The term containing b^6 is -210 a^6 b^6
The given expansion can be solved by using the Binomial expansion
The binomial expansion for two terms (a + b) raised to the power n is given by
(a+b)^n = Σ[tex]a^{n-k} * b^k[/tex] * n!/k!(n-k)!
To find term contain b^6 we use the formula
Use the formula T r+1 =(−1) ⁿCr [tex]a^{n-r} * b^r[/tex]
Putting n=10,
we get 10-r=6
r=4
Therefore,
it is the fourth term ,
T = (-1)^3 10!/4!6! [tex]a^{10-6} * (b^2)^4[/tex]
= -1 x 10x9x8x7/4x3x2=-210 [tex]a^6 b^6[/tex]
Hence the term containing b^6 is -210 a^6 b^6
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Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following:
18 Pennies 19 Dimes
16 Nickels 20 Quarters
What is the probability that you reach into the jar and randomly grab a dime and then, without replacement, a penny? Express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of picking a dime and then a penny without replacement is 0.0651.
What is the probability?Probability is used to determine the odds that a random event would happen. The probability the event happens is 1 and the probability that the event does not happen is 0.
The more likely the event is to occur, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability of picking a dime and then a penny without replacement = (number of dimes / total number of coins) x (number of pennies / total number of coins - 1)
(19 / 73) x (18 / 72) = 0.0651
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A medical insurance policy requires Harold to pay the first $550 of her hospital expense. The insurance company will then pay 75% of the remaining expense. Harold estimates the total bill to be about $20,500. Apart from that Harold also had to pay 12% of $450 fee for prescription medications and a $250 late fee if she pays the bill after September 30. How much will Harold's total payment be if he pays on October 2nd?
Harold's total payment is $5,841.50.
What is Harold's total payment?Percentage is the fraction of a quantity that is expressed as a number out of hundred. The sign used to represent percentages is %. Percentages are a measure of frequency.
The total bill Harold would pay is the sum of the first $550, 25% of the remaining bill, 12% of the fee for prescription medications and the late payment fee since she paid after September 30.
Amount of total bill that Harold would pay = (100 - 75)% x (20,500 - 550)
25% x 19,950 = $4,987.50
Amount of the prescription medications Harold pays : 12% x 450 = $54
Total bill - $550 + $4,987.50 + $54 + $250 = $5,841.50
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The digit 3 in 5,630, is 10 times the value of the digit 3 in 342.
The digit 3 in 5,630, is not 10 times the value of the digit 3 in 342. It's false.
How to calculate the value?It should be noted the question has to do with place value. In this case, the digit 3 in 5,630 gives a value of 30.
On the other hand, the digit 3 in 342 is 300.
Therefore, we can see that the digit 3 in 5,630, is not 10 times the value of the digit 3 in 342.
Therefore, the correct option is false.
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The digit 3 in 5,630, is 10 times the value of the digit 3 in 342. True or. false?
0,0 as center of dilation 1/4 and a =10,6
The new coordinates after the dilation with scale factor 1/4 is
a' = (5/2 , 3/2)
To get the new coordinates when the point is dilated is to multiply the scale factor with the coordinates of the point.
According to the question we have been given that
center of dilation = (0,0)
Scale factor = 1/4
coordinate of the point, a = (10,6)
To get the new coordinates we will multiply the given coordinates by the scale factor that is ,
a' = 1/4*(10,6)
= (10*1/4 , 6*1/4)
a' = (5/2 , 3/2)
Hence the new coordinates after the dilation is a' = (5/2 , 3/2)
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At Food Lion you can buy 5 cans of greens for $2.60 how much will it cost to buy three cans of green beans at the same unit price
What is 8 + x/3 = 13
line gh contains points G(-2,6) and H(5,-3) what is the slope of gh?
The slope of line gh is [tex]\frac{-9}{7}[/tex] .
Line Slope is a measure of the slope and direction of a line . The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. The slope of a line can be calculated from two points on the line. Given the coordinates of two points, we can use the equation for the slope of the line which is given by [tex]m=\frac{y_2-y_!}{x_2-x_1}[/tex] .......(1) where [tex](x_1,y_1)[/tex] is the coordinate of first point and [tex](x_2,y_2)[/tex] is the coordinate of second pointWe have given two points G(-2,6) and H(5,-3) .
Putting [tex]x_1=-2,y_1=6[/tex] and [tex]x_2=-5 ,y_2=-3[/tex] in equation (1) , we get
[tex]m=\frac{-3-6}{5-(-2)} \\\\m=\frac{-9}{5+2}\\\\m=\frac{-9}{7} \\[/tex]
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Find the z-intercepts and the coordinates of the vertex for the parabola y=x2+6x+5 if there is more than one x intercept awpweate them with commas
The x-intercepts of the parabola are (-1,0) and (-5,0) and the coordinates of the vertex are ( -3 , - 4 ).
