The following table shows the distance from the bus stop as a function of time: Time (in minutes) x Distance (in meters) f(x) 0 45 3 40 6 35 9 30 12 25 Find and interpret the meaning of the x-intercept in this scenario. (45, 0); the distance away from the bus stop (27, 0); the time it takes to reach the bus stop (45, 0); the time it takes to reach the bus stop (27, 0); the distance away from the bus stop

The probability that all a randomly chosen student has a schedule that excludes music theory, using the combination formula, is of:

p = 1/14.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

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

Without simplifying it, the probability that all a randomly chosen student has a schedule that excludes music theory is of:

\(p = \frac{C_{4,3}}{C_{8,3}}\)

The numeric value for each of these combinations is given as follows:

Hence the probability is given as follows:

p = 4/56.

The division of 56 by 4 has a quotient of 14, hence the simplified probability is of:

p = 1/14.

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To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.

To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.

What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).

What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value

step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)

Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)

Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11

Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)

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(a) Since all values are greater than 10, the sampling distribution is normally distributed.

(b) The mean of the sampling distribution is 0.23.

(c) The standard deviation of the sampling distribution is 0.1288.

(d) The probability that the difference in sample proportions (senior - junior) of students with parking passes is greater than 30% is -0.56.

In the given question, at Westville High School there are 315 seniors and 389 juniors.

65% of the seniors have parking passes and 42% of the juniors have parking passes.

The statistics teacher selects a SRS of 30 seniors and a separate SRS of 30 juniors.

Let be the difference in the sample proportions of seniors and juniors that have parking passes.

(a) We have to find the shape of the sampling distribution.

n1*p1 = 0.65*30 = 19.5 > 10

n1*(1 - p1) = (1 - 0.65)*30 = 10.5 > 10

n2*p2 = 0.42*30 = 12.6 > 10

n2*(1 - p2) = (1 - 0.42)*30 = 17.4 > 10

Since all values are greater than 10, the sampling distribution is normally distributed.

(b) We have to find the mean of the sampling distribution.

Mean = p1 - p2

Mean = 0.65 - 0.42

Mean = 0.23

(c) We have to calculate and interpret the standard deviation of the sampling distribution.

Pooled proportion, P' = (x1 + x2)/(n1 + n2)

P' = (0.65*30 + 0.42*30)/(30 + 30)

P' = 0.535

Standard deviation = √P'(1-P')*(1/n1 + 1/n2)

Standard deviation = √0.535(1- 0.535)*(1/30 + 1/30)

Standard deviation = 0.1288

(d) We have to find the probability that the difference in sample proportions (senior - junior) of students with parking passes is greater than 30%.

The test statistic, z = Mean - delta/√P'(1- P')*(1/n1 + 1/n2)

z = 0.23 - 0.30/0.1288

z = -0.56

The p-value is 0.7118. [Using NORMSDIST(z-value)]

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Here, we need to find the monthly and the weekly growth rate

The monthly growth rate is 99.33 ounces and the weekly growth rate is 22.9 ounces

Weight at birth = 8 ounces

Weight at one year =75 ounces

1 pound = 16 ounces

75 pounds = 1200 ounces

Additional weight after birth = Weight at one year - Weight at birth

= 1200 ounces - 8 ounces

= 1,192 ounces

There are 12 months in a year

Growth rate per month = Additional weight after birth / 12

= 1,192 / 12

= 99.33 ounces per month

There are 52 weeks in a year

Growth rate per week = Additional weight after birth / 52

= 1,192 / 52

= 22.9 ounces per week

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Using point estimation, the sample proportion falls between 0.2 and 0.4.

The sample distribution offers details on the point estimator to choose. If the distribution's mean matches the actual value of the population parameter, the estimator is considered to be impartial. As a result, the population percentage p and the sample proportion p ought to be quite similar.

The correct option is C, because the average of 0.2 and 0.4 is 0.3

At a large university it is known that 30% of the students live on campus. The director of student life is going to take a random sample of 500 students. Which of the following is most likely to occur?

a.) The sample proportion falls between 0.3 and 0.5.

b.) The sample proportion falls between 0.1 and 0.3.

c.) The sample proportion falls between 0.2 and 0.4.

d.) The sample proportion falls between 0.25 and 0.35.

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Answer:

the third angle of the triangle is 62°

62 grad

Step-by-step explanation:

Answer:13.93

Step-by-step explanation:

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

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Answer:

6 has the exponent of 1,  meaning that 6 does not need to be multiplied by it self. So it is simpily six.

9.332622e+157 or 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

What is Factorial?

The product of all positive integers less than or equal to a given positive integer, indicated by that integer plus an exclamation point, is known as Factorial in mathematics.

The approximate value of 100! is 9.3326215443944E+157.

The number of trailing zeros in 100! is 24.

The number of digits in 100 factorial is 158.

