Answer:
a) 6
Step-by-step explanation:
Expanding the polynomial using the formula:
[tex]$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $[/tex]
Also
[tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]
I think you mean [tex]210x^6y^4[/tex]
We can deduce that this term will be located somewhere in the middle. So I will calculate [tex]k= 5; k=6 \text{ and } k =7[/tex].
For [tex]k=5[/tex]
[tex]$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$[/tex]
Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just [tex]x^{n-k} y^k[/tex]
For [tex]k=6[/tex]
[tex]$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$[/tex]
What is the value of the expression
9r-5s+3 to the 3rd power if r=2/3 and s= -2
Answer:
43
Step-by-step explanation:
(9r-5s+3^3)
Let r = 2/3 and s = -2
(9 * 2/3-5* -2+3^3)
(6+ 10+27)
43
Answer:
[tex] \huge \boxed{43}[/tex]Step-by-step explanation:
[tex]9r - 5s + {3}^{3} [/tex]
plug the values
[tex] = 9 \times \frac{2}{3} - 5 \times ( - 2) + {3}^{3} [/tex]
Reduce the numbers with Greatest Common Factor 3
[tex] = 3 \times 2 - 5 \times ( - 2) + {3}^{3} [/tex]
Multiply the numbers
[tex] = 6 + 10 + 27[/tex]
Calculate the sum of positive numbers
[tex] = 43[/tex]
Hope I helped..
Best regards!
Reflecting the graph of y = cos x across the y-axis is the same as reflecting it
across the x-axis.
True or Fale
Reflecting the graph of y = cos(x) is across the x-axis is the same as taking y = -cos(x). Reflecting across the y-axis is the same as taking cos(-x). However, cos(-x) is actually equal to cos(x), not -cos(x), so these two are not equivalent (diagram attached).
I have also attached a graph of these functions. The green line is the reflection over the y-axis, which is the same as the original function. The blue line is the reflection over the x-axis.
A backpack is on sale for 40% off the regular $50 price. What is the sale price?
$40
$30
$20
$10
Answer:
$30
Step-by-step explanation:
i think i did the right math
Answer:
Hey there!
40% of 50 dollars is 20
Thus, the price of the backpack is now 50-20, or 30 dollars.
Hope this helps :)
What is the measure of MN?
A. 45
B. 29
C. 74
D. 37
Answer:
45°
Step-by-step explanation:
There are sets of formulas you can refer to for different situations like this. In your case here, you need to apply the formula and solve for the unknown. My work is in the attachment.
Answer: 45 degrees
Step-by-step explanation:
(1 mark)
13.
The time to finish a certain work decreases as the number of worker increases
in number. What kind of proportion is illustrated in the situation?
Answer:
Inverse proportion
Step-by-step explanation:
Inverse proportion: in this type of relation, two quantities proportion such that one decreases and other increases or vice-versa.
So, in the given question when the number of workers increases, time is taken for certain work decreases.
So, Inverse proportion is the correct answer.
Which of the following shapes, when flopped, will always coincide with the original shape?
Which of the following inequalities matches the graph? (1 point)
x<5
x>5
y<5
y>5
Answer:
x≤5Step-by-step explanation:
The line is vertical, so it is on x
the line is on x=5
the line is whole so it is less or greater than and equal to
the shaded part is to the left, so it is less than
So, the inequality represented by the graph is x≤5
if the edges of the base of a rectangular prism are 8 cm and 6 cm, and the diagonal is 10√2, what is the volume of the solid?
Answer:
221.12 cm^3
Step-by-step explanation:
Imagine that you have the 6cm side of the prism base facing you, and that you cut the prism in half through the vertex. Doing this will form two triangles. The hypotenuse of the triangle is the same as the "diagonal" that is 10√2 cm. The base of this triangle is half of the 6" side, or 3 cm.
Use the Pythagorean Theorem to determine the height (h) of the prism:
h^2 + 3^2 = (10√2)^2, or
h^2 = 200-9 = 191
Then the height is √191 cm
and the base area is 6cm times 8 cm, or 48 cm^2
and so we end up with the volume V = (1/3)(base area)(height), or
V = (1/3)(48 cm^2)(√191 cm), or
roughly 221.12 cm^3
Monica tosses a fair 6-sided die. If the roll is a prime number, then she wins that amount of dollars (so that, for example, if she rolls 3, then she wins 3 dollars). If the roll is composite, she wins nothing. Otherwise, she loses 3 dollars. What is the expected value of her winnings on one die toss? Express your answer as a dollar value to the nearest cent.
Answer:
Expected win = $15.17 to the nearest cent.
