9514 1404 393
Answer:
64k^6 -64k^5 +(80/3)k^4 -(160/27)k^3 +(20/27)k^2 -(4/81)k +1/729
Step-by-step explanation:
The row of Pascal's triangle we need for a 6th power expansion is ...
1, 6, 15, 20, 15, 6, 1
These are the coefficients of the products (a^(n-k))(b^k) in the expansion of (a+b)^n as k ranges from 0 to n.
Your expansion is ...
1(2k)^6(-1/3)^0 +6(2k)^5(-1/3)^1 +15(2k)^4(-1/3)^2 +20(2k)^3(-1/3)^3 +...
15(2k)^2(-1/3)^4 +6(2k)^1(-1/3)^5 +1(2k)^0(-1/3)^6
= 64k^6 -64k^5 +(80/3)k^4 -(160/27)k^3 +(20/27)k^2 -(4/81)k +1/729
PLEASE HELLLPP!!!! What is the value of B for the following solid figure? 6 in. 2 8 in. 2 4 in. 2 3 in. 2
The value of B in the prism is 21 in²
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
The given figure is a prism.
And,
B is the base of the prism.
Now,
The base of the prism is a rectangle.
So,
Area of a rectangle.
= length x width
= 7 x 3
= 21 in²
Thus,
The value of B in the prism is 21 in²
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In general, the larger a sample is: a. The more difficult it becomes to avoid atypical cases. b. The greater the standard deviation becomes. c. The smaller the standard deviation becomes. d. The more closely it represents the population. e. The more likely it is that it will be biased.
Answer:
d
Step-by-step explanation:
Larger samples more closely resemble the population from which they come.
Think of the difference between sampling hundreds of people from a town, perhaps asking them if they've ever ordered fast food. If you go to McDonald's and ask customers as they come out, you wouldn't expect those answers to represent the entire population of the town, right?
A convenience store purchased a magazine and marked it up 100% from the original cost of $2.30. A week later, the store placed the magazine on sale for 50% off. What was the discount price?
Answer:
$2.30
Step-by-step explanation:
The original price is $2.30 an it goes up by 100% which means another 2.30. So add 2.30 and 2.30 together you get 4.60 now divide that by two since the magazine is 50% off and you get the original price which was 2.30
The discount price would be an amount of $2.30.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100.
The convenience store bought a magazine for $2.30 and increased the price by 100%. A week later, the retailer reduced the price of the magazine by half.
As per the given situation, the required solution would be as:
The original price is $2.30, then it increases by 100%, or another $2.30. So add 2.30 and 2.30 to get 4.60, then split that by two because the magazine is 50% discounted to obtain the original price of 2.30.
⇒ $2.30 + $2.30
⇒ $4.60
⇒ $4.60 / 2
⇒ $2.30
Therefore, the discount price would be amount of $2.30.
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solve the exponential equation 2^2x +2^x+1 -8
Answer: can you tell me what the x= to because I can’t solve it like that if you give me what the x= to I tell you the answer
Step-by-step explanation:
Answer:
2^x+4^x-7
Step-by-step explanation:
HELPPPPPPPPPP- pleaseeee T^T
Answer:
Step-by-step explanation:
A
Answer:
A. 2x6+4
Step-by-step explanation:
It is really the only one that works, there are two rows of 6 with 4 extra
LUVP is an example of:
Simplify the expression:
9f2 - 10 - 1 + 2/2 + -772
Answer:
4f^2-11
Step-by-step explanation:
In circle M with m
Round to the nearest hundredth.
We know that the area of a sector is given by:
[tex]A = \dfrac{\pi r^2\alpha}{360}[/tex]
Where α is the angle in degrees and r is the radius. We have:
r = 9α = 82°Evaluating:
[tex]A = \dfrac{\pi r^2\alpha}{360} = \dfrac{\pi(9)^2\cdot 82}{360} = 57.96\ u^2[/tex]
Jamie wants to make a playlist with 8 songs on her iPod. She has 50 songs to choose from, including 15 songs from Maroon 5. Janine's iPod won't allow any song to appear more than once in a playlist. How many 8-song playlists contain no songs by Maroon 5? Suppose Janine decides to let her iPod select an 8-song playlist at random.
Answer:
the answer is that she would have to pick 4and let the iPod pick 4
Each week, the price of oranges at the farmer's market increases by 20%.
The price of oranges this week is $4.50.
What was the price last week?
Will give brainliest to correct answer.
The price of orange last week was $3.75
An equation is used to show the relationship between two or more numbers and variables.
The price of oranges increases by 20% each week.
The price of oranges this week is $4.50. Hence:
Price of orange last week (x) is given by:
4.5 = x + 20% of x
4.5 = x + 0.2x
1.2x = 4.5
x = 3.75
The price of orange last week was $3.75
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Caroline has a rock stuck in her Jeep’s tire
Answer:
oh no
Step-by-step explanation:
sorry about that I guess
QUICK PLEASE HELP!!
