1,000,000,000 social Security numbers can be formed using the numerals 0-9.
What is combination?A combination is grouping or sub-setting of items from a set where the order in which the selection is being made does not matter.
The formula for combination is:[tex]^{n}C_r = \frac{n!}{(n-r)!r!}[/tex]
where, n = Total number of items to be selected from.
r = Number of items to be selected.
According to the given problem,
Social security number contains nine digits.
A digit can be any number between 0-9.
For the first digit there are 10 choices which is 0-9 and the amount of numbers to be chosen is 1.
Thus there are [tex]^{10}C_{1}[/tex] ways for filling up first spot.
Similarly for the second digit , numbers available are 10 and numbers to be chosen is 9.
Thus there are [tex]^{10}C_{1}[/tex] ways for achieving this.
Same for third, fourth .. . . ninth digit.
Using the formula of combination, total number of ways would be,
= [tex]9 ~times~~ ^{10}C_{1}[/tex]
= [tex](\frac{10!}{1!\times (10-1)!})^9[/tex]
= 1000,000,000 ways
Hence we can conclude that there are 1000,000,000 ways of choosing 10 numbers from 0 to 9 for nine spots.
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Solving for Circumference of a Penny A penny is 1.9 cm wide. What is the circumference of a penny? Approximate using mc001-1.jpg = 3.14 and round the answer to the nearest tenth if necessary.
Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.
To find the circumference of a penny, we use the formula for the circumference of a circle:
Circumference = π * diameter
Since the penny's width is given (which is the same as the diameter), we can plug in the values:
Circumference = 3.14 * 1.9 cm
Now, calculate the circumference:
Circumference ≈ 5.966 cm
Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.
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Kurt bought a bike for $149.95. Eric bought a bike that had been $169.50 but was marked 1/5 off. How much less did Eric’s bike cost than Kurt’s?
After calculating the discount and subtracting it from the original price, Eric's bike cost $135.60, which is $14.35 less than Kurt's bike that cost $149.95.
To determine how much less Eric paid for his bike compared to Kurt's bike, we need to calculate the discount Eric received and subtract it from the original price of his bike. Then, we'll compare it to the price Kurt paid for his bike.
First, we calculate Eric's discount by multiplying the original price of the bike, $169.50, by 1/5 (which represents the 20% discount):
$169.50 times 15= $33.90.
Now, subtract this discount from the original price to find out how much Eric paid for the bike:
$169.50 - $33.90 = $135.60.
Finally, to find out how much less Eric's bike cost than Kurt's, we subtract the price Eric paid from the price Kurt paid:
$149.95 - $135.60 = $14.35.
Eric's bike cost $14.35 less than Kurt's.
what is the simplest form of this expression w^2(-4w^2-2)+(-5w^2)(-2w^2-2)
What do you call a person who makes face all day long
A clockmaker is the answer
A probability close to 1/2 indicates a chance event is ________ to occur
Likely, unlikely, or neither likely nor unlikely
Please help
Each chair installed in the new chapel requires 24 inches of clearance. If each row cannot be greater than 35 feet in length, how many chairs may be placed in each row?
(write as an inequality and solve)
The solution is 17 chairs
The number of chairs placed is 17 and the inequality equation is 2x < 35 , where x is the number of chairs
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of chairs be represented as x
Now , the inequality equation will be
Each chair installed in the new chapel requires 24 inches of clearance
So , 24 inches = 2 feet
And , each row cannot be greater than 35 feet
So , the number of 2 feet chairs = 2x
And , 2x cannot be greater than 35 feet
Substituting the values in the equation , we get
2x < 35 be equation (1)
Divide both sides of the equation by 2 , we get
x < 17.5
x < 17 chairs
Therefore , the value of x is 17 chairs
Hence , the number of chairs is 17 chairs
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Solve the system of equations. y = 7x + 43 y = 2x + 13 a. ( -6, 1) c. ( 6, 1) b. ( 6, -1) d. No solution
Sebby has 330 for singing lessons he paid 20 for each lesson how many lessons has he attended if he still has 210 left
name the following triangle according to its angles and sides: 120 degrees, 35 degrees, 25 degrees
Final answer:
The triangle with angles of 120 degrees, 35 degrees, and 25 degrees is classified as an obtuse scalene triangle because it has one angle greater than 90 degrees and all angles of different measures.
