Answer:
The number of ways she can choose four albums for display with at least two from Diana Kroll is from the sixteen albums is 665 ways
Step-by-step explanation:
1) The number of ways she can choose 2 albums of Diana from the 5 Diana Kroll albums is 5!/(2!(5 - 2)!) = 10 ways
Choosing the other 2 albums from the remaining 11 albums gives;
11!/(2!(11 - 2)!) = 55 ways
Total number of ways is then 10 × 55 = 550 ways
Choosing 3 from the 5 Diana Kroll albums is 5!/(3!(5 - 3)!) = 10 ways
Choosing the other 1 album from the remaining 11 albums gives;
11!/(1!(11 - 1)!) = 11 ways
Total number of ways is then 10 × 11 = 110 ways
Choosing 4 from the 5 Diana Kroll albums is 5!/(4!(5 - 4)!) = 5 ways
Choosing the other 0 album from the remaining 11 albums gives;
11!/(0!(11 - 0)!) = 1 way
Total number of ways is then 5 × 1 = 5 ways
Total number of ways = 550 + 110 + 5 = 665 ways
2) In the indirect method, we first find the number of ways to choose 4 albums out of the 16 albums, then we subtract the number of cases where there are 1 and 0 Diana Kroll albums as follows;
16!/(4!(16 - 4)!) = 1820 ways
With 1 Diana Kroll album gives
5!/(1!(5 - 1)!)×11!(3!(11 - 3)!) = 825 ways
With 0 Diana Kroll album gives
5!/(0!(5 - 0)!)×11!(4!(11 - 4)!) = 330 ways
Total number of ways with at least 2 Diana Kroll albums = 1820 - 825 - 330
Total number of ways with at least 2 Diana Kroll albums = 665 ways.
is 1.25 the same as 25%?
Answer:
No
Step-by-step explanation:
1.25 as a percentage is 125%.
25% as a decimal is 0.25.
What is the height of the prsim if there is 3 meters,2 meters, and the volume is 36 cublic meters
Answer: The height is 6 meters
Step-by-step explanation:
3 * 2 *h = 36 where h is the height
6h = 36
h = 6
Answer:
The answer is 6
Step-by-step explanation:
Because you would have to get 6h=36 alone so you would have to divide 6 by both sides. which gives you h=6
Dawn is going scuba diving. Which situation would be modeled by a positive number?
Answer:
on the dive boat deck
Step-by-step explanation:
Answer:
the above is right
Step-by-step explanation:
Which of the following represents a rotation of triangle XYZ, which has vertices (-4,7), Y(6,2), and Z (3,-8) about the origin by 90 degrees? HELP PLS options: A: X (-7,-4) Y(6,-2) Z(-8,3) B: X(7,-4) Y(-2,6) Z (3,-8) C: X (-7,-4) Y(-2,6) Z (8,3) D: X(7,-4) Y (-2,6) Z (-3,8)
Answer:
The best option is B: X' = (-7,-4), Y' = (-2,6), Z'=(8, 3).
Step-by-step explanation:
Each vertex can be represented as a vector with regard to origin.
[tex]\vec X = -4\cdot i + 7\cdot j[/tex], [tex]\vec Y = 6\cdot i + 2\cdot j[/tex] and [tex]\vec Z = 3\cdot i -8\cdot j[/tex].
The magnitudes and directions of each vector are, respectively:
X:
[tex]\|\vec X\| = \sqrt{(-4)^{2}+7^{2}}[/tex]
[tex]\|\vec X\| \approx 8.063[/tex]
[tex]\theta_{X} = \tan^{-1}\left(\frac{7}{-4} \right)[/tex]
[tex]\theta_{X} \approx 119.744^{\circ}[/tex]
Y:
[tex]\|\vec Y\| = \sqrt{6^{2}+2^{2}}[/tex]
[tex]\|\vec Y\| \approx 6.325[/tex]
[tex]\theta_{Y} = \tan^{-1}\left(\frac{2}{6} \right)[/tex]
[tex]\theta_{Y} \approx 18.435^{\circ}[/tex]
Z:
[tex]\|\vec Z\| = \sqrt{3^{2}+(-8)^{2}}[/tex]
[tex]\|\vec Z\| \approx 8.544[/tex]
[tex]\theta_{Z} = \tan^{-1}\left(\frac{-8}{3} \right)[/tex]
[tex]\theta_{Z} \approx 290.556^{\circ}[/tex]
Now, the rotation consist is changing the direction of each vector in [tex]\pm 90^{\circ}[/tex], which means the existence of two solutions. That is:
[tex]\vec p = r \cdot [\cos (\theta \pm 90^{\circ})\cdot i + \sin (\theta \pm 90^{\circ})\cdot j][/tex]
Where [tex]r[/tex] and [tex]\theta[/tex] are the magnitude and the original angle of the vector.
