5. PA license plates have 3 letters followed by 4 numbers.
a. If the same letter or number can be repeated, how many can be made?
b. If the same letter CANNOT be repeated, how many can be made?

Answers

Answer 1

Answer:

A. 175,760,000

B. 156,000,000

Step-by-step explanation:

For part A:

There are 26 letters in the alphabet.  Therefore, if there are 3 spots to use 26 letters, that is represented as [tex]26^3[/tex].  As for numbers, there are 10 digits from 0-9.  So if there are 4 spots for numbers, the total possible number of sequences is [tex]10^4[/tex].  So you simply multiply [tex]26^3[/tex] and [tex]10^4[/tex] to get 175,760,000 possible combinations.

For part B:

If the same letter can't be repeated, instead of using an exponent, we have to use a factorial, but only for the 3 digits required in the license plate.  These are called permutations and can be expressed as [tex]_2_6P_3[/tex], which is the same as saying 26 x 25 x 24.  Since there is no change to number of numbers, that remains the same.

[tex]_2_6P_3 * 10^4 =26*25*24*10^4=156,000,000[/tex]


Related Questions

2. Sally charges $8.50 an hour to babysit for the first hour and $7.50 an hour each additional hour. Write an expression to
represent the cost Sally charges if x is the number of hours after the first hour.

Answers

Answer:

c = 8.50 + 7.50x

Step-by-step explanation:

c = 8.5 + 7.50x

PLEASE HELP In 2010 the population of India was 1,231,000,000. By 2016, the population had increased by 7.5%.The land area of India is 1, 269,000 miles. What was the population density of India in 2016?

Complete the density statement below, round your answer to the nearest whole number

The population density of India in 2016 was

per

Answers

Answer:

The population density of India in 2016 was of 1042.8 habitants per miles squared.

Step-by-step explanation:

Population density:

Number of habitants divided by land area.

In 2010 the population of India was 1,231,000,000. By 2016, the population had increased by 7.5%.

This means that India's population in 2016 was given by:

1,231,000,000*1.075 = 1,323,325,000

The land area of India is 1, 269,000 miles squared:

1,323,325,000/1,269,000 = 1042.8 habitants per miles squared.

The population density of India in 2016 was of 1042.8 habitants per miles squared.

What is the equation of the graph below? y=1/2sinx y=1/2cosx y=1/2sin2x

Answers

Answer:

24

Step-by-step explanation:

I just did it in class. it was hard but you just have to think about the question

Katie's baby took 3 naps. Each nap was
of an hour long
How long did the baby nap in all? Move numbers to the blanks to answer the question.

Answers

Answer:

the answer is 3 hours

Step-by-step explanation:

it just makes sense

Evaluate: 5 - 3x when X = -2

Answers

Answer:

Rewrite the equation as 5-3-2. -2 is x, as it says in the problem. All you have to do is solve, so you're answer will result in 0. :)

Answer:

Replace the variable x  

with -2   in the expression.

5 − 3 x

Step-by-step explanation:

4) If the sum of two numbers is 64, and the larger number is 3 less than 3 times the
smaller number. Find the smaller number.

Answers

Answer:

19

i hope this is the correct answer.

From the equation, the smaller number is 67/4.

What is an equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x = smaller number and

y = bigger number

Then we can formulate an equation

x +y = 64 and y = 3x-3

Substituting y into

x+y = 64, we get the equation

[tex]x + 3x -3 = 64\\\\4x = 67\\\\x = \frac{67}{4}[/tex]

To learn more about equation: https://brainly.com/question/10413253

#SPJ2

1) Find the missing measures of this
isosceles triangle below .
48°
B.
C
MAC

Answers

Answer:

B measures 66°

C measures 66° .Sum of all angels is 180° .

Find the volume of the cone. Round your answer to the nearest hundredth.
A) 129.72m^3
B) 134.04m^3
C) 137.71m^3
D) 143.04

Answers

Answer:

can we get the figure plz

An article reported that for a sample of 58 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 164.55. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.) 611.81 , 696.51 ppm

Answers

Answer:

95% Confidence Interval = (611.81 ppm, 696.51 ppm)

Step-by-step explanation:

The formula for Confidence Interval is given as:

Confidence Interval = Mean ± z × s /√n

Mean = the sample mean/average = 654.16

s = the sample standard deviation = 164.55

z = z score of 95% confidence interval = 1.96

Confidence Interval =

654.16 ± 1.96 × 164.55/√58

= 654.16 ± 42.348

Hence,

654.16 - 42.348

= 611.812

Approximately to two decimal places = 611.81 ppm

654.16 + 42.348

= 696.508

Approximately to two decimal places = 696.51 ppm

Therefore, the 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected is (611.81 ppm, 696.51 ppm).

