Answer:
Step-by-step explanation:
Another very interesting problem
If the candles were all of a different color, then the first candle (randomly chosen) would be 7. The second candle would be any one of 6. Third would be any one of the remaining 5, then 4 then 3 then 2 then 1
The abbreviated way of writing that is 7! which means that the number of different ways would be
7*6*5*4 *3*2*1
However this problem is not that simple The complexity comes from the fact that there are colors that are duplicated.
That event is handled by dividing 7! /by 3! and another 3!
The result is 140
3! = 3*2*1 = 6
So you would take 7! and divide by 6*6
5040/36 = 140
This problem is much more difficult than any of the others.
There are 9 different ways the seven candles can be arranged in the kinara.
Explanation:The given problem is asking for the number of different ways that the seven candles can be arranged in the kinara for the celebration of Kwanzaa. Since there are seven candles, we can solve this problem by finding the number of permutations of seven objects. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects we are arranging.
First, we calculate the number of ways to arrange the red candles. Since there are three identical red candles, this can be represented as 3P3 = 3! / (3 - 3)! = 3! / 0! = 3! / 1 = 3.Next, we calculate the number of ways to arrange the green candles. Similar to the red candles, this can be represented as 3P3 = 3! / (3 - 3)! = 3! / 0! = 3! / 1 = 3.Finally, we calculate the number of ways to arrange the black candle. Since there is only one black candle, there is only 1P1 = 1! / (1 - 1)! = 1! / 0! = 1! / 1 = 1.To find the total number of arrangements, we multiply the number of ways to arrange each set of candles together. Therefore, the total number of different ways the seven candles can be arranged in the kinara is 3 * 3 * 1 = 9.
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What is the answer to: (51 + 11.22 + 35.92)?
Answer:
It would equal 98.14
Step-by-step explanation:
If a right triangle has sides of length a, b and c and if c is the largest, then it is called the "hypotenuse" and its length is the square root of the sum of the squares of the lengths of the shorter sides (a and b). assume that variables a and b have been declared as doubles and that a and bcontain the lengths of the shorter sides of a right triangle: write an expression for the length of the hypotenuse.
Assuming this is for a programming language like c++, then the expression might look like
c = sqrt(a*a + b*b)
or you can use the pow function (short for power function)
c = sqrt( pow(a,2) + pow(b,2) )
writing "pow(a,2)" means "a^2"; similarly for b as well.
the length of hypotenuse can be found using the formula [tex]c = \sqrt{a^2+b^2}[/tex]
The pytharogas theorem states that:
[tex]hypotenuse^2 = perpendicular^2+ base^2[/tex]
The Pythagorean Theorem relates the length of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by:
[tex]a^2 + b^2 = c^2[/tex]
This can be rewritten, solving for c:
[tex]c = \sqrt{a^2+b^2}\\\\[/tex]
Thus, the length of hypotenuse can be found using the formula [tex]c = \sqrt{a^2+b^2}[/tex]
If two angles are supplementary, which is the sum of their measurements? A. 45o B. 90o C. 120o D. 180o
Two supplementary angle when added together need to equal 180 degrees.
Answer:
Two supplementary angle when added together need to equal 180 degrees.
Step-by-step explanation:
Please help! Write the slope-intercept form of the equation for the line.
a. y=-8/7x-3/2
b. y=-3/2x+7/8
c. y=-7/8x-3/2
d. y=7/8x-3/2
Answer:
C
Step-by-step explanation:
The slope intercept of a line is y=mx +b where
m is the slope which is calculated as the vertical distance divided by the horizontal distance between two points.b is the y-intercept for value on the y-axis for which the line crosses it.This graph crosses the y-axis (the vertical line) halfway between -1 and -2. This is -3/2. This means only answers a, c, and d are options.
The graph moves up from -3/2 to its next point at (-4,0). We calculate the slope using:
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=0\\y_1=-1.5[/tex] and [tex]x_2=-4\\y_2=2[/tex]
[tex]m=\frac{2-(-1.5)}{-4-0}[/tex]
[tex]m=\frac{2+1.5}{-4}=\frac{3.5}{-4} =-0.875[/tex]
This decimal is equivalent to -7/8. This means C is the answer.