Solution I ([tex]+90^{\circ}[/tex])
[tex]\vec p_{X} = 8.063\cdot [\cos (119.744^{\circ}+90^{\circ})\cdot i + \sin (119.744^{\circ}+90^{\circ})\cdot j][/tex]
[tex]\vec p_{X} = -7\cdot i -4\cdot j[/tex]
[tex]\vec p_{Y} = 6.325\cdot [\cos(18.435^{\circ}+90^{\circ})\cdot i+\sin(18.435^{\circ}+90^{\circ})\cdot j][/tex]
[tex]\vec p_{Y} = -2\cdot i +6\cdot j[/tex]
[tex]\vec p_{Z} = 8.544\cdot [\cos(290^{\circ}+90^{\circ})\cdot i +\sin(290^{\circ}+90^{\circ})\cdot j][/tex]
[tex]\vec p_{Z} = 8.029\cdot i +2.922\cdot j[/tex]
Solution II ([tex]-90^{\circ}[/tex])
[tex]\vec p_{X} = 8.063\cdot [\cos (119.744^{\circ}-90^{\circ})\cdot i + \sin (119.744^{\circ}-90^{\circ})\cdot j][/tex]
[tex]\vec p_{X} = 7\cdot i +4\cdot j[/tex]
[tex]\vec p_{Y} = 6.325\cdot [\cos(18.435^{\circ}-90^{\circ})\cdot i+\sin(18.435^{\circ}-90^{\circ})\cdot j][/tex]
[tex]\vec p_{Y} = 2\cdot i -6\cdot j[/tex]
[tex]\vec p_{Z} = 8.544\cdot [\cos(290^{\circ}-90^{\circ})\cdot i +\sin(290^{\circ}-90^{\circ})\cdot j][/tex]
[tex]\vec p_{Z} = -8.029\cdot i -2.922\cdot j[/tex]
The rotated vertices are: i) X' = (-7,-4), Y' = (-2,6), Z'=(8.029, 2.922) or ii) X' = (7,4), Y' = (2,-6), Z' = (-8.029, -2.922). The best option is B: X' = (-7,-4), Y' = (-2,6), Z'=(8, 3).
find the values of a and b such that x^2+2x+2=(x-a)^2+b
Answer:
a = -1
b = 1
Step-by-step explanation:
Step 1: Isolate x's
x² + 2x = -2
Step 2: Complete the Square
x² + 2x + 1 = -2 + 1
(x + 1)² = -1
Step 3: Move everything to 1 side
(x + 1)² + 1 = 0
And we have our answer.
Answer:
A=1 and b=1
Step-by-step explanation:
arcs and circles formula? can someone help me find the answer?
Answer:
9.2 cmHere,
The length of an arc of a sector with theta nag radius'r' is:
[tex] \frac{theta}{360} 2\pi \: r[/tex]
CD=?
Radius=7.9 cm
theta=66.4
Length of CD
[tex] \frac{66.4}{360} \times 2 \times \pi \times 7.9 \\ = \frac{66.4}{360} \times 2 \times 3.14 \times 7.9 \\ = 9.1506 \\ = 9.2 \: cm[/tex]
Hope this helps...
Good luck on your assignment..
Is this function linear or nonlinear y=1/2x^{2}
will give brainliest
Answer:
nonlinear
Step-by-step explanation:
The word 'linear' means something having to do with a line. On a Cartesian Plane, a linear characteristic is a feature wherein the graph is a straight line. The line can cross in any direction, but it's always an instant line. A non-linear function has a shape that isn't an immediate line
The graph is nonlinear because it is not a straight line.
please mark me brainliest!
Answer:
Nonlinear.
Step-by-step explanation:
Since x is being squared, the equation is actually a parabola. The power of x has to be 1 for the function to be a linear function, so this equation is nonlinear.
Hope this helps!
the area of a rectangular sandbox can be expressed as 72xy + 18x the width of the sandbox is 9x what is the perimeter of the sandbox
Answer:
18x +16y +4
Step-by-step explanation:
The area is the product of length and width, so the length is ...
A = LW
L = A/W = (72xy +18x)/(9x) = 8y +2
The perimeter is double the sum of length and width:
P = 2(L +W) = 2(8y +2 +9x)
P = 18x +16y +4 . . . . the perimeter of the sandbox
HURRY I NEED HELP PLEASE IM STUCK! :(
Answer:
0.6 then calculate which expression is equal to that
Step-by-step explanation:
arccos = cos^-1
Put that in calculator
Work out the length of AB. Give your answer to 3 significant figures
Answer:
D = 9.80
Step-by-step explanation:
To find AB, we'll use the distance formula:
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
D = [tex]\sqrt{(10-1)^2+(3-7)^2}[/tex]
D = [tex]\sqrt{(9)^2+(-4)^2}[/tex]
D = [tex]\sqrt{81+16}[/tex]
D = [tex]\sqrt{96}[/tex]
D = 9.80 (Upto 3 sfs)
A function is a relation where each input value is assigned to
Which statement is true regarding the graphed functions?
A. f(4) = g(4)
B. f(4) = g(-2)
C. f(2) = g(-2)
D. f(-2) = g(-2)
Answer:c. F(2)=g(-2)
Step-by-step explanation:
A line is defined by the equation 2x + 4y = -8. Determine the equation of
another line that will creare a linear system with
(a) no solution
(b) many solucions
(c) one solution
Answer:
so turn it into the other form:
2x+4y=-8
4y=-2x-8
y=-0.5-2
then:
a) y=-0.5x+44
b) y=-0.5x-2 (itself)
c) y=-55x-2 (they cut each other in (0,-2)
Work out x. Give reasons for your answer.
Answer:
The measurement for x is 80°
Step-by-step explanation:
In the picture, we see two parallel lines cut by a transversal line. Since the lines are cut by a transversal, then there are a few things we should know that can help us find the value of x.
Corresponding angles are congruent. Angles that are right beside each other (such as ∠CBD and ∠CBA) are a linear pair. This means that they have a total measurement of 180° when added together.Now that we know these things, we can use this information to find the measurement of ∠CBA. We do this by subtracting 100 from 180 because ∠CBA and ∠CBD are a linear pair. Once we know the measurement of this angle, then it will be much easier to find the value of x.
180 - 100 = 80
So, the measurement of ∠CBA is 80°. Now, ∠CBA and ∠x are corresponding angles so this means that they have the same measurements. If the measurement of ∠CBA is 80°, then the measurement of ∠x is also 80°
x = 80°
here is a sequence of numbers: 64,49,36,25,16. What is the name given to these numbers
Answer:
These are squares of numbers 8 to 4.
Step-by-step explanation:
The given sequence of numbers is given as:
64, 49, 36, 25, 16
First of all let us factorize each number:
[tex]64 = 8 \times 8\\49 = 7 \times 7\\36 = 6 \times 6\\25 = 5\times 5\\16 = 4\times 4\\[/tex]
We can see that every number is obtained by multiplying some other number by itself.
For example, 64 is obtained by multiplying 8 with itself i.e. 8 multiplied with 8.
49 is obtained by multiplying 7 with itself i.e. 7 multiplied with 7.
and so on.
So, each number is a square of some number.
The numbers are in decreasing order. (64 to 16)
i.e. we have square of numbers here.
Square of 8, square of 7, square of 6, square of 5, square of 4,
Generalizing the terms:
[tex]a_n = (9-n)^2[/tex] where n is from 1 to 5
The name given to the sequence is:
Square of (9-n) where n is from 1 to 5.
OR
square of numbers, numbers from 8 to 4 in decreasing order.
2. in a geometric progression
the first term is 64 and the
fourth term is 27. Calculate
(a) the common ratio
Answer:
0.75 or 3/4
Step-by-step explanation:
If we call the common ratio r, since 4 - 1 = 3 we can write:
64 * r³ = 27
r³ = 27/64
r = ∛(27/64) = ∛27 / ∛64 = 3 / 4
Answer:
(a) the common ratio = 3/4.
Step-by-step explanation:
First term a1 = 64
The fourth term a4 = a1 r^3 = 27
So a1 r^3 / a1 = 27/64
r^3 = (27/64)
r = ∛ (27/64
= 3/4.
The world record for the largest collection of bookmarks is 71 235 bookmarks. Find the closest benchmark for each: a) in thousands _______________ b) in hundreds _______________ c) in tens _______________
Answer:
A: 71,235,000
B: 71,235,00
C: 71,240
Step-by-step explanation: Round by thousands, hundreds and tens.
