Consider a random variable X with the following probability
distribution:
P(X=0) = 0.08, P(X=1) = 0.22,
P(X=2) = 0.25, P(X=3) = 0.25,
P(X=4) = 0.15, P(X=5) =
0.05
Find the expected value of X and t

Answer:

30 cents per ounce

Step-by-step explanation:

$9.60 for 2 pounds:

$4.75 for 1 pound.

1 pound= 16 ounces

2 pounds= 32 ounces

$9.50 divided by 32= 0.296 cents per ounce

rounded: 30 cents per ounce

Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as = 2 * 10^-7

A canonical, normal, or standard form of a mathematical object is a conventional manner of presenting that item as a mathematical expression in mathematics and computer science. It is frequently the one that gives the simplest representation of an item and allows it to be identified in a unique fashion.

A quantity is said to be stated in standard form if it is written as the product of a power of ten and a number higher than or equal to one but less than ten (or scientific notation).

The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as follows:

=3.6 * 10^-5 / (1.8 * 10^2)

= (3.6 / 1.8) * (10^-5 / 10^2)

= 2 * 10^-7

Therefore, the answer in standard form is 2 * 10^-7.

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The range of the 200 measurements is 17 cm and one of the measurements is 49.5 cm, it is possible for another measurement to be 34 cm (option d).

To determine if a particular measurement can be one of the 200 measurements, we need to consider the range of the measurements and the given measurement of 49.5 cm. The range is calculated by subtracting the smallest measurement from the largest measurement. In this case, the range is 17 cm. Since the given measurement is 49.5 cm, the smallest measurement would be 49.5 - 17 = 32.5 cm.

Considering the options provided, only 34 cm falls within the range of possible measurements (32.5 cm to 49.5 cm). Therefore, 34 cm could be another one of the 200 measurements.

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Answer: True False True true

Step-by-step explanation:

Answer:

true

false

true

true

Step-by-step explanation:

Answer: 12 Hershey bars is the better buy

Step-by-step explanation: If you get 24 Hershey bars (12 x 2) your price will be $6.24 and if you get 24 Butterfingers (8 x 3) your price will be $6.72

The probability that a randomly chosen plate contains the number 2222 is 0.000028 approximately.

The probability that a randomly chosen plate contains the sub-string HI is 0.002548  approximately.

Given that:

The license plate was in the form of 3 letters followed by 3 digits or 2 letters followed by 4 digits.

Part (A)

Let A be the way the symbol is three letters followed by three numbers, and B be the way two letters followed by four numbers.

Repetition is allowed here. There are 26 alphabetic characters and 10 unique digits.

If 3 letters followed by 3 numbers, the selection method is:

   26 × 26 × 26 × 10 × 10 × 10

⇒ (26)² ×(10)⁴ = 6760000

The number of possibilities is 17576000 + 6760000 = 24336000

contains the digits 2222.

That is, the first two letters can be any alphabet, but the remaining digits he must be 2222. Disk contains number 2222:

   (26) ² = 676

Probability that randomly selected disk contains number 2222:

676/24336000 ≈ 0.000028

Part (B):

Selected disk contains substring HI Number of possibilities:

3 letters followed by 3 digits, the disc has Un

26 × 1 ×10³ × 1 × 26 ×10³

2 letters followed by 4 digits, the number of possible ways is as follows.

1 × 10⁴

So the total number of ways a randomly chosen plate contains the substring HI is:

620000/24336000 ≈ 0.002548

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Answer:

Grade can make 55 bracelets

Step-by-step explanation:

2640/48 = 55

Answer:

55

Step-by-step explanation:

2640 divided by 48

the answer is 55

Answer:

30

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

48 + 3x = 54

3x= 54-48

3x= 6

x= 2

Answer:

225 inches

Step-by-step explanation:

15 x 15 = 225

Answer:

C) 5x+3

Step-by-step explanation:

2x+5-x+3x+x-2

2x-x+3x+x+5-2

x+3x+x+3

4x+x+3

5x+3

Answer: 7 Plates

Step-by-step explanation:

Use Algebra

1. Write this as an algebraic equation.

a) 6N + 12P = 132

b) N + P = 15

2. Now solve this equation. You will get an answer of 8 Napkins and 7 Plates.

Answer:

11 don't ask 11

Step-by-step explanation:

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

The mean of a standard normal distribution is zero (0). The standard deviation of a standard normal distribution is one (1).

A standard normal distribution is a special case of the normal distribution with a mean of zero and a standard deviation of one. It is a commonly used probability distribution in statistics, and its properties make it easy to standardize and compare different normal distributions. The value of the mean of a standard normal distribution is zero.

The standard normal distribution is important in hypothesis testing, confidence intervals, and calculating Z-scores. The value of standard deviation of a standard normal distribution is one.