A parabola is a graphical representation of a function of the form y=g(x) where g(x) is a quadratic polynomial of x.
The locus of a point which is equidistant point also known as focus and equidistant from a given line known as directrix forms a parabola.The general equation of a parabola is given by y =4a(x-h)²+k(h, k) is the vertex of the parabola.The given equation of the parabola is y = x² + 6x + 5
to find the x-intercepts we have to take the value of y at zero.
∴ x² + 6x + 5 = 0
or, x² + 5x + x + 5 = 0
or, x (x + 5) + 1 ( x + 5 ) = 0
or, (x+5)(x+1)=0
either x=-5 or x=-1
Therefore the x-intercepts of the graph is (-1,0) and (-5,0)
Now to find the vertex of the parabola:
y = x² + 6x + 5
or, y = x² + 2·x·3 + 3² - 4
or, y = (x + 3)² - 4
Therefore from the above equation we can say that the vertex of the parabola is at ( -3 , - 4 ).
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At its farthest, the earth is about 9.52 * 10 ^ 7 miles from the sun. Light travels from the sun at a speed of around 1.2 * 10 ^ 6 miles per minute. How many minutes does it take for the light to travel from the Sun to the Earth? Show your calculations and write in standard form.
The number of minutes to take for the light to travel from the sun to the earth is 7.93×[tex]10^{1}[/tex] minutes.
The distance between the earth and sun=9.52×[tex]10^{7}[/tex] miles
The speed of the light from sun=1.2×[tex]10^{6}[/tex] miles per minutes
Speed=Distance/Time
Time= Distance/Speed
Substitute the values in the equation
Time taken for the light to travel from the sun to the earth = The distance between the earth and sun ÷ The speed of the light from sun
Substitute the values in the equation
=9.52×[tex]10^{7}[/tex]÷ 1.2×[tex]10^{6}[/tex]
=(9.52÷1.2)×[tex]10^{7-6}[/tex]
=7.93×[tex]10^{1}[/tex] minutes
Hence, the time taken for the light to travel from the sun to the earth is 7.93×[tex]10^{1}[/tex] minutes
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ASAP can someone help me with this will mark you brainliest
Answer:
C
Step-by-step explanation:
hope this helps!
The area of a square is the square of the length of a side
The area of a square is the square of the length of a side is a^2.
The quantity of space occupied within the square can be used to calculate the size of a square using mathematics. We'll go over the equation for calculating the square's area below. It is mainly known for its geometric quadrilaterals. The simplest definition of a square is a regular polygon with four equal sides. A square has all the same facts and characteristics as regular polygons.
The number of square units that are anticipated to fill a square is used to describe the area of a square. The area is typically defined as the area included by the confines of a level article or 2D figure.
Mathematical Area of Square Formula = a×a=a^2.
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8 - (6 - 8x) = 4x + 5
The value of the x in the linear equation is a 3/4.
According to the statement
We have to find that the value of the x.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
8 - (6 - 8x) = 4x + 5
Now we have to solve this
Then
8 - (6 - 8x) = 4x + 5
8 - 6 + 8x = 4x + 5
Now, rearrange the above written terms for the value of the x
2 + 8x = 4x + 5
4x = 3
x =3/4.
So, The value of the x in the linear equation is a 3/4.
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The formula t = √ h 4 represents the time t in seconds that it takes an object to fall from a height of h feet. If a rock falls from 125 feet, estimate how long it will take the rock to hit the ground. Estimate the square root to the nearest integer before dividing. Express your answer as a decimal. about __ seconds
Answer: How in the world would anybody answer this
Step-by-step explanation: I don't know!
Rectangular paintings hang on the wall of an art gallery. One painting has a area of 24 square feet and another has an area of 32 square feet the paintings have whole number side lengths and have one pair of side lengths in common. What could the common side lengths be?
The common side length of the paintings is 8 feet
What are areas?The area of a shape is the amount of space on the shape
How to determine what common side lengths could be?The given parameters are
Area of painting 1 = 24 square feet
Area of painting 2 = 32 square feet
Express the areas as the product of their factors
So, we have
24 = 2 * 2 * 2 * 3
32 = 2 * 2 * 2 * 4
Multiply the common factors
Common factors =2 * 2 * 2
Evaluate the product
Common factors = 8
This represents the common side length
Hence, the common side length of the paintings is 8 feet
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Please Help! I will give you brainlist and +20 points:)
Thx:)
Answer:-
Step-by-step explanation:
Step 1 1.2r = 0.6r-3
Step 2 .6r = -3
Step 3 -3 divided by .6 = -5
Answer: -5
Given that A, O & B lie on a straight line segment, evaluate the size of the smallest angle.
