There are 28 ways for Mary to put the plants on the sills.
We can use the Binomial Theorem to solve this problem.
We have 6 plants and 3 sills, so we have6 + 3 − 1 = 8 total objects.
Since we have 8 objects, we can use the Binomial Theorem to expand [tex](x + y)^{8}[/tex].
The coefficient [tex]x^{6} y^{2}[/tex] will be the number of ways for Mary to put the plants on the sills. We can expand [tex](x + y)^{8}[/tex]
using the Binomial Theorem:
[tex](x + y)^{8}=(\left\ {{8}\atop {0}} \right. )x^{8}+ (\left\ {{8}\atop {1}} \right. )x^{7}y+(\left\ {{8}\atop {2}} \right. )x^{6}y^{2} +(\left\ {{8}\atop {3}} \right. )x^{5}y^{3} +(\left\ {{8}\atop {4}} \right. )x^{4}y^{4}+(\left\ {{8}\atop {5}} \right. )x^{3}y^{5} +(\left\ {{8}\atop {6}} \right. )x^{2}y^{6} +(\left\ {{8}\atop {7}} \right. )x^{1}y^{7} +(\left\ {{8}\atop {8}} \right. )y^{8}[/tex]
Since we are only interested in the coefficient of [tex]x^{6} y^{2}[/tex] , we can ignore all terms that do not have [tex]x^{6}[/tex] and [tex]y^{2}[/tex].
Therefore, we are left with [tex](\left\ {{8}\atop {2}} \right. )x^{6}y^{2}[/tex]
[tex](\left\ {{8}\atop {2}} \right. )=\frac{8!}{2!(8-2)!} =\frac{8!}{2!6!} =\frac{8*7*6!}{2!6!} =28\\[/tex]
Therefore, there are 28 ways for Mary to put the plants on the sills.
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Determine the equation, in vertex form, for the following parabolas.
A. The graph below
B. has a vertex at (−2, 5) and passes (b) through the point (2, 0)
5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.
We need to determine the equation, in vertex form, for the following parabolas.
How to find the equation, in vertex form?We can find the parabola's equation in vertex form following two steps:
Step 1: Use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)²+k.
Step 2: Find the value of the coefficient a by substituting the coordinates of the point into the equation written in step 1 and solving for a.
Now, substitute (−2, 5) in y=a(x−h)²+k
⇒y=a(x−(-2))²+5
Now, substitute (2, 0) in y=a(x−(-2))²+5.
0=a(2+2)²+5
⇒a=-5/16
So, y=-5/16(x+2)²+5
⇒16y=-5(x²+4x+4)+5
⇒16y=-5x²-20x-20+5
⇒5x²+20x+16y-15=0.
Therefore, 5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.
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I need the answers asap
Answer:
The red is the pre-image. The blue is after the 1st transformation. The green is after the 2nd transformation.
Step-by-step explanation:
This is because; you can see the tiny marks. 1 mark next to the letter represents 1 transformation while 2 marks next to letter symbolize the 2nd transformation! I hope this helped you :D
If an equilateral triangles sides are 8 inches long, what is the height?
I think it’s 8.48 but i’m not sure.
Answer:
6.93
Step-by-step explanation:
formula to find height of equilateral triangle is [tex]\frac{\sqrt{3} }{2} *A[/tex] A is the side of the equilateral triangle
Answer:
6.93 inches
(first option listed)
Step-by-step explanation:
we can find the height of this triangle by turning it into a right triangle, and then using the Pythagorean Theorem
(process shown in photo)
hope this helps!! have a lovely day :)
Mateo is making lemonade. he needs 1 1/4 cups of suger.If he can only find 1/8 cup measuring cup.What should you suggest he do.
Answer:
Mateo can measure out the sugar 10 times using the 1/8 measuring cup because 10 times 1/8 equals 1 1/4
Step-by-step explanation:
I need help with this problem.
x3+4x
Answer: x=0 x=2i x=-2i
if your factoring: x(x^2+4)
Step-by-step explanation:
(if your solving for x)
[tex]x^{3} +4x\\x(x^{2} +4)\\\\x=0\\\\x=\frac{-b}{2a}\frac{+}{-} \frac{\sqrt{b^2-4ac}}{2a} \\\\x=\frac{0}{2}\frac{+}{-} \frac{\sqrt{0^2-16}}{2} \\x={0}}\frac{+}{-} \frac{\sqrt{-16}}{2} \\[/tex]
[tex]x={0}}\frac{+}{-} \frac{4i}{2} \\\\\\x=\frac{+}{-}2i[/tex]
Which of the following is a true statement about functions?
