Juan and his friends played a game in which sticky darts were thrown onto a playing board. To start the game, Juan threw a dart randomly onto the board. Describe the likelihood of getting each score. 8 points: 16 points: more than 0 points:

Answers

Answer 1

Answer:

8 points:  unlikely

16 points:   impossible

more than 0 points:   likely

Step-by-step explanation:

Answer 2

Answer:

8 points:  

✔ unlikely

16 points:  

✔ impossible

more than 0 points:  

✔ likely

i did the test hope this helped


Related Questions

how many are 4 x 4 ?​

Answers

16, think of 4 plus 4 plus 4 plus 4.

PLEASE HELP!

Fill in the reason for statement 3 in proof below:

SAS
AA
SSS

Answers

Answer:

SAS

Step-by-step explanation:

ΔABD ~ ΔECD is similar through:

S - because ED = CD (Given)

A - same angle ∠D (Statement 2)

S - because AD = BD (Given)

Cheers!

Answer:

SAS

Step-by-step explanation:

You can notice that you have ED/AB = CD/BD You have one common angle

Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like 2 of the songs. With the random feature on your​ player, each of the 12 songs is played once in random order. Find the probability that among the first two songs played ​(a) You like both of them. Would this be​ unusual? ​(b) You like neither of them. ​(c) You like exactly one of them. ​(d) Redo​ (a)-(c) if a song can be replayed before all 12 songs are played.

Answers

Answer:

The answer is below

Step-by-step explanation:

We have the following information:

Number of songs you like = 2

Total number of songs = 12

a) P(you like both of them) = 2/12 x 1/11 = 0.015

This is unusual because the probability of the event is less than 0.05

b) P(you like neither of them) = 10/12 x 9/11  = 0.68

c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30

d) If  a song can be replayed before all 12,

P(you like both of them) = 2/12 x 2/12  =0.027

This is unusual because the probability of the event is less than 0.05

P(you like neither of them) = 9/12 x 9/12  = 0.5625

P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25

Which of the following graphs is described by the function given below?
y = 2x^2 + 8x + 3

Answers

Answer:

Option A

Step-by-step explanation:

Equation of the given quadratic function is,

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

  = 2(x² + 4x + 4 - 4) + 3

  = 2(x + 2)² - 8 + 3

  = 2(x + 2)² - 5

By comparing this equation with the equation of a quadratic function in vertex form,

y = a(x - h)² + k

Here (h, k) is the vertex of the parabola

Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)

Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.

Option (A). Graph A will be the answer.

In a race, Brian Collins has to cross 10 hurdles. The probability that he clears a hurdle is 2/3. Find P(clears all hurdles).

Answers

Answer:

1024/59049

Step-by-step explanation:

P( clear hurdle) = 2/3

There are 10 hurdles

P ( clear all hurdles) = P( clear hurdle) * P( clear hurdle)...... 10 times

                                 = 2/3 * 2/3 *....... 10 times

                                  = (2/3) ^ 10

                                  =1024/59049

Answer:

1024/59049, 1.7%

Step-by-step explanation:

One way to do it would to be simply multiply 2/3 by itself 10 times

2/3 x 2/3 x 2/3 x 2/3 and so on

That would be a really long equation so instead we can use exponents to shorten it. We can simply just do 2^10/3^10

2^10=1024

3^10=59049

1024/59049, 1.7%

Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was​ red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.

Answers

Answer:

With replacement = 14/49without replacement = 3/7

Step-by-step explanation:

Since there are  2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.

Probability that at least 1 ball was​ red, given that the first ball was replaced before the second can be calculated as shown;

Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.

Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49

Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49

The probability that at least 1 ball was​ red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49

If the balls were not replaced before the second draw

Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21

Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21

The probability that at least 1 ball was​ red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:

2 + 5 = X7 = X

(2/7 + 2/7) / 2 = X (0.285 + 0.285) / 2 = X 0.285 = X

(2/7 + 1/6) / 2 = X (0.28 + 0.16) / 2 = X 0.451 / 2 = X 0.225 = X

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Learn more about probability in https://brainly.com/question/14393430

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 58 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = (b) Find an expression for the number of cells after t hours. P(t) = (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr

Answers

Answer:

a) k=2.08 1/hour

b) The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

c) 977,435,644 cells

d) 2.033 billions cells per hour.

e) 2.81 hours.

