Answers
Answer:
B
Step-by-step explanation:
P(7,r) = 5040
[tex]P(n,r)=\dfrac{n!}{(n - r)!}\\\\\\n = 7 \\\\\dfrac{7!}{(7 - r)!}=5040\\\\\\7! = (7-r)!*5040\\\\(7-r)!=\dfrac{5040}{7*6*5*4*3*2*1}\\\\\\(7-r)!=\dfrac{5040}{5040}\\\\\\(7-r)!=1\\\\[/tex]
(7 - r)! = 1!
7 -r = 1
7 = 1 + r
7 - 1 = r
r = 6
Answer:
12. B or C
13. C
14. A
15. A
Step-by-step explanation:
These problems involve various counting techniques. For combinations and permutations, there are formulas to aid in the counting. For other situations, you may need to list possibilities.
__
12.P(7, r) = 5040 . . . . . given
P(7, r) = 7!/(7 -r)! = 5040
5040/(7 -r)! = 5040 . . . . . evaluate 7!
(7 -r)! = 1 . . . . . . . . . . . multiply by (7-r)!/5040
We know that both 0! and 1! = 1, so this has two solutions:
7 -r = 0 ⇒ r = 7
7 -r = 1 ⇒ r = 6
Both choices B and C are correct.
The attached calculator output confirms this result.
__
13.The formula of choice C is correct:
C(n, r) = n!/((n-r)!r!)
__
14.The number of permutations of the 9 letters is reduced by the numbers of permutations of letters that are indistinguishable. That is, the 9 letters can be rearranged 9! ways, but the 4 Es are indistinguishable, so a factor of 4! must be removed from that result. Similarly, the two Ns and two Ss are indistinguishable, so additional factors of 2! must be removed. The number of arrangements is ...
9!/(4!2!2!) . . . . matches choice A
__
15.The 5 students can be arranged in 5 consecutive chairs in P(5, 5) = 5! = 120 ways. Those 5 consecutive chairs can start in chairs 1 through 6, so there are 6×120 = 720 ways the 5 students can sit together in 10 chairs.
Related Questions
Expand. (1-4m)(m^2-3m+8) your answer should be a polynomial in standard form.
Answers
Answer:
13m²−35m+8−4m³
Step-by-step explanation:
Expand (1 − 4m)(m² − 3m + 8) by multiplying each term in the first expression by each term in the second expression.
1m² + 1 (−3m) + 1 ⋅ 8 − 4m ⋅ m² − 4m (−3m) − 4m ⋅ 8
Simplify terms.
13m²−35m+8−4m³
The graph below represents the relationship between the number of days a book is overdue and the library fine charged. A graph titled Library Fines. The horizontal axis shows days overdue and the vertical axis shows the fine (dollars). The line shows an increase to $10 at 19 days overdue, then constant. Christen returned an overdue book to the library. Her fine was the same as it would have been if she returned the book the previous day. Which of the answer choices below could be the number of days Christen’s book is overdue? 10 14 18 22
Answers
Answer:
(d) 22
Step-by-step explanation:
For numbers of days above 19, the fine is constant. The answer choice that is above 19 is 22. For 22 days overdue, the fine will be the same as for 21 days overdue: $10.
22 could be the number of days
Answer:
D. 22
Step-by-step explanation:
A fair die is rolled 3 times what is the probability that is comes up 1 at least Once
Answers
The final question on Walter's science exam was an essay question. Walter's essay
was 175 words long. This was 5 times more words than the minimum number of
required words. Which equation can be used to find n, the minimum number of
required words?
A 5 + n = 175
B 5 x 175 = n
C 175 - 5 = n
D5n = 175
Answers
Answer:
D
Step-by-step explanation:
If n=minimum number of required words and the essay is 175 words long which is 5 times more words than the minimum number of required words, you multiply n with 5 and equate to 175. To get n, you divide 175 with 5(175/5) which is 35 words.
Please help!!!!!!!!!!!!!!