The smallest angle on the line will be 36°
What do you understand by straight line segment?A line segment seems to be a straight line that connects two places. A line segment does indeed have a predetermined length. A ruler can be used to determine the shortest distance between the two points.
What is another name for a straight angle?A straight angle in geometry is an angle with a vertex point of 180 degrees. It basically generates a straight line with sides that point in opposite directions first from the vertex. It is also known as "flat angles."
According to the given data:We know the the sum of the straight angle is = 180°
So,
(5a + 18) + (48 - a) + (8a -30 ) = 180°
5a - a + 8a + 18 +48 - 30 = 180°
12a + 36 = 180°
12a = 180 - 36
a = 12°
So putting the value of a in the equation:
(5a + 18) = 5 *12 + 18 = 78°
(48 - a) = 48 - 12 = 36°
(8a -30 ) = 96 - 30 = 66°
36° < 66° <78°
So the smallest angle on the line will be 36°
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Write an equation that can be used to solve the problem. Find the solution to the problem. Angles A and B are complementary angles. Determine the measures of angles A and B if angle A is 8 times the size of angle B.
Answer:
A = 80
B = 10
Step-by-step explanation:
a + b = 90
a = 8b
above are the two equations that we will used to find A and B.
substitute in 8b for a in the first equation.
a + b = 90
8b + b = 90 Combine like terms
9b = 90 Divide both sides by 9
b = 10
If b is 10, than a must be 80.
sam sent a email to 3 friends on monday. each of these friends then sent a email on tuesday. on wensday each of those friends then sent a email to 3 friends write the prime factorization of the number of emails that were sent on wensday
7. A paper clip weighs 0.5 grams and an empty envelope weighs 6.75 grams.
Han adds paper clips one at a time to an empty envelope. Complete the table
with the weight of the envelope w(n), in grams, after n paper clips have been
added.
2012 3
a.
w(n)
6.75
The total weight of the envelop after n paper clips have been added is w(n) = 0.5n + 6.75
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let w(n) represent the total weight of the envelop with n paper clips. A paper clip weighs 0.5 grams and an empty envelope weighs 6.75 grams. Hence:
w(n) = 0.5n + 6.75
The total weight of the envelop after n paper clips have been added is w(n) = 0.5n + 6.75
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which inequality is true
Answer:
The answer is C. 5π > 15
Step-by-step explanation:
5π = 15.7
15.7 is greater than 15
the nth term of 1,3,5,7, … is
Answer: an=2(n-1)+1
Step-by-step explanation:
1,3,5,7, …
As the terms progress in the sequence, each term get increased by 2 to get to the next term. Hence, the change is linear and can be modeled with the function y=2(x-1)+1 where y=term value, x=term number and 1 is the first term in the sequence.
y=2(x-1)+1
an=2(n-1)+1 ==> n=term number while an=term value. an=nth term
If Jessie can answer multiplication problems at a rate of 6 problems every 20 seconds. If she has a 10 minute test with 175 questions on it, will she finish in time?
Answer:
yes
Step-by-step explanation:
to solve this you must first find her rate
6 / 20 is her rate
you want to know how many she can do in ten minutes so we must find how many seconds are in 10 minutes
10 * 60 = 600
175 / 600 is the rate needed fro the test
now make them have the same denominator
6 / 20 is also 180 / 600
175/600 is less than 180/600 so yes she will finish the test in time
What are the slope and the y-intercept of the linear function that is represented by the equation y=9x-2
Answer:
Gradient: 9
Y-intercept: -2
Step-by-step explanation:
The equation of a line is expressed in this format:
y = mx + c
Where m is the gradient (slope) of the line, and c is the y intercept.
The equation in the question is already in this format, meaning the values can be read directly from it without needing any rearranging.
m = 9, c = -2.
Jay sells his smartphone to Louise and makes a 20% profit. Louise then sells the
smartphone after a year to Angel, and makes a 10% loss. Louise sold the smartphone
to Angel for £652. How much did Louise pay for the smartphone, and how much did
Jay pay for the smartphone originally?
Answer:
Jay paid £573.76 for the smart phone originally.
Solve the system of equations.
