Find the 2 consecutive integers whose squares have a difference of 259

1. Independent random samples arise when one random sample is split into groups differing by an observed feature is incorrect.

2. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

1. Independent random samples arise when individuals in a sample are randomly assigned to experimental groups, data is recorded repeatedly on a random sample of individuals, or random samples are selected separately. The statement that one random sample is split into groups differing by an observed feature does not accurately describe independent random samples.

2. The margin of error in a confidence interval represents the range of values within which the true population parameter is likely to fall. It is calculated by taking half of the width of the confidence interval. Therefore, the correct answer is that the margin of error is equal to half the width of the confidence interval.

In summary, the incorrect statement is that independent random samples arise when one random sample is split into groups differing by an observed feature. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

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Answer:

16 square feet is left uncovered.

Explanation:

Essentially, you’re trying to find the difference between the area of the door and the area of the poster. The area formula for a basic rectangle is l • w (length times width.) We have both of those dimensions for the separate shapes, so you can go ahead & do that math separately (as shown in the attachment!) Then, you subtract the area of the poster from the area of the door, and you have your answer. As always, I hope this is accurate & helpful! Good luck on your test, friend. Best wishes <3

Answer:

1406.7 in^3

Explanation:

The volume of a cylinder with radius r and height h is given by

Now in our case h = 7 in, r = 16 /2 = 8 in, and in we use pi = 3.14, the above gives

which gives

Rounded to the nearest tenth this is

Answer:

The formula to calculate volume of a cylinder is given by the product of base area and its height. Volume of a cylinder = πr2h cubic units.

Step-by-step explanation:

Answer:

The vertex will be at ( -1,-2)

Step-by-step explanation:

g(x) = |x + 1| - 2.

The vertex of g(x) = |x |  is ( 0,0)

y = f(x) + C C < 0 moves it down  

y = f(x + C) C > 0 moves it left

We shift this  to the left 1 unit and down 2 units

( 0 -1, 0-2)

The vertex will be at ( -1,-2)

Given: g(x) = |x + 1| - 2.

We start at g(x) = |x| at (0, 0)

c < 0 moves it down

y = f(x) + c

2 units down

c > 0 moves it left

y = f(x + c)

1 unit to the left

After the shift, we see the vertex being at (-1, -2).

Best of Luck!

Answer:

c is your answer to the question

1. a) The median is 148. b) The midrange is 148. c) The sample mean is 81.8. d) The sample standard deviation is 76.08. 2. The probability that Sam will get a parking ticket given that he parked in a no-parking zone is 0.06.

1. a) Find the median. The median is the middle value when the data set is arranged in order from smallest to largest. Since there are five numbers, the middle number will be the third one when they are arranged in order. So, the median is 148.

3, 30, 71, 148, 157

b) Find the midrange. The midrange is the average of the maximum and minimum values in the data set. The maximum value is 157, and the minimum value is 3.

Midrange = (157 + 3) / 2 = 80

c) Find the sample mean. The sample mean is the average of all the values in the data set.

Sample mean = (3 + 30 + 148 + 157 + 71) / 5 = 81.8

d) Find the sample standard deviation. To find the sample standard deviation, we need to use the formula:

s = √ [ Σ(xi - x)² / (n - 1) ]

where:

xi = each value in the data set

x = the sample mean

n = the sample size

Σ = the sum of

Using the given values:

s = √ [( (3 - 81.8)² + (30 - 81.8)² + (148 - 81.8)² + (157 - 81.8)² + (71 - 81.8)² ) / (5 - 1) ]

s = √ [23148.16 / 4]

s = √ [5787.04]

s = 76.08

2. The probability that Sam parks in a no-parking zone and gets a parking ticket is 6%, and the probability that Sam cannot find a legal parking space and has to park in the no-parking zone is 20%.

Let A be the event that Sam parks in a no-parking zone and B be the event that Sam gets a parking ticket.

We want to find P(B|A), the probability that Sam will get a parking ticket given that he parked in a no-parking zone.

Using Bayes' theorem:

P(B|A) = P(A|B) x P(B) / P(A)

P(B) = 0.06 (given)

P(A|B) = the probability that Sam parked in a no-parking zone given that he got a parking ticket. This is not given directly, but we can use the information that Sam parks in a no-parking zone with a probability of 20%, and out of those times he gets a parking ticket with a probability of 6%. So:

P(A|B) = P(A and B) / P(B)

P(A and B) = P(B|A) x P(A) = 0.06 x 0.20 = 0.012

P(A|B) = P(A and B) / P(B) = 0.012 / 0.06 = 0.2

P(A) = the probability that Sam parks in a no-parking zone, whether or not he gets a ticket. This is 20% (given).

So, substituting into Bayes' theorem:

P(B|A) = P(A|B) x P(B) / P(A) = 0.2 x 0.06 / 0.20 = 0.06

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The bearing of H from P is 243°26′

In mathematics, an angle is a measure of the amount of rotation between two lines or planes. It is measured in units of degrees or radians. An angle is formed by two rays that have a common endpoint called the vertex. The rays are the sides of the angle and the vertex is the point where the rays meet.

An angle is defined by its measure, which is the amount of rotation between the two rays. The most common way to measure angles is in degrees, where a full rotation is equal to 360 degrees. Another way to measure angles is in radians, where a full rotation is equal to 2*pi radians.

Let the bearing of H from P be represented by x°.

tanθ=3060=0.5

θ=tan−1(0.5)=26.565°

x=180°+(90−26.565)

x=180+63.435=243.435°

= 243°26′

Hence, the bearing of H from P is 243°26′

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The correct statement for the 95% confidence interval is given by

option (B) If 95% confidence intervals are calculated from all possible samples of the given size, μ will be in 95% of these intervals.

Confidence interval = 95%

Population mean μ

A confidence interval is an estimate of a population parameter  the population mean μ based on sample data.

The interpretation of a 95% confidence interval is that ,

Sample from the population and construct 95% confidence intervals,

Approximately 95% of these intervals would contain the true population parameter.

Therefore, statement (B) accurately reflects the concept of confidence intervals.

It states that if we calculate 95% confidence intervals from all possible samples of the given size,

The true population mean μ will be within 95% of these intervals.

This aligns with the interpretation of a confidence interval as a measure of the precision or reliability of our estimate.

The other statements which are not accurate,

(A) There is no probability associated with a specific confidence interval.

Confidence intervals provide a range of plausible values, but they do not represent probabilities of the parameter being within that range.

(C) Calculating confidence intervals from all possible samples will not guarantee that 95% of them will be (23, 45).

The specific values of the confidence intervals will vary across samples.

(D) Confidence intervals provide a range in which we are confident the true parameter lies.

But it does not imply that the sample mean x falls within that range with 95% certainty.

(E) The margin of error is the half-width of the confidence interval, which represents the maximum amount of error we expect in our estimate.

Here, the margin of error would be (45 - 23) / 2 = 11, not 22.

Therefore , for the confidence interval 95% option B is correct.

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Answer is in the file below

tinyurl.com/wtjfavyw

The division of 4 · x² + 10 · x - 4 by 2 · x - 1 is equal to (2 · x + 6) + 2 / (2 · x - 1).

In this problem we find a second grade polynomial, also known as quadratic function, being divided by a first grade polynomial, also known as linear function. The complete procedure is shown below:

The resulting polynomial is (2 · x + 6) + 2 / (2 · x - 1).

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The relationship between x and y is y = 0.25x + 1.

Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form. One of the formulas used to get a line's equation is the slope-intercept formula. Y = mx + b is the slope-intercept formula for a line with slope m and y-intercept b. Any point on the line is (x, y) in this case.

Given,

A basket with 4 apples weighs 2 pounds.

