Answer:
[tex]\large\boxed{_4P_3>_4C_3}[/tex]
Step-by-step explanation:
[tex]\left\begin{array}{ccc}_nP_r=\dfrac{n!}{(n-r)!}\\\\_nC_r=\dfrac{n!}{r!(n-r)!}\end{array}\right\}\Rightarrow\dfrac{n!}{(n-r)!}>\dfrac{n^!}{r!(n-r)!}\Rightarrow_nP_r>_nC_r\\\\\text{because}\\-\text{the nominators are the same}\\-\text{the denominator}\ (n-r)!\ \text{is graeter than the denominator}\ r!(n-r)![/tex]
[tex]\text{Let's check our example:}\\\\n!=1\cdot2\cdot3\cdot4\cdot...\cdot n\\\\_4P_3=\dfrac{4!}{(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1!}=\dfrac{24}{1}=24\\\\_4C_3=\dfrac{4!}{3!(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1\cdot2\cdot3\cdot1!}=\dfrac{24}{6}=4\\\\24>4\Rightarrow_4P_3>_4C_3[/tex]
[tex]nPr = \dfrac{n!}{(n-r)!} \\ \\ nCr = \dfrac{n!}{r!(n-r)!}\\ \\ \Rightarrow nPr > nCr\\ \\ \Rightarrow \boxed{4P3 > 4C3}[/tex]
What is the inverse of y=^x3
Answer:
Inverse of y=x^3 is f^-1(x) = ∛x
Step-by-step explanation:
We need to find the inverse of y=x^3
Step 1:
Interchange the variables:
x= y^3
Step 2: Now solve to find the value of y
=> y^3 = x
taking cube root on both sides of the equation
∛y^3 = ∛x
y=∛x
Step 3: Replace y with f^-1(x)
f^-1(x) = ∛x
So inverse of y=x^3 is f^-1(x) = ∛x
Which point is an x-intercept of the quadratic function f(x)=(x-4)(x+2)
Answer:
x = - 2 or x = 4
Step-by-step explanation:
To find the x- intercepts let f(x) = 0, that is
(x - 4)(x + 2) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 2 = 0 ⇒ x = - 2
The x- intercepts are at x = - 2, x = 4
Which expression represents the amount of punch Milena will need for her party?
g + 20
3g
3g + 20
3(20)
Answer:3g+20 on edg
Step-by-step explanation:
Since the guests equals g and 3 cups per guest it would be 3g+ extra 20 so the answer would be 3g+20
Which is a trait of all seed plants?
Answer:
All seed plants share two characteristics. They have vascular tissue and use seeds to reproduce. In addition, they all have body plans that include leaves, stems, and roots. Most seed plants live on land.
Step-by-step explanation:
All seed plants have the ability to produce seeds. Seeds contain an embryo and stored food and can withstand harsher conditions, staying dormant until conditions for growth are ideal. This trait is seen across all seed plants, which includes both gymnosperms and angiosperms.
Explanation:All seed plants, also known as spermatophytes, share a key characteristic that they have the ability to produce seeds. This is a common trait and allows seed plants to reproduce. Seeds contain an embryo and stored food wrapped in a protective coat. They can withstand harsher conditions and can stay dormant until the conditions for growth are favorable. Seed plants include gymnosperms, such as conifers, and angiosperms, which are flowering plants.
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The vertex of this parabola is at (-3, -2). Which of the following could be its equation?
Answer:
y = a(x + 3)² - 2 where a is any real number except 0.Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (-3, -2) → h = -3 and k = -2.
Substitute:
[tex]y=a(x-(-3))^2+(-2)=a(x+3)^2-2[/tex]
The equation of parabola is , [tex]y= -2(x+3)^{2} - 2[/tex]
What is a parabola?Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.What are the 4 types of parabola?There are three types of parabolas. The three forms are: vertex form, standard form and intercept form. Each form provides you a different key feature for the graph.What is parabola and examples?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.What is equation of parabola?[tex]y = a(x- h)^{2} + K[/tex].
According to the question:
Applying value in equation gives.
[tex]y= -2(x-(-3))^{2} -2\\[/tex]
[tex]y= -2(x+3)^{2} - 2[/tex]
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Write the real number 12 as a complex number in form of a+bi
[tex]12+0i[/tex]
.....................
