By definition of the binomial coefficient,
[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]
so we have
[tex]C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)[/tex]
as required.
Write a slope-intercept equation for a line that passes through (-2,1) and (3,-14).
Steve bought a new car for $22,000 but paid 93% of the list price. How much was the list price
Answer:
approximately $23,655.91 (rounded to the nearest hundredths place)
Step-by-step explanation:
[tex]22,000=0.93x\\x=23,655.91[/tex]
10 problems for 50 points
Answer:
1. F
2. F
3. T
4. F
5. F
6. T
7. T
8. F
9. F
10. T
Step-by-step explanation:
1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.
2. They do not lie on the same line.
3. Points A, B, C, D all lie in the same plane therefore making them coplanar.
4. Points X, Y do not lie in the same plane as A, B.
5. Point X does not lie in the same plane as C, D, B
6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.
7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.
8. Plane AXY cannot be defined as point X and Y are not in a plane.
9. Lines AB and CD cannot both be in a different plane.
10. Both rays sum up to equal Line XY.
3x + 4 divided by 2 = 9.5
Answer:
2.5
Step-by-step explanation:
First divide 4 by 2
Second, you want x on a side by itself. So you would move 2 over to 9.5. But since 2 is positive, you would subtract 2 from 9.5
Third, you need to get x by itself. So you would divide by 3 on both sides because division cancels out multiplication which is what 3x is. And then you end up with 2.5
3x + 4 / 2 = 9.5
3x + 2 = 9.5
3x = 7.5
3x/3 = 905/3
x = 2.5
And if you want to check it, just substitute 2.5 for x
3(2.5) + 4 / 2 = 9.5
7.5 + 4 / 2 = 9.5
7.5 + 2 = 9.5
9.5 = 9.5
14 A ladder 10m long leans against a wall and make 45" with the ground. What is the height of the wall? 14 A ladder 10m long leans against a wall and make 45 " with the ground . What is the height of the wall ?
Answer:
A 10m ladder is leaning against a wall. The ladder makes an angle of 78o with the ground. How high up the wall does the ladder reach? Please include a diagram in the answer.
Th function you need is the sine function. The sine of 78° is about 0.978. That is the ratio of the opposite side (wall) over the hypotenuse (ladder) of the right triangle in this problem.
10 m · sin 78° = 10 m · 0.978 = 9.78 meters.
The ladder reaches 9.78 meters up on the wall.
Step-by-step explanation:
Factoring using GCF 15cd + 30c^2d^2
Answer:
15cd(1 + 2cd)
Step-by-step explanation:
greatest common factor is 15cd
[tex]15cd*1 + 15cd*2cd\\= 15cd(1 + 2cd)[/tex]
DJ Erin is making a playlist for work; he is trying to decide what 10 songs to play and in what order they should be played.
Step 2 of 2 : If he has his choices narrowed down to 3 country, 6 pop, 7 disco, and 3 hip-hop songs, and he wants to play all 7 disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.
Using the combination and the arrangements formula, it is found that the number of possible playlists is given by:
[tex]7.98 \times 10^8[/tex]
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
7 disco songs are taken from a set of 7.3 remaining songs are taken from a set of 3 + 6 + 3 = 12 songs.Hence, without considering the order, the number of playlists is given by:
[tex]C_{7,7}C_{12,3} = \frac{7!}{7!0!} \times \frac{12!}{3!9!} = 220[/tex]
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, the 10 musics are arranged, hence the number of playlists, considering the order, is given by:
[tex]n = 10! \times 220 = 798336000 = 7.98 \times 10^8[/tex]
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The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.
A 2-row table with 10 columns. The first row is labeled time (minutes) with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4, 4.5. The second row is labeled temperature (degrees Celsius) with entries 75, 79, 83, 86, 89, 91, 93, 94, 95, 95.5.
According to the line of best fit, at what time will the temperature reach 100°C, the boiling point of water?
5
5.5
6
6.5.
According to the given table the line of best fit is
f(x)=4.54x+77.84
The term "line of best fit" describes a line that passes across a scatter plot of data points and best captures their connection. Statisticians often utilise regression analysis software or manual computations to arrive at the geometric equation for the line using the least squares approach. A straightforward linear regression study of two or more independent variables will provide a straight line.
