15. The average battery life of 2800 manufactured cell phones is recordedand normally distributed. The mean battery life is 12 hours with astandard deviation of 1.0 hours. Find the number of phones whohave a battery life in the 13 to 14 range.*

Answer: In decimal form, 14.85

Answer in fraction form: 297/20

Step-by-step explanation:

Answer:

D 1/16

Step-by-step explanation:

(1/2)^4=.0625

.0625= 1/16

A formula that describes the average revenue per person is:

average revenue per person = 1.4w

Average revenue per person is the ratio of the total revenue received to the number of people. It is calculated by dividing total revenue by the number of people.

We have:

Total revenue formula, M = 350w⁴

Total number of people formula, T = 250w³

Thus,

Average revenue per person = M/T

Average revenue per person = 350w⁴/250w³

Average revenue per person = 1.4w

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The values Matilda use are A. x = 10 and y = 2

Since Matilda uses the polynomial identity (2x−y)² =4x²− 4xy + y² to show that 18² = 324, we choose the value of x = 10 and y = 2 since 2x - y = 2(10) - 2 = 20 - 2 = 18

Substituting the values of the variables into the polynomial identity, we have

(2x − y)² = 4x²− 4xy + y²

(2(10) − 2)² = 4(10)²− 4(10)(2) + 2²

(20 − 2)² = 4(100)− 4(10)(2) + 4

(20 − 2)² = 400 − 80 + 4

18² = 320 + 4

324 = 324

Since both the Left hand side and right hand side of the polynomial equation are equal, then x = 10 and y = 2

So, the values Matilda use are A. x = 10 and y = 2

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Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Answer:

The probability that they will teach different courses is \(\frac{2}{3}\).

Step-by-step explanation:

Sample space is a set of all possible outcomes of an experiment.

In this case we will write the sample space in the form (x, y).

Here x represents the course taught by the first part-time instructor and y represents the course taught by the second part-time instructor.

Denote every course by their first letter.

The sample space is as follows:

S = {(P, P), (P, I), (P, S), (I, P), (I, I), (I, S), (S, P), (S, I) and (S, S)}

The outcomes where the the instructors will teach different courses are:

s = {(P, I), (P, S), (I, P),(I, S), (S, P) and (S, I)}

The probability of an events E is the ratio of the number of favorable outcomes to the total number of outcomes.

\(P(E)=\frac{n(E)}{N}\)

Compute the probability that they will teach different courses as follows:

\(P(\text{Different courses})=\frac{n(s)}{n(S)}=\frac{6}{9}=\frac{2}{3}\)

Thus, the probability that they will teach different courses is \(\frac{2}{3}\).

Answer:

132

Step-by-step explanation:

X is smaller number

x + 71 is larger number.

x+ (x+71)=193

2x = 193-71

2x=122

x=61

x+71=largest number

61+71=132 largest numher

check answer

x+(x+71)=193

61+132=193

Answer:

The larger of the two numbers is 132.

Step-by-step explanation:

let x be the larger number and y be the smaller number.

x + y = 193 [Equatio#1]

x = y +71 [Equation#2]

substitute x from equation #2 into equation # 1:

(y+71) + y = 193

2y = 193 - 71

2y = 122

y = 61

substitute this value of y back into equation #2 to solve for x:

x = (61)+71

x= 132

the larger number is 132.

The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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The domain of function A and function B are compared by the statement of Option A: The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1.

What is a function?

A function is a fundamental concept in mathematics that relates a set of inputs (also known as the domain) to a corresponding set of outputs (sometimes referred to as the codomain). For each input, there exists exactly one output, and the output can be linked to its corresponding input in a unique manner.

The domain of a function refers to the set of all possible input values for which the function can produce an output.

In Function A, the domain consists of all real numbers greater than 0, since it is a logarithmic function that can take any positive number as an input.

In contrast, the domain of Function B includes all real numbers greater than or equal to 1, since it is a square root function that begins at (1,0) and continues to infinity.

