Diego planted a 8 inch tall magical beanstalk. The height of the beanstalk increases by 16% each day.Write a function ff that determines the height of the beanstalk in inches in terms of the number of days tt since Diego planted the beanstalk f(t)=f(1)/f(0)=f(2)/f(1)=f(5.28)/f(4.28)=For any value of x, what is the value of f(x+1)/f(x)?

Answer:

a) 13% of people did not experience problems with an online transaction.

b) 36.54% of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website

c) 46.11% of people experienced problems with an online transaction and contacted customer-service representatives.

Step-by-step explanation:

a. What percentage of people did not experience problems with an online transaction?

87% of people have experienced problems with an online transaction. So 100 - 87 = 13% of people did not experience problems with an online transaction.

b. What percentage of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website?

87% of people have experienced problems with an online transaction. Forty-two percent of people who experienced a problem abandoned the transaction or switched to a competitor′s website.

Then:

0.87*0.42 = 0.3654

36.54% of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website.

c. What percentage of people experienced problems with an online transaction and contacted customer-service representatives?

87% of people have experienced problems with an online transaction. Fifty-three percent of people who experienced problems contacted customer-service representatives.

Then:

0.87*0.53 = 0.4611

46.11% of people experienced problems with an online transaction and contacted customer-service representatives.

Step-by-step explanation:

y=7x-10

Answer:

[tex]\huge \boxed{y=7x-10}[/tex]

Step-by-step explanation:

[tex]-7x+y=-10[/tex]

[tex]\sf Add \ 7x \ on \ both \ sides.[/tex]

[tex]-7x+y+7x=-10+7x[/tex]

[tex]y=7x-10[/tex]

Answer:

See the answers below.

Step-by-step explanation:

[tex]a.\:\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2x^2-x-5-\left(2a^2-a-5\right)}{x-a}\\\\=\frac{2x^2-x+a-2a^2}{x-a}\\\\=\frac{2\left(x+a\right)\left(x-a\right)-1\left(x-a\right)}{x-a}\\\\=\frac{\left(x-a\right)\left[2\left(x+a\right)-1\right]}{x-a}\\\\=2x+2a-1\\\\\\b.\:\frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{2\left(x+h\right)^2-\left(x+h\right)-5-\left(2x^2-x-5\right)}{h}\\\\=\frac{2\left(x^2+2xh+h^2\right)-\left(x+h\right)-5-\left(2x^2-x-5\right)}{h}\\[/tex]

Expand and simplify to get:

[tex]=\frac{2h^2+4xh-h}{h}\\\\=\frac{h\left(2h+4x-1\right)}{h}\\\\=2h+4x-1[/tex]

Best Regards!

Answer:

a. The distribution is bell-shaped and symmetric: True.

b. The distribution is bell-shaped and symmetric: True.

c. The probability to the left of the mean is 0: False.

d. The standard deviation of the distribution is 1: True.

Step-by-step explanation:

The Standard Normal distribution is a normal distribution with mean, [tex] \\ \mu = 0[/tex], and standard deviation, [tex] \\ \sigma = 1[/tex].

It is important to recall that the parameters of the Normal distributions, namely, [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] characterized them.

We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where [tex] \\ x[/tex] is the raw score that we want to standardize.

Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:

(a) True or False: The distribution is bell-shaped and symmetric

Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.

(b) True or False: The mean of the distribution is 0.

Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

If [tex] \\ x = \mu[/tex]

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

[tex] \\ z = \frac{0}{\sigma}[/tex]

[tex] \\ z = 0[/tex]

Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.

(c) True or False: The probability to the left of the mean is 0.

Answer: False. The probability to the left of the mean is not 0. The cumulative probability from [tex] \\ -\infty[/tex] until the mean is 0.5000 or [tex] \\ P(-\infty < z < 0) = 0.5[/tex].

(d) True or False: The standard deviation of the distribution is 1.

Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.

In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, [tex] \\ x - \mu[/tex], by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, [tex] \\ \sigma[/tex].

In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.

Answer:

A: true

B: true

C: false

D: true

Answer:

The length of the short side is 14.5 units, the length of the other short side is 18.5 units, and the length of the longest side is 23.5 units.

Step-by-step explanation:

The Pythagorean Theorem

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

                                                     [tex]a^2+b^2=c^2[/tex]

Applying the Pythagorean Theorem  to find the lengths of the three sides we get:

[tex](x)^2+(x+4)^2=(x+9)^2\\\\2x^2+8x+16=x^2+18x+81\\\\2x^2+8x-65=x^2+18x\\\\2x^2-10x-65=x^2\\\\x^2-10x-65=0[/tex]

Solve with the quadratic formula

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\mathrm{For\:}\quad a=1,\:b=-10,\:c=-65:\quad x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}\\\\x_{1}=\frac{-\left(-10\right)+ \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5+3\sqrt{10}\\\\x_{2}=\frac{-\left(-10\right)- \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5-3\sqrt{10}[/tex]

Because a length can only be positive, the only solution is

[tex]x=5+3\sqrt{10}\approx 14.5[/tex]

The length of the short side is 14.5, the length of the other short side is [tex]14.5+4=18.5[/tex], and the length of the longest side is [tex]14.5+9=23.5[/tex].