Explanation:
To classify the triangle with angles of 120 degrees, 35 degrees, and 25 degrees, we first confirm that the sum of its angles is 180 degrees, which is true for any plane triangle. Given this sum, we can classify the triangle based on its angles and sides.
A triangle with one angle greater than 90 degrees is called an obtuse triangle, as it has an obtuse angle (greater than 90 degrees). Since this triangle has a 120-degree angle, it fits that definition. Furthermore, because all the angles are different, we can classify it as a scalene triangle, meaning all sides have different lengths. Therefore, the correct classification for this triangle is an obtuse scalene triangle.
7.Kristy baked 18 cookies. She took 2/3 of the cookies to work. How many cookies did she NOT take to work? 4 6 8 12
The area of a circle is 68 square centimeters find the diameter
is .8801 positive or negative
Write the vertex form of the equation of the parabola which has a vertex of (0,0) and contains the point (1,2). A. Y=2x^2. B. Y=2(x-1)^2. C. Y=x^2. D. Y=(x+1)^2+1
The vertex form of the equation of a parabola with a vertex at (0,0) and passing through the point (1,2) is [tex]y=2x^2.[/tex]
The vertex form of a parabola is given by: [tex]y = a(x - h)^2 + k[/tex] where (h, k) is the vertex of the parabola.
In this case, the vertex is (0, 0), so h = 0 and k = 0.
Therefore, the equation becomes: [tex]y = a(x - 0)^2 + 0.[/tex] Simplifying further, the equation becomes: [tex]y = ax^2[/tex].
Now, we need to find the value of 'a.' To do this, we can use the given point (1, 2). Substitute these values into the equation:
[tex]2 = a(1)^2[/tex].
Therefore, 'a' is 2. So, the final equation in vertex form is: [tex]y = 2x^2.[/tex]
So, the correct answer is A. [tex]Y = 2x^2.[/tex]
Which line would be the line of best fit for the scatter plot?
The first line is the line of best fit for this given disperse plot.
"A disperse plot is a kind of plot or numerical graph involving Cartesian directions to show values for regularly two factors for a bunch of information.
On the off chance that the focuses are coded, one extra factor can be shown."
For a particular scatter plot, four different lines are drawn here.
We know, a line drawn on a disperse plot fits it the best is the line that is nearer to a large portion of the places.
a triangle with an area of 202.5 has a height that measures 15 find its base
Circumference is 4 what is the radius and area of the circle
a 15-oz iced tea at a certain restaurant had 135 calories. How many calories are there in a 22-oz iced tea?
The solution is, There are 198 calories in a 22-oz iced tea.
What is multiplication?
In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
a 15-oz iced tea at a certain restaurant had 135 calories.
now we have to find that, How many calories are there in a 22-oz iced tea.
i.e. we have
15/135 = 22/?
let, x calories are there in a 22-oz iced tea.
now, 15/135 = 22/x
or, x = 22 x 135 / 15
we have,
22 x 135 = 2970
2970/15 = 198
so, x = 198
There are 198 calories in a 22-oz iced tea.
Hence, The solution is, There are 198 calories in a 22-oz iced tea.
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A sandwich shop offers the following toppings. How many two topping sandwiches can you make?
-lettuce
-tomato
-bacon
-cheese
-mustard
A sandwich shop offers the following toppings. How many two topping sandwiches can you make?
-lettuce
-tomato
-bacon
-cheese
-mustard
Solution:
There are five toppings available and the five toppings are lettuce, tomato, bacon, cheese, mustard.
We need to make 2 topping sandwiches.
So, we can select any 2 toppings from the available 5 toppings
So, we must use combination here
So, the number of two topping sandwiches is 5 combination 2
Or, Number of 2 topping sandwiches= 5 C 2
The formula is, n C r =[tex]\frac{n!}{(n-r)!r!}[/tex]
So, The number of 2 topping sandwiches= 5 C 2 =[tex]\frac{5!}{(5-2)!2!}[/tex]
The number of 2 topping sandwiches=[tex]\frac{5!}{(3)!2!}[/tex]
The number of 2 topping sandwiches=[tex]\frac{(5*4*3*2*1)}{(3*2*1)(2*1)}[/tex]
The number of 2 topping sandwiches=[tex]\frac{120}{12}[/tex]
The number of 2 topping sandwiches=10
that is,
lettuce, tomato(1)
lettuce, bacon(2)
lettuce, cheese(3)
lettuce, mustard(4)
tomato,bacon(5)
tomato,cheese(6)
tomato,mustard(7)
bacon,cheese(8)
bacon, mustard(9)
cheese,mustard(10)
Answer: So, there are 10 possible two topping sandwiches
Graph the data from the table below. Describe the parent function as linear, square root, cube root, cubic, or quadratic.
