Total subsets of a set containing 9 elements having more than 2 elements = 466
What is a set?
A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things. A set with a single element is a singleton, while a set with no elements is an empty set. A set can either be infinite or have a finite number of items. If all of the items in two sets are identical, then the sets are equal. Modern mathematics is rife with sets. In fact, since the first part of the 20th century, Zermelo-Fraenkel set theory has been the de facto method for constructing solid foundations for all areas of mathematics.
C₉³+C₉⁴+C₉⁵+C₉⁶+C₉⁷+C₉⁸+C₉⁹
C₉³ = 84 subsets consisting of 3 elements
C₉⁴ = 126 subsets consisting of 4 elements
C₉⁵ = 126 subsets consisting of 5 elements
C₉⁶ = 84 subsets consisting of 6 elements
C₉⁷ = 36 subsets consisting of 7 elements
C₉⁸ = 9 subsets consisting of 8 elements
C₉⁹ = 1 subsets consisting of 9 elements
Total subsets of the set having 9 elements containing more than 2 elements = 84+126+126+84+36+9+1
= 466
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To pass a course with a B grade a student must have an average of 80 or greater. The students grades on three test are 80, 81 and 70. Find what score the student must get on the next test to get a B average or better.
Given that the student's grades on three tests are 80, 81 and 70
Let the student's grade on the fourth test be X
In order to pass the course, the student must have an average of 80 or greater.
Hence,
[tex]\begin{gathered} \frac{80+81+70+X}{4}\ge80 \\ \frac{231+X}{4}\ge80 \\ 231+X\ge320 \\ X\ge320-231 \\ X\ge89 \end{gathered}[/tex]The score the student must get on the next test to get a B average or better is greater than or equal to 89
Lily is making kool-aid. She uses 1/4 cup of sugar for every 2/3 cups of kool-aid. how 4many cups of sugar does she need to make 4 cups of kool aid. HELP PLS
Lily needs 3/2 cup of sugar to make 4 cups of kool-aid.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Lily is making kool-aid. She uses 1/4 cup of sugar for every 2/3 cup of kool-aid which is given in the question.
We have to determine the number of cups of sugar she needs to make 4 cups of kool-aid.
Let the number of cups of sugar would be x she needs to make 4 cups of kool-aid.
As per the given information, we can write the ratio as:
1/4 cup of sugar : 2/3 cup of kool-aid = x cup of sugar : 4 cup of kool-aid
⇒ 1/4 ÷ 2/3 = x ÷ 4
⇒ (1/4) / (2/3) = x / 4
⇒ (1/4) × (3/2) = x / 4
⇒ 3/8= x / 4
⇒ x = (3 × 4)/8
⇒ x = 12/8
⇒ x = 3/2
Therefore, she needs 3/2 cups of sugar to make 4 cups of kool-aid.
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Which combination could the coach buy?Click on the correct answer.Remember, the coach1) needs to buy at least 4 bats and atleast 8 balls2) cannot spend more than $1206 bats, 10 balls12-3 bats, 10 balls84 bats, 9 balls-4-110T14812x24y2815x + 5y = 120
It is important to know that the yellow area represents all the possible solutions because there all the areas intercept. So, among the options, the correct one is 4 bats, 9 balls because it represents (3,10) which is inside the yellow region.
Hence, the answer is option 3.Luisa bought 4.4 kilograms of apples. How
many ounces of apples did she buy? Use the
conversion rates 1 kilogram = 2.20 pounds
and 1 pound = 16 ounces. Round to the
nearest ounce.
True or false?
By issuing a patent, the government can give a company monopoly power.
Answer:
this is true
Step-by-step explanation:
Summary
Give an example of a proportional relationship and write an equation that represents the relationship.
The proportional relationship is represented by the formula, y = kx, which demonstrates that y increases at the same rate as x does
Relationships between two variables that are proportional occur when their ratios are equal.
Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.The ratio of the constant values of two proportional quantities is known as the proportionality constant.When either the ratio or product of two changing values results in a constant, that pair of values is said to be in proportion.The Direct Variation and Inverse Variation types of proportions between the two provided values determine the value of the proportionality constant.The direct proportionality formula, y = kx, demonstrates that y increases at the same rate as x does. The cost per item (y), which is inversely proportional to the number of things purchased (x), is represented by the symbol y x.By using the indirect proportionality formula, y = k/x, it can be seen that when y rises, x falls, and vice versa.Therefore the proportional relationship is represented by the formula,
y = kx .