Answer:

Minimum = 25

First quartile = 58

Second quartile = 72

Third quartile = 80

Maximum = 98

Step-by-step explanation:

Answer:

15.74% of the player's serves were between 115 mph and 145 mph

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

[tex]\mu = 100, \sigma = 15[/tex]

What percentage of the player's serves were between 115 mph and 145 mph

This is the pvalue of Z when X = 145 subtracted by the pvalue of Z when X = 115.

X = 145

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

[tex]Z = \frac{145 - 100}{15}[/tex]

[tex]Z = 3[/tex]

[tex]Z = 3[/tex] has a pvalue of 0.9987

X = 115

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

[tex]Z = \frac{115 - 100}{15}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

0.9987 - 0.8413 = 0.1574

15.74% of the player's serves were between 115 mph and 145 mph

Answer:

$1733.67

Step-by-step explanation:

Simple interest rate formula: A = P(1 + r)^t

Simply plug in your known variables

A = 1700(1 + 0.04)^0.5

A = 1733.67

Remember that t is time in years.

Answer:

a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12

c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.

d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.

Step-by-step explanation:

Let the event that a student does homework regularly be H.

The event that a student passes the course be P.

- 60% of her students do homework regularly

P(H) = 60% = 0.60

- 95% of the students who do their homework regularly generally pass the course

P(P|H) = 95% = 0.95

- She also knows that 85% of her students pass the course.

P(P) = 85% = 0.85

a) The probability that a student will do homework regularly and also pass the course = P(H n P)

The conditional probability of A occurring given that B has occurred, P(A|B), is given as

P(A|B) = P(A n B) ÷ P(B)

And we can write that

P(A n B) = P(A|B) × P(B)

Hence,

P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')

From Sets Theory,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

P(H n P) = 0.57 (from (a))

Note also that

P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)

0.60 = P(H n P') + 0.57

P(H n P') = 0.60 - 0.57

Also

P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)

0.85 = P(H' n P) + 0.57

P(H' n P) = 0.85 - 0.57 = 0.28

So,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

Becomes

0.03 + 0.28 + 0.57 + P(H' n P') = 1

P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12

c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.

Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,

P(A n B) = 0.

But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.

Hence, the two events aren't mutually exclusive.

d. Are the events "pass the course" and "do homework regularly" independent? Explain

Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when

P(A|B) = P(A)

P(B|A) = P(B)

P(A n B) = P(A) × P(B)

To check if the events pass the course and do homework regularly are mutually exclusive now.

P(P|H) = 0.95

P(P) = 0.85

P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671

P(H) = 0.60

P(H n P) = P(P n H)

P(P|H) = 0.95 ≠ 0.85 = P(P)

P(H|P) = 0.671 ≠ 0.60 = P(H)

P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)

None of the conditions is satisfied, hence, we can conclude that the two events are not independent.

Hope this Helps!!!

Answer:

n =32

Step-by-step explanation:

If 1 contestant is eliminated each round

then of 1024contestants

32 left

1024/32=32

Answer:

n=32

Step-by-step explanation:

Answer:

-45/2 - 12/2 = -57/2

Step-by-step explanation:

Substitute 15 for x in the given equation:  y = (-3/2)x - 6 becomes

y = (-3/2)(15) - 6 = -45/2  -  6 when x = 15.  This is equivalent to -57/2

Answer:

The number of employees classified into groups as shown below:

1 - 10: 3 6 (2companies)

11-20: 16 (1 company)

21-30: 25, 26, 27 (3 companies)

31-40: 34, 35, 35, 35, 36 (5 companies)

41-50: 41, 43, 48, 48 (4 companies)

Hope this helps!

Answer:

11-20 is 1

31-40 is 5

Step-by-step explanation:

Just count the amount

Hope that helps :D

Answer:

  see attached

Step-by-step explanation:

The attachments show the initial (brown) and final (blue) positions of the phone. The spreadsheet shows all the intermediate locations and the formulas used to determine them.

The two reflections cancel the total of 180° of CW rotation, so the net result is simply a translation. That translation is up by 9 units.

__

Translation up adds to the y-coefficient; translation right adds to the x-coefficient. Down or left use negative values.