Slope intercept form:

y = mx + b

Equation:

2 = 4m +b ..(1)

A basket with 12 apples weighs 4 pounds

4 = 12m + b ... (2)

Solving,

2 = 4m + b

4 = 12m + b

4 = 8m

Divide the second equation by 8:

2 = 4m + b

m = 0.25

b = 1

The relationship between x and y is y = 0.25x + 1.

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Answer:

9+11i

Step-by-step explanation:

The probability that a particular driver had fewer than two speeding violations is 0.825.

To find the probability that a particular driver had fewer than two speeding violations, we will analyze the given data:

Number of Violations - Number of Drivers
0 - 115
1 - 50
2 - 15
3 - 10
4 - 6
5 or more - 4

Total number of drivers: 200

1: Identify the number of drivers with fewer than two speeding violations. This includes drivers with 0 and 1 violations.

0 violations: 115 drivers

1 violation: 50 drivers

2: Add the number of drivers with 0 and 1 violations together.

115 + 50 = 165 drivers

3: Calculate the probability by dividing the number of drivers with fewer than two speeding violations (165) by the total number of drivers (200).

Probability = 165 / 200

4: Convert the fraction to a decimal and round to three decimal places.

Probability = 0.825

Hence, there is a 0.825 probability that a particular driver had fewer than two speeding violations.

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The expected number of rolls required until two different faces appear when rolling a die repeatedly is 1 + 6/5. This is explained by considering probabilities of different outcomes, using the concept of expected value.

In the first roll, there are 6 equally likely outcomes corresponding to each face of the die. Therefore, the probability of obtaining a different face in the first roll is 5/6. If this happens, the experiment ends with just one roll.

If the first roll results in the same face, the experiment continues. In the second roll, there are now 5 equally likely outcomes remaining, and the probability of obtaining a different face is 4/5. If a different face appears in the second roll, the experiment ends with two rolls.

Continuing this pattern, in the third roll, the probability of obtaining a different face is 3/5. Similarly, in the fourth roll, the probability is 2/5, and in the fifth roll, the probability is 1/5.

To find the expected number of rolls, we multiply each probability by the corresponding number of rolls and sum them up. This gives us

(1× 5/6) + (2× 1/6× 4/5) + (3×1/6× 1/5) = 1 + 6/5, which is the expected number of rolls until two different faces appear.

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Answer:

Answer:

10.4 inches per minute

Step-by-step explanation:

52 ft -> 60 mins

624 in -> 60 mins

10.4 -> 1 min

Hello User,

Answer:

10.4 in per min

Step-by-step explanation:

First multiply 52 by 12 to get inches per hour. 624 in per hour. Then make it 624 inches in 60 minutes. Divide 624 by 60 to get 10.4. So it's speed in inches per minute is 10.4 in per min.

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer:

angle 3=83(vertically opposite angles are equal)

angle 5=angle 3(alternate interior angles) so = 83

angle 7 =angle 5 ( vertically opposite angles)

angle 2 +angle 1=180 (linear pair ) so angle 1 + 180-83=97

angle 4 = angle 2 (VOA)=97

angle 6 =angle 4 (AIA)=97

angle 8 =angle 6(VOA)=97

hope it helped plz mark me as brailiest

Step-by-step explanation:

Answer:

Line 2 and Line 4 are perpendicular

Step-by-step explanation:

Line 2: y=1/5x−3

Line 4: y+1=−5(x+2)

The missing sides of the special right triangles are listed below:

Case 1: y = √2 · 13, x = 13

Case 2: x = y = 15√2

Case 3: x = 6, y = 3√3

Case 4: x = 17√3, y = 17

Case 5: x = y = 10

Case 6: x = 50, y = 25

Case 7: x = y = 4√7

Case 8: x = 16√3, y = 8√3

Case 9: x = 11√3, y = 33

Case 10: x = 3√2, y = 2√6

Case 11: x = √10, y = 2√5

Case 12: x = 4√7, y = 8√21

Herein we find twelve cases of special right triangles whose missing sides must be determined by using the following rules:

45 - 90 - 45 Right triangle

r = √2 · x = √2 · y

30 - 60 - 90 Right triangle

x = (1 / 2) · r

y = (√3 / 2) · r = √3 · x

Where:

Case 1

y = √2 · 13

x = 13

Case 2

x = y = 15√2

Case 3

x = 3 / (1 / 2)

x = 6

y = 3√3

Case 4

x = 34 · (√3 / 2)

x = 17√3

y = 34 · (1 / 2)

y = 17

Case 5

x = y = 10

Case 6

x = 25√3 / (√3 / 2)

x = 50

y = 25√3 / √3

y = 25

Case 7

x = y = 2√14 · √2 = 2√28 = 4√7

Case 8

x = 24 / (√3 / 2)

x = 48 / √3

x = 16√3

y = 24 / √3

y = 8√3

Case 9

x = 22√3 · (1 / 2)

x = 11√3

y = 22√3 · (√3 / 2)

y = 33

Case 10

x = √18

x = 3√2

y = √6 / (1 / 2)

y = 2√6

Case 11

x = √10

y = √20

y = 2√5

Case 12

x = 4√21 / √3

x = 4√7

y = 4√21 / (1 / 2)

y = 8√21

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Answer:

-3/10

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-6-(-9))/(-3-7)

m=(-6+9)/-10

m=3/-10

m=-3/10

a) The union of all nonempty bit strings of length not exceeding n (⋃ni=1Ai) is the set of all nonempty bit strings of length 1 to n.

b) The intersection of all nonempty bit strings of length not exceeding n (⋂ni=1Aj) is an empty set, as there are no common bit strings among all Ai sets.

a) To find ⋃ni=1Ai, follow these steps:
1. Start with an empty set.
2. For each i from 1 to n, add all nonempty bit strings of length i to the set.
3. Combine all sets to form the union.


b) To find ⋂ni=1Aj, follow these steps:
1. Start with the first set A1, which contains all nonempty bit strings of length 1.
2. For each set Ai (i from 2 to n), find the common elements between Ai and the previous sets.
3. As there are no common elements among all sets, the intersection is an empty set.

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The solution of the initial value problem y' = 2xy² ; y(1) = 1/2 is y(x) = -1/(x² - 3)

An initial value problem is a differential equation that contains the initial values of the variables of the differential equation.

Given the initial value problem

y' = 2xy² ; y(1) = 1/2

So, we solve the differential equation as follows

y' = 2xy²

dy/dx = 2xy²

Separing the variables, we have

dy/y² = 2xdx

Integrating both sides of the equation, we have

∫dy/y² = ∫2xdx

∫dy/y² = 2∫xdx

We know that ∫xⁿ = xⁿ⁺¹/(n + 1)

So, integrating the expressions, we have

y⁻²⁺¹/(-2 + 1) = 2x¹⁺¹/(1 + 1)

y⁻¹/(-1) = 2x²/2 + c

-y⁻¹ = x² + c

Given that y(1) = 1/2, substituting these into the equaqtion, we have

-y⁻¹ = x² + c

-(1/2)⁻¹ = 1² + c

-2 = 1 = c

c = -2 - 1

c = -3

So, -y⁻¹ = x² + c

-y⁻¹ = x² - 3

Dividing through by - 1, we have

y⁻¹ = -(x² - 3)

Taking the inverse of both sides, we have

y(x) = -1/(x² - 3)

So, y(x) = -1/(x² - 3)

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Answer:

64% male

36% female

Step-by-step explanation:

We know

A class has 50 students, 18 female, and 32 male.

If a representative is chosen in their class, what is the probability of having a male?

32 divided by 50, times 100 = 64%

So, 64% that the representative is male.

If a representative is chosen for their class, what is the probability of having a female?