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What is the interquartile range of the sample data represented on the stem and leaf diagram below?
0 | 2 3 5 7 9
1 | 3
2 | 1 2 3
The interquartile range of the sample data represented on the stem and leaf diagram is 21.
What is the interquartile range?
IQR(interquartile range) is the difference between the third and first quartile.
The range of a set of data is the difference between the largest and smallest values. The difference is specific; the range of a set of data is the result of subtracting the sample maximum and minimum.
Range = Maximum value - Minimum value
Range = 23 - 02 = 21
We know that the range is the difference between the smallest and the largest value and in the interval we write it as:
From a to b where a is the smallest value and b is the maximum value.
Hence, The interquartile range of the sample data represented on the stem and leaf diagram is 21.
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how much bags of fertilizer will brett need to cover the entire garden.
Area A = ?
Bag area covers = 54 ft2
Square Area S = 18ft X 18 ft
. = 324 ft2
Then now divide S/B
S/B = 324/54
. = 36/6
. = 6
Then answer is
Brett will need 6 bags of fertilizer
What is 75.6 divided by 4
Answer:
18.9
Step-by-step explanation:
Calculators, haha
whats the average for 62,81,72,60,100,79
Answer:
75.66
Step-by-step explanation:
62, 81, 72, 60, 100, 79
To find the average, add all the numbers together then divide by how many numbers there are.
62 + 81 + 72 + 60 + 100 + 79 = 454
454 ÷ 6 = 75.66 or rounded 76
I hope this helps!
S
SOLUTION
Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows
the relationship between the perimeter of an equilateral triangle and the
perimeter of a regular pentagon. What is the perimeter of the pentagon?
A 20
B 50
C 100
D 150
Nikia chose A as the correct answer. How might she have gotten that answer?
The perimeter of pentagon is 150 so option D is correct.
Given:
Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows the relationship between the perimeter of an equilateral triangle and the perimeter of a regular pentagon.
3(3x-10) = 5(x+10)
9x - 30 = 5x + 50
9x - 5x = 30 + 50
4x = 80
divide by 4 on both sides
4x/4 = 80/4
x = 80/4
x = 20.
perimeter of pentagon = 5(x+10)
= 5(20+10)
= 5*30
= 150.
Therefore the perimeter of pentagon is 150 so option D is correct.
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Graph 10 and its opposite. HHHHHHHHHHHHHH -201816141210-8-6-4-2 0 2 4 6 8 101214161820 0-0 0-0 - 0 0 < PREV 1 7
The opposite of 10 is -10.
Graph 10 and -10 on the number line.
The numbers are represented by points (dots) on the number line.
Find a point N on the segment with endpoints K(-2, -3) and L(4,3) that partitions thesegment, starting at point K, 1/3 of the way to point L.
First find the length of the segment KL
Apply the formula for distance between two points as;
d = √{y2-y1}^2 + {x2-x1}^2 where
y1= -3 , y2 = 3 , x1 = -2 and x2 = 4
d= √ {3--3}^2 + { 4--2}^2
d= √ 9^2 + 6^2
d= √ 81 + 12
d= √93 = 9.6
So the length of the segment is 9.6
From point K {-2, -3} , find 1/3 of the length to locate point L
This will be : 1/3 * 9.6 =3.2
This means point L is 3.2 units from point K, now apply the distance formula to find x and y coordinates for L, where K is {-2,-3} and L {x,y}
d = √{y2-y1}^2 + {x2-x1}^2
3.2 = √{y--3}^2 + {x--2}^2
3.2 =√ {y+3}^2 +{x+2}^2
3.2^2 = {y+3}^2 + {x+2}^2
10.3 = y^2 + 6y + 9 + x^2 +4x +4
10.3 = y^2 + 6y +x^2 +4x +9+4
10.3 = y^2 + 6y +x^2 +4x +13
0=y^2 +6y +x^2 +4x +13-10.3
0= y^2 +6y +x^2 +4x +2.7
y^2 + 6y +x^2 +4x +2.7 = 0
{-0.9,-0.5)
Find the percent change and tell whether it is a percent decrease orincrease.Original amount: 30End amount: 45
Step 1
Since the end amount is greater than the original amount, it is, therefore, percentage increase
Step 2
Calculate the percentage increase
The formula is given by
[tex]\begin{gathered} \text{Percentage increase =}\frac{Increase}{\text{Original}}\times100 \\ \text{Increase}=\text{ }45\text{ - 30 = 15} \\ \end{gathered}[/tex][tex]\text{Percentage increase =}\frac{15}{30}\times100=\text{ 50 percent}[/tex]The answer is therefore 50%
calculate the mean of each data set below. can you find any shortcuts that allow you to find the mean without having to d much calculation
a. 6, 10, 6,10
b. 11, 12, 12, 13, 12
c 0, 5, 4, 8, 0, 7
In the rectangle below, R V=3 x+8, S V=6 x-4, and m∠ V R S=54°. Find the value of x and m∠ V U R
From the information given about the above quadrilateral, that is, the rectangle x is equal to 4, and m∠VUR is equal to 36°.
