Q1
The sum of the first 68 positive odd integers is ?

Q2
The degree of recurrence relation an = 2an-2 + 5an-49 is ??

Q3
In how many ways can an organization containing 19 members elect a president, treasurer and secretary (assuming no person is elected to more than one position)?

Q4
The Greatest Common Divisor (GCD) of 28 × 37 × 58 and 23 × 33 × 54 is ??

Answer: We know that for any circle with radius r the formula for the area and circumference of the circle is given as: Area of circle=πr². ... Hence, to describe the relationship between the area of a circle and its circumference. The Area of circle is 1/2 times the radius times the circumference.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The statement that correctly describes a normal distribution is, the approximate percent of values lying within three standard deviation of the mean is 49.85%. approximately 68% of the values are greater than the mean value.

For the standard normal distribution, 68% of the observations lie within 1 standard deviation of the mean; 95% lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean.

The Standard Normal curve, shown here, has mean 0 and standard deviation 1. If a dataset follows a normal distribution, then about 68% of the observations will fall within of the mean , which in this case is with the interval (-1,1).

In normally distributed data, about 34% of the values lie between the mean and one standard deviation below the mean, and 34% between the mean and one standard deviation above the mean. In addition, 13.5% of the values lie between the first and second standard deviations above the mean.

The approximate percent of values lying within three standard deviations of the mean is 49.85%. A. Approximately 68% of the values lie within one standard deviation of the mean.

Therefore,

The statement that correctly describes a normal distribution is, the approximate percent of values lying within three standard deviation of the mean is 49.85%. approximately 68% of the values are greater than the mean value.

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Answer:6 ounce of cereal are left in  the box

Step-by-step explanation:

Total amount of cereal = 16 ounce

Amount of cereal eaten by Tina= 3/8 X16= 6ounce

Amount of cereal eaten by Lane= 1/4 X16= 4ounce

Amount of cereal left = Total amount of cereal -Amount of cereal eaten by Tina and Lane

=16- ( 6+4)

16-10

= 6 ounce of cereal remaining

A slope of 15 simply means that the rate of change of the value on the y-axis with respect to the x-axis is equal to 15.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting an assumed data points into the slope formula, we have the following;

Slope (m) = (80 - 20)/(6 - 2)

Slope (m) = 60/4

Slope (m) = 15.

In this context, we can reasonably infer and logically deduce that a slope of 15 denotes the rate of change of a straight line on a graph.

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Answer:

See below

Step-by-step explanation:

I'm not positive that this is right, but I'll try.

No, and no. 6 is not a perfect cube, and that is a multiple of 3.

8 is a perfect cube that is not a multiple of three.

I hope this helps, sorry if I'm wrong.

Answer:

x=22

Step-by-step explanation:

We would do the opposite so "six less" we would add 6 to 38. 6+38= 44 and "twice a number" we would divide by 2. 44 /2= 22. So the answer would be 22.

Hope this helps! :)

Answer:

Answer is 22

Step-by-step explanation:

38+6=44

44 ÷ 2= 22

:)

Answer:

x = 106 degrees

Step-by-step explanation:

we can create a triangle with angles x, 30, and 26+18.

that means x + 30 + (26 + 18) = 180.

move the constants to one side to get x = 180 - 30 - (26 + 18) = 106

The surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.

What is the surface area of the cylinder?

To find the surface area of a cylinder, we need to find the sum of the areas of its curved surface (lateral area) and its two circular bases.

The formula for the lateral area of a cylinder is L = 2πrh, where r is the radius and h is the height. The formula for the area of each circular base is B = πr^2.

We are given that the height of the cylinder is 11 inches and the radius is 8 inches. Therefore, we can calculate:

L = 2πrh = 2 × 3.14 × 8 × 11 = 549.52 in²

B = πr^2 = 3.14 × 8^2 = 200.96 in²

The total surface area is the sum of the lateral area and the two base areas:

Surface area = L + 2B = 549.52 + 2(200.96) = 951.44 in²

Hence, the surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.