Step-by-step explanation:

We have a model of exponential growth.

We know that the population duplicates every 20 minutes (t=0.33).

The initial population is P(t=0)=58.

The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

For t=0, we have:

[tex]P(0)=Ce^0=C=58[/tex]

If we use the duplication time, we have:

[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]

Then, we have the model as:

[tex]P(t)=58e^{2.08t}[/tex]

The relative growth rate (RGR) is defined, if P is the population and t the time, as:

[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]

In this case, the RGR is k=2.08 1/h.

After 8 hours, we will have:

[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]

The rate of growth can be calculated as dP/dt and is:

[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]

For t=8, the rate of growth is:

[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]

(2.033 billions cells per hour).

We can calculate when the population will reach 20,000 cells as:

[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]

An industrial psychologist conducted an experiment in which 40 employees that were identified as "chronically tardy" by their managers were divided into two groups of size 20. Group 1 participated in the new "It's Great to be Awake!" program, while Group 2 had their pay docked. The following data represent the number of minutes that employees in Group 1 were late for work after participating in the program.

Does the probability plot suggest that the sample was obtained from a population that is normally distributed? Provide TWO reasons for your classification.

Answers

Answer:

The probability plot of this distribution shows that it is approximately normally distributed..

Check explanation for the reasons.

Step-by-step explanation:

The complete question is attached to this solution provided.

From the cumulative probability plot for this question, we can see that the plot is almost linear with no points outside the band (the fat pencil test).

The cumulative probability plot for a normal distribution isn't normally linear. It's usually fairly S shaped. But, when the probability plot satisfies the fat pencil test, we can conclude that the distribution is approximately linear. This is the first proof that this distribution is approximately normal.

Also, the p-value for the plot was obtained to be 0.541.

For this question, we are trying to check the notmality of the distribution, hence, the null hypothesis would be that the distribution is normal and the alternative hypothesis would be that the distribution isn't normal.

The interpretation of p-valies is that

When the p-value is greater than the significance level, we fail to reject the null hypothesis (normal hypothesis) and but if the p-value is less than the significance level, we reject the null hypothesis (normal hypothesis).

For this distribution,

p-value = 0.541

Significance level = 0.05 (Evident from the plot)

Hence,

p-value > significance level

So, we fail to reject the null or normality hypothesis. Hence, we can conclude that this distribution is approximately normal.

Hope this Helps!!!

Brainliest for the correct awnser!!!!! Which of the following is the product of the rational expressions shown below?

Answers

Answer:

A.

Step-by-step explanation:

Multiply straight across:

[tex]\frac{2}{x+1}\cdot \frac{5}{3x}=\frac{10}{3x(x+1)}[/tex]

Simplify:

[tex]=\frac{10}{3x^2+3x}[/tex]

This cannot be simplified further.

Answer:

[tex] \boxed{\sf \frac{10}{3 {x}^{2} + 3x}} [/tex]

Step-by-step explanation:

[tex] \sf Expand \: the \: following: \\ \sf \implies \frac{2}{x + 1} \times \frac{5}{3x} \\ \\ \sf \implies \frac{2 \times 5}{3x(x + 1)} \\ \\ \sf 2 \times 5 = 10 : \\ \sf \implies \frac{ \boxed{ \sf 10}}{3x(x + 1)} \\ \\ \sf 3x(x + 1) = (3x)(x) + (3x)(1) : \\ \sf \implies \frac{10}{ \boxed{ \sf (3x)(x) + (3x)(1)}} \\ \\ \sf (3x)(x) = 3 {x}^{2} : \\ \sf \implies \frac{10}{ \boxed{ \sf 3 {x}^{2}} + (3x)(1) } \\ \\ \sf (3x)(1) = 3x : \\ \sf \implies \frac{10}{3 {x}^{2} + 3x} [/tex]

Fake Question: Should Sekkrit be a moderator? (answer if you can) Real Question: Solve for x. [tex]x^2+3x=-2[/tex]

Answers

Answer:

x = -2 , -1

Step-by-step explanation:

Set the equation equal to 0. Add 2 to both sides:

x² + 3x = -2

x² + 3x (+2) = - 2 (+2)

x² + 3x + 2 = 0

Simplify. Find factors of x²  and 2 that will give 3x when combined:

x²  + 3x + 2 = 0

x               2

x               1

(x + 2)(x + 1) = 0

Set each parenthesis equal to 0. Isolate the variable, x. Note that what you do to one side of the equation, you do to the other.

