==========================================================
Explanation:
We have five slots which we can label A,B,C,D,E
There are 8 choices for slot AThen 7 choices for B6 for C5 for D4 for EWe start at 8 and count down by 1 each time until all slots are accounted for. Then multiply out those items: 8*7*6*5*4 = 6720
--------------
Another approach is to use the nPr permutation formula.
Plug in n = 8 and r = 5.
[tex]n P r = \frac{n!}{ (n-r)! }\\\\8 P 5 = \frac{8!}{ (8-5)! }\\\\8 P 5 = \frac{8!}{ 3! }\\\\8 P 5 = \frac{8*7*6*5*4*3!}{ 3! }\\\\8 P 5 = 8*7*6*5*4\\\\8 P 5 = 6720\\\\[/tex]
In the second to last line, the "3!" factorial terms cancel out.
We have the string 8*7*6*5*4 show up again to help reinforce the previous section.
20. Factor the trinomial.
Factors of 40: (1, 40) (2, 20) (4, 10) (5, 8)
---Using these factors will help us find a pair that adds up to -13 and multiplies to equal 40
-5 + -8 = -13
-5 x -8 = 40
(v - 8)(v - 5)
The trinomial can be factored into the following expression (v - 8)(v - 5).
Hope this helps!
Graph the function g(x)=−[tex]\frac{1}{3}[/tex](x+2)(x+8)
Answer:
Step-by-step explanation:
Comment
If you do not have a graphing calculator the best thing to use is Desmos. Desmos is free -- anyone can use it and and the graphs can be used here on Brainly. I've downloaded the graph for you.
There are a couple of things you should notice.
The most downward point is (-5,-3)
The largest root is x = -2
The smallest root is x = - 8
Notice the roots are the opposite of what you are given. You will eventually learn how to do all of these things.
An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Select the diagrams that would represent the types of animals adopted.
How many of each type of animals were adopted?
There are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Combine ratio dogs:ferrets:cats = 5:1:9
Let's suppose the number of ferrets is x then:
5x + x + 9x = 45
15x = 45
x = 3
Ferrets x = 3
Dogs = 5x = 5(3) = 15
Cats = 9x = 9(3) = 27
Thus, there are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Learn more about the ratio here:
brainly.com/question/13419413
#SPJ1
In this figure, AB || CD and m/1 = 110°
A
1/2 B
4 3
What is mZ5?
5/6
8 7
Answer is 105 degrees.
Explanation:
Given two parallel lines AB and CD and a transversal cutting the two lines.
We know that when a transversal cuts two parallel line,
i) corresponding angles would be equal
ii) Interior angles total to 180
iii) alternate angles are equal.
In the picture given we have corresponding angles as
(2,6) . Hence angle 2 = angle 6.
Angle 6 = 75 (given)
Hence angle 2 =75.
Angles 1 and 2 are supplementary because they form a linear pair.
Hence angle 1 = 180-75
Angle 1 =105
Please help with 6 and 7
Answer:
6. The number is [tex]-5[/tex]
7. The two numbers are [tex]10[/tex] and [tex]11[/tex]
Step-by-step explanation:
Question six can be re-worded to create the following expression:
[tex]-2=\frac{4x+10}{5}[/tex]
Solve for x to find the number:
[tex]-2=\frac{4x+10}{5}\\-10=4x+10\\-20=4x\\\frac{-20}{4} = x\\-5 = x[/tex]
Question seven can be solved by first listing the constraints (assuming x is smaller than y):
x and y are less than 20[tex]x + 1 = y[/tex][tex]3x - 8 = 2y[/tex]To get the numbers, we can create a system of linear equations. First, solve for [tex]y[/tex] in each expression:
[tex]y = x+1[/tex]
[tex]2y = 3x-8\\y = \frac{3}{2}x - 4[/tex]
Solve for [tex]x[/tex]:
[tex]x+ 1 = \frac{3}{2}x - 4\\x + 5 = \frac{3}{2}x\\5 = \frac{3}{2}x - x\\5 = \frac{1}{2}x\\10 = x[/tex]
Solve for [tex]y[/tex]:
[tex]y = x + 1\\y = 10 + 1\\y= 11[/tex]
Answer:
see explanation
Step-by-step explanation:
(6)
let n be the number then the sum of 4 times the number and 10 is 4n + 10
so
[tex]\frac{4n+10}{5}[/tex] = - 2 ( multiply both sides by 5 to clear the fraction )
4n + 10 = - 10 ( subtract 10 from both sides )
4n = - 20 ( divide both sides by 4 )
n = - 5
(7)
let the consecutive integers be n and n + 1 , then
3n = 2(n + 1) - 8 ← distribute parenthesis and simplify right side
3n = 2n + 2 - 8
3n = 2n - 6 ( subtract 2n from both sides )
n = - 6 and n + 1 = - 6 + 1 = - 5
the 2 integers are - 6 and - 5
HELP ASAP PLEASE, this is the last question i promise T^T
WILL MARK BRAINLIEST AND GIVE POINTS
find the perimeter of a circular sector if the diameter of its circle equals 10cm and its arc length = 10cm. equals = ......... cm.
