14. What is the Kaplan-Meier estimator used for? Estimating the probability density function of a continuous random variable. Estimating the mean of a discrete random variable. Estimating the survival function from right-censored data. Estimating the cumulative distribution function of a continuous random variable.

Answer:

Let's use variables to represent the unknowns:

Let x be the number of psychology textbooks sold.

Then, the number of history textbooks sold is 2x (twice the number of psychology textbooks sold).

The problem tells us that the total number of textbooks sold is 237, so we can set up an equation:

x + 2x = 237

Simplifying and solving for x:

3x = 237

x = 79

Therefore, 79 psychology textbooks were sold and 2x = 158 history textbooks were sold.

Step-by-step explanation:

The constant of proportionality between the plant's height and time in weeks is 2 inches/week. So,correct answer is (D) 2.

The constant of proportionality is a factor that relates two variables that are directly proportional, indicating the ratio of change between them.

We can use the given information to determine the constant of proportionality between the plant's height and time in weeks.

The plant's height increased by 6 - 0 = 6 inches in the first three weeks (from week 0 to week 3). Therefore, the rate of growth during this period was 6 inches / 3 weeks = 2 inches/week.

Similarly, the plant's height increased by 10 - 6 = 4 inches during the next two weeks (from week 3 to week 5), so the rate of growth during this period was 4 inches / 2 weeks = 2 inches/week.

Finally, the plant's height increased by 14 - 10 = 4 inches during the last two weeks (from week 5 to week 7), so the rate of growth during this period was also 4 inches / 2 weeks = 2 inches/week.

Since the plant grows at a constant rate, we can assume that the rate of growth was 2 inches/week throughout the entire period from week 0 to week 7.

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a. The surface area of the outer square pyramid is 11.25 square centimeters. b. The side length of the inner square pyramid is 2.25 centimeters.

a. To find the surface area of the outer square pyramid, we need to calculate the area of each of its faces and add them together. The outer square pyramid has four triangular faces and a square base.

Area of a triangular face = (1/2) x base x height

Area of a triangular face = (1/2) x 1.5 cm x 3 cm = 2.25 cm²

The area of the square base can be found using the formula for the area of a square:

Area of square base = side length²

Area of square base = 1.5 cm x 1.5 cm = 2.25 cm²

Therefore, the total surface area of the outer square pyramid is:

Surface area = 4 x area of triangular face + area of square base

Surface area = 4 x 2.25 cm² + 2.25 cm²

Surface area = 11.25 cm²

Therefore, the surface area of the outer square pyramid is 11.25 square centimeters.

b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. Let's call the side length of the inner square pyramid "x". Since the ratio of the dimensions is 2:3, we know that the side length of the outer square pyramid is (3/2)x.

The volume of a square pyramid can be calculated using the formula:

Volume = (1/3) x base area x height

Since the two pyramids are similar, the ratio of their volumes is the cube of the ratio of their corresponding side lengths:

Volume of inner pyramid / Volume of outer pyramid = (x / (3/2)x)³ = (2/3)³

We also know that the volume of the outer pyramid is:

Volume of outer pyramid = (1/3) x base area x height

The height of the two pyramids is the same, since they are stacked on top of each other, so we can write:

Volume of inner pyramid / Volume of outer pyramid = (1/3) x base area of inner pyramid / (1/3) x base area of outer pyramid

Simplifying this expression, we get:

(x / (3/2)x)³ = (1/3) x² / (1/3) (3/2x)²

Solving for x, we get:

x = (3/2)²

x = 2.25

Therefore, the side length of the inner square pyramid is 2.25 centimeters.

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The complete question is :

a. For the outer square pyramid, the side length of the base is 1.5 centimeters and the height of one of the triangular faces is 3 centimeters. What is the surface area of the outer square pyramid?

b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid?

The y-intercept is (0, -20) and the x-intercept is (20, 0).

what is an algebraic expression?

An algebraic expression is a mathematical phrase consisting of variables, numbers, and mathematical operations. It can include variables (such as x, y, or z), constants (such as 2, 3, or 4), and operators (such as +, -, *, or /) that combine these elements.

For example, 2x + 3y - 4 is an algebraic expression that contains the variables x and y, the constants 2, 3, and 4, and the operators + and -. It does not contain an equal sign and does not represent an equation, but it can be simplified or evaluated for specific values of the variables. Algebraic expressions are commonly used in algebra and other branches of mathematics to represent mathematical relationships and solve problems.

The given equation is y = -32 + 12.

To find the y-intercept, we set x = 0 and solve for y:

y = -32 + 12

y = -20

So the y-intercept is (0, -20).To find the x-intercept, we set y = 0 and solve for x:

0 = -32 + 12

20 = x

So the x-intercept is (20, 0).

Therefore, the y-intercept is (0, -20) and the x-intercept is (20, 0).

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Answer:

x = 18

Step-by-step explanation:

[tex]\frac{6}{7}=\frac{x}{21} \\\\6*21=7*x\\\\126=7x\\\\x=18[/tex]

Therefore, the two possible values for AC are approximately 13.266 cm and 16.734 cm.

An assortment of similarly spaced out points in a plane make up a circle. The center is where the point is located, but the radius is the distance from the center. Two times the radius equals the diameter.

We can see that triangle ADC is a right triangle since it's inscribed in a semi-circle (the smaller circle). So we can use the Pythagorean theorem to find AC:

AC² = AD² - CD²

Since AD is the radius of the larger circle (15 cm) and CD is the radius of the smaller circle (7 cm), we have:

AC² = 15² - 7²

AC² = 176

AC = √(176)

AC ≈ 13.266 cm

So one possible value for AC is approximately 13.266 cm.

Now let's consider the other intersection point, D. We can see that triangle BDC is also a right triangle since it's inscribed in a semi-circle (the smaller circle). So we can use the Pythagorean theorem again to find BD:

BD² = BC² + CD²

Since BC is the radius of the larger circle (15 cm) and CD is the radius of the smaller circle (7 cm), we have:

BD² = 15² - 7²

BD² = 176

BD = √(176)

BD ≈ 13.266 cm

Since BD is a diameter of the larger circle, we have:

AC + BD = 2 * 15 = 30

So the other possible value for AC is:

AC = 30 - BD

AC ≈ 16.734 cm

Therefore, the two possible values for AC are approximately 13.266 cm and 16.734 cm.

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The area of the given figure is 94.29 [tex]in^{2}[/tex].

An object of area is how much space it takes up in 2-D. It is the measurement of object is unit squares than , completely cover the surface of a closed figure. The square unit, is frequently expressed as square inches, square feet,square meter,etc. is the accepted unit of area.

A shape is created by combining multiple  shapes is known as a composite figure. We add up all of outside sides of shape to find the perimeter. We  calculate the areas of each independently, and then add the resulting areas to determine the area.

First of all ,we will find the area of, the triangle.

The formula for area of a triangle =[tex]\frac{1}{2} *base* height[/tex].

According to question ,

base of triangle = 10 in.

Height of triangle =11 in.

value of base and height  substitute in formula than we get,

area of a triangle =[tex]\frac{1}{2} * 10 * 11[/tex]

area of a triangle= 1* 5*11

area of a triangle= 55 [tex]in^{2}[/tex].

Now,we will find the area of semi circle,

The formula for area of semi circle  =[tex]\frac{1}{2} \pi r^{2}[/tex]

According to question ,

[tex]r=\frac{10}{2} =5 in.[/tex] and use [tex]\pi =\frac{22}{7}[/tex]

area of semi circle=

[tex]=\frac{1}{2} *\frac{22}{7}*5^{2} \\\\=\frac{1}{2} *\frac{22}{7}*25\\\\=\frac{11}{7}*25}\\\\=1.57*25\\\\=39.29 in^{2}[/tex]

Now,area of given shape =

[tex]55 in^{2}+39.29 in^{2}\\\\=94.29 in^{2}[/tex]

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Answer:

Step-by-step explanation:

∠ADB = ∠CDB = 90°  (equal angles on a straight line are complimentary)

BD=BD                          (common side)

AD = CD                         (D is midpoint of AC)

∴[tex]\triangle[/tex]ABD ≡ [tex]\triangle[/tex]CBD          (SAS)  

I hope this is useful.

The value of the given product or expression is =1,

An algebraic equation is said to have an algebraic identity if it is true regardless of the values of its variables. An equality that remains constant when the values of the variables change are known as an algebraic identity, to put it simply. Algebraic identities are routinely used to factor polynomials more rapidly and efficiently.

Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The principles of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables. In an algebraic expression, both constants and variables can be employed. Any amount that is added before a variable and then multiplied by is a coefficient.

The given product can be solved by the algebraic identity,

[tex]a^2+2ab+b^2=(a+b)^2\\a^2-2ab+b^2=(a-b)^2[/tex]

[tex]899^2-2*899*898+898^2\\=(899-898)^2\\=1[/tex]

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a. Probability of candidate being forecast as the winner ≈ 17.78%

b. Probability of candidate being forecast as the winner ≈ 99.65%

c. Probability of candidate being incorrectly forecast as the winner ≈ 1.58%

d. 95% confidence interval for the true percentage of the candidate's vote ≈ (0.449, 0.651)

e. No, there is not sufficient evidence at 90% level of confidence that she has won the election.

a. If the population percentage of the candidate's vote is 50%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.50:

P(X ≥ 55) = 1 - P(X < 55) = 1 - binomial distribution (54, 100, 0.50, true)

≈ 0.1778

b. If the true percentage of the candidate's vote is 60%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.60:

P(X ≥ 55) = 1 - P(X < 55) = 1 - binomial distribution (54, 100, 0.60, true)

≈ 0.9965

c. If the true percentage of the candidate's vote is 49%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.49:

P(X ≥ 55) = 1 - P(X < 55) = 1 - binomdist(54, 100, 0.49, true) ≈ 0.0158

d. The 95% confidence interval for the true percentage of the candidate's vote can be calculated using the following formula:

CI = p ± zα/2 × √(p×(1-p)/n)

where p is the sample proportion (55/100=0.55), zα/2 is the critical value for a 95% confidence interval (1.96), and n is the sample size (100).

Substituting the values, we get:

CI = 0.55 ± 1.96 × √(0.55×(1-0.55)/100) ≈ (0.449, 0.651)

e. If 55% of a sample of 300 indicated that they have voted for her, the sample proportion is p=0.55 and the sample size is n=300. We can calculate the standard error of the sample proportion using the following formula:

SE = √(p×(1-p)/n) ≈ √(0.55×(1-0.55)/300) ≈ 0.0316

The margin of error for a 90% confidence interval can be calculated by multiplying the standard error by the critical value for a 90% confidence interval, which is approximately 1.645:

ME = 1.645 × SE ≈ 0.052

The 90% confidence interval for the true proportion can be calculated as:

CI = p ± ME ≈ 0.55 ± 0.052 ≈ (0.498, 0.602)

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Answer:

not possible since 3 + 4 < 8

The probability that you choose a 7 out of the deck of cards is P(A)= 1/13.

There are 52 cards in a standard deck of cards, with four of each type of card: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. Let event A be choosing a 7 out of a deck of cards. Identify the numbers of each of the following:

There are cards in the sample space. There are cards in event A. There are cards in the sample space. There are cards in event A. Probability that you choose a 7 out of the deck of cards is P(A)= 1/13. There are 52 cards in a standard deck of cards, with four of each type of card: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

We have to find out the probability of choosing 7 out of a deck of cards. The sample space is the total number of possible outcomes. Here, a standard deck of cards has 52 cards, so there are 52 possible outcomes. There are four 7s in the deck. So, there are 4 possible successful outcomes. Event A is defined as choosing a 7 out of a deck of cards.

Since there are four 7s, there are 4 possible outcomes in event A. Therefore, There are 52 cards in the sample space. There are 4 cards in event A. P(A) is the probability of choosing a 7 out of a deck of cards.

P(A) = number of successful outcomes/number of possible outcomes= 4/52= 1/13

Therefore, the probability that you choose a 7 out of the deck of cards is P(A)= 1/13.

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Answer:

Step-by-step explanation:

2a = -b - d + c

     = c - b - d

x = c/2 - b/2 - d/2

The vector a in terms of other vectors for the given vectors in the image is  c/2 - b/2 - d/2.

A vector is a quantity that determines both an object, its magnitude, and its direction.

The resultant vector is obtained when the tail of one vector is attached to the head of another vector such the resultant vector is formed from the sum of the two vectors.

Let a be the total vector of the given figure.

The vectors are written as:

2a = -b - d + c

a = c - b - d

a = c/2 - b/2 - d/2

Hence, the vector a in terms of other vectors is  c/2 - b/2 - d/2.

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The regular price of one baseball bat is $80.40.

A discount is a drop in a product's or service's price. It is often provided by the vendor as an inducement to lure customers into making a purchase. Often, the discount is indicated as a percentage or a dollar amount off the list price.

The standard price and the discount rate must be known in order to determine a discount. Often, the discount rate is expressed as a percentage. We multiply the usual price by the discount rate to determine the discount amount.

Given that, coach buys 5 identical baseball bats for a total of $327.45.

Thus,

5P = 327.45

P = 65.49

So one bat cost him 65.90.

Now, the regular cost of the bat will be:

Price = 65.90 + 14.50

Price = 80.40

Hence, the regular price of one baseball bat is $80.40.

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We can conclude after answering the provided question that We can see from the diagram that the sides of triangle XYZ are of varying lengths. As a result, XYZ is a scalene triangle.

A triangle is a closed, double-symmetrical object made up of three line segments called sides that meet at three points called vertices. Triangles can be identified by their sides and angles. Based on their sides, triangles can be equilateral (equal factions), isosceles, or scalene. Triangles can be acute (all angles less than 90 degrees), okay (one angle equal to 90 degrees), or orbicular (all angles greater than 90 degrees) (all angles greater than 90 degrees). A triangle's region can be calculated using the formula A = (1/2)bh, where a represents the neighborhood, b represents the triangle's base, and h represents the triangle's height.

We can see from the diagram that the sides of triangle XYZ are of varying lengths. As a result, XYZ is a scalene triangle.

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The statement is True. According to the Central Limit Theorem, in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n).

1. The Central Limit Theorem states that the distribution of the sample means of a large sample size will approach a normal distribution, regardless of the original distribution of the population from which the sample is drawn.
2. For a sufficiently large sample size, the mean of the sample means will approach the population mean (μ) and the standard deviation of the sample means will approach the population standard deviation divided by the square root of the sample size (σ/sqrt(n)).
3. Therefore, in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n).

This is the case because the Central Limit Theorem states that the distribution of sample means is approximately normal, regardless of the original distribution of the population from which the sample is drawn.

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Step-by-step explanation:

we simply use the definitions in the main expression.

f(x) = -3x²

therefore,

f(x + h) = -3(x + h)² = -3(x² + 2hx + h²) = -3x² - 6hx - 3h²

so, we have

((-3x² - 6xh - 3h²) - -3x²)/h

(-3x² - 6xh - 3h² + 3x²)/h

(-6xh - 3h²)/h

this is then

-6x - 3h

and for the limit of h going to 0 this is -6x.

Step-by-step explanation:

let the smallest angle = x

tan x = 5/8

x = arctan 5/8

x = 32°

Answer: The smallest angle of the triangle is 32°

Step-by-step explanation:

Given: 

one side of the triangle= 8 cm

The other side of the triangle = 5 cm

Angle between AB and BC = 90°

⇒ ∠ABC = 90°

ΔABC is a right angled triangle

Use trigonometric function: For X

tanx= AB/CB

tanx= 8/5

x=tan-1 (8/5)

x= 58°

Use trigonometric function: For Y

tany= BC/AB

tany=5/8

y=tan-1 (5/8)

y = 32°

Making 32° be the smallest angle of the triangle

Answer:

Step-by-step explanation:

If the value of the car has decreased by 44%, it still retains 56% of its value. Thus, the solution for the depreciation is 63,765(.56) = $35,708.40

Answer:

[tex]\huge\boxed{\sf 48.3 \ miles}[/tex]

Step-by-step explanation:

Given that,

1 day = 6.9 miles

1 × 7 days = 6.9 × 7 miles

[tex]\rule[225]{225}{2}[/tex]

Answer:

7 days = 48.3 miles

Step-by-step explanation:

Given information,

→ Ronald bikes 6.9 miles every day.

Now we have to,

→ Find the distance travelled in 7 days.

General formula we use,

→ Distance travelled × Number of days

Then the distance travelled will be,

→ Miles × Days

→ 6.9 × 7

→ 48.3 miles

Hence, the answer is 48.3 miles.

Answer:

h(t) = 40 cos(π/22.5 t) + 10.