This equation represents a line with a slope of [tex]\( -\frac{7}{8} \)[/tex](meaning the line slopes downward from left to right) and a y-intercept of [tex]\( -\frac{3}{2} \)[/tex](where the line crosses the y-axis). The correct answer is option c
The slope-intercept form of the equation of a line is [tex]\( y = mx + b \),[/tex] where m represents the slope of the line, and b represents the y-intercept (where the line crosses the y-axis).
Let's analyze each option:
a.[tex]\( y = -\frac{8}{7}x - \frac{3}{2} \):[/tex]
- Slope [tex]\( m = -\frac{8}{7} \)[/tex]
- y-intercept [tex]\( b = -\frac{3}{2} \)[/tex]
b. [tex]\( y = -\frac{3}{2}x + \frac{7}{8} \):[/tex]
- Slope [tex]\( m = -\frac{3}{2} \)[/tex]
- y-intercept[tex]\( b = \frac{7}{8} \)[/tex]
c.[tex]\( y = -\frac{7}{8}x - \frac{3}{2} \):[/tex]
- Slope [tex]\( m = -\frac{7}{8} \)[/tex]
- y-intercept [tex]\( b = -\frac{3}{2} \)[/tex]
d.[tex]\( y = \frac{7}{8}x - \frac{3}{2} \):[/tex]
- Slope[tex]\( m = \frac{7}{8} \)[/tex]
- y-intercept[tex]\( b = -\frac{3}{2} \)[/tex]
Among the given options, the correct slope-intercept form is option c:
[tex]\[ \boxed{y = -\frac{7}{8}x - \frac{3}{2}} \][/tex]
Two less than three– fourths of a number is ten. What is the number?
A. 10 2/3
B. 13 1/3
C. 15 1/3
D. 16
Answer:
Option D. 16
Step-by-step explanation:
Let
x ----> the number
we know that
The linear equation that represent this problem is equal to
[tex]\frac{3}{4}x-2=10[/tex]
Solve for x
Multiply by 4 both sides
[tex](4)*\frac{3}{4}x-2*4=10*4[/tex]
[tex]3x-8=40[/tex]
Adds 8 both sides
[tex]3x-8+8=40+8[/tex]
[tex]3x=48[/tex]
Divide by 3 both sides
[tex]3x/3=48/3[/tex]
[tex]x=16[/tex]
therefore
The number is 16
Estimate the same of 9.327 + 5.72 + 4.132 to one decimal place?
Answer:
19.2
Step-by-step explanation:
[tex]\\\text{Consider the sum}\\\\9.327 + 5.72 + 4.132\\\\\text{To add the numbers, we add the whole parts together and the decimal parts together}\\\text{so we have}\\\\\ \ 9.327\\5.720\\4.132\\----\\19.179\\\\\text{we need to round the final answer to one decimal place.}\\\text{observe that the second digit after the decimal point is 7, which is greater than 5}\\\\\text{so we'll increase the digit before it by 1, so the sum of the numbers}\\\text{to one decimal place is }19.2[/tex]
if m ║ n and m ∠5 = 65°, what is m ∠1?
Answer:
65
Step-by-step explanation:
Since <5 and <1 are corresponding angles and m is parallel to n
<5 = <1
<5 =65
so <1 = 65
Suppose that Spain has a workforce of 22.85 million people, and that the average salary for each person is €24,200 annually. Spain has imports of €290.85 billion and exports of €200.13 billion. If the Spanish government levies a 7% tariff on exports, an 18% tariff on imports, and a 21% income tax, how will the revenue gained from tariffs and the revenue gained from income tax compare?
D. The government will earn €49.7616 billion more from income tax than from tariffs.
Step-by-step explanation: According to E2020
Answer:
The answer is D: The government will earn €49.7616 billion more from income tax than from tariffs.
