The no. of subsets with at least one odd number is ²⁰C₁₀ - 1
We have the sample set to be {1, 2, 3, 4, ... 20}
Now we need to make subsets of 10 from these 20 elements.
Hence, the number of possible subsets of 10 elements will be
²⁰C₁₀
Now, there are 10 odd elements in the given sample set.
Hence the number of sets that contain at least 1 odd element
= Total no. of possible sets - no. of possible sets with no odd no.
Now since there are only 10 even numbers, there can be only one such set possible.
Hence no. of the subsets with at least one odd number is
²⁰C₁₀ - 1
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an integer is called parity-monotonic if its decimal representation $a 1 a 2 a 3 \dots a k$ satisfies $a i < a {i 1}$ if $a i$ is odd, and $a i > a {i 1}$ if $a i$ is even. how many four-digit parity-monotonic integers are there?
The total number of four-digit parity-monotonic integers is 432*1 = 24.
Parity-monotonic four-digit integers countWe can solve this problem by counting the number of parity-monotonic integers in each of the four digits individually and then multiplying the counts together.
For the first digit, we must have [tex]$1 \leq a_1 \leq 4$[/tex] as the integer must be four-digit.For the second digit, we must have [tex]$0 \leq a_2 < a_1$[/tex] if [tex]$a_1$[/tex] is odd and [tex]$a_1 < a_2 \leq 9$[/tex] if [tex]$a_1$[/tex] is even.For the third digit, we must have [tex]$0 \leq a_3 < a_2$[/tex] if [tex]$a_2$[/tex] is odd and [tex]$a_2 < a_3 \leq 9$[/tex] if [tex]$a_2$[/tex] is even.For the fourth digit, we must have [tex]$0 \leq a_4 < a_3$[/tex] if [tex]$a_3$[/tex] is odd and [tex]$a_3 < a_4 \leq 9$[/tex] if [tex]$a_3$[/tex]is even.By counting the possible values of [tex]$a_1$[/tex], [tex]$a_2$[/tex], [tex]$a_3$[/tex] and [tex]$a_4$[/tex] independently, we have:
[tex]$a_1$[/tex] has 4 possibilities[tex]$a_2$[/tex] has 3,2,1 possibilities depending on [tex]$a_1$[/tex] is even or odd[tex]$a_3$[/tex] has 2,1,2,1 possibilities depending on [tex]$a_2$[/tex] is even or odd[tex]$a_4$[/tex] has 1,0,1,0 possibilities depending on [tex]$a_3$[/tex] is even or oddThus, the total number of four-digit parity-monotonic integers is 432*1 = 24.
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What is the solution to this system of
equations?
s 6x – 2y = 8
1-3x + y = -4
According to the elimination method, the solution of the system of equation has infinite number of solutions.
In math the term elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables
Here we know that the equations are
=> 6x - 2y = 8 ---------------(1)
=> -3x + y = -4 ------------------(2)
when we simplify the equation (1) by dividing the terms by 2, then we get
=> 3x - y = 4
Now, we have to add the two equation then we get the result as,
=> (-3x + 3x) +( -y + y) = (-4 + 4)
=> 0 + 0 = 0
Hence the system has an infinite number of solutions.
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3/5 less than a number, and the result is squared
Answer:
(n - 3/5)²
Step-by-step explanation:
(n - 3/5)²
The point (6, -2) is reflected over the and-axis. What are the coordinates resulting point, A?
The price of a new car was $22,800 in April. However, the price of the car was reduced by 5% in May. Find the price in May.
In May, the price of the car was ? % as compared to
the price of the car in April.
Answer: To find the price of the car in May, we can use the formula:
New price = Original price - (Original price x Discount rate)
In this case, the original price is $22,800, and the discount rate is 5%, which can be written as 0.05.
So, the new price in May is:
New price = 22700 - (22700 x 0.05)
New price = 22700 - 1135
New price = $21,565
So, the price of the car in May was $21,565.
