Answer: A. 210
Step-by-step explanation:
We know that the number of combinations of n things taking r at time is given by expression :-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] (1)
The given expression : [tex]^{10}C_{6}[/tex] which basically gives the number of combinations of 10 things taking 6 at a time.
Using (1) , we have
[tex]^{10}C_{6}=\dfrac{10!}{6!(10-6)!}\\\\=\dfrac{10\times9\times8\times7\times6!}{6!4!}\\\\=\dfrac{10\times9\times8\times7}{4!}\ \ [\text{Cancel }6!\text{ from numerator and denominator}]\\\\=\dfrac{10\times9\times8\times7}{4\times3\times2\times1}\\\\=210[/tex]
Hence, the correct answer is A. 210 .
Simplify but do not evaluate. 2 to the power of 3 times 2 to the power of 4.
A ball is kicked upward with an initial velocity of 56 feet per second. The ball's height h (in feet) can be expressed as a function of time t (in seconds) by the equation h = -16t2 + 56t. How much time does the ball take to return to the ground?
A) 1.75 seconds
B) 2.50 seconds
C) 2.75 seconds
D) 3.50 seconds
Answer:
D) 3.50 seconds
Step-by-step explanation:
You are interested in the positive value of t such that h=0. Substituting 0 for h, we get ...
0 = -16t^2 +56t
0 = -16t(t -3.5) . . . . . factored form
The product is zero when the factors are zero. Here, the factor of interest is ...
0 = t-3.5
3.5 = t . . . . . add 3.5 to both sides
The ball takes 3.5 seconds to return to the ground.
Final answer:
The ball takes D. 3.5 seconds to return to the ground.
Explanation:
To find the time it takes for the ball to return to the ground, we need to set the height function h equal to 0 and solve for t.
So, we have the equation -16t^2 + 56t = 0.
Factoring out t, we get t(-16t + 56) = 0.
Setting each factor equal to 0, we find that t = 0 or t = 3.5.
Since time cannot be negative, we disregard the t = 0 solution.
Therefore, the ball takes 3.5 seconds to return to the ground.
Find the area of an equilateral triangle with a radius 6 square root of 3. Leave your answer in simplest radical form
Final answer:
The area of the equilateral triangle with a radius of 6√3 is 27√3 square units.
Explanation:
An equilateral triangle has all three sides equal in length and all three angles equal to 60 degrees. In this case, the radius of the circumscribed circle is given as 6√3. This radius is equal to the length of the side of the equilateral triangle.
To find the area of an equilateral triangle, we can use the formula A = (sqrt(3)/4) * s^2, where s is the length of the side of the triangle.
Substituting the given value of the radius into the formula, we have:
A = (sqrt(3)/4) * (6√3)^2 = (sqrt(3)/4) * 108 = 27sqrt(3).
Therefore, the area of the equilateral triangle is 27sqrt(3) square units.
What are the coordinates of the vertex for f(x) = 2x^2 + 4x + 9?
(−2, 4)
(−1, 7)
(1, 15)
(2, 9)
Which transformations map the strip pattern onto itself
Answer: a horizontal translation and a 180 rotation
Step-by-step explanation:
name the property used in each equation. then find the value of n.
2.) 1·n=8
3.) 28·n=0
4.) 0+n=22
5.) 1/4·n=1
Samuel drove 28 miles in 32 minutes. Beverly drove 42 miles in 48 minutes.
Are the ratios of miles to minutes for Samuel and Beverly proportional?
Answer:
Yes. Ratios of miles to minutes for Samuel and Beverly are proportional
Step-by-step explanation:
Samuel's speed can be calculated as following:
[tex]28/32=0,875[/tex]
0,875 miles per minute.
On the other hand Beverly's speed can be calculated as following:
[tex]42/48=0,875[/tex]
0,875 miles per minute
If we convert the speed to mile per hour:
[tex]0,875*60=52,5[/tex]
It can be easily seen that both Samuel and Beverly drove at the same speed at 52,5 miles per hour.
Liams entire school is traveling by bus to the new aquarium there are 665 boys and 473 girls in liams school if each bus can hold 45 students how many buses will be needed.
Eleven less than a number is more than seventeen in number form
The Smiths plan to recarpet their family room, which measures 15 ft. by 20 ft. How many square yards of carpet are needed?
Answer: [tex]33\frac{1}{3}[/tex] square yards of carpet is needed.
