σ) = 5.2 oz

mean (μ) = 10 oz

Number of students (n) = 120

As we know,

P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])

                        = P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])

                        = P (z > 1.86)

                        = 1 - P ( z < 1.86)

                        = 1 - 0.862394

                        = 0.137606

Thus, P( z > 12.7 oz.) = 0.137606

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Answer:

After the price deduction, the retail price would be $42

Step-by-step explanation:

Complete the square.

\(z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0\)

\(\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4\)

Use de Moivre's theorem to compute the square roots of the right side.

\(w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)\)

\(\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2\)

Now, taking square roots on both sides, we have

\(z^2 + \dfrac12 = \pm w^{1/2}\)

\(z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2\)

Use de Moivre's theorem again to take square roots on both sides.

\(w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)\)

\(\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}\)

\(w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)\)

\(\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}\)

To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

Based on the calculations, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Assuming the following parameters for triangle ABC:

For the slope of BC, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2.

For the slope of CA, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3.

For the slope of AB, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4.

Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.

Since side AB is perpendicular to side QC, we have:

m₁ × m₂ = -1

Slope of AB × Slope of QC = -1

Slope of QC = (k - 4)/(h - 2)

4 × (k - 4)/(h - 2) = -1

(4k - 16)/(h - 2) = -1

4k - 16 = -h + 2

4k + h = 18    .......equation 1.

Similarly, we have the following:

Slope of BC × Slope of AH = -1

-3/2 × (k)/(h + 2) = -1

3k/(2h + 4) = 1

3k = 2h + 4

3k - 2h = 4     .......equation 2.

Solving eqn. 1 and eqn. 2 simultaneously, we have:

8k + 2h = 36

3k - 2h = 4

11k = 40

k = 40/11.

For the value of h, we have:

h = -4k

h = -4 × (40/11)

h = -160/11

Therefore, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).

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Answer:

3

Step-by-step explanation:

3

(

2

+

5

)

=

−

7

(

2

−

1

0

)

+

5

{\color{#c92786}{3(2x+5)}}=-7(2x-10)+5

3(2x+5)=−7(2x−10)+5

6

+

1

5

=

−

7

(

2

−

1

0

)

+

5

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\(\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}\)

\(3(2x + 5) = - 7(2x - 10) + 5 \\ 6x + 15 = - 14x + 70 + 5 \\ 6x + 14x = 70 + 5 - 15 \\ 20x = 75 - 15 \\ 20x = 60 \\ x = \frac{60}{20} \\ x = 3\)

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____________________

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꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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One of the main features of the normal distribution is that it is asymptotic, it means that the curve gets closer to the x-axis but never touches it. This statement is true.

The normal probability curve approaches the horizontal axis asymptotically i.e., the curve continues to decrease in size on both ends away from the middle point or the maximum ordinate point but it never touches the horizontal axis.

It extends infinitely in both directions from minus infinitely to plus infinity. As the distance from the mean increases, the curve approaches the baseline more and more closely.

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To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

A option is correct

Step-by-step explanation:

We know that one foot contain 12inches so 12 inches is equal to one foot

There are 36 inches is equivalent to 3 feet which scales is the correct answer would be option (E).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We know that one foot contains 12 inches.

Therefore 12 inches equal one foot

According to option (E),

36 inches is equivalent to 3 feet.

Therefore, the correct answer would be an option (E).

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The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

Step-by-step explanation:

At a pay of 12$ per hour at 8 hours a day you will make 94$ a day or 658$ a week.

Answer:

180x - x²

Step-by-step explanation:

Since the yard has 360 yd. of fencing, hence the perimeter of Rick's lumberyard has 360 yd.

Given that the yard is x yards long. Let y represent the width of the yard. Hence:

Perimeter of the yard = 2(length + width) = 2(x + y)

Substituting:

360 = 2(x + y)

180 = x + y

y = 180 - x

Therefore the width of the yard is (180 - x) yard.

The area of the yard is the product of the length and the width, hence:

Area (A) = length * width

A = x * (180 - x)

A = 180x - x²

Expression for the area as a function of its length will be, Area = (180x - x²) square yards

It's given in the question,

Since, length of the fence = Perimeter of the rectangular area

And Perimeter of the rectangular area = 2(length + width)

By substituting the values of area and the length in the expression,

360 = 2(x + width)

180 = x + width

Width = (180 - x) yards

Since, area of a rectangle is given by the expression,

Area = Length × Width

By substituting the values in the expression,

Area = x(180 - x)

        = (180x - x²) square yards

      Therefore, expression for the area in terms of its length will be, Area = (180x - x²) square yards.

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Answer:

\(x=11\)

Step-by-step explanation:

An undefined slope is a vertical line on a graph. This means it isn't equal to a y-value, but rather an x-value instead. All values of y work for this function, just as long as the x-coordinate is 11.

Answer:

D. It aids a company in not having to calculate an inventory cost for each individual item.

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Answer:

m=3

Step-by-step explanation:

m= 7-1= 6

    5-3= 2

then you simplify    

    3

m= 1 which also equals 3

I am not very good at explaining on this but i hope this helps :)

Answer:20 m/s

Step-by-step explanation:

Answer:

20 m/s

Step-by-step explanation:

700 ÷ 35 = 20 m/s

Answer:

We draw two balls. We know that one of them is orange.

Let's suppose that the first one is the orange.

Then after drawing that, we know that there are 5 balls left in the urn, and only one will be orange.

Then the probability of drawing the other orange ball is equal to the quotient between the number of orange balls and the total number of balls.

P1 = 1/5.

And now let's consider the other case, where we know that in the second draw we will draw an orange ball.

Then the probability of drawing an orange ball in the first draw is equal to the quotient between the number of orange balls (at the beginning we have 2) and the total number of balls (6)

P2 = 2/6

As those represent different cases (we assume different conditions for each one), the probability that we draw two orange balls, knowing for sure that we will draw one, is equal to the sum of these probabilities.

P = P1 + P2 = 1/5 + 2/6 = 6/30 + 10/30 = 16/30 = 8/15

The fraction of the plot of land not occupied by the flowers is 0.0625 or 1/16.

Let's calculate the fraction of the plot of land that is not occupied by the flowers.

Given that initially, 1/4 of the land is allocated for orchids, we have 1 - 1/4 = 3/4 of the land remaining.

After planting the orchids, 2/3 of the remaining land is allocated for roses. Therefore, the fraction of land allocated for roses is (2/3) * (3/4) = 2/4 = 1/2.

Subtracting the land allocated for roses from the remaining land, we have 3/4 - 1/2 = 1/4 of the land remaining.

Finally, 0.75 of the remaining land is allocated for tulips. Therefore, the fraction of land allocated for tulips is 0.75 * (1/4) = 0.1875.

To find the fraction of the plot of land not occupied by the flowers, we subtract the fractions of land allocated for flowers from 1:

1 - (1/4 + 1/2 + 0.1875) = 1 - 0.9375 = 0.0625.

Therefore, the fraction of the plot of land not occupied by the flowers is 0.0625.

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Answer: y = 90°

Step-by-step explanation:

55.30786941 = sin-1 (148/180)   round to 55.3°  angle x

34.69213059 = cos-1 (148/180) . round to 34.7°  "angle z" at right

34.7 +55.3 = 90

Sum of All angles of the triangle = 180°  180 -90 = 90

If angle x is 55.7 and angle z is 34.7° Angle y must be 90°

Ratio of inscribed arcs = ratio of chord to diameter