Suppose we have a random sample of size n = 5 from a continuous uniform distribution on the interval [0, 1]. Find the probability that the third largest observation in the
sample is less than 0.7.

The function [4x⁻⁴ - 3x ³ + 6x -10]/ x +1 is described accordingly.

The graph of the function [4x⁻⁴ - 3x³ + 6x - 10]/(x + 1) represents a rational function.

It may exhibit vertical asymptotes at x = -1, where the function approaches infinity or negative infinity.

The graph can also have x-intercepts and may show different behavior based on the values of x.

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Full question

Describe the [4x⁻⁴ - 3x ³ + 6x -10]/ x +1

The length of AB in the triangle is 9 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Therefore, the side AB can be found as follows:

AC = 27 units

CD = 9 units

DB = 3 units

Therefore, let's find the height of the triangle. AD is an angle bisector. Angle bisector theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Using angle bisector theorem,

AC / AB =  CD / DB

Therefore,

27 / AB = 9 / 3

cross multiply

AB = 81 / 9

AB = 9 units

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An equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, −2) is y = 3x - 5.

Here, we have,

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

m represent the slope.

x and y represent the points.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 6)/(0 + 3)

Slope (m) = -1/3.

For the equation of line g, we have:

y - 6 = (x + 3)

y - 6 = -1/3(x + 3)

y = -x/3 + 1 + 6

y = -x/3 + 7

Therefore, the slope, m = -1/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1/3 × m₂ = -1

m₂ = 3

At data point (1, -2), an equation of this line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - (-2) = 3(x - 1)

y + 2 = 3x - 3

y = 3x - 5

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The following table shows the number of hours 45 hospital patients slept for one night. Use the table to answer the questions:Hours of Sleep | Patients0-2 | 53-5 | 96-8 | 179-11 | 2212-14 | 10a) How many patients slept between 6 and 11 hours?A total of 22 patients slept between 6 and 11 hours.

To find out, we need to add the number of patients who slept for 6-8 hours (17) and those who slept for 9-11 hours (5). Therefore, 17+5=22.b)

The mode is the value that occurs most frequently in the data set. In this case, the mode is the number of hours that the highest number of patients slept.

From the table, we can see that 9-11 hours is the mode because 22 patients slept for that number of hours, which is more than any other number of hours.c)

The median is the middle value in the data set when the data are arranged in numerical order. In this case, we have 45 patients, so we need to find the middle value between the 22nd and 23rd patients. These patients slept for 9-11 hours, so the median is 9-11 hours.

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Answer:

504 voice cracks per week
72 voice cracks per day

Step-by-step explanation:

If Danny's voice cracks every 20 minutes, we can calculate the number of times his voice cracks in a day and in a week.

Number of times his voice cracks in a day:

There are 60 minutes in an hour, so there are 60/20 = 3 intervals of 20 minutes in an hour.

Since there are 24 hours in a day, Danny's voice cracks 3 times per hour * 24 hours = 72 times in a day.

Number of times his voice cracks in a week:

Since there are 7 days in a week, we can multiply the number of times his voice cracks in a day by 7.

Danny's voice cracks 72 times per day * 7 days = 504 times in a week.

The value of length of side AB is,

⇒ AB = 5 units

We have to given that;

The figure is shown a trapezoid.

Hence, By using Pythagoras theorem we get;

⇒ AB² = 4² + (5.25 - 2.25)²

⇒ AB² = 16 + 3²

⇒ AB² = 16 + 9

⇒ AB² = 25

⇒ AB = √25

⇒ AB = 5 units

Therefore, The value of length of AB is,

⇒ AB = 5 units

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The relative change in average television sizes is 5.94%.

To calculate the absolute change in average television sizes, we subtract the initial average size from the final average size:

Absolute change = Final average size - Initial average size

Absolute change = 42.8 inches - 40.4 inches

Absolute change = 2.4 inches

Therefore, the absolute change in average television sizes from the time of Joseph's deployment to the time he returned is 2.4 inches.

To calculate the relative change in average television sizes, we divide the absolute change by the initial average size and then multiply by 100 to express it as a percentage:

Relative change = (Absolute change / Initial average size) × 100

Relative change = (2.4 inches / 40.4 inches) × 100

Relative change = 0.05940594× 100

Relative change = 5.94%

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The  mean is 5.907, and the standard deviation is 0.677.

To construct a binomial probability distribution, we need the parameters n and p, where n is the number of trials and p is the probability of success in each trial.

From the provided data, it appears that we have the probability distribution for a binomial random variable X with n = 6 trials. The probabilities are as follows:

P(0) = 0.0156

P(1) = 0.0938

P(2) = 0.2344

P(3) = 0.3125

P(4) = 0.2344

P(5) = 0.0938

P(6) = 0.0156

The sum of these probabilities should be equal to 1.

Now, let's compute the mean (μ) and standard deviation (σ) using the formulas:

μ = np

σ = √(np(1 - p))

So, p = P(success)

= P(1) + P(2) + P(3) + P(4) + P(5) + P(6)

= 0.0938 + 0.2344 + 0.3125 + 0.2344 + 0.0938 + 0.0156

= 0.9845

Now, we can calculate the mean and standard deviation:

μ = np = 6 x 0.9845 ≈ 5.907

σ = √(np(1 - p))

= √(6 x 0.9845 x (1 - 0.9845))

= 0.677

Therefore, the mean is 5.907, and the standard deviation is 0.677.

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Answer:

C

Step-by-step explanation:

(i)

given a triangle with 2 sides and the included angle known

to find the third side use the Cosine rule

a² = b² + c² - 2bc cosA

adapting the formula to describe Δ PQR

r² = p² + q² - 2pq cosR

here r = PQ, p = QR = 7.6 , q = PR = 8.4 and ∠ R = 62° , then

r² = 7.6² + 8.4² - (2 × 7.6 × 8.4 × cos62° )

  = 57.76 + 70.56 - 59.942

  = 128.32 - 59.942

  = 68.376 ( take square root of both sides )

r = [tex]\sqrt{68.378}[/tex]

  ≈ 8.27

that is PQ ≈ 8.27 cm ( to 2 decimal places )

(11)

the area (A) is then calculated as

A = [tex]\frac{1}{2}[/tex] pq sinR

  = 0.5 × 7.6 × 8.4 × sin62°

  ≈ 28.2

that is area of Δ PQR ≈ 28.2 cm² ( to 1 decimal place )

Answer:

c

Step-by-step explanation:

I think it's c I might be wrong though not sure

Answer: Total visitors =1500

Step-by-step explanation:

By rounding off each no. nearest to 100 is :

185=200, 349=300, 107=100, 355= 400. 451= 500

By adding round off  no. i.e.200+300+100+400+500= 1500

So total no. of visitors were 1500

Answer:

S = π(6^2) + π(6)(9) = 90π

= about 283 cm^2

Using π = 3.14:

S = 90(3.14) = about 283 cm^2

(a) The given sequence 2,4,8,..... is a geometric sequence, that is, the common ratio of the sequence is the same.

The next term, that is, the fourth term of the sequence can be found with the help of the nth term formula of G.P.(Geometric progression) which is given as

Aₙ = arⁿ⁻¹ where a is the first term and r is the common ratio.

Aₙ = (2)(2)⁴⁻¹

    = (2)(2)³

    = 16

(b) Putting n= 1,2,3,4 one by one in 2ⁿ, we have

2¹ =2

2²=4

2³=8

2⁴= 16

Now evaluating n²-n+2 by putting n=1,2,3,4

Putting n=1, we have

n²-n+2 = (1)²-1+2

            = 1-1+2=2

Putting n=2, we have

n²-n+2 = (2)²-2+2

            = 4-2+2

            =4

Putting n=3, we have

n²-n+2 = (3)²-3+2

            = 9-3+2

            = 6+2

            =8

Putting n=4, we have

n²-n+2 = (4)²-4+2

           = 16-4+2

           = 14

Now evaluating n³-5n²+10n-4 by putting n=1,2,3,4

Putting n=1,

(1)³-5(1)²+10(1)-4

= 1-5+10-4

= -4+6

= 2

Putting n=2,

(2)³-5(2)²+10(2)-4

= 8-20+20-4

= 4

Putting n=3,

(3)³-5(3)²+10(3)-4

=27-45+30-4

=8

Putting n=4,

(4)³-5(4)²+10(4)-4

=20  

c) 2ⁿ is a geometric sequence, but the other two do not have the same ratio and hence their nth term can not be found by G.P.

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Answer:

A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Step-by-step explanation:

The diameter of a sunflower pollen grain is [tex]3.0 * 10^{-5}[/tex] meters.

The diameter of a ginger pollen grain is [tex]1.5 * 10^{-4}[/tex] meters.

We can divide the diameter of the sunflower pollen grain by the diameter of the ginger pollen grain to compare the sizes of these grains.

This gives us:

[tex]\frac{3.0 * 10^{-5} }{1.5 * 10^{-4 }}= 0.2[/tex]

This means that a sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

So the answer is A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Answer: Your answer is B. A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Step-by-Step Explanation: Take them both and divide them (3.0*10^(-5))/(1.5*10^(-4)) Solving the equations first and that makes:

Scientific Notation 2⋅10^−1

Or expanded form 0.2

Hope it helped :D

The probability that a randomly selected point within the square falls in the red-shaded square is approximately 0.4444, or 44.44%.

To find the probability that a randomly selected point within the square falls in the red-shaded square, we need to compare the areas of the red square and the larger square.