To find the percentage of the price of the car in May as compared to the price of the car in April, we can use the formula:
(New price / Original price) x 100
In this case, the new price is $21,565 and the original price is $22,800
(21565 / 22700) x 100 = 0.95 x 100 = 95%
Therefore, in May, the price of the car was 95% as compared to the price of the car in April.
Step-by-step explanation:
Can anyone help?- I need it by 11:30.
Answer:
See Below
Step-by-step explanation:
5. [tex]3.1 + (8.6 + m)\\3.1 + 8.6 + m\\11.7 + m[/tex]
take expression out of brackets by distribution (multiplying both by 1), then add
6. [tex]((\frac{2}{3})(t)) (1\frac{1}{2})\\(\frac{2}{3}t) (1\frac{1}{2})\\(\frac{2}{3}t) (\frac{3}{2})\\\frac{6}{6} t\\t[/tex]
Simplify the expression in the brackets by multiplying them together, once done turn the mixed fraction back into improper fraction in order to multiply the two together. Once done, simplify the expression
7. [tex]4(x + 8)\\4x + 32[/tex]
I would argue that factored form is the most simplified but regardless using the distribution rule you multiply both numbers within the bracket in order to get rid of it
8. [tex]4t + 7 + 2t - 2\\6t + 5[/tex]
This is just combining like terms and simplifying
a car magazine is comparing the top speed in miles per hour of 15 different sports cars. the speeds are included in the table below. top speeds 267.71 253 187 247.16 188 250.4 240.10 224 195 212 248.5 190 205 202 245 use a calculator to create a histogram for the data. use the default window size. what is the result?
The result of a histogram of the given data is 0.8.
There are a few steps to use a TI-83, TI-83 plus, or TI-84 calculator is used to create the histogram.
1. First, the process is to press the STAT key and then press ENTER.
2. Enter the data into column L1.
3. In the third step with all of the data entered, press the 2nd key and then press the Y= key to open the STAT PLOT menu.
4. After that press ENTER and make sure that Plot1 is set to On.
5. Use the directional keys to navigate to the Type selector, move the selection to the third type in the top row, and press ENTER.
6. Make sure that Xlist is set to L1 as this needs to be the same column as the list that the data were entered into previously. If it is not, highlight the value for Xlist and press 2nd and the 1 key for list L1.
7. Finally, press the ZOOM key and then press 9 in order to change the zoom to ZoomStat. When this is finished, the correct histogram will display on the calculator.
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A ball is thrown upward at an angle of elevation of 28 degrees with a force of 19n. How much of that force is horizontal and how much of that force is vertical?
19N force act in upward direction with angle of elevation 28 degrees has horizontal and vertical force is given by 16.78N and 8.92N respectively.
Angle of elevation while thrown a ball upward 'α' = 28 degrees
Force 'F' is equal to 19N.
While throwing a ball force is applied in two possible direction are:
Horizontal direction and Vertical direction.
For horizontal direction :
let 'x' represents the horizontal direction
cosα = x / F
⇒ cos28° = x / 19
⇒ x = 19 cos 28°
⇒ x = 19 × 0.8829
⇒ x = 16.78N
For Vertical direction :
let 'y' represents the vertical direction
sinα = x / F
⇒ sin28° = y / 19
⇒ y = 19 sin 28°
⇒y = 19 × 0.4695
⇒ y = 8.92N
Therefore, the horizontal force and vertical force for the given angle of elevation is equal to 16.78N and 8.92N respectively.
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Simplify (4s+7 -2S) +4 (3s-5^2) 
Answer:
14S -93
Step-by-step explanation:
(4s+7 -2S) +4 (3s-5^2)
= 2S +7 +12S -4*25
=14S -93
a certain corner of a room is selected as the origin of a rectangular coordinate system. if a fly is crawling on an adjacent wall at a point having coordinates (1.7, 0.6), where the units are meters, what is the distance of the fly from the corner of the room?