Step-by-step explanation:

The function that models Amelia's height, h, at time t can be written as:

h(t) = r cos(ωt) + a

where:

r is the radius of the ferris wheel (40 m)

a is the initial height of the cart above the ground (10 m)

ω is the angular velocity of the ferris wheel, which is equal to 2π divided by the time for one complete rotation (T)

T is the time for one complete rotation, which is given as 45 seconds

To find ω, we can use the formula:

ω = 2π/T

ω = 2π/45

ω = π/22.5

Substituting the values into the function, we get:

h(t) = 40 cos(π/22.5 t) + 10

Therefore, the function that models Amelia's height, h, at time t since she got on the ride is h(t) = 40 cos(π/22.5 t) + 10.

Based on the above, the 7 melons together will weigh about 21,000 grams.

We know that 2 melons of the same size together weigh 6 kg, therefore each melon weighs:

6kg / 2 = 3kg

To know how many grams the 7 melons weigh, we first need to know how many grams a kilogram weighs:

1kg = 1000g

So each melon weighs 3 kg * 1000 g/kg = 3000 g.

Therefore, 7 melons equal to the ones Alberto bought will weigh:

7 * 3000g = 21,000g

Therefore, the 7 melons together will weigh 21,000 grams.

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See text below

Alberto bought 2 melons of the same size and together they weigh 6 kg. How many grams will 7 melons equal to the ones Alberto bought weigh?

The hypotenuse measures 3 cm in length. (Using the Pythagorean theorem: c2 = a2 + b2 where c is the hypotenuse and a and b are the other two sides.)

According to the Pythagorean theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the legs. This formula may be used to get the hypotenuse length of a right triangle with sides that are 4 and 5 cm long.

With the Pythagorean theorem in use, we have:

2 hypotenuse Equals 4 + 5

(2)Hypotenuse = (16 + 25)

Hypotenuse 2 equals 41

When we square the two sides, we obtain:

41 cm is the hypotenuse.

Hence, the right triangle's hypotenuse measures around 6.4 cm in length (rounded to one decimal place).

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It will take the Stand family approximately 29.17 hours to reach Disneyland, including the breaks taken every two hours.

The total time taken can be calculated as:

Here, distance = 860 miles, speed = 60 mph, and breaks are taken every two hours, which means 430 miles of driving before each break.

So, the equation becomes:

Simplifying the equation, we get:

Therefore, it will take the Stand family approximately 29.17 hours to reach Disneyland, including the breaks taken every two hours.

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The shaded region representing the possible combinations of ticket sales is given by the image presented at the end of the answer.

The region containing the possible combinations is obtained using a system of inequalities, for which the variables are given as follows:

The amounts cannot be negative, as they are countable amounts, hence:

Each member of the team must make a minimum of $300, hence:

60x + 20y ≥ 300.

They cannot sell more than 10 tickets, hence:

x + y ≤ 10.

The graph containing the region that respects these four constraints is given by the image presented at the end of the answer.

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The brown cows produced more milk than the white cows in the given situation.

"Same amount" means that two or more quantities are equal to each other in terms of their numerical value or quantity.

To find out whether the brown cows produce more milk or the white cows, we can make a ratio of milk produced by both the herds in one day.

For this, let’s assume the amount of milk produced by a white cow in one day is “w” and the amount of milk produced by a brown cow in one day is “b”.

Then, The amount of milk produced by eight white cows in 1 day = 8w.

The amount of milk produced by six brown cows in 1 day = 6b.

The amount of milk produced by six white cows in 1 day = 6w.

The amount of milk produced by ten brown cows in 1 day = 10b.

According to the given condition, both herds produce the same amount of milk in one day.

Therefore, 8w × 10 = 6w × 86w × 5/3

                               = 10b5w/4 = 5b/2b

                               = (5w/4) × (2/5)

                               = w/2

We can say that a brown cow produces double the milk produced by a white cow. Hence, brown cows produced more milk than the white cows in the given situation.

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Answer:

8pi

Step-by-step explanation:

Since the triangle is a 30-60-90 triangle, the hypotenuse is 2 times the shortest side and the second longest side is sqrt3 times the shortest side. Since it is given that the second longest side is 4sqrt3, this means that the shortest side is 4, so the hypotenuse is 8.

Because of this, the diameter is 8, which means the radius is half of the diameter, which is 4.

The formula for circumference is 2*pi*r, and since r is 4, we can plug this in to get 2*pi*4, which is 8pi.

Answer:

-51 would be the answer for this equation.

Step-by-step explanation: