The number of ways Dr. Orchid can arrange all 9 paintings is 362880 and the number of ways she can choose the paintings she wishes to display is 126.
What is combination?Combination is the way of arrangement or the collection of items in the particular order. The order of this group of items does not matter in the combination type of arrangement.
Dr. Orchid has 9 paintings she wants to hang side by side on her walls.
a)Number of ways she can arrange all 9 paintings-Total number of paintings is 9. She wants to arrange them side by side. Thus, the number of ways, she can arrange all 9 paintings is,
[tex]9!=9\times8\times7\times6\times5\times4\times3\times2\times1\\9!=362880[/tex]
b) Number of ways she can choose the paintings she wishes to display.She wants to display 4 of the paintings. The number of arrangement of 4 painting from 9 paintings is,
[tex]^9C_4=\dfrac{9!}{(9-4)!4!}\\^9C_4=\dfrac{9\times8\times7\times6\times5!}{5!\times4\times3\times2\times1}\\^9C_4=126[/tex]
Thus, the number of ways Dr. Orchid can arrange all 9 paintings is 362880 and the number of ways she can choose the paintings she wishes to display is 126.
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What lines are parallel?
A: y=3x-2 and y=1/3x-3
B: y=x and y=3
C: y=0 and y=3
Please explain the answer!!! Will give brainliest!!!
Answer:
C
Step-by-step explanation:
y=0 gives the straight horizontal line passing through (0,0)
y=3 also gives straight horizontal line passing through (0,3)
In order to find out which two lines are parallel, let's find the slope of each line first.
The slope of the line y=3x-2 is 3.
The slope of the line y=1/3x-3 is 1/3
The slope of the line y=x is 1
The slope of the line y=3 is 0
The slope of the line y=0 is 0
Now, if two lines have the same slope, they are parallel to each other.
So if a line's slope is 0, the line parallel to it has a slope of 0.
So the parallel lines here are ↓
y=0 and y=3
hope helpful ~
Determine the length of the missing side.
Answer:
5
Step-by-step explanation:
pythagorean triple is 5-12-14 or use pythagorean theorem
b=[tex]\sqrt{ 13^{2} -12^{2} }=\\\sqrt{169-144} =\\\sqrt{25} =5[/tex]
Answer: 5
Step-by-step explanation: The square root of 13²- 12²
P is a rectangle with length 40 cm and width x cm. Q is a rectangle with width y cm. P The length of Q is 25% more than the length of P. The area of Q is 10% less than the area of P. Work out the ratio x : y x cm Give your answer in its simplest form. 40 cm Q y cm
From rectangle P and Q, the ratio of x to y is 25/18
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
Area of P = 40 * x = 40x cm²
Area of Q = y * (1.25 * 40) = 50y cm²
Given that area of Q = 90% if P = 0.9(40x) = 36x cm²
50y cm² = 36x cm²
x/y = 50/36 = 25/18
From rectangle P and Q, the ratio of x to y is 25/18
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I’m confused please help!
Answer:
See below
Step-by-step explanation:
c will be tha same as the labelled angle = 99 degrees
then c + b = a straight line = 180
99 + b = 180
b = 81 degrees
Bob has 30 coins, which are all dimes and quarters. If the total amount of money he has
is $4.80, how many of each coin does he have?
Answer:
that means he will have 25.2
select the equivalent expression (3^3*6^6)^-3
Answer: Choice B and Choice D
Step-by-step explanation:
4^-2 * 7^-2= 16*49=784
Answer:
B & C
Step-by-step explanation:
[tex]4^-^2*7^-^2[/tex] is equal to [tex]\frac{1}{784}[/tex]
[tex]\frac{1}{28^2}[/tex] is also requal to [tex]\frac{1}{784}[/tex]
[tex]\frac{7^-^2}{4^2}[/tex] is also equal to [tex]\frac{1}{784}[/tex]
pls help with this maths question... feels like I'm missing something easy ;/
Answer:
10.34 cm.