A certain corner of a room is selected as the origin of a rectangular coordinate system. A fly has coordinate (1.7, 0.6). The distance of the fly from the corner of the room is 1.8 meters.
Suppose we have a point having coordinate (x,y). Then the horizontal axes, vertical axis, and the distance from the origin form a right triangle which its base is x and y.
Hence, we can find the distance of the point (x,y) from the origin using the Pythagorean Theorem.
In this case, the origin is a certain corner of the room. The coordinate of the fly is (1.7, 0.6) meters.
Using the Pythagorean Theorem:
distance = sqrt (1.7² + 0.6²)
distance = sqrt (2.89 + 0.36)
distance = sqrt (3.25)
distance = 1.8 meters
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WHICH one doesn’t belong
9 16
25 43
NUMBER 1
from Pam Wilson
From the set of numbers 9, 16, 25, 43 , the number does not belong to the group is prime number 43.
Set of numbers are 9, 16 , 25, 43.
9 is the composite number with 1, 3, 9 as factor.
It is perfect square of 3 also.
16 is the composite number with 1, 2, 4, 8,16 as factors.
It is perfect square of 4 also.
25 is the composite number with 1, 5, 25 as factors.
It is perfect square of 5 also.
43 is not a composite number.
It has only two factors 1, 43.
43 is a prime number.
It is not a perfect square of any number.
Here 43 does not belong to the group.
Therefore, the number which does not belong to the group from 9,16, 25, 43 is 43.
The above question is incomplete, the complete question is :
Which number does not belongs to group ?
9, 16, 25, 43.
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Sara says if you subtract 19 from my number and multiply the difference by -6 the result is -96,
what is saras number
PLEASE PLAE PLASE PALSE PLASEP APLSASEP PLASEP PLEASE PLAESESEEPZ.
The art teacher has 48 paintbrushes. She puts 8 paintbrushes on each table in her classroom. How many tables are in her classroom?
Answer:
6 Tables
Step-by-step explanation:
48 tables divided by 8 paintbrushes equals 6 tables.
In a survey of 50 first graders, 30% said their favorite food is hot dog. Which box is correctly set up to show this?
The probability that the number of first graders who have liked the hot dog is 15
In math the term probability is defined as a number that reflects the chance or likelihood that a particular event will occur
Here we have know that in a survey of 50 first graders, and then 30% said their favorite food is hot dog.
Here we have to find the probability that the number of first graders who have liked the hot dog
As we know that the number of first graders is 50.
And here we also know that 30% of them are liked the hot dog.
Then it can be calculated as,
=> 50 x 30%
=> 50 x 30/100
=> 15.
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in a negatively skewed distribution of exam scores, bender scored at the mean, fry scored at the median, and lela scored at the mode. who had the highest score?
Lela had the highest score.
Now, According to the question:
A skewed distribution is neither symmetric nor normal because the data values trail off more sharply on one side than on the other. In business, you often find skewness in data sets that represent sizes using positive numbers.
In a negatively skewed distribution, higher values are more frequent than lower values causing the distribution to present a longer left-tail. This implies in a median higher than the mean and in a mode higher than the median:
mean < median < mode.
Therefore, since Lela scored at the mode, Lela had the highest score.
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5b-2c + 3)-d, a +2b-c+d, 2-d + 3c + a
The sum of the given expression will be 2a+7b+-d.
What are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now
Given expressions are 1.5b-2c+3-d 2.a+2b-c+d 3.2-d+3c+a
By adding these
=a+a+5b+2b-2c-c+3c-d+d-d
=2a+7b-d
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Use the figure shown for Items 1–4. In the figure, m∠IJL=0.5 m∠JIK.
Triangle I J K with side I J congruent to side J K. Segment J L is drawn from vertex K perpendicular to base I K such that it bisects the base. Segment I L has length 3 x and is congruent to segment L K which has length 2 x plus 5.
Select all the statements that must be true.