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The probability that a cell phone user makes or receives less than 12 calls per day is 0.3971.

To find P(x < 12), we need to standardize the value of 12 using the formula: z = (x - μ) / σ where z = z-score, x = value of interest, μ = mean, and σ = standard deviation.

Substituting the values, we get:

z = (12 - 13.1) / 4.3

z = -0.25581

Using a calculator, we can find the probability that z is less than -0.25581, which is:

P(z < -0.25581) = 0.3971

P(z < -0.25581) = 39.71%.

Full question "Suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. Find P (x <12)".

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Answer:

a^2+20a+24

Step-by-step explanation:

Answer:

your answer is   a^2 + 20a + 24

Step-by-step explanation:

The amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square is 16.67

In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.

By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.

In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:

=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).

If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.

If the owner counted 7 trees in the first square, the formula would be

=> (7 / 70) x (2500 / 12) = 16.67.

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Complete Question:

To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here.

7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5

Answer:

Zero Point

Step-by-step explanation:

The correct statements regarding the pth percentile of a continuous random variable are: the area under the curve to the left of the pth percentile is equal to p, and the area under the curve to the right of the pth percentile is equal to (1-p).

In general, when considering the pth percentile of a continuous random variable, the following statements are always true:

1. The area under the curve to the left of the pth percentile is equal to p: This statement is correct. The pth percentile is the value below which p percent of the data falls. Therefore, the area under the curve to the left of the pth percentile represents p percent of the total area.

2. The area under the curve to the right of the pth percentile is equal to (1-p): This statement is also correct. Since the total area under the curve is equal to 1, the remaining area to the right of the pth percentile is (1 - p).

3. The pth percentile is positive: This statement is not necessarily true. The pth percentile can be positive, zero, or negative depending on the distribution of the random variable. It is possible for a significant portion of the data to fall below zero, resulting in a negative pth percentile.

Therefore, the correct statements are:

- The area under the curve to the left of the pth percentile is equal to p.

- The area under the curve to the right of the pth percentile is equal to (1-p).

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Answer: B

Step-by-step explanation:

Answer:

x is greater than or equal to 4

Step-by-step explanation:

divide both sides by two, treating it as an equation

so x is greater than or equal to 4

Greetings again.

The answer is (-3,6)

Explanation:

As explained in the your previous question about eliminating the term.

We can either eliminate x-term or y-term to find/solve another term first. But It's easier to eliminate the term without multiplying to make both terms the same.

By adding/subtracting vertically for two equations. We get that the adding y and -y makes them 0.

Therefore, we eliminate y-term to solve x first.

\(\left \{ {{2x+y=0} \atop {3x-y=-15}} \right. \\5x=-15\\\)

I explained about adding/subtracting vertically.

Basically, 2x+3x = 5x

y - y = 0

0 - 15 = -15

That's how to get 5x = -15

\(x=-3\)

Because it is the system of two linear equations. We need to find the y-term too.

Therefore, substitute x = -3 in any given equations. I suggest you to substitute x = -3 in the equation with less coefficient value.

So I'll substitute x = -3 in 2x+y = 0 instead because the first equation has less coefficient than the second equation.

\(2x+y=0\)

Substitute x = -3 in the equation.

\(2(-3)+y=0\\-6+y=0\\y=6\)

Therefore, when x = -3, y = 6. Since you want the answer as an ordered pair. The answer is (-3,6)

The 3 represent the degree of the freedom in the given equation.

According to the statement

we have to find that the in the given statement the digit is 3 is represented the term and we have to find that term.

So, For this purpose, we know that the

The given statement is:

X^2(3) = 8.4, p < .05,

From this it is clear that the

Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample.

This represent the independent values in the given statement also.

So, The 3 represent the degree of the freedom in the given equation.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

In the result X^2(3) = 8.4, p < .05, what is 3 represent from the given questions?

a. the observed value

b. the critical value

c. the significant level

d. degrees of freedom

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The surface area of a sphere with a radius of 2 units is approximately 50.24 square units, and the surface area of a sphere with a radius of 4 units is approximately 200.96 square units.