Tess and Dan have $24.00 each to spend at a book fair, where all students receive a 15% discount. They both want to purchase a copy of the same book, which normally sells for $24.50 plus 10% sales tax. To check if she has enough to purchase the book, Tess takes 15% of $24.50 and subtracts that amount from the normal price. She takes 10% of the discounted selling price and adds it back to find the purchase amount. Dan takes 85% of the normal purchase price and then computes 110% of the reduced price. Is Tess correct? Is Dan correct? Do they have enough money to purchase the book? Explain your answer using complete sentences.

Answers

Answer:

Tessa is correct. They have enough money.

Please read Comfort Zone on Wattpad!!!!!!

Solve for V . 7v-20=-6(v-1) Simplify your answer as much as possible.

Answers

Answer:

v = 2

Step-by-step explanation:

You can start by distributing -6:

7v - 20 = -6v + 6

To combine the like x terms, you can add 6v to both sides:

7v - 20 = -6v + 6

+6v          +6v

13v - 20 = 6

Now add 20 to both sides to isolate the x term:

13v - 20 = 6

      +20   +20

13v = 26

You can divide by 13 on both sides to find v,

13v = 26

÷13    ÷13

v = 2

Answer:

v= 2

Step 1: Simplify both sides of the equation.

7v−20=−6(v−1)  

7v+−20=−6v+6

7v−20=−6v+6

Step 2: Add 6v to both sides.

7v−20+6v=−6v+6+6v

13v−20=6

Step 3: Add 20 to both sides.

13v−20+20=6+20

13v=26

Step 4: Divide both sides by 13.

13v/13   = 26/13  

v=2

Solve the system of equations using substitution.

4x – y = 7
3y – 12x = –21

(3, 5)

(6, 17)

no solution

infinite solutions

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

solve  by substitution:

solve equation 1 for y: - y = 7 - 4x; divide by -1 to simplify into y = -7 + 4x

Substitute - 7 + 4x into the second equation to obtain:

3(-7 + 4x) - 12x = -21, which yields:

-21 + 12x - 12x = -21, which simplifies 0 = 0

a result of 0 = 0 means infinite solutions such as:

(2,1), (3, 5), (4, 9), (5, 13), (6, 17)....

Answer:

infinite soulutions

Step-by-step explanation:

i just did it and it was right on ed2021...

PLEASE HELP ME ON THIS

Answers

Answer: C

Step-by-step explanation:

What is the solution to the system of equations below?
y = 2/5 x -3 and x = -10
-
A= (-10, -7)
B= (-10, -1)
C= (-7, -10)
D= (-1, -10)
WILL MARK FIRST CORRECT ANSWER BRAINLIEST

Answers

Answer:

here u go gurly

Step-by-step explanation:

Determine the value of angle ABC?

Answers

Answer:it is about 90-93 degrees and also it is a obtuse

Step-by-step explanation:

it is simple because it the other side to the right says 98 if you put it in it position it is alittle bigger so thats how i got my answer

Answer:

∠ ABC = 62°

Step-by-step explanation:

The inscribed angle ABC is half the measure of its intercepted arc AC

AC = 360° - (138 + 98)° = 360° - 236° = 124° , then

∠ ABC = [tex]\frac{1}{2}[/tex] × 124° = 62°

What is the area of the shape

Answers

The answer is : 72 sq. Ft. Because you have to measure the ones who are on the diagonal line so if you multiply 8 by 9 you get 72 and that’s the answer hope I helped.

20 PTS! WILL MARK BRAINLIEST
A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 157 square units, and the area of the cross-section of the cylinder is 50π square units. Based on this information, which argument can be made?

The volume of the square prism is one third the volume of the cylinder.
The volume of the square prism is half the volume of the cylinder.
The volume of the square prism is equal to the volume of the cylinder.
The volume of the square prism is twice the volume of the cylinder.

Answers

Answer:

The volume of the square prism is equal to the volume of the cylinder.

Step-by-step explanation:

As per the information depicted the volume of the square prism is equal all to the volume of the cylinder. Hence option C is correct.