What is a quadrilateral?A quadrilateral is a four-sided polygon with four edges and four corners in geometry. The name comes from the Latin words quadri, a variation of four, and latus, which means "side."
The results above are derived as follows:
To find x note that the diagonals of a triangle are congruent. This means that RT = SU.
⇒ 3x + 8 = 6x - 4 (add 4 to both sides)
3x + 8 + 4 = 6x - 4 + 4
3x + 12 = 6x (Collect like terms over the equation sign)
12 = 6x - 3x
12 = 3x (divide both sides by three)
x = 12/3
x = 4
To derive m∠VUR,
Recall the properties of a rectangle:
Opposites sides a parallelOpposite sides are equalAll internal angles measure 90°The diagonals of a rectangle are equal.Also, note that;
SRU = 90°
hence
∠VRU = ∠SRU - ∠VRS
that is:
∠VRU = 90 -54 = 36°
If ∠VRU = 36°, then
∠VUR = 36° [The diagonals of a rectangle are equal.]
Hence ΔRVU is an Isosceles triangle. Since this is true, and it is also true that the two angles opposite to the equal sides of an isosceles triangle are congruent to each other,
Then indeed, ∠VUR = 36°
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counselor at a summer camp are assigned beds to the campers Jackson is assign a bed and then Eva is assigned one are these two events dependent or independent
Solution;
The events are independent
Ron's Tea Shop has caffeinated tea and decaffeinated tea. During the lunchtime rush, the tea shop served 25 teas in all, 20% of which were caffeinated. How many caffeinated teas did the tea shop serve?
The number of caffeinated teas that the tea shop serve is 5.
How to calculate the percentage?Number of teas served = 25 teas.
Percentage that was caffeinated.= 20%
Therefore the number that was caffeinated will be the percentage multiplied by the number of teas. This will be:
= 20% × 25
= 0.2 × 25
= 5
Therefore, 5 are caffeinated
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please answer this using the foil method[tex] {9x}^{2} + 60x + 100[/tex]
Answer
Given expression
[tex]9x^2+60x+100[/tex]By factorization, we have
[tex]\begin{gathered} 9x^2+30x+30x+100 \\ 3x(3x+10)+10(3x+10) \\ (3x+10)(3x+10) \end{gathered}[/tex]Now to check, using FOIL method, we have
F = First, i.e 3x(3x) = 9x²
O = Outer = 3x(+10) = +30x
I = Inner = +10(3x) = +30x
L = Last = +10(+10) = +100
Is tim correct? explain why or why not and provide three examples that prove whether or not tim’s statement is correct
Given:
[tex]\text{Tim has the expression x}^2[/tex]Yes, Tim is correct.
Expression is having the square so , wheather the input is negative or positive the output will always gives the positive values.
All real inputs will give the positive output.
Example:
[tex]\begin{gathered} (-2)^2=4 \\ (-1.1)^2=1.21 \\ 5^2=25 \end{gathered}[/tex]help me with geometry proof, pls I did really bad on this homework and I need help, This is what I hard:State. Just.segment AB ll DC; Given
Answer:
Triangle ABC is congruent to DCE by SAS Theorem.