a) 10
b) 20
c) 30
d) 40
an explanation for future reference would be greatly appreciated, thank youuu <33
Answer:
A= 10
Step-by-step explanation:
[10 + 2/360˚(10)]
Which of these tables does NOT represent a function?
I'm a bit stuck, I need help
Let's consider all the trig identities, to help us with the problem:
⇒ (look at the attached image for help with that)
After looking at all the trig identity, let's look at the problem given to us:
⇒ cos(θ) = [tex]\frac{5}{13}[/tex]
⇒ we know that sec(θ) = 1 / cos(θ) = 1 / (5/13) = 13/5
Thus: sec(θ) = 13/5, which just so happens to be Choice (D)
Answer: sec(θ) = 13/5 or Choice (D)
Hope that helps!
Find the area of the kite
Answer:
180
Step-by-step explanation:
(10×11)+(10×7)=110+70
The area of the kite is expressed as 1/2 × (Product of its diagonals)
In this case, we have;
Diagonal₁ - 10 + 10 feet = 20 feetDiagonal₂ - 7 + 11 feet = 18 feetTherefore, when we substitute the diagonals in the formula, we get;
⇒ 1/2 × (Product of its diagonals)⇒ 1/2 × (20 × 18)When simplified, we get;
⇒ 1/2 × (20 × 18)⇒ 1/2 × (360)⇒ 360/2 = 180 ft²Therefore, the area of the kite is 180 ft².
Learn more about area of kites: https://brainly.com/question/12796559
I need help finding the value of x which is the base of a triangle.
Answer:
sqrt(13)
Step-by-step explanation:
The entire base is 4, so 1/2 of the base is 2
We can use the pythagorean theorem
a^2 = b^2 = c^2
2^2 + 3^2 = x^2
4+9 = x^2
13 = x^2
Taking the square root of each side
sqrt(13) = x
Check the picture below.
GIVE A GOOD DETAILED AND ORIGINAL ANSWER FOR BRAINLIEST
Question 3(Multiple Choice Worth 5 points)
(08.03 MC)
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length followed by inches in parentheses. There are markings from 11 to 14 on each line at intervals of one. For the top line there are 3 dots above the second mark, 4 dots above the third mark, and 3 dots above the fourth mark. For the bottom line there are 3 dots above the first mark, 5 dots above the second mark, and 2 dots above the third mark.
Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?
Group B, because three children in the group have the least forearm length of 11 inches
Group A, because three children in the group have the least forearm length of 11 inches
Group A, because seven children have a forearm length longer than 12 inches
Group B, because two children have a forearm length longer than 12 inches
Using the dot plot, the correct option regarding the group that appears to have the longer average forearm length is:
Group A, because seven children have a forearm length longer than 12 inches
What does a dot plot show?A dot plot shows the number of times each measure appears in the data-set.
In this problem, Group A has 3 students with forearm length of 14 inches, while group B have none. Group A also has more students with forearm length of 13 inches, and less of 11 and 12(lower values). Hence the correct option is given by:
Group A, because seven children have a forearm length longer than 12 inches.
More can be learned about dot plots at https://brainly.com/question/24912483
#SPJ1
PLSSS HELP IF YOU TURLY KNOW THISS
If 25% of the people in a small town are voters and there are 2360 voters, what is the population of the town?
