what are the first 5 terms of the sequence generated by the formula an= 2(n!)

Answer:

Check the explanation

Step-by-step explanation:

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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

150 students in a tenth grade high school class take a survey about which video game consoles they own. 60  students answer that one of their consoles is a Playstation, 50 answer that one of their consoles is an Xbox. Out  of these, there are 20 who have both systems.

Let A be the event that a randomly selected student in the class has a Playstation and B be the event that the  student has an XBOX. Based on this information, answer the following questions.

a) What is P(A), the probability that a randomly selected student has a Playstation?

b) What is P(B), the probability that a randomly selected student has an XBOX?

c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?

d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he  or she has an XBOX?

Answer:

a) P(A) = 2/5

b) P(B) = 1/3

c) P(A and B) = 2/15

d) P(A | B) = 2/5

Step-by-step explanation:

Total no. of students = 150

No. of students having playstation = 60

No. of students having xbox = 50

No. of students who have both playstation and xbox = 20

a) What is P(A), the probability that a randomly selected student has a Playstation?

P(A) = No. of students having playstation/Total no. of students

P(A) = 60/150

P(A) = 2/5

b) What is P(B), the probability that a randomly selected student has an XBOX?

P(B) = No. of students having xbox/Total no. of students

P(B) = 50/150

P(B) = 1/3

c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?

The probability that a students has a Playstation and an Xbox is given by

P(A and B) = P(A)*P(B)

P(A and B) = (2/5)*(1/3)

P(A and B) = 2/15

d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he or she has an XBOX?

The conditional probability is given by

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

P(A | B) = (2/15)/(1/3)

P(A | B) = 2/5

Alternatively:

P(A | B) = P(A∩B)/P(B)

Where P(A∩B) is given by

P(A∩B) = No. of students who have both playstation and xbox/Total no. of students

P(A∩B) = 20/150

P(A∩B) = 2/15

P(A | B) = P(A∩B)/P(B)

P(A | B) = (2/15)/(1/3)

P(A | B) = 2/5

Answer: 27.42 ft

Step-by-step explanation:

To find the perimeter first we must find the circumference of the circles.

You can easily find the diameter by subtracting and you get 6.

Using the circle circumference formula c=2piR you get 9.42.

9.42 is our circumference of one circle.

You don't need to divide this by 2 because you already have 2 halves of a circle.

Next add all the sides which is 18.

Add this to the circumference we calculated earlier which gives you 27.42 ft.

Answer:

i think its c

Step-by-step explanation:

Answer:

C: Columns: likes roller coasters, doesn’t like roller coasters; rows: likes water rides, doesn’t like water rides

Step-by-step explanation:

Like variables need to be together on the columns and rows

Answer:

a) 0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92

b) A score of 89.8 marks the lowest 25 percent of the distribution

c) A score of 145.48 marks the highest 5 percent of the distribution

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 106, \sigma = 24[/tex]

(a) What proportion of children aged 13 to 15 years old have scores on this test above 92 ?

This is 1 subtracted by the pvalue of Z when X = 92. So

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

[tex]Z = \frac{92 - 106}{24}[/tex]

[tex]Z = -0.58[/tex]

[tex]Z = -0.58[/tex] has a pvalue of 0.2810

1 - 0.2810 = 0.719

0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92

(b) What score which marks the lowest 25 percent of the distribution?

The 25th percentile, which is X when Z has a pvalue of 0.25. So it is X when Z = -0.675.

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

[tex]-0.675 = \frac{X - 106}{24}[/tex]

[tex]X - 106 = -0.675*24[/tex]

[tex]X = 89.8[/tex]

A score of 89.8 marks the lowest 25 percent of the distribution

(c) Enter the score that marks the highest 5 percent of the distribution

The 100-5 = 95th percentile, which is X when Z has a pvalue of 0.95. So it is X when Z = 1.645

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

[tex]1.645 = \frac{X - 106}{24}[/tex]

[tex]X - 106 = 1.645*24[/tex]

[tex]X = 145.48[/tex]

A score of 145.48 marks the highest 5 percent of the distribution

Final answer:

Using z-scores and the properties of a normal distribution, it was calculated that approximately 71.90% of children score above 92. The score marking the lowest 25 percent is approximately 90.20, and the score that marks the highest 5 percent of the distribution is around 145.88.