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The equation for growth is  \(f(t) = 5. (1.25)\) x can be stated in the formula f(t) = abx, where a = 5 and b = \(1.25\) . The growth rate in this case is the value of b, which is the quantity by which the function increases over time.

The given growth formula is:

\(f(t) = 5(1.25)^t\)

Here, t represents time, and f(t) represents the value of the function at time t.

The growth rate of a function is the rate at which its value increases over time. In this case, the growth rate is determined by the base of the exponential function, which is 1.25. The base represents the factor by which the function grows at each time step.

The growth rate can be calculated as follows:

Growth rate = (1 + growth factor) - 1

where the growth factor is the factor by which the function grows at each time step, which in this case is  \(1.25\) .

Therefore, the growth rate can be calculated as:

Growth rate  \(= (1 + 1.25) - 1 = 0.25 or 25%\)

Therefore, the growth rate of the given function is \(25%.\)

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The statement suggesting that larger groups are more effective than smaller groups is false. Smaller groups tend to have better communication, efficiency, and individual participation.

The statement suggests that larger groups, specifically groups of twenty to thirty people with representatives from multiple subgroups, are more effective than smaller groups of six to eight people. However, this statement is generally considered false for several reasons:

Larger groups can face challenges in communication and coordination. With more members, it becomes more difficult to ensure effective information sharing, active participation, and clear decision-making. Small groups often have better communication and coordination due to fewer individuals involved.

Smaller groups tend to be more efficient and productive. In larger groups, there can be increased time spent on managing diverse opinions and reaching consensus, which can slow down the decision-making process and hinder productivity. Smaller groups can often make quicker decisions and accomplish tasks more efficiently.

Larger groups may result in reduced individual participation. Some members may feel less inclined to contribute or may be overshadowed by more dominant personalities. In smaller groups, each member can have a more significant impact and be actively engaged in the group's work.

Smaller groups tend to foster better group dynamics and cohesion. It is easier for members to develop strong relationships, trust, and a shared sense of purpose in smaller groups. Larger groups can struggle with maintaining cohesiveness and a sense of belonging.

While larger groups may have certain advantages, such as a broader range of perspectives and resources, the statement disregards the potential drawbacks of managing larger groups effectively. Overall, smaller groups often exhibit better communication, efficiency, and individual participation, making the statement false in general.

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Answer:

n = -8

Step-by-step explanation:

-12n - 19 = 77

       +19   +19

-12n = 96

n = -8

Answer:

N = -8

Step-by-step explanation:

-12n - 19 = 77

-12n = 77 + 19 = 96

n = 96/-12

n = -8

Given:

The total number of marbles are 26.

Red marbles=10

Black marbles=8

Green marbles=8

The two marbles are drawn randomly,

To find the probability that both marbles are green,

The probability that first marbles chosen is green,

Condition is given that the first is not returned before the second one is drawn.

Now the we have 7 green marbles and total marbles are 25.

Probability is given by,

The total probability of getting both green marbles without replacement is,

Answer: Probability is 0.08615.

A one-way ANOVA is a statistical test used to compare the means of four populations in this case. Thus, the degrees of freedom for the F-statistic in this one-way ANOVA are (df1, df2) \(= (3, 78)\).

The degrees of freedom are essential for calculating the F-statistic, which helps determine whether there are significant differences among the population means.

To calculate the degrees of freedom for the F-statistic, we need to determine the numerator degrees of freedom (df1) and the denominator degrees of freedom (df2). For df1 (numerator degrees of freedom), it is equal to the number of populations (groups) minus 1.

In this case, there are four populations,

So: df1 \(= 4 - 1 = 3\)

For df2 (denominator degrees of freedom), it is equal to the total sample size (N) minus the number of populations (groups).

The total sample size is given as \(18 + 22 + 20 + 22 = 82\).

So: df2 \(= 82 - 4 = 78\)

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The simplified form of 37 / (√12 + √√(3√3)1) is\((74 - 37\sqrt{(3^(1/4))) } / (2\sqrt{3} - 3^(1/4)\sqrt{3} ).\)

To simplify the given expressions without using a calculator, let's break down each expression step by step:

Simplifying 2√8 - 4√32 + 3√50:

First, let's simplify the square roots individually:

√8 = √(4 × 2) = √4 × √2 = 2√2

√32 = √(16 × 2) = √16 × √2 = 4√2

√50 = √(25 × 2) = √25 × √2 = 5√2

Now, substitute these values back into the original expression:

2√8 - 4√32 + 3√50 = 2(2√2) - 4(4√2) + 3(5√2)

= 4√2 - 16√2 + 15√2

= (4 - 16 + 15)√2

= 3√2

Therefore, the simplified form of 2√8 - 4√32 + 3√50 is 3√2.