Step-by-step explanation:
First we need to calculate the angle between the hour and minute hand
We see that there are 5 * 5-minute intervals between the 2 hands and the clock has 12 * 5-minute intervals, so:
This is 5/12 * 360 = 150 degrees,
So we apply the Cosine Rule to the triangle:
x^2 = 4.5^2 + 6.2^2 - 2*4.5*6.2cos150
= 107.014
x = √107.14 = 10.34.
Missing length is 10.3cm to 1.d.p
The clock is a circle divided into 12
360/12=30 degrees for each part
1) 7 to 8
2) 8 to 9
3) 9 to 10
4) 10 to 11
5) 11 to 12
5 parts
30 x 5 = 150 degrees
We've got an angle between 2 lengths - cosine rule comes to mind for me.
a = root 6.2^2 + 4.5^2 - 2x6.2 4.5 x cos 150
= 10.34476764
length is 10.3cm to 1.d.p
(the others are to 1.d.p too)
Hope this helps!
For which value of x is the equation 2(1+x)=x+3
Tisha and her scout troop are heading to the Swing Time zipline park. They plan to purchase
the group package. With the package, the cost per person is $5 less than the normal cost for
an individual. There are 12 scouts in Tisha's troop. Her troop leader called ahead and found
that the total cost for the group will be $150. What is the normal cost for an individual?
Answer:
$17.5
Step-by-step explanation:
divide 150 by 12 to get 12.5. 12.5 is what they paid per-person with the discount. add 5 to get 17.5 and that is the on-discounted price
The normal cost for an individual is $17.50.
Let's denote the normal cost for an individual as "N."
According to the given information, with the group package, the cost per person is $5 less than the normal cost for an individual. So, the cost for each scout in Tisha's troop is "N - $5."
There are 12 scouts in Tisha's troop, so the total cost for the group is given as $150.
We can set up an equation based on the total cost:
Total Cost = Cost per Person × Number of People
$150 = (N - $5) × 12
Now, let's solve for the normal cost for an individual (N):
$150 = 12N - $60
12N = $150 + $60
12N = $210
N = $210 / 12
N = $17.50
So, the normal cost for an individual is $17.50.
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Help and show work please I beg u!
The graph of a linear function is shown on the grid.
Which equation is best represented by this graph?
Answer:
C
Step-by-step explanation:
Because thats the answer
Which of the following functions has a rate of change that stays the same?
A:y = 4x+10
B:y=-4x+10
C:y = 3^x
D:y = x² + 2
Answer:
C:y = 3^x
Step-by-step explanation:
The answer is C because the rate of change is always -6.
helpppp will give brainlistdhd
Answer:
S18 = 288
Step-by-step explanation:
find the first and last term.
n = 1
a1 = 2 x 1 - 3
a18 = 2 x 18 - 3
(simplify the expression)
a1 = -1
a18 = 33
(use the formula for the sum of a finite arithmetic series)
a1 + a18
S18 = 18 x ---------------------
2
(use the substitute) substitute -1 for a1 and 33 for a18
-1 + 33
S18 = 18 x ---------------------
2
simplify the expression and ur done hope this helped x
ps. wheres my head :)
Which factored form is equivalent to the expression x^2 + 5x + 4? A) (x + 2)(x + 3) B) (x + 4)(x + 1) C) (x + 5)(x − 1) D) (x − 4)(x + 1)
option B.
Calculations ↓
First, let's think of two numbers so that :
if we multiply these numbers, we'll get 4if we add these numbers, we'll get 5These numbers are :
4 and 1
Plug these numbers here :
(x+4) (x+1)
So the correct factored form of this expression is
Option B) (x+4)(x+1)
[tex]\footnotesize\text{hope\:helpful~}}[/tex]
A vending machine that takes only dimes and
quarters contains 30 coins, with a total value of
$4.20. How many of each coin are there?
a. Subtraction Property of Equality
b. Addition Property of Equality
c. Division Property of Equality
d. Multiplication Property of Equality
Answer:
The correct answer would be option A; Subtraction Property of Equality
Step-by-step explanation:
This is because you are subtracting 3 on both sides of the equation to go from;
x + 3 = 17
to
x = 14
Hope this helps!