Step-by-step explanation:
Given: The dimensions for the carpet is 15 ft. by 20 ft.
We know that area ( in square units ) of a rectangle is given by :-
[tex]Area=length\times width[/tex]
Therefore, area of the required carpet is given by :-
[tex]Area=20\times15=300\text{ square feet}[/tex]
We know that 1 feet =1/3 yard
Now,
[tex]300\text{ square feet}=300\times\frac{1}{3}\times\frac{1}{3}\\=\frac{100}{3} \text{square yards}=33\frac{1}{3}\text{ square yards}[/tex]
Hence, [tex]33\frac{1}{3}[/tex] square yards of carpet is needed.
one horsepower is equal to how many foot pounds of work per second
which ratio is proportional to 10/24
A 20/36
B 5/8
C 35/84
D 5/6
Answer:
C 35/84
Step-by-step explanation:
The given ratio is less than 1/2. Only one answer choice is less than 1/2: 35/84.
__
The given ratio reduces to 5/12. The reduced ratios of the answer choices are ...
A 5/9
B 5/8
C 5/12 . . . . your answer
D 5/6
what is 32 percent of 60
A piece of cloth is folded into a square with a side length measuring x inches. When it is unfolded, it has an area of x2 + 27x + 162 square inches.
Which could be the dimensions of the rectangular piece of cloth when it is unfolded? Remember, the area of a rectangle can be determined using the formula A = lw.
we need to factor the expression
[tex] x^{2} + 27x + 162 [/tex]
Equate to zero the expression
[tex] x^{2} + 27x + 162=0 [/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex] x^{2} + 27x =-162 [/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex] x^{2} + 27x +182.25=-162+182.25 [/tex]
[tex] x^{2} + 27x +182.25=20.25 [/tex]
Rewrite as perfect squares
[tex] (x+13.5)^{2}=20.25 [/tex]
[tex] (x+13.5)=(+/-)4.5 [/tex]
[tex] x1=-13.5+4.5= -9 [/tex]
[tex] x2=-13.5-4.5= -18 [/tex]
Hence
[tex] x^{2} + 27x + 162 =(x+9)*(x+18) [/tex]
Remember that the area of the rectangle is equal to
[tex] A=L*W [/tex]
therefore
the answer is
the dimensions of the rectangular piece of cloth could be
[tex] L=(x+18)\ inches\\ W=(x+9)\ inches [/tex]
in the fraction 3/5 which statement best describes the denominator
What is the exact value for the expression the square root of 56. − the square root of 14. + the square root of 126.? Simplify if possible.
the square root of 14.
4 the square root of 14.
2 the square root of 42.
8 the square root of 42.
...?
Answer:
B- [tex]\sqrt(56)-\sqrt(14)+\sqrt(126)=14.966[/tex]
Step-by-step explanation:
Given equation : square root of 56 − the square root of 14 + the square root of 126 or [tex]\sqrt(56)-\sqrt(14)+\sqrt(126)[/tex]
Solution of the equation :
[tex]\sqrt(56)-\sqrt(14)+\sqrt(126)[/tex]
= [tex]2\sqrt(14)-\sqrt(14)+3\sqrt(14)[/tex]
= [tex]\sqrt(14)(2-1+3)[/tex]
= [tex]4\sqrt(14)[/tex]
=14.966
Now,
square root of 14 =√14 =3.7414 the square root of 14 = 4√14 = 14.9662 the square root of 42= 2√42 = 12.9618 the square root of 42 = 8√42= 51.845Therefore, Option B is correct
Fill in the missing numbers to complete the factorization. Some of the numbers could be negative. Type the numbers in increasing order.
x 3 + 2x 2 - x - 2 = (x +
Answer:
[tex]x^3+2x^2-x-2=(x+1)(x-1)(x+2)[/tex]
Step-by-step explanation:
We have given equation : [tex]x^3+2x^2-x-2=(x+[/tex]
To find : the missing numbers
We have given that missing numbers complete the factorization
so, we find the factors of the given equation
[tex]x^3+2x^2-x-2=0[/tex]
with the help of graph(attached) we find the roots of the equation or you can also take help of hit n trial method.
Roots of the equation are = 1,-1,-2
therefore the factors are (x+1)(x-1)(x+2)
and the missing terms are the factors of the equation = (x+1)(x-1)(x+2)
Answer:
[tex](x-1)>(x+1)>(x+2)[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^3+2x^2-x-2[/tex]
Factorizing the above equation, we get
[tex](x+1)(x^2+x-2)[/tex]
[tex](x+1)(x^2+2x-x-2)[/tex]
[tex](x+1)(x(x+2)-1(x+2))[/tex]
[tex](x+1)(x-1)(x+2)[/tex]
which is the required factorized form of the given equation.
Now, the numbers in increasing order are:
[tex](x-1)>(x+1)>(x+2)[/tex]
A certain small factory employs 98 workers of these 10 recieve a wage of 150 dollars per day and the rest recieve 85.50 dollars a day to the management a week is equal to 6 working days how much does the factory pay out for each week
Answer:
The factor payout for each week is $54144. Below is the explanation
Step-by-step explanation:
Given:
There are 98 employs
10 of them receive $150 per day
88 of them receive $85.50 per day.
There are 6 working days in a week.
To find:
Let's find the wage per week by multiplying the wage per day by the number of people and the number of days in a week.
10 of them receive $150 per day.
So, they will receive $150*10*6
Which is simplified as $9000.
88 of them receive $85.50 per day
So, they will receive $85.50*88*6
Which is simplified to $45144.
So, the sum of wages for both would be $9000+$45144.
Add them together, which gives $54144.
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Of the students in ms. dancer's class, 6 walk to school. this represents 30% of her students. how many students are in ms. dancer's class?
The function p(t) represents the value of a new car t years after it was manufactured.
p(t)=24,525(0.94)^t
What does the value 0.94 represent in this situation?
The value of the car increases by 94% each year.
The value of the car decreases by 94% each year.
The value of the car is 0.94 times the value of the car the previous year.
The initial value of the car is 0.94.
Answer:
The value of the car is 0.94 times the value of the car the previous year.
Sarah's age is five less than twice her sister's age. Sarah is fifteen years old.
Which equation could you use to solve for the age of Sarah's sister?
2x - 5 = 15
2(15) - 5 = x
15 = 5 - 2x
15 - 5 = 2x
Which term describes a rate in which the second quantity is 1?
unit rate
percent
proportion
ratio
What segment is an altitude of triangle ABC?
segment AC
segment BC
segment BD
segment CD
...?
Marietta drives her tow truck 312 miles in 8 hours. What is her average speed in miles per hour? Be sure to include the equation for speed in your answer.
The average speed in miles per hour is 39mi/hr
How to calculate Speed of a bodySpeed is the ratio of distance with respect to time. The formula for calculating speed is expressed as:
Speed = Distance/Time
Given the following
Distance = 312 miles
Time = 8 hours
Substitute
Speed = 312/8
Speed = 39mi/hr
Hence the average speed in miles per hour is 39mi/hr
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The equation √7-x=x 5 has two possible solution.
Answer:
What is the extraneous solution of the equation? Answer: x= -9
What is the true solution of the equation? Answer: x= -2
This is the correct answer.
Hoped this helped!
Hillary wants to go on the latin club trip to italy it cost 2730 for the trip the trip is 30 weeks away and she wants to make equal weekly payments how much money altogether does hillary need to pay at the end of week eight
How many square feet of outdoor carpet will need for this hole
Answer:
[tex]Area=63 square foot[/tex]
Step-by-step explanation:
The dimensions of the outdoor carpet which is rectangle in shape are:
L=6 ft and w=12 ft.
The dimensions of the indoor carpet that is triangle in shape are:
b=3 ft and h=9 ft.
Now, area of the outdoor= Area of the green region-Area of triangular region
[tex]Area=l{\times}b-\frac{1}{2}{\times}b{\times}h[/tex]
[tex]Area=6(12)-\frac{1}{2}{\times}3{\times}6[/tex]
[tex]Area=72-9[/tex]
[tex]Area=63 square foot[/tex]
Thus, the area of the outdoor carpet is 63 square foot.
Find the domain and range of the relation and determine whether it is a function.
Domain: positive integers; range: positive integers; no, it is not a function.
Domain: x > 3; range: y > 0; yes, it is a function.
Domain: all real numbers; range: all real numbers; yes, it is a function.
Domain: x ³ 0; range: y > 3; no, it is not a function.
Answer:
y>0
Step-by-step explanation:
graph the fraction 1/2 on the number line.
the number of equally sized spaces needed between 0 and 1 is ?
The gross weight of a package and its contents is 11 pounds 5 ounces . If the packaging weighs 1 pound 15 ounces , what's the net weight of the contents