Hence, as asked by the question we need to find the time at which the tempurature will become 100°C.
To find that let us put f(x)=100 and find out the value of x for which it is satisfied.
4.54x+77.84=100
⇒[tex]x=\frac{100-77.84}{4.54}=4.88[/tex]
⇒x≈5
Therefore the time at which the tempurature is 100°C is 5 minutes.
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i needs a help please
Answer:
Step-by-step explanation:
Givens
x intercept =
(1,0) (5,0)The vertex is at 3, 4
The vertex is upside down.
Solution
(x - 1) and (x - 5) produce the two roots.
There must be 1 minus somewhere so that the quadratic goes upside down.
Answer
y = - (x -1)(x - 5)
Yolanda invests $30,000 in an account that offers a compound interest rate of 7.9% per year. Which of the following is the correct equation for how much Yolanda will have in year 10?
The correct option will be Option D: [tex]P_{10} =30000(1+0.079)^{10[/tex]
The compounds interest can be estimated by using the following formula
[tex]A =P(1+r/n)^{nt[/tex]
where
A: the final amount
P: the initial investment
r: the interest rate (in decimal)
n: the number of times the interest will be compounded per year
t: the time (in year)
Given in the problem that
the initial investment is $30,000 and the time period is 10 years,
so P=30000 and
t=10
As we know The interest will be compounded one time per year
n=1.
now for converting the interest rate into decimal form, we will divide the rate of interest by 100.
r=7.9/100
⇒r=0.079
putting above values in the above formula
[tex]A =P(1+r/n)^{nt[/tex]
⇒ [tex]A =30000(1+0.079/1)^{(1)(10)[/tex]
⇒ [tex]A =30000(1+0.079)^{10[/tex]
⇒[tex]P_{10} =30000(1+0.079)^{10[/tex]
Therefore correct option is Option D: [tex]P_{10} =30000(1+0.079)^{10[/tex]
By completing the above equation to find the total amount
[tex]P_{10} =30000(1+0.079)^{10[/tex]
⇒[tex]P_{10} =30000(1.079)^{10[/tex]
⇒[tex]P_{10} =64170.54[/tex]
Yolanda will have to pay $64,170.54 in her account after ten years.
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What is the domain of the given function?
{x|x = -6, -1, 0, 3}
{y ly=-7, -2, 1, 9}
{x|x=-7, -6, -2, -1, 0, 1, 3, 9}
y ly=-7, -6, -2, -1, 0, 1, 3, 9}
Step-by-step explanation:
Easy buddy....
_________________________________
Remember, from now on, wherever the function domain is asked
They mean the same inputs or xs of the function.
Now you can answer them yourself but I like to help you to do it buddy.
_________________________________
The first function's domain is :
D = { -6 , -1 , 0 , 3 }
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
The second function's domain is :
D = { -7 , -6 , -2 , -1 , 0 , 1 , 3 , 9 }
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
The domain of the function in the table given is:
A. {x|x = -6, -1, 0, 3}.
In any given function, all x-values (input) make up the domain of the function, while corresponding y-values (output) make up the range of the function.
In the table given, the x-values (input) are -6, -1, 0, and 3.
Therefore, the domain of the function in the table given is:
A. {x|x = -6, -1, 0, 3}.
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The amount left from you net income after your fixed expenses have been paid.
The profit is the amount left from you net income after your fixed expenses have been paid.
The amount earned by an individual or corporation after costs, allowances, and taxes is referred to as net income. Net income in company is what remains after all costs, such as salaries and wages, the cost of goods or raw materials, and taxes, have been paid.
Profit is a financial gain, specifically the sum obtained over that which was used to acquire, maintain, or produce the good or service.
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Hence the profit is the amount left from you net income after your fixed expenses have been paid.
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Which property of real numbers IS shown below?
3 + ((-5) + 6) = (3 + (-5)) + 6
The associative property of real numbers is shown in the number expression 3 + ((-5) + 6) = (3 + (-5)) + 6
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have a number expression:
= 3 + ((-5) + 6) = (3 + (-5)) + 6
As we know in the associative property:
a + (b + c) = (a + b) + c
= (3 + (-5)) + 6
Thus, the associative property of real numbers is shown in the number expression 3 + ((-5) + 6) = (3 + (-5)) + 6
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f(x) = 3x² + 7x + 2, what is f(5)?
