Select the correct answer from each drop-down menu. if f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4).

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:

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:

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.

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:

Just connect points Y and D with a straight line to make YD. Do the same for YE and YF, just attach Y to points E and F with a straight line.

Answer:

[tex]z=-1.49[/tex]

Step-by-step explanation:

[tex]\text{Standard Score, z} =\dfrac{X-\mu}{\sigma} $ where:\\\\Mean Pulse rate, \mu =67.3$ beats per minute\\Standard Deviation, \sigma = 10.3$ beats per minute.\\[/tex]

For a male student who has a measured pulse rate of 52 beats per  minute.

Raw Score, X =52 beats per  minute.

Therefore:

[tex]\text{Standard Score, z} =\dfrac{52-67.3}{10.3}\\z=-1.49[/tex]

Since the usual pulse rates are within 2 standard deviations of the mean, a z-score of -1.49 tells us that the selected student's pulse rate is within the usual pulse rates.

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:

Minimum = 25

First quartile = 58

Second quartile = 72

Third quartile = 80

Maximum = 98

Step-by-step explanation:

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:

$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:

No The reactions are not inverses to each other

Step-by-step explanation:

f(x) = 3x + 27

Let f(x) be y

y= 3x+27

subtracting 27 on both sides

3x = y - 27

x= (y-27)/3

= y/3 - 9

inverse function is x/3 -9 not x/3 + 9

Therefore, not an inverse

Hope it helps...

Answer:

Sugar:

Honey:

Sugar substitute:

Step-by-step explanation:

35 + 14 + 21 = 70

35 out of 70 = 50%

14 out of 70 = 20%

21 out of 70 = 30%

Hope this helps!

Answer:

0.0164 probability that exactly 11 black balls are drawn

Step-by-step explanation:

The balls are drawn without replacement, so we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

In this question:

Total of 88 + 88 = 176 balls, so [tex]N = 176[/tex]

33 balls are drawn, so [tex]n = 33[/tex]

We want 11 black balls(sucesses), so [tex]n = 11[/tex]

There are 88 black balls, so [tex]k = 88[/tex]

Then

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 11) = h(11,176,88,33) = \frac{C_{88,11}*C_{88,22}}{C_{176,33}} = 0.0164[/tex]

0.0164 probability that exactly 11 black balls are drawn

Answer:

261.71

Step-by-step explanation:

The calculation of days is shown below:-

[tex]X = \mu + Z\sigma[/tex]

where,

Mean = 270

standard deviation is 8

And, the normsinv is -1.036

Now placing these values to the above formula

So, the number of days is

= 270 + (-1.036433389)  × 8

= 270 + (-8.29146711)

= 261.708533

or

= 261.71

Therefore for computing the number of days we simply applied the above formula and for (-1.036433389) please find in the attachment.

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:

8

Step-by-step explanation:

2,3,5,11,13,14

Mean= 8

Standard deviation= 4.830

Answer:

The volume formula for a cylinder is V = πr²h. We are solving for h and we know that V, π and r are 86, 3.14, 3 respectively so we can write:

86 = 3.14 * 3² * h

86 = 28.26 h

h = 3.04

Answer:

i found the question mark ;)

Step-by-step explanation:

Problem 1

y = tan(3x+4)

f(x) = tan(3x+4)

f ' (x) = 3sec^2(3x+4) .... apply derivative chain rule

dy/dx = f ' (x)

dy = f ' (x) * dx

dy = ( 3sec^2(3x+4) ) * dx

Now plug in x = 5 and dx = 0.3

dy = ( 3sec^2(3*5+4) ) * 0.3

dy = 0.920681 which is approximate

Make sure your calculator is in radian mode.  Calculus textbooks will be in radian mode for the special sine limit definition [tex]\lim_{x\to0}\frac{\sin x}{x} = 1[/tex] to be true.

===========================================================

Problem 2

We'll have the same derivative function and same x value. The only difference is that dx = 0.6 this time.

dy = f ' (x) * dx

dy = ( 3sec^2(3*5+4) ) * 0.6

dy = 1.84136 approximately

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.

Step-by-step explanation:

In my opinion maybe he has spent 98%

Answer: k = 5

Step-by-step explanation:

Box A has more counters than box B

3 * 4 = 12

4 + 8 = 12

So if k was equal to 4, then both boxes would have the same amount.

3 * 5 = 15

5 + 8 = 13

15 > 13

If k was equal to 5, then Box A would contain more counters than Box B.

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 and Step-by-step explanation: Congruent triangles are triangles with the same three sides and same three angles.

There many ways to determine if 2 triangles are congruent.

One of them is ASA or Angle, Side, Angle and it means that if two angles and the included side of one triangle are equal to the corresponding angles and side on the other triangle, they are congruent.

In this case, angle MRQ and angle NQR are equal. The included side of both triangles are the same QR, so it can be concluded that triangle QNR is congruent to triangle RMQ.

The image in the attachment shows the angles and their included side, which are colored.

Answer:

4

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

There is the same amount of teachers in each department of the school.

He asks 7 different departments of the school and collects the data he wants to.

I think it is not bias

Answer:

no

Step-by-step explanation:

This sample of teachers in the school is not likely to be biased.

Hey there! :)

Answer:

[tex]-25m^{6}n^{9}[/tex]

Step-by-step explanation:

The product rule means that when multiplying variables with exponents, the exponents must be added together. Therefore:

[tex](-5m^{5}n^{6})(5mn^{3}) =[/tex]

[tex]-25m^{5+1}n^{6+3} =[/tex]

Simplify:

[tex]-25m^{6}n^{9}[/tex]

This is your answer!

Answer: z = 55.

Step-by-step explanation:

we want to find values of k that make this inconsistent.

x - 2y + 4z = 3

4x + 5y + kz = 9

y + 3z = 2

First, can you can see that k never can make some of the equations linearly dependent because of how constructed is the set. Now, let's see if there are values of k that give problems to our system.

To see it, let's solve the system.

from the third equation we can write y = 2 - 3z, and we can replace it into the first two equations:

x - 2(2 - 3z) + 4z  = 3

4x + 5(2 - 3z) + kz = 9

simplify both equations and get

x  + 10z = 7

4x  + ( k - 15)*z = - 1

from the first equation, we have that:

x = 7 - 10z

we can replace it into the other equation:

4*(7 - 10z) + (k - 15)*z = -1

28 - 40z + (k -15)*z = -1

(k - 55)*z = -29

z = -29/(k - 55)

here you can see that the only value of z that has problems is z = 55, because we never can have a 0 in the denominator.

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.

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