To find the surface area of a sphere with radius rr, we can use the formula S(r)=4πr2S(r)=4πr2.

Let's substitute the given values into the formula:

For r=2r=2, we have:

S(2)=4π⋅22S(2)=4π⋅22

S(2)=4π⋅4S(2)=4π⋅4

S(2)=16πS(2)=16π

For r=4r=4, we have:

S(4)=4π⋅42S(4)=4π⋅42

S(4)=4π⋅16S(4)=4π⋅16

S(4)=64πS(4)=64π

Now, let's approximate the values to two decimal places using a calculator:

S(2)≈16⋅3.14≈50.24S(2)≈16⋅3.14≈50.24

S(4)≈64⋅3.14≈200.96S(4)≈64⋅3.14≈200.96

Therefore, S(2)≈50.24S(2)≈50.24 and S(4)≈200.96S(4)≈200.96 (rounded to two decimal places).

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Answer:

432, 36, 3

Step-by-step explanation:

Divide each # by 12

Answer: 432, 36, 3

Step-by-step explanation:

You can divide 746,496 by 12 to get 62,208.

You can divide 62,208 by 12 to get 5,184.

You can continue dividing by 12 to get:

5,184 ÷ 12 = 432

432 ÷ 12 = 36

36 ÷ 12 = 3

Therefore, the next three terms are 432, 36, and 3.

I hope this helps!

In order to determine which inequality represents a graph, you need to look at the inequality and identify if the equation is an open or closed interval. If it is an open interval, it will be represented by a dashed line on the graph. If it is a closed interval, it will be represented by a solid line on the graph.

1. Look at the inequality and identify if the equation is an open or closed interval.

2. If it is an open interval, it will be represented by a dashed line on the graph.

3. If it is a closed interval, it will be represented by a solid line on the graph.

4. Determine the starting and ending points of the inequality, and plot them on the graph.

5. Draw the line that connects the two points, either dashed or solid, depending on whether the interval is open or closed.

6. Shade the area of the graph that is represented by the inequality.

7. Label the graph with the inequality, the points, and the shading.

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True, an iterative algorithm will usually run faster than an equivalent recursive algorithm. This is because iterative algorithms use loops to repeat a set of instructions, whereas recursive algorithms call themselves repeatedly until they reach a base case.

An iterative algorithm will usually run faster than an equivalent recursive algorithm. This is because recursive algorithms often involve function calls, which have overhead costs such as saving and restoring the call stack. In contrast, iterative algorithms use loops and do not require the same overhead, making them more efficient in terms of both time and memory usage.

However, it's important to note that some problems may be more elegantly or intuitively solved using recursion, even if it's less efficient. The repeated function calls in a recursive algorithm can lead to slower performance and higher memory usage compared to the more direct approach of an iterative algorithm.

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Answer:

x = 8.98782862707

Step-by-step explanation:

Base on the given we can infer that we are solving for x:

Given equation:

1000x+27x+5.5=9236

Combine similar terms

1027x + 5.5 = 9236

Subtract both side by 5.5

1027x + 5.5 = 9236

             -5.5      -5.5

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

1027x = 9230.5

Now divide both sides by 1027x

9230.5 / 1027

x = 8.98782862707

[RevyBreeze]

Answer:

48

Step-by-step explanation:

-12 x -4 = 48 (When we multiply two negetive numbers, the product becomes positive )

Answer:

48

Step-by-step explanation:

i did the quiz

The quotient of expression is \(\rm x^2+2x+3\).

Given that,

Expression; \(\rm\dfrac{ (x^3 + 3x^2 + 5x + 3) }{ (x + 1)}\)

We have to determine,

The quotient of expression?

According to the question,

To determine the quotient of expression following all the steps given below.

Simplify the expression,

\(\rm =\dfrac{ (x^3 + 3x^2 + 5x + 3) }{ (x + 1)}\\\\= \dfrac{ (x^3 + 2x^2 + 3x + x^2+2x+ 3) }{ (x + 1)}\\\\ = \dfrac{ x(x^2+ 2x+ 3) + 1(x^2+2x+ 3) }{ (x + 1)}\\= \dfrac{ (x^2+ 2x+ 3) (x+1) }{ (x + 1)}\\\\= x^2+2x+3\)

Hence, The required quotient of expression is \(\rm x^2+2x+3\).