What is the square prism?

A square prism is thee dimensional cuboid with a base and the top has an equal square while the remaining four faces have a rectangle and the opposite side angles of the square prism are congruent and parallel to each other.

As a square prism have the least two lengths that are equal to each other. Hence the volume of the square prism is equal to the volume of the cylinder as they have the same height and area of cross-section.

Find out more information about the square prism.

brainly.com/question/4315703

Select ALL of the expressions that are equivalent to 3(8-4x)
24 - 4x
12x - 24
24 - 12x
-12x + 24
2(12 - 6x)

Answers

Step-by-step explanation:

24-12x,and 2(12-6x)

hope it helps

G(x)=3(x/2)
If you input 2 into g(x), what do you get for an output?

Enter your answer in the simplest form in the space provided below.

(If your answer is a decimal number, round it to two decimal places.)

Example answer: 42.63

Answers

Answer:

[tex]g(x) = 4[/tex]

Step-by-step explanation:

Given

[tex]g(x) = 3\frac{x}{2}[/tex]

Required

Find g(2)

This is calculated as:

[tex]g(x) = 3\frac{x}{2} \\[/tex]

Substitute 2 for x

[tex]g(x) = 3\frac{2}{2}[/tex]

[tex]g(x) = 3+1[/tex]

[tex]g(x) = 4[/tex]

Which is the equation of the given line?

Answers

Answer:

y = 1

Step-by-step explanation:

since its a horizantal line

if u take any 2 points and find the slope, for example if we take points (1, 1) and (4, 1) the slope will be 0/3 which is zero

y = 0x + b

so there is basically no x in this case

so y = b

now plug in a point from the line, (1, 1)

y = mx + b

y = 0x + b

1 = 0(1) + b

1 = 0 + b

1 = b

b = 1

final equation:

y = 0x + 1

y = 1

What is the answer using synthetic division? -6x^3+18^2-7x-b divided by x-2

Answers

Answer:

[tex]-6x^{3} + 322-7x - \frac{b}{x}[/tex]

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Please help fasst???!!! Plzzzx

Answers

Answer:

y = 10(½)^(x)

Step-by-step explanation:

In writing exponential functions passing through points, we will just substitute the x and y values in each case into y = ab^(x).

Now, for point (-1, 20), the exponential function is; 20 = ab^(-1)

20 = a/b

For the point (1, 5), the exponential function is; 5 = ab^(1)

5 = ab

From 20 = a/b, we have; a = 20b

Thus, putting 20b for a in 5 = ab, we have;

5 = 20b(b)

b² = 5/20

b² = 1/4

b = √(1/4)

b = 1/2

Since a = 20b, then;

a = 20 × 1/2

a = 10

Thus, from y = ab^(x), we have;

y = 10(½)^(x)

find the are of the triangle​

Answers

Answer:

It’s a, 49

Step-by-step explanation:

Area is length x width so you would count how long the triangle is and how wide it is so
7 x 7 is 49

The odds of winning a rifle are 1:9 the probability of winning a carnival game is 0.15 does the raffle or the carnival game give you better chance of winning

Answers

Answer:

Hence the carnival game gives you better chance of winning.

Step-by-step explanation:

Let the event of win be given by 1/10 in the game of rifle then the event of loose is given by 9/10

the

Odds in favor of a game are given by  = P(Event)/ 1- P(Event)

Odds in favor of winning a rifle are given by = 1/10/ 1- 1/10

                                                                         =1/10/9/10

                                                                          =1/9

                                                                             = 0.111

The probability of winning aa rifle game is 0.111

The probability of winning the carnival game is 0.15

Comparing the two probabilities   0.111:0.15

The probability of  winning carnival game is greater than winning a rifle game

0.15>0.11

Hence the carnival game gives you better chance of winning.

What is the probability of spinning a yellow?
What is the probability of spinning an odd number?
What is the probability of spinning a number less than 5?

Answers

Answer:

Answer given below

Step-by-step explanation:

P (spinning yellow) = 2 / 8 = 1 / 4

P (Spinning an odd number) = 4 / 8 = 1 / 2

P ( spinning a number less than 5) = 4 / 8 = 1 / 2

Hope it helps

The probability of spinning a yellow is 1/4.

The probability of spinning an odd number is 1/2.

The probability of spinning a number less than 5 is 1/2.