Step-by-step explanation:
What is the equation of the line that contains the point (3,-1) and has the same slope as the the line y=1/3x+5
Answer:
y = 1/3x - 2
Step-by-step explanation:
Line y = 1/3x + 5 has slope 1/3, so the line we are looking for also has slope 1/3.
y = 1/3x + b
We know a point, so we plug in the values of x and y, and we solve for b.
y = 1/3x + b
-1 = (1/3)(3) + b
-1 = 1 + b
b = -2
Now that we know b, the equation is:
y = 1/3x - 2
To take a taxi, it costs \$3.00$3.00 plus an additional \$2.00$2.00 per mile traveled. You spent exactly \$20$20 on a taxi, which includes the \$1$1 tip you left. How many miles did you travel?
Answer:
8 miles
Step-by-step explanation:
Given:
To take a taxi initial cost = $ 3.00
Per mile cost = $ 2.00
Total spent = $20
Tip Given = $ 1
To find:
Total miles traveled=?
Solution:
Now the total cost f the ride was $ 20
As we see that initial cost for all the trips would stay the same
Let someone travels x miles
then according to the given
Initial cost + 2 * miles traveled + tip = total cost
Putting from the given values it becomes
3 + 2 * x + 1 = 20
Now we have to find x here which is the total miles traveled
solving the above equation
3+1+2x=20
4+2x=20
2x=20-4
2x=16
dividing both sides by 2
x =8 miles
so total miles travelled by the person is 8 miles
Answer: 8 miles you traveled.
Step-by-step explanation:
solve this identifying holes, vertical asymptotes, and horizontal asymptotes for
f(x)=x²+7x+12/-x²-3x+4
[tex]x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{Vertical asymptotes:}\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\\boxed{x=-4\ and\ x=1}\\\\\text{Horizontal asymptotes:}[/tex]
[tex]\lim\limits_{x\to\pm\infty}\dfrac{x^2+7x+12}{-x^2-3x+4}=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\dfrac{7}{x}+\dfrac{12}{x^2}\right)}{x^2\left(-1-\dfrac{3}{x}+\dfrac{4}{x^2}\right)}=\dfrac{1}{-1}=-1\\\\\boxed{y=-1}[/tex]
What is the radical expression that is equivalent to the expression
(35)^1/4?
Enter your answer as a radical.
For example, if your answer is
3√14,
enter it like this: cuberoot(14)
Hello from MrBillDoesMath!
Answer:
fourthroot(35)
Discussion:
The question is a bit unclear as to the desired answer.... but here goes!
(35)^1/4 is the fourth root of 35, that is, symbolically, fourthroot(35).
Note the fourth root of a number is the same as the square root of the square root of the number.
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
6y + 2x - 2y - 3x
PLEASE HELP ASAP THANK YOU
Answer:
4y-x
Step-by-step explanation:
Combine like-terms.
6y-2y and -3x+2x
Do the Math
4y and -x
4y-x
The height, h(t), in feet of an object thrown into the air with an initial upward velocity of 63 feet per second is given by the formula h(t) = -16t2 + 63t, where t is the time in seconds. What is the height, in feet, of the object after 3 seconds?
Answer:
The height of the object after 3 seconds is 45 feets.
Step-by-step explanation:
The height of an object thrown into the air with an initial upward velocity of 63 feet per second is given as
[tex]h(t)=-16t^2+63t[/tex]
Where, h(t) is height of the object in feet and t is the time in seconds.
We have to find the height of the object after 3 seconds. So, substitute t=3.
[tex]h(3)=-16(3)^2+63(3)[/tex]
[tex]h(3)=-16(9)+189[/tex]
[tex]h(3)=-144+189[/tex]
[tex]h(3)=45[/tex]
Therefore height of the object after 3 seconds is 45 feets.
To calculate the height of an object after 3 seconds using the equation h(t) = -16t^2 + 63t, substitute t with 3 and solve. This results in a height of 45 feet.
To find the height after 3 seconds, we substitute t with 3 into the equation, getting h(3) = -16(3)2 + 63(3). Calculating this step-by-step, we first find the square of 3, which is 9, and then multiply it by -16 to get -144. Next, we multiply 63 by 3 to get 189. Adding these two results together, we end up with 45 feet. Therefore, the height of the object after 3 seconds is 45 feet.
Please answer this question !! 98 points and brainliest!!
