True of False?
1. The Central Limit Theorem (CLT) states that the sample mean is normally distributed whenever the population size is sufficiently large, even if the underlying population distribution is skewed.
2. Suppose that a set of data has been collected over time. A time plot of the data set shows an increasing trend. This means that we have evidence that the observations are not iid (independent, identically distributed).
3. The U.S. Census Bureau reported in 2014 that the mean salary for statisticians was $96,000. A researcher speculates that the mean salary is too high for statisticians who have limited work experience (less than 2 years of work experience). To put this theory to the test, the researcher took a random sample of 45 statisticians who had limited work experience (less than 2 years of work experience) and recorded their 2014 annual salary. You have been asked to use the data to test (at a 10% level) the following hypotheses: H0: μ = 96,000 versus Ha: μ < 96,000.
The hypotheses involve the parameter μ. Is this definition for the parameter correct or incorrect?
"μ = the population mean salary for all statisticians reported by the U.S. Census Bureau in 2014."

Answer:

841000

Step-by-step explanation:

Because the shape is symmetrical in regards to the sides and base. Therefore, the equation can be written as either 29*29*10*10*10 or 29^2*10^3

The decimal equivalent of the hex number 0x3F is 63.

To convert the hex number 0x3F to its decimal equivalent, we need to multiply each digit by the corresponding power of 16 and sum them up.

Starting from the rightmost digit, we have:

Now, we multiply each digit by the corresponding power of 16:

Finally, we sum up the results:

(15 * 1) + (3 * 16) = 15 + 48 = 63

Therefore, the decimal equivalent of the hex number 0x3F is 63.

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The perimeter of the given figure is 19.

A shape's perimeter is calculated mathematically using the idea of perimeter. You sum together the lengths of all the sides to find the perimeter.

The perimeter of triangle can be expressed as

P=a+b+c

where the abc are the sides of the triangle, since we were given right angle  triangle we can us trigonometry to find the remaining side.

\(8^2 = a^2 + 4.7^2\\a^2= 8^2 - 4.7^2\\ a^2= 64 - 22.09 \\ a^2 = 41.91\\\\a = 6.47\)

The perimeter = 4.7 + 8 + 6.47

=19.17

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Answer:

$150

Step-by-step explanation:

Well we know that 10% is going to equal 1/10 of 100%.

So now just multipy 15% times 10 to get the original price.

Answer:

A

Step-by-step explanation:

Slope is 4   so for every + 1 change in 'y'   'x' will change by 4

A looks good..... y increases by one from the given point and x increased 4

The probability of selecting an even number card is: 50%

The number of the cards are given as:

4, 5, 6 and 7

Now, an even number are defined as any number that can be exactly divided by 2. Even numbers always end up with the last digit as 0, 2, 4, 6 or 8. Some examples of even numbers are 2, 4, 6, 8, 10, 12, 14, 16.

A number which is not divisible by “2” is called an odd number. An odd number always ends in 1, 3, 5, 7, or 9. Examples of odd numbers: 51 , − 543 , 8765 , − 97 , 9 , etc.

Thus, we have 4 cards and the even number are 2. Thus:

P(even) = 2/4 = 0.5

= 50%

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Answer:

Step-by-step explanation:

a) To find the probability that the operators of the towing service do not miss any calls for assistance during their 30-minute lunch break, we need to calculate the probability of zero requests occurring during that time.

The Poisson distribution can be used to model the number of events in a given time interval. In this case, with a rate of λ = 4 per hour, we can adjust it to the 30-minute time interval. The average number of requests during the lunch break is given by λ' = λ * t = 4 * (30/60) = 2, where t is the time interval in hours.

Using the Poisson distribution formula, the probability of zero requests during the 30-minute lunch break is given by P(X = 0) = (e^(-λ')) * (λ'^0) / 0! = (e^(-2)) * (2^0) / 0! = e^(-2) ≈ 0.1353.