Answers
Answer:
312.29 square feet
Step-by-step explanation:
[tex]w = \sqrt{ {d}^{2} - {l}^{2} } = \sqrt{ {25}^{2} - {18}^{2} } \\ [/tex]
w = 17.35
A= l × w
= 18 × 17.35
= 312.29 square feet
Find the equation for the line that passes through the points (-4,1) and(2,+3)
Answers
y=2x+1
Teresa has lived one-fourth of her life in England, one-fifth in Ireland, one-third in France and 13 years in
Switzerland. Assuming she lived in no other countries, how many years old is she?
Will give BRAINLIST
Answers
Answer:
She is 60 years old
Step-by-step explanation:
The first thing we can do is convert each fraction to have a common denominator. The LCM of 5, 3, and 4 is 60.
[tex]\frac{1}{4} =\frac{15}{60}[/tex]
[tex]\frac{1}{3} =\frac{20}{60}[/tex]
[tex]\frac{1}{5} =\frac{12}{60}[/tex]
Add the numerators:
[tex]15+12+20=47/60[/tex]
Meaning that the time she lived in Switzerland is the remaining 13/60, and since she lived there for 13 years that means she lived for a total of 60 years because the numerator and denominator both equal 60.
#LearnWithBrainly
Answer:
Teresa is 60 years old------------------------------
Let the age of Teresa be x.
Set up equation:
x(1/4 + 1/5 + 1/3) + 13 = xMultiply both sides by 3*4*5 = 60 to clear fraction:
x(60/4 + 60/5 + 60/3) + 13*60 = 60xx(15 + 12 + 20) + 780 = 60x47x + 780 = 60x60x - 47x = 78013x = 780x = 780/13x = 60What is the trigonometric ratio for cos N?
Enter your answer, as a simplified fraction.
Answers
Answer
=12/13
Step-by-step explanation:
I have done it before:)
At a high school football game, the amount of concession items sold over the first 5 weeks of the season is shown below.
Answers
Based on the quantity of the various items sold at the concession stand, the items that show a linear relationship include:
Hot dogs.Nachos. Why are these items showing a linear relationship?Items that show a linear relationship are those that are either increasing or decreasing by the same amount overtime.
Change in Hotdogs:
= 142 - 131 = 120 - 109
= 11 = 11
Hotdogs are changing by the same amount.
Change in Soft drinks:
= 161 - 154 = 147 - 133
= 7 = 14
Change in Pretzels
= 96 - 64 = 120 - 112
= 32 = 8
Change in Nachos:
= 111 - 97 = 153 - 139
= 14 = 14
Therefore, the only items that are linear are the Hotdogs and Nachos.
Find out more on linear relationships at https://brainly.com/question/837754.
Slope: Tutorial
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10 11
The slope of the line in the graph is
(If your answer is a fraction, write it in simplified terms.)
I’m
Answers
Answer:
Step-by-step explanation: just write from 2 to 11 one by one
....pleaseee....helpppppp................
Answers
Answer:
16 ounces
Step-by-step explanation:
one pound is sixteen ounces
1 pound = 16 ounce
How do you solve the picture AND DO NOT TELL ME YOU DO NOT KNOW lol
Answers
I don't know use a calculator
Do you guys know what 4m - 2m + 3
Answers
Answer:
2m + 3 I think.
Step-by-step explanation:
4m - 2m = 2m. So just put that in the equation now and poof. 2m + 3
What is the answer to 4-(-6)+(-4)+3x0
Answers
Answer:
9
Step-by-step explanation:
Follow PEMDAS
[tex]4-(-6)+(-4)+3x\\4+6-4+3x\\6+3x\\6+3=9[/tex]
Answer:
6
Step-by-step explanation: [tex]4-\left(-6\right)+\left(-4\right)+3\times0[/tex]
Apply the Inverse Property of Addition
[tex]-\left(-6\right)+3\times0[/tex]
Apply Zero Property of Multiplication
[tex]-\left(-6\right)[/tex]
Determine the sign
[tex]6=YOUR\ ANSWER[/tex]
I hope this helps you
:)
Please help if you know anything about triangles!!