A. KL=15
B. JL bisects IK
C. ΔIJK is equilateral.
D. JL is the perpendicular bisector of IK
E. JL=2LK
The true statements are:
A. KL=15
B. JL bisects IK
D. JL is the perpendicular bisector of IK
What is perpendicular?Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular sign, ⊥ , can be used to visually depict the state of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.
Given:
We have a triangle IJK.
m∠IJL=0.5 m∠JIK.
Side IJ ≅ side JK.
JL ⊥ IK.
It bisects the base.
That means,
JL bisects IK and JL is the perpendicular bisector of IK.
So, IL = LK.
3x = 2x + 5
x = 5
KL=15.
Therefore, A, B and D are the true statements.
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on a fair die whose faces are numbered consecutively starting from 1, the probability of rolling an even number is less than twice the probability of rolling a multiple of 3. which could be the number of sides on the die?
Answer:
iam sorry
i don't know the answer
The difference between the water levels for high and low tide was 3. 6 feet. Write and solve an equation to find the water level at high tide
The difference between the water levels for the high and low tide was 3. 6 feet. the equation to find the water level at high tide x = y + 3.6, where High Tide Water Level = x and Low Tide Water Level = y.
In simple form it will be High Tide Water Level = Low Tide Water Level + 3.6. To explain this equation, the water level at high tide is equal to the water level at low tide plus 3.6 feet. The variable 'x' represents the water level at high tide, while the variable 'y' represents the water level at low tide. By adding 3.6 feet to the water level at low tide, we can find the water level at high tide.
For example, if the water level at low tide is 4 feet, the water level at high tide would be 4 + 3.6 = 7.6 feet. To find the water level at high tide for any given low tide water level, one can simply add 3.6 feet to the known low tide water level. This equation can be used to accurately calculate the water level at high tide for any given low tide water level.
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dilate figure ABCD by a cale factor of 3 with the center of dilation at the origin
the slope of A'B' is= 1.2 ,The length of A'C' in triangle is = 3q unit.
When we dilate a triangle and the center of the dilation is at the center of the triangle, the only thing that changes are the coordinates of the summits of the triangle.
The angles remain the same, so do the slope.
So, since the slope of AB is equal to -1.2, the slope of A'B' will also be -1.2.
They say the dilation factor was 3, that means the length of every side was multiplied by 3. So, if the length of AC is q units, the length of A'C' is 3q units.
The complete question is-
ΔABC is dilated by a scale factor of 3 with the origin as the center of dilation to form ΔA′B′C′. The slope of AB is -1.2. The length of AB is p units, the length of AC is q units, and the length of BC is r units.
The slope of AB is (?). The length of is (?) units.
the slope of AB is?
A. 1.2 B. -1.2 C. -3.6
The length of AC is ?
A. 1/3q
B. 3q
C.-1.2p
D. (p+q+r)
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An octagon with vertices at (-4, 2), (-2,5), (1,5), (3, 2), (3, -6), (1, -3), (-2, -3),
and (4, -6) was dilated by a scale factor of 3 and with a center of dilation at the
origin. What are the coordinates of the vertices of the dilated octagon
Coordinates of the vertices of the octagon after dilation by scale factor 3 are (-12, 6), (-6,15), (3,15), (9, 6), (9, -18), (3, -9), (-6, -9),and (12, -18).
Original coordinates of the vertices of an octagon are :
(-4, 2), (-2,5), (1,5), (3, 2), (3, -6), (1, -3), (-2, -3), and (4, -6).
Scale factor is equal to 3
Figure transformed using dilation of scale factor of 3 with center of dilation at the origin.
Coordinates of the new vertices after dilation of the octagon.
(-4×3, 2×3) = ( -12, 6)
(-2 ×3,5×3) = ( -6 , 15)
(1 ×3,5×3) = ( 3 ,15)
(3×3, 2×3) = ( 9,6)
(3×3, -6×3) = ( 9, -18)
(1 ×3, -3×3) = ( 3 , -9)
(-2×3, -3×3) = ( -6 , -9)
(4×3, -6×3) = (12, -18)
Therefore, the new coordinates of the vertices after dilation are (-12, 6), (-6,15), (3,15), (9, 6), (9, -18), (3, -9), (-6, -9),and (12, -18).