Therefore, the probability that the operators do not miss any calls for assistance during their lunch break is approximately 0.1353.

b) To find the probability that the operators need to wait no more than 10 minutes for their first call after returning from lunch, we can calculate the cumulative probability of the first request occurring within the 10-minute time frame.

Using the exponential distribution with a rate parameter of λ = 4 requests per hour, we can adjust it to the 10-minute time interval. The average number of requests during the 10 minutes is given by λ' = λ * t = 4 * (10/60) = 2/3, where t is the time interval in hours.

The probability of the first request occurring within the 10-minute time frame is given by P(X ≤ 1/6) = 1 - e^(-λ') * Σ(λ'^k / k!), where the summation is taken from k = 0 to k = 1/6.

Calculating this probability yields P(X ≤ 1/6) ≈ 0.0801.

Therefore, the probability that the operators need to wait no more than 10 minutes for their first call after returning from lunch is approximately 0.0801

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Answer: To find the product of the four given expressions, you can use the distributive property to expand each expression and then multiply the terms.

(2x + 1)(x + 2) = (2x + 1)(x) + (2x + 1)(2) = 2x^2 + 2x + x + 2 = 3x^2 + 3x + 2

(2x + 3y)(x + y) = (2x + 3y)(x) + (2x + 3y)(y) = 2x^2 + 3xy + 2xy + 3y^2 = 2x^2 + 5xy + 3y^2

(x + 3y)(2x + y) = (x + 3y)(2x) + (x + 3y)(y) = 2x^2 + 3xy + xy + 3y^2 = 3x^2 + 4xy + 3y^2

(2x+3)(x - 1) = (2x+3)(x) + (2x+3)(-1) = 2x^2 + 3x - 2x - 3 = 2x^2 - x - 3

So the product of the four given expressions is 3x^2 + 3x + 2, 2x^2 + 5xy + 3y^2, 3x^2 + 4xy + 3y^2, and 2x^2 - x - 3.

From the table, the average daily change in the share price from d = 5 to d = 20 is of 11.

The average rate of change of a function p(x) over an interval [a,b] is given by:

\(A = \frac{p(b) - p(a)}{b - a}\)

In this problem, rate over the interval d = 5 to d = 20, hence \(a = 5, b = 20\).

The values of the function are \(p(5) = 39, p(20) = 204\).

Hence:

\(A = \frac{p(b) - p(a)}{b - a}\)

\(A = \frac{204 - 39}{20 - 5}\)

\(A = 11\)

The average daily change in the share price from d = 5 to d = 20 is of 11.

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The probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

This is a binomial distribution problem, where we have n = 15 trials and the probability of success (a patient having hyperextending joints) is p = 0.2.

A. To find the probability that exactly 5 of the 15 patients have hyperextending joints, we can use the formula for the binomial probability mass function:

P(X = 5) = (15 choose 5) * 0.2^5 * 0.8^10

where (15 choose 5) is the number of ways to choose 5 patients out of 15. Using a calculator, we get:

P(X = 5) = 0.188

So the probability that exactly 5 of the 15 patients have hyperextending joints is 0.188, or about 18.8%.

B. To find the probability that no more than 7 of the 15 patients have hyperextending joints, we need to add up the probabilities of having 0, 1, 2, ..., 7 patients with hyperextending joints. We can use the cumulative distribution function (CDF) of the binomial distribution:

P(X ≤ 7) = Σ(P(X = k)) for k = 0 to 7

Again, using a calculator, we get:

P(X ≤ 7) = 0.985

So the probability that no more than 7 of the 15 patients have hyperextending joints is 0.985, or about 98.5%.

C. To find the probability that more than 7 of the 15 patients have hyperextending joints, we can use the complement rule:

P(X > 7) = 1 - P(X ≤ 7)

We already know from part (B) that P(X ≤ 7) = 0.985, so:

P(X > 7) = 1 - 0.985 = 0.015

Therefore, the probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.

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Answer:

D

Step-by-step explanation:

i took the test

The equivalent expressions of \((x^{6} )^{-3}\) will be \((x )^{-18}\).