Explanation:

To solve the problems about normal distribution and interpreting IQ scores, we use the properties of the normal curve and z-scores. Z-scores help us understand how far away a particular score is from the mean, in terms of standard deviations.

Part (a): Proportion of Children With Scores Above 92

We first calculate the z-score for 92 using the formula: z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. With μ = 106 and σ = 24, the z-score for 92 is (92 - 106) / 24 = -0.5833. Using a standard normal distribution table, we find that the proportion of children scoring above 92 corresponds to the area to the right of the z-score, which is approximately 0.7190. Therefore, the proportion of children aged 13 to 15 with scores above 92 is 0.7190.

Part (b): Lowest 25 Percent of the Distribution

The score marking the lowest 25 percent of the distribution corresponds to the 25th percentile or a z-score of about -0.675. We convert this z-score back to the original scale using the formula: X = μ + zσ, which yields X = 106 + (-0.675)(24) = 90.20. Thus, the score marking the lowest 25 percent is approximately 90.20.

Part (c): Highest 5 Percent of the Distribution

To find the score that marks the highest 5 percent, we locate the z-score that corresponds to the 95th percentile, which is about 1.645. Applying the conversion formula, we get X = 106 + (1.645)(24) = 145.88. Therefore, the score marking the highest 5 percent is approximately 145.88.

Answer:

so the answer is b i did the quiz

Step-by-step explanation:

What is the total surface area of the solid?

A rectangular prism with a length of 14 centimeters, width of 10 centimeters and height of 6 centimeters. A rectangular pyramid with 2 triangular sides with a base of 14 centimeters and height of 11 centimeters, and 2 triangular sides with a base of 10 centimeters and height of 12 centimeters.

558 square centimeters

702 square centimeters

842 square centimeters

982 square centimeters

Answer:

B but i could be wrong

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Universal Set, U=37

Number who play basketball, n(B)=25

Number who are under six feet, n(U)=15

Number of those who do not play basketball and are six feet or taller, n(B∪U)'=5

From set theory.

U=n(B)+n(U)-n(B∩U)+n(B∪U)'

37=25+15-n(B∩U)+5

37=45-n(B∩U)

Therefore:

n(B∩U)=45-37=8

Therefore, the number of people at the party who play basketball and are under six feet tall is 8.

The number of people at the party who play basketball and are under six feet tall is 1510. These people belong to both the group of basketball players and the group of people under six feet tall.

To answer this question, we first need to understand who are the people at the party who play basketball and are under six feet tall. This group of people belongs to both the basketball players group represented by BB and the group of people under six feet tall, represented by U. We are looking for the intersection of these two groups, represented by |B∩U|.

Out of the 3737 people at the party, 2525 of them play basketball. From these 2525 basketball players, we don't know directly how many are under six feet tall. However, we are told that 1515 people at the party are under six feet tall. We also know that 5 people are over six feet tall and do not play basketball.

Therefore, to find out how many under six feet basketball players there are, we can subtract the 5 people who are over six feet and do not play basketball from the total of the ones who are under six feet: 1515 - 5 = 1510. So, there are 1510 people at the party who play basketball and are under six feet tall.

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Answer:

Step-by-step explanation:

Im going to assum the wall your talking about is the one at the bottom.

It is divided into two equal trapezoids, so we can find the area of one trapezoid, multiply it by 2 to find the area of the entire wall.

A= (1/2)(b1+b2)(h)

Where b1 and b2 are the two parrellel sides, and h is the height of the trapezoid.

A= .5*(9+6)(8/4)   We divide by 8 by 2 because we are finding the area of one trapezoid which is half the height of the wall.

A= 30 ft squared.

2A= area of whole wall

2*30=60

The entire wall is 60 sq. ft.

2. The area you need to cover need to cover is 60 sqft.

Rolls of wallpaper are rectangular.

