Answer:
2625 different numbers
Step-by-step explanation:
General outlineCombinatoricsSpecial circumstancesPartitioning the situationConclusionPart 1. CombinatoricsThis type of problem is classified as a "Combinatorics" problem: Counting up the number of ways something can happen.
Many times when attempting to count a large number of items, patterns are recognized and shortcuts to count are developed so that one doesn't need to physically count all of the items. Perhaps the trickiest part of counting with these shortcuts is to ensure that one does not over-count (counting a scenario more than once), although it is equally important that we don't under-count (fail to count a situation that applies).
Part 2. Special circumstancesIt should be noted that for a number to be a 4 digit number, it must have 4 digits, and thus the first digit must not be zero (despite that that would be an even digit, the number itself would not be a 4 digit number).
Part 3. Partitioning the situationThere are 2 main scenarios:
1. All 4 digits are even
2. Exactly 3 digits are even (meaning that exactly one digit is odd).
There are two sub-cases to Scenario 2:
2.1. The first digit is odd, and all three of the other digits are even.
2.2. The first digit is even, and exactly two of the other digits are even (meaning that exactly one of the last three digits is odd).
None of scenarios 1, 2.1, and 2.2 overlap, so we're not over-counting:
If all 4 digits are even, then there can't be exactly 3 even digits. If the first digit is odd, then not all 4 digits are even nor is the first digit even. If exactly two of the last three digits are even, then not all 4 digits are even, nor are all three of the last digits even.Further, this is all of the possibilities for a 4 digit number with least three even digits, so we're not under-counting.
Scenario 1 -- All 4 digits are even.
If all 4 digits are even, then the first digit has fours choices (2,4,6,8), and the next 3 digits each have 5 choices (2,4,6,8,0).
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.1 -- The first digit is odd, and all three of the other digits are even
If the first digit is odd, there are 5 choices for the first digit (1,3,5,7,9), and the next 3 digits each have 5 choices (2,4,6,8,0).
[tex]5*5*5*5=625\text{ choices}[/tex]
Scenario 2.2 -- The first digit is even, and exactly two of the other digits are even
If the first digit is even, there are 4 choices for the first digit (2,4,6,8), and if exactly two of the next 3 digits are even, then there are 5 choices for each of the two even digits (2,4,6,8,0), and 5 choices for the odd digit (1,3,5,7,9), and there are "3 permuted by 2" ways of ordering those three digits.
[tex]4* \left [(5*5*5) * {}_3 \! P_2 \right ]=\\\\=4*\left [5*5*5 * \dfrac{3!}{2!} \right ]\\\\=4*\left [ 5*5*5 * \dfrac{3*2*1}{2*1} \right ] \\\\=4*\left [5*5*5 * 3 \right ] \\\\=1500\text{ choices}[/tex]
Scenario 2.2 broken down (calculated without using the permutation operation) -- The first digit is even, and exactly two of the other digits are even
Then either the second digit is odd (scenario 2.2.1), the third digit is odd (scenario 2.2.2), or the fourth digit is odd (scenario 2.2.3).
Scenario 2.2.1. The second digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second digit is odd: 5 choices for the odd digit (1,3,5,7,9)
The third and fourth digits are even: 5 choices for each even digit (2,4,6,8,0).
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.2.2. The third digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second and fourth digits are even: 5 choices for each even digit (2,4,6,8,0).
The third digit is odd: 5 choices for the odd digit (1,3,5,7,9)
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.2.3. The last digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second and third digits are even: 5 choices for each even digit (2,4,6,8,0).
The last digit is odd: 5 choices for the odd digit (1,3,5,7,9)
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenarios 2.2.1, 2.2.2, and 2.2.3 comprise all of Scenario 2.2, so [tex]500+500+500=1500\text{ choices}[/tex]
Part 4. ConclusionHow many ways can a 4 digit number be formed where at least 4 of the digits are even?
This is the sum of the choices from Scenario 1, Scenario 2.1, and Scenario 2.2, so [tex]500+625+1500=2625\text{ choices}[/tex].