Answers
Step-by-step explanation:
125 + 30 + 25 + b is equal to 180 degree 19 + y equal to 180 degree equal to 180 - 190 equal to - -10
A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form
best describes the total volume of the cylinder? Use the formula V = 3.14r^2h for the volume of a
cylinder
Answers
Answer:
The answer is A!
Step-by-step explanation:
area of the base = pi*(4x+2)^2 = pi*(16x^2 +16x +4)
volume of cylinder = pi*r^2 *h
V = pi *(16x^2 +16x +4)(5x+4) = pi*(80x^3 +80x^2 +20x +64x^2 +64x +16) =
= pi*(80x^3 +144x^2 +84x +16)
Answer:
Step-by-step explanation:
The volume of a cylinder can be thought of as the area of a circle, scaled by the height of the cylinder. The formula for the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]
Plug in the radius, and the height:
[tex]V=\pi (4x+2)^2(5x+4)[/tex]
Use FOIL to expand the squared binomial:
[tex]V=\pi (16x^2+16x+4)(5x+4)[/tex]
Bring out the binomial to the front of the trinomial:
[tex]V=\pi [(5x+4)(16x^2+16x+4)][/tex]
The process to multiply a trinomial by a binomial involves multiplying the trinomial by each term of the binomial:
[tex]V=\pi [(5x+4)(16x^2+16x+4)]=\pi [5x(16x^2+16x+4)+4(16x^2+16x+4)][/tex]
The rest is just distributing and tedious algebra:
[tex]V=\pi [(80x^3+80x^2+20x)+(64x^2+64x+16)][/tex]
Combine like terms and order the terms from highest exponent to lowest exponent. That is the definition of standard form:
[tex]V=\pi [80x^3+144x^2+84x+16][/tex]
[tex]V=4\pi [20x^3+36x^2+21x+4][/tex]
the following shape has 1 pair of parallel sides. 3, 5, 8, 2, 6
Answers
To identify the shape with one pair of parallel sides, we need to consider the given set of numbers: 3, 5, 8, 2, 6.
A shape with one pair of parallel sides is a trapezoid. In a trapezoid, two sides are parallel while the other two sides are non-parallel.
Looking at the given set of numbers, we can form the sides of a trapezoid by pairing the numbers in the following way: 3, 5, 8, 2, 6.
The sides of the trapezoid can be represented as follows:
Parallel sides: 3 and 5 (forming the top and bottom sides)
Non-parallel sides: 8, 2, 6 (forming the slanted sides)
Therefore, the given set of numbers forms a trapezoid with one pair of parallel sides.
For such more question on trapezoid
https://brainly.com/question/1410008
#SPJ8
Magan decides to research the relationship between the length in inches and the
weight of a certain species of catfish. He measures the length and weight of a number
of specimens he catches, then throws back into the water. After plotting all his data,
he draws a line of best fit. Based on the line of best fit, what would you predict to be
the length of a catfish that weighed 40 pounds?
Answers
Based on the line of best fit, the length of this catfish can be predicted to be 38 inches.
Given the following data:
Weight of catfish, x = 40 pounds.What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.
From the graph of the data, we have the following linear equation:
[tex]y=\frac{1}{2} x+18[/tex]
Substituting the value of x, we have:
[tex]y=(\frac{1}{2} \times 40 )+18\\\\y=20+18[/tex]
y = 38 inches.
Read more on scatterplot here: https://brainly.com/question/6592115
Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).
-3x-y - 1
-2x+2y = 10
Add Work
> Next Question
Answers
Answer:
2x + 3y = 12 …equation 1
x– y = 1 … equation 2
To solve it by elimination method, let us multiply the second equation by 3
3x — 3y = 3 …equation 3
Now add the first and third equation
5x = 15
x = 3
From equation 2, y = x-1
y = 2
Hence x = 3, y = 2.