Point Z is equidistant from the sides of ΔRST. Point Z is equidistant from the sides of triangle R S T. Lines are drawn from the point of the triangle to point Z. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. Which must be true? Line segment S Z is-congruent-to line segment T Z Line segment R Z is-congruent-to line segment B Z AngleCTZ Is-congruent-to AngleASZ AngleASZ Is-congruent-to AngleZSB
Answer:
AngleASZ Is-congruent-to AngleZSB
Step-by-step explanation:
The incenter of a triangle is a point inside a triangle that is equidistant from all the sides of a triangle. The incenter is the point formed by the intersection of all the three angles of the triangle bisected. The lines drawn from the incenter to the sides of the triangle forming right angles to the sides are congruent.
If Point Z is equidistant from the sides of ΔRST, point Z is the incenter of triangle RST. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. This lines are therefore congruent to each other, i.e. ZA = ZB = ZC.. Since the angles of the sides of the triangles are bisected to form the incenter, therefore:
AngleASZ Is-congruent-to AngleZSB
Answer:
AngleASZ Is-congruent-to AngleZSB
Step-by-step explanation:
D is the correct answer
6. Trail Bike Rentals charges a $16 fixed fee plus $8 per hour for renting a bike. Matt paid $72
to rent a bike. How many hours did Matt use the bike? Write an equation to represent this
scenario and solve for the variable. (2 marks)
Answer:
[tex]C =8t+16\\7\ hours[/tex]
Step-by-step explanation:
Given that, Fixed charge = $16
Per hour charge for renting the bike = $8/hour
To find:
If Matt paid $72 to rent a bike, for how many hours did he rent the bike?
Solution:
Let 't' be the time for which Matt rents the bike.
1 hour charge for the bike rent = $8
't' hour charge for the bike rent = $8 [tex]\times t[/tex]
Total Charge for the bike = Charge for renting the bike for t hours + fixed charge
Let 'C' be the total charge, so the equation becomes:
[tex]C = 8t + 16[/tex]
Given that C is $72, we need to find t:
[tex]72 = 8t+16\\\Rightarrow 8t=72-16\\\Rightarrow 8t=56\\\Rightarrow t = 7\ hours[/tex]
So, he rented the bike for 7 hours.
The equation is: [tex]C = 8t + 16[/tex]
ILL MARK YOU BRAINLIEST :))))) if you apply the changes below to the linear parent function, f(x)=|x|, what is the equation of the new function Shift 4 units left Shift 2 units up
Answer:
f(x) = |x + 4| + 2.
Step-by-step explanation:
When you shift the function to the left, the x-value changes, so you put the change within the absolute value. Also, within the absolute value, when you shift things to the right, you minus, and when you shift to the left, you add.
When you shift the function up, the y-value changes, so you put the changes outside of the absolute value. Shifting up means adding and shifting down means subtracting.
Hope this helps!
Hello! Someone please help ASAP
Answer:
A.
Step-by-step explanation:
Since g(x) is the graph of f(x) but vertically stretched, the only viable option is g(x) = 2x² because the rest of the equations are vertically shrunk.
Meggy was solving the following equation: 3x + 5 = 64 She concluded that the value of x is [tex]x=19.6666...[/tex] Is she correct?
Answer:
Yes, she is correct.
Step-by-step explanation:
[tex]3x+5=64\\\\3x+5-5=64-5\\\\3x=59\\\\\frac{3x}{3}=\frac{59}{3}\\\\ \frac{59}{3}=19\frac{2}{3}\\\\19\frac{2}{3}=19.666...\\\\ \text{Therefore}:\\x=\boxed{19.666...}[/tex]
The digit of 6 is repeating.
A tank is 4 feet long, 6 feet wide and 10 feet
tall. How much water can that tank hold?
Answer:
Volume = 240 feet³
Step-by-step explanation:
We'll find it's volume
Volume = [tex]Lenth *Width*Height[/tex]
Where Length = 4, Width = 6, Height = 10
Volume = 4 * 6 * 10
Volume = 240 feet³
What is the answer to question
Answer:
A
Step-by-step explanation:
I literally don't know how to explain this
The graph of a line passes through the two points (-2, 1) and (2, 1). What is the equation of the line written in general
form?
Oy - 1= 0
Ox-y+1 = 0
OX+ y - 1= 0
Answer:
y - 1 = 0.
Step-by-step explanation:
First off, we need to find the slope between the two points. That would be (1 - 1) / (2 - -2) = 0 / 4 = 0.