Step-by-step explanation:
Expected win = (1/6)*(1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) = 15.167 or $15.17 to the nearest cent.
The positive expected value means that Monica wins 1.17 dollars on average for each roll.
==================================================
Explanation:
The sample space is {1,2,3,4,5,6} to represent the outcomes of the die.
Of that list, {2,3,5} are prime numbers. Note that 1 is not a prime number. It's not composite either. So Monica will lose money when she rolls a 1. If she rolls {4,6} then she wins 0 dollars.
For any single roll, the probability of landing on that value is 1/6
Multiply 1/6 by each winning amount. Then add up the products
(1/6)*(-3) + (1/6)*(2) + (1/6)*(3) + (1/6)*(0) + (1/6)*(5) + (1/6)*(0)
-3/6 + 2/6 + 3/6 + 5/6
(-3+2+3+5)/6
7/6
1.17 approximately
Monica will get about 1.17 dollars per roll on average. She only loses money on average if the expected value was negative.
The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the sequence 2, -6, 18, -54, ...? an = 2 · 3n - 1 an = 2 · (-3)n - 1 an = 3 · 2n - 1 an = -3 · 2n - 1
Answer:
The second choice
Step-by-step explanation:
So first we would plug in the first term which is 2 so we would get [tex]an=2[/tex] times [tex]rn-1[/tex] so next we would see that the common ration is -3 since every time the number is being multiplied by -3. so then our equation would be [tex]an= 2[/tex] times [tex]-3n-1[/tex]. Now we would just find the choice that matches and it would be the second choice.
Answer:
option 2
Step-by-step explanation:
First term [tex]a_{1} = 2\\[/tex]
common ratio = r = second term ÷ first term
= -6 ÷2 = -4
Plug in the values of [tex]a_{1}[/tex] & r in the formula
[tex]a_{n} = a_{1}*r^{n-1}\\\\\\a_{n}=2 * (-3)^{n-1}[/tex]
A square is shown below. Which expression can be used to find the area, in square units, of the shaded triangle in the square? Fraction 1 over 4 • 6•6 Fraction 1 over 2 •3•3
Fraction 1 over 4 •3•3
Fraction 1 over 2 •6•6
Answer:
Area = [tex]\frac{1}{2} (6)(6)[/tex]
Step-by-step explanation:
Area of Triangle = [tex]\frac{1}{2} (Base)(Height)[/tex]
Where Base = 6 , Height = 6
Area = [tex]\frac{1}{2} (6)(6)[/tex]
Area = 3 * 6
Area = 18 units^2
Answer:
Hey there!
The area of the shaded triangle covers exactly half the square.
Thus, first we find the area of the square, which is 6x6, or 36.
Finally, half of that is 1/4 times 6x6.(Fraction 1 over 2 •6•6 is correct)
Let me know if you need more help :)
Write this number in standard form. 300+80+0.9+0.06+0.001
Hey there! I'm happy to help!
First, let's add the hundreds and the tens.
300+80=380
We see that there is nothing in the ones place, so we keep our ones place 0 and we move onto adding the tenths.
380+0.9=380.9
We add the hundredths.
380.9+0.06=380.96
And finally, we add the thousandths.
380.96+0.001=380.961
Therefore, this number in standard form is 380.961.
Have a wonderful day! :D
Answer:
380.961
Step-by-step explanation:
300+80=380
0.9+0.06+0.001=.961
380+.961=380.961
since there is nothing in the ones place, keep it 0.
Triangle ABC is described below. Find all possible values for B, C, and c.
A= 121.59, a = 27.9 cm, b = 52.6 cm
Apply the rules regarding the use of significant digits to each angle and
length after all computations are complete.
Answer:
c = 27.9
B = 62.13°
C = 89.90°
Step-by-step explanation:
We are given the following values:
A= 121.59°, a = 27.9 cm, b = 52.6 cm
a) Finding side c
We would use Pythagoras Theorem
c² = a² + b²
c = √(a² + b²)
c = √(27.9² + 52.6²)
c = 59.54cm
≈ Approximately = 59.5cm
b) Finding B
We would be using Cosine rule to find Angle B
Cos B = a² + b² - c²/2ab
B = arc cos ( a² + c² - b²/2ac)
B = arc cos( 27.9² + 59.5² - 52.6²/ 2 × 27.9 × 59.5)
B = 62.13268°
B = 62.13°
c) Finding C
We would be using Cosine rule to find Angle C
Cos C = a² + b² - c²/2ab
C = arc cos ( a² + b² - c²/2ab)
C = arc cos( 27.9² + 52.6² - 59.5²/ 2 × 27.9 × 52.6)
C = 89.9°
fleur wants to make tables and chairs. She has a total of 150 wooden boards and 330 nails. 17T + 6C ≤ 150 represents the number of tables T and chairs C she can make with 150 Wooden boards. 34T + 27C ≤ 330 represents the number of tables and chairs she can make with 330 nails. Does Fleur have enough boards and nails to make 3 tables and 9 chairs? Choose 1 answer: (Choice A) Fleur has enough boards and nails. (Choice B) Fleur has enough boards but not enough nails. (Choice C) Fleur has enough nails but not enough boards. (Choice D) Fleur has neither enough boards nor enough nails.