90° CW does this: (x, y) ⇒ (y, -x)

Reflection across y does this: (x, y) ⇒ (-x, y)

Reflection across x does this: (x, y) ⇒ (x, -y)

Answer:

  56.25°

Step-by-step explanation:

The definition of the cosine function tells you that

  cos(B) = BC/BA

  B = arccos(BC/BA) = arccos(5/9)

  B ≈ 56.25°

Answer:

a) 0.9332 = 93.32% drink 2 cups per day or more.

b) 0.8413 = 84.13% drink no more than 4 cups per day

c) The minimum number of cups consumed by a heavy coffee drinker is 4.52.

d) 86.86% probability that the mean number of cups per day is greater than 3

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

[tex]\mu = 3.2, \sigma = 0.8[/tex]

a. What proportion drink 2 cups per day or more?

This is 1 subtracted by the pvalue of Z when X = 2. So

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

[tex]Z = \frac{2 - 3.2}{0.8}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

1 - 0.0668 = 0.9332

0.9332 = 93.32% drink 2 cups per day or more.

b. What proportion drink no more than 4 cups per day?

This is the pvalue of Z when X = 4.

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

[tex]Z = \frac{4 - 3.2}{0.8}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

0.8413 = 84.13% drink no more than 4 cups per day

c. If the top 5% of coffee drinkers are considered "heavy" coffee drinkers, what is the minimum number of cups consumed by a heavy coffee drinker?

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

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

[tex]1.645 = \frac{X - 3.2}{0.8}[/tex]

[tex]X - 3.2 = 1.645*0.8[/tex]

[tex]X = 4.52[/tex]

The minimum number of cups consumed by a heavy coffee drinker is 4.52.

d. If a sample of 20 men is selected, what is the probability that the mean number of cups per day is greater than 3?

Sample of 20, so applying the central limit theore with n = 20, [tex]s = \frac{0.8}{\sqrt{20}} = 0.1789[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 3.

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

By the Central Limit Theorem

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

[tex]Z = \frac{3 - 3.2}{0.1789}[/tex]

[tex]Z = -1.12[/tex]

[tex]Z = -1.12[/tex] has a pvalue of 0.1314

1 - 0.1314 = 0.8686

86.86% probability that the mean number of cups per day is greater than 3

Answer:

4

Step-by-step explanation:

9.8 +12x+y-7

2.8+12x+4y

Answer:

[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]

And we can find this probability using the normal standard table with this difference:

[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(1539,1580)[/tex]  

Where [tex]\mu=1400[/tex] and [tex]\sigma=\sqrt{10000}= 100[/tex]

We are interested on this probability

[tex]P(1539<X<1580)[/tex]

And we can solve the problem using the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]

And we can find this probability using the normal standard table with this difference:

[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]

Step-by-step explanation:

In my opinion maybe he has spent 98%

Answer:

(a) The standard error of the mean is 0.091.

(b) The probability that the sample mean will be less than $7.75 is 0.0107.

(c) The probability that the sample mean will be less than $8.10 is 0.9369.

(d) The probability that the sample mean will be more than $8.20 is 0.0043.

Step-by-step explanation:

We are given that the average price for a movie in the United States in 2012 was $7.96.

Assume the population standard deviation is $0.50 and that a sample of 30 theaters was randomly selected.

Let [tex]\bar X[/tex] = sample mean price for a movie in the United States

The z-score probability distribution for the sample mean is given by;

                              Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where,  [tex]\mu[/tex] = population mean price for a movie = $7.96

            [tex]\sigma[/tex] = population standard deviation = $0.50

            n = sample of theaters = 30

(a) The standard error of the mean is given by;

     Standard error  =  [tex]\frac{\sigma}{\sqrt{n} }[/tex]  =  [tex]\frac{0.50}{\sqrt{30} }[/tex]

                                =  0.091

(b) The probability that the sample mean will be less than $7.75 is given by = P([tex]\bar X[/tex] < $7.75)

  P([tex]\bar X[/tex] < $7.75) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{7.75-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z < -2.30) = 1 - P(Z [tex]\leq[/tex] 2.30)

                                                         = 1 - 0.9893 = 0.0107

The above probability is calculated by looking at the value of x = 2.30 in the z table which has an area of 0.9893.

(c) The probability that the sample mean will be less than $8.10 is given by = P([tex]\bar X[/tex] < $8.10)

  P([tex]\bar X[/tex] < $8.10) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{8.10-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z < 1.53) = 0.9369

The above probability is calculated by looking at the value of x = 1.53 in the z table which has an area of 0.9369.

(d) The probability that the sample mean will be more than $8.20 is given by = P([tex]\bar X[/tex] > $8.20)

  P([tex]\bar X[/tex] > $8.20) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{8.20-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z > 2.63) = 1 - P(Z [tex]\leq[/tex] 2.63)

                                                         = 1 - 0.9957 = 0.0043

The above probability is calculated by looking at the value of x = 2.63 in the z table which has an area of 0.9957.