(x + 2) = 0

x + 2 (-2) = 0 (-2)

x = 0 - 2

x = -2

(x + 1) = 0

x + 1 (-1) = 0 (-1)

x = 0 - 1

x = -1

x = -2 , -1

~

Answer:

x = -2       OR      x = -1

Step-by-step explanation:

=> [tex]x^2+3x = -2[/tex]

Adding 2 to both sides

=> [tex]x^2+3x+2 = 0[/tex]

Using mid-term break formula

=> [tex]x^2+x+2x+2 = 0[/tex]

=> x(x+1)+2(x+1) = 0

=> (x+2)(x+1) = 0

Either:

x+2 = 0    OR     x+1 = 0

x = -2       OR      x = -1

P.S. Ummmm maybe...... Because he usually reports absurd answers! So, Won't it be better that he could directly delete it. And one more thing! He's Online 24/7!!!!!

Find the remainder when f(x)=2x3−x2+x+1 is divided by 2x+1.

Answers

Step-by-step explanation:

it can be simply done by using remainder theorem.

The National Safety Council (NSC) estimates that off-the-job accidents cost U.S. businesses almost $200 billion annually in lost productivity (National Safety Council, March 2006). Based on NSC estimates, companies with 50 employees are expected to average three employee off-the-job accidents per year. Answer the following questions for companies with 50 employees.a. What is the probability of no off-the-job accidents during a one-year period (to 4 decimals)?b. What is the probability of at least two off-the-job accidents during a one-year period (to 4 decimals)?c. What is the expected number of off-the-job accidents during six months (to 1 decimal)?d. What is the probability of no off-the-job accidents during the next six months (to 4 decimals)?

Answers

Answer:

a. 0.0498 = 4.98% probability of no off-the-job accidents during a one-year period

b. 0.8008 = 80.08% probability of at least two off-the-job accidents during a one-year period.

c. The expected number of off-the-job accidents during six months is 1.5.

d. 0.2231 = 22.31% probability of no off-the-job accidents during the next six months.

Step-by-step explanation:

We have the mean during a period, so we use the Poisson distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Companies with 50 employees are expected to average three employee off-the-job accidents per year.

This means that [tex]\mu = 3n[/tex], in which n is the number of years.

a. What is the probability of no off-the-job accidents during a one-year period (to 4 decimals)?

This is [tex]P(X = 0)[/tex] when [tex]\mu = 3*1 = 3[/tex]. So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

0.0498 = 4.98% probability of no off-the-job accidents during a one-year period.

b. What is the probability of at least two off-the-job accidents during a one-year period (to 4 decimals)?

Either there are less than two accidents, or there are at least two. The sum of the probabilities of these events is 1. So

[tex]P(X < 2) + P(X \geq 2) = 1[/tex]

We want [tex]P(X \geq 2)[/tex]. Then

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0498 + 0.1494 = 0.1992[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1992 = 0.8008[/tex]

0.8008 = 80.08% probability of at least two off-the-job accidents during a one-year period.

c. What is the expected number of off-the-job accidents during six months (to 1 decimal)?

6 months is half a year, so [tex]n = 0.5[/tex]

[tex]\mu = 3n = 3*0.5 = 1.5[/tex]

The expected number of off-the-job accidents during six months is 1.5.

d. What is the probability of no off-the-job accidents during the next six months (to 4 decimals)?

This is P(X = 0) when [tex]\mu = 1.5[/tex]. So

[tex]P(X = 0) = \frac{e^{-1.5}*1.5^{0}}{(0)!} = 0.2231[/tex]

0.2231 = 22.31% probability of no off-the-job accidents during the next six months.