(b) 3x + y = 10
Since we have one equation and 2 variables, it cannot be solved by the elimination method.
To solve this, we can go for trial and error
Say y = 1, x = 3 or x = 5, y = —5
(c) x – 3y=1 …eq 1
3x – 2y + 4 = 0 …eq 2
Multiply eq 1 by 3, 3x — 9y = 3 …eq 3
Eq 2 — eq 3,
7y = —7
y = —1, x = —2 Ans
Hope it helps!!!!!!!brainliest pls!!!!!!!!!!!The expression for thrice of a number m is m +3. true or false
Answers
Answer:
False
Step-by-step explanation:
[tex]the \: expression \: is \: 3x[/tex]
Answer:
false
Step-by-step explanation:
thrice a number means 3 times the number
if the number is m then thrice the number is
3 × m = 3m
You are buying carpet to cover a room that measures 42 ft by 42 ft. The carpet cost $ 25 per square yard. How much will the carpet cost?
Answers
Explanation:
3 feet = 1 yard
14*(3 feet) = 14*(1 yard) .... multiply both sides by 14
42 feet = 14 yards
The carpet is 14 yards by 14 yards.
Its area is 14*14 = 196 square yards.
Since it costs $25 per square yard, this means the total cost is 25*196 = 4900 dollars
Item 1
The Diamond Rule says two factors, m and n, must multiply to get to the top number and add to get to the bottom number.
What are the possible values for m and n?
9 and 4
-9 and 4
6 and 6
-6 and -6
-6 and 6
-9 and -4
Answers
The diamond rule creates a system of equation for variables m and n
The possible values of m and n are 8 and 4 or 4 and 8
How to determine the possible values of m and n.The question is incomplete; so I will make use of the attached figure
When the diamond rule is applied to the figure, we have the following equations
[tex]mn = 32[/tex]
[tex]m + n = 12[/tex]
Make n the subject, in the second equation
[tex]n = 12 - m[/tex]
The first equation becomes
[tex](12 - m)m = 32[/tex]
Expand
[tex]12m - m^2 = 32[/tex]
Rewrite as:
[tex]-m^2 + 12m - 32 = 0[/tex]
Multiply through by -1
[tex]m^2 - 12m + 32 = 0[/tex]
Expand
[tex]m^2 - 4m - 8m + 32 = 0[/tex]
Factorize
[tex]m(m - 4) - 8(m - 4) = 0[/tex]
Factorize
[tex](m - 8)(m - 4) = 0[/tex]
Solve for m
m = 8 or m = 4
Recall that:
[tex]n = 12 - m[/tex]
So, we have:
n = 12 - 8 or n = 12 - 4
Solve
n = 4 or n = 8
Hence, the possible values of m and n are 8 and 4 or 4 and 8 (using the attached figure)
Read more about equations at:
https://brainly.com/question/2972832
solve the system substitution y= 4x + 1 and 3x+2y =13
Answers
Given :
[tex]{\qquad \sf \dashrightarrow y= 4x + 1 \: –––– \sf \: (i)}[/tex]
[tex]{\qquad \sf \dashrightarrow 3x + 2y = 13 \: –––– \sf \: (ii)}[/tex]
Now, Substituing the value of y in equation (ii) :
[tex]{\qquad \sf \dashrightarrow \: 3x + 2y = 13 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 3x + 2(4x + 1) = 13 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 3x + 8x + 2 = 13 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 11x + 2 = 13 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 11x = 13 - 2 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: 11x = 11 }[/tex]
[tex]{\qquad \sf \dashrightarrow \: x = \dfrac{11}{11} }[/tex]
[tex]{\qquad \sf \dashrightarrow \bf \: x = 1 }[/tex]
Now, substituting the value of x in equation (i) :
[tex]{\qquad \sf \dashrightarrow y= 4x + 1}[/tex]
[tex]{\qquad \sf \dashrightarrow y= 4(1) + 1}[/tex]
[tex]{\qquad \sf \dashrightarrow y= 4 + 1}[/tex]
[tex]{\qquad \bf \dashrightarrow y= 5}[/tex]
Please show work and thanks
Answers
Answer:
2
Step-by-step explanation:
If ABC is equilateral, its angles are all equal to each other and each one measures 60°.