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Question
Two boxes need to be wrapped in paper (with no overlap). Both boxes are in the shape of right rectangular prisms.
Box A measures 0.8 feet high, 0.6 feet long, and 1 foot wide. Box B measures 1.4 feet high, 0.5 feet long and 1.2 feet wide.
The wrapping paper costs $6.79 per 80 square feet.
What is the cost of wrapping both boxes?
Enter your answer in the box.
$
Answer:
0.82
Step-by-step explanation:
A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76
B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96
total 9.72
cost = $6.79* 9.72/80 =$0.82
Answer:
0.92
Step-by-step explanation:
Which property is being demonstrated?
3^9/3^4=3^9-4=3^5
quotient of powers property
power of a product property
product of powers property
power of a quotient property
From the given example we can say that , the given expression is in the form of quotient of a powers property.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expression,
3^9 / 3^4
= 3^(9-4)
= 3^(5)
So,
if a^m / a^n = a^(m-n)
Its in the form of quotient of powers property.
And from above we can say that, The given expression also in the form of quotient of powers property.
Hence, From the given example we can say that , the given expression is in the form of quotient of a powers property.
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The population of a city in 2015 was 36,000. The population is increasing at 15% per year.
Part A: Write an exponential equation that models the population, P(x), where x represents the number of years since 2005.
Part B: Based on your equation, what was the population in 2020? Show how you obtained your answer.
A: The exponential function for the situation is P(t) = 36,000 × (1 + 0.15)^t.
B: The population in 2020 was 72,396.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The population of a city in 2015 is 36,000 and it is increasing at 15% per year.
Model this using an exponential equation of the form -
P(t) = P0 × (1 + r)^t
Where -
P(t) is the population after t years
P0 is the initial population in 2015 (36,000)
r is the rate of growth (0.15)
t is the number of years since 2015
So the exponential equation that models the population is -
P(t) = 36,000 × (1 + 0.15)^t
Part B:
To find the population in 2020, substitute t = 5 (2020 - 2015) into the equation -
P(5) = 36,000 × (1 + 0.15)^5
P(5) = 36,000 × 1.15^5
P(5) = 36,000 × 2.011
P(5) = 72396
Calculating this gives us a population of approximately 72,396 in 2020.
To obtain this answer, the exponential equation that models the population, P(t), is used where t represents the number of years since 2015, with the given information that population in 2015 was 36,000 and it's increasing at 15% per year and substitute the value of 5 for t.
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in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?
Lisa and Joe put $46 towards the gift
How much money did Lisa and Joe put towards the gift?Let's call the amount of money that Sara put in "x".
Joe put in twice that amount, so he put in 2x.
Lisa put in ten dollars more than Sara, so she put in x + 10.
Together, Sara, Joe, and Lisa put in x + 2x + (x + 10) = $58.
Evaluate the like terms, so we have
4x + 10 = 58.
Subtracting 10 from both sides, we get
4x = 48.
Dividing both sides by 4, we find that
x = $12.
So Sara put in $12, Joe put in $24, and Lisa put in $22.
The total amount put by Lisa and Joe is $24 + $22 = $46.
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Complete question
Three friends are put their money together to buy a $58 gift. Joe put in twice the amount of money as Sara. Lisa put in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?
The sum of the ages of Jaren and his brother, Daniel is 40. Four years ago, Daniel was 3 times as old as Jaren. Calculate
(i) Jaren's present age
(ii) the age of Daniel when Jaren was born
Answer:
(i) Let's call Jaren's current age J. According to the problem, the sum of J and Daniel's age is 40.
If we also know that four years ago, Daniel was 3 times Jaren's age, we can set up the following equation:
J + (J+4) = 40
Solving for J, we find that Jaren's present age is 18.
(ii) When Jaren was born, Daniel would have been 18 + 4 = 22 years old.