Answer:
12+0i
Step-by-step explanation:
Which is equivalent
Answer:
[tex]x^\frac{5}{3} y^\frac{1}{3}[/tex]
Step-by-step explanation:
This question is on rules of rational exponential
where the exponential is a fraction, you can re-write it using radicals where the denominator of the fraction becomes the index of the radical;
General expression
[tex]a^\frac{1}{n} =\sqrt[n]{a}[/tex]
Thus [tex]\sqrt[3]{x} =x^\frac{1}{3}[/tex]
Applying the same in the question
[tex]\sqrt[3]{x^5y} =x^\frac{5}{3} y^\frac{1}{3}[/tex]
=[tex]x^\frac{5}{3} y^\frac{1}{3}[/tex]
Answer: Second option
[tex](x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]
Step-by-step explanation:
By definition we know that:
[tex]a ^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]
In this case we have the following expression
[tex]\sqrt[3]{x^5y}[/tex]
Using the property mentioned above we can write an equivalent expression for [tex]\sqrt[3]{x^5y}[/tex]
[tex]\sqrt[3]{x^5y} = (x^5y)^{\frac{1}{3}}[/tex]
[tex](x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]
Therefore the correct option is the second option
What is the measure of arc AC? Enter your answer in the box. AC is (7x-2) degrees. ABC is inscribed with (2.5x + 4) degrees
Answer:
The measure of arc AC is equal to 33°
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
∠ABC=(1/2) arc AC
substitute the values
(2.5x+4)=(1/2)(7x-2)
solve for x
5x+8=7x-2
7x-5x=8+2
2x=10
x=5
Find the measure of arc AC
arc AC=(7(5)-2)=33°
Final answer:
The measure of arc AC can be calculated by using the inscribed angle theorem and solving the equation 2×(2.5x + 4) = 7x - 2, which represents the relationship between the inscribed angle and its intercepted arc.
Explanation:
To determine the measure of arc AC, we need to consider the relationship between the inscribed angle of a circle (ABC in this case) and the corresponding arc (arc AC).
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. This relationship allows us to set up the equation (2.5x + 4) degrees = 0.5×((7x-2) degrees).
By solving this equation, we can find the value of x, and consequently, the measure of arc AC.
substitute the values
(2.5x+4)=(1/2)(7x-2)
solve for x
5x+8=7x-2
7x-5x=8+2
2x=10
x=5
Find the measure of arc AC
arc AC=(7(5)-2)=33°
Consider a graph of the equation y = 2x - 1. What is the y-intercept?
Answer:
[0, -1]
Step-by-step explanation:
According to the Slope-Intercept Formula y = mx + b, b is your y-intercept, and in the above raisin, you have your answer in place of that b.
Answer:
[0, -1], or just -1
The product of the polynomials (2ab + b) and (a2 – b2)
Answer:
= 2a³b - 2ab² + a²b - b³
Step-by-step explanation:
We multiply the each term in the first polynomial by each in the other as follows.
2ab(a² - b²) + b(a² - b²)
We then open the brackets and get the following.
2a³b - 2ab² + a²b - b³
We can not simplify the product further than this since it has no like terms.
Answer:
First is C
Second is 2
Step-by-step explanation:EDGE 2021
subtract the polynomials (3x^2-11x-4)-(x-2)(2x+3)
Answer:
[tex]x^2-10x+2[/tex]
Step-by-step explanation:
Multiply out the two monomials first because of PEMDAS.
[tex](-x + 2) * (2x + 3)=-2x^2+x+6[/tex]
Now add them together.
[tex]3x^2-11x-4-2x^2+x+6=x^2-10x+2[/tex]
Triangle ABC is a right triangle. Find the measure of side b. Round to the nearest hundredth.
A) 6.13 cm
B) 6.71 cm
C) 9.53 cm
D) 10.54 cm
E) 12.45 cm
Answer:
Applying the trigonometric functions, 8/b=Tan40
b=8/Tan40
Answer:
C) 9.53 cm
Step-by-step explanation:
We know this is a right triangle, so we can use trig relations
tan A = opposite side/ adjacent side
tan 40 = 8/b
Multiply each side by b
b tan 40 = 8
Divide each side by tan 40
b tan 40 / tan 40 = 8 / tan 40
b = 8/ tan 40
b = 9.534028741
5 - 7 second power + 6 - 7 second power + 5 - 7 second power + 6 - 7 second power + 10 - 7 second power + 10 - 7 second power
ANSWER: -252
HOW TO GET IT:
Simply follow PEMDAS. Solve each exponent first, then do the rest.