Look below at image attached
The true statement about functions is D. If f and g are functions, then (f + g)(-2) = (g + f)(-2).
How to depict the information?It should be noted that a function is used to define the relationship that's exist between rte variables.
In this case, when f and g are functions, then (f + g)(-2) = (g + f)(-2).
Therefore, the correct option is D.
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Tracy made a Venn diagram to compare the numbers of students in her English and history classes. How many students are in Tracy's English class?
The total number of persons that are ion Tracy's English class is given as 21.
How to find the persons in the English Class
We have the Venn diagram showing that there are 14 people in English
15 people in history
While there is a number of 7 students intersecting the two subjects.
Hence the people that attend both history and English are 7.
From here we would know that an English class would be made up of 14 + 7 persons
= 21 persons.
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A bag contains 39 colored marbles. There are 6 blue marbles, 14 red marbles, 8 yellow marbles, and 11 clear marbles. What is the ratio of blue marbles to red marbles?
Answer:
[tex]6:14=3:7[/tex]
Step-by-step explanation:
There are 6 blue marbles and 14 red marbles, so the ratio of blue marbles to red marbles [tex]=6:14=3:7[/tex]
4 (-15 - 3p ) - 4 (-p + 5 )
A. (-8p - 80)
B . ( -13p - 80 )
C. ( -8p + 80 )
D ( 8p - 80)
Answer:
Answer A is correct
Step-by-step explanation:
4 (-15 - 3p ) - 4 (-p + 5 )
First, solve the brackets.
-60 - 12p + 4p - 20
Combine like terms.
- 80 - 8p
∴ - 8p - 80
The difference of two numbers is 8, and the sum of the squares of these two numbers are 320. what are the numbers
Answer:
There are two sets of numbers that meet the criteria:
1) 8 and 16, or
2) -8 and -16
Step-by-step explanation:
Let's call the two numbers A and B.
We are told:
1) A-B=8, and
2) A^2 + B^2 = 320
Rearrange 1) to solve for A:
A=8+B
Use this value of A in the second equation:
A^2 + B^2 = 320
(8+B)^2 + B^2 = 320
(64+ 16B + B^2) + B^2 = 320
2B^2 + 16B + 64 = 320
B^2 + 8B + 32 = 160
B^2 + 8B + 32 = 160
B^2 + 8B - 128 = 0
(B+16)(B-8)=0
B is either -16 or +8
Assuming B = 8
Then from A-B=8 we find that A = B+8 and A = 16
Does A^2 + B^2 = 320?
(16)^2 + (8)^2 = 320?
256 + 64 = 320? YES
--------------------------------
Assuming B=-16
If B=-16, then from A-B=8 we find that A = 8+(-16) and A = -8
Does A-B=8?
-8 - (-16) = 8? YES
Does A^2 + B^2 = 320?
(-8)^2 + (-16)^2 = 320?
64 + 256 = 320? YES
Find x in the following 45°-45°-90° right triangle. Geometry!!! pls help
Answer:
6
Step-by-step explanation:
A farmer plants the same amount every day, adding up to 413 acres at the end of the year. If the year is 58 over, how many acres has the farmer planted?
Using proportions, it is found that the farmer has planted 258 acres.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
He plants 413 acres during the entire year, hence, considering he plants an equal amount daily, and the year is 5/8 over, the amount he has planted is:
A = (5/8) x 413 = 258 acres.
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Prism A and Prism B have the same volume. Which could be the dimensions of prism B. Please help!
Question : Prism A and Prism B have the same volume. Which could be the dimensions of prism B?
Prism A :
Length = 8 feet
Width = 4 feet
Height = 5 feet
Prism B:
Length = ? feet
Width = ? feet
Height = ? feet
Option 1:
Length = 6 feet
Width = 10 feet
Height = 2 feet
Option 2:
Length = 4 feet
Width = 4 feet
Height = 10 feet
Option 3:
Length = 5 feet
Width = 4 feet
Height = 7 feet
Option 4:
Length = 8 feet
Width = 4 feet
Height = 6 feet
Here, the dimensions of the prism B will be length = 4 feet, width = 4 feet, and height = 10 feet.
We know that if the a and b be the length and width of the base respectively and c be the height of a prism, then the volume of the prism is abc.
Given that
length of 1st prism = 8 feet
width of 1st prism = 4 feet
height of 1st prism = 5 feet
So volume of 1st prism = 8 * 4 * 5 = 160 feet³
Now the volume of 1st and 2nd prisms are the same.
So, we have to check the options for length, width, and height of the 2nd prism.
1st option:
Height = 6 feet
Width = 10 feet
Length = 2 feet
So, volume = 6 * 10 * 2 = 120 feet³
Then the 1st option is incorrect.