Calculate the area of a square with side length 12 cm
Answer:
144 cm^2
Step-by-step explanation:
A square has equal sides, and so if one side is 12 cm, so are the rest.
So 12 * 12 = 144.
Answer:
c
Step-by-step explanation:
Lisa used 6 2/3 feet of rope to make a jump rope. She also used 4 1/5 feet of rope to make a leash for her dog. Which expression could be used to determine the amount of rope, in feet, that lisa used? (A) 10+2 /15 (B) 10+3/8 (C) 6+4+10/15+3/15 (D) 6+4+3/15+3/15
Answer:
(C) 6+4+10/15+3/15
Step-by-step explanation:
2/3=10/15
1/5=3/15
6+4+13/15
10 13/15
find area of the shaded portion of the figure
Answer:
[tex]\sf C) \quad 57 \frac34 \:cm^2[/tex]
Step-by-step explanation:
To find the shaded area, subtract the area of the semicircle from the area of the rectangle.
Formulae
[tex]\textsf{Area of a rectangle}=\textsf{width} \times \textsf{length}[/tex]
[tex]\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Diameter of a circle}=2r \quad \textsf{(where r is the radius)}[/tex]
Area of rectangle
Given dimensions of the rectangle:
width = 7 cmlength = 11 cmSubstituting these values into the formula:
[tex]\implies \textsf{Area}=\textsf{7} \times \textsf{11}=77\: \sf cm^2[/tex]
Area of semicircle
Diameter of semicircle = 11 - 2 - 2 = 7 cm
⇒ Radius (r) = 7 ÷ 2 = 3.5 cm
[tex]\textsf{let}\: \pi=\dfrac{22}{7}[/tex]
[tex]\implies \textsf{Area}=\dfrac12 \left(\dfrac{22}{7}\right) (3.5)^2=19.25\: \sf cm^2[/tex]
Area of shaded region
= area of rectangle - area of semicircle
= 77 - 19.25
= 57.75
[tex]\sf =57 \frac34 \:cm^2[/tex]
You are one of 22 people whose name will be drawn for a prize. What is the probability that your name will be drawn first? Express your answer as a fraction.
Answer:
1/22
Step-by-step explanation:
Its 1/22 because that is the total probability of your name being drawn for the prize
A gold, a silver, and a bronze medal are awarded in an Olympic event. In how many possible ways can the medals be awarded for a 200-meter sprint in which there are 8 runners
Answer:
1320 ways
Step-by-step explanation:
an olympic event getting a gold medal is not equal to getting a silver or a bronze medal. Hence, we will use the concept of permutation for this problem as order matters here. Hence, there are 1320 ways in which 8 runners can get these 3 medals
Every day when Brandon arrives at work he must decide to either take the stairs or use the elevator to get to his office on the third floor. What type of decision is this
Answer:
would you rather, i think
Is 2.67034165508… rational or unrational?
Answer:
Unrational
Step-by-step explanation:
Step 1: Determine what is rational and unrational
"A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction, so any number that does not fit the definition of a rational number."
Step 2: Now determine what our number fits into
Since our decimal isn't a whole number, isn't a fraction, and it is a decimal that continues to either repeat or just continues. Therefore, our number would fit into the unrational category. If our number is just 2.67034165508 then it would be a rational number since it ends. However, since we have the ... at the end that means that it continues and therefore falls into the unrational category.
Answer: Unrational
The function h(x) is given in the table above.
Which of the following choices shows the
average rate of change of the function over the
interval 2 ≤ x ≤ 6?
