The California license plate has one number followed by three letters followed by three numbers. How many different license plates are possible? Do not use commas in your answer. Answer:

9.8 +12x+y-7

2.8+12x+4y

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.

Step-by-step explanation:

In my opinion maybe he has spent 98%

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:

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:

B. I and II only.

Step-by-step explanation:

A person who is 61 inches tall is predicted to weight 104.6 pounds according to the regression model.

[tex]y(61)=-115+3.6(61)=-115+219.6=104.6[/tex]

The slope of the linear regression model indicates the rate of change of the predicted variable in function of a unit change in the independent variable. In this case, for each additional inch in height, the predicted weight will increase, on average by 3.6 pounds, as indicated by the slope of this model.

As the slope m=3.6 is positive, the correlation is positive: when the independent variable increases, the predicted variable also increases.

A] Both I and II are correct.

Weight = - 115 + 3.6 (Height)

Here, 115 is the autonomous weight at 0 level of height, it is the intercept.  3.6 is the slope, representing change in weight due to change in height. Slope implies that : For every additional inch of height, the predicted weight will increase, on average by 3.6 pounds.                                                                    So, II is True

At height = 61 inches, weight = - 115 + 3.6 (61) = - 115 + 219.6 = 104.6             So, I is  True

Regression shows cause effect relationship (of height on weight). Correlation shows just co-relationship in direction of variables' movement. Nevertheless, positive regression correlation increases the probability of positive correlation (instead of negative correlation)                                           So, III is false

https://brainly.com/question/7656407?referrer=searchResults

Answer: He would need at least a 95

Step-by-step explanation:

First I found the current average by adding 72, 74, 89, and 90 which equals 325.

Second, I worked backwards to see what the sum of his grades had to be by multiplying 84 times 5. 84 times 5 = 420

Now that we have both the current and the target sum, we find the difference by doing 420-325 which equals 95.

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:

The p-value of the test is 0.1515.

Step-by-step explanation:

The hypothesis for the test can be defined as follows:

H₀: The mean level of arsenic is 80 ppb, i.e. μ = 80.

Hₐ: The mean level of arsenic is greater than 80 ppb, i.e. μ > 80.

As the population standard deviation is not known we will use a t-test for single mean.

It is provided that the sample mean was, [tex]\bar X=91[/tex].

The adjusted sample provided is:

S = {57, 64, 70, 82, 84, 123}

Compute the sample standard deviation as follows:

[tex]\bar x=\farc{57+64+70+82+84+123}{6}=80\\\\s=\sqrt{\frac{1}{6-1}\times [(57-80)^{2}+(64-80)^{2}+(70-80)^{2}+...+(123-80)^{2}]}=23.47[/tex]

Compute the test statistic value as follows:

 [tex]t=\frac{\bar X-\mu}{\s/\sqrt{n}}=\frac{91-80}{23.47/\sqrt{6}}=1.148[/tex]

Thus, the test statistic value is 1.148.

Compute the p-value of the test as follows:

 [tex]p-\text{value}=P(t_{n-1}<t)[/tex]

                [tex]=P(t_{6-1}<1.148})\\\\=P(t_{5}<1.148})\\\\=0.1515[/tex]

*Use a t-table.

Thus, the p-value of the test is 0.1515.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.1515 > α = 0.05

The null hypothesis will not be rejected at 5% level of significance.

Thus, concluding that the mean level of arsenic in chicken from the suppliers is 80 ppb.

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:

[tex]m ^ {3/7}[/tex]

Step-by-step explanation:

=> [tex]\sqrt[7]{m^3}[/tex]

[tex]\sqrt[7]{}= ^\frac{1}{7}[/tex]

=> [tex]m^{3*1/7}[/tex]

=> [tex]m ^ {3/7}[/tex]

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:

[tex]-p^4+4p^3-5p^2+8p-6[/tex]

I hope this help you :)

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:

The probability that the sampling distribution of sample porportions is less than 77% is P(p<0.77)=0.1106.

Step-by-step explanation:

We know that the population proportion is π=0.81.

We want to know the probability that the sampling distribution of sample proportions, with sample size n=144, is less than 0.77.

The sampling distributions of sampling proportions has a mean and standard deviation calculated as:

[tex]\mu_p=\pi=0.81\\\\\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.81\cdot 0.19}{144}}=\sqrt{0.001068}=0.0327[/tex]

Then, we calculated the z-score for p=0.77:

[tex]z=\dfrac{p-\pi}{\sigma_p}=\dfrac{0.77-0.81}{0.0327}=\dfrac{-0.04}{0.0327}=-1.2232[/tex]

The probability that the sample proportion is less than 0.77 is:

[tex]P(p<0.77)=P(z<-1.2232)=0.1106[/tex]

Answer:

V= 1/3 h π r²

hope it helps

Answer:

The answer is Y = 6.3973.

Note: Kindly find an attached document of the complete question to this solution

Sources: The complete question was researched from Quizlet site.