What is the recursive formula for the geometric sequence with this explicit
formula?
The recursive formula for the geometric sequence is given as follows:
D.
[tex]a_1 = 9[/tex].[tex]a_n = a_{n-1} \times \left(-\frac{1}{3}\right)[/tex]What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
With a recursive formula, it is given by:
[tex]a_n = a_{n-1} \times q[/tex]
For this problem, the first term and the common ratio are:
[tex]a_1 = 9, q = -\frac{1}{3}[/tex]
Then the recursive formula is:
D.
[tex]a_1 = 9[/tex].[tex]a_n = a_{n-1} \times \left(-\frac{1}{3}\right)[/tex]More can be learned about geometric sequences at https://brainly.com/question/11847927
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These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
Help
simplest terms.
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.
The probability of drawing two yellow balls if they're not replaced exists 1/45.
What is probability?
The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.
Number of yellow marbles be 2
Number of pink marbles be 3
Number of blue marbles be 5
Total number of marbles = 2+3+5 = 10
The probability of removing the first yellow ball = 2/10
Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.
Probability of drawing the second yellow ball = 1/9.
Probability of drawing two yellow balls if they're not replaced
= 2/10 × 1/9
= 2/90
= 1/45
The probability of drawing two yellow balls if they're not replaced exists 1/45.
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Mr. Omwoyo, the principal of Maili Mbili Secondary would wish to cover the floor of the new administration block using square tiles. The floor is a rectangle of sides 12.8m by 8.4m. Find the area of the largest tiles in cm² which can be used to fit exactly without cutting.
Answer:
hi play truth and dare to with me in g met
The range, a measure of variability, Group of answer choices is the difference between the largest (L) and smallest (S) value in a list of scores is the most informative when used to describe data sets without outliers includes only two values in its computation, regardless of the number of scores in a distribution all of the above
The correct answer is all of the above.
Why is the range the most convenient measure of variability?
Your data's spread from the lowest to the greatest value in the distribution is indicated by the range. The calculation of this variability index is the simplest. Simply subtract the lowest value from the highest value in the data set to determine the range.How do you find the range?
The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response.Learn more about range
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A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true?
Based on the calculations, the true statements are:
A. The angular velocity is 10π rad/sec.
E. The angular velocity is 600π rad/min.
How to calculate the angular velocity?Mathematically, angular velocity can be calculated by using this formula:
ω = θ/t
Where:
ω is the angular velocity.θ is the angle.t is the time.Note: 1/2 revolution = 0.5 × 2π = π radians.
Substituting the given parameters into the formula, we have;
ω = θ/t
ω = π/0.1
ω = 10π rad/s.
Next, we would convert the time in seconds to minutes:
ω = 10π × 60
ω = 600π rad/min.
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Complete Question:
A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true? Check all that apply.
A. The angular velocity is 10π rad/sec.
B. The angular velocity is 10π rad/min.
C. The angular velocity is 60π rad/min.
D. The angular velocity is 600π rad/sec.
E. The angular velocity is 600π rad/min.
Answer:
A,
Step-by-step explanation:
Edge202
The line plot shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
The measure that best describes the data is the median and the measure that might mislead the data is the mode
How to determine the mean, median and mode?The mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{20* 2 + 50 * 3 + 60 * 6 + 70 * 3 + 80 * 4 + 90 * 4 + 100 * 2 + 130 * 1}{25}[/tex]
This gives
[tex]\bar x = \frac{1770}{25}[/tex]
[tex]\bar x = 70.8[/tex]
So, the mean is 70.8
The median is the middle number, and the position is calculated using
Median = (n + 1)/2 th
This gives
Median = (25 + 1)/2 th
Median = 13th
The 13th element is 70
So, the median is 70
The mode is the data element with the highest frequency.
So, the mode is 60
The measure that best describes the dataThe line plot has outliers at 20 and 130.
This is so because 20 and 130 are far from other data values
When a dataset has an outlier, the best measure is the median
Hence, the measure that best describes the data is the median.