At her favorite sneakers store Nyeema saved $48 because of a
sale.
If the sneakers normally cost $120. How much did she save?​

Answers

Answer:

40%

Step-by-step explanation:

We can find what percent 48 is of 120 by dividing:

48/120 = 0.4 or 40%

So, she saved 40% from the original price.

Select the correct answer.
If two angles of a triangle have equal measures and the third angle measures 90º, what are the angle measures of the triangle?
ОА.
60°, 60°, 60°
OB.
459,909, 90°
Ос.
30°, 30°, 90°
OD.
45°, 45°, 90°

Answers

Answer:

OD. 45,45,90

Step-by-step explanation:

Which set of numbers can represent the lengths of the sides of a triangle? A. {1,2,3} B. {3,5,7} C. {3,9,14} D. {4,4,8}

Answers

B

To form a triangle, the sum of any 2 sides of a triangle must be greater than the measure of the third side. For B, 3+5>7 works.

The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.

What is a triangle?

Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.

That is to say, 3+5 = 8 is greater than the third side which is 7.

Therefore, the set of numbers the would represent a triangle are 3,5,7.

Learn more about triangle here:

https://brainly.com/question/17335144

#SPJ1

Identify the segments that are parallel, if any, if ∠ADH≅∠ECK

Answers

Answer:

DF and CG

Step-by-step explanation:

Two or more segments are said to be parallel is the angle between them is [tex]180^{0}[/tex]. While two segments are said to be perpendicular when the angle between them is [tex]90^{0}[/tex].

The given figure is a parallelogram. A parallelogram is a quadrilateral with a pair of parallel opposite sides.

In the given question if ∠ADH ≅ ∠ECK , then the parallel segment would be DF and CG.

A class of 30 music students includes 13 who play the​ piano, 15 who play the​ guitar, and 9 who play both the piano and the guitar. How many students in the class play neither​ instrument?

Answers

I am not to sure but I think it’s 2 because you might not need to include the 9 students and 15 plus 13 equals 28 and you would have 2 left .

Answer: 2

Step-by-step explanation:

As given, out of 30 students, 15 play guitar and 13 play piano, thats 28.

Among these, 9 play both the guitar and the piano.

That means, only 2 remaining students play neither instrument. (30-15-13)

Alexandra has $15 to buy drinks for her friends at the baseball game. Soda
costs $2.75 and bottled water costs $2.00. This relationship can be
represented by the inequality 2758+2w $ 15. Three of Alexandra's friends
asked for water. Which inequality represents the number of sodas she can
buy?
A. OS 85 3.27
B. 85 3.27
C. OSSS3
D. 853

Answers

Answer:

C

Step-by-step explanation:

write an equation for the costs:

if x is the number of sodas

and y is the number of waters

2.75x + 2y <= 15

(<= is less than or equal to)

if we substitute 3 for y

we get 2.75x + 2(3) <= 15

2.75x + 6 <= 15

2.75x <= 9

9 / 2.75 = 3.2727

however, you cannot buy part of a soda

so, round to 3

you also cannot buy negative sodas

so, the answer is C

15 3/4% is equal to which decimal?

Answers

15 3/4% as a decimal would be 0.1575 if I’m not mistaken

Answer:

2/4%

Step-by-step explanation:

Which value of x makes 7+5(x-3)=227+5(x−3)=227, plus, 5, left parenthesis, x, minus, 3, right parenthesis, equals, 22 a true statement? Choose 1 answer:

Answers

Answer:

7 + 5(x - 3) = 22

5(x - 3) = 15

x - 3 = 3

x = 6

Answer:

x = 6

Step-by-step explanation:

Step 1: Distribute 5

7 + 5x - 15 = 22

Step 2: Combine like terms

5x - 8 = 22

Step 3: Add 8 to both sides

5x = 30

Step 4: Divide both sides by 5

x = 6

HELP !!!..... ASAP PLS

Answers

Step-by-step explanation:

the average change H = Δy/ Δx

so H = ( f(4) - f(2) )/ (4 -2) = ( 0 -1 ) / 2 = -1/2

Will anyone help me with geometry ASAP!? Please!? In desperate help!!!