I WILL MARK BRAINLIEST!!!
You have $10. If you and 3 of your friends want to go to the movies, what does the ticket price need to be for you to be able to buy all 4 tickets?
Answer:
$2.50
Step-by-step explanation:
$10/4 = $2.50
√625/1000
simplification
please do in process
Answer:
[tex] \frac{1}{40} [/tex]
Step-by-step explanation:
[tex] \frac{ \sqrt{625} }{1000} = \frac{ \sqrt{5 \times 5 \times 5 \times 5} }{1000} = \frac{5 \times 5}{1000} = \frac{25}{1000} [/tex]
Reducing the fraction will give -
[tex] \frac{25}{1000} = \frac{25}{25 \times 40} = \frac{1}{40} [/tex]
Not sure if these are right plz help will give brainliest
Answer:
they all seem right to me g!
Step-by-step explanation:
Cassie is going to dinner and a movie with some friends. The movie starts at 7:30 p.m. The restaurant
is 15 minutes from the theater, and dinner will take one hour. If Cassie
lives 20 minutes from the restaurant, what time should she leave her house?
Answer:5:55pm
Step-by-step explanation:
7:30-0:20=7:10-1:00=6:10-0:15=5:55pm
someone help please
Answer:
r=5
Step-by-step explanation:
r³=125
=r⁵=125
=5x5x5
=125
Answer: R is 5
Step-by-step explanation:
5•5•5=125
9 gal and 1 pt - 2pt
please complete the question so we can help you out!! :)
The ratio of yellow blocks to red blocks is 3:5, and the ratio of blue blocks to red blocks is 7:2.
What is the ratio of yellow blocks to blue blocks?
=========================================================
Explanation:
The ratio of yellow to red is 3:5. This could mean we have any of the following situations (pick one):
3 yellow, 5 red6 yellow, 10 red9 yellow, 15 redand so on. In general, we would have 3x yellow blocks and 5x red blocks. The ratio 3x:5x reduces to 3:5 when dividing both parts by x. The x is some positive whole number. The order is important because yellow must be listed first, then red second.
The same idea applies to the other ratio 7:2, which is the blue to red. In that case, we could have...
7 blue, 2 red14 blue, 4 red21 blue, 6 red28 blue, 8 red35 blue, 10 red42 blue, 12 redand so on. Notice that items in bold (in each list) have "10 red" as part of it. This is directly from the fact we multiply the 5 and 2 to get 5*2 = 10.
So we can connect the two ratios to have: 6 yellow, 10 red, 35 blue.
The ratio of yellow to blue is 6:35. This is the final answer. We cannot reduce this ratio any further due to 6 and 35 having no common factors other than 1. It's the same as saying the fraction 6/35 can't be reduced further.
PLEASE HELPP !! The ceiling of Stacy's living room is a square that is 25 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 25 ft, but she doesn't know how long it is. Solve for the length of the diagonal of Stacy's ceiling in two ways: (a) Using the Pythagorean Theorem. (b) Using trigonometry . Round each answer to the nearest whole number and make sure to show all your work( Hint: the answers should be the same!)
Answer:
a) d = 36 ft. ( using Pithagoras´theorem )
b) d = 36 ft ( Using ( function sin ) trigonometry
Step-by-step explanation:
a) Using Pythagoras´Theorem:
Diagonal (d) is the hypothenuse of a right triangle of side 25 feet, and according to Pythagoras´Theorem in a right triangle.
d² = a² + b²
In this particular case a = b = 25 feet then
d² = (25)² + ( 25)²
d = √ 2 * (25)²
d = √2 * 25
d = 1,414*25
d = 35,35
d = 36 ft.
b) Using trigonometry:
We know that sin 45° = cos 45° = √2 / 2
In a right triangle
sin α = opposite side / hypothenuse (d)
sin 45° = √2 / 2 = 25/ d
√2 *d = 2* 25
d = 50/√2
d = 50 / 1,414
d = 35,36
d = 36 ft
HELP HELP HELP HELP
What is the equation of the trend line in the scatter plot ?
Answer:
Equation would be: y = [tex]\frac{4}{7} x + 4[/tex]
Hope this helps!
What steps to get the principle of a 30 year loan at 5.5%?
Harold purchased a new snowmobile. The dealer gave him an option to pay the purchase price of x dollars at 100 dollars per month for y months. He would pay the remaining balance amount the following month. Which type of payment plan did the dealer offer Harold?