So, we would have an equation y = mx + b, where m is the slope and b is the y-intercept. Since the slope is 0, we have y = 0x + b, or y = b.
If you examine the coordinates, y always equals 1. So, b = 1, and y = 1.
y = 1
y - 1 = 0.
Hope this helps!
In a game the average score was 60 time score was 5/2 of the average what was Tim’s score?
Answer:
in my own reasoning not sure if I am correct
Step-by-step explanation:
first it said Tim score was 5/2 of the of the average score
and the average score is 60
so that will be 5/2 × 60 which is
= 150
If weight is an explanatory variable and cost is the corresponding response variable which of these would be represented by the y-axis on a scatterplot A. Weight B. Neither weight nor cost C. Both weight and cost D. Cost
Answer:
D. Cost
Step-by-step explanation:
In a scatter diagram we have that the x axis corresponds to the explanatory variable or also called the independent variable, since it is the value that is entered in the equation and does not depend on another.
While the y-axis corresponds to the response variable or also called the dependent variable since it is the value of the result of the equation
In this case, the explanatory variable is weight, that is, on the x-axis the weight would go and the cost is the response variable and would go on the y-axis, therefore, the answer is D. Cost
Annie and Xenas each arrive at a party at a random time between 2:00 and 4:00. Each stays for 45 minutes and then leaves. What is the probability that Annie and Xenas see each other at the party?
Answer:
P(meet) = 55/64
P(meet) = 0.8594
P(meet) = 85.94%
Therefore, there is a 85.94% probability that Annie and Xenas see each other at the party.
Step-by-step explanation:
Let A denote Annie and X denotes Xenas.
The total time is 2 hours (2:00 to 4:00)
Both A and X stays for 45 minutes or 3/4 hours
The probability that A and X do not meet is given by
P(Not meet) = (3/4)/2 × (3/4)/2
P(Not meet) = 9/64
So the probability that A and X will meet is given by
P(meet) = 1 - P(Not meet)
P(meet) = 1 - 9/64
P(meet) = 55/64
P(meet) = 0.8594
P(meet) = 85.94%
Therefore, there is a 85.94% probability that Annie and Xenas see each other at the party.
The partial receipt below shows the money, in dollars, Ryan spent at an online clothing retailer.
PRODUCT
QTY
PRICE
TOTAL
Socks
3
2.00
6.00
V-Neck
2
8.00
16.00
Shorts
1
15.00
15.00
What does 8.00 mean in this situation?
Choose 1 answer:
Ryan bought 8.00 V-Necks,
The price of each V-Neck Ryan bought was 8.00 dollars.
Answer:
Option (B)
Step-by-step explanation:
Picture attached shows a table having 4 columns,
Column 1). Name of products
Column 2). Quantity of each item
Column 3). Unit price of each item.
Column 4). Total value of each item.
8.00 lies in the column (3) which represents the price of each V-neck Ryan bought.
Therefore, Option (B) will be the answer.
Answer:
B
Step-by-step explanation:
had this question also
complete both I will give brainliest question if answer correct
Answer:
1. 5 3/4 - 2 1/4 = 3 1/12 2. 7 2/3 + 2 1/5 = 9 13/15
Step-by-step explanation:
1. 5 3/4 - 2 1/4
subtract the numbers on the side 5-2=3
subtract the fraction 3/4-1/4=2/4
reduce 2/4=1/2
add them together 3+1/2=3 1/2
2. 7 2/3 + 2 1/5
subtract the numbers on the side 7+2=9
find LCD of 2/3 and 1/5=
10/15+3/15=13/15
add them together 9+13/15=9 13/15
Answer: [tex]a)\ 3\dfrac{1}{2}[/tex]
[tex]b)\ 9\dfrac{13}{15}[/tex]
Step-by-step explanation:
a)
[tex].\quad 5\dfrac{3}{4}\\-\\.\quad\underline{ 2\dfrac{1}{4}}\\\\.\quad 3\dfrac{2}{4}\div\dfrac{2}{2}\quad =\quad \large\boxed{3\dfrac{1}{2}}[/tex]
b)
[tex].\quad 7\dfrac{2}{3}\times \dfrac{5}{5}=7\dfrac{10}{15}\\+\\.\quad 2\dfrac{1}{5}\times \dfrac{3}{3}=\underline{2\dfrac{3}{15}}\\\\.\qquad \qquad \quad \ \large\boxed{9\dfrac{13}{15}}[/tex]