Answer:
x > -3
Step-by-step explanation:
5x+ 7 > 2(x-1)
Distribute the 2 on each side
5x+7 > 2x -2*1
5x+7 > 2x-2
Subtract 2x from each side
5x-2x +7 > 2x-2x-2
3x + 7>-2
Subtract 7 from each side
3x+7-7>-2-7
3x>-9
Divide by 3 on each side
3x/3 >-9/3
x > -3
You need about one and a half hours to set up a computer workstation. At this rate how many hours should it take you to set up seven of these workstations?
Answer: About 10.5 hours
When 4 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution.
Answer:
-1
Step-by-step explanation:
because if you put it in a equation for you get x^2-4=3x therefore you use the quadratic formula and solve the two answers you get are 4 and -1 so since its negative solution it must be -1 must be the square
The negative solution for a quadratic equation, set up to represent the expression 'When 4 is subtracted from the square of a number, the result is 3 times the number', is -1.
Explanation:The subject of this question is a quadratic equation. If we let n be the number, the provided question can be rewritten as:
n² - 4 = 3n
To solve this equation for n, we rearrange terms to get a standard quadratic equation:
n² - 3n - 4 = 0
We can solve this equation using the quadratic formula:
n = [-b ± sqrt(b² - 4ac)] / (2a)
Substituting the values a = 1, b = -3, c = -4 into the formula, we obtain:
n = [3 ± sqrt((-3)² - 4 × 1 × -4)] / (2 × 1)
which simplifies to:
n = [3 ± sqrt(9 + 16)] / 2 = [3 ± sqrt(25)] / 2 = [3 ± 5] / 2
Thus we have two solutions:
n = 8/2 = 4 and n = -2/2 = -1
Since we are looking for the negative solution, the number we are looking for is -1.
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How do you recognize if a binomial is a difference of perfect squares and how is the pattern used to factor the binomial?
Answer:
A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
Step-by-step explanation:
A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.
A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answer:
Its the graph at the bottom right.
Step-by-step explanation:
Adding f(x) and g(x) we get
-x^2 + 3x + 5 + x^2 + 2x
= 5x + 5 = (f+ g)(x)
This has a slope of 5 and a y-intercept of 5, so its bottom right graph.
(f + g)(x) is a composite function of f(x) and g(x), and it is represented by graph (c)
The functions are given as:
[tex]\mathbf{f(x) = -x^2 + 3x + 5}[/tex]
[tex]\mathbf{g(x) = x^2 + 2x}[/tex]
To calculate (f + g)(x), we make use of the following formula
[tex]\mathbf{(f + g)(x) = f(x) + g(x)}[/tex]
So, we have:
[tex]\mathbf{(f + g)(x) = -x^2 + 3x + 5 + x^2 + 2x}[/tex]
Collect like terms
[tex]\mathbf{(f + g)(x) = x^2-x^2 + 3x+ 2x + 5 }[/tex]
Evaluate the like terms
[tex]\mathbf{(f + g)(x) = 5x + 5}[/tex]
The above function is a linear function.
A linear function is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where m represents the slope, and c represents the y-intercept
So, by comparison:
[tex]\mathbf{m = 5}[/tex]
[tex]\mathbf{c = 5}[/tex]
The graph that has a slope of 5, and a y-intercept of 5 is graph (c)
Hence, graph (c) represents (f + g)(x)
Read more about composite functions at:
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Help me please!!! 30 points! :)
The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. Which type of function best models this situation?
A) exponential
B) linear
C) quadratic
D) radical
Answer: Exponential
$35,000(1.03)^x
Step-by-step explanation:
Answer:
The answer is exponential hope this helps mark me brainliest.
What is the slope of the line through (-7,-2)(−7,−2) and (-6,7)(−6,7)? Choose 1 answer: Choose 1 answer: (Choice A) A -\dfrac19− 9 1 (Choice B) B -9−9 (Choice C) C 99 (Choice D) D \dfrac19 9 1
[tex]\bf (\stackrel{x_1}{-7}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{7-(-2)}{-6-(-7)}\implies \cfrac{7+2}{-6+7}\implies \cfrac{9}{1}\implies 9[/tex]
Drag and drop numbers into the boxes so that the paired values are in a proportional relationship.
x 1 3 _____ 5 8
y 4 12 16 20 _____
4
12
32
8
36
Answer:
4 and 32
Step-by-step explanation:
We are given paired values for two variables x and y and we are to fill in the missing values such that they are in a proportional relationship.