Carrie wants to know what the probability is that a card drawn randomly from a deck will be an ace.her sample space includes all 52 cards in a standard deck.Which of these outcomes compose the event
Mr Jones spent 156 to attend a college football game .twenty percent of this cost was for a parking pass.he spent the remainder of the money on two tickets for the game .what was the price per ticket
Which does NOT appear in an algebraic expression?
A. a number
B. a variable
C. an equal sign
D. a multiplication symbol
A. What there-dimensional figure can be assembled from this net?
Answer:__________
B. If each square has a side length of 48 cm, write an expression for the surface area.
Answer:__________
C. Calculate the volume of the figure above given the side length of 48 cm. Use a formula. SHOW YOUR WORK.
D. What would happen to the volume of the figure if you reduce the side length by 25%? Explain your reasoning.
____________________________________________________________
Mitch does not know the correct answer to two multiple choice questions. The choices are A,B,C, and D. If Mitch just guesses, what is the probability that Mitch will guess both answers correctly?
Final answer:
Mitch has a 1/16 probability of guessing both multiple-choice answers correctly when randomly guessing among four options.
Explanation:
If Mitch guesses on two multiple-choice questions with choices A, B, C, and D, the probability of guessing both correctly is calculated as follows: The probability of correctly guessing one question is 1/4 (since there are 4 possible choices, and only one is correct). To find the probability of guessing both correctly, we multiply the probabilities of each independent event. Thus, the probability of guessing the first question correctly AND the second question correctly is 1/4 × 1/4 = 1/16.
You bought 5 folders that cost x dollars each, a calculator for $45, and a set of pens for $3. a. 5x + 48 c. 5x + 45x + 3x b. 5 + 45 + 3
Find an equation for the inverse of the relation y=6x-3. Show how you found the inverse equation.
The inverse of the relation y=6x-3 is y = (x + 3) / 6.
To find an equation for the inverse of the relation y=6x-3, we need to follow a series of steps which involves swapping the variables, and then solving for the new y.
Start with the initial equation: y = 6x - 3.
Swap the variables x and y: x = 6y - 3.
Solve for y to find the inverse relation: Add 3 to both sides to get x + 3 = 6y, then divide both sides by 6 to isolate y, resulting in y = (x + 3) / 6.
Diane is baking cookies. She bakes four dozen sugar cookies, three dozen butter cookies, and two dozen chocolate chip cookies. She gives away 2 dozen sugar cookies, 2.5 dozen butter cookies, and 1.5 dozen chocolate chip how many cookies does she have left? ( Give an exact number of cookies).
Find the quotient. (14x^3-21x^2 +28x)/(7x)
The calculated quotient of the expression (14x³ - 21x² + 28x) ÷ 7x is 2x² - 3x + 4
How to evaluate the quotient expression
From the question, we have the following parameters that can be used in our computation:
(14x³ - 21x² + 28x) ÷ 7x
Factor out x in the numerator
So, we have
(14x³ - 21x² + 28x) ÷ 7x = x(14x² - 21x + 28) ÷ 7x
Evaluate the quotient
(14x³ - 21x² + 28x) ÷ 7x = (14x² - 21x + 28) ÷ 7
Divide through by 7
(14x³ - 21x² + 28x) ÷ 7x = 2x² - 3x + 4
Hence, the quotient of the expression is 2x² - 3x + 4
The sum of the ages of two people is 32. The difference is their ages is 4. What is the age of the younger person ?
there are 54 people at the party. 18 of them are wearing red, what percent of them are not wearing red
There are 54 people at the party.
18 people are wearing red which means that 36 people are not wearing red
54 - 18 = 36
The fraction [tex]\frac{36}{54}[/tex] represents the 36 people at the party that are wearing no red. We can find what percent of the people at the party are not wearing red by turning [tex]\frac{36}{54}[/tex] into a percent.
[tex]\frac{36}{54}[/tex] can be reduced to [tex]\frac{2}{3}[/tex] by dividing both the numerator and denominator by the greatest common factor of 36 and 54.
2 ÷ 3 = 0.667
0.667 × 100 = 66.67%
Therefore, 66.67% of the people at the party are not wearing red