Answer:
[tex]{x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 [/tex]
Step-by-step explanation:
This too follows the as same process as
https://brainly.com/question/27201053recall binomial theorem,
[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]
Given binomial:
(x+8)⁵comparing it to (a+b)ⁿ , we acquire:
[tex]a \implies x[/tex][tex]b\implies 8[/tex][tex]n\implies 5[/tex]Now substitute:
[tex] \displaystyle (x +8 {)}^{5} = \sum _{k = 0} ^{5} \binom{n}{k} {a}^{5- k} {b}^{k} [/tex]
To convert the summation into a sum, substitute the values from k=0 to k=5 into the expression which yields
[tex] \displaystyle (x + 8{)}^{5} = \binom{5}{0} {x}^{5 - 0} \cdot {8}^{0} + \binom{5}{1} {x}^{5 - 1} \cdot {8}^{1} + \binom{5}{2} {x}^{5 - 2} \cdot {8}^{2} + \binom{5}{3} {x}^{5 - 3} \cdot {8}^{3} + \binom{5}{4} {x}^{5- 4} \cdot {8}^{4} + \binom{5}{5} {x}^{5 - 5} \cdot {8}^{5} \\ \implies(x + 8 {)}^{5} = \binom{5}{0} {x}^{5} \cdot 1 + \binom{5}{1} {x}^{4} \cdot {8} + \binom{5}{2} {x}^{3} \cdot 64+ \binom{5}{3} {x}^{2} \cdot 512 + \binom{6}{4} {x}^{1} \cdot 4096+ \binom{5}{5} {x}^{0} \cdot 32768\\ \implies(x + 8{)}^{5} = 1 \cdot {x}^{5 } \cdot 1 + 5\cdot{x}^{4} \cdot {8} + 10 \cdot {x}^{3} \cdot 64+ 10 \cdot {x}^{2} \cdot 512 + 5 \cdot{x}^{1} \cdot 4096+ 1 \cdot {x}^{0} \cdot 32768 \\ \implies \boxed{ (x + 8 {)}^{5} = {x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 }[/tex]
and we're done!
The temperature in Toronto was 14 F. The temperature that same night fell to -5 F. What was the difference in temperatures?
A.) 9 degrees
B.) 11 degrees
C.) 19 degrees
D.) 21 degrees
Answer:
a 9 degrees
Step-by-step explanation:
so I'm not sure but if this is the right answer I think it's 9 so basically you do 14-5=9
Can someone help me with these questions
Answer:
Step-by-step explanation:
When you take the n-th root of a number, you can rewrite the expression by taking it to the 1/n-th power. For example:
[tex]\sqrt[n]{x} =x^\frac{1}{n}[/tex]
For the first expression, we can use this proprtery to get:
[tex]\sqrt[5]{a^x} =(a^x)^\frac{1}{5}[/tex]
Using exponent rules, you can combine the exponents by simply multiplying them to get:
[tex]a^\frac{x}{5}[/tex]
Moving on to the second expression. It is now the square root, or equivalently a 1/2 power. If we break up the terms under the radical into powers of 2, we can cancel a lot of the terms:
[tex]\frac{\sqrt{81a^3b^1^0} }{\sqrt{3}a } =\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }[/tex]
The a^2 and b^10 can be taken out of the radical because they have perfect roots:
[tex]\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }=ab^5\frac{\sqrt{81a} }{\sqrt{3}a }[/tex]
The square root of 81 has a perfect root of 9. We have:
[tex]ab^5\frac{\sqrt{81a} }{\sqrt{3}a }=9ab^5\frac{\sqrt{a} }{\sqrt{3}a }[/tex]
You can divide 9 and the square root of 3 by breaking up 9 into a product:
[tex]\frac{(3*3)ab^5}{\sqrt{3} } \frac{\sqrt{a} }{a }=3\sqrt{3} ab^5\frac{\sqrt{a} }{a }[/tex]
Simply by cancelling the 'a' terms to get:
[tex]3\sqrt{3} ab^5\frac{\sqrt{a} }{a }={3\sqrt{3}}\sqrt{a}b^5=3b^5\sqrt{3a}[/tex]
Your friend operates a business and has the following demand curve. Complete the table, and use the information provided to find your friend’s profit-maximizing price and level of output
A demand curve shows the quantity demanded of a product at each price.
What is a demand curve?Your information is incomplete as the table isn't given. Therefore, an overview will be given.
A demand curve simply means a graphical representation of the relationship between price and quantity demanded.
In this case, a demand curve shows the quantity demanded of a product at each price. The profit maximizing price is when the marginal cost equals marginal revenue.
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The profit-maximizing price is when the marginal cost equals marginal revenue.
An individual’s utility-maximizing choices can lead to a demand curve.