The measure that might mislead the dataThe measure that might mislead the data is the mode
This is so the highest occurring value does not necessarily represent the dataset
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John's dad is 30 years old than john. if john were three times ad old as he is now,he would still be younger than his dad. what is the oldest that john could be right now
john could be right now 45
What is word problem in math?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."
According to the question:
John's dad is 30 years old than john .In essence, x = y -30 .................equation 1And
john were three times ad old as he is now.y=3xSolution for the above equation:
[tex]x=y-30, y=3 x \quad\\ \quad x=15, y=45[/tex]
steps:
[tex]x=y-30 \\y=3 x[/tex]
Substitute :[tex]$y=3 x$[/tex]
[tex][x=3 x-30][/tex]
[tex]for $$x=3 x-30: \quad x=15[/tex]
For [tex]$y=3 x$[/tex]
Substitute: [tex]$x=15$[/tex]
[tex]y=3 \cdot 15[/tex]
Simplify:
[tex]y=45[/tex]
The solutions to the system of equations are: [tex]$x=15, y=45$[/tex]
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Which of the following terms is defined as a set of all points in a plane that are a given distance from a point?
O Circle
O Line segment
O Parallel line
O Ray
Answer:
circle
Step-by-step explanation:
any point on the circumference of a circle is equidistant from the centre.
1. Find the Principal when S.l. = 100 Rate = 5% per annum Time = 2 years.
The principal is 1000
SI = PRT/100
Simple interest = 100
Rate = 5%
Time = 2 years.
SI = PRT/100
100 = (P × 5 × 2)/100
10000 = 10P
P = 10000/10
P = 1000
Aaron has a loan of 1250£ He pays simple intrest 0.5% per month for eight months Calculate the total amount of interest Aaron pays
What is the -value in the solution to this system of linear equations?y
4 + 5 = −12xy
-2 + 3 = −16xy
The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.
What is a system of linear equations?Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.
When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.
From the given information:
4x + 5y = -12 --- (1)
-2x + 3y = -16 ----- (2)
From equation (1)
4x+5y+(−5y) = −12 + (−5y) (Add -5y to both sides)
4x = −5y − 12
Divide both sides by 4
[tex]\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}[/tex]
[tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]
Replacing the value of x in [tex]\mathbf{ \dfrac{-5}{4}y-3}[/tex] into equation (2); we have:
[tex]=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}[/tex]
[tex]\mathbf{\dfrac{11}{2}y+6 =-16}[/tex]
Simplifying both sides of the equation, we have:
[tex]\mathbf{\dfrac{11}{2}y+6-6 =-16-6}[/tex]
[tex]\mathbf{\dfrac{11}{2}y=-22}[/tex]
Cross multiply
11y = -44
y = -4
Replace the value of y = -4 into [tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]
[tex]\mathbf{x= \dfrac{-5}{4}(-4)-3}[/tex]
x = 2
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The probability of a student buying coffee before class is 30%. The probability of a student buying a muffin before class is 40%. The probability of a student buying tea before class is 20%. The probability a student buys coffee AND a muffin before class is 15%. The probability a student buys tea AND a muffin before class is 10%. What is the probability that a student buys coffee OR a muffin before class
The probability that a student buys coffee OR a muffin before class is 55%
How to determine the probability?The given parameters are:
P(Coffee) = 30%
P(Muffin) = 40%
P(Tea) = 20%
P(Coffee and Muffin) = 15%
P(Tea and Muffin) = 10%
The probability that a student buys coffee OR a muffin before class is
P(Coffee or Muffin) = P(Coffee) + P(Muffin) - P(Coffee and Muffin)
This gives
P(Coffee or Muffin) = 30% + 40% - 15%
Evaluate
P(Coffee or Muffin) = 55%
Hence, the probability that a student buys coffee OR a muffin before class is 55%
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HELP PLEASE!)
A square pyramid has surface that is covered in dark glass. The sides of the pyramid are 456 feet in length. The slant height of the pyramid is 185 feet.
