The question is an illustration of permutation and combinations.
The number of ways she can choose 4 out of the 7 paintings is 35The number of ways she can arrange 4 out of the 7 paintings is 840The given parameters are:
[tex]\mathbf{n = 7}[/tex]
[tex]\mathbf{r = 4}[/tex]
(a) Choose 4 of 7 paintings
Choosing 4 of 7 paintings implies combination.
So, we have:
[tex]\mathbf{^nC_r = \frac{n!}{(n - r)!r!}}[/tex]
Substitute values for n and r
[tex]\mathbf{^7C_4 = \frac{7!}{(7 - 4)!4!}}[/tex]
[tex]\mathbf{^7C_4 = \frac{7!}{3!4!}}[/tex]
Expand
[tex]\mathbf{^7C_4 = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4 !}}[/tex]
[tex]\mathbf{^7C_4 = 35}[/tex]
Hence, the number of ways she can choose 4 out of the 7 paintings is 35
(b) Arrange 4 of 7 paintings
Arranging 4 of 7 paintings implies permutation.
So, we have:
[tex]\mathbf{^nP_r = \frac{n!}{(n - r)!}}[/tex]
Substitute values for n and r
[tex]\mathbf{^7P_4 = \frac{7!}{(7 - 4)!}}[/tex]
[tex]\mathbf{^7P_4 = \frac{7!}{3!}}[/tex]
Expand
[tex]\mathbf{^7P_4 = \frac{7 \times 6 \times 5 \times 4 \times 3!}{3!}}[/tex]
[tex]\mathbf{^7P_4 = 840}[/tex]
Hence, the number of ways she can arrange 4 out of the 7 paintings is 840
Read more about permutation and combinations at:
https://brainly.com/question/15301090
[tex]\sf x-5=16[/tex]
Answer:
x=21
Step-by-step explanation:
[tex]x-5=16[/tex]
[tex]x-5+5=16+5[/tex] (Add 5 to bth sides)
[tex]x=21[/tex]
Use synthetic division to find the result when 4x^3+3x^2– 8x – 7 is divided by x+1.
Winter fills 2/5 of a water bottle in 1/4
of a minute. How many bottles can
Winter fill in 1 minute?
Answer:
1.6 (decimal), 1 6/10 (proper), and 8/5 (improper)
Step-by-step explanation:
If it’s 2/5 in 1/4 and to get one while you need four 1/4 you need to multiply to get how much it can fill in that 4/4. To do this multiply 2/5 by 4 which is 1.6 (decimal) and 1 6/10 fractional. Or if you want it improper, 8/5
write the equation
it passes through (0,-2) and is perpendicular to the graph of y=5x+7
Step-by-step explanation:
the line passes through (0,-2) and perpendicular to the graph of y=5x+7.
solution :
the slope = -1/5
the equation :
y+2 = -1/5 (x-0)
y = -1/5x - 2
Identify the parallel lines.
Answer:
lines m and n
Step-by-step explanation:
Uhh parallel lines are basically lines that have the same slope.
There are only three lines, lines m, n, and t
It can't be t because it's traversing lines m and n
so it has to be lines m and n
Hope that helps, let me know if you have any further questions
ISOSCELES
EQUILATERAL
SCALENE
Answer:
scalene because all the angles are different in an isosceles triangle 2 angles are the same
Answer:
Scalene triangle
Step-by-step explanation:
the answer is the scalene triangle
Find the area and perimeter of
the parallelogram:
17ft
12ft
15ft
Answer:
Hi there!
Here is your answer...
The Area of the Parallelogram is:
[tex]204ft^{2}[/tex]The Perimeter of the Parallelogram is:
[tex]64ft[/tex]
Step-by-step explanation:
To find the Area of a Parallelogram you must first identify the Base and Height. In this instance the Base would be the top and bottom which we know are 17ft in length. The Height would be the dotted line that we know it 12ft tall. The next step would be to Multiply the Base by the Height. That would give us 204. After we add the correct units we have [tex]204ft^{2}[/tex].
To find the Perimeter we would simply add together all side lengths. We know that the top and bottom are equal to 17ft and the left and right are equal to 15 feet. This gives us 17+17+15+15. Which would equal 64, add the units and it becomes [tex]64ft[/tex].
Area=base x height
Perimeter = base + base + angle +angle
(angle is the side length.)
guys pls help me!!!!!!
Answer:
x= 55
y=125
Step-by-step explanation:
y = 180 - 55
hope it's correct
need a well explained ans ...
● no spams needed
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Question : 1Cost price of the T.V. is :
[tex]₹ \: 15000[/tex]Question : 2The scooter cost him :
[tex]₹ \: 21000[/tex]The solution is in attachment ~
Which point is the vertex?
C
B
A
None of the above
A bank fee increased by 200% from $7.20. What is the charge for the new bank fee
Hello!
Answer:
21.6
Steps:
7.20 increase 200% =
7.20 × (1 + 200%) = 7.20 × (1 + 2) = 21.6
Which equation represents a line which is parallel to the y-axis?
Answer:
x= 3
Step-by-step explanation:
I hope this helps but if there are options lmk
Answer:x= -2
Step-by-step explanation:
can someone please help me with this
Answer:
Perimeter = 18m
Area = 18m²
Step-by-step explanation:
On a rectangle, opposite sides have equal lengths. This means to find the perimeter you would do (3 × 2) + (6 × 2) which is 6 + 12 = 18
The perimeter is 18m
To find the area, you would do length × width. The length is 6 and the width is 3 so 6 × 3 is 18
The area is 18m²
Hope this helps!
Which number equals (34)−2?
Answer:
32
Step-by-step explanation:
HELP PLSSS THIS IS HARD SOMEONEEE
Answer:
correct option is f(x,y) -----> ( -y,x) option 1.
Answer:
correct option is f(x,y) -----> ( -y,x) option 1.
Step-by-step explanation:
Write the equation parallel to y=−1/4x (meaning with a slope of −1/4) but passing through the point (−12,1).
Answer: y=1/4x+4
Step-by-step explanation:
Parallel means the new equation will have the same slope.
y= 1/4x+b
We don't know the b value yet but we can plug in coordinates to solve. We can use the one provided since it has to be a value of this equation.
1= 1/4(-12)+b
1= -3+b
b= 4
y=1/4x+4
PLEASE HELP WILL MARK BRAINLIEST NO FAKE ANSWERS OR WILL BE REPORTED
Evaluate the expression IN EXPONENTIAL FORM
Answer:
-10 × -10= 100
dkfofjdnrjf
137.8×3.5 with explanation
Answer:
482.3
Step-by-step explanation:
because 137.8 times 3.5 is
482.3
What is the number 18 written in a+bi form
Answer:
Step-by-step explanation:To see that
i
−
18
=
−
1
note that
i
1
=
√
−
1
i
0
=
1
i
−
1
=
1
√
−
1
i
−
2
=
1
−
1
=
−
1
i
−
18
=
(
i
−
2
)
9
=
(
−
1
)
9
=
−
1
The number 18 in the form of complex numbers will be written as 18 + 0i.
What are complex numbers?Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfies the equation i² = 1.
The given number is 18. The number in the form of a complex number can be written as:-
Complex number = a + bi
Complex number = 18 + 0i
Therefore, the number 18 in the form of complex numbers will be written as 18 + 0i.
To know more about complex numbers follow
https://brainly.com/question/2801231
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The diagram below represent the rate of making copies on a copy machine. Which table represent this rate?
Answer:
its B
Step-by-step explanation:
at sunrise,the temperature outside was 5 below zero . by noon the temperature dropped 27. what was the temprature at noon
Answer:
-32
Step-by-step explanation:
hope this helps you with the question
Can someone help me with this?
Answer:
they are correct
Step-by-step explanation:
Answer:
317m
Step-by-step explanation:
I am not sure its the perimeter (p) you need because thats what i understood.
p=2(109.7)+2(48.8)=317m
what is 26 divide 7,124
Answer:
1/274
Step-by-step explanation:
Solution 1: Use a fraction simplifier calculator :)
Solution 2: divide by 2 first, then test to find 13, and your there.
Answer: There are two answers ( just for explanation ) 1. 0.0036496350364964 2. 274
Step-by-step explanation:
1. If we do 26 divided by 7124 answer is = 0.0036496350364964 ( check the pic-div1, div2, div3 )
2. If we do 7124 divided by 26 answer is = 274 (check pics-div4, div5)
Describe the translation of the point to its image. (-2,-3) to (-2,4)
Up 8 Units, Hope this helps :)
Find the value of f(5) for the function f(m) = 1 - 4(m/2) *
Answer:
f(m) = -9
Step-by-step explanation:
We replace m with 5 in the function.
f(m) = 1 - 4(m/2) becomes f(5) = 1 - 4(5/2)
then we solve the numbers in the parenthesis first
= 1 - 4 (5/2)
= 1 - 4 (2.5)
= 1 - 10
= -9
please help me, thank you! :)
Answer:
x=-4
Step-by-step explanation:
2(x+6)=4
2x+12=4
2x=4-12
2x=-8
x=-4
Answer:
x = -4
Step-by-step explanation:
First distribute 2 among everything in the parentheses. So now you'll have 2x + 12 = 4
Next subtract 12 on both sides to get -8.
Lastly divide 2 on both sides to get x = -4
Hope this helps :)
Simplify (3x^2y^3)^3
Answer:
27 x^( 6 )y^( 9)
Step-by-step explanation:
A polynomial function of degree 4 with real coefficients could have -3, 1+i, 1-i, and -3,7i as its zeros. true or false
Using complex numbers concepts, it is found that the statement is false.
When a complex number is a root of a polynomial function, it's conjugate also has to be.
A complex number has the format [tex]a + bi[/tex], and it's conjugate is [tex]a - bi[/tex].In this problem:
Real root -3.Complex-conjugate roots 1 + i and 1 - i.Complex root -3 + 7i.The conjugate of -3 + 7i also has to be a root, which would make the polynomial of the 5th degree, as it would have 5 roots, thus, the statement is false.
A similar problem is given at https://brainly.com/question/24450834
Ryan has 15 meters of stereo wire He used 7/8 of the wire to hook his new speakers. How much wire did he use?
Answer:
13.125 meters
Step-by-step explanation:
7/8 times 15
Show that (√7+i√3/√7-i√3 + √7-i√3/√7+i√3) is real
Answer:
Step-by-step explanation:
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]
On taking LCM, we get
[tex]\rm \: = \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]
and
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]
So, using these Identities, we get
[tex]\rm \: = \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{2(7 - 3)}{7 + 3} [/tex]
[tex]\rm \: = \: \dfrac{2 \times 4}{10} [/tex]
[tex]\rm \: = \: \dfrac{4}{5} [/tex]
Hence,
[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]