in constructing a confidence interval for the mean, the z distribution provides a result nearly identical to the t distribution when n is large. (True or False)

Using arrangements and combination, it is found that there are \(8.65 \times 10^7\) different schedules possible.

-------------------------------------------

Combination formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

-------------------------------------------

\(T = C_{13,2}C_{8,2}C_{11,2} = \frac{13!}{2!11!} \times \frac{8!}{2!6!} \times \frac{11!}{2!9!} = 120120\)

-------------------------------------------

\(6!(120120) = 720(120120) = 86486400\)

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Answer:

A) v = f(x) = 96 -32x

B)the velocity when x = 0

V = 96 ft/s

The velocity when x =4

V = -32 ft/s

C). Time when v= 0

3 seconds = x

Step-by-step explanation:

f(x) = 96x -16x^2

The above equation represents the position of the object at x time along the x axis.

The velocity will be determined by differentiating the equation with respect with x

f(x) = 96x -16x^2,

D f(x)/Dx= 96 -2(16x)

D f(x)/Dx= 96 -32x

v = f(x) = 96 -32x

The velocity when x = 0

v = f(x) = 96 -32x

V = f(0) = 96-32(0)

V = 96 ft/s

The velocity when x = 4

v = f(x) = 96 -32x

V = f(4) = 96-32(4)

V = 96 - 128

V = -32 ft/s

Time when v= 0

v = f(x) = 96 -32x

0= 96 -32x

-96= -32x

-96/-32=x

3 seconds = x

After 2 years there will be 6257 research papers published from now if the Dr. Carey's area of expertise has been increasing by 3% every year.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent \(\rm y = a^x\)

where a is a constant and a>1

We have:

The number of research papers in Dr. Carey's area of expertise has been increasing by 3% every year.

We are assuming there is exponential increase.

So,

After 2 years the published research papers (a)

a = 34,176(1 + 0.03)²

Because increasing by 3%(0.03) every year.

a = 34176(1.03)²

a = 36257.31 ≈ 36257 research papers

Thus, after 2 years there will be 6257 research papers published from now if the Dr. Carey's area of expertise has been increasing by 3% every year.

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3x² + 2x - 4 = 0

Δ = b² - 4.a.c

Δ = 2² - 4 . 3 . -4

Δ = 4 - 4. 3 . -4

Δ = 52

x = (-b +- √Δ)/2a

x' = (-2 + √52)/2.3    

x'' = (-2 - √52)/2.3

x' = 0,8685170918213297    

x'' = -1,5351837584879966

2 Decimal places

x' = 0,87

x'' = -1,54

Answer: .8685

Step-by-step explanation:

This table shows the frequency of each number obtained after throwing the die 35 times

To prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.

Numbers: 1, 2, 3, 4, 5, 6

Frequency: 5, 14, 6, 4, 5, 1

Based on the given numbers, the frequency table would look like this:

Number   | Frequency

1                      5

2                     14

3                      6

4                      4

5                      5

6                       1

This table shows the frequency of each number obtained after throwing the die 35 times.

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The value of the integer number is -1

The statement is given as:

The sum of an integer and 7 times the next consecutive odd integer is 6

Let the integer value be x

So, the next consecutive odd integer is x + 2

When represented as an equation, we have

x + 7(x + 2) = 6

Open the bracket

x + 7x + 14 = 6

Evaluate the like terms

8x = -8

Divide both sides by 8

x = -1

Hence, the value of the integer number is -1

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Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

Given, a number 2,016

we have to find the place and face value of 6 in the given number 2,016.

So, the Place value of 6 in the given number is ones.

Ones is the place value of the digit 6 in the number 2,016

Also, the Face value of 6 in the given number is 6.

6 is the face value of the digit 6 in the number 2,016

Hence, Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

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Answer:

25 ounce bag

Step-by-step explanation:

In linear equation, 48 coins does Mark have.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                      Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

let

x = number of coins Mark has

Number of coins Joey have = 9 + 1  /3 x

Hence,

25 = 9 + 1  / 3 x

25 - 9 = 1 / 3 x

16 = 1 / 3 x

cross multiply

x = 16 × 3

x = 48 coins

Therefore, number of coins Mark have = 48 coins

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The complete question is -

Write an equation for the word problem below

Joey has 25 collectible coins which is 9 more than 1/3 the number Mark has. How many coins does Mark have?

The required distance between the points  (−1,6) and (−1,7). is 1 unit.

Given that,
using the distance formula to evaluate the distance between the points  (−1,6) and (−1,7).

Distance is defined as the object traveling at a particular speed in time from one point to another.

Here,
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Substitute the values in the above equation,
D = √[[-1 + 1]² + [7 - 6]²]
D = √[0 + 1]
D = 1

Thus, the required distance between the points  (−1,6) and (−1,7). is 1 unit.

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Answer:

4n + 5

Step-by-step explanation:

This equation cannot be simplified further

Unless you meant 4n + 7 = 2

Then the answer would be -1.25

Answer:

4n+5 hope this helps

Step-by-step explanation:

4n+7-2

4n+5

The answer to this Question based on survey is 12.5%

What is survey?