Find the lateral surface area to determine the square feet of glass needed to cover the surface of the pyramid.
Answer choices
376,656 ft^2
42,180 ft^2
337,440 ft ^2
168,720 ft^2
PLEASE HELP IM SO STUCK
Answer:
-4
Step-by-step explanation:
Slope = y/x
1. y=12 x=-3
12/-3=-4
2. y=8, x=-2
8/-2 = -4
3. y=4, x=-1
4/-1 = -4
4. 0/0 = 0
5. y=-4, x=1
-4/1 = -4
Hope it helps I had this question last year on Acellus.
The ratio of the number of galleons to the number of galleys in the spanish armada is 5 : 1 . what missing information could be used to find the total number of galleons to galleys in the spanish armada ?
The amount of the galleys or the number of galleys.
If given the amount of galleons, you can find the amount of galleys by dividing the number of given galleons by 5.
If given the amount of galleys, you can find the amount of galleons by multiplying the number of given galleys by 5.
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Find the value of cos F rounded to the nearest hundredth, if necessary. E 6 F 8 10 D
Answer:
cosF = 0.6
Step-by-step explanation:
cosF = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{6}{10}[/tex] = 0.6
Answer:
Cos F = 0.6
Step-by-step explanation:
Trigonometry ratios:[tex]\sf \boxed{\bf \ Cos \ F = \dfrac{adjacent \ side \ of \ \angle F}{hypotenuse}}[/tex]
[tex]\sf =\dfrac{EF}{DF}\\\\=\dfrac{6}{10}\\\\= 0.6[/tex]
The general term of a sequence is T(n)=n+2/n+3, find the value of T(1)*T(2)*T(3)*……….*T(100).
Answer:
T(1)=1+2(1)+3=6
T(2)=2+2(2)+3=9
T(3)=3+2(3)+3=12
T(100)=100+2(100)+3=303
An athletic coach conducted an experiment to test whether a four-week stretching and flexibility program reduces the number of muscular injuries that occur during athletic events. the coach randomly selected 30 athletes from several sports and randomly assigned 15 athletes to the four-week program. the remaining 15 athletes did not participate in any type of flexibility program during the four weeks. which statements about this study are true?
Answer:
The remaining 15 athletes did not participate in any type of flexibility program
A manufacturing firm has adopted a new layout for its production process, which is intended to increase worker productivity. With the old layout, mean daily output was 200 units. A manager wants to test the null hypothesis that with the new layout, mean daily output is no greater than 200, against the alternative hypothesis that it is greater than 200. Assume that daily output levels are approximately normally distributed, with standard deviation 18 units. Which sampling distribution is the basis for this hypothesis test? Letter (see multiple choices in the instructions)
Since the standard deviation for the population is known, the z-distribution is used as the sampling distribution basis for this hypothesis test.
When to use the t-distribution and the z-distribution?If the population standard deviation is known, the z-distribution is used.If the population standard deviation is not known, only the sample standard deviation, the t-distribution is used.In this problem, the standard deviation for the population is known, hence the z-distribution is used.
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Which statement correctly describes the expression 19×4?
A. Both factors are negative, so the product will be positive.
B. One factor is positive and one factor is negative, so the product will be positive.
C. Both factors are positive, so the product will be negative.
D. Both factors are positive, so the product will be positive.
Answer:
D. Both factors are positive, so the product will be positive.
please match the following pairs of lines with their descriptions:
The following pairs of lines should be matched with their descriptions as follows:
y = 2x/3 + 4 and y = -3x/2 + 9; perpendicular lines.y = 4x/5 + 8 and y = 5x/4 + 8; neither parallel nor perpendicular lines.y = 5x/6 + 8 and y = 5x/6 + 2; parallel lines.What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.
This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
What are perpendicular lines?Perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).
The condition for two parallel lines.In Mathematics, the condition for perpendicularity of two lines is:
m₁ × m₂ = -1
Given the following equations:
y = 2x/3 + 4 and y = -3x/2 + 9; 2/3 × -3/2 = -1.
y = 4x/5 + 8 and y = 5x/4 + 8; neither parallel nor perpendicular lines.
y = 5x/6 + 8 and y = 5x/6 + 2; 5/6 = 5/6.
