what is the approximate area of the shaded sector in the circle shown below

Answer:

60 different meal packages are possible.

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In this question:

4 types of drinks

5 types of sandwiches.

3 types of chips.

They are independent events, so, by the fundamental counting principle:

4*5*3 = 60

60 different meal packages are possible.

Answer:

[tex]\bar x = 1.4896[/tex]

[tex]Median = 1.525[/tex]

7 is an outlier

Step-by-step explanation:

Given

See comment for dataset

Solving (a): The mean

The mean is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{2.53 +1.33 +0.64 +2.55 +0.67 +0.57 +............+2.03 +1.78}{50}[/tex]

[tex]\bar x = \frac{74.48}{50}[/tex]

[tex]\bar x = 1.4896[/tex]

Solving (b): The median

First, we sort the data:

[tex]0.01, 0.01, 0.08, 0.14, 0.24, 0.35, 0.57, 0.64, 0.65, 0.67,[/tex]

[tex]0.69, 0.74, 0.81, 0.82, 0.92, 0.99, 1.01, 1.04, 1.15, 1.16, 1.33,[/tex]

[tex]1.41, 1.45, 1.48, 1.52, 1.53, 1.58, 1.61, 1.62, 1.73, 1.77, 1.78, 1.84,[/tex]

[tex]1.98, 2.01, 2.02, 2.03, 2.06, 2.06, 2.31, 2.41, 2.53, 2.55, 2.59,[/tex]

[tex]2.66, 2.74, 2.74, 2.77, 2.77, 2.91[/tex]

The median position is:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{50 + 1}{2}[/tex]

[tex]Median = \frac{51}{2}[/tex]

[tex]Median = 25.5th[/tex]

This means that the median is the average of the 25th and the 26th item.

So:

[tex]Median = \frac{1.52+1.53}{2}[/tex]

[tex]Median = \frac{3.05}{2}[/tex]

[tex]Median = 1.525[/tex]

Solving (c): Is 7 an outlier

Yes; 7 is an outlier.

Because the range of the dataset (0.01 to 2.92) is far from 7.

9514 1404 393

Answer:

  B.  F(-9/2, 0), x = 9/2

Step-by-step explanation:

One definition of a parabola is that it is all of the points that are equidistant from the focus and the directrix. Among other things, this means the parabola "wraps around" the focus, and opens away from the directrix.

The focus is on the axis of symmetry, so shares a coordinate with the vertex. Since the vertex is a point on the parabola, it is equidistant from the focus and directrix—halfway between them.

The given equation has x get more negative as y increases, so the parabola opens to the left. This means the focus will be a point on the -x axis. Only one answer choice meets that requirement:

  focus: (-9/2, 0), directrix: x = 9/2

__

The equation of a parabola with its vertex at the origin can be written as ...

  x = 1/(4p)y^2

In this case, we have 4p = -18, so p = -9/2. This is the distance from the vertex to the focus. The negative sign means the focus is to the left of the vertex, and its x-coordinate is -9/2 (as noted above).

Answer: [tex]\dfrac{x^2+1}{2}[/tex]

Step-by-step explanation:

Given

[tex]f(x)=\sqrt{2x-1}[/tex]

We can write it as

[tex]\Rightarrow y=\sqrt{2x-1}[/tex]

Express x in terms of y

[tex]\Rightarrow y^2=2x-1\\\\\Rightarrow x=\dfrac{y^2+1}{2}[/tex]

Replace y be x to get the inverse

[tex]\Rightarrow f^{-1}(x)=\dfrac{x^2+1}{2}[/tex]

To prove, it is inverse of f(x). [tex]f(f^{-1}(x))=x[/tex]

[tex]\Rightarrow f(f^{-1}(x))=\sqrt{2\times \dfrac{x^2+1}{2}-1}\\\\\Rightarrow f(f^{-1}(x))=\sqrt{x^2+1-1}\\\\\Rightarrow f(f^{-1}(x))=x[/tex]

So, they are inverse of each other.

Answer:

4x^2-9x+7+\frac{x-2}{x^2+x+1}

Step-by-step explanation:

Here is a hopefully helpful answer! :)

Step-by-step explanation:

5

Sigma (10(n-1) + 3)

n=1

Answer:

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 15.4 inches, and standard deviation of 3.5 inches.

This means that [tex]\mu = 15.4, \sigma = 3.5[/tex]

16 items are chosen at random

This means that [tex]n = 16, s = \frac{3.5}{\sqrt{16}} = 0.875[/tex]

What is the probability that their mean length is less than 16.8 inches?

This is the p-value of Z when X = 16.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{16.8 - 15.4}{0.875}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452.

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

Answer:a

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

X is equal to 70 degrees because angle x and the angle that is 70 degrees are alternate interior angles.

These are alternate interior angles. If two angles are alternate interior angles they are congruent. That means x is also 70 degrees.

Answer:

- 8

Step-by-step explanation:

56 ÷ (- 7)

56 ÷ - 7

- 8

Answer:

-8

Step-by-step explanation:

A positive number divided by a negative one results in a negative quotient.

Thus, 56 ÷ (–7) = -8

Answer:

282.12 ft

Step-by-step explanation:

Please find attached a graphical illustration of the question

We are given the value of the opposite side and we are to determine the value of the adjacent side. Thus, tan would be used

Tan 65 = opposite / adjacent

2.1445 = 605 / x

x = 605 / 2.1445

x = 282.12 ft

Answer:

209

Step-by-step explanation: guyci you y tf7itfit 6tuit6yci7v uvtfi7ftyvg hkvyucoyvyvhj gku citctvo utictgvuk h jh hj vvuk

c A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

vvvv A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

vv A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

v A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

Answer:

4xy² + 3x -5 polynomial example

example of a polynomial

this one has 3 terms

Dividing

polynomial division

Polynomials can sometimes be divided using the simple methods shown on Dividing Polynomials.