A. 6/4
B. -3/2
C.-7/6
D. -1
Rate of change
h(6)-h(2)/6-23-9/6-2-6/4-3/2Option B
Brady dilates an oblique prism by a scale factor of 2/3. Determine the scale factors for perimeter, area, and Volume. (Answer as a fraction)
Using proportions, it is found that:
The scale factor for the perimeter is of [tex]\frac{2}{3}[/tex].The scale factor for the area is of [tex]\frac{4}{9}[/tex].The scale factor for the volume is of [tex]\frac{8}{27}[/tex].What is a proportion?A proportion is a fraction of a total amount.
For the perimeter, as it is given in units, the scale factor is the same, hence it is of [tex]\frac{2}{3}[/tex].
For the area, as it is given in units squared, the scale factor is squared, hence:
[tex]\left(\frac{2}{3}\right)^2 = \frac{4}{9}[/tex]
For the volume, as it is given in cubic units, the scale factor is eleveted to the third power, hence:
[tex]\left(\frac{2}{3}\right)^3 = \frac{8}{27}[/tex]
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answer this super simple word problem for so many points
Answer:
60kph
Step-by-step explanation:
Distance = Rate X Time
640 = r x 4+ (r+5) x 7
640 = 4r + 7r + 35
640=11r + 35
640 - 35 = 11r
605 = 11r
r = 605 / 11
r= 55 kph
r=55 =5 =60 kph is the speed of the train
To see if the answer is right: 55 x 4 + 60 x 7 = 220 + 420 = 640 km
Whats 38240 divided by 4
Answer:
9560
Step-by-step explanation:
Use a calculator or do long division.
You can also divide by 2 twice.
38240/2 = 19120
19120/2 = 9560
Answer: 9560
Answer:
9560
Step-by-step explanation:
30000÷4=7500
8000÷4=2000
200÷4=50
40÷4=10
0÷4=0
7,500+2,000+50+10+0=9,500+60=9,560
which fraction is equivlent to 8/10
Answer:
4/5 or 16/20
Step-by-step explanation:
did my best with the info provided
Answer:
4/5
Step-by-step explanation:
8/10 = 80% 1. / the fraction by 2
4/5 = 80%
The endpoints of a
diameter of a circle are (2,
4) and (-4, 7). What is the
standard form of the
equation
of this circle?
I know one of the answer is not c
Hurry i got like 30 mins left and a girl is tired
Answer:
2nd option
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
the centre is at the midpoint of the endpoints of the diameter.
The coordinates of the centre is the average of the coordinates of the endpoints.
centre = ( [tex]\frac{-4+2}{2}[/tex], [tex]\frac{7-1}{2}[/tex] ) = ([tex]\frac{-2}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = (- 1, 3 )
the radius is the distance from the centre to either of the endpoints
using the distance formula to calculate r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]
with (x₁, y₁ ) = (- 1, 3 ) and (x₂, y₂ ) = (2, - 1 )
r = [tex]\sqrt{(2-(-1))^2+(-1-3)^2}[/tex]
= [tex]\sqrt{(2+1)^2+(-4)^2}[/tex]
= [tex]\sqrt{3^2+16}[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
then equation of circle is
(x - (- 1) )² + (y - 3)² = 5² , that is
(x + 1)² + (y - 3)² = 25
In 2010, Cameron invested $10,000 in an account that earns 8. 5% interest compounded monthly. How much money would Cameron have gained by 2025?
Answer:
Step-by-step explanation:
First, we need to calculate how many years will earn percent.
2010---->2025= 15 years elapsed. Now we have our time, we need to plug it in our compound interest formula=
Principal(rate+1)^time or A=P(1+R)^t
10,000(0.085+1)^15
=$33,997.43
To calculate how much Cam earned, you need to subtract from original amount.
=$33,997.43-10,000=
---->$23997.43
Please mark me brainiest :)