The area of the larger square is given by the formula:

Area = side length x side length

In this case, the side length of the larger square is 3 units, so its area is:

Area of larger square = 3 x 3 = 9 square units

The area of the red square is given by the formula:

Area = side length x side length

In this case, the side length of the red square is 2 units, so its area is:

Area of red square = 2 x 2 = 4 square units

To find the probability, we divide the area of the red square by the area of the larger square:

Probability = Area of red square / Area of larger square

Probability = 4 / 9

Therefore, the probability that a randomly selected point within the square falls in the red-shaded square is approximately 0.4444, or 44.44%.

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Answer:

To calculate the future value of an investment compounded annually, we can use the formula:

Future Value = Principal Amount * (1 + Interest Rate)^(Number of Periods)

In this case, the principal amount is $3200, the interest rate is 2.4% (or 0.024), and the investment is compounded annually for 4 years.

Plugging these values into the formula, we get:

Future Value = $3200 * (1 + 0.024)^4

Calculating the exponent first:

(1 + 0.024)^4 = 1.024^4 = 1.09985925696

Multiplying the principal amount by the exponent:

Future Value = $3200 * 1.09985925696

Future Value ≈ $3,519.47

Therefore, the investment will be worth approximately $3,519.47 after 4 years when compounded annually at a rate of 2.4%.

Step-by-step explanation:

Answer:

57° + 108° + p = 180°

165° + p = 180°

p = 15°

Answer:

3a units^2

Step-by-step explanation:

Area = 6ah^2 + 9a = 1/2(b1 + b2) × (4h^2 + 6)

Simplify: 6ah^2 + 9a = 2h^2(b1 + b2) × 3(b1 + b2)

Factor out b1 + b2:

6ah^2 + 9a = (2h^2 + 3)(b1 + b2)

Express sum of lengths (divide both sides by 2h^2 + 3):

(b1 + b2) = 6a^2 + 9a / 2h^2 + 3

= 3 units^2

So, the sum of the lengths is 3 units^2 (in terms of a).

[tex]$\sigma={\sqrt {\frac {529+196+169+16+196+400+400}{7}}}$[/tex]The formula for calculating standard deviation is  [tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{n}}}[/tex], where

[tex]\sigma[/tex] is the population standard deviation, [tex]n[/tex] is the population size, [tex]x_{i}[/tex] is each value from the population, and [tex]\mu[/tex] is the population mean. We can substitute each value into the formula and simplify, which gives us our standard deviation.

[tex]$\sigma={\sqrt {\frac {(57-34)^{2}+(48-34)^{2}+(47-34)^{2}+(38-34)^{2}+(20-34)^{2}+(14-34)^{2}+(14-34)^{2}}{7}}}$[/tex]

[tex]$\sigma={\sqrt {\frac {(23)^{2}+(14)^{2}+(13)^{2}+(4)^{2}+(-14)^{2}+(-20)^{2}+(-20)^{2}}{7}}}$[/tex]

[tex]$\sigma={\sqrt {\frac {529+196+169+16+196+400+400}{7}}}$[/tex]

[tex]$\sigma={\sqrt {\frac {1906}{7}}}$[/tex]

[tex]$\sigma = \sqrt{272.285714286}$[/tex]

[tex]$\sigma \approx 16.5010822156$[/tex]

Our answer is [tex]$\sigma \approx 16.5010822156$[/tex], or, for convenience, [tex]$\sigma \approx 16.501082$[/tex], which is the most digits you'll probably need for any calculations you make.

Hope this helps!

The  average density of the planet is approximately 5.6g/cm³

The formula for density is expressed as;

D = m/v

Such that;

From the information given, we have that;

Volume = 1.02×10⁹ km³

Mass = 5.683 × 10²¹ kg

Convert the parameters

Volume = 1.02×10²⁴cm³

Mass = 5.683 × 10²⁴g

Substitute the values, we have;

Density = 5.683 × 10²⁴g/1.02×10²⁴cm³

Density = 5.6g/cm³

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You need to buy 29 feet of lumber to frame the outside of the sandbox.

To calculate the total amount of lumber you need to buy to frame the outside of the sandbox, you need to calculate the perimeter of the box.

The formula to calculate the perimeter of a rectangle is:

Perimeter = 2×(Length + Width)

Given that the dimensions of the sandbox are 6.3 ft. by 8.2 ft., we can substitute the values into the formula:

Perimeter = 2×(6.3 ft. + 8.2 ft.)

Perimeter = 2 × (14.5 ft.)

Perimeter = 29 ft.

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Answer:

I'm sorry, but you haven't provided any information about the function F(x). In order to determine the value of x when F(x) equals 7, I need to know the specific form or equation of the function. Could you please provide more details or the equation of F(x)?

Step-by-step explanation:

The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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The distance from the house that should place the base of the ladder is approximately 5.95 feet.