For x, we have the following paired values:
[tex]1, 3, ___, 5, 8[/tex]
So from the given options, 4 fits the best here which is greater than 3 and lesser than 5.
And for y, we have:
[tex]4, 12, 16, 20, ___[/tex]
Here, 32 fits the best from all the options as it is the next (available) number after 20.
What is the greatest common factor of the two terms in the expression x^5y^2+x^2y^7z
The greatest common factor of [tex]x^5y^2[/tex] and [tex]x^2y^7z[/tex]is [tex]x^2y^2[/tex].
Explanation:To find the greatest common factor (GCF) of two or more terms, we need to identify the largest possible number that divides both terms evenly. In this case, we have two terms,[tex]x^5y²[/tex]and [tex]x²y^7z.[/tex]
Firstly, let's simplify the terms by removing any common factors. Here, we can see that both terms have 'x' and 'y' in common. So, let's remove them from both terms to simplify them.
[tex]x^5y²[/tex]becomes [tex]x^3y²[/tex]
[tex]x^2y^7z[/tex]becomes [tex]x^2y^5z[/tex]
Now, let's look for any common factors between these simplified terms. We can see that both terms have 'x' raised to the power of 2 in common. So, let's remove this factor from both terms.
[tex]x^3y²[/tex] becomes xy²
[tex]x^2y^5z[/tex] becomes [tex]xy^3z[/tex]
Now, let's look for any further common factors between these simplified terms. We can see that both terms have 'y' raised to the power of 2 in common. So, let's remove this factor from both terms.
xy² becomes xy
[tex]xy^3z[/tex] becomes xyz
Finally, we can see that both simplified terms now share a common factor of 'xy'. Therefore, 'xy' is the greatest common factor (GCF) of our original two terms, which is x²y² when we replace 'x' and 'y' with their original powers.
Eileen collected 98 empty cans to recycle and Carl 82 cans. They packed a equal number of cans into each of three boxes. How many cans were in each box?
Answer: 60 cans in each box
Step-by-step explanation:
98+82=180
180/3=60
Which scenario would make someone vulnerable to identity theft? A. including a Social Security number on an income tax form B. missing monthly payments on a car loan for three months C. opening a credit card account to purchase a household appliance D. using a public library computer to access confidential bank information
Answer:
The correct answer is option D
Step-by-step explanation:
The use of personal information though a public computer can make personal information prone to adulteration and misuse as identity theft
When a Social Security number is mentioned on an income tax form it remains private and does not get exposed. Like wise missing monthly payments for a car loan has no relevance to data stealing. In case of opening a credit card account, the information provided are secured with the availed banking service
Answer:
Randell uses a computer at a public library to view his bank account online.
Step-by-step explanation:
Using a publicly accessible computer to view sensitive information can lead to that information being divulged to others using the same computer.
There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders. How many band members are sixth graders? How many band members are seventh graders? What percentage of the band members are eighth graders?
Answer:
The band members of sixth graders are 28.
The band members of seventh graders are 14.
The percentage of the band members eighth graders are 40% .
Step-by-step explanation
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
There are 70 students in the school band.
40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.
Now first find out the band members are sixth graders .
Percentage = 40%
Total value = 70
Put in the formula
[tex]40 = \frac{Number\ of\ band\ members\ are\ sixth\ graders\times 100}{70}[/tex]
[tex]Number\ of\ band\ members\ are\ sixth\ graders = \frac{40\times 70}{100}[/tex]
[tex]Number\ of\ band\ members\ are\ sixth\ graders = \frac{2800}{100}[/tex]
[tex]Number\ of\ band\ members\ are\ sixth\ graders = 28[/tex]
Therefore the number of band members are from sixth graders are 28 .
Now first find out the band members are seventh graders .
Percentage = 20%
Total value = 70
[tex]20 = \frac{Number\ of\ band\ members\ are\ seventh\ graders\times 100}{70}[/tex]
[tex]Number\ of\ band\ members\ are\ seventh\ graders = \frac{20\times 70}{100}[/tex]
[tex]Number\ of\ band\ members\ are\ seventh\ graders = \frac{1400}{100}[/tex]
[tex]Number\ of\ band\ members\ are\ seventh\ graders = 14[/tex]
Therefore the number of band members are from seventh graders are 14.