Answer::
Choice B : fleur has enough boards but not enough nails
Answer:
Fleur has enough boards but not enough nails.
Step-by-step explanation:
T = 3
C = 9
substitute
tina bought a notebook for $6.59 a backpack for 24.95 and a pen for $4.98
Answer: 36.52 dollars she spent
What is the slope of the line?
Answer:
y=-3x+4
Step-by-step explanation:
Use rise/run to find slope. Rise= -3, Run= 1
Y-Intercept is found where the line intersects y.
Answer:
The slope of the line is -3.
Step-by-Step Explanation:
You need to find any two points on the line.
I'll chose (0, 4) and (2, -2).
To find slope, you need to use the formula m = y2 - y1 divided by x2 - x1.
m = y2 - y1 / x2 - x1
m = (-2 - 4) / (2 - 0)
m = -6 / 2
Then you must reduce to lowest terms.
m = -3
help i want help plz help me
Answer:
SA = 384 in ^2
Step-by-step explanation:
The surface area of a cube is given by
SA = 6 S ^2 where s is the side length
SA = 6 * (8) ^2
SA = 6 * 64
SA = 384 in ^2
Answer:
384 in^3
Step-by-step explanation:
To find the surface area of a cube, you have to multiply 6(the number of sides on a cube) by *(8)^2. When you plug it in, you get 384 in^3.
Please help me out , Currently stuck on this problem
Answer: it will be 3.7 cuz its perpendicular
have a good day, hey thechesguy nice name and the guy under copied from me.
(will mark brainliest if correct)
Answer:
A = 27π
P =
Step-by-step explanation:
Well if it follows the same proportions as a square then the dotted line is 6 cm.
Triangle
So the area of a triangle is b*h / 2
b = 6
h = 6
6*6 = 36
36 / 2 = 18
A = 18cm^2
So to find the missing side or c we do 6^2 + 6^2 = c^2,
36 + 36 = c^2
72 = c^2
≅8
6 + 6 + 8
= 20cm
Half circle
Now the area of a semicircle is,
pi r^2 / 2
So if the diameter is 6 then the radius is 3.
So we do 3*3 = 9
9 * pi = 9π^2
Perimeter: 6π
____________________________________________________________
Thus,
the area is 27π and the perimeter 26π.
Hope this helps :)
Sphere A has a radius of 24 centimeters, and sphere B has a diameter of 42 centimeters. The radius of sphere A is
multiplied by what factor to produce the radius of sphere B?
c
+ N100 N
AN
Mark this and return
Save and Exit
Answer:
multiply by a factor of 7/8
Step-by-step explanation:
sphere A radius is 24 and Sphere B radius is 21
24x=21
x = 7/8
Answer:
multiply by a factor of 7/8
The function f(x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2,–1)} Which equation is true?
Answer:
y = -6x + 6
Step-by-step explanation:
To make an equation you need to find the slope first
To do that use the expression y2-y1/x2-x1 (-6)
Now plug that in to y = mx + b
Lastly you substitute any coordinate and find b
y = -6x + 6
Answer:C
Step-by-step explanation:
The points (3,0) and (6,4) are adjacent vertices of a square, What is the area of the square, in unit squared? HELP PLS
Answer: 25
Step-by-step explanation:
Find the distance from (3, 0) to (6,4). That is the side length (s).
Area (A) = s²
[tex]s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\s^2=(x_2-x_1)^2+(y_2-y_1)^2\\\\s^2=(6-3)^2+(4-0)^2\\\\s^2=3^2+4^2\\\\s^2=9+16\\\\s^2=25\\\\\\A=s^2\\\\\large\boxed{A = 25}[/tex]
Answer:
25 units squared
Step-by-step explanation:
Distance between (3, 0) and (6, 4)
√(3-6)²+(0-4)² = 5
Area = 5 * 5 = 25 units squared
*PLEASE ANSWER* If we decrease a dimension on a figure, how is the figure’s area affected? a.) The area decreases. b.) The area becomes 0. c.) The area increases. d.) The area remains the same.
Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.
The area of the figure decreases when the dimension is decreased
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the figure be represented as ABCD
where ABCD is a rectangle
Now , the measures of the sides of the rectangle be
The length of the rectangle = L
The width of the rectangle = W
And , Area of Rectangle = Length x Width
On simplifying , we get
Area of rectangle = LW
when the dimension of one of the unit is decreased , we get
when L = L/2
Area of rectangle = ( LW) / 2
So , the area of the figure is decreased bu ( 1/2 )
Hence , the area of the figure decreases
To learn more about area of rectangle click :
https://brainly.com/question/15225905
#SPJ3
what's four to the six power times four to the seventh power
Answer:
67,108,864 or 4^13
Step-by-step explanation:
4^6*4^7=4^13 you basically just add the exponents since the base is the same.
Since these two powers have the same base of 4, you can multiply
them together by simply adding their exponents to get 4¹³.
This idea is called the product rule.
A common mistake in this problem would be to multiply
the bases together and give an answer of 16¹³.
It's important to understand however that the 4's in this problem can't
be multiplied together because they're not coefficients, they're bases.
When applying your exponent rules, your base will never change.
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x -4
h(x) = 3
h(x) =
77 X
This is the same as h(x) = x/4
In decimal form, it would be h(x) = 0.25x
=============================================
Explanation:
Inverses undo the original function. The original function tells us to take any input (x) and multiply by 4 to get the output y = f(x) = 4x
To get the inverse, we reverse the operation applied here. The opposite of multiplication is division. So we'll divide by 4 instead of multiply by 4. This is why the answer is x/4 or (1/4)x
-----------
Another approach is to do the following: Replace f(x) with y. Swap x and y. Solve for y
f(x) = 4x
y = 4x
x = 4y
4y = x
y = x/4
h(x) = x/4
We end up with the same result as before.
-----------
Extra info:
For any real number x, the following two equations are true
h( f(x) ) = x
f( h(x) ) = x
A man flips a coin repeatedly until he obtains a heads. This probability setting describes _______ events. answer quick pls
Answer: I'm sure it describes experimental events? Is that an option? Because he's experimenting by flipping the coin. If not, just contact me! :)
Here and happy to help.
Find the partial sum of the first 4 terms of the series:
5n + 2
n=1
60
58
85
None of these
Answer:
[tex]\large \boxed{\sf \ \ \sum_{n=1}^{n=4} (5n + 2) = 58 \ \ }[/tex]
Step-by-step explanation:
Hello,
We need to compute the following:
[tex]\displaystyle \sum_{k=1}^{k=4} (5\cdot k + 2)= (5*1+2) + (5*2+2)+ (5*3+2) + (5*4+2)\\\\=7 + 12 + 17 + 22 = 19 + 39 = 58[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
help pls. Find the period of the graph shown below.
Answer:
Option A. π
Step-by-step explanation:
The period of a simple harmonic motion is the time taken to make one complete circle or oscillation.
Considering the graph given above, we can see that at the completion of one circle, the angle θ, has value as pi (π).
This value is equivalent to the period of the graph.
Therefore, the period of the graph shown above is π.
Of 28 students taking at least one subject, the number taking Math and English but not History equals the number taking Math but not History or English. No student takes English only or History only, and six students take Math and History but not English. The number taking English and History but not Math is 5 times the number taking all three subjects. If the number taking all three subjects is even and non-zero, the number taking English and Math but not History is
Answer:
The answer is 5 students taking English and Math but not History
Step-by-step explanation:
The total students are 28 which are divided into 5 possible groups with no students taking either English only or History only:
Taking Math only Taking English and Math but not HistoryTaking Math and History but not EnglishTaking English and History but not MathTaking triple subjectsThe number of students in group 3 is 6. Hence, the total number in group 1, 2, 4 and 5 is: 28 - 6 = 22
Also, the number of students in group 4 is five times the number in group 5, therefore: group 2 + group 5 = 6 times group 5
Additionally, the number of students in group 1 equals that in group 2.
Hence, the equation is: 6 x group 5 + 2 x group 2 = 22 => group 2 = 11 - 3 x group 5 => group 2 = 5 because group 5 is an even number and non-zero, it must be 2.
Given the figure below, find the values of x and z.
Answer:
z = 96; x = 8.
Step-by-step explanation:
z = 96. This is because the angle measuring z degrees is a vertical angle of the angle measuring 96 degrees, which means that the two angles are congruent.
The angle measuring 5x + 44 degrees forms a straight angle with the 96 degree angle. That means that the measurements of the two angles will add to be 180 degrees.
5x + 44 + 96 = 180
5x + 140 = 180
5x = 40
x = 8
Hope this helps!