3x + 48 + 32 = 9
3x+3y +32=3
2x + 4y + 32 = 8
Answer:
It will be (x=1.y=6.z=-6
Answer:
Choice b
(x = 1, y = 6, z = -6)
Step-by-step explanation:
The system of equations is
3x + 4y + 3z = 9 (1)
3x + 3y + 3z = 3 (2)
2x + 4y + 3z = 8 (3)
Subtract (2) from (1) to eliminate the 3x and 3y terms and solve for y
(1) - (2)
==> 3x + 4y + 3z - (3x + 3y +3z) = 9 - 3
==> 3x + 4y + 3z - 3x - 3y - 3z = 6
(3x-3x) + (4y-3y) + (3z-3z) = 6
4y - 3y = 6
y = 6
Subtract (3) from (1) to isolate the x term
(3x - 2x) + (4y-4y) + (3z-3z) = 9 -8
x = 1
Divide equation (2) on both sides by 32 to eliminate the coefficients
Equation (2) ÷ 3
==> (3x + 3y + 3z) / 2 = 3/3
==> x + y + z = 1 (4)
Substitute the values of x and y in Equation (4)
1 + 6 + z = 1
7 + z = 1
Subtract 7 from both sides
==> z = 1-7 = 6
Answer:
(x = 1, y = 6, z = -6)
Larry had 6312
feet of rope. He used 1813
feet to tie down a load of lumber on one trailer and then he used 1556
feet to tie down another load on a second trailer. About how much rope does Larry have left? Choose the best estimate.
Responses
A 29 feet29 feet
B 31 feet31 feet
C 28 feet28 feet
D 30 feet30
The feet of rope that Larry has left will be 29 feet.
How to calculate the value?Total number of feet of the rope = 63 feet
Feet that were used = 15.56 + 18.13 = 16 + 18 = 34 feet
Therefore, the feet of rope that Larry has left will be:
= 63 - 34
= 29
Therefore, the feet of rope that Larry has left will be 29 feet.
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Answer: 29 feet
Step-by-step explanation:
if you take 3/10 of a number and add 2 , you get 17
Step-by-step explanation:
Are you asking for the number?
Math on the Spot There are tiger barbs in a aquarium and giant danios in a aquarium. Write a numerical expression to represent the greatest total number of fish that could be in both aquariums. Use the rule and the table to solve this problem. The rule for the number of fish in an aquarium is to allow of water for each of length.
Math on the Spot There are tiger barbs in a 30-gallon aquarium and giant danios in a 20-gallon aquarium. Write a numerical expression to represent the greatest total number of fish that could be in both aquariums. Use the rule and the table to solve this problem. The rule for the number of fish in an aquarium is to allow 1 gallon of water for each inch of lengnth
A numerical expression to represent the greatest total number of fish that could be in both aquariums is; Number in Tiger barb + number in giant danios
The Greatest number of fishes that could be in both aquariums is; 14
How to solve Algebra word problems?
We are given that;
Tiger barbs = 30 gallon aquarium
Giant danios = 20 gallon aquarium
Greatest number of fishes that could be in both aquariums;
Tiger barb = volume / length
Tiger barb = 30 / 3
Tiger barb = 10 fishes
Giant danios = volume / length
Giant danios = 20 /5
Giant danios = 4 fishes
Hence, the greatest total number of fishes in both aquarium is :
Number in Tiger barb + number in giant danios
= 10 + 4 = 14
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Complete question is;
There are tiger barbs in a 30-gallon aquarium and giant danios in a 20-gallon aquarium
Use the rule to solve this problem. The rule for the number of fish in an aquarium is to allow 1 gallon of water for each inch of length.
Giant Danio=5 inch length
Tiger barb=3 inch length
What is the correct numerical expression that represents the greatest total number of fish that could be in both aquariums?
Differential Equations Dilemma
Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the
following functions that vanishes identically.
f(x) = 4x, g(x) = 2x², h(x) = 8x-12x²
Enter the non-trivial linearcombination.
(16)4x + (__)2x²+ (__)(8x-12x²) = 0
The equation with nontrivial linear combination is (16)4x + ( -48 )2x²+ (-8 )(8x-12x²) = 0
We can solve this problem following some steps.
Let's assume the value is A for blank one and it is B for blank two.
Now we can rewrite the equation as,
(16)4x + (A) 2x²+ (B)(8x-12x²) = 0
Or, 64x + 2Ax² + 8Bx - 12Bx² = 0
After rearrangement, we can write this equation as,
x ( 64 + 8B) + x²( 2A - 12B) = 0
We can consider the whole equation as zero, only when the coefficient of both x and x² is zero, To complete a nontrivial combination, we have to write,
∴ ( 64 + 8B) = 0 [ Coefficient of x ]
Or , 8B = -64
Or, B = -64/8 = -8
Again following the previous concept we can also write, ( 2A - 12B ) = 0
[ Coefficient of x² ]
Now, we should put the value of B = -8
∵ ( 2A - 12B ) = 0
Or, 2A + 96 = 0
Or, 2A = - 96
Or, A = - 48
So, the value of A is -48, and the value of B is -8
Now we can conclude,
(16)4x + ( -48 )2x²+ ( -8 )(8x-12x²) = 0
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Nine billion , two hundred forty-six million,seventy-three thousand ,one hundred eighty-nine
In digits
Answer:
9,246,073,189
Step-by-step explanation:
Answer:
9,246,793,189
Step-by-step explanation:
its 9 billion which have nine zeros in behind
and others do it by yourself