18 divided by 50, times 100 = 36%

So, 36% that the representative is female.

The solution of the periodic function is explained below.

A periodic function is a function that repeats its values after a certain interval of time, called its period.

The periodic function f(t) is defined on its period –2 ≤ t ≤ 2 and is described by the formula:

f(t) = t^2, when -2 ≤ t < 0

f(t) = -t^2, when 0 ≤ t ≤ 2

a) Plotting the function on the interval -8 ≤ t ≤ 8 would show us the repeating pattern of the function. To plot the function, we need to evaluate it for different values of t and plot the corresponding points on the coordinate plane.

b) The period of the function can be found by determining the smallest interval in which the function repeats. In this case, the period of the function is 2.

c) To determine whether the function is odd or even, we need to check if f(-t) = f(t) or f(-t) = -f(t). In this case, the function is an even function as f(-t) = f(t).

d) The mean value of the function on its period can be found by finding the average value of the function over one period. This is given by the formula:

(1/period) * ∫_0^period f(t) dt

e) The Fourier coefficients of the function can be found by using the formula:

ak = (2/period) * ∫f(t) cos(kπt/period) dt

bk = (2/period) * ∫f(t) sin(kπt/period) dt

f) The Fourier series of the function can be found by using the Fourier coefficients. This is given by the formula:

=> f(t) = a0/2 + ∑_(n=1)^∞

g) The first four terms of the Fourier series can be found by finding the first four values of the sum in the Fourier series formula. To find the explicit form, we need to evaluate the integrals and the sums.

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Using trigonometric ratio, the length of BE is 10 units, the value of sin B is 0.64 and cos B is 0.64 respectively

This is the ratio between the angles and sides of a right-angle triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In this problem, we have that

1)

Using tangent of B

tan B = opposite / adjacent

tan B = NE / BE

3/4 = 7.5 / BE

BE = 7.5 / 0.75

BE = 10

2)

To find sin B, we need to calculate the hypothenuse of the triangle which we will use Pythagoras's theorem

NB² = BE² + NE²

NB² = 10² + 7.5²

NB = 12.5

sin B = NE / NB

sin B = 7.5 / 12.5

B = sin⁻¹ (7.5 / 12.5)

B = 0.64

3)

cos B = BE / NB

cos B = 10 / 12.5

B = cos⁻¹ (10/12.5)

B = 0.64

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The interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

The graph of the two functions alongside their equations are the given parameters of this question

The functions are given as:

f(x) = 5x - x^2

g(x) = 3x - 0.5x^2

When the graphs of two curves or lines intersect on a coordinate plane, it means that the point of intersection represents where the graphs have equal value

In this case, it represents

f(x) = g(x)

Substitute the known values in the above equation

5x - x^2 = 3x - 0.5x^2

So, the interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

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The value of p-hat (the sample proportion) is 0.24, or 24% if total number of skittles in a sample is 300 out of which 72 skittles are purple.

The sample proportion, denoted by p-hat, is the proportion of purple skittles in the sample. We can calculate p-hat by dividing the number of purple skittles by the total number of skittles in the sample

p-hat = number of purple skittles / total number of skittles in sample

In this case, we have

Number of purple skittles = 72

Total number of skittles in sample = 300

Therefore,

p-hat = 72/300 = 0.24

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In the discrete distribution the probability that x equals 5 is 0.51

A discrete probability distribution counts occurrences that have countable or finite outcomes. This is in contrast to a continuous distribution, where outcomes can fall anywhere on a continuum

The summation of the discrete probabilities must be always equal 1,

The probaility of 2 is 0.16

The probaility of 6 is 0.30

The probaility of 8 is 0.21

We need to find The probaility of 5

To find the probaility of 5, we can subtract the probaility of all other numbers from 5.

Probability (X = 5) = 1 - (0.25+0.16+0.08) = 0.51

Therefore, in the discrete probability distribution the probability that x equals 5 is 0.51

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