Suppose a license plate must contain 3 letters followed by 4 digits. Letters and digits can be repeated. How many different license plates are possible that end with 5 as the last digit?
There are 17,576,000 possible license plates consisting of 3 letters followed by 4 digits.
Fundamental Counting Principles:
The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation.
When something can be done m different ways and n different ways,
there are then [tex]m*n[/tex] ways to accomplish both.
Based on the given information, since the letters and digits may be repeated, there are:
26 ways to fill in the first letter
26 ways to fill in the second letter
26 ways to fill in the third letter
10 ways to fill in the first digit
10 ways to fill in the second digit
10 ways to fill in the third digit and
1 way to fill in the first digit (as the last digit end with 5)
Thus, by Fundamental Principle of Counting, there are 17,576,000 possible license plates.
26 x 26 x 26 x 10 x 10 x 10 x 1 = 17,576,000
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A small tree was planted at a height of 5 feet. The tree has been planted for 15 months, and is now 42.5 feet tall. Which equation could be used to find x, the average number of feet the tree grew each month?
A.
15x + 5 = 42.5
B.
5x + 15 = 42.5
C.
15x + 42.5 = 5
D.
42.5x + 5 = 15
The equation that shows the height of the tree is 42.5 = 15x + 5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The slope intercept form of the linear equation is:
y = mx + b
where m is the slope and b is the initial value.
Let y represent the height of the small tree and x represent the average number of feet the tree grew each month. Hence:
A small tree was planted at a height of 5 feet. Hence, b = 5.
The tree has been planted for 15 months, and is now 42.5 feet tall. This makes:
42.5 = 15x + 5
The equation is 42.5 = 15x + 5
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In this number sentence, both triangles represent the same number. 32 - (triangle) = (triangle) - 8. What number do the triangles represent?
Answer:
Δ = 20
Step-by-step explanation:
let triangle be Δ , then
32 - Δ = Δ - 8 ( subtract 32 from both sides )
- Δ = Δ - 40 ( subtract Δ from both sides )
- 2Δ = - 40 ( divide both sides by 2 )
Δ = 20
If the growth factor of function f is k times the growth factor of function g, what is the value of k?
The value of k depends on the specific functions f and g and their growth rates. The growth factor is a measure of how quickly a function grows relative to another function. To determine the value of k, you would need to compare the growth rates of f and g.
Finding Value of kHere's how you can do to finding the value of k:
Define the functions f and g and specify their growth rates.Express the growth rate of f in terms of the growth rate of g.Solve for k.For example, if f(n) = n² and g(n) = n, then the growth rate of f is proportional to n² and the growth rate of g is proportional to n. To find the value of k, we can write:n² = k * n
Dividing both sides by n, we get:n = k
So in this case, the value of k is 1.This is just a simple example, and the specific value of k will depend on the growth rates of the specific functions you're comparing.
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Actors competing in a 42 mile bicycle race he’s already completed 18 miles of the racing is traveling at a constant speed of 12 mph when one starts the race what is traveling at a constant speed for 16 mph. Our constant speed could want to travel to catch up with Hector at the finish line explain.
In 4 hours, and 30 minutes (or 4.5 hours), Wanda will catch up to the hector.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Hector competing in a 42-mile bicycle race he’s already completed 18 miles of the racing and is traveling at a constant speed of 12 mph.
Let x = the hours needed for Wanda to catch up to Hector.
Hector has already completed 18 miles. Hector travels at 12 miles per hour.
After x more hours, Hector will travel
18 + 12x miles
Wanda travels at 16 miles per hour. In x hours, she travels
16x miles
If Wanda catches up to Hector, then
16x = 18 + 12x
4x = 18
x = 4.5 hours
Therefore, Wanda will catch up to the hector at 4 hours, 30 minutes (or 4.5 hours).
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Complete question:
How many terms are there in the following expression:
-12x + 15y -17x + 16y
Answer:
4 terms
Step-by-step explanation:
-12x
15y
-17x
16y
How is (8÷ 2) + (4 x 7) written as a verbal description?
A t-shirt printer can produce 40 tank tops with logos in 5 hours. At this rate, how many tank tops with logos can they printer produce in 7 hours?
Answer: It should be 56
Step-by-step explanation:
first we know for 40 tank-tops with logos can be finished in 5 hours, but we need to know how many shirts can be printed in 7 hours.
First we have x as 40 and y as 5. How many times can 5 go into 40?.. 8 times. So now we have 8. 8 x 7=56
X=56
Y=8
I hope this helps! Just to make sure it may not be correct, very sorry if it didn't work! Have a nice day/night!
-GreenteaStudys
if you draw five cards at random from a standard deck of 52 cards, what is the probability that there are at least 4 distinct characters (letters or numbers)?
If you draw five cards at random from a standard deck of 52 cards, the probability that there are at least 4 distinct characters (letters or numbers) is 0.8406.
This probability is calculated using the combination formula. The formula states that the number of possible outcomes when selecting r items from a set of n is equal to n!/(r! (n-r)!). consider a deck of 52 cards, each with a unique letter or number. When selecting 5 cards at random, the probability of there being at least 4 distinct characters is the same as the probability of there being exactly 4 distinct characters.
This is because if there are 4 distinct characters, there must be a fifth card with a character that has already been drawn. Therefore, the probability of there being at least 4 distinct characters is the same as the probability of there being exactly 4 distinct characters. Since there are 52 possible characters and we are selecting 5 cards, the probability can be calculated using the combination formula and is equal to 0.8406.
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7. A portrait without its frame has
a height 1.5 times its width w,
in inches. Its frame is 4 in. wide
all along its perimeter. What is
an expression for the area of the
framed portrait in terms of w?
Simplify your expression and write
it in standard form.
The expression for the area of the framed portrait in terms of w is: A = [tex]1.5w^{2}[/tex] + 12w + 64.
How to simplify an expression?Simplifying an expression means to write it in its simplest form by combining like terms and removing any redundant or unnecessary elements. There are several techniques you can use to simplify expressions, including:
Combining like terms: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms. To simplify an expression, you can add or subtract like terms.
Distributing: Distributing means multiplying a constant or variable by each term within a set of parentheses. For example, if you have the expression 2(x + 3), you can distribute the 2 to each term within the parentheses: 2x + 6.
Factoring: Factoring means finding a common factor among a set of terms and grouping them together. For example, if you have the expression [tex]x^{2}[/tex] + 4x, you can factor out the x: x(x + 4).
Simplifying rational expressions: Rational expressions are expressions that have one fractional term. To simplify a rational expression, you can cancel out common factors in the numerator and denominator.
Let's call the width of the portrait w and the height h. We know that the height of the portrait is 1.5 times its width, so h = 1.5w.
The area of the portrait is the product of its width and height: A = w * h = w * 1.5w = [tex]1.5w^{2}[/tex].
The width of the frame is 4 inches all along its perimeter, so the total width of the framed portrait is w + 4 + 4 = w + 8.
The total height of the framed portrait is h + 4 + 4 = h + 8 = 1.5w + 8.
The area of the framed portrait is the product of its width and height: A = (w + 8) * (1.5w + 8) = (w + 8) * 1.5w + 8 * (w + 8) = 1.5w^2 + 12w + 64.
So, the expression for the area of the framed portrait in terms of w is: A = [tex]1.5w^{2}[/tex] + 12w + 64.
This expression is already in standard form.
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Write the slope-intercept form of the equation of the line satisfying the given conditions.
Through (-2,4); slope: -3/4
Write the equation in slope-intercept form.
(Simplify your answer. Type your answer in slope-intercept form.)
I’m pretty sure it’s y = 0x+4
I need help with getting an answer for these
Answer:
Step-by-step explanation:
(-1, 6/5) = logbase4(5x^2) etc
only 5 = ln(x+5) = ln (x-1) + ln(x+1)
only 3 = log(x-1) etc.
(-1, 5) = e^x^2 = e^4x+5
Use the information given to answer the question.
One U.S. dollar is equivalent to about 6 Chinese yuan.
One U.S. dollar is equivalent to about 334 Saudi riyal.
Danny has 48 yuan and 84 riyal. What is the equivalent value of this money in U.S. dollars?
Answer:
I'm not sure but it might be 8 42/167
Step-by-step explanation:
At a small high school, 5 students took Mrs. Jones's AP Statistics class last year. The student's names are Ashley, Brayden, Carmen, Dale, and Eve. Ashley, Brayden, and Carmen each got a 5 on the AP Statistics exam. Mrs. Jones would like to use the results of these 5 students to demonstrate how to create a sampling distribution of the sample proportion for simple random samples of size n = 2 for her current students. a) What is the value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam? Explain. b) Using the table provided, list all 10 possible simple random samples of size n = 2, and for each sample calculate the sample proportion of students who got a 5 on the AP Statistics exam. The first one is completed for you. SRS n = 2 А, В P 1 c) Using the number line provided, create a dotplot to display the sampling distribution of p. d) is the sample proportion an unbiased estimator of the population proportion? Explain.