The factorial of 100 is calculated, through its definition, this way:

               100! = 100 • 99 • 98 • 97 • 96 … 3 • 2 • 1

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Answer: y-9 = 2(x-1)

Step-by-step explanation:

The program is an illustration of loops and conditional statements and the part of the complete program is

n = int(input())

for i in range(1,n+1):

  if not(i%3 == 0 or i%5==0):

The program written in Python where comments are used to explain each line is as follows:

#This gets input for n

n = int(input())

#This iterates through n

for i in range(1,n+1):

  #If the current number is not a multiple of 3 and 5

  if not(i%3 == 0 or i%5==0):

      #This prints the number

      print(i,end="")

  else:

      #This prints "Fizz", if the current number is a multiple of 3

      if i%3 == 0:

          print("Fizz",end="")

      #This prints "Buzz", if the current number is a multiple of 5

      if i%5==0:

          print("Buzz",end="")

  #This prints a new line

  print()

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The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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Answer: Maybe a

Step-by-step explanation:

I mean it is confusing but still look over it

Answer:

The bottom one looks correct

Step-by-step explanation:

Any number from 1-infinity will make that true

Answer:

Alex can buy "3" socks

Step-by-step explanation:

75- 25 =50

50- 29.99 = 20.01

20.01/ 6.26= 3.02

Since you can't get a portion of a sock you just take the first number (which is 3). Therefore, Alex can only buy three socks.  

Answer:

it would take 99 minutes

Answer:

99 minutes!

Step-by-step explanation:

Answer:

2/4 = 0.5

0.578

Step-by-step explanation:

so sin(π/4) is √2/2 squaring this gets your first answer

second answer is just plug and chug in a calculator

Answer:

i not know what you need me to help you

Step-by-step explanation:

The total cost of the taxi ride is given by the equation A = $ 19.25

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of taxi ride be represented as A

Now , the equation will be

The initial cost for the pickup = $ 3.50

The cost of the ride per mile = $ 1.75

The cost for riding 9 miles = 9 x cost of the ride per mile

Substituting the values in the equation , we get

The cost for riding 9 miles = 9 x 1.75 = $ 15.75

So , the total cost of taxi ride A = initial cost for the pickup + cost for riding 9 miles

The total cost of taxi ride A = 3.50 + 15.75

The total cost of taxi ride A = $ 19.25

So , if the ride is m miles long , the cost is A = 3.50 + ( 1.75 )m

Hence , the equation is A = $ 19.25

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Answer:

21i² + 45i + 24

Step-by-step explanation:

Answer:

-5-4i

Step-by-step explanation:

The total number of students in Ms. Morales's class is either 20 or 30, depending on the value of x.

Let the ratio of boys to girls in Ms. Morales's class be 3x:7x, where 3x represents the number of boys and 7x represents the number of girls.

The total number of students in the class is equal to the sum of the number of boys and the number of girls, which is 3x + 7x = 10x.

We don't know the value of x, but we do know that the class size is between 22 and 34 students.

Therefore, we can set up an inequality based on the total number of students:

22 ≤ 10x ≤ 34

Dividing all parts of the inequality by 10, we get:

2.2 ≤ x ≤ 3.4

Since x represents a whole number of students, the possible values for x are 3 (if there are 30 students in the class) or 2 (if there are 20 students in the class).

If x = 3, then the total number of students is:

10x = 10(3) = 30

If x = 2, then the total number of students is:

10x = 10(2) = 20

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Answer:

81989970383

Step-by-step explanation:

The given shape of the distribution is not symmetric.

Given that, a box plot shows donations in dollars to charity.

We need to describe the shape of the distribution.

Donations to Charity ($) =

20 40 60 80 100 120 140 160 180 200 220

so, as we can see,

The shape of the distribution is not symmetric since the lengths of each box and whisker are not the same. There is an outlier at 220.

Hence, the given shape of the distribution is not symmetric.

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a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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The area of each part of the figure is Triangle B = 10 square units and Triangle A = 17.5 square units. The area of the whole figure is 27.5 square units.

A two-dimensional surface, like the surface of a shape or object, can be measured in terms of area. Usually, it is expressed in square quantities like square metres (m2) or square feet (ft2). By multiplying the length and breadth of a rectangle, or by applying particular formulas for other forms, such as base times height divided by two for a triangle, one can determine the area of a shape.

From the given figure we observe that the base of the slanted figure has true base length of 5 units.

Thus, for triangle B the area is:

Triangle B = 1/2(b)(h)

Triangle B = 1/2(5)(4) = 10 square units.

For triangle A we have:

Triangle A = 1/2(5)(7) = 35/2 = 17.5 square units.

The area of the whole figure is:

A = 10 + 17.5 = 27.5 square units.

Hence, the area of each part of the figure is Triangle B = 10 square units and Triangle A = 17.5 square units. The area of the whole figure is 27.5 square units.

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Answer:

triangle

Step-by-step explanation:

i dont know if there should be picture attached

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer: 355

Step-by-step explanation:

Hope this helps !