Answer:
x=11800
Step-by-step explanation:
make a proportion:
2360/.2=X/1
2360(1)=.2x
x=11800
pls help me find all missing sides and angles. ;-;
Answer:
see explanation
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180° , then
∠ BAC + 51° + 90° = 180°
∠ BAC + 141° = 180° ( subtract 141° from both sides )
∠ BAC = 39°
using the tangent ratio in the right triangle
tan51° = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{12.8}[/tex] ( multiply both sides by 12.8 )
12.8 × tan51° = AC , then
AC ≈ 15.8 ( to 1 dec. place )
using the cosine ratio in the right triangle
cos51° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{12.8}{AB}[/tex] ( multiply both sides by AB )
AB × cos51° = 12.8 ( divide both sides by cos51° )
AB = [tex]\frac{12.8}{cos51}[/tex] ≈ 20.3 ( to 1 dec. place )
which is closer to 12? 11.96 or 12.0321
Answer:The answer is 12.0321
Step-by-step explanation:
Please belpppp don’t understand
Answer:
[tex]\huge 3w^2\sqrt[4]{2\:w^{3}}[/tex]
Step-by-step explanation:
[tex]\huge\sqrt[4]{162\:w^{11}}[/tex][tex]=\huge\sqrt[4]{81*2\:w^{8}*w^{3}}[/tex][tex]=\huge\sqrt[4]{3^4*2\:(w^{2})^4*w^{3}}[/tex][tex]=\huge 3w^2\sqrt[4]{2\:w^{3}}[/tex] (Elements with power 4 within the radical will come out and the rest will be within the radical sign)Helpppp meeeeee pleaseeeee
Answer:
C. 54 tens
Step-by-step explanation:
54×10=540
54tens=540
Answer:
54 tens
Step-by-step explanation:
This is like regular multiplication, sort of.
54 x 10= 540
540=54
giving brainliest help asap
Answer:
12,30
Step-by-step explanation:
Hence the numbers can either be (6,60) or (12,30), but as both the numbers are greater than 6 so the answer is (12,30)
(A-5)² + (B- 3)² = 18 B=A-2 A = ?, B = ?
Answer:
A = 8 and B = 6
Step-by-step explanation:
Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".
(A - 5)² + (B - 3)² = 18 -----> Original equation
(A - 5)² + ((A - 2) - 3)² = 18 -----> Plug in B = A - 2
(A - 5)² + (A - 5)² = 18 -----> Subtract
(A² - 10A + 25) + (A² - 10A + 25) = 18 -----> Expand parentheses
2A² - 20A + 50 = 18 ------> Add like terms
2A² - 20A + 32 = 0 -----> Subtract 18 from both sides
2(A² - 10A + 16) = 0 -----> Remove common factor
2(A - 2)(A - 8) = 0 -----> Factor within parentheses
A = 2 -----> Find A - 2 = 0
A = 8 -----> Find A - 8 = 0
Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.
When A = 2:
B = A - 2 -----> Original equation
B = 2 - 2 -----> Plug in A = 2
B = 0 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(2 - 5)² + (B - 3)² = 18 ------> Plug in A = 2
(-3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
When A = 8:
B = A - 2 -----> Original equation
B = 8 - 2 -----> Plug in A = 8
B = 6 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(8 - 5)² + (B - 3)² = 18 ------> Plug in A = 8
(3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.
Find the surface area of the cylinder. Use 3.14 for $\pi$ .
a can with a radius of 60 millimeters and a height of 160 millimeters
A can with a radius of 60 mm and a height of 160 mm. Then the surface area of the cylinder will be 1808640 mm³.
How do find the lateral surface area of a cylinder?The lateral surface area of a cylinder is also called the curved surface area of the cylinder.
Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
Then, the lateral surface area of that cylinder is:
SA = πr²h
A can with a radius of 60 mm and a height of 160 mm. Then the surface area of the cylinder will be
SA = π x (60)² x 160
SA = 3.14 x 3600 x 160
SA = 1808640 mm³
Learn more about the lateral surface area of a cylinder here:
https://brainly.com/question/11385509
#SPJ1
Which of the following is a radical equation?
Ox√3=13
O x+√3=13
O√x+3=13
O x+3=√13
Answer:
The answer would be: √x+3=13
Step-by-step explanation:
A radical equation is an equation with at least one variable put on a radical form. In this question, there is only one kind of variable which is x. Then, you need to find the equation where x is in the radical form. The radical form can be expressed with square root symbol.
The option with √x would be only √x+3=13
Shenika factored the polynomial completely. what is the value of a? 5x3 35x2 6x 42 (5x2 a)(x b) 1 5 6 7
Factorising the polynomial 5x³ + 35x² + 6x + 42, the value of A is 6.
Factorisation of polynomialFactorising a polynomial simply means to decompose the polynomial into a product of two or more polynomials.