Now find out the percentage of the eighth graders of the band members.
Total number of band members = sixth graders members + seventh grade members + eighth graders members
As sixth graders members = 28
seventh grade members = 14
Total number of band members = 70
Put in the above
70 = 28 + 14 + eighth graders members
70 - 42 = eighth graders members
28 = eighth graders members
Put in the percentage formula
[tex]Percentage = \frac{28\times 100}{70}[/tex]
[tex]Percentage = \frac{2800}{70}[/tex]
Percentage = 40%
Therefore the percentage of the band members are eighth graders is 40 %.
Answer:
The band members of sixth graders are 28.
The band members of seventh graders are 14.
The percentage of the band members eighth graders are 40% .
Step-by-step explanation
Formula
As given
There are 70 students in the school band.
40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.
Now first find out the band members are sixth graders .
Percentage = 40%
Total value = 70
Put in the formula
Therefore the number of band members are from sixth graders are 28 .
Now first find out the band members are seventh graders .
Percentage = 20%
Total value = 70
Step-by-step explanation:
Therefore the number of band members are from seventh graders are 14.
Now find out the percentage of the eighth graders of the band members.
Total number of band members = sixth graders members + seventh grade members + eighth graders members
As sixth graders members = 28
seventh grade members = 14
Total number of band members = 70
Put in the above
70 = 28 + 14 + eighth graders members
70 - 42 = eighth graders members
28 = eighth graders members
Put in the percentage formula
Percentage = 40%
Therefore the percentage of the band members are eighth graders is 40 %.
What is the quotient (3x2 + 4x − 15) ÷ (x + 3)?
Answer: (3x-5)
Step-by-step explanation:
first we set it up x+3[tex]\sqrt{3x^2 +4x-15}[/tex]
we want to get rid of 3x^2 first so, x*3x= 3x^2
then we subtract x+3[tex]\sqrt{3x^2 +4x-15}[/tex]
distribute :3x*3=9x - (3x^2 +9x)
0 -5x
now we want to get rid of -5x, we use -5
-5(x+3)=-5x-15 x+3[tex]\sqrt{-5x-15}[/tex]
-(-5x-15)
0, so reminder of 0
What is the fourth term of the expansion of the binomial (2x + 5)5? A. 10x2 B. 5,000x2 C. 1,250x3 D. 2,000x3
Answer:
B would be the answer for this question.
Step-by-step explanation:
Answer: The fourth term is [tex]5000x^2.[/tex]
Step-by-step explanation: We are given to find the fourth term in the expansion of the following binomial :
[tex]B=(2x+5)^5.[/tex]
We know that
the r-th term in the expansion of the binomial [tex](a+x)^n[/tex] is given by
[tex]T_r=^nC_ra^{n-(r-1)}b^{r-1}.[/tex]
For the given term, we have
n = 5 and r = 4.
Therefore, fourth term is given by
[tex]T_4\\\\=^5C_{4-1}(2x)^{5-(4-1)}5^{4-1}\\\\=^5C_3(2x)^25^3\\\\=\dfrac{5!}{3!(5-3)!}\times4x^2\times125\\\\\\=\dfrac{5\times4}{2\times1}\times 500x^2\\\\=5000x^2.[/tex]
Thus, the fourth term is [tex]5000x^2.[/tex]
A formula for electrical circuits states that E=P/\I where E represents the force in volts, P represents power in watts, and I represents current in amps. Solve this formula for I. Then find I when the force E = 3.6 volts and the power P = 45 watts.
Answer:
[tex]I=12.5[/tex] amp
Step-by-step explanation:
The formula is,
[tex]E=\dfrac{P}{I}[/tex]
where,
E = Electromotive force in volts,
P = Power in watts,
I = Current in amps.
Given values are,
E = 3.6 volts,
P = 45 watts,
I = ??
Putting the values,
[tex]\Rightarrow 3.6=\dfrac{45}{I}[/tex]
[tex]\Rightarrow I=\dfrac{45}{3.6}=12.5[/tex] amp