What is the demand curve?Demand can be defined as the total amount of goods or services that consumers are willing and able to purchase at a given price.
In Economics, there are primarily two (2) factors that affect the availability and the price at which goods and services are sold or provided, these are demand and supply.
The marginal decision rule—generally produce downward-sloping demand curves.
This section shows how an individual’s utility-maximizing choices can lead to a demand curve.
Hence, The profit-maximizing price is when the marginal cost equals marginal revenue.
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The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean mu = 18 sec and standard deviation sigma = 1.2 sec. what percentage of the runners have times less than 14.4 sec? 0.15% 0.30% 0.60% 2.50%
The percentage of the runners having times less than 14.4 sec is 0.15%. Then the correct option is A.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The times of all 15 years old who run a certain race are approximately normally distributed with a given mean μ = 18 sec and standard deviation σ = 1.2 sec.
The percentage of the runners has times less than 14.4 sec.
Then the z-score will be given as
[tex]\rm z = \dfrac{X - \mu}{\sigma }\\\\\\z = \dfrac{14.4 - 18}{1.2}\\\\\\z = -3[/tex]
Then the percentage will be
[tex]\rm P(z < -3)=0.00135 = 0.135 \% \approx 0.15 \%[/tex]
More about the normal distribution link is given below.
https://brainly.com/question/12421652
Answer:
A. 0.15%
Step-by-step explanation:
edge 2022
Jasmin rakes at two different houses. it takes her 2 1/3 hours to rake leaves at the first. it takes her 1/2 of that time to rake at the second house. how long does it take jasmin to rake at the second house?
Answer:
Jasmin rastrilla en dos casas diferentes. le toma 2 1/3 horas rastrillar las hojas al principio. le toma 1/2 de ese tiempo rastrillar en la segunda casa. ¿Cuánto tiempo tarda el jazmín en rastrillar en la segunda casa?
Step-by-step explanation:
what are the x- intercepts of the graph that represents y=(x+1)(x+5)
Answer:
x= -1 and x= -5
Explanation
y=(x+1)(x+5)
set both equations equal to 0
x+1=0 and x+5=0
subtract each constant from the appropriate side
x= -1 x=-5
HELP ME PLEASE! 20 POINTS!!!
In terms of π, what is the volume of the sphere? Refer to your STAAR 8th Grade Math Reference Sheet for the appropriate formula.
Question 6 options:
360π cubic feet
1800π cubic feet
27000π cubic feet
36000π cubic feet
Answer:
is in the shape of a sphere
diameter = 60 feet
radius = r = 60/2 = 30 feet
Step-by-step explanation:
volume of sphere = 4/3 × π × r³
= 4/3 × π × 30³
=4/3π × 27,000
= 36000π cubic feet
Answer:
36000π cubic feet
Step-by-step explanation:
Given :
Diameter of sphere = 60 feetSolving :
Volume = 4/3πr³But 2r = d or r = d/2Therefore, volume is :⇒ 4/3π(d/2)³⇒ 4/24πd³⇒ 1/6πd³⇒ 1/6 x 60 x 60 x 60 x π⇒ 10 x 3600π⇒ 36000π cubic feetBananas cost $0.48 per pound. If you spent $1.84, how many pounds of bananas did you
purchase?
Answer:
3 pounds of bananas
Step-by-step explanation:
1.84 ÷ 0.48 = 3.8333etc
since you can't buy 4 pounds with the money you have its 3 pounds of bananas
The price of a train ticket consists of an initial fee of $5dollar sign, 5 plus a fee of $2.75dollar sign, 2, point, 75 per stop. Julia has $21 dollar sign, 21 and would like to travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket.
Answer:
17 stops on 1 ticket
Step-by-step explanation:
Answer:
17 stops on 1 ticket
Step-by-step explanation:
Y^2-9y+2. Y=6 evaluat the expression
[tex] \huge\mathbb\orange{ANSWER} [/tex]
[tex] \mathsf\green{y = 6}[/tex]
[tex] \mathsf \purple{{y}^{2} - 9y + 2}[/tex]
[tex] \mathsf \pink{ {6}^{2} - 9(6) + 2}[/tex]
[tex] \mathsf \purple{36 - 54 + 2}[/tex]
[tex] \mathsf \pink{ - 16}[/tex]
[tex] \mathbb\green{Hope\:It\:Helps} [/tex]
A bag of cement weighs 50 kg. A lorry carrying 5 t of cement breaks down. the cement is then transported in a pick up which can carry 10 bags at a time. how many trips does the pick-up make?
Answer:
10 trips
Step-by-step explanation:
50kg in a bag, 4535.92 kg in 5 tons
4535.92kg/50kg = 90.7184
90/10 = 9 trips
but there's still 0.7184 bag left, so the pick-up would need to make 10 trips.