Therefore, let's factorise 5x³ + 35x² + 6x + 42 and find the value of A
(5x² + A)(x + B)
Therefore,
5x³ + 35x² + 6x + 42
5x³ + 6x + 35x² + 42
x(5x² + 6) + 7(5x² + 6)
Therefore,
(5x² + 6)(x + 7)
Therefore, the value of A is 6
learn more on factorisation here; https://brainly.com/question/1415111
#SPJ4
Freida has 12 red apples and 15 green apples. She is going to share the apples equally among 8 people and keep any extra apples for herself. How many apples will Freida keep for herself?
Answer: 3 apples
Step-by-step explanation:
Given:
12 red apples
15 green apples
8 people
Freida
..............................................................................................................................................
12 + 15 = 27
Since she is going to give the apples equally among 8 people,
27 / 8 = 3 remainder 3
Each of the 8 people will get 3 apples each.
Freida will get the remaining 3 apples.
Write the quadratic equation in standard form:
5x^2+7+3x=-3x
Answer:
5x²+6x+7=0
Step-by-step explanation:
Yeah. I think it's the answer
Answer:
5x² + 6x + 7 = 0
Step-by-step explanation:
Standard form of quadratic equation :
Ax² + Bx + C = 0Solving :
5x² + 7 + 3x = -3x5x² + 7 + 3x + 3x = 05x² + 6x + 7 = 0Find the circumference and area of the circle to the nearest hundredth. Use 3.14 for π. Round to the nearest hundredth if necessary.
54 cm
The circumference of the circle is about
cm.
The area of the circle is about
cm2.
The circumference of the circle is about 339 cm.
The area of the circle is about 9, 156 cm∧ 2
NOTE :
The circumference of a circle is known to be the perimeter of the circle.
It is determined using ;
Circumference, C = 2 π r
The area of a circle is known to be the axis occupied by the circle in a two-dimensional plane.
It is determined using ;
Area, A = π r ∧2
How to determine the area and circumference of a circle
Parameters:
π = 3.14
radius, r =54 cm
Circumference, C = 2 π r = 2 × 3.14 × 54 = 339. 12 cm
Circumference , C in the nearest hundredth = 339 cm
Area, A = π r∧ 2 = 3. 14 × 54 × 54 = 9,156.24 cm∧ 2
Area, A in the nearest hundredth = 9,156 cm∧2
Thus, the circumference of the circle in the nearest hundredth is 339cm and the area of the circle in the nearest hundredth is 9, 156 cm∧2
A car with a cost price of $5200 is
sold at a profit of 15%. Calculate the
selling price
Answer:
We are given the initial price of a car and we are also told that the car sold for a 15% profit which means that the price that the car was sold for is 15% more than it's initial price. This is just a simple multiplication problem which we multiply the initial price by the total percentage plus 0.15
[tex]Sold\ Price = Initial\ Price *(Total\ Percentage+Profit\ Percentage)[/tex]
[tex]Sold\ Price = \$5200*(1+0.15)[/tex]
[tex]Sold\ Price = \$5200*(1.15)[/tex]
[tex]Sold\ Price = \$5980[/tex]
Therefore, our final answer is that the selling price was $5980
Hope this helps!
Find the length of the third side. If necessary, write in simplest radical form
Answer:
7.2
Step-by-step explanation:
(6)^2 + (4)^2
36 + 16
52
square root of 52 = 7.2
The majority of Americans spend most of their income on:
housing.
A.food.
B.health care.
C.entertainment.
A bakery produces eight different kinds of pastry, one of which is eclairs. Assume there are at least twenty five pastries of each kind. Suppose the bakery has only ten eclairs but has at least twenty five of each of the other kinds of pastry. Suppose in addition to having only ten eclairs, the bakery has only eight napoleon slices. How many different selections of twenty five pastries are there
There are 142506 different selections of twenty-five pastries
How to determine the number of different selections?The given parameters are:
Pastry, n = 6Pastries to select, r = 25The number of different selections is calculated using:
[tex]C(n + r - 1,r) = \frac{(n + r - 1)!}{r!(n - 1)!}[/tex]
The above formula is used because repetitions are allowed.
So, we have:
[tex]C(6 + 25 - 1,25) = \frac{(6 + 25 - 1)!}{25!(6 - 1)!}[/tex]
Evaluate the sum and difference
[tex]C(30,25) = \frac{30!}{25!5!}[/tex]
Evaluate the expression
C(30,25) = 142506
Hence, there are 142506 different selections of twenty-five pastries
Read more about combination at:
https://brainly.com/question/11732255
#SPJ4
please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answer:
6.5
Step-by-step explanation:
9.1^2-6.4^2 is 41.85
square root of that is 6.469...