Use the Bisection Method up to five iterations and find the root to 3 decimal places for the following:
f(x) = x2 − 3x + 1 in the interval [0, 1]
A.
0.375
B.
0.438
C.
0.406
D.
0.391
Answer:
D. 0.391
Step-by-step explanation:
You want the approximate solution to f(x) = x² -3x +1 = 0 on the interval [0, 1] using 5 iterations of the Bisection Method.
IterationThe Bisection Method makes one iteration by finding the function value at the midpoint of the interval. The midpoint replaces the end of the interval whose function value has the same sign. At the end of one iteration, the midpoint of the halved interval is calculated.
Start:
f(0) = 1, f(1) = -1. Interval: [0, 1]; midpoint: 1/2
First iteration:
f(1/2) < 0. Interval: [0, 1/2]; midpoint: 1/4
Second iteration:
f(1/4) > 0. Interval: [1/4, 1/2]; midpoint: 3/8
Third iteration:
f(3/8) > 0. Interval: [3/8, 1/2]; midpoint: 7/16
Fourth iteration:
f(7/16) < 0. Interval: [3/8, 7/16]; midpoint: 13/32
Fifth iteration:
f(13/32) < 0. Interval: [3/8, 13/32]; midpoint: 25/64
SolutionThe approximate solution after 5 iterations is x ≈ 25/64 ≈ 0.391.
__
Additional comments
The approximate solution in the interval to full calculator precision is 0.38196601125. The exact solution is 1.5-√1.25.
You will notice that the function values for the ends of the interval [0, 1] are [positive, negative]. So, when the function value at the midpoint is negative, that point replaces the right end of the interval.
Of course, the midpoint is the average of the interval end values.
On average, it takes about 3.3 iterations to improve the accuracy of the solution by 1 decimal place.
You can model the arch of the fireplace using the equation y =-1/9(x+18)(x-18) when x and y are measured in inches. The x-axis represents the floor. Find the width of the arch at floor level
The width of the arch at floor level is 18 inches.
Substitute x = 0 into the equation.
y = -1/9(0+18)(0-18)
Solve for y.
y = -1/9(-18)(18)
y = 18
Therefore, the width of the arch at floor level is 18 inches.
A linear system can be algebraically solved using the substitution approach. One y-value is substituted for another in the substitution procedure. Finding the value of the x-variable in terms of the y-variable is the method's most straightforward step.
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Chris opens up a new visa credit card and credit line with U. S. Bank. He is paying a 15% annual percentage rate (APR) on all new purchases. If he has a current balance of $2,800 on this credit card, how much does he owe in interest to the back next month?
Chris owes $35 in interest to the back next month.
We know that a credit card's interest rate is nothing but the price one pay for borrowing money. This is called the annual percentage rate (APR).
The Interest paid is calculated by the formula:
I = PTR ÷ 100
where P = Principal amount ,
R= rate of interest in percentage ,
and T= period.
Here, P = $2800,
R = 15%
T= 1 year
Using above formula,
I = (2800 x 15 x 1) ÷ 100
I = 420.
He will pay an interest of 420 ÷ 12= $35 per month.
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chooe all of the following expreion which are even for all value of n
2n8
5n10
2n3
n2
4n-14
All of the expressions 2n8, 5n10, 2n3, n2, and 4n-14 are even for all values of n because all of the coefficients of n are even numbers.
2n8, 5n10, n2, 4n-14
2n8 : This expression is even for all values of n because the coefficient of n is an even number (2).
5n10 : This expression is even for all values of n because the coefficient of n is an even number (5).
2n3 : This expression is even for all values of n because the coefficient of n is an even number (2).
n2 : This expression is even for all values of n because the coefficient of n is an even number (1).
4n-14 : This expression is even for all values of n because the coefficient of n is an even number (4).
All of the expressions 2n8, 5n10, 2n3, n2, and 4n-14 are even for all values of n because all of the coefficients of n are even numbers.
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