A = L*W and they told us the width is 2 ft. and we know the area we need to cover is 60 ft so we can subsitute those in to figure out the length.

60= L*2

L= 30 ft

You need at least 30 feet in length to cover the whole wall.

Answer:

[tex]\frac{(21)(5.437)^2}{41.402} \leq \sigma^2 \leq \frac{(21)(5.437)^2}{8.034}[/tex]

[tex] 14.996 \leq \sigma^2 \leq 77.278[/tex]

And the confidence interval for the deviation would be obtained taking the square root of the last result and we got:

3.9<σ<8.8

Step-by-step explanation:

Data given:

65.2 71.9 72.8 73.1 73.1 73.5 75.5 75.7 75.8 76.1 76.2 76.2 77.0 77.9 78.1 79.6 79.7 79.9 80.1 82.2 83.7 93.8

The sample mean would be given by:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

We can calculate the sample deviation with this formula:

[tex]s = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]

And we got:

s=5.437 represent the sample standard deviation

[tex]\bar x[/tex] represent the sample mean

n=22 the sample size

Confidence=99% or 0.99

The confidence interval for the population variance is given by:

[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]

The degrees of freedom given by:

[tex]df=n-1=22-1=21[/tex]

The Confidence is 0.99 or 99%, the value of significance is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical values are:

[tex]\chi^2_{\alpha/2}=41.402[/tex]

[tex]\chi^2_{1- \alpha/2}=8.034[/tex]

And the confidence interval would be:

[tex]\frac{(21)(5.437)^2}{41.402} \leq \sigma^2 \leq \frac{(21)(5.437)^2}{8.034}[/tex]

[tex] 14.996 \leq \sigma^2 \leq 77.278[/tex]

And the confidence interval for the deviation would be obtained taking the square root of the last result and we got:

3.9<σ<8.8

Answer:

The answer is 42 centimeters.

Step-by-step explanation:

HOPE THIS HELPED!

Answer:

Given:

Sample size, n = 11

P = 0.5

a) The shape of the histogram will be symmetrical. This is because the probability of getting heads and tails is equal.

b) The histogram is centered at

p = 0.5 (because of equal probability of obtaining heads and tails).

c) How much variability would you expect among these​ proportions?

Here, we are to find the standard deviation.

Let's use the formula:

[tex] \sigma = \sqrt{\frac{pq}{n}} [/tex]

Where

p = 0.5(probability of getting heads)

q = 0.5 (probability of getting tails)

Therefore

[tex] \sigma = \sqrt{\frac{0.5 * 0.5}{11}} [/tex]

= 0.0227 ≈ 0.023

The standard deviation is 0.023

d) A normal model should not be use here because the success/failure condition is violated, since each student only flips the coin 11 times, it impossible to obtain both at least 10 heads and at least 10 tails. Here, the sample size is too small.

Answer:

The value of G is 3/8 .

Step-by-step explanation:

In order to solve G, you have to divide 2/3 to both sides :

[tex] \frac{2}{3} \times G = \frac{1}{4} [/tex]

[tex] \frac{2}{3} \times G \div \frac{2}{3 } = \frac{1}{4} \div \frac{2}{3} [/tex]

[tex]G = \frac{1}{4} \times \frac{3}{2} [/tex]

[tex]G = \frac{3}{8} [/tex]

Answer:

3/8

Step-by-step explanation:

Convert to common denominator which would be 12.

8/12 x G=3/12

Then divide 3/12 by 8/12 and you get 3/8

If you add a pic maybe I could help but for now I cant

Answer:k(-7)=-89

Step-by-step explanation:

since k(t)=10t - 19

K(-7)=10(-7)-19

k(-7)=-70-19

k(-7)=-89

Answer:

The lateral area of the cylinder is 678cm²

Step-by-step explanation:

To calculate the lateral area of ​​the cylinder we have to calculate the circumference and multiply it by the height

To solve this problem we need to use the circumferenc formula of a circle:

c = circumference

r = radius = 9cm

π = 3.14

c = 2π * r

we replace with the known values

c = 2 * 3.14 * 9cm

c = 56.52cm

The length of the circumference is 56.52cm

lateral area = c * h

56.52cm  * 12cm = 678.24 cm²

round to the nearest whole number

678.24 cm² = 678cm²

The lateral area of the cylinder is 678cm²

Answer:

c-678 cm2

Step-by-step explanation:

what i got on edg 2020

Answer:

178

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

A relation is a function when there is exactly one output for each input. That is the case in this table, so the relation between the original price and sale price is a function.