Answers

Answer:

14.  C   41

15. k = 72

Step-by-step explanation:

14.

For parallel lines, alternate exterior angles must be congruent.

3x - 43 = 80

3x = 123

x = 41

15.

The sum of the measures of the angles of a triangle is 180 deg.

k + 33 + 75 = 180

k + 108 = 180

k = 72

Answer:

1. 32

2. 41

3. 72

Step-by-step explanation:

which equation represents the graph function?

Answers

Answer:

[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]

Step-by-step explanation:

First, notice that since the graph of the function is a line, we have a linear function.

To find the equations for linear functions, we need the slope and the y-intercept. Recall the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

We are given the point (0,3) which is the y-intercept. Thus, b = 3.

To find the slope, we can use the slope formula:

[tex]\displaystyle m=\frac{\Delta y}{\Delta x} =\frac{2-3}{3-0}=-1/3[/tex]

Therefore, our equation is:

[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]

15% as a fraction in its lowest terms is:

-3/20
-5/100
-1/15
-3/100

Answers

Answer:

3/20

Step-by-step explanation:

15%

15/100

/5  /5

3/20

The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle

Answers

Answer:

width = 4.5 m

length = 14 m

Step-by-step explanation:

okay so first you right down that L = 5 + 2w

then as you know that Area = length * width so you replace the length with 5 + 2w

so it's A = (5 +2w) * w = 63

then 2 w^2 + 5w - 63 =0

so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14

compute the missing data in the table for the following exponential function f(x)={1/4}

Answers

I can’t see the table, more info plz

Answer:

1/256

Step-by-step explanation:

The table shows a chain of fractions for f(x), x1 is 1/4, x2 is 1/16 and x3 is 1/64. All you need to do is multiply the denominator by 4 and put 1 over it. 64*4 = 256, adding the 1 as the numerator gives us the answer of 1/256 as x4.

In a particular year, the mean score on the ACT test was 19.6 and the standard deviation was 5.2. The mean score on the SAT mathematics test was 546 and the standard deviation was 126. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal placesFind the z-score for an ACT score of 26. The Z-score for an ACT score of 26 is ______ .

Answers

Answer:

0.11

Step-by-step explanation:

Let the random variable score, X = 26; mean, ∪ = 19.6; standard deviation, α = 5.2

By comparing P(0≤ Z ≤ 26)

P(Z ≤ X - ∪/α) = P(Z ≤ 26 - 19.6/5.2)

= P(Z ≤ 1.231)

Using Table: P(0 ≤ Z ≤ 1) = 0.39

P(Z > 1) = (0.5 - 0.39) = 0.11

∴ P(Z > 26) = 0.11

how many types of progression in mathematics?

Answers

There are three different type


Explain

In math , there are three different type , they are arithmetic progression ( Ap) , Geometric progression and Harmonic



Arithmetic Progression - When a fix constant is added to each number except the first number.

For example : 2,4,6,8,10..... Here 2 is added each time to get the next number.


2. Geometric Progression - When a fix constant is multiplied to each number except the first number.

For example : 2,6,18,54.... Here 3 is multiplies each time to get first number.

3. Harmonic - a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression.

For example : 1/2 , 1/4 , 1/6, 1/8 ....

¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5

Answers

Answer:

The series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Step-by-step explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ; [tex]X_n=2n+1[/tex]

If we put n = 1, then;

[tex]X_1=(2\times 1)+1[/tex]

[tex]X_1 = 2+1 = 3[/tex]

If we put n = 2, then;

[tex]X_2=(2\times 2)+1[/tex]

[tex]X_2 = 4+1 = 5[/tex]

If we put n = 3, then;

[tex]X_3=(2\times 3)+1[/tex]

[tex]X_3 = 6+1 = 7[/tex]

If we put n = 4, then;

[tex]X_4=(2\times 4)+1[/tex]

[tex]X_4 = 8+1 = 9[/tex]

Hence, the series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3

Answers

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

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