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

From the spinner

Blue region = 3

Red region= 1

Yellow region = 2

Purple region = 2

So, the probability of getting Yellow

P (spinning yellow) = 2 / 8

                                = 1 / 4

and, the probability of getting odd number

P (Spinning an odd number) = 4 / 8

                                               = 1 / 2

and, the probability of getting less than 5

P ( spinning a number less than 5) = 4 / 8

                                                         = 1 / 2

Learn more about Probability here:

https://brainly.com/question/30034780

#SPJ7

Find the inverse for each relation:

1. [(4,2),(5,1),(6,0),(7,-1)}

Answers

Answer:

the inverse for each relation:

1. [(4,2),(5,1),(6,0),(7,-1)} is

{(2,4),(1,5),(0,6),(-1,7)}

How much did each notebook and each binders cost

Answers

Answer:

Each notebook cost $3 and each binder cost $4.

Step-by-step explanation:

Do some trial and error when plugging in certain numbers for each notebook and each binder.  You should get $3 and $4 when plugging it in.

the value of y is directly proportional to the value of x. if y =35 when x=140, what is the value y when x=70

Answers

Answer:

17.5

Step-by-step explanation:

35÷y = 140 ÷ 70

or, 35 = 2y

or, y= 17.5

ARE the square root of the positive integer irrational? if not given an example of the square root of a number that is a rational number​

Answers

9514 1404 393

Answer:

  no; √4 = 2

Step-by-step explanation:

If an integer is the square of another integer, its square root is rational. For example, 9 = 3², so √9 = 3, a rational number.

The square root of an integer is irrational if and only if the integer is not a perfect square.

The Sine Function

The average number of customers per day at a home improvement store is given in the following table. The sine regression equation was found to be y = 29.882sin (0.887 x 1.271) + 85.635, where x represents the day where 1 = Sun of the week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use this model to predict the average number of customers on Tuesday. Round to the nearest customer.

a. 70
b. 67
c. 71
d. 64

Please select the best answer from choices provided

Answers

Answer:

D. 64

Step-by-step explanation:

I calculated it logically

Other Questions
Identify two technologies developed during World War II, and explain how these technologies affected the war's outcome. What is the zero of function f?f(x)=7^3Vx+12-12 40% of what is 35?help please 28. Briana Miller deposited a check for $543.00 and a check for $231.12. She received$60.00 in cash. What was her total deposit? Where does gene visit finny after he returns from summer school? Simplest form X^3-X^2+16x-16 On a scale drawing, the height of a tree is 3.75 inches. If the scale of the drawing is 1 in. : 50 ft, how tall is the tree?Geometry The crayon balloon is made up of a cone and a cylinder. What is the volume, in cubic inches, of the crayon balloon?A) 69.12 B) 75.40 C) 138.23 D) 276.46 You go to the doctor and he gives you 11 milligrams of radioactive dye. After 12 minutes, 7.75 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived Drag each label to the correct location on the image. Not all labels will be used.Match the labels with the symbols on the weather map. Do you agree with Milton Babbit's idea that modern composers should forget about the audience and retreat to writingIn private for themselves and other music professionals? What conclusion can you draw from the following picture?A taxi cab on a busy three-lane street. There are shops in the background.a.you are in a big city, probably NYCb.there seems to be a lot of traffic c.it is probably loud in this cityd.all of the abovePlease select the best answer from the choices provided Sample Means: PracticeQuestion 1 of 5Select the correct answer.A class is gathering data on the amount of time spent watching videos each day. Each student collected 10 pieces of data and willcompile that data to determine a population mean. One student, Megan, has a sample mean of 45.67.Which statement must be true about this situation?The population mean is also 45.67.oThe population mean must be less than 45.67.oThere is not enough information to make a conclusion about the population mean.The population mean must be greater than 45.67.SubmitReset What is the solution to the equation below round your answer to two decimal decimal places log4 x=2.1A. x=8.40B. x=18.38C. x=8.17D. x=19.45 Which source of evidence for evolution is the weakest? How do you find the vertex of this?y = 1/2 (x 8)(x + 10) A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 6 types of drinks to choose from, 3 types of sandwiches, and 4 types of chips. How many different value meal packages are possible? A baseball has a diameter of 4.3 inches. Find the volume of the baseball. Round your answer to the nearest tenth. Use 3.14 for . If a =5 and b=3 what is the value of the 2a-3b+3a I need helppppppppppp