There will be 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 when repeated digits are allowed by fundamental counting principle.
What is fundamental counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting simplifies the approach to selection by taking into account all of the possible choices and their combinations in order to calculate the Probability.
Here,
Since there are 6 digit given,
In first place, there are 6 ways to arrange the digits. In second place, there are 6 ways to arrange the digits. In third place, there are 6 ways to arrange the digits.
This way,
6×6×6=216 ways
When repeated digits are allowed by the fundamental counting principle, 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6.
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The figure shows two parallel lines, j and k, cut by two transversals, t₁ and t₂.
What is the value of m<3, in degrees, if m<5 = 70° and m<2 = 60°?
the figure for m3 in the above question is 50
hello can someone help me pls
Answer:
sum= 1080
Step-by-step explanation:
Answer:
The sum of an octagon is always 1080 degrees. The interior angles are usually all equal to 135 degrees, but this is an irregular octagon, making that not the case. Because the angles are not all equal, that does not mean that the octagon's sum is any different. Thus, the sum of the interior angles is 1080 degrees.
Hope this helps!
Given that D( x ) = 2 x , select all of the following that are true statements.
D( x ) is a direct variation.
D( x ) is a function.
D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4)
x is the dependent variable.
D(6) = 3
F(x)=x^2+1 what is f(f(x))?
Answer:
f(f(x)) = [tex]x^{4}[/tex] + 2x² + 2
Step-by-step explanation:
to evaluate f(f(x)), substitute x = f(x) into f(x)
f(f(x))
= f(x² + 1)
= (x² + 1)² + 1 ← expand factor using FOIL
= [tex]x^{4}[/tex] + 2x² + 1 + 1
= [tex]x^{4}[/tex] + 2x² + 2
Answer:
[tex]f[f(x)]=x^4+2x^2+2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2+1[/tex]
To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):
[tex]\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}[/tex]
Find the probability P(0.21 distribution.
The probability of the value of (0.21) distribution using the normal distribution table is: 0.3166
What is Probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.
In the question, we have
Probability of (0.21 < z <1.28)
= P(z < 1.28) - P(z < 0.21)
Probability of value for z
= 1.28 using z table is 0.8997
=> P(z < 1.28)
= 0.8997
probability of value for z = 0.21
Now, find the value of the probability using the normal distribution table:
using the z table of 0.21; we get:
The value of z is: 0.5832
=> P(z < 0.21) = 0.5832;
The value of Probability of (0.21 < z <1.28)
= Probability of (z < 1.28) - Probability of (z < 0.21)
= 0.8997 - 0.5832
= 0.3165
~ 0.3166
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Gaste el 30% de lo que no gaste, si hubiera gastado el 40% de lo que no hubiera gastado, entonces ahora tendría 30 dólares menos de los que tengo
Veremos que originalmente tenias $300, y el valor de la compra fue de $90
¿Cuanto dinero tenía originalmente?Definamos X como la cantidad original de dinero. Ahora trabajaremos con porcentajes.
Sabemos que tu gastaste 30% de esto, entonces lo que te sobra es:
0.7*X
Sabemso qe si hubieras gastado el 40% (en este caso te sobra 0.6*X), te sobrarian 30 dolares menos, entonces podemos escribir:
0.7*X = 0.6*X + $30
Resolviendo para X
0.7*X - 0.6*X = $30
0.1*X = $30
X = $30/0.1 = $300
Originalmente tenias $300 dolares, y gastaste:
$300*0.3 = $90
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During 75 days, rain fell on 3/5 of the day. On how many days did rainfall?