Answer:
112
Step-by-step explanation:
How many degrees does Earth turn in one hour?
Answer:
15 degrees
Step-by-step explanation:
Answer:
The earth turns 15 degrees in one hour. Hope this helps!
Step-by-step explanation:
if x²+X+1=0 then what is the value of x²⁰¹⁵ + x²⁰¹³ + x
Since [tex]x^2 + x + 1 = 0[/tex] means [tex]x^2+x = -1[/tex], we have for any [tex]n[/tex] the recursive relation
[tex]x^n (x^2 + x) = x^{n+2} + x^{n+1} = -x^n \implies x^{n+2} = -x^{n+1} - x^n[/tex]
Let [tex]f(x)=x^{2015}+x^{2013}+x[/tex]. Substitution using the recursive rule generates an alternating power-reduction pattern:
[tex]f(x) = \left(-x^{2014} - x^{2013}\right) + x^{2013} + x = -x^{2014} + x[/tex]
[tex]f(x) = -\left(-x^{2013} - x^{2012}\right) + x = x^{2013} + x^{2012} + x[/tex]
[tex]f(x) = \left(-x^{2012} - x^{2011}\right) + x^{2012} + x = -x^{2011} + x[/tex]
[tex]f(x) = -\left(-x^{2010} - x^{2009}\right) + x = x^{2010} + x^{2009} + x[/tex]
[tex]f(x) = \left(-x^{2009} - x^{2008}\right) + x^{2009} + x = -x^{2008} + x[/tex]
[tex]f(x) = -\left(-x^{2007} - x^{2006}\right) + x = x^{2007} + x^{2006} + x[/tex]
and so on.
Notice that in the equivalent forms of [tex]f(x)[/tex] involving 3 terms, the largest power of [tex]x[/tex] is a multiple of 3, and the next largest power is 1 less. This means after so many iterations of substitutions, we would end up with
[tex]f(x) = x^3 + x^2 + x[/tex]
Then by factorizing, the expression of interest reduces to
[tex]f(x) = x (x^2 + x + 1) = x \times 0 = \boxed{0}[/tex]
||
Writing ratios for real-world situations
There are 3 red marbles and 8 blue marbles in a bag.
Answer:
3:11 or 8:11
Step-by-step explanation:
I think your missing some imformation! I'm guessing the ratio of picking a red marble is 3:8 while a blue marble is 8:3
help me please ! due soon!
Answer:
Step-by-step explanation:
Comment
An x intercept occurs when y = 0. So the table shows three of them.
Answer
There are 3 x values when y = 0. They are
x = - 1x = 2x = 3Answer: A. [tex](-1, 0)[/tex]
Step-by-step explanation:
The x-intercept is every point where y=0. To see this, we should look at the table's f(x) section to find any zeroes.
According to the table and this knowledge, one x-intercept of this continuous function is [tex](-1, 0)[/tex].
I hope this helps! Pls mark brainliest!! :)
Which equation represents a circle with a center at (-5,5) and a radius of 3 units?
Answer:
[tex] {(x + 5)}^{2} + {(y - 5)}^{2} = 9 [/tex]
Two regular polygons X and Y are such that the number of sides of X is
3 more than the number of sides of Y. If the sum of the exterior angles
of X and Y is 117°, how many sides has .X?
Based on the indices of the regular polygons, the number of sides that X has is 8. See the computation below.
What is the analysis for the above solution?Assuming that X has G number of sides; and
Y has H number of sides, this means that:
G-H = 3 ...........1
Recall that the formula for the exterior angles is:
360/n; where n is number of sides
X = 360/G
Y = 360/H
(360/G) + (360/H) = 117°.......2
Solving 1 and 2 simultaneously, we obtain:
G= 8 and
H = 5
Thus, X has 8 sides.
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find the area of the shaded portion in each of the following
Answer:
30.5 cm^2
Step-by-step explanation:
General outlineFind the area of the full circleFind the area of the rectangleFind the difference (full circle area - rectangle area)Step 1. Find the area of the full circleRecall the formula for the area of a circle: [tex]A_{circle}=\pi r^2[/tex] where [tex]\pi \approx 3.14[/tex], and "r" is the radius of the circle (distance from center to any point on the edge).