The dealer gave Harold
The dealer gave Harold (a deferred payment plan, an installment plan with a down payment, a rent to own plan) The expression for the amount of Harold’s last payment is (x-100y, 100y-x, x-100+y, x+100-y)
Answer:
the healer gave Harold a deferred payment plan. The expression for the amount of Harold’s last payment is x - 100y
Step-by-step explanation:
The dealer gave Harold an installment plan with a down payment. The expression for the amount of Harold’s last payment is x-100y.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
An installment plan is a type of payment plan in which the purchase price is paid in a series of payments, rather than all at once. A down payment is an initial payment made when purchasing a costly item, such as a car or house, with the intention of paying the remaining balance in a series of payments.
The expression for the amount of Harold's last payment is x - 100y. This is because the monthly payments are 100 dollars and there are y months of payments, so the total amount of payments made is 100y. The remaining balance is the original purchase price minus the total amount of payments made, which is x - 100y.
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Let a, β, y be the three interior angles of any triangle, and try to prove that cos(a+β+y) = -1.
[tex]prove \: that \: \cos( \alpha + \beta + \gamma ) = - 1[/tex]
Given:
[tex]\alpha, \beta, \gamma[/tex] are three interior angles of any triangle.
To prove:
[tex]\cos (\alpha+\beta+\gamma)=-1[/tex]
Solution:
According to the angle sum property of a triangle, the sum of all three interior angle of a triangle is always 180 degrees.
It is given that, [tex]\alpha, \beta, \gamma[/tex] are three interior angles of any triangle.
Using the angle sum property of triangles, we get
[tex]\alpha+\beta+\gamma =180^\circ[/tex] ...(i)
We need to prove,
[tex]\cos (\alpha+\beta+\gamma)=-1[/tex]
Taking LHS, we get
[tex]LHS=\cos (\alpha+\beta+\gamma)[/tex]
[tex]LHS=\cos (180^\circ)[/tex] [Using (i)]
[tex]LHS=-1[/tex]
[tex]LHS=RHS[/tex]
Hence proved.
Julie's recipe for lemonade made 2 quarts. What did she need to
multiply each ingredient by to make 8 gallons?
Answer:
She needs 16 recipe to make 8 gallons
A A rug is 6 feet long and w feet wide. Which expression
does NOT represent the perimeter of the rug in feet?
Circle the correct answer.
A) 2(67/8+w)
B) 2w-13 6/8
C) 2(67/8+w
D) 6 7/8+ w+ 6 7/8 + w
Answer:C
Step-by-step explanation:
Answer:
2(6 7/8) + w
Step-by-step explanation:
Disclamer: NOT 2(6 7/8 + w)
Please help it's important
Answer:
cos 24 =x/17
cross multiply
cos 24 × 17=x
0.913 × 17 =x
0.669=x
x = 0.669
PLZ HELP FIRST RIGHT GETS BRAINLEST
A summer camp has 20 boys and 20 girls. Each day, all camper names are put in a hat, and one name is drawn to receive a prize. What are the odds in favor of boys names being drawn on three out of three nights?
Answer:
[tex]\frac{1}{8}[/tex] or [tex]\frac{9}{78}[/tex]
(see explanation)
Step-by-step explanation:
This problem is asking about compound probability, what is the probability of this even happening three times in a row.
Since there are 20 boy's names and 20 girl's names in the hat, one can say that half of the names in the hat. Assume that after drawing it from the hat, the name is put back into the hat. Therefore, on each night, there is a half-chance of the event happening. To find the probability of the event, one must multiply ([tex]\frac{1}{2}[/tex]) by itself (3) times,
[tex](\frac{1}{2})(\frac{1}{2})(\frac{1}{2})\\=\frac{1}{8}[/tex]
In this case, assume that after each drawing the name is not replaced into the hat. This means that after every draw, one must subtract (1) from both the numerator and denominator of the fraction when the fraction is in the un-simplified form.
[tex](\frac{1}{2})(\frac{19}{39})(\frac{18}{38})[/tex]
Simplify,
[tex](\frac{1}{2})(\frac{19}{39})(\frac{9}{19})[/tex]
[tex]\frac{9}{78}[/tex]
ax - 8 = x + 2
If x = 2 on the equation above, what is the value of a?
Answer:
a=2
Step-by-step explanation:
ax-8=x+2
when x=2
2a-8=2+2
2a=4+8
2a=12
a=12/2=6
The compound interest on the account with .01% interest rate in 5 years
compounded quarterly with an initial deposit of $1,000.
Answer:
The interest generated will be $ 51.20.
Step-by-step explanation:
To determine the compound interest on the account with 0.01% interest rate in 5 years compounded quarterly with an initial deposit of $ 1,000, the following calculation must be performed:
1,000 x (1 + 0.01 / 4) ^ 4x5 = X
1,000 x (1 + 0.0025) ^ 20 = X
1,000 x 1.0025 ^ 20 = X
1,000 x 1.05120 = X
1,051.20 = X
1,051.20 - 1,000 = 51.20
Therefore, the interest generated will be $ 51.20.
