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
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Match the pairs of equivalent expressions.
i would say y + 2/5y is the equivalent expression of 7/5y and y - 2/5y is the quivalent expression of 3/5y but im not sure
What is the equation of the line in point slope form with a slope of m=-2/3 passing through the point (-5,-2)
Answer:
[tex]m=− 32 ≈−0.666666667[/tex]
Step-by-step explanation:
0.4(-1.08) = ?
what is the product?
Answer: -0.432
Step-by-step explanation:
0.4*1.08 would be 0.432 add the negative sign to get -0.432
The product of 0.4 and -1.08 is -4.240.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
To multiply 0.4 and 1.08, we need to follow few steps
first multiply as if there is no decimal.
Next, count the number of digits after the decimal in each factor.
Finally, put the same number of digits behind the decimal in the product.
0.40
1.08
___________
240
000+
040++
____________
4.240
As there is a negative sign infront if 1.08, we will put minus sign to the product value
So 0.4(-1.08) is -4.240
Hence the product of 0.4 and -1.08 is -4.240.
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Simplify the expression to a + bi form: (10 + 6i)(- 2 - 4i)
[tex] \Large{\boxed{\sf (10 + 6i)(-2 - 4i) = 4 - 52i}} [/tex]
[tex] \\ [/tex]
Explanation:To find the algebraic form, also called 'a + bi form', of the given complex number, we will have to expand its expression using FOIL method.
[tex] \\ [/tex]
[tex] \Large{ \sf \: \underline{FOIL \: method \text{:}}} \\ \\ \Large{\boxed{\sf (A + B)(C + D) = AC + AD + BC + BD}} [/tex]
[tex] \\ [/tex]
Let's identify our coefficients and expand the given expression:
[tex] \sf (\underbrace{\sf 10}_{A} + \overbrace{\sf 6i}^{B})(\underbrace{\sf -2}_{C} \overbrace{\sf -4i}^{D}) = 10 \times (-2) + 10 \times (-4i) + 6i \times (-2) + 6i \times (-4i) \\ \\ \\ \sf = -20 - 40i - 12i - 24i^2 = -20 - 52i - 24i^2 [/tex]
[tex] \\ [/tex]
In the complex number system, i² = -1. Therefore, our final answer is:
[tex] \sf (10 + 6i)(- 2 - 4i) = -20 - 52i - 24(-1)= \boxed{\boxed{\sf 4 - 52i}} [/tex]
[tex] \\ \\ [/tex]
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How is email a useful component of online banking?I. Email alerts can be used to warn you before you overdraw your account.II. You can have your bank statements emailed to you, getting them to you faster.III. Only emailed bank statements can be used to support electronically-filed tax returns.a.I onlyb.II onlyc.I and II onlyd.I, II, and III
Answer:
c
Step-by-step explanation:
Find the sum of the first twelve terms of the sequences 3, -6, 12, -24,..
Show your work.
Answer:
3, -6, 12, -24, 48, -96, 192, -384, 768, -1536, 3072, -6144...
×-2
Geometric sequence
In a United States flag, the length of the union is fly, and the width is 13 of the hoist. 7 If the fly is 6 feet, how long is the union. 2 5 of the
Answer: These American flag measurements ratios are: (A) Height (hoist) of the flag = 1.0; (B) Width (fly) of the flag = 1.9; (C) Union height (Hoist of the canton) = 0.5385 (A × 7/13, spanning seven stripes);
Step-by-step explanation:
Hope this helps!
Answer:
cut.ly/4Ivk
Step-by-step explanation:
This link should help cut.ly/4RIvk
(Type an ordered pair, using integers or decimals)
Answer:
(0,-3) is the correct answer because e-3 is on the y axis
Answer:
-5,0
Step-by-step explanation:
The x-intercept is where the line intercepts the x-axis
What is the value of each minor gridline?
Answer:
Minor Gridlines will separate units that are traced or delineated by major gridlines. They will also only appear for value axes.
I hope this helps
QUESTION 12
Maria bought 6 books for a total of $360.00. Math books cost $80.00 and science books cost $50.00. How many science books did she buy? Your
answer should be a number only.
Answer: 4 science and 2 math books
Step-by-step explanation:
Let M and S stand for the numbers of math and science books.
We know that M+S = 6 books
and M*80 + S*50 = $360
Rearance the first: M = 6-S
Use this definition of M in the second equation:
(6-S)*80 + S*50 = $360
480-80S + 50S = 360
-30S = - 120
S = 4
Use S=4 in the first equation (M=6-S) to find the number of math books, 2.
Check to see if there number work:
4*($50)= $200
2*($80)= $320160
Total is $360. It works.
B.
E.
20 cm
7 cm
11 cm
-
Find volume
Step-by-step explanation:
The volume of cylinder = [tex]\pi r^{2}h[/tex]
The radius of cylinder = 20 ÷ 2 = 10
The volume of cylinder = [tex](\frac{22}{7})(10^{2} )(7)[/tex]
= [tex](22)(100)[/tex] = 2200
please give me a brainliest answer
Answer:
Volume of cylinder = 2,198 cmSolution:
volume of a cylinder = area of base(pi × radius²) × altitude (height)
Volume = πr² × altitude
V = 3.14 × 10² × 7
V = 3.14 × 100 × 7
V = 314 × 7
V = 2,198 cm
y=3x-1 identify the slope and y-intercerpt
Answer:
Step-by-step explanation:
y = 3x - 1
whatever is in front of the x is the slope. It has to be a number of some kind. I don't think complex numbers count, but don't quote me on that.
The y intercept is the number on the right that is not associated with x. In this case it is - 1.
Change 32/6 to a mixed number in lowest terms .
Answer:
5 1/3
Step-by-step explanation:
true or false Typically, a plot begins with conclusions that introduce the characters and the conflict they face.
Answer:
Hello!!
The correct answer is false. The exposition begins with conclusions that introduce the characters and the conflict they face
Hope this helps!!
Please help me solve this
Answer:
the answer will be something like 18
[tex]f(x)=\frac{2x}{x-1}[/tex]
[tex]f(a); f(a+h); \frac{f(a+h)-f(a)}{h}[/tex]
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $2.40 and the cost of a large greeting card is $3.70. How much would it cost to get 2 small greeting cards and 3 large greeting cards? How much would it cost to get x small greeting cards and y large greeting cards?
Answer:
1)15.9
depends on what x and y are but put 15.9 ig
Step-by-step explanation:
Answer:
cost of smalls + cost of larges so the answer is 2.40+3.70
Step-by-step explanation:
What is the solution and answer of this question:
3 log 10 + 9 log 10
Answer:
12
Step-by-step explanation:
the answer is 12 ndndbdbdndnfnnfnfnfnfnfnfnfnfn
Five hundred students were surveyed about their favorite activity. The results are shown in the table.ActivityPercent of StudentsVideo Games25Hiking22Reading19Bike Riding18Movies16How many more students prefer playing video games to bike riding?studentsListen to the complete questionTools are not currently accessible
Answer:
Video game- 25
Bike riding - 18
Subtract them and you will get the answer.
= 7
In the figure, s//t Find the m\1
will give brainliest
The answer is 115 degrees
I NEED HELP ASAP I WILL MARK BRAINLIEST :’]
The question is “Find the equation of the line. Use exact numbers.”
Answer:
y=x-5
Step-by-step explanation:
Which statement correctly compares the function shown on this graph with
the function y = 4x + 2?
8
7
6
5
1
543 2
1 2 3 4
5
A. The function shown on the graph has a greater rate of change, but
a lower starting point.
B. The function shown on the graph has a greater rate of change and
a higher starting point.
C. The function shown on the graph has a smaller rate of change, but
a higher starting point.
The given highest power of x in the given function, y = 4·x + 2, is 1,
therefore, the graph of the function is a straight line.
The statement that correctly compares the function shown on the graph
with the function; y = 4·x + 2 is; C. The function shown on the graph has a
smaller rate of change but a higher starting point.
Reasons:
The given function is; y = 4·x + 2
Comparing with the equation for a straight line; y = m·x + c, we have;
The rate of change or slope, m = 4
The y-intercept, starting point, c = 2
Two points on the function shown on the graph are; (0, 4), and (-2, -2)
The slope of the given graph is therefore;
[tex]m = \dfrac{4 - (-2)}{0 - (-2) } = \dfrac{6}{2} = 3[/tex]
The rate of change of the graph, m = 3
The equation of the graph is therefore;
y - 4 = 3·(x - 0)
Which gives;
y = 3·x + 4
The y-intercept, starting point of the graph, is therefore, c = 4
Which gives;
The function shown on the graph has a higher starting point but a smaller rate of change than the given function.
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Do the following: Ayie says that 7-³ is the same as – 7³. Write an explanation of how Ayie should interpret 7-³, then show her how each expression results in a different value.
Can you use mechanical pencils on the PSAT?
Answer:
no
Step-by-step explanation:
only number 2 pencils im pretty sure
What is..Simplify 15.8
Answer:
simplify of 15.8 is 16
Step-by-step explanation:
please mark me as brainliest
Answer:
15 4/5
Step-by-step explanation:
Perform the indicated operation. Show all necessary work. a -2-(-9) b -2 -9 c -2- (-9)-(-2
please help i need to finish a test
Answer:
a=7 b=11 c=9
Step-by-step explanation:
-2-(9) -2-(9) = -2+9=7 b -2-9=-11 c -2-(-9)-(-2) = -2+9+2=9
Answer:
Is the other answer correct?
Step-by-step explanation:
for cases of n objects taken n at a time the number of possible combinations is _____________ the number of possible permutations.
Answer:
I believe your answer is less than or equal to. I hope this helps.
The length of a 10-minute video is decreased by 45% when the video is edited. What is the length of the edited video?
Answer:
The edited video would now be 5 Minutes 50 Seconds
Step-by-step explanation:
10-4.5=5.5
To subtract any percentage from a number, simply multiply that number by the percentage you want to remain. In other words, multiply by 100 percent minus the percentage you want to subtract, in decimal form. To subtract 20 percent, multiply by 80 percent (0.8).
Step-by-step explanation:
its 5.5 mins
here are the methods
1-0.45= 0.55 0.55*10= 5.5
or
its
45/100= 0.45 0.45*10min= 4.5 10mins-4.5mins= 5.5 mins
50 POINT QUESTION!!!!
f(x)=12x^(2)+4x-5
find the zeroes of the function...
Answer is in picture below
:)
8TH GRADE MATH PLEASE HELP!!
Answer:
C.
Step-by-step explanation:
\sqrt{35} = 5.916079783
Its the Closest one
Answer:
C is the correct answer
[tex] \sqrt{35 } = 5.91 \\ [/tex]