This means that any number greater than or equal to 1 can be used as an input to produce a corresponding output.

It is essential to define the domain of a function accurately to ensure that the function is well-defined and to avoid potential errors or ambiguities in mathematical computations.

Therefore, the correct statement is A.

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1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

Answer:

Step-by-step explanation:

3/4 : 1/8 =

3/4 x 8 =

24/4 =

6

Answer:

The second choice

40

Step-by-step explanation:

All the ratos are 10:1

20/2 = 10/1 ==> 10:1

80/8 = 10/1 ==> 10:1

120/12 =10/1 => 10:1

For a 40 serving size the ratio is
40/6 = 20/3 not equal to  10/1

The correct options regarding the statistical measures in this problem are given as follows:

3. The IQR remains a 2.

7. Mean 84º.

To find the quartiles, we need to consider the median, which is the middle value of a data-set, hence:

For question 3, adding the shoe size of 8, the ordered data-set is given by:

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8, 8.5.

Hence:

Hence the IQR is given by:

IQR = 8 - 6 = 2.

Thus the correct option is:

The IQR remains a 2.

For question 7, the second lowest value would remain the second highest value. The only measure that considers all the values to be calculated is the mean, hence the correct option is:

Mean 84º.

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Answer:

Step-by-step explanation:

Remark

Area of an entire circle = pi * r^2

Area of a sector = angle / 360 * pi * r^2

Givens

angle = 140

radius = 8

Solution

Area = (140/360) * 3.14 * 8^2

Area =0.3889 * 3.14 * 64

Area = 78.15

Answer:

78.15

Step-by-step explanation:

The line on the graph is a thick line not dashed. This indicates there is an equal to sign attached to the inequality

We only have two options with equal to attached to the inequality

The shading is towards the negative side of y axis (coming down)

So the right option will have a less than and equal to sigh attached:

Using Pythagorean theorem, the height of Oscar's dog house, at its tallest point, is approximately 7.81 feet.

What is Pythagorean Theorem?

The Pythagorean Theorem is a fundamental concept in mathematics that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem is expressed mathematically as:

a² + b² = c²

Now,

Let's height of the house = "h":

Using Pythagoras

a² + b² = c²

Where "a" and "b" are the lengths of the slanted sides and "c" is the height of the house. We know that "a" and "b" are both 5 feet long, and the bottom of the house is 6 feet across. Let's use this information to find "c":

a = b = 5 feet

b = 6 feet

c² = a² + b²

c² = 5² + 6²

c² = 25 + 36

c² = 61

c = √(61)

c ≈ 7.81 feet

So the height of Oscar's dog house, at its tallest point, is approximately 7.81 feet.

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Answer:

24 shots

Step-by-step explanation:

\(\frac{15}{y}= \frac{63}{100}\)

y × 63 = 15 × 100

63y = 1500

63y ÷ 63 = 1500 ÷ 63

\(y=23\frac{17}{21}\)

Answer:

(1/2, -1/2)

Step-by-step explanation:

To find a midpoint add the two x's and divide by 2 so -1+2 / 2 = 1/2

add the two y's and divide by 2 so 4-5 / 2 = -1/2

Put the two numbers together as a coordinate (1/2, -1/2)

"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).

The expression "log 2 - log 4" can be simplified using                   logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."

The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:

A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.

B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.

C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.

D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.

Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.

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Answer:

12.2

Step-by-step explanation:

7^2 + 10^2 = C^2

49 + 100 = C^2

149 = C^2

√149 = 12.2

C= 12.2

To calculate the mean, median, and mode, we first need to know what each of these terms represents. The mean, also known as the average, is the sum of all the values divided by the total number of values. To find the mean, add up all of the values and divide by the number of values. The median is the middle value in a set of data when it is arranged in order from least to greatest. The mode is the value that occurs most frequently in a set of data. Here's an example to illustrate these concepts:

Let's say we have a set of data consisting of the following values: 2, 5, 5, 7, 8, 10, 12. To find the mean, we add up all of the values and divide by the number of values. In this case, the sum of the values is 49 (2+5+5+7+8+10+12) and there are 7 values, so we divide 49 by 7 to get the mean, which is approximately 7. To find the median, we first need to arrange the data in order from least to greatest: 2, 5, 5, 7, 8, 10, 12. The middle value is 7, so that is the median. To find the mode, we look for the value that occurs most frequently. In this case, 5 occurs twice, which is more than any other value, so the mode is 5.
In conclusion, the mean, median, and mode are all measures of central tendency that can be used to describe a set of data. The mean is the average value, the median is the middle value, and the mode is the value that occurs most frequently. When calculating these measures, it is important to carefully consider the data and choose the appropriate method for finding each value.

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The mean and the variance of the poisson distribution are;

Mean = 2.66

Variance = 1.277

The formula for the PMF of a Poisson distribution is;

p(x:λ) = [e^(-λ) * λ^(x)]/x! for x = 0, 1, 2......

Thus;

p(x = 0) =  [e^(-λ) * λ^(0)]/0!

e^(-λ) = 0.07

λ = - In 0.07

λ = 2.66

That is the mean

Variance is square root of standard deviation;

Variance = √√(2.66)

Variance = 1.277

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Answer:

2.65926003693 for mean and variance.

Step-by-step explanation:

First of all, when it comes to Poisson distributions, the mean and variance equal the same thing. Here we can find the mean using e^-(lambda)=0.07 therefore lambda= -ln(0.07) which equals 2.65926003693 for both.

The probability that at least one of the codes will have repeating digits is 0.4712.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Here, The probability of a pin being repeated is 14.7%

⇒ 14.7/100

After Eliminating the decimal point;

⇒ 14.7/100 = 147/1000

Hence,

The probability that a pin, if selected will have a repeating digit format = 147/1000

The probability of a pin not having repeating digits format is,

⇒ 1 - 147/1000

⇒ 853/1000

If four codes are selected at random (without replacement), the probability that all four of the codes will not have repeating digits format is,

⇒ (853/1000) x (852/999) x (851/998) x (850/997)

⇒ 0.5288

Thus, The probability that at least one of them will have repeating digits is,

⇒ 1 - 0.5288

⇒ 0.4712

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Answer: i think the answer is A

Step-by-step explanation:i think bc i is a quadratic function

Answer: D

Step-by-step explanation:

A and B don't make sense, since the maximum value > 0, and the function is more negative than positive. C and D are our remaining answers. C would be incorrect, since if X reaches \infinity , the function isn't infinite. The only way to make C correct, is a sudden spike in the function to infinity. So, the only correct answer is D.

Hope this helps (please respond if I'm wrong)

Answer:

$362.5

Step-by-step explanation:

Given that :

x : _____ 230 ______340 ______ 590

P(x): ____0.25______0.55 _____ 0.20

To obtain the expected value E(x) of the outcome ; we can use the formula :

E(x) = Σ(x * P(x))

E(x) = (230 * 0.25) + (340 * 0.55) + (590 * 0.20)

E(x) = 57.50 + 187 + 118

E(x) = 362.50

The variance of X-bar is 12.25.

To find the variance of the sample mean (X-bar) for a normally distributed population, we can use the formula:

Variance of X-bar = (Population Variance) / (Sample Size)

In this case, the population mean (μ) is 138 and the standard deviation (σ) is 14. The population variance (σ^2) can be calculated as the square of the standard deviation, which gives us 14^2 = 196.

Since we are sampling with a batch size of 16, the sample size is also 16.

Now we can substitute these values into the formula:

Variance of X-bar = 196 / 16 = 12.25

Therefore, the variance of X-bar is 12.25.

It's important to note that the sample mean (X-bar) is an unbiased estimator of the population mean (μ). The smaller the sample size, the greater the variability of X-bar around the population mean.

As the sample size increases, the variance of X-bar decreases, indicating a more precise estimate of the population mean.

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Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

Answer:

-8,4

Step-by-step explanation:

because the slope is slightly 0n 5 and 4