Answer:

25%

Step-by-step explanation:

Plz mark me brainliest.

Answer:

25%

Step-by-step explanation:

Answer:

She uses 1.7475 cups of flour.

Step-by-step explanation:

This question can be solved using a rule of three.

For each batch of cookies:

Two and one-third cups of flour.

So [tex]2 + \frac{1}{3} = 2.33[/tex] cups.

If she makes three-fourths of a batch of cookies, how much flour does she use?

3/4 = 0.75 batch of cookies. How much flour?

1 batch - 2.33 cups.

0.75 batches - x cups

x = 2.33*0.75

x = 1.7475

She uses 1.7475 cups of flour.

Answer:

1 3/4

Step-by-step explanation:

Answer: 16.5

Step-by-step explanation:

[tex]\frac{99}{6} = 16.5[/tex]

Answer:

What i got is 16.5 hope this helps!

Answer:

 b = 16

Step-by-step explanation:

Answer:

-6b-12+8 which simplifies to -6b-4

Step-by-step explanation:use distrubutive property and then combine like terms

Answer:

Quadratic function (assuming 4x2 is 4x^2)

Step-by-step explanation:

Linear functions are ax+b=y

Quadratic is ax^2+b=y

Cubic is ax^3+b=y

The equation 4x² + 8x - 7 is a Quadratic equation.

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ 4x² + 8x - 7

Now,

Clearly, In the equation;

The highest power of a variable is two.

And, we know that;

In the quadratic equation, the highest power of a equation is two.

Thus, The equation 4x² + 8x - 7 is a Quadratic equation.

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Answer:

Step-by-step explanation:

The formula for finding the volume is

Volume = length × width × height

Volume of the given prism is

Volume = 3 × 4 × 5 = 60 inches³

The formula for determining the surface area of a rectangular prism is expressed as

Surface area = Ph + 2B

Where

P represents perimeter of base

h represents height of prism

B represents base area

Perimeter of base = 2(length + width)

P = 2(3 + 4) = 14 inches

B = 3 × 4 = 12 inches

h = 5 inches

Surface area = 14 × 5 + 2 × 12 = 94 inches²

For another prism,

Assuming h = 3, length = 10 and width = 2, then

Volume = 3 × 10 × 2 = 60 inches³

P = 2(10 + 2) = 24 inches

B = 10 × 2 = 20 inches

Surface area = (24 × 3) + (2 × 20) = 112 inches²

If we keep changing the values, the surface area will always be greater than 94 inches².

Therefore, there is no rectangular prism with the same volume but less surface area.

Answer:

its 60 for volume, but for the area i don't know

Step-by-step explanation:

Let y represent the y-coordinate of point A.

We have been given that point B has coordinates (5,1) The x-coordinate of point A is 0. So coordinates of point A would be (0,y)

The distance between point A and Point B is 13 units.

We will use distance formula to solve our given problem.

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let point A [tex](0,y)=(x_2-y_2)[/tex] and point A [tex](5,1)=(x_1,y_1)[/tex].

Upon substituting coordinates of both points in distance formula, we will get:

[tex]13=\sqrt{(0-5)^2+(y-1)^2}[/tex]

[tex]13=\sqrt{25+y^2-2y+1}[/tex]

[tex]13=\sqrt{y^2-2y+26}[/tex]

Let us square both sides as:

[tex]13^2=(\sqrt{y^2-2y+26})^2[/tex]

[tex]169=y^2-2y+26[/tex]

[tex]169-169=y^2-2y+26-169[/tex]

[tex]0=y^2-2y-143[/tex]

[tex]y^2-2y-143=0[/tex]

Upon splitting the middle term, we will get:

[tex]y^2-13y+11y-143=0[/tex]

[tex]y(y-13)+11(y-13)=0[/tex]

[tex](y-13)(y+11)=0[/tex]

Now we will use zero product property.