From the diagram, the radius is 5cm.
[tex]A_{circle}=\pi r^2[/tex]
[tex]A_{circle}=(3.14)(5[cm])^2[/tex]
[tex]A_{circle}=78.5[cm^2][/tex]
Step 2. Find the area of the rectangleRecall the formula for the area of a rectangle: [tex]A_{rectangle}=bh[/tex] where "b" is the base of the rectangle (length of bottom or length of top), "h" is the height of the rectangle (distance from bottom to top).
From the diagram, the base is 8cm, and the height is 6cm.
[tex]A_{rectangle}=bh[/tex]
[tex]A_{rectangle}=(8[cm])(6[cm])[/tex]
[tex]A_{rectangle}=48[cm^2][/tex]
Step 3. Find the difference (full circle area - rectangle area)Having found the areas for each of the first parts, we can find the difference to find the shaded area:
[tex]A_{shaded}=A_{circle}-A_{rectangle}[/tex]
[tex]A_{shaded}=(78.5[cm^2])-(48[cm^2])[/tex]
[tex]A_{shaded}=30.5[cm^2][/tex]
X: 4x^2+16 -20=0
What is x
Answer:
[tex]\boxed{\sf x = 1, \ x = -5}[/tex]
Explanation:
[tex]\rightarrow \sf 4x^2 + 16x - 20 = 0[/tex]
[tex]\rightarrow \sf 4(x^2 + 4x - 5) = 0[/tex]
[tex]\rightarrow \sf x^2 + 4x - 5 = 0[/tex]
[tex]\rightarrow \sf x^2 + 5x -x- 5 = 0[/tex]
[tex]\rightarrow \sf x(x + 5) -1(x+ 5) = 0[/tex]
[tex]\rightarrow \sf (x-1)(x+ 5) = 0[/tex]
[tex]\rightarrow \sf x = 1, \ x = -5[/tex]
s x – 5 a factor of the function f(x) = x3 – 5x2 + 7x – 35? Use the Remainder Theorem to justify your answer.
By using the remainder theorem we found that ( x - 5 ) is the factor of function f(x) = x³ – 5x² + 7x – 35.
What is factorization?Factorization is defined as splitting the polynomial into its most simplified form. This factor satisfies the polynomials from which it is extracted.
The factorization by using the Remainder theorem.
x - 5 ) x³ – 5x² + 7x – 35.( x ² + 7
x³ - 5x²
______________
00 7x - 35
7x - 35
-------------------------
00
Here the function is completely divided by the factor x - 5 therefore
by using the remainder theorem we found that ( x - 5 ) is the factor of function f(x) = x³ – 5x² + 7x – 35.
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7
2
3
Mark this and return
f(x)
The functions f(x) and g(x) are graphed.
3
-6-5-4-3-2-1₁-
"AssessmentViewer(Ant
N
5
-2+
-3-
6
g(x)
7
2 3 4 5 6 x
8
Which represents where f(x) = g(x)?
Of(2)= g(2) and f(0) = g(0)
f(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)
Save and Exit
Answer: Option 1
Step-by-step explanation:
The graphs intersect at x=0 and x=2, meaning f(2)=g(2) and f(0)=g(0).
The functions have the intersecting points at x = 2 and x = 0 and the relation is f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the first function be represented as f ( x )
Let the second function be represented as g ( x )
Now , the function f ( x ) is a parabolic function and g ( x ) is a linear function
And , the intersecting points of both f ( x ) and g ( x ) are
x = 2 and x = 0
So , both the functions f(x) and g(x) intersect at two points, one at x = 2 at the x-axis in the graph and one at y = 4 at y-axis of the graph
Therefore , f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )
Hence , the functions are solved
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100 adults were asked how they keep fit.
Each adult goes to the gym, runs or cycles.
45 of these adults are female.
30 of the 52 adults who go to the gym are female.
35 adults run.
9 males cycle.
One of the females is chosen at random.
Write down the probability that she runs.