Simplifying 37 / (√12 + √√(3√3)1):

Let's start by simplifying the radicals:

√12 = √(4 × 3) = √4 × √3 = 2√3

√√(3√3)1 = √(3√3)

\(= (\sqrt{3} )^{(1/2) }\times \sqrt{3}\)

\(= 3^(1/4) \times \sqrt{3}\)

Now, substitute these values back into the original expression:

37 / (√12 + √√(3√3)1) \(= 37 / (2\sqrt{3} + 3^{(1/4)} \times \sqrt{3} )\)

To simplify further, we can factor out √3:

37 / (√12 + √√(3√3)1) \(= 37 / (\sqrt{3} (2 + 3^{(1/4)}))\)

Now, rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:

\(37 \times(\sqrt{3} (2 - 3^{(1/4)})) / (\sqrt{3} (2 + 3^{(1/4)})) \times (\sqrt{3} (2 - 3^{(1/4)})) / (\sqrt{3} (2 - 3^(1/4)))\)

Simplifying further, we get:

\(37(2 - 3^{(1/4)}) / (2\sqrt{3} - 3^{(1/4)}\sqrt{3} )\)

\(= (74 - 37\sqrt{(3^{(1/4)})) / (2\sqrt{3} - 3^{(1/4)}\sqrt{3} )}\)

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Answer:

B. 12.40

Step-by-step explanation:

Add all the hours

Total profit divided by the amount of hours

Because the sample statistic centers around a different value than the population parameter, the sample mean absolute deviation is a biased estimator of the population mean absolute deviation.

Reason Behind a Biased Estimator

The expected value (average) of all the sample absolute deviations must match the population absolute deviation in order for the absolute deviation to function as an unbiased estimator. It does not, however, which makes the values of sample mean absolute deviation behave as a  biased estimator.

Brief Description of Sample Mean Absolute Deviation

The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection. It is a statistical summary of statistical variability or dispersion.

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Answer:

5i + 2

Step-by-step explanation:

(5-2i)(i)

5i - 2i^2

i^2= -1

5i -2(-1)

= 5i + 2

Answer:

- 1

Step-by-step explanation:

Multiplying a negative quantity by a negative quantity results in a positive.

Also multiplying by 1 leaves the other value as is, then

- 1 × - \(\frac{7}{11}\) = \(\frac{7}{11}\)

Answer:

We know that 6 squared equals 36, and we know that 5 squared is equal to 25. SO we know that 30 must lie somewhere between those two numbers. It is greater than 5, but less than 6 because 25 is less than 30 and 36 is greater than 30.

Answer:

-3

Step-by-step explanation:

The area enclosed by the ellipse with equation x^2/a^2 + y^2/b^2 = 1 is given by the formula pi * a * b. This formula applies to ellipses with semi-axes a and b. The proof involves solving the equation for y and obtaining the equation of the ellipse in the first quadrant.

To find the area enclosed by the ellipse x²/a² + y²/b² = 1, we begin by solving the equation for y. This gives us y²/b² = 2 - x²/a² or y = ± (b/a)√(a² - x²). Since the ellipse is symmetric with respect to both axes, the total area A is four times the area in the first quadrant.

In the first quadrant, the equation of the ellipse becomes:

y = (b/a)√(a² - x²) for 0 ≤ x ≤ a.

To determine the area, we integrate this equation with respect to x over the interval [0, a]. Substituting x = a sinθ and differentiating, we find dx = a cosθ dθ.

By changing the limits of integration, we note that when x = 0, sinθ = 0, so θ = 0; and when x = a, sinθ = 1, so θ = π/2. Thus, the integral becomes 1/4A = ∫[0,π/2] (b/a)(a cosθ)(a dθ).

Simplifying, we have 1/4A = (b/a) * a² ∫[0,π/2] cosθ dθ. The integral of cosθ over [0,π/2] is sinθ evaluated at the limits, which gives:

sin(π/2) - sin(0) = 1 - 0 = 1.

Therefore, we have 1/4A = (b/a) * a² * 1, which simplifies to 1/4A = a * b. Multiplying both sides by 4, we get A = π * a * b, which proves that the area of an ellipse with semi-axes a and b is given by the formula π * a * b.

In particular, when the ellipse is a circle with radius r, we can substitute a = b = r, yielding A = π * r^2. Thus, we have proven the well-known formula for the area of a circle.

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The required explanation for log of base 10 is described.

The ability of logarithms to solve exponential problems is a large part of their strength. Examples of this include sound (measured in decibels), earthquakes (measured on the Richter scale), starlight brightness, and chemistry (pH balance, a measure of acidity and alkalinity).

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

The logarithm can be rewritten using the general rule. The common logarithm, which has a base of 10 always, is what you're dealing with when the log has no base.

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To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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