Step-by-step explanation:

Solution

Given that:

The regression  equation is given below:

Y = - 0.3302 + 0.0672 x₁ + 0.6735 x₂ + 0.9980 x₃

Now,

When x₂ = 5, x₁ = 50, x₃ = 0

Y = - 0.3302 + 0.0672 * 50 +0.6735 * 5

Y=  - 0.3302 + 3.36 + 3.3675

Y = 6.3973

Therefore the time (hour) it will take for the driver to make five deliveries on a 50 mile journey not during rush hour is 6.3973.

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:

b) -1/9

Step-by-step explanation:

Given

              [tex]a_{n} = \frac{(-1)^{n} }{2n-1}[/tex]

First term

              [tex]a_{1} = \frac{(-1)^{1} }{2(1)-1} = -1[/tex]

second term

            [tex]a_{2} = \frac{(-1)^{2} }{2(2)-1} = \frac{1}{3}[/tex]

Third term

           [tex]a_{3} = \frac{(-1)^{3} }{2(3)-1} = \frac{-1}{5}[/tex]

Fourth term

          [tex]a_{4} = \frac{(-1)^{4} }{2(4)-1} = \frac{1}{7}[/tex]

Fifth term

         [tex]a_{5} = \frac{(-1)^{5} }{2(5)-1} = \frac{-1}{9}[/tex]

Answer:

B

Step-by-step explanation:

right on edge 2021

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:

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:

Slope: -1/2 Y-intercept: 1

Step-by-step explanation:

Slope: The line goes across 2 units, for every 1 unit down, so -1/2

Y-intercept: The line intersects the Y axis at 1

Answer:  Choice B.  slope = -1/2,  y intercept = 1

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

Explanation:

The line goes downhill as we move from left to right. This means the slope is negative. We can rule out anything that has a positive slope. The answer is between A and B.

We can rule out choice A because the y intercept is actually 1 (not 2) because it crosses the y axis here. The only thing left is choice B.

The slope is -1/2 because moving from (0,1) to (2,0) means we move down 1 unit and over to the right 2 units.

slope = rise/run = -1/2

rise = -1 indicates a drop of 1

run = 2 means we move to the right 2 units

-----------

You can use the slope formula to get the same result

I'll use the two points (0,1) and (2,0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 1)/(2 - 0)

m = -1/2

You could use any other two points you want as long as they are on the diagonal line.

Answer:

y = 1/2x + 1

Step-by-step explanation:

Step 1: Find slope

(1-0)/(0+2) = 1/2

Step 2: Write equation

y = 1/2x + 1

Answer:

2*2  * 2*2   * 2*3

Step-by-step explanation:

96 =16 *6

Break these down, since neither 16 nor 6 are prime

    = 4*4 * 2*3

4 in not prime, but 2 and 3 are prime

   = 2*2  * 2*2   * 2*3

All of these are prime

Answer:

22, 23

Step-by-step explanation:

Just got it right on edge 2021

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:

P(F | D) = 47.26%

There is a 47.26% probability that the foreman forgot to shut off the machine the previous night.

Step-by-step explanation:

A foreman for an injection-molding firm admits that on 23% of his shifts, he forgets to shut off the injection machine on his line.

Let F denote the event that foreman forgets to shut off the machine.

Failure to shut down at night causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 5% to 15%.

Let D denote the event that the mold is defective.

If the foreman forgets to shut off the machine then 15% molds get defective.

P(F and D) = 0.23×0.15

P(F and D) = 0.0345

If the foreman doesn't forget to shut off the machine then 5% molds get defective.

P(F' and D) = (1 - 0.23)×0.05

P(F' and D) = 0.77×0.05

P(F' and D) = 0.0385

The probability that the mold is defective is

P(D) = P(F and D) + P(F' and D)

P(D) = 0.0345 + 0.0385

P(D) = 0.073

The probability that the foreman forgot to shut off the machine the previous night is given by

∵ P(B | A) = P(A and B)/P(A)

For the given case,

P(F | D) = P(F and D)/P(D)

Where

P(F and D) = 0.0345

P(D) = 0.073

So,

P(F | D) = 0.0345/0.073

P(F | D) = 0.4726

P(F | D) = 47.26%

Answer:

3.5

Step-by-step explanation:

To find the mean, add up all the numbers

(8+0+3+3+1+7+4+1+4+4) = 35

Then divide by how many numbers there are

35/10 = 3.5

The mean is 3.5

Answer:

Step-by-step explanation:

- Mean- The AVERAGE OF ALL NUMBERS: You add up all the numbers then you divide it by the TOTAL NUMBER of NUMBERS!

8+0+3+3+1+7+4+1+4+4=35

35/10=3.5

35

Answer:

94

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

<1 = 29+65

   =94

Answer:

94°

Step-by-step explanation:

Angles in a triangle add up to 180°

[tex]180-65-29=86[/tex]

Angle 2 = 86°

Angles on a straight line add up to 180°

[tex]180-86=94[/tex]

Angle 1 = 94°

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:

Option B

Step-by-step explanation:

<r = 32 degrees (alternate angles )

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