The probability that a female chosen runs = 0.24
How to find the probability?We are given;
Number of adults surveyed = 100
Total number of females = 45
Total Number of Males = 55
Number of female adults that go to gym = 30
Number of adults that run = 35
Number of males that cycle = 9
Thus;
From the probability table attached, we can say that;
Number of females that can run = 11
Probability that she runs = 11/45
Probability that she runs = 0.24
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The reverse of the number 129 is 921, and these add to 1050, which is divisible by 30.
How many three-digit numbers have the property that, when added to their reverse,
the sum is divisible by 30?
Answer:
Step-by-step explanation:
Write the number as [tex]abc[/tex] and use the divisibility rules for 10 and 3. From the rule for 10, we know that the last digit of [tex]abc+cba[/tex] is [tex]o[/tex], hence [tex]a+c=10[/tex]. Thus the options are [tex]a=1[/tex] & [tex]c=9[/tex], [tex]a=2[/tex], & [tex]c=8[/tex], etc.
From the rule for 3, namely that the digit sum must be divisible by 3, we find that [tex]2a+2b+2c=20+2b[/tex] is divisible by [tex]3[/tex]. By hand it's easy to check that [tex]b=2,5,8[/tex] are the only options that work.
So there are 9 choices for [tex]a[/tex] and [tex]c[/tex] and [tex]3[/tex] for [tex]b[/tex] , giving 27 total.
[tex]4x {}^{2} + 20x + 25[/tex]
using appropriate identity factories the following
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's Solve ~
[tex]\qquad \sf \dashrightarrow \: 4 {x}^{2} + 20x + 25[/tex]
[tex]\qquad \sf \dashrightarrow \: 4 {x}^{2} + 10x + 10x + 25[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x(2x + 5) + 5(2x + 5)[/tex]
[tex]\qquad \sf \dashrightarrow \: (2x + 5) (2x + 5)[/tex]
[tex]\qquad \sf \dashrightarrow \: (2x + 5) {}^{2} [/tex]
or
[tex] \sf{\qquad \sf \dashrightarrow \: 4x² + 20x + 25 } [/tex]
[tex] \sf{\qquad \sf \dashrightarrow \: (2x)² + (2 \sdot 2x \sdot 5) + (5)²} [/tex]
[ it's similar to expression - a² + 2ab + b² that is equal to (a + b)² ]
so, let's use this identity here to factorise :
[tex] \sf{\qquad \sf \dashrightarrow \: (2x + 5)²} [/tex]
I hope it was helpful ~
which expression is equivalent to...
Answer:
[tex]\frac{y^{12} }{5}[/tex]Step-by-step explanation:
1) Cancel [tex]x^5[/tex].
[tex]\frac{9y^{16} }{45y^4}[/tex]
2) Take out the constants.
[tex]\frac{9}{45} \times\frac{y^{16} }{y^4}[/tex]
3) Simplify [tex]\frac{9}{45}[/tex] to [tex]\frac{1}{5}[/tex].
[tex]\frac{1}{5} \times\frac{y^{16} }{y^4}[/tex]
4) Simplify.
[tex]\frac{y^{16} }{5y^4}[/tex]
5) Use Quotient Rule: Use Quotient Rule: [tex]\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}[/tex].
[tex]\frac{{y}^{16-4}}{5}[/tex]
6) Simplify [tex]16-4[/tex] to [tex]12[/tex].
[tex]\frac{y^{12} }{5}[/tex]
4.5x + 9 -1/2x = -3.75 +5 1/2 + 5.25
Answer:
x = -1/2 = -0.5
Step-by-step explanation:
4.5x + 9 -1/2x = -3.75 +5 1/2 + 5.25
⇔ (4 1/2 - 1/2)x + 9 = (5 1/2 + 5 1/4) - 3 3/4
⇔ 4x + 9 = 10 3/4 - 3 3/4
⇔ 4x + 9 = 10 - 3
⇔ 4x + 9 = 7
⇔ 4x = 7 - 9
⇔ 4x = -2
⇔ x = -2/4
⇔ x = -1/2
⇔ x = -0.5
Chico, California, hosts the annual Silver Dollar Fair.
In 2016, contestants competed in the Inaugural World Silver Dollar
Pancake Eating Championship, where they had 8 minutes to eat as
many one-ounce silver dollar pancakes as possible.
Answer: what is the question
Step-by-step explanation:
