In a small state, the license plate for a car begins with two letters, which may be repeated, and ends with three digits, which also may be repeated. How many license plates are possible in that state?

Answer:

different slope same intercept

Step-by-step explanation:

g(x)= 3x+3

this means they both intercept the y axis at 3 but the incline of g is much greater then f since the slope is much larger.Hope this is what you were looking for

Answer:

Mean = 3x

Step-by-step explanation:

Mean = [tex]\frac{SumOfObservations}{TotalNumberOfObservations}[/tex]

Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]

Mean = [tex]\frac{15x}{5}[/tex]

Mean = [tex]\frac{15x}{5}[/tex]

Mean = 3x

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78

The probability of failure, q would be 1 - p = 1 - 0.78 = 0.22

n = 6

a) Mean = np = 6 × 0.78 = 4.68

b) Variance = npq = 6 × 0.78 × 0.22 = 1.0

c) Standard deviation = √npq = √(6 × 0.78 × 0.22) = 1.0

d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0

Answer:

9:20

Step-by-step explanation:

The ratio of the surface area of similar solid is equal to the square of the ratio of their corresponding linear measures.

If the ratio of their corresponding linear measures is a:b, the surface area ratio will be (a/b)².

Therefore, (A/B )² = 9/16

square root both sides A/B = √9/√16 A/B = 3/4 A:B = 3:4

The ratio of volume of two similar solid is the ratio cube of their corresponding linear measures.

Therefore, (B/C)³ = 27/125 cube root both sides B/C = 3/5 B:C = 3:5

To make the ratio equivalent A:B:C = 9:12:20

A:C = 9:20

Answer:

The probability that a group of 15 randomly selected skiers will overload the gondola = (3.177 × 10⁻⁵¹)

(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)

Step-by-step explanation:

Complete Question

A ski gondola carries skiers to the top of the mountain. If the Total weight of an adult skier and the equipment is normally distributed with mean 200 lb and standard deviation 40 lb.

Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola.

Solution

For 15 people to exceed 5000 lb, each person is expected to exceed (5000/15) per skier.

Each skier is expected to exceed 333.333 lb weight.

Probability of one skier exceeding this limit = P(x > 333.333)

This becomes a normal distribution problem with mean = 200 lb, standard deviation = 40 lb

We first standardize 333.333 lbs

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (333.333 - 200)/40 = 3.33

To determine the required probability

P(x > 333.333) = P(z > 3.33)

We'll use data from the normal distribution table for these probabilities

P(x > 333.333) = P(z > 3.33) = 1 - P(z ≤ 3.33)

= 1 - 0.99957

= 0.00043

So, the probability that 15 people will now all be above this limit = (probability of one person exceeding the limit)¹⁵ = (0.00043)¹⁵

= (3.177 × 10⁻⁵¹)

(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)

Hope this Helps!!!

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Work Shown:

Substitute y = 1 into the first equation. Basically we replace every y with 1. From here we solve for x

3x+y = 7

3x+1 = 7

3x+1-1 = 7-1 .... subtracting 1 from both sides

3x = 6

3x/3 = 6/3 .... dividing both sides by 3

x = 2

We have x = 2 pair up with y = 1. The two equations intersect at (2,1)

As a check, plugging (x,y) = (2,1) into the first equation should lead to a true statement

3x+y = 7

3(2)+1 = 7

6+1 = 7

7 = 7 and it does lead to a true statement

The graph is shown below.

Answer:

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

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 = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761[/tex]

What is the probability that the mean of this sample is less than 15.99 ounces of water?

This is the pvalue of Z when X = 15.99. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{15.99 - 16.15}{0.0761}[/tex]

[tex]Z = -2.1[/tex]

[tex]Z = -2.1[/tex] has a pvalue of 0.0179

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

Answer: 44

Step-by-step explanation:

This is a confusing problem to look at, so use PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction).

5 * (-4) + (1 - (-3)^2)^2      simplify inside the parenthesis

5 * (-4) + (1 - 9)^2

5 * (-4) + (-8)^2                simplify exponents

5 * (-4) + 64                     multiply

-20 + 64                          finally, addition

44

Answer:

255

Step-by-step explanation:

use calculator

Answer:

255

Step-by-step explanation:

∑ᵢ₌₁⁸ 2ⁱ⁻¹

Using brute force method:

S = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷

S = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128

S = 255

Using formula:

S = a₁ (1 − rⁿ) / (1 − r)

S = 1 (1 − 2⁸) / (1 − 2)

S = 255

Answer: d + 28

Step-by-step explanation:

Answer:

d+28

Step-by-step explanation:

it is easier to remeber that you should always flip the wording so for this on "d" would be first then add the 28

Answer:

the answer is the last option, c :8.

Answer:

D. No comma because the total probability is not equal to 1.

Step-by-step explanation:

Given the distribution:

[tex]\left|\begin{array}{c|cccccc}x&0&1&2&3&4&5\\ P(x)&1/25&1/5&1/2&3/4& 1/50&1/100\end{array}\right|[/tex]

The sum of the probabilities

[tex]\sum P(x)=1/25+1/5+1/2+3/4+ 1/50+1/100\\\sum P(x) =1.52 \neq 1[/tex]

Therefore, the distribution is not a probability distribution because the total probability is not equal to 1.

The correct option is D.

Answer:

The probability that a student arriving at the ATM will have to wait is 67%.

Step-by-step explanation:

This can be solved using the queueing theory models.