Answer:
144
Step-by-step explanation:
5-7 = 2 2^2 + 6 = 10 - 7 = 3^2 = 9 + 10 = 19 - 7 = 12^2 = 144
I hope this helps even if I am too late! :)
The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?
Answer:
2+3
Step-by-step explanation:
Shirts cost $20 each and ties cost $12 each. Write an expression for the cost of s shirts and t
ties.
20 + 12
g(x) = x3 + 6x2 + 12x + 8
Determine the function's value when x = -1
g(x)
g(-1) = -3
9(-1) = 0
9(-1) = 1
g(-1) = 27
64
125
Answer:
g(-1) = 5 - 4 = 1
Step-by-step explanation:
Please use " ^ " to denote exponentiation: g(x) = x^3 + 6x^2 + 12x + 8.
Substitute -1 for x in this equation: g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8
Then: g(-1) = -1 + 6 - 12 + 8, or
g(-1) = 5 - 4 = 1
Answer:
The answer is C
Step-by-step explanation:
I just took the test and got it right.
Hopefully this helps you :)
pls mark brainlest ;)
A die is rolled. What is the probability of rolling the following?
a multiple of 2 or a multiple of 5
Answer:
2/3 chance (67%)
Step-by-step explanation:
Multiples of 5:
(5)
Multiples of 2:
(2)
(4)
(6)
This is a 4/6 chance or 2/3
[tex]|\Omega|=6\\|A|=3+1=4\\\\P(A)=\dfrac{4}{6}=\dfrac{2}{3}\approx67\%[/tex]
Find each product or quotient. Use significant digits.
0.0505 m X 665 m
6th grade-Write an inequality to represent the situation: The temperature stayed above -15 degrees. Thanks guys!
Let temperature = T
"The temperature stayed above -15 degrees. " means that the temperature is always greater than -15 degrees.
Therefore,
-15 degrees < T
Evaluate b^2 for b=9
Answer: It's 81
Step-by-step explanation:
So, if B= 9 then it's 9^2 which is 9 x 9 = 81
Hope my answer has helped you and if not i'm sorry.
Rewrite the function by completing the square.
f(x) = x2 – 10x + 44
+
f(x) = (x+
Answer:
[tex]f(x)=(x-5)^{2}+19[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-10x+44[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-44=x^{2}-10x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)-44+25=x^{2}-10x+25[/tex]
[tex]f(x)-19=x^{2}-10x+25[/tex]
Rewrite as perfect squares
[tex]f(x)-19=(x-5)^{2}[/tex]
[tex]f(x)=(x-5)^{2}+19[/tex]
Find the quotient. Simplify your answer.
y-4/y ÷ 6/y
Answer: [tex]\frac{y-4}{6}[/tex]
Step-by-step explanation:
To find the quotient asked, you need to make the division indicated.
You can follow these steps:
1. Find the reciprocal of [tex]\frac{6}{y}[/tex]. You need to turn it upside down. Then you get that the recriprocal is:
[tex]\frac{y}{6}[/tex]
2. Now you must multiply [tex]\frac{y-4}{y}[/tex] by [tex]\frac{y}{6}[/tex]:
[tex](\frac{y-4}{y})(\frac{y}{6})=\frac{(y-4)(y)}{(y)(6)}[/tex]
3. Simplifying, you get that the quotient is:
[tex]=\frac{y-4}{6}[/tex]
Which of the symbols correctly relates the two numbers ?
Answer:
C. >
Step-by-step explanation:
The answer is C. because 65 is greater than 56!
Determine if the two figures are congruent and explain your answer.
Answer:
They can be congurent depending on which two figures you are using
Step-by-step explanation:
The four folded parts of an envelope are opened up to create this figure. What is the surface area of one side of the unfolded envelope?