What is the square of the sum of the first 5 Square numbers?
Answer:
3025
Step-by-step explanation: Add the first five square numbers together then square that.
1²+2²+3²+4²+5² = 55
55² = 3025
American Eagle is having a 60 % clearance sale on all summer merchandise. The consumer purchased $342.57 of the summer merchandise. What is the final cost to the consumer? Sales tax is 5%.
Answer:
$143.88
Step-by-step explanation:
Look at image above...
I did not add this to the picture but to get the new total of $137.03, you need to subtract $205.54 (the 60% off) from the original total.
Find the derivative of 9x³ + 4x² + x + 3 at x = 3.
Answer:
268
Step-by-step explanation:
Derivative Rule
dy/dx (xⁿ) = nxⁿ⁻¹On deriving,
dy/dx = 9x³ + 4x² + x + 3dy/dx = 27x² + 8x + 1Substitute x = 3
dy/dx = 27(3)² + 8(3) + 1dy/dx = 243 + 24 + 1dy/dx = 268Solution:
268
=============================
[tex]\sf \bold{ \rightarrow } \ y = 9x^3 + 4x^2 + x + 3[/tex]
[tex]\sf \bold{ \rightarrow } \ \dfrac{dy}{dx} = \dfrac{d}{dx} ( \ 9x^3 + 4x^2 + x + 3 \ )[/tex]
[tex]| | \ \mathrm{ If \ y = x^n , \ then \ \frac{dy}{dx} = nx^{n-1}} \ | |[/tex]
[tex]\sf derivative \ of \ constant \ is \ always \ 0 \ || \ \sf\dfrac{d}{dx}\left(a\right)=0 \ ||[/tex]
solving step wise
[tex]\sf \bold{ \rightarrow } \ \dfrac{d}{dx} ( 9x^3) + \dfrac{d}{dx}(4x^2) + \dfrac{d}{dx}(x )+ \dfrac{d}{dx}(3 )[/tex]
[tex]\sf \bold{ \rightarrow } \ \sf ( 3(9x^{3-1}) +2(4x^{2-1}) + (1)(x^{1-1} )+ 0[/tex]
[tex]\sf \rightarrow 27x^2+8x+1+0[/tex]
[tex]\sf \rightarrow 27x^2+8x+1[/tex]
when x = 3
[tex]\sf \hookrightarrow 27(3)^2+8(3)+1[/tex]
[tex]\sf \hookrightarrow 243+24+1[/tex]
[tex]\sf \hookrightarrow 268[/tex]
zelma buys p pounds of bananas for 40 cents per pound. she pays the clerk with a $20 bills. The clerk Subtract The total cost of the banana from the $20 bill to determine the amount of change to give zelma. which expression represents the amount of change Zelma should received?
[tex]A.p-20
B.20-40p
C.20-0.40p
D.0.40p-20
Answer:
B
Step-by-step explanation:
The amount of change Zelma should receive is 20-0.40p, or 20 dollars minus the total amount of the bananas (each pound multiplied by 40 cents).
Answer: Simple the answer is c.
Step-by-step explanation:
First start out with 20 witch is a full number and subtract .40 p from 20
.40 is the cost of each banana and p is the amount of bananas that will be purchased.
Debbie has 65 tubs of yogurt and 16 boxes of granola. All four kids continue to eat the same amount of food each morning. Which kind of food will get used up first?_________
show your calculations and explain how you figured it out.
The kind of food that will finish and get used up first is the boxes of granola.
What is word problem?Word problem in mathematics is the use of critical understanding of the problem which then employs basic arithmetic operations, fractions, ratios, algebraic expression, etc to solve real-life problems.
From the parameters given:
Debbie has = 65 tubs of yogurtThe boxes of granola = 16The number of kids that consume the same quantity of both food types = 4The time at which the 65 tubs of yogurt will finish:
= 65/4
= 16th rounds with a remainder of 1 tub
The time at which 16 boxes of granola will finish:
= 16/4
= 4th round
A tub of yogurt is roughly 17 ounces while a box of granola is 1 ounce.
Therefore, we can conclude that the kind of food that will finish and get used up first is the boxes of granola.
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What are the y-intercept and the horizontal asymptote of g(x) = 4x + 3?
(0, 3); y = 4
(0, 4) ; y = 3
(0, 5) ; y = 4
(0, 7) ; y = 3
Using exponential function concepts, it is found that that the y-intercept and the horizontal asymptote are given by, respectively:
(0, 3); y = 4
What is an exponential function?It is modeled by:
[tex]y = ab^x + c[/tex].
In which:
a is the initial value.b is the rate of change.y = c is the horizontal asymptote.In this problem, the equation is:
[tex]y = 4^x + 3[/tex].