Answer:
Step-by-step explanation:
a) The value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam, is 3/5. This is because out of the 5 students, 3 (Ashley, Brayden, and Carmen) got a 5 on the AP Statistics exam.
b) The 10 possible simple random samples of size n = 2 are:
Ashley, Brayden; P = 2/2 = 1
Ashley, Carmen; P = 2/2 = 1
Ashley, Dale; P = 1/2 = 0.5
Ashley, Eve; P = 1/2 = 0.5
Brayden, Carmen; P = 2/2 = 1
Brayden, Dale; P = 1/2 = 0.5
Brayden, Eve; P = 1/2 = 0.5
Carmen, Dale; P = 1/2 = 0.5
Carmen, Eve; P = 1/2 = 0.5
Dale, Eve; P = 0/2 = 0
c) To create the dotplot for the sampling distribution of p:
Label the number line with 0, 0.5, 1
For each sample proportion calculated, place a dot above the corresponding value on the number line
Repeat this process for all sample proportions
d) Yes, the sample proportion is an unbiased estimator of the population proportion. This means that on average, the sample proportion will equal the population proportion. In other words, the mean of the sampling distribution of the sample proportion will equal the population proportion.
find the equation of the line perpendicular to 5y = 2x - 4 which passes through (0,7)
Answer: To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the original line and use the point-slope form of a line.
The equation of the original line is 5y = 2x - 4, which we can rearrange to get y = (2/5)x - 4/5. The slope of this line is 2/5. The negative reciprocal of the slope is -5/2.
Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the slope -5/2 and the point (0, 7), we get:
y - 7 = -5/2 (x - 0)
y - 7 = -5/2 x
y = -5/2 x + 7
So the equation of the line perpendicular to 5y = 2x - 4 and passing through (0, 7) is y = -5/2 x + 7.
Step-by-step explanation:
(2a^2 - 5a + 10) - (a^2 - 9)
How do you answer this?
Answer:
a^2 -5a + 19
Step-by-step explanation:
(2a^2 - 5a + 10) - (a^2 - 9)
= (2a^2 - 5a + 10) - a^2 + 9 [Distribution]
= a^2 -5a + 19
PLEASE HELP
X =
(15x - 30)°
T
Answer:
x=1°
Step-by-step explanation:
I gave my explanation in the previous question. Now, I can just solve:
(15x-30)°=45°
15x°=15°
x=1°
PLEASE MARK AS BRAINLIESTwhat is the domain and range
John had 72 flyers supposed around town last week he posted 1/3of them this week he posted 5/6 of the remaining flyers how many flyers has he still not posted
Answer:
8 posters
Explanation:
first you need to find how many he posted the first week. You do this by multiplying 72 by 1/3, or 72/3. That is 24. Then, you need to subtract that amount, 72-24 is 48. Then, you need to figure out how many he posted the second week. To do that, you need to figure out what 1/6 of 48 is first. So you would need to divide 48 by 6, which equals 8. So if John posted 5/6 of 48, you then need to multiply 8 by 5, equaling 40. If john posted 40 of his 48, then 48-40 is 8, meaning he has 8 posters to post.
Big ideas math 7.4.
Based on the properties of a rhombus, the measure of each numbered angle is:
m<1 = 36°
m<2 = 72°
m<3 = 72°
m<4 = 72°
m<5 = 36°
What are the Properties of a Rhombus?The two set of opposite sides of a rhombus are parallel to each other.Opposite angles have the same measure.The diagonals bisect each of the angles.Using the properties mentioned above, we can solve for the numbered angles as explained below:
ED and FG are parallel, therefore, m<3 = 72° (alternate interior angles)
m<4 = 72° [bisected angles of a rhombus by the diagonal]
m<2 = m<4 (alternate interior angles)
m<2 = 72°
m<1 = 180 - m<2 + 72 [sum of a triangle]
Substitute:
m<1 = 180 - 72 + 72
m<1 = 36°
m<5 = m<1 [opposite angles are equal in a rhombus]
m<5 = 36°
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Find the slope of the line that passes through (-3,-7) and (7,9)
Answer:
Step-by-step explanation:
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
Slope = (y2 - y1) / (x2 - x1)
Plugging in the given points, we get:
Slope = (9 - (-7)) / (7 - (-3))
= 16 / 10
= 1.6
So the slope of the line passing through (-3, -7) and (7, 9) is 1.6.
Answer:
m = 8/5
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
(-3,-7) and (7,9)
We see the y increase by 16 and the x increase by 10, so the slope is
m = 16/10 = 8/5
So, the slope is 8/5
Two families attend a performance of the Circus Mage. The cost of a ticket for adult is
1.5 times higher than that of a child ticket. Clothilde buys a ticket for her, for her
husband and for her 2 children. She pays $90 in all, taxes included. Her friend Naomie
buys tickets for her 4 children and herself. Clothilde thinks that going to the circus
costs her less than Naomie. Is she right?
Clothilde thinks that going to the circus costs her less than Naomie and she is right
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let the cost of 1 child be "c"
Let the cost of 1 adult be "a"
Given a=1.5c
Clothilde buys a ticket for her, for her
husband and for her 2 children.
=> She buys for 2 adults and 2 children
price = 2a+2c
Substitute a=1.5c
price = 2(1.5c )+2c
= 3c+2c
= 5c
Naomie
buys tickets for her 4 children and herself.