Answer:

You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. but you're worried that only 100 students will show up to vote. how often will the underdog (the one with 45% support) win? to find out, you set up a simulation.

a. describe-how-you-will-simulate a component.

b. describe-how-you-will-simulate a trial.

c. describe-the-response-variable

Step-by-step explanation:

Part A:

A component is one voter's voting. An outcome is a vote in favor of our candidate.

Since there are 100 voters, we can stimulate the component by using two random digits from 00 - 99, where the digits 00 - 64 represents a vote for our candidate and the digits 65 - 99 represents a vote for the under dog.

Part B:

A trial is 100 votes. We can stimulate the trial by randomly picking 100 two-digits numbers from 00 - 99.

And counted how many people voted for each candidate.  Whoever gets the majority of the votes wins the trial.

Part C:

The response variable is whether the underdog  wins or not.

To calculate the experimental probability, divide the number of trials in which the simulated underdog wins by the total number of trials.

Answer:

Step-by-step explanation:

thats the answer...

just:  Expand the polynomial using the FOIL method.

Answer:

(x-1)(x-1)=(x-1)² because it's the same thing multiplied by itself

Using FOIL method:

(x-1)(x-1)=

x²-x-x+1=

x²-2x+1

Answer:

0.495 probability that Jim and Molly take counters of different colours

Step-by-step explanation:

For each trial, there are only two possible outcomes. Either a blue counter is picked, or a red counter is picked. The counter is put back in the bag after it is taken, which means that we can use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that the counter is red is 0.45

This means that [tex]p = 0.45[/tex]

Jim taken a counter, then Molly:

Two trials, so [tex]n = 2[/tex]

What is the probability that Jim and Molly take counters of different colours?

One red and one blue. So this is P(X = 1).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{2,1}.(0.45)^{1}.(0.55)^{1} = 0.495[/tex]

0.495 probability that Jim and Molly take counters of different colours

Answer:

Option B

Step-by-step explanation:

<r = 32 degrees (alternate angles )

<r = <n = 32 degrees (vertical angles)

Answer:

[tex]distance=\sqrt{32}[/tex]  , which agrees with answer "c" in your list of possible options

Step-by-step explanation:

Use the formula for distance between two points [tex](x_1,y_1)[/tex], and [tex](x_2,y_2)[/tex] on the plane:

[tex]distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance= \sqrt{(4-8)^2+(-7-(-3))^2} \\distance= \sqrt{(-4)^2+(-4)^2} \\distance=\sqrt{16+16}\\distance=\sqrt{32}[/tex]

Answer:

6x(x - 6y +2)

Step-by-step explanation:

Step 1: Write out expression

6x² - 36xy + 12x

Step 2: Factor out x

x(6x - 36y + 12)

Step 3: Factor out 6

6x(x - 6y + 2)

That is the most we can do. We can only take GCF to factor. Since we don't have an y² term we do not have binomial factors.

Answer:

if the sequence is:

12, 13, 13, 14, 14 etc, and each term keeps growing up, the sequence obviusly diverges.

Now, if the sequence is

1/2, 1/3, 1/3, 1/4, 1/4, 1/5 , 1/5

so the terms after the first one repeat, we could group the terms with the same denominator and get:

1/2, 2/3, 2/4, 2/5..... etc.

So the terms after the first one are aₙ = 2/n.

Now, a criteria to see if a sequence converges if seing if:

[tex]\lim_{n \to \infty} a_n = 0[/tex]

and here we have;

[tex]\lim_{n \to \infty} 2/n[/tex]

that obviusly tends to zero, so we can conclude that this sequence converges.

then the limit is:

There exist a n' such that for any n > n' then IL -aₙI < ε

where L is the limit

I2/n - 0I = I2/nI < ε

then this is true if n > 2/ε = n'

Answer:

  x = -1

Step-by-step explanation:

The usual approach to these is to square the radicals until they are gone.

  [tex]\displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}[/tex]

Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.

The solution is x = -1.

_____

Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.

Answer:

Unit rate = 81  riders/ car.

Step-by-step explanation:

Given

729 riders in 9 cars

we have to find unit rate in terms of riders per car

let the the riders per car (i.e rate) be x.

If there are 9 cars then

total no. of riders in 9 cars = no. of cars *  riders per car = 9*x = 9x

given that 729 riders in 9 cars

then

9x = 729

=> x = 729/9 = 81

Thus, riders per car =  x = 81.

Unit rate is 81 riders per car.

Answer:

D.

Step-by-step explanation:

One slope is positive and one negative, so one line should go up and one down. B or D.

y = 1/2 x - 1 line goes up and y-int. = - 1.  Answer D.

y = - 1/2 x + 3 line goes up and y-int. = 3.  Answer D.