It is a question answer based campaign in which opinions from large audiences are recorded and used for data analytics

Solution:

The elected official claims that he 70% people agree on a particular case

lets remember what he claims but yhis was not based on the survey

But survey of 100 people showed that 80% of agreed with that same particular case

but both can't be true at same time hence difference in their answers is

80-70/80 * 100

= 12.5%

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Answer:

\(\mu =2.16\) --- Mean

\(\sigma^2 = 1.4944\) -- Variance

\(\sigma = 1.222\) --- Standard deviation

Step-by-step explanation:

Given

\(\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.12} & {0.2} & {0.2} & {0.36} & {0.12} \ \end{array}\)

Solving (a): The population mean

This is calculated as:

\(\mu = \sum x * P(x)\)

So, we have:

\(\mu =0*0.12 + 1 * 0.2 + 2 * 0.2 + 3 * 0.36 + 4 * 0.12\)

\(\mu =2.16\)

Solving (b): The population variance

First, calculate:

\(E(x^2)\) using:

\(E(x^2) = \sum x^2 * P(x)\)

So, we have:

\(E(x^2) = 0^2*0.12 + 1^2 * 0.2 + 2^2 * 0.2 + 3^2 * 0.36 + 4^2 * 0.12\)

\(E(x^2) =6.160\)

So, the population variance is:

\(\sigma^2 = E(x^2) - \mu^2\)

\(\sigma^2 = 6.16 - 2.160^2\)

\(\sigma^2 = 6.160 - 4.6656\)

\(\sigma^2 = 1.4944\)

Solving (c): The population standard deviation

This is calculated as:

\(\sigma = \sqrt{\sigma^2}\)

\(\sigma = \sqrt{1.4944}\)

\(\sigma = 1.222\)

Let 'x' represents the advance ticket,

Let 'y' represents the same-day ticket.

Therefore,

The combined cost of one advance ticket and the same ticket is $60, and it can be represented mathematically below.

Secondly, the sum of 25 advance tickets and 40 same-day tickets is $2025. Mathematically,

Let us now combine the equations together,

Let us make x the subject of the formula in equation (1),

Now let us substitute the 'x' into equation (2), and solve for y.

Let us now substitute the value of y into equation 3 to solve for x,

Hence, Advance ticket is $25,

Same-day ticket is $35.

The average rate of change for the interval from x =  7 to x =  8 is 35.  

To calculate the average rate of change for the interval from x =  7 to x =  8, we need to find the difference in y- values and divide it by the difference inx-values within that interval.

Let's calculate it step by step using the given table  

For the interval from x =  7 to x =  8  x1 =  7, y1 = -37  x2 =  8, y2 = -2   Difference in y- values Δy =  y2- y1 = -2-(- 37) =  35  

Difference inx-values Δx =  x2- x1 =  8- 7 =  1  

Average rate of change =  Δy/ Δx =  35/ 1 =  35  

Thus, the average rate of change for the interval from x =  7 to x =  8 is 35.   Note: It's important to mention that the values calculated then are grounded solely on the given data. Please  insure you  corroborate the  delicacy of the  handed data and  environment before using the answer in any important or critical  operations.

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The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.

The correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."

The standard error of the sample proportion can be calculated using the formula:

SE = √[p*(1-p) / n]

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:

SE = sqrt[0.37*(1-0.37) / 100] = 0.048

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

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The correct option is (b) i.e. the total perimeter of the fence is 7x + y − 4 feet.

What is Perimeter?

Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a polygon, circle, or ellipse. It is the sum of the lengths of all the sides or arcs that make up the shape. For example, the perimeter of a square is the sum of the lengths of all its sides, while the perimeter of a circle is the circumference, which is the distance around the circle. The perimeter is often measured in units such as centimeters, meters, or feet, depending on the context of the problem.

Given : sides of the fence

            s₁ = 4x + 5

            s₂ =  y − 7

            s₃ = 3x − 2

We know that, perimeter of a triangle is sum of all three sides.

So, Perimeter of the fence =  s₁+ s₂+ s₃

                                            = 4x + 5 + y − 7 + 3x − 2

                                            = 7x + y - 4 ft.

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The height of the building can be  649.44 ft

What is angle of elevation ?

angle of elevation states that the angle which is formed between line of sight and horizontal line.

Given,  the base of the triangle is 1.75 mile. The angle opposite of the tall side, x, is 4 degrees.

height of the building is an unknown variable (x) .

tan(angle) = opposite length /adjacent length.

Opposite length is x, adjacent length is 1.75 mile, angle is 4 degrees.

tan(4º) = x / 1.75

rearrange for x

x = 1.75*tan(4º) = ~1.75*0.0699  miles.

x = ~0.123

Now to get feet, just multiply by 5,280 ft in one mile

Height of the building is 0.123 miles * 5280 ft/mile = 649.44 ft

Hence , The height of the building can be  649.44 ft .

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

5696

Step-by-step explanation:

i assume you are referring to tax of 16%

16/100 x 35600 = 5696

Answer:

the 2nd and 3rd one I believe

Answer:

2 hours

Step-by-step explanation:

divide 4 by 2 to get 2. Do this becasue 3 is 6 divided by 2.

The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.

When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.

In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.

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Answer:

2⁵ x 3

Step-by-step explanation:

2 x 2 x 2 x 2 x 2 is the same as 2⁵[multiplying 2 with itself for 5 times]

Answer:

5 hours 20 minutes

Step-by-step explanation:

Distance traveled to be 20 miles apart

180 - 20 = 160 miles

Combined speed

14 + 16 = 30 mph

time = distance / speed

t = 160/30

t = 5 1/3 hours

t = 5 hours 20 minutes

Answer:

5 hours and 20 minutes

Step-by-step explanation:

it will take them 5 hours and 20 minutes.

1/6 off means the regular price for that item should be: $88.8

Work:

The sale = $74 ÷ 5 × 1 = $14.8

=> The regular price = $14.8 x 6 = $88.8