Hence the horizontal asymptote is y = 3, and the y-intercept is y when x = 0, hence:
[tex](0,y) = (0, 4^0 + 3) = (0, 4)[/tex]
Which means that the first option is correct.
More can be learned about exponential function concepts at https://brainly.com/question/25537936
Answer:
B. (0, 4) ; y = 3
Step-by-step explanation:
I took the exam for algebra 2
What the answer rate you 5 star
Answer:
This is a net
Step-by-step explanation:
Good Luck!!
Help me due in 5 mins!
Hi ..
I really need help on this one
Answer:
LCM of 3 and 2 is 6
so, firstly we had to make the denominator same:-
[tex] \frac{2(2a + 1) + 3(3a - 1)} {6} [/tex]
[tex] \frac{4a + 2 + 9a - 3}{6} [/tex]
[tex] \frac{13a - 1}{6} [/tex]
Step-by-step explanation:
hope this helps you!!!
XxITSCHOCOLOVERxX
The simplified equation of [tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex] is [tex]\frac{13a-1}{6}[/tex]
How to simplify an equation?[tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex]
[tex]\frac{2a+1}{3}+\frac{3a-1}{2} = \frac{2(2a+1)+3(3a-1)}{6}[/tex]
open the bracket in the numerator
Therefore,
[tex]\frac{2(2a+1)+3(3a-1)}{6}=\frac{4a+2 + 9a-3}{6}[/tex]
combine like terms in the numerator
[tex]\frac{4a+2 + 9a-3}{6}=\frac{4a+9a+2-3}{6}[/tex]
Hence,
[tex]\frac{4a+9a+2-3}{6}=\frac{13a-1}{6}[/tex]
Therefore, the final equation is as follows
[tex]\frac{2a+1}{3}+\frac{3a-1}{2}=\frac{13a-1}{6}[/tex]
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Pls pls pla help it lol
Mr. Ramirez made 5 sandwiches. He cut each sandwich in half. How many half sandwiches does he have?
Answer:
10
Step-by-step explanation:
If you cut each sandwich in half and count how many halves there are, you are essentially multiplying it by 2. 5 times 2 is 10. Therefore, your answer is 10. Hope this helps:)
What is 3 inches converted to feet?
Write your answer as a fraction in simplest form. 6
3 in=3 x 1 in
Answer:
1/4 feet
Explanation:
12 inches = 1 feet1 inches = (1/12) feet3 inches = (1/12)*3 feet3 inches = 1/4 feetSo
1in=1/12ftHence.
3in3(1/12)3/121/4ft0.25ftWhich of the following tables represents a proportional relationship?
A
y=4x
8/2=4. .and the rest too have the same value
solve pls brainliest
Answer:
$645.89
Step-by-step explanation:
Determine if S could lie on the perpendicular bisector of QR with the given coordinates
Q(-5 , 4), R(8 ,3) , S(-2,-5)
Step-by-step explanation:
The distance between two points, and is given by:
The endpoints are: Q(-5, -1), R(3, 7)
Point S is (4,-2).
The distance of S to Q is:
The distance of S to R is:
Gerard has 365 baseball cards he puts as many of them into piles of 100 how many piles of 100 does he make
Your class of 96 students is going on a field trip to the aquarium.
You filled one school bus, and the second school bus had 6 seats left
over. Write and solve an equation to determine how many students
s can fit on one school bus.
Answer:
51 seats
Step-by-step explanation:
96 = 2 buses minus six seats
96 = 2x -6
102 = 2x
102/2 = x
51 seats
Four roommates want to split the price of a computer. How much will each roommate pay? Write an equation and solve it by using the information in the table. A 2-column table with 4 rows. Column 1 is labeled Electronics with entries Mp3 player, computer, tablet, smart phone. Column 2 is labeled Sale Price in dollars with entries 39, 299, 199, 78. $49. 75 $74. 75 $156 $1196.
The division is one of the four fundamental arithmetic operations. The amount that is needed to be paid by each friend is $74.75.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
As it is given that the total cost of the computer is $299, it is needed to be split between four friends. Therefore, the price will be paid by the four friends equally which can be written as,
[tex]\text{Amount paid by each friend}=\dfrac{\text{Total cost of computer}}{\text{Number of friends}}\\\\\\\text{Amount paid by each friend}=\dfrac{\$299}{4} = \$74.75[/tex]
Thus, the amount that is needed to be paid by each friend is $74.75.
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i really need
help on this work it is really difficult help plsss
Answer: 105 square feet
Step-by-step explanation: The answer is 105 square feet because find the area of the pool by multiplying 12 and 20 to get 240. You then want to find the area of the total space. Add 3 to 12 and add 3 to 20. Then multiply 23 by 15 to get 345. You then want to subtract 345 - 240 to get rid of the extra space to get your answer of 105.