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Answer:

|x| - |-x| = 0

Step-by-step explanation:

Answer:

no se

Step-by-step explanation:

no se

The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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(a) The value of k is 81/14 for which f(x, y) is a joint probability density. (b) The marginal density of Y is f_Y(y) = (81/14) (18 - 6y). (c) P(X ≤ 1.5 | Y = 3.5) is approximately 0.1667.

To find the value of k and demonstrate that f(x, y) is a joint probability density function, we need to perform the following steps:

(a) Normalize the joint probability density function:

To find the value of k, we integrate f(x, y) over the entire range of x and y and set it equal to 1.

∫∫f(x, y) dx dy = 1

∫∫k(6 - x - y) dx dy = 1

Since the limits of integration are not provided, we assume that x and y both range from 0 to 6.

∫[0 to 6] ∫[0 to 6] k(6 - x - y) dx dy = 1

Solving this double integral:

\(\[k \int_{0}^{6} (6x - \frac{x^2}{2} - xy) \, dy = 1\]\[k \int_{0}^{6} (6x - \frac{x^2}{2} - xy) \, dy = 1\]\)

\(k[6xy - (x^2)y/2 - (y^2)/2]\) evaluated from 0 to 6 = 1

\(k[36x - 18x^2 + 6]\) evaluated from 0 to 6 = 1

k[(216 - 648 + 6) - (0 - 0 + 6)] = 1

k[174] = 1

k = 1/174 = 81/14

Therefore, k = 81/14.

(b) Finding the marginal density of Y:

To find the marginal density of Y, we integrate the joint probability density function f(x, y) with respect to x over its entire range.

\(f_Y(y)\)= ∫[0 to 6] f(x, y) dx

Substituting the value of k:

\(f_Y(y)\) = (81/14) ∫[0 to 6] (6 - x - y) dx

\(f_Y(y) = (81/14) [6x - (x^2)/2 - xy]\) evaluated from 0 to 6

\(f_Y(y) = (81/14) [(36 - 18 - 6y) - (0 - 0 - 6y)]f_Y(y) = (81/14) (18 - 6y)\)

Therefore, the marginal density of Y is \(f_Y(y) = (81/14) (18 - 6y).\)

(c) Finding the conditional density of X given Y = y and evaluating P(X ≤ 1.5 | Y = 3.5):

The conditional density of X given Y = y is given by:

\(f_{X|Y}(x|y) = f(x, y) / f_Y(y)\)

Substituting the values:

\(f_{X|Y}(x|y) = (81/14) (6 - x - y) / (81/14) (18 - 6y)\\f_{X|Y}(x|y) = (6 - x - y) / (18 - 6y)\)

To evaluate P(X ≤ 1.5 | Y = 3.5), we integrate the conditional density function over the range of x from 0 to 1.5:

P(X ≤ 1.5 | Y = 3.5) = ∫[0 to 1.5] f_X|Y(x|3.5) dx

P(X ≤ 1.5 | Y = 3.5) = ∫[0 to 1.5] (6 - x - 3.5) / (18 - 6(3.5)) dx

P(X ≤ 1.5 | Y = 3.5) = ∫[0 to 1.5] (2.5 - x) / 9 dx

Solving this integral:

P(X ≤ 1.5 | Y = 3.5) = [(2.5x - (x²)/2) / 9] evaluated from 0 to 1.5

P(X ≤ 1.5 | Y = 3.5) = [(2.5(1.5) - (1.5²)/2) / 9] - [(2.5(0) - (0²)/2) / 9]

P(X ≤ 1.5 | Y = 3.5) = (3.75 - 2.25) / 9

P(X ≤ 1.5 | Y = 3.5) = 1.5 / 9

Therefore, P(X ≤ 1.5 | Y = 3.5) is approximately equal to 0.1667.

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