2nd option:
Height = 4 feet
Width = 4 feet
Length = 10 feet
So, volume = 4 * 4 * 10 = 160 feet³
Then the 2nd option is correct.
Therefore, the dimensions of the prism B will be length = 4 feet, width = 4 feet, and height = 10 feet. The 2nd option is correct.
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Solve for n.
11(n – 1) + 35 = 3n
n = –6
n = –3
n = 3
n = 6
? Question
Kim sells fruit at the farmers market. Her week starts out slow, but she gets much busier later in the week. The sequence that
represents the total kilograms of a fruit she sold the first 4 days of a week is 5, 15, 45, and 135.
Of(n) = 5(3)-1
Of(n) = 3(5)-1
□ f(n) =
(3)"
Of(n) =
(3)"
f(n) = (5)"
E Save &
Identify the explicit and exponential forms of the function, f (n), representing the number of kilograms of fruit sold on the
nth day.
Select all the correct answers.
Submit
Using a geometric sequence, the formula for the number of kilograms of fruit sold on the nth day is:
[tex]f(n) = 5(3)^{n - 1}[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For this problem, the first term and common ratio are given as follows:
[tex]a_1 = 5, q = 3[/tex]
Hence the function can be written as:
[tex]f(n) = 5(3)^{n - 1}[/tex]
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Write the number which is seventeen less than ten
thousand and four:
A number which is 17 less than 10,004:
10,004-17=9987
Hope it helps!
Each leg of a 45°-45°-90° triangle measures 14 cm. what is the length of the hypotenuse? 7 cm 7 startroot 2 endroot cm 14 cm 14 startroot 2 endroot cm
Answer:
[tex]14\sqrt{2}[/tex]
Step-by-step explanation:
In a 45°-45°-90° triangle, the legs = x and the hypotenuse = [tex]x\sqrt2}[/tex]
x = 14
[tex]x\sqrt{2} =14\sqrt{2}[/tex]
Answer:
d
Step-by-step explanation:
14 startroot 2 endroot cm
An American roulette wheel has 38 slots: two slots are numbered 0 and 00, and the remaining slots are numbered from 1 to 36. Find the probability that the ball lands in an odd-numbered slot. Write your answer as a whole number or reduced fraction.
Answer:
9/19
Step-by-step explanation:
To write the probability as a fraction, put the total number on the bottom and put the number of ways the event can happen, put that on top.
They said there are 38 slots. That's the total, it goes on the bottom.
Landing on an Odd Number is the event we're looking at. There are 18 ways that can happen: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35
That number 18 (bc 18 ways to get an odd number) goes on top.
P(Odd) = 18/38
Always simplify when possible.
18/38
= 9/19
What is the slope of the line that goes through the points (-4,2) and (8,5)?
The slope of a straight line passing through the points (-4, 2) and (8, 5) is 1/4.
What is Slope of a straight line?
The slope of a straight line measures the rate of change of variable 'y' with respect to independent variable 'x'. Mathematically -
m = (y₂ - y₁)/(x₂ - x₁) = tan Ф
Given is a line that passes through the points (-4, 2) and (8, 5).
The slope of a straight line passing through two points is given by -
m = (y₂ - y₁)/(x₂ - x₁)
The coordinates given are (-4, 2) and (8, 5).
Substituting them in the formula, we get -
m = (y₂ - y₁)/(x₂ - x₁)
m = (5 - 2)/(8 + 4)
m = 3/12
m = 1/4
Therefore, the slope of a straight line passing through the points (-4, 2) and (8, 5) is 1/4.
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help meee please i need help
Answer:
81pi
Step-by-step explanation:
You are asking yourself the area of pi*r^2 could with r as 9. pi*9^2. solve and you get 81pi :D
If the probability is 50% what is the probability of getting 2 goals out of 5?
please help!
Using the binomial distribution, it is found that there is a 0.3125 = 31.25% probability of getting 2 goals out of 5.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 5, x = 2, p = 0.5.
Hence the probability is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]
0.3125 = 31.25% probability of getting 2 goals out of 5.
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In triangle ABC, m∠ABC = (4x – 12)° and
m∠ACB = (2x + 26)°. Yin says that if x = 19, the triangle must be equilateral. Is he correct? Justify your answer.
Triangle A B C is shown. Angles A B C and B C A are congruent.
The value of ∠ABC is 64 degree at x = 19 degree ,therefore Yin is not right about the value of x .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that
m∠ABC = (4x – 12)°
m∠ACB = (2x + 26)°
Let m∠ACB = y degree
It is asked that if x =19 degree , is the triangle equilateral
m∠ABC = (4x – 12)° = 4 *19 -12 = 64 degree
As in an equilateral triangle , the angles are all equal and equal to 60 degree.
If the value of ∠ABC is 64 degree at x = 19 degree ,therefore Yin is not right about the value of x .
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Answer:No, Yin is not correct. If
x = 19, the measure of angle ABC = 4(19) – 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.
Step-by-step explanation: Because ;0
Select all of the solutions to the equation.
The solution to the equations is; +1/2, -1/2, +√2, and -√2.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given;
[tex]4x^4 + 7x^2 - 2 = 0\\\\[/tex]
The factored form of the polynomial regression
[tex](4x^2 -1)(x^{2} + 2)[/tex]
So,
[tex](4x^2 -1) = 0\\\\4x^2 = 1\\\\x = \pm \dfrac{1}{2}[/tex]
Also,
[tex](x^{2} + 2) = 0\\\\x^{2} = - 2\\\\x = \pm \sqrt{2}[/tex]
Hence, the solution to the equations are;
+1/2, -1/2, +√2, and -√2.
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Answer:
ABCF
Step-by-step explanation:
An electronics shop sells only TVs, phones and tablets. Number sold Select all of the statements below that are true. Number of electronic devices sold 80 60- 40 20 0 Monday Tuesday Wednesday Day Key TV Phone Tablet The largest total number of electronic devices sold was on Wednesday The smallest number of TVs sold was on Monday The same number of phones was sold on each of Monday, Tuesday and Wednesday On Tuesday, more tablets were sold than any other type of electronic device An electronics shop sells only TVs , phones and tablets . Number sold Select all of the statements below that are true . Number of electronic devices sold 80 60 40 20 0 Monday Tuesday Wednesday Day Key TV Phone Tablet The largest total number of electronic devices sold was on Wednesday The smallest number of TVs sold was on Monday The same number of phones was sold on each of Monday , Tuesday and Wednesday On Tuesday , more tablets were sold than any other type of electronic device
A graph is a way to represent a lot of data in such a visual format. The correct statements are A, B, and D.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
The statement that is correct about the given table is,
A.) The largest total number of electronic devices sold was on Wednesday.
B.) The smallest number of TVs sold was on Monday.
D.) On Tuesday, more tablets were sold than any other type of electronic device
hence, the correct statements are A, B, and D.
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Solve |1-4x| > 7
(x-1.5
(xlx < -1.5 UX>1.5)
(xx<-1.5 UX > 2)
If [tex]1-4x\ge0[/tex], then by definition of absolute value
[tex]|1-4x| = 1-4x > 7 \implies 4x < -6 \implies x < -\dfrac32[/tex]
On the other hand, if [tex]1-4x<0[/tex], then
[tex]|1-4x| = -(1-4x) = -1 + 4x > 7 \implies 4x > 8 \implies x > 2[/tex]
So, the overall solution to the inequality is interval union
[tex]\left(x < -\dfrac32\right) \cup (x > 2)[/tex]
A 40 percent discount on a sweater resulted in a saving of $14.40. Find the original price.
Answer:
$36
Step-by-step explanation:
14.40 is 40% of 36.
Answer:
$36
Step-by-step explanation
40/100 = 14.4/?
100 * 14.4 = 1440
1440 / 40 = 36
What is the sum of the series infinity e n-1 -3(3/8)^n?
the answer for the question above is 9/5
a property sells for one and a half million dollars. the five owners each receive a fifth of the money.
how much money does each owner receive?
Answer: Each owner gets $300000
Step-by-step explanation:
one and a half million is 1500000
then divide by 5
you get $300000
A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are
The correct hypothesis that can be set up for this test is given as
H0: mu = 5.8
Ha: mu ≠ 5.8
What is a statistical hypothesis?This is the method of inference that is made in a statistical testing in order to know if the dat available is able to support the claims that have been made.
What the manufacturer wants to know is the average filling of the machine. If it is within 5.8 or not.
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George bought socks for "$"300 and planned to sell them for $6 a pair. write an inequality to find the minimum number of socks he has to sell in order to make a profit of more than 210.
The inequality 6s - 300 > 210 represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.
In the question, we are given that George bought socks for $300.
Therefore, George's total cost = $300.
We assume the number of pairs of socks George sells to be s.
The unit price per pair quoted by George = $6
Therefore, George's total sales = $6s.
We know that the profit over a transaction is given as the difference between sales and costs, that is,
The profit = The total sales - the total costs,
or, profit = 6s - 300.
In the question, we are required to make a profit of more than 210.
This can be shown by the inequality,
6s - 300 > 210.
Thus, the inequality 6s - 300 > 210 represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.
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