=> She buys for 1 adult and 4 children
price = a+4c
Substitute a=1.5c
price = 1.5c +4c
= 5.5c
5c < 5.5c
So, Clothilde thinks that going to the circus costs her less than Naomie and she is right
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Jimmy collected 100 pounds of aluminum cans to recycle.He plans to collect an additional 35 pounds each day. Write the equation for the total pounds,P, of aluminum cans after w weeks. What does the slope and y-intercept represent? How long will it take Rufus to collect 1000 pounds of cans?
Maria and Gabriella each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Maria spent $114 on 10 ft² of grass sod and 9 geraniums. Gabriella spent $90 on 5 ft² of grass sod and 10 geraniums. What is the cost of one ft² of grass sod and the cost of one geranium?
Maria and Gabriella each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Maria spent $114 on 10 ft² of grass sod and 9 geraniums. Gabriella spent $90 on 5 ft² of grass sod and 10 geraniums. What is the cost of one ft² of grass sod and the cost of one geranium?
Answer:
$11/ft^2 of grass, $12/geranium
Step-by-step explanation:
sally has 20 water bottles he gives 10 to jerry how many does sally have left?
If sally has 20 water bottles and then he gives 10 to jerry, the number of water bottles he have left is 10.
According to the question, it is given that :
Total number of water bottles sally had = 20 water bottles
Number of water bottles, Sally gives to jerry = 10 water bottles
Number of water bottles sally have left are
Total number of water bottles sally had - Number of water bottles sally gives to jerry
Number of water bottles sally have left = 20 - 10
Number of water bottles sally have left = 10 water bottles
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help please xxxxxxxxxxxx
Part A
BOXES The diagram shows the dimensions of a box used by a manufacturing company to
ship products.
s+2
s+3
What is the volume of the box? Write the expression in standard form.
the difference of their volumes of the boxes is 2lh+2bh+2lb+4b+4l+4h+8.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
Let the 1st box have length l, width b and height h.
So the 2nd box will have l+2, b+2 and h+2.
volume of 1st box is l*b*h.
volume of 2nd box is (l+2)*(b+2)*(h+2)= (lb+2l+2b+4)(h+2)
=lbh+2lh + 2bh+4h+2lb+4l+4b+8
The difference of their volumes = 2lh+2bh+2lb+4b+4l+4h+8
Hence the difference of their volumes of the boxes is 2lh+2bh+2lb+4b+4l+4h+8.
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william has a 26 2626-liter glass tank. first, he wants to put some marbles in it, all of the same volume. then, he wants to fill the tank with water until it's completely full. if he uses 85 8585 marbles, he will have to add 20.9 20.920, point, 9 liters of water. what is the volume of each marble?
The volume of each marble in a 26 liter glass tank is 12.
The tank's volume is listed as 26.
The tank requires 20.9 liters of water to fill when 85 marbles are placed inside.
So the volume of 85 marble
= 26-20.9 = 5.1
So, volume of each marble
= 5.1/85 = 0.06
Therefore, the volume that will be covered if William wishes to use 200 marbles is:
200*0.6 = 12
Therefore, the volume of marbles in a 26 litre tank is equal to 12
Water will therefore be needed to fill the tank.
= 26 - 12 = 14
Therefore, The volume of each marble in a 26 liter glass tank is 12.
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Complete question:
William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. If he uses 85 marbles, he will have to add 20.9 liters of water. What is the volume of each marble? How much water is necessary if William uses 200 marbles?
what is the probability that a randomly selected patient is admitted for something other than coronary care?
The probability that a randomly chosen patient will be admitted for a reason other than coronary care is equal to one less than the likelihood that they will be admitted for that reason.
The likelihood that a randomly chosen patient will be admitted for a reason other than coronary care is equal to 1 less than the likelihood that they will be admitted for that reason. For instance, if the chance of being admitted for coronary care is 0.25, the chance of being admitted for a different reason is 0.75. This is due to the requirement that the total number of outcomes must equal 1. Accordingly, if one outcome has a 0.25 probability, then the chance of every other outcome must equal 0.75. As a result, the likelihood that a randomly chosen patient will be admitted for a reason other than coronary care is equal to 1 minus the likelihood that they will be admitted for that reason.
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How many solutions does the system of equations have?
A. No solution
B. Four solutions
C. Exactly one solution
D. Infinitely many solutions
Answer:
C. Exactly one solution
Step-by-step explanation:
You want to know the number of solutions of the system of equations shown in the graph.
Point(s) of intersectionA solution to a system of equations is the set of points on a graph where all of the equations are satisfied simultaneously. For a system of two linear equations, it will be the point(s) where the lines intersect.
Here, the lines intersect at one point, so there is exactly one solution.