[tex]8x-44 =60\\8x = 16 \rightarrow x = 2[/tex]
There is a rectangular field in Sheffield Park that is 4 meters long and 2 meters wide.
What is the area, in square meters, of the field?
Answers
Answer:
8 m^2
Step-by-step explanation:
4x2=8 and if it needs to be in sq meters it is 8 m^2 (m^2 means meters squared)
Explanation
Area = length(width)
Wendy bought an $80 dress on sale for 40% off. How much did she pay for the dress?
Answers
Solution:
We know that:
Discounted price: Original price - (Original price × Discount)Original cost of dress: $80Discount: 40%This means that:
Discounted price of dress: 80 - (80 × 40%)Step-1: Convert "40%" into a fraction.
40% = 40/100Step-2: Find the discounted price.
Discounted price of dress: 80 - (80 × 40/100)Discounted price of dress: 80 - (4 × 40/5)Discounted price of dress: 80 - (4 × 8)Discounted price of dress: 80 - 32Discounted price of dress: $48!!!PLEASE HELP!!!
What is one of the solutions to the system of equations graphed here?
(Look at the image for the answer it’s multi choice)
Answers
Answer:
B. (-5,-4)
Step-by-step explanation:
The answer must be at the point where the two functions intersect. They meet at the points (-5,-4) and (2,0). Since (2,0) is not an answer choice, (-5,-4) must be the answer.
In Diagram 5, POQ is the diameter of the circle with centre O .Find the area, in cm², of the shaded region. Use 22/7
Answers
Answer:
B) 236.25
Step-by-step explanation:
POQ is a diameter of circle with centre O having diameter 21 cm. Whereas radius is 21/2 cm (as radius is considered as half of the diameter).
Assume that the tip of the triangle that touches the circle is point 'N'. So,
NO = radius = 21/2 cm
At present time we have a triangle of radius or height 21/2 cm, base 21 cm is enclosed in circle of diameter 21 cm. And are asked to find the area of the remaining region or you can say asked to find area of the shaded region.
Shaded region = Area of Circle - Area of Triangle
= πr² - 1/2 × b × h
= 22/7 × 21/2 × 21/2 - 1/2 × 21 × 21/2
= 21/2 × 1/2 [ 22/7 × 21 - 21 ]
= 21/4 [ 22 × 3 - 21 ]
= 21/4 [ 66 - 21 ]
= 21/4 [ 45 ]
= 21 × 11.25
= 236.25
Hence, the area of the shaded region is 236.25 cm².
Find the total area of the irregular polygon shown? * m 11 m 36 sqm 84 sq.m 88 sqm
Answers
Answer:
100
Step-by-step explanation:
Split it into 3 different rectangles, find the area of each, and add them together.
Rectangle 1: length=11 width=4 11×4=44
Rectangle 2: length=11-9=2 width=6 2×6=12
Rectangle 3: length=11 width=4 11×4=44
44+12+44=100
Solve for x. Leave your answer in simplest radical form.
Answers
Answer:[tex]2\sqrt{3}[/tex]
Step-by-step explanation:
Use pytha. theorem on leftmost triangle and get sqrt(13)
Use it again on the other triangle: 13+b^2=25
First, we find the hypotenuse of the first triangle
(Use the pythagorean theorem) : [tex]3^{2} + 2^{2} = 9 + 4 = 13[/tex]
So, the length of the side = [tex]\sqrt{13}[/tex]
Now, we find x :
x(squared) = [tex]5^{2} -\sqrt{13} ^{2}[/tex] = 25 - 13 = 12
-> x = [tex]\sqrt{12}[/tex] = 2[tex]\sqrt{3}[/tex]