Answer:45
Step-by-step explanation:
75*3/5
Expand and simplify (x + 3)(x + 5)
Answer:
expanded: x^2+8x+15
Step-by-step explanation:
(x+3)(x+5)
x^2+5x+3x+15
help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Can't be solved
Step-by-step explanation:
Using Pythagoras theorem,
H2= O2 + A2 (where, H= Hypotenuse,O=Opposite,A=Adjacent)
The hypotenuse,H=7feet long
If the opposite side of the triangle is 4 feet longer than the adjacent side, then;
O=A+4
while, A=A
,then using H^2= O^2 + A^2(The 2 are power,that is square)
7^2 = (A+4)^2 + A^2
49= (A+4)(A+4) + A^2
49=A^2 +4A+4A+16 + A^2
49=A^2+8A+16+A^2
(collect like terms)
49-16=A^2+A^2+8A
33=2A^2+8A
Then a quadratic equation,
2A^2+8A=33
2A^2+8A-33=0,
using (-b+/-√4ac) /2a
where b=8, a=2, c=-33
[-8 +/-√4*2*(-33) ]/2(2)
-8 +/-
Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios. A 2-column table has 3 rows. Column 1 is labeled Silver paints (parts) with entries 3, blank, blank. Column 2 is labeled Green paint (parts) with entries 4, blank, blank. Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check all that apply. 4:5 6:8 5:6 9:12
The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.
What are Equivalent Ratios?Equivalent ratios can be described as ratios that have the same values when compared to each other. For example, 8/16, 4/8 and 1/2 re equivalent ratios because:
8/16 = 1/2
4/8 = 1/2
Therefore, 8:16 = 4:8 = 1:2.
Given the table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, the ratio is: 3:4.
This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.
Therefore:
6/8 = 3/4
9/12 = 3/4
6/8 = 9/12 = 3/4
This implies that 6:8, 9:12 and 3:4 are all equivalent ratios.
Therefore, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
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help!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
5/6 is closest to 1 and 2/5 is closest to 1/2 so the difference is closest to 1/2.
a publisher reports that 45% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 300 found that 37% of the readers owned a particular make of car. determine the p-value of the test statistic. round your answer to four decimal places.
The test statistic's p-value is -2.785.
According to A publisher, 45% of its readers own a particular make of car.
Claim: An executive in marketing would like to test the claim that the percentage is different from what is reported.
[tex]H_{o}[/tex]: p = 0.45
[tex]H_{a}[/tex]: p ≠ 0.45
a random sample of 300 found that 37% of the readers owned a particular make of car.
= 37% × 300
= (37 ÷ 100) × 300
X = 111
n= 300
One sample proportion test should be used.
p-vector = x ÷ n,
p-vector = 111 ÷ 300
p-vector = 0.37
The test statistic's formula,
= [tex]\frac{p-q}{\sqrt{\frac{pq}{n} } }[/tex]
test statistic = [tex]\frac{0.37- 0.45}{\sqrt{\frac{0.45(1-0.45)}{300} } }[/tex]
≈ -2.7851
thus, the p-value of the test statistic is -2.7851.
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How to do this equation (1 + 3)²
Answer:
your answer is 16
Step-by-step explanation:
So, to solve (1 + 3)²
first add 1 and 3
then you will get 4
and your equation would be (4)²
then you just square 4.
(4)² > 4x4 = 16
hope this helps (can you mark as brainiest pls)
I am stuck on this. Can someone help me with my math homework
Answer: -5,5 = B
Step-by-step explanation:
Julia reads 25% of a book in 100 minutes. How much time is needed to finish the book?
Answer:
400 minutes
Step-by-step explanation:
25 % *4 =100 %
100*4=400 minutes
A school needs to buy new notebook and desktop computers for its computer lab. The
notebook computers cost $200 each, and the desktop computers cost $400 each.
How many total computers would someone buy if they get 12 notebooks and 15
desktop computers? How many total computers would someone buy if they get n
notebooks and d desktop computers?
Total computers, 12 notebooks and 15 desktop computers:
Total computers, n notebooks and d desktop computers:
Answer: 27
Step-by-step explanation:
Well we already know that n is 12 and d is 15
So based on what I see we do n + d which would equal 27.