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive the equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

The given expression is;

\((x^{6} )^{-3}\)

Required to Determine the equivalent expression.

First, we need to evaluate the expression in the bracket:

Apply the following law of indices:

\((x^a)^b = x ^{ab}\)

So:

\((x^{6} )^{-3}\)

becomes

\((x )^{6 \times -3}\\\\\)

\((x )^{-18}\)

Hence: the equivalent expressions of \((x^{6} )^{-3}\) will be \((x )^{-18}\).

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Answer:

No thanks I don't feel like it

Step-by-step explanation:

I don't feel like it

Answer:

C. 37 miles

Step-by-step explanation:

0.50 + 1.50 = 20

        -1.50     -1.50

0.50 = 18.50

18.50 / 0.50 = 37

Answer:

x^2+6x+8 or (x+2)*(x+4)

Step-by-step explanation:

area = length * width

area = (x+2)*(x+4)

(just expanded the brackets)

area  = x^2+6x+8

Answer:

x^2+6x+8

Step-by-step explanation:

The initial way to represent the area of the entire rectangle is (x+2)*(x+4).

With this, we can multiply the two together using the FOIL method (First, Outside, Inside, Last).

x*x=x^2
x*4=4x
2*x=2x
2*4=8

Add these together, and you get your final answer:
x^2+6x+8

To check whether AB exists or not, we have to consider the dimension of both matrices. Matrix A is 1 × 4 and matrix B is 1 × 2. Since the number of columns of matrix A is equal to the number of rows of matrix B, we can multiply A and B.

Therefore, AB exists. The matrix product AB can be obtained by multiplying the elements of row i of matrix A with the elements of column j of matrix B and summing the results, for 1 ≤ i ≤ m and 1 ≤ j ≤ p. Moreover, AB will have a dimension of m × p. So, the dimension of the product AB is 1 × 1. The product AB is a scalar quantity. In order to calculate AB, we have to write matrices A and B in terms of their elements as shown below: A=[1 4 -3 5],

Hence, the product AB exists. It is equal to 5. In linear algebra, matrix multiplication is an important operation that involves multiplying two matrices. The product of two matrices is only defined if the number of columns in the first matrix is equal to the number of rows in the second matrix. If this condition is met, then we can perform the matrix multiplication. where 1 ≤ i ≤ m and 1 ≤ j ≤ p and k is the index of summation, and n is the common dimension of A and B. We replace the values of matrices A and B in the formula, and calculate the product of AB. We find that AB is equal to 5. Therefore, the product AB exists, and it is equal to 5.

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Answer:

10,830

Step-by-step explanation:

Answer:

3/10

Step-by-step explanation:

Of means multiply

2/5 * 3/4

Rewriting

2/4 * 3/5

1/2*3/5

3/10

Answer:

y = 3x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 12 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

To find c substitute (1, - 2 ) into the partial equation

- 2 = 3 + c ⇒ c = - 2 - 3 = - 5

y = 3x - 5 ← equation of parallel line

Step-by-step explanation:

d = √(x2-x1)²+(y2-y1)²

d = √(-3-(-3))²+(-7-(-5))²

d = √ 0+(-2)²

d = √4

d = 2 units

The probability of getting at most 4 and yellow is 1/12.

In this problem, we are given two events: rolling a number that is at most 4 on a six-sided die and spinning the spinner and landing on yellow.

To find the probability of getting at most 4, we first need to determine how many outcomes on the die will satisfy this condition. There are four possible outcomes that meet this requirement: rolling a 1, 2, 3, or 4. Since there are six possible outcomes in total (rolling a 1, 2, 3, 4, 5, or 6), the probability of rolling at most 4 is 4/6, which simplifies to 2/3.

Next, we need to determine the probability of spinning the spinner and landing on yellow. There are five equally-sized sections on the spinner, so the probability of landing on yellow is 1/5.

To find the probability of both events happening, we multiply their individual probabilities. This is because the two events are independent; the outcome of the first event (rolling the die) does not affect the outcome of the second event (spinning the spinner).