Step-by-step explanation:
Since AB is parallel to DC, we can say that BC is congruent to CE and AC is congruent to DE, then:
If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangle is congruent.
Triangle ABC is congruent to DCE by SAS Theorem.
What is the congruence correspondence, if any, that
will prove the given triangles congruent?
A) ASA
B)SAS
C) SSS
D) none
Answer:
A) ASA
Step-by-step explanation:
You want to know the relevant congruence postulate given the markings of angles and sides shown in the diagram.
MarkingsThe arc and hash marks show on the angles mean the angles with matching markings are congruent. Two angles are shown as congruent to their corresponding angles in the other triangle.
The hash mark on the sides mean the sides with matching markings are congruent. One side between the marked angles is shown as congruent to the corresponding side in the other triangle.
The letters A and S in the congruence postulate designations refer to corresponding Angles and Sides, respectively. So, two angles with a side between them would be identified as ASA.
The ASA congruence postulate applies.
Option A) ASA is the correct answer for the given triangle in the question. ASA is the congruence correspondence.
What is congruence correspondence?
Each triangle's vertices must match one another exactly. This expression signifies that each triangle's side and angle measurements match up with a side or angle of the other triangle. To have a one-to-one correspondence, triangles don't necessarily have to be congruent, but when they are, knowing the correspondence of the triangles is important to determine precisely which sides and which angles are congruent.
According to congruence postulate,
Angles with matching markings are congruent if an arc or hash mark appears on them. The relationship between two angles and the corresponding angles in the other triangle is demonstrated.
The hash marks on the sides indicate that the markings on the sides that match are consistent. The opposite triangle's equivalent side is shown to be congruent to the side between the highlighted angles.
The congruence postulate designations begin with the letters A and S, which stand for matching Angles and Sides, respectively. Therefore, ASA would be used to describe two angles with a side in between them.
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which statement would justify selecting plan B instead of plan A?Plan A: C = 30dPlan B: C = 25d + 15
We have two rental car plans.
We have to compare them to find the one that offers the minimum cost.
Plan A has no fixed fee but has a cost of $30 per day:
[tex]C=30d[/tex]Plan B has a fixed fee of $15 and a cost per day of $25:
[tex]C=25d+15[/tex]We expect the plan A to have a smaller cost for few days, while plan B becomes more convenient when we increase the number of days.
We can calculate the break even point when both costs are the same:
[tex]\begin{gathered} C_A=C_B \\ 30d=25d+15 \\ 30d-25d=15 \\ 5d=15 \\ d=\frac{15}{3} \\ d=5 \end{gathered}[/tex]Then, we know that for less than 5 days, Plan A is more convenient.
For more than 5 days, Plan B is more convenient.
For exactly 5 days, the decision is indifferent as both plans will have the same total cost.
Answer: The only statement that would justify selecting Plan B instead of A is if Marcus rents a car for 5 days.
Write a specific formula to describe the variation: Q varies jointly with the square of the inverse of the sum of b and R; Q = 4 when b = 2, R = 8.
Given the following variation
[tex]Q\propto\frac{1}{(b+R)^2}[/tex]Introducing the constant of proportionality c as shown below
[tex]\begin{gathered} Q=c\times\frac{1}{(b+R)^2} \\ Q=\frac{c}{(b+R)^2} \end{gathered}[/tex]Q=4, when b=2, R= 8
Let use the above values of Q, b, and R to find the value of c as shown below:
[tex]\begin{gathered} 4=\frac{c}{(2+8)^2} \\ 4=\frac{c}{10^2} \\ 4=\frac{c}{100} \\ c=4\times100 \\ c=400 \end{gathered}[/tex]Let us substitute c in the formula as shown below
[tex]Q=\frac{400}{(b+R)^2}[/tex]Hence, the specific formula to describe the variation is
Q= 400/(b+R)²
Determine the values of x in the equation x^2 = 81. Please help
x = −9
x = ±9
x = ±40.5
x = 40.5
The value of x in the quadratic equation is ±9.
As equation is [tex]X^{2}[/tex] = 81
Taking square root on both sides
⇒ [tex]\sqrt{x^{2} } = \sqrt{81}[/tex]
⇒ X = ± 9
∴ The value of X is ± 9
The roots of the given quadratic equation are +9 and -9.