Cube root of 426 give your answer to the nearest integer
Answer:
3
Step-by-step explanation:
Explain how the distributive property cam be used to eliminate the fractions in the equation 1/5x +8 = 1/10x + 9
We will use the distributive property to take a common factor in the next step:
(1/5)*x - (1/10)*x = (1/5 - 1/10)*x
Using that we will see that the solution is x = 10.
How can we use the distributive property?The distributive property can be written as:
A*(B + C) = A*B + A*C
Now we have the equation:
(1/5)*x + 8 = (1/10)*x + 9
If we group like terms we get:
(1/5)*x - (1/10)*x = 9 - 8
Here we apply the property, we can rewrite the left side as:
(1/5)*x - (1/10)*x = (1/5 - 1/10)*x
Then we can write:
(1/5)*x - (1/10)*x = 9 - 8
(1/5 - 1/10)*x = 1
(1/10)*x = 1
x = 10*1
x = 10
And that is the solution.
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Which expression equals 9/10 ?
O 5√10+4√10
O5 10+4 10
O 5√10+43/10
O 5 10+4 10
Answer:
The second answer:
5cubrt10 + 4cubrt10
Step-by-step explanation:
In order to get a cubrt10 answer you have to add cubrt10's.
The first answer has squareroots, so that's a no.
The last two have cubrt + sqrt, which cannot be simplified.
5cubrt10 + 4cubrt10 = 9cubrt10
Peggy pays an annual fee of $10.75 to belong to an online music club and download songs at a reduced price. Last year she downloaded 105 songs altogether. Non-members pay $0.35 more per song download than members. Suppose Daniel is not a member of the club and downloaded 85 songs last year. If Daniel and Peggy both paid the same total amount, what is the cost per download for members and for non-members? Let x represent the cost of downloading a song for members. Set up and solve an equation.
the equation representing amount paid by Peggy and Daniel for songs is
105x = 29.75the cost per download for members and for non-members
members = $0.28non-members = $0.35How to determine the amount paid by membersfrom the question the following information can deduced
Daniel is not a member of the club and downloaded 85 at rate of $0.35
total amount paid by Daniel
= 85 * 0.35
= 29.75
Peggy is a member and downloaded 105 songs at a rate of $x
Total amount paid by Peggy
= 105 * $x
= 105x
equating both amounts
105x = 29.75
cost of downloading a song for members, x0.28
105x = 29.75
x = 29.5 / 105
x = 0.28
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please help!!!!! math functions
Answer:
A and C
Step-by-step explanation:
For every x value, there should be at most 1 y value.
B and D violate that constraint.
Jonshelle is developing a new bread recipe. The relationship between cups of water, w, and cups of flour, f, is a=2/5b. What is the scale factor of flour to
water?
Answer: the i8 49
Step-by-step explanation:98493
Eddie is on holiday in Italy
Eddie has €150 to spend on gifts. He buys 1 pair of sunglasses for €70
3 pairs of shorts for €15 each
He also wants to buy a pair of trainers costing €40
Has Eddie got enough money to buy the trainers?
Answer:
No
Step-by-step explanation:
Total money = €150
1 pair of sunglasses = €70
3 pairs of shorts = €15 × 3 = €45
then, Total = €70 + €45 + x
€150 = €115 + x
x = €150 - €115
x = €35
Which means Eddie got only €35 left on him which is not enough for him to buy the trainers
if they are 180 percent of people not satisfied with there car and there is 820 people somewhat satisfied, and 1500 people are completely satisfied. what is the percent of people who are completely satisfied with their car
Answer:
Completely satisfied with their car: 60.00%
Step-by-step explanation:
I'll assume that "180 percent of people not satisfied . ." is meant to read "180 people not satisfied . . ."
Add the people in the groups to find a total. Then divide the numeber of people in each group by the total. This will provide a decimal number which can be multiplies by 100% to give the breakdown requested.
Group Count Percent(%)
Not S. 180 7.20
Somewhat S. 820 32.80
Completely S. 1500 60.00
Total People: 2500 100.00%
Y'all someone PLEASE help me!!! This is due tonight!!!!!!!!!!!!!
The complete two-column proof that shows that ΔAKZ ≅ ΔAKC by AAS is explained below.
What is the AAS Congruence Theorem?The AAS congruence theorem states that if two angles and one non-included side in one triangle have measures that are equal to the two corresponding angles and a corresponding side of another triangle, the two triangles are therefore congruent to each other.
In the image above, we are given two triangles that share a common side, AK. We are informed that line AK bisects an angle, ZKC, and also angles Z and C are congruent.
Therefore, using the information we are given, the two-column proof that can be written to show that the triangles are congruent by the AAS is explained below.
Statements Reasons
1. ∠Z ≅ ∠C 1. Given
AK bisects ∠ZKC
2. ∠ZKA ≅ ∠CKA 2. Definition of bisection
3. AK ≅ AK 3. Reflexive property
4. ΔAKZ ≅ ΔAKC 4. AAS
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Which of The following Best describes the transformation of Y=x^2 so that the resulting equation is as follows?
Y=(x-3)^2+4
By using the concept of translation, it can be inferred that
The graph of the equation is translated 3 units to the left and 4 units down
What is translation?
Translation is a transformation which changes the position of a figure without changing the shape and size of the figure.
The given equation is
[tex]y = (x +3)^2 + 4[/tex]
This means the parabola [tex]y = x^2[/tex] is first translated 3 units to the left and then translated 4 units up.
So the first option is correct.
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Can someone help me on this
The algebra properties associated to each case are listed below:
Case 1: Distributive property
Case 3: Associative property (multiplication)
Case 5: Existence of inverse (addition)
What algebra properties are used in algebraic expressions?
In this question we find three algebraic expressions, in which we need to determine what algebra property is used. The most important properties in real algebra are listed below:
Reflexive property of equalities.Symmetric property of equalities.Transitive property of equalities.Compatibility property (addition, multiplication)Commutative property (addition, multiplication).Associative property (addition, multiplication).Existence of inverse (addition, multiplication).Modulative property (addition, multiplication).Distributive property.Now we proceed to determine the property associated to corresponding operation:
Case 1
9 · (x + y) = 9 · x + 9 · y → Distributive property
Case 3
[8 · (3 / 2)] · 15 = 8 · [(3 / 2) · 15] → Associative property (multiplication)
Case 5
(6 · x + 1) + (- 6 · x + 1) = 0 → Existence of inverse (addition)
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Triangle ABC has vertices A(0, -1), B(6, 5), and C(-4, 3). Which statement about triangle ABC is true?
The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.
What is a right triangle?A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.
The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;
d² = (x₂ - x₁)² + (y₂ - y₁)²
The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;
[tex]\overline{AB}^2[/tex] = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2
[tex]\overline{AC}^2[/tex] = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2
[tex]\overline{BC}^2[/tex] = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)
72 + 32 = 104
Therefore; [tex]\overline{AB}^2[/tex] + [tex]\overline{AC}^2[/tex] = [tex]\overline{BC}^2[/tex]
ΔABC is a right triangle
The slopes of the equation of the lines of the sides of the triangle are;
Slope of side AB = (5 - (-1))/(6 - 0) = 1
Slope of side BC = (3 - 5)/(-4 - 6) = 0.2
Slope of side AC = (3 - (-1))/(-4 - 0) = -1
Therefore;
[tex]\overline{AB}[/tex] ⊥ [tex]\overline{AC}[/tex]
Which gives;
A true statement about triangle ΔABC is that ΔABC is a right triangle a nd the lengths of the sides of the triangle are differentLearn more about the Pythagorean theorem in mathematics here:
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evaluate the expression and enter expression and enter your answer in the box below -3•(6+2)+232÷8
Answer:
5
Step-by-step explanation:
Distribute 1st
-3 x 8 +232 /8
Multiply -3 and 8
-24 +232 /8
Divide 232 and 8
-24+29
Add -24 and 29
5
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
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