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1. What is the approximate area of circle A?
2. What is the approximate area of circle B?
3. What is the approximate area of the shaded region 1 (between the square and circle A)?
4. What is the approximate area of shaded region 2 (between circles A & B)?
The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.
The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.
The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.
The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.
How to estimate geometric areas
In this situation we have a square whose side length is known and two circles whose radii have to be estimated. By direct inspection we find that the diameter of circle A is two thirds of the length of the square side (l), in inches and the diameter of circle B is the half of the diameter of the former. Now we proceed to find the key dimensions of the figure:
Circle A
Diameter: 16 inches
Radius: 8 inches
Circle B
Diameter: 8 inches
Radius: 4 inches
The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.
The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.
The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.
The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.
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A graphing calculator is recommended.
Use the graphical method to find all solutions of the system of equations, rounded to two decimal places.
y=e^x+e^-x
y=5-x^2
Dont bother answering if you won't show how you got it
The solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)
How to solve the system of equations?The system of equations is given as
y=e^x+e^-x
y=5-x^2
See attachment for the graph of both equations
From the attached graph, the curve intersect at
(-1.189, 3.587) and (1.189, 3.587)
Hence, the solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)
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An equilateral triangle and a square both have perimeters of 48 inches. What is the ratio of the length of the side of the triangle to the length of the side of the square
Answer: 4:3
Step-by-step explanation:
The side length of the triangle is 48/3 = 16.
The side length of the square is 48/4 = 12.
So, the ratio is 16:12 = 4:3.
Write an equation of the line passing through the point (8, 2) that is parallel to the line 6x - 9y = -7.
The equation passing through the point ()8, 2 and parallel to 6x - 9y = -7 is y = 6 / 7x - 2 / 7
How to find equation of a line?The equation of the line passes through the point (8, 2) and it is parallel to 6x - 7y = -7.
The equation of a line can be represented as follows;
y = mx + b
where
m = slope
b = y-intercept
Therefore, parallel line have the same slope.
6x - 7y = -7
7y = 6x + 7
y = 6 / 7 x + 1
m = 6 / 7
Hence, using (8, 2)
2 = 6 / 7 (8) + b
2 = 16 / 7 + b
b = 2 - 16 / 7
b = 14 - 16/ 7
b = - 2 / 7
Hence, the equation is y = 6 / 7x - 2 / 7
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FIRST CORRECT ANSWER WILL GET BRAINLIEST
Answer:
They are parallel.
Step-by-step explanation:
They have the same slope, 7, and different y-intercepts, 4, -1/4, so they are parallel.
Quick Please
(order from least to greatest)
please and thank you
Answer:
√(3 , √(π , 2
Step-by-step explanation:
ascending order
Which could be the entire interval over which the function, f(x), is positive? a 2-column table with 8 rows. the first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. the second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20.
The entire interval over which the function, f(x), is positive is (-∞,1).
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Each element of X receives exactly one element of Y when a function from one set to the other is used. The set X is referred to as the function's domain, while the set Y is referred to as the function's codomain.
According to the question,
The function has positive values corresponding to the interval from negative infinity to one.
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Nathan buys a bottle of water for $1.25, gum for $0.50, and a book for $3.95. the sales tax is 10%. what is the sales tax for the things he buys
Answer:
$0.75, which is
75 cents
Step-by-step explanation:
First add the cost of all the items.
1.25 + .50 + 3.95
= 5.70
To find 10% of 5.70, change the percent to a decimal and multiply.
10% is .10
5.70 × .10 = .57
The tax is 57 cents. This can be written as $0.57
The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.
The sine, cosine, cosecant, and secant functions have period 2π; the tangent and cotangent functions have period π.
Definition for Period of a Trigonometric Function :
The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.
If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. Period is the interval between two occurrences of the wave.
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