Therefore, the probability of getting at most 4 and yellow is the product of the probability of getting at most 4 (2/3) and the probability of getting yellow (1/5), which equals 2/15.

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The domain of the function can be written in the form of interval as  (-∞, ∞).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The function is given as y = aˣ.

Its domain can be found as follows,

For x = 0, y is a⁰ = 1.

For x = n, where n > 0, y is given as,

y = aⁿ, which is greater than zero.

For x = n, where n < 0, y is given as,

y = a⁻ⁿ

⇒ y = 1/aⁿ

Thus, the given function is valid for all real numbers.

Which implies its domain is (-∞, ∞).

Hence, the domain of the given function is obtained as (-∞, ∞).

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2x-6y= 36-4x is the equations create a system of equations with no solution.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, 2x-6y= 36-4x is the equations create a system of equations with no solution.

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The probability of winning the minimum award is 1/68230. In a lottery, the top cash prize was $634 million going to three lucky winners. Players pick four different numbers from 1 to 55 and one number from 1 to 46.

A player wins a minimum of $350 by correctly matching two numbers drawn from the white balls (1 through 55) and matching the number on the gold ball (1 through 46).

A player must match two numbers from 1 to 55 and a number from 1 to 46 to win a minimum of $350. This may be expressed as follows: A possible number of ways to select two numbers from 55 = 55C2 = (55 × 54) / (2 × 1) = 1485. A possible number of ways to select one number from 46 = 46C1 = 46.

The probability of matching the numbers in any of the selected combinations is as follows:P (matching the gold ball) = 1/46 (Since only one number is drawn from 46)P (matching any 2 numbers from the white balls) = (2/55) × (1/54) = 1/1485 (There are 2 ways to select two balls from 55, so the probability is multiplied by 2)P (winning a minimum of $350) = P (matching any 2 white balls) × P (matching gold ball) = (1/1485) × (1/46) = 1/68230.

The probability of winning the minimum award is 1/68230.

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The simplified answer for the given value (3x²y⁵)³  is 27x⁶y¹⁵.

The first step is to find the cube of the values inside the bracket

⇒  (3x²y⁵)³= (3³ × (x²)³ × (y⁵)³)

⇒ 3³ × x⁶ × y¹⁵

⇒ 27x⁶y¹⁵

Hence,  the simplified answer for the given value (3x²y⁵)³  is 27x⁶y¹⁵.

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The volume of the solid obtained by rotating the region bounded by y = x and y = 2x² about the line y = 2 is π/24 units cube.

option D.

The volume of the solid obtained by rotating the region bounded by y = x and y = 2x² about the line y = 2 is calculated as follows;

y = 2x²

x² = y/2

x = √(y/2) ----- (1)

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

Solve (1) and (2) to obtain the limit of the integration.

y =  √(y/2)

y² = y/2

y = 1/2 or 0

The volume obtained by the rotation is calculated as follows;

V = 2π∫(R² - r²)

V = 2π ∫[(√(y/2)² - (y)² ] dy

V = 2π ∫ [ y/2  - y² ] dy

V = 2π [ y²/4 - y³/3 ]

Substitute the limit of the integration as follows;

y = 1/2 to 0

V = 2π [ 1/16  -  1/24 ]

V = 2π [1/48]

V = π/24 units cube

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1. Indian

2.South

3.Africa

4.stormyy

A function representing the line that includes the points (3,3) and (-6,15) is 3y=-4x+21.

The given coordinate points are (3,3) and (-6,15).

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Now, slope=(y2-y1)/(x2-x1)

= (15-3)/(-6-3)

= 12/(-9)

= -4/3

Substitute m=-4/3 and (x, y)=(3, 3) in y=mx+c, we get

3=-4/3 (3) +c

c=7

Put, m=-4/3 and c=7 in y=mx+c, we get

y=-4/3 x+7

3y=-4x+21

Therefore, a function representing the line that includes the points (3,3) and (-6,15) is 3y=-4x+21.

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