How to solve a quadratic equation?An equation of degree 2 containing a single variable is known as the quadratic equation. . Its general form is [tex]Ax^{2}+ Bx^{} + C[/tex], where variables are x and constants are a, b, and c.
Examples are [tex]X^{2}[/tex] = ± 3, [tex]X^{2}[/tex] = ±9, [tex]X^{2}[/tex]=4 or any real number.
Some other examples are [tex]x^{2} + 2X+2[/tex], etc.
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solve im giving 40 points ASAP
A point P on the line segment starting at A and ending at B can be parameterized by
[tex]p(t) = (1-t)(-2,-4) + t (6,1)[/tex]
with [tex]0\le t\le1[/tex].
If AP/PB = 3/2, then point P is 3/5 of the length of AB from A, and 2/5 of the length of AB from B. So the coordinates of P are obtained at [tex]t=\frac35[/tex], and we find
[tex]p\left(\dfrac35\right) = \left(1-\dfrac35\right)(-2,-4) + \dfrac35 (6,1) = \boxed{\left(\dfrac{14}5, -1\right)}[/tex]
let k(x)=3h(x)+4x^4/g(x). given the following table of values, find k'(-1)
k(x)=3h(x)+4x^4/g(x). given the following table of values, k'(-1) will be 3.
What is differentiation?A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative. the procedure for determining a function's derivative, or rate of change, in mathematics. Differentiation is the method used to calculate a function's derivative. The derivative is the rate at which two variables, x and y, change relative to one another.
Given Data
k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]
k(x) = -3h'(x) + 4[tex]\frac{4x^{3} g(x)- x^{4}g'(x) }{gx^{2} }[/tex]
k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g(-1)}{g(-1)^{2} }[/tex]
k'(-1) = -3(-1) + 4(0)
k(-1) = 3 + 0
k'(-1) = 3
k(x)=3h(x)+4x^4/g(x). given the following table of values, k'(-1) will be 3.
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the measure of <1 is 39°. find the measure of the Adjacent angle to <1.
Explanation
by the graph we can conclude
[tex]\text{angle}\measuredangle1+angle\measuredangle2=90[/tex]if
angle1=39
replace,
[tex]\begin{gathered} \text{angle}\measuredangle1+angle\measuredangle2=90 \\ \text{39}+angle\measuredangle2=90 \\ \text{subtract 39 in both sdies} \\ \text{39}+angle\measuredangle2-39=90-39 \\ angle\measuredangle2=51 \end{gathered}[/tex]I hope this helps you
which of the following is a key property of the quadratic parent function?it is in quandrants I and IIIt is not a functionit is not a parabolaits vertex is in quandrant III
quadrants
In this case, we'll have to carry out several steps to find the solution.
Step 01:
We must analyze the statements to find the solution.
Step 02:
it is in quadrants I and II ==> True
It is not a function ==> False
it is not a parabola ==> False
its vertex is in quandrant III ===> False
The answer is:
It is in quadrants I and II
The owner of two hotels is ordering towels. He bought 24 hand towels and 5 bath towels for his hotel in Washington, spending a total of $151. He also ordered 26 hand towels and 66 bath towels for his hotel in Lancaster, spending $830. How much does each towel cost?
The first step is to state the system of equations that represent this situation.
Let x and y be the cost of a hand towel and a bath towel respectively.
The equation that represents the money spent for the towels of the hotel in Washington is:
[tex]24x+5y=151[/tex]The equation that represents the money spent for the towels of the hotel in Lancaster is:
[tex]26x+66y=830[/tex]Solve the given system of equations by equalization:
[tex]\begin{gathered} y=\frac{151-24x}{5} \\ y=\frac{830-26x}{66} \\ \frac{151-24x}{5}=\frac{830-26x}{66} \\ 66(151-24x)=5(830-26x) \\ 9966-1584x=4150-130x \\ 1584x-130x=9966-4150 \\ 1454x=5816 \\ x=\frac{5816}{1454} \\ x=4 \end{gathered}[/tex]It means that a hand towel costs $4.
Use this value to find y:
[tex]\begin{gathered} y=\frac{151-24(4)}{5} \\ y=\frac{151-96}{5} \\ y=\frac{55}{5} \\ y=11 \end{gathered}[/tex]A bath towel costs $11.