A. 25 square centimeters
B. 37 square centimeters
C. 50 square centimeters
D. 64 square centimeters
Answer:
Option C. 50 square centimeters
Step-by-step explanation:
we know that
The surface area is equal to the area of four triangles plus the area of rectangle
so
[tex]SA=2[\frac{1}{2}(4)(2)]+2[\frac{1}{2}(6)(3)]+(6)(4)[/tex]
[tex]SA=8+18+24[/tex]
[tex]SA=50\ cm^{2}[/tex]
Answer:
C
Step-by-step explanation:
The total area comprises of the rectangle (area is base * height) and the 4 triangles (area = 1/2 * base * height).
Area of rectangle = 6 * 4 = 24
Area of top triangle = 1/2 * 6 * 3 = 9
Area of bottom triangle = 1/2 * 6 * 3 = 9
Area of rightside triangle = 1/2 * 4 * 2 = 4
Area of leftside triangle = 1/2 * 4 * 2 = 4
Let's add them up and find the correct answer:
Area = 24 + 9 + 9 + 4 + 4 = 50
Joshua likes to read he read 6 books when he was 6 years old every year he doubled the number of book he read the previous year how many total books did he read between the ages of 6 and 10?
When Joshua Is 6 he reads 6 books, when he is 7 he reads 12 books, when he turns 8, he reads 24 books, when he turns 9 he reads 48 books, when Joshua turns 10 he reads 96 books
6+12+24+48+96=186
The answer is C
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Answer:
Joshua read 186 books form 6 to 10 years of age.
Step-by-step explanation:
Joshua reads 6 books at the age of 6.
He doubled the number of books he read the previous years.
Now the sequence will be a geometric sequence as
6, 12, 24, ......
We have to calculate the number of books he read from 6 years to 10 years of his age.
Since sum of n terms of a geometric sequence is given by
[tex]S_{n}=\frac{a(r^{n}-1 )}{r-1}[/tex]
where a = first term
r = common ratio
n = number of terms
[tex]S_{5}=\frac{6(2^{5}-1 )}{2-1}[/tex]
= [tex]\frac{6(32-1)}{1}[/tex]
= 6×31
= 186 books
Therefore Joshua read 186 books form 6 to 10 years of age.
Here is a table of values for y = f(x).
x 0 5 10 15 20 25 30 35 40
f(x) 5 6 7 8 9 10 11 12 13
Mark the statements that are true.
A. 5) = 6
B. The domain for f(x) is the set {5, 6, 7, 8, 10, 11, 12, 13).
O
C. The range for fx) is all real numbers.
D. f15) = 8
Answer:
A, D
Step-by-step explanation:
for this table:
x 0 5 10 15 20 25 30 35 40
f(x) 5 6 7 8 9 10 11 12 13
A, assuming it's supposed to say f(5)=6, is true since 5 in x corresponds to 6 in f(x)
B is false, since the domain would be the set of all numbers in x, since domain corresponds to input (x) and range corresponds to output (f(x))
C is false, the range is not all real numbers since it is a defined set of numbers
D is true, since 15 in x corresponds to 8 in f(x)
Therefore, A and D are true
Solve the equation log4(x + 20) = 3
Answer:
x = 44
Step-by-step explanation:
log4(x + 20) = 3
Raise each side to the power of 4
4^ log4(x + 20) = 4^3
x+20 = 4^3
x+20 = 64
Subtract 20 from each side
x+20-20 = 64-20
x = 44
Compute the permutation. 8 P 4 32 1,680 6,720
ANSWER
[tex]^8P_4=1680[/tex]
EXPLANATION
The given permutation is
[tex]^8P_4.[/tex]
Recall the formula for permutation
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
We substitute n=8, and r=4 to obtain:
[tex]^8P_4=\frac{8!}{(8-4)!}[/tex]
[tex]^8P_4=\frac{8!}{4!}[/tex]
Recall the factorial expansion
[tex]n! = n \times (n - 1) \times (n - 2)...3 \times 2 \times 1[/tex]
We apply this expansion to get:
[tex]^8P_4=\frac{8 \times 7 \times 6 \times 5 \times 4!}{4!}[/tex]
[tex]^8P_4=8 \times 7 \times 6 \times 5[/tex]
[tex]^8P_4=1680[/tex]
Which polygon has an interior angle sum of 1080°?
Step-by-step explanation:
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent.Answer:
Octagon
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides, so
180° (n - 2) = 1080° ( divide both sides by 180° )
n - 2 = 6 ( add 2 to both sides )
n = 8 ← octagon