[tex](y-13)=0, (y+11)=0[/tex]

[tex]y=13, y=-11[/tex]

Therefore, the possible coordinates of point A would be [tex](0,-11)[/tex] and [tex](0,13)[/tex].

Answer:

[tex]\binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} }[/tex]

Step-by-step explanation:

First, find the magnitude of the vector:

[tex] |v| = \sqrt{( {(7)}^{2} + {( - 3)}^{2}) } \\ = \sqrt{(49 + 9)} \\ = \sqrt{58} [/tex]

Then, divide each component of the vector by the magnitude to get the unit vector and rationalise:

[tex]unit \: vector = \binom{ \frac{7}{ \sqrt{58} } }{ \frac{ - 3}{ \sqrt{58} } } \\ = \binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} } [/tex]

Final answer:

Mrs. Golden will need 26 squares of silver paper to cover her bulletin board, and there will not be any pieces left over.

Explanation:

To find out how many 1-foot squares Mrs. Golden needs to cover her bulletin board, we first need to calculate the area of the bulletin board. The area of a rectangle can be found by multiplying the length and width. In this case, the length is 6.5 feet and the width is 4 feet, so the area is 6.5 feet x 4 feet = 26 square feet.

Since the silver paper comes in 1-foot squares, we can divide the area of the bulletin board by the area of each square to find out how many squares are needed. In this case, we divide 26 square feet by 1 square foot, giving us a result of 26 squares.

There will not be any pieces left over because 26 squares fully cover the area of the bulletin board. If there were any remaining space, we would need a fraction of a square to cover it.

Journal entry

Explanation:

                                  Books of (----Limited)

                                      Journal Entry

Date         Account Title and Explanation            Debit         Credit

              Cash / Bank                          A/c  Dr.     $750,000

                To Unearned Subscription A/c                               $750,000

                            (Being Unearned Subscription)

Computation:

Amount of Unearned Subscription =  25,000 × $30

Amount of Unearned Subscription =  %750,000

Answer:

The zeros are x1=4.45 and x2=-0.45.

x1 is between 4 and 5.

x2 is between -1 and 0.

Step-by-step explanation:

We have the function:

[tex]y(x) = x2 - 4x-2[/tex]

As this is a quadratic function, we can calculate the zeros of the function with the quadratic equation:

[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot 1\cdot(-2)}}{2\cdot 1}\\\\\\x=\dfrac{4\pm\sqrt{16+8}}{2}\\\\\\x=\dfrac{4\pm\sqrt{24}}{2}\\\\\\x=\dfrac{4\pm4.9}{2}=2\pm2.45\\\\\\x_1=2+2.45=4.45\\\\x_2=2-2.45=-0.45[/tex]

The zeros are x1=4.45 and x2=-0.45.

x1 is between 4 and 5.

x2 is between -1 and 0.

The two real zeros of the quadratic equation are located between -1 and 4.

To determine between which consecutive integers the real zeros of the function y(x) = x² - 4x - 2 are located, we can use the quadratic formula.

The quadratic formula is given as:

x = (-b ± √(b² - 4ac)) / (2a)

In the equation y(x) = x² - 4x - 2, we have a = 1, b = -4, and c = -2.

Let's substitute these values into the quadratic formula to find the values of x:

x = (-(-4) ± √((-4)² - 4(1)(-2))) / (2(1))

x = (4 ± √(16 + 8)) / 2

x = (4 ± √24) / 2

x = (4 ± 2√6) / 2

x = 2 ± √6

From the quadratic formula, we find that the real zeros of the function are x = 2 + √6 and x = 2 - √6.

To determine between which consecutive integers these real zeros are located, we can compare the values to the nearest integers.

x = 2 + √6 is approximately 4.45

x = 2 - √6 is approximately -0.45

Therefore, the real zeros of the function are located between the consecutive integers -1 and 4.

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Answer:

22650

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

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