We can start by modeling the situation as a right triangle. Doing this will allow us to use basic trigonometric functions to determine how far the base of the ladder should be placed from the house. Imagine the house makes a 90 degree angle with the ground. The ladder gets propped against the house, making a 75 degree angle with the ground. We can use the fact that cos(75°) = base distance/length of ladder to figure out the length of the base. Multiplying both sides by length of ladder we get, length of ladder × cos(75°) = base distance. Now, by plugging in the length of the ladder we find that base distance = 5 2381/2500 or roughly 5.95 feet.

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Given statement solution is :- "3 and 5 - 1," the mean is 3.5, the median is 5, and there is no mode.

To find the mean, median, and mode for the given numbers, let's start by organizing the numbers in ascending order:

For "3 and 5":

Ascending order: 3, 5

Mean:

To find the mean, we sum up all the numbers and divide the total by the count of numbers.

Mean = (3 + 5) / 2 = 8 / 2 = 4

Median:

The median is the middle value in a set of numbers when they are arranged in ascending order. Since we have two numbers, the median is the average of the two middle numbers.

Median = (3 + 5) / 2 = 8 / 2 = 4

Mode:

The mode is the value that appears most frequently in a set of numbers.

In this case, there is no repeating value, so there is no mode.

For "3 and 5 - 1":

Ascending order: 2, 5

Mean:

Mean = (2 + 5) / 2 = 7 / 2 = 3.5

Median:

Median = 5 (since we have two numbers, the median is the average of the two middle numbers, which is 5 in this case)

Mode:

Again, there is no repeating value, so there is no mode.

Therefore, for "3 and 5," the mean and median are both 4, and there is no mode.

For "3 and 5 - 1," the mean is 3.5, the median is 5, and there is no mode.

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Answer:

Step-by-step explanation:

[tex]\frac{15}{7} or \frac{26}{9}[/tex]

The (g.f)(x)  of the two functions is:

(g.f) (x) = 6x + 37

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To find (g.f) (x), follow the steps below:

1. Substitute the value of f(x) into the function g(x).

2. Then simplify the expression.

That is:

f(x) = 3x+18

g(x) = 2x+1

Thus, we have:

(g.f) (x) = g(f(x))

(g.f) (x) = g(3x+18)

(g.f) (x) = 2(3x+18) + 1

(g.f) (x) = 6x+36 + 1

(g.f) (x) = 6x + 37

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The marginal cost for the fifth unit is $50. Hence, the correct option is b. $50.

To find the marginal cost for the fifth unit, we need to calculate the change in total cost when moving from producing 4 units to producing 5 units.

Total cost consists of both fixed costs and variable costs. The fixed costs remain constant regardless of the number of units produced, so they do not contribute to the marginal cost.

Variable costs, on the other hand, increase as more units are produced. The change in variable costs from producing 4 units to producing 5 units is $150 - $100 = $50.

Therefore, the marginal cost for the fifth unit is $50.

Hence, the correct option is b. $50.

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a.)The expression of David's money as a fraction would be = 2/3×h

b.) The amount of money they have together would be = $40.

To determine the fraction of Henry's money that is of David's, the following steps needs to be considered.

Let d represent David's money

Let h represent Henry's money

a.) Therefore, Fraction of Henry's money that belongs to David;

d = 2/3×h ----> 1

b.) d= 60+ h----->2

Substitute d= 60+h in equation 1;

60+h = 2/3h

60= 2/3h-h

60 = -1/3h

h= 60/3

h= -20

The total amount of money they both have= 60-20 = $40

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Complete question:

1/2 of David's money is 2/3 of Henry's money.

a) Express David's $ as a fraction of Henry's $.

b) If David has $60 more than Henry, how much money to they have altogether.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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The percent increase in Newark's population from 2010 to 2020 is 11.98%.

By comparing percent increases, the greatest percent increase occurred in the 1840s - 1850s decade with 124.83%.

To get percent increase, we have to find difference between the population in 2020 and 2010, divide it by the population in 2010, and then multiply by 100.

Population in 2010: 277,140

Population in 2020: 310,350

Percent increase = ((310,350 - 277,140) / 277,140) * 100

Percent increase = (33,210 / 277,140) * 100

Percent increase = 11.983113228

Percent increase = 11.98%.

To know decade with the greatest percent increase, we need to calculate percent increase for each decade and compare the values.

Percent increase for each decade goes as follows:

1840s to 1850s:

= ((38,864 - 17,290) / 17,290) * 100

≈ 124.83%

1850s to 1860s:

= ((71,941 - 38,864) / 38,864) * 100

≈ 85.08%

1860s to 1870s:

= ((105,059 - 71,941) / 71,941) * 100

≈ 45.87%

2010s to 2020s:

= ((310,350 - 277,140) / 277,140) * 100

≈ 11.97%

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