We have a mean rate of arrival of:

[tex]\lambda=1/3\,min^{-1}[/tex]

We have a service rate of:

[tex]\mu=1/2\,min^{-1}[/tex]

The probability that a student arriving at the ATM will have to wait is equal to 1 minus the probability of having 0 students in the ATM (idle ATM).

Then, the probability that a student arriving at the ATM will have to wait is equal to the utilization rate of the ATM.

The last can be calculated as:

[tex]P_{n>0}=\rho=\dfrac{\lambda}{\mu}=\dfrac{1/3}{1/2}=\dfrac{2}{3}=0.67[/tex]

Then, the probability that a student arriving at the ATM will have to wait is 67%.

Answer:

0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In this question:

[tex]m = 0.5, \mu = \frac{1}{0.5} = 2[/tex]

What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours?

[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4)[/tex]

In which

[tex]P(X \leq 1) = 1 - e^{-2} = 0.8647[/tex]

[tex]P(X \leq 0.4) = 1 - e^{-2*0.4} = 0.5507[/tex]

So

[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4) = 0.8647 - 0.5507 = 0.314[/tex]

0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours

Answer: -5, 6, and 9

Step-by-step explanation:

Step-by-step explanation:

least to greatest

-5 6 9

Answer:

option a (-1,-1/2)

Step-by-step explanation:

apply mid point formula

Answer:

8 and 9

Step-by-step explanation:

√64 = 8

√81 = 9

√74 falls inbetween those 2

Answer:

U are finding the slope. so the vertical line is ur rise(x value) and the horizontal line is ur y value. Hopefully that helped

Answer:

See the answers below. Thanks!

Step-by-step explanation:

(a). Option F is the correct choice. "There are two mutually exclusive outcomes, success or failure."

(b). P(X=15) = 0.1702

(c). P(X<15) = 0.0673

(d). P(X>=15) = 1 - P(X<15) = 0.9327

(e). P(13<=X<=15) = 0.1482

Best Regards!

Answer:

4 categories are shown in rows.

2 categories are shown in columns.

12 14 year olds.

82 people were polled.

Answer:

the same

Step-by-step explanation:

Answer:

The two solutions can be +10 and -10

Step-by-step explanation:

b^2 - 100 = 0

b^2 = 100

Take the root of both sides

b = +- 10

b = +10 , b = -10

Answer:

cooking ( mesurments )

gardening ( landscape )

designing ( art )

shopping for the best price ( aka money counting )

car rides ( figuring out distance and time )

sewing.

hope this helped :)

Step-by-step explanation:

Answer:

The population of interest is all the students at the University, to find their parking times.

Step-by-step explanation:

Sampling

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

Here, the population of interest is all New York state residents.

An administrator inconspicuously followed 250 students and carefully recorded their parking times.

Sample of 250 students at the University.

So the population of interest is all the students at the University, to find their parking times.

Answer:

First option is the right choice.

Step-by-step explanation:

x/95 = 15/19

x = 75

Best Regards!

Answer:

Option A

Step-by-step explanation:

Triangle ABC and DEF are similar.

Taking proportion of their sides to find the value of the unknown.

=> x/15 = 95/19

Cross Multiplying

=> 19x = 1425

Dividing both sides by 9

=> x = 75

26.

Step-by-step explanation:

To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...

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

With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.

[tex]10^2+24^2=c^2[/tex]

[tex]100+576=c^2[/tex]

Add the legs together.

[tex]676=c^2[/tex]

Now, since c is squared we will have to find the square root of 676.

[tex]\sqrt{676}[/tex]

= 26

Answer:

Both piecewise functions have a linear portion and a quadratic portion.  The y-intercepts of both linear pieces are the same, 2.  The quadratics are both open upward, but have different y-intercepts (one at 1, one at 2).  The linear portion of the first function is decreasing, while the linear portion of the second function is increasing.

Step-by-step explanation:

Comparing and contrast of the functions are shown in below.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The given piecewise functions are;

⇒ f (x) = { - x + 2 ; x < 0

         = { x² + 1 ; x > 0

Now, Comparison and contrast of the above piecewise functions are,

The similarities are;

1) Both piecewise functions are linear when x < 0.

2) Both piecewise functions are quadratic when x > 0.

3) The magnitude the slope of the linear part both function are equal.

4) The leading coefficient of the quadratic function are the same.

5) The y-intercept of the linear function are equal, therefore, the linear functions in f(x) and g(x) intersect on the y-axis.

6) The domain of the linear and quadratic functions are the same.

The contrasts (differences) in the function are;

1) The slope of the linear function of g(x) is positive and the slope of the linear function of f(x) is negative.

2) The y-intercept of the quadratic function in f(x) is +1, while the y-intercept of the quadratic function in g(x) is +2.

3) The quadratic function in f(x) and g(x) have graphs that do not intersect.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ7

Answer: H - 46

Step-by-step explanation:

Primeter = 2(l + w)

50 = 2{(3m+2) + (m-5)}

25 = 3m+2 +m -5

25 = 4m -3

m = 28/4 = 7

l = 3m+2 = 23 cm

w = m-5 = 2 cm

Area = l x b

= 23 x 2 = 46 sq. cm.

Answer:

21°

Step-by-step explanation:

All angles in a triangle add up to 180°.

180 - 31 - 128

= 21

The measure of the third angle is 21°.

Answer:

1/12 of a dozen is 1

Step-by-step explanation:

One dozen means 12. If you ask for 1/12 of 12, you multiply 12 and 1/12. You should get 1 as your answer.