But sometimes it is better to use "Long Division" (a method similar to Long Division for Numbers)

Numerator and Denominator

We can give each polynomial a name:

x² + 2x -7 (numerator)

_________

x-2 (denominator)

[tex] \times - {}^{2} \sqrt{ \times {}^{2} } + 2 \times - 7[/tex]

Both polynomials should have the "higher order" terms first (those with the largest exponents, like the "2" in x2).

then :

divide: the first term of the numerator

by the first term of denominator and put that answer

multiply the denominator by that answer, put that below the numerator

subtract to create a new polynomial

repeat using the polynomial

Answer:

36

Step-by-step explanation:

Simple:

(4)(3)+2((5)(3)−2)−2

=12+2((5)(3)−2)−2

=12+2(15−2)−2

=12+(2)(13)−2

=12+26−2

=38−2

=36

Answer:

Hence the correct option is Option b that is the same for each interval.

Step-by-step explanation:

The PDF for Uniform distribution in [a,b] is given by  

[tex]f(x)=\frac{1}{b-a}~~~~~~a\leq x\leq b[/tex]  

So the probability that the random variable assumes a value in​ [a,b] is given by  

[tex]\int_{a}^{b}f(x)dx=\int_{a}^{b}\frac{1}{b-a}dx=1[/tex]

Therefore the correct option is b. the same for each interval.

Answer:

182

2.0239

3.97

(178, 186)

Step-by-step explanation:

Given :

Sample mean, n = 250

Sample mean, xbar = 182

Sample standard deviation, s = 32

Point estimate for the mean ;

According to the central limit theorem ; for n > 30, the sample mean equal to the population mean.

Hence, point estimate of mean cholesterol level for men is 182

B.) The standard error = s/√n

s= 32 ; n = 250

Standard error = 32/√250 = 2.0239

C.) Margin of error :

TCritical * standard error

TCritical at 95% ; df =250 -1 = 249 = 1.96

1.969 * 2.0239 = 3.966 = 3.97

D.) The confidence interval :

Point estimate ± margin of error

182 ± 3.97

182 - 3.97 = 178.03

182 + 3.97 = 185.97

(178, 186)

Answer:

see graph

Step-by-step explanation:

Answer:

The first option you gave, fourth one, fifth one. This is what I think, the question is formatted badly and hard to read.

Step-by-step explanation:

Answer:

1,4,5

Step-by-step explanation:

Answer:

A = 16.3

Step-by-step explanation:

take angle A as reference angle

using cos rule

cos A =adjacent /hypotenuse

cos A =24/25

cos A = 0.96

A = [tex]cos^{-1} (0.96)[/tex]

A = 16.26

A = 16.3 (after converting to nearest tenth)

Answer:

Cos A = 24/25

Step-by-step explanation:

cos A = adj side / hypotenuse

Cos A = 24/25

Answer:

they would have bike 544 miles together with each other.

Step-by-step explanation:

since Elsa went more than Linda Linda had to stop while Elsa kept going.

Answer: 34767.2

Step-by-step explanation:

given p = $16,000, n = 14 years, y = 5.7%

amount in bank after 14 years = p ( 1 + </100)

= 16,000 (1 + 5.7/ 100) 14

= 34767.2

Answer:

Step-by-step explanation:

Required formula:

Substitute values and solve:

Answer:

Dominic ate [tex]\frac{2}{6}[/tex]  of the pizza.

Step-by-step explanation:

First you want to convert the fractions so they all have the same denominator (bottom number in the fraction.) That will make it a lot easier to add and subtract with them.

[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]

So Shawn ate 1/6 of the pizza, and Ryan ate 3/6 of the pizza. To find what else makes up the whole pizza (what Dominic ate) we add 1/6 and 3/6, then subtract from the whole.

[tex]\frac{1}{6}[/tex] + [tex]\frac{3}{6}[/tex] = [tex]\frac{4}{6}[/tex]

[tex]\frac{6}{6}[/tex] - [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{6}[/tex]

Therefore Dominic ate [tex]\frac{2}{6}[/tex]  of the pizza.

Answer:

Yes there is alternative way in solving and arithmetic sequence .An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

Answer:

A = 2.1 ft^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 ( 2.8)(1.5)

A = 2.1 ft^2

Answer:2.1

Step-by-step explanation:

The formula of finding the area of a triangle is A=. 1/2*b*h

A=1/2*2.8*1.2

A=1/2* 4.2

A=2.1

Answer:

2.28% of faculty members work more than 58.6 hours a week.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average full-time faculty member in a college works an average of 53 hours per week. Standard deviation of 2.8 hours.

This means that [tex]\mu = 53, \sigma = 2.8[/tex]

What percentage of faculty members work more than 58.6 hours a week?

The proportion is 1 subtracted by the p-value of Z when X = 58.6. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{58.6 - 53}{2.8}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

1 - 0.9772 = 0.0228

0.0228*100% = 2.28%

2.28% of faculty members work more than 58.6 hours a week.

Answer:

Step-by-step explanation:

For this case we have the following equation:

An equivalent way to write this equation is to multiply both sides of the equation by a scalar.

When multiplying both sides of the equation by 100 we have:

By doing distributive property we have:

Answer:

An equation that is equivalent is:

Answer:

3 white to 5 yellow

the third choice

Step-by-step explanation:

white     9 parts

yellow   15 parts

9 white to 15 yellow

Divide by 3

3 white to 5 yellow