Answer:
17C5+11C5
Step-by-step explanation:
Well there are 17 and chooses 5 that's 17C5
there are 11 men abd chooses 5 that's 11C5
so add them up
17C5+11C5
The combination helps us to know the number of ways an object can be selected without a particular manner. The number of ways in which 5 men and 5 women can be selected is 2,858,856.
What is Permutation and Combination?Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be selected without a particular manner. A combination is denoted by 'C'.
[tex]^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given that from a group of 17 women and 11 men, a researcher wants to randomly select 5 women and 5 men for a study.
Now, the number of ways for selection can be written as,
Number of ways in which men can be selected = ¹¹C₅ = 462
Number of ways in which women can be selected = ¹⁷C₅ = 6188
Further, the number of ways for selection can be written as,
Number of ways = Number of ways in which men can be selected × Number of ways in which women can be selected
Number of ways = 462 × 6188
Number of ways = 2,858,856
Hence, the number of ways in which 5 men and 5 women can be selected is 2,858,856.
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one-third of a number is subtracted from 11.The result is one and half times the original number. what is the number.
If 11 is subtracted from 3 times the number, the result is the square of 5 less than the number. What are the set of numbers that satisfy
Top Hat Soda has 300,000 milliliters of cola to bottle. Each bottle holds 500 milliliters. How many bottles will the cola fill?
Answer:
600 bottlesStep-by-step explanation:
Given that Top Hat Soda has 300,000 millilitres of cola to bottle and,
a bottle is 500 millilitres in capacity.
To find the amount of bottles that will fill the Top Hat Soda,
we have to divide Top Hat Soda by the 500 millilitres bottle
we have:
Number of bottles needed to fill Top Hat Soda= 300,000/500 = 600 bottles.
Hence 600 bottles will fill the Top Hat Soda
You have $95 in your bank account. Each week you plan to deposit $9 from your allowance and $10 from your paycheck. The equation b=95+(10+9)w gives the amount b in your account after w weeks. How many weeks from now will you have $220 in your bank account?
There will be $220 in the account after ___ weeks
Answer:
7 weeks
Step-by-step explanation:
b=95+(10+9)w
Combine like terms
b=95+(19)w
Let b = 220
220 = 95 + 19w
Subtract 95 from each side
220-95 = 19w
125 = 19w
Divide each side by 19
125/19 = w
6.578947368
Round up
After 7 week
Find the missing value.
Hint: Use the number line to find the missing value.
-4 -
9
{
--15
开
15
-10
-5
0
5
10
Answer:
5
Step-by-step explanation:
-4 = x - 9
I hope this helps! :)Answer:
5
Step-by-step explanation:
5 - 9 = -4
Joan weighs 10 pounds less than her older sister. The average of the two sisters’ weights is 85 pounds. How much does Joan’s older sister weigh?
Answer:
Joan's older sister weighs 90 pounds
Step-by-step explanation:
x = older sister
x - 10 = Joan
(x + (x-10))/2 = 85
2x - 10 = 170
2x = 180
x = 90
Answer:
90 pounds
Step-by-step explanation:
We can set up an equation to find their weights.
Let's start by naming Joan's weight x.
Her sister's weight would then be x+10, since Joan weighs 10 pounds less.
To find the average between 2 numbers, you need to add them together, then divide by 2.
So we can set up the following equation:
(x+x+10)/2=85
Now let's isolate x.
We can first multiply both sides by 2.
x+x+10=170
Combine like terms.
2x+10=170
Subtract 10 from both sides.
2x=160
Subtract both sides by 2.
x=80
Joan weighs 80 pounds.
x+10 is her sister's weight.
80+10=90
Joan's older sister weighs 90 pounds.
Please help, urgent... Which transformation can not be used to prove that triangle ABC is congruent to triangle DEF?
Answer:
Dilation
Step-by-step explanation:
Dilation can only be used to prove that certain figures are similar
3/4 + z = 5/6 what does z equal
Answer:
1/12
Step-by-step explanation:
3/4 + z = 5/6
Subtract 3/4 from each side
3/4 -3/4+ z = 5/6-3/4
z = 5/6 -3/4
Get a common denominator of 12
z = 5/6 *2/2 -3/4 *3/3
z = 10/12 - 9/12
z = 1/12
A is (1, –2) and B is (3, 6).
a. Find the length of AB.
b. Find the mid-point of AB.
c. Find the equation of the perpendicular
bisector of AB.
Answer:
I know mid point is (2,2)
Step-by-step explanation:
95°
6rº + 47°
r_ degrees
Answer:
r = 8°
Step-by-step explanation:
95° = 6r° + 47° ( vertically opposite angles are equal)
6r° = 95° - 47°
6r = 48°
r = 48°/6
r = 8°
Answer: r = 8
Step-by-step explanation:
The angles a VOA vertically opposite angles which means they are congurent and equal
6r + 47 = 95
6r = 95 - 47
6r = 48
r = 48/6
r = 8
please click thanks and mark brainliest if you like :)
help! ill give brainliest
Answer:
84 square inches is the correct answer.
Step-by-step explanation:
I am 100% sure of that.
Hope this helps....
Have a nice day!!!!
If the dimensions of a rectangle are 2x + 1 by x + 1, find its area, in terms of x.
Answer:
3x + 1
Step-by-step explanation:
Area Of a rectangle = L x B
= 2 + 1 + 1
= 2 + + 1
= 2 + + 1
= 3 + 1
Answer From Gauth Math
-8+4x-12=-4(2x-8) help me plz
Answer:
x = 13/3Step-by-step explanation:
[tex]-8+4x-12=-4\left(2x-8\right)\\\\\mathrm{Group\:like\:terms}\\\\\mathrm{Subtract\:the\:numbers:}\:-8-12=-20\\\\4x-20=-4\left(2x-8\right)\\\\\mathrm{Expand\:}-4\left(2x-8\right):\quad -8x+32\\4x-20=-8x+32\\\\\mathrm{Add\:}20\mathrm{\:to\:both\:sides}\\4x-20+20=-8x+32+20\\\\Simplify\\\\4x=-8x+52\\\\\mathrm{Add\:}8x\mathrm{\:to\:both\:sides}\\\\4x+8x=-8x+52+8x\\\\\mathrm{Simplify}\\\\12x=52\\\\\mathrm{Divide\:both\:sides\:by\:}12\\\\\frac{12x}{12}=\frac{52}{12}\\\\x=\frac{13}{3}[/tex]
Answer:
Step-by-step explanation:
-8+4x-12 =-8x+32
4x+8x=32+8+12
12x=52
x=52\12
x=41.3
Help anyone can help me do this question,I will mark brainlest.
Answer:
10. x is 15; y is \sqrt104. 11. \sqrt5
Step-by-step explanation:
for 10:
first we find the face on the left side; which according to the pythagorean theorem x is 144 + 81 =225 = x = 15. and y is 11^2 + y^2 = 225 = 225 - 121 = y^2 = y = the square root of 104.
for 11:
144 + y^2 = 169 = y^2 = 25 = y = 5. because the two sides are equivalent, the base is also 5 for the left part of the triangle. therefore, 5^2 + 5^2 = x^2 which means x is the square root of 5.
What kind of polygon is bounded by the line segments passing through points A, D, C, and E? What is the sum of the interior angle measures for this polygon?
Answer:
Step-by-step explanation:
Answer:
The polygon formed through points A, D, C, and E is a quadrilateral. The sum of the interior angle measures for any quadrilateral is 360°.
Step-by-step explanation:
mΖΗ - 67
pleas please please help!! i’m doing angles
Answer:
could u take a picture of the angles please
Step-by-step explanation:
2. find out the h.c.f
2a , 1st exp= a2 + ab
= a(a+b)
2nd exp = a2-b2
= (a+b) (a-b)
HCF = (a+b)
b, 1 st exp= (a+b)2
= (a+b)(a+)
2 nd exp = a2-b2
= (a+b) ( a-b)
HCF = (a+b)
c, 1 st exp= (a-1)2
= (a+1) (a-1)
2nd exp= a2-1
= (a+1)(a-1)
HCF = (a-1)
d, 1st exp= (x-2)(x-3)
= x(x-3)-2(x-3)
= x2 - 3x - 2x + 6
= x2- 5x+ 6
= x2 - (3+2)x + 6
=x2 -3x-2x+ 6
= x(x-3) -2(x-3)
=(x-3)(x-2)
2 nd exp = (x+2) (x-3)
= x( x-3) + 2 (x-3)
= x2 - 3 x+ 2x -6
= x(x-3) + 2(x-3)
=(x-3) ( x+ 2)
HCF = (x-3)
According to the graph, what is the value of the constant in the equation
below?
A. 30
B. 72
C. 60
D. 15
Greetings from Brasil...
As stated in the statement:
HEIGHT = CONSTANT ÷ WIDTH
H = C ÷ W
so, isolating the variable C....
C = H · W
choosing any point on the graph...
(2; 30) ⇒ W = 2 and H = 30
C = H · W
C = 30 · 2
C = 60The value of the constant in the equation shown in the figure would be, 60. Hence option C is true.
Given that,
The graph is the relation between Height and width.
As is given in the graph:
Height = Constant / Width
We observe that the graph passes through (2,30), (5,12), (10,6), (30,2)
So, by using any one point we may get the value of constant( since it is a fixed quantity)
Hence, using the point (2,30)
Width = 2
And, Height = 30
So, we get:
Constant = 2 × 30
= 60
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PLEASE help!!!
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.
Answer:
Step-by-step explanation:
The shaded regions consist of a triangle and a semicircle
Area of shaded regions = Area of Triangle + Area of semicircle
Area of Triangle = (h x b) ÷ 2
Height, h = 10 cm
Base, b = 8 cm
Are of the triangle component = (10 x 8) ÷ 2
= 80 ÷ 2
= 40 cm^2
Area of semicircle = πr^2 ÷ 2
Diameter, D = 8 cm
Radius, r = 8 cm ÷ 2 = 4 cm
Are of the semicircle component = [π(4^2) ÷ 2)
= 16π ÷ 2
= 16π cm^2
Total area of shaded regions
= (40+16π) cm^2
= 8 (5 +2π) cm^2
Answer:
[tex]\boxed{\sf Area = 8\pi + 40\ cm^2}[/tex]
[tex]\boxed{\sf Perimeter = 4\pi + 22\ cm}[/tex]
Step-by-step explanation:
Area of the figure:
Firstly: Area of semicircle:
[tex]\sf \frac{\pi r^2}{2} \\Where\ r = 4 \ cm\\\frac{\pi (4)^2}{2} \\\frac{16 \pi}{2}\\8 \pi \ cm^2[/tex]
Then Area of Triangle
[tex]\sf 1/2 (Base)(Height)\\1/2(10)(4)\\10*2\\20\ cm^2[/tex]
Area of Figure = Area of Semicircle + 2(Area of triangle)
=> 8π + 2(20)
=> 8π + 40 cm²
Perimeter of Semicircle:
Firstly, we'll have to find the hypotenuse
[tex]\sf c^2 = a^2+b^2\\c^2 = 4^2+10^2\\c^2 = 16+100\\c^2 = 116\\c = 11\ cm[/tex]
Then, Perimeter of the semi-circle:
=> πr
Where r = 4 cm
=> 4π
Now, the perimeter of the whole figure:
=> 4π + 2(11)
=> 4π + 22 cm
How do I solve for x.
Answer:
x = 17
Step-by-step explanation:
(whole secant) x (external part) = (whole secant) x (external part)
(x+7) * 7 = ( 13+8) *8
(x+7) * 7 = ( 21) *8
Divide each side by 7
x+7 = 21/7 *8
x+7 = 3*8
x+7 = 24
Subtract 7
x = 17
Answer:
The answer is x = 17
Though I think the other guy explained it better
HURRY PLZ WILL GIVE BRAINIEST IF I CAN 4f+4+3d-6-3f
Answer:
3d + f -2
Step-by-step explanation:
= 4f+4+3d-6-3f
= f+3d-6
= 3d+ f - 6
On the circle below, tangent line BC¯¯¯¯¯ is constructed by striking an arc from point D that intersects circle A at point B. The measure of EC¯¯¯¯¯ is 8 units and other measures are shown on the diagram below. Enter the distance from point D to point B.
Answer:
[tex]\huge\boxed{BD = 12\ units}[/tex]
Step-by-step explanation:
If AB = 5 , then AE = 5 [Radii of the same circle]
So,
AC = AE + EC
AC = 8+5
AC = 13 units
Now, Using Pythagorean theorem to find the missing side i.e. BD because tangent strikes the circle at 90 degrees making the triangle a right angled triangle
[tex]c^2=a^2+b^2[/tex]
Where c = AC , a = BD and b = AB
[tex]13^2 = BD^2+5^2[/tex]
169 = BD² + 25
Subtracting 25 to both sides
169 - 25 = BD²
BD² = 144
Taking square root on both sides
BD = 12 units
Simplify 3 squared 2 ⋅ 3 squared 5
Answer:
45
Step-by-step explanation:
(
3
√
5
)
2
9
√
5
2
Rewrite
√
5
2
as
5
.
9
⋅
5
Multiply
9
by
5
.
45
Answer:
2187
Step-by-step explanation:
I'm guessing you meant ^ as squared? Therefore, our equation is [tex]3^23^5[/tex]. We can simplify using the rule of exponents, giving us [tex]3^7[/tex]. [tex]3^7=2187[/tex].
20° + 2pº
70°
p =
degrees
[tex]\\ \sf\longmapsto 20°+2p=70[/tex]
[tex]\\ \sf\longmapsto 2p=70-20[/tex]
[tex]\\ \sf\longmapsto 2p=50[/tex]
[tex]\\ \sf\longmapsto p=\dfrac{50}{2}[/tex]
[tex]\\ \sf\longmapsto p=25[/tex]
If A= and then find : 2A + 3B
Step-by-step explanation:
Answer:
Step-by-step explanation:
13824 = 2a*3b
13824= 6ab
Ab = 13824/6
A= 13824/b
B= 13824/a
In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP? one half the area of circle L one third the area of circle L one half the circumference of circle L one third the circumference of circle L
Question
In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP?
• one half the area of circle L
• one third the area of circle L
• one half the circumference of circle L • one third the circumference of circle L
Answer:
• one third the circumference of circle L
Step-by-step explanation:
In the question, we are told that:
In circle L, arc MNOP is 120° and the radius is 5 units.
We are asked to find the statement amongst the options that describes the arc length MNOP of Circle L
Step 1
Find the Area of circle
Area of a circle = πr²
r = 5 units
Area of a circle = π × 5²
Area of a circle = π × 25
Area of a circle = 78.53981634 square units
Step 2
Find the arc length of a circle
Arc length = 2πr × θ /360
r = 5 units
θ = 120°
Arc length = 2 × π × r × 120/360
Arc length = 2 × π × r × (1/3)
Arc length = 2 × π × 5 × (1/3)
Arc length = 10.47198 units
Step 3
Circumference of a circle = 2πr
= 2 × π × 5
= 31.415926536 units
Since the Circumference of a circle = 2πr
Arc length of the circle for the above calculation, = 2πr × 1/3
Therefore, the statement that best describes the arc length MNOP of Circle L is:
" the arc length MNOP is one third the circumference of circle L"
Answer:
the arc length MNOP is one third the circumference of circle L
Step-by-step explanation:
i fishie yupo
Let X denote the block rate of the host hotel for a particular conference, and let Y denote the lowest room rate available in the host hotel outside of the conference block. For a conference that requires a two-night hotel stay, which one of the following expressions represents the least amount of discount on the conference registration fee that, according to the article, would be sufficient to deter conference attendees from employing the ROB strategy in choosing accommodations?
A. X+Y2X+Y2
B. X−Y2X−Y2
C. X−YX−Y
D. X+YX+Y
E. 2(X−Y)
Answer:
C. X-Y X-Y
Step-by-step explanation:
The question asks to identify the least amount of discount on the conference registration. If the registration discount is at least half of the possible saving of ROB then all attendees will stay within the block. X is the block rate and Y is the non block rate. The saving for staying two nights outside the block is 2 (X-Y)
Which of the following lists of three numbers could form the side lengths of a triangle? [tex]A. $10, 20, 30$B. $122, 257, 137$C. $8.6, 12.2, 2.7$D. $\frac{1}{2}, \frac{1}{5}, \frac{1}{6}$[/tex]
Answer:
B. 122, 257, 137
Step-by-step explanation:
The triangle inequality rule states that the sum of any two sides of a triangle must be greater than the third side. If A, B and C are sides of a triangle then A + B > C, A + C > B, B + C > A
Testing for the options:
1) 10, 20, 30
10 + 20 (= 30) is not greater than 30. It cannot form a triangle
2) 122, 257, 137
122 + 137 (259) is greater than 257. It can form a triangle
3) 8.6, 12.2, 2.7
8.6 + 2.7 (11.3) is not greater than 12.2. It cannot form a triangle
4) 1/2, 1/5, 1/6
1/5 + 1/6 (11//30) is not greater than 1/2. It cannot form a triangle
Patrick raced round a 440 metre circular track and stopped suddenly after 900 metres . How far was she from the starting point at the 900 metre mark ? Solve
Answer:
20 meters
Step-by-step explanation:
The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.
So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.
The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be [tex]900-880=20[/tex] meters from the starting point.
2500 feet is to how many meters
Answer: is 762 meters
Step-by-step explanation:
One foot is equal to 0.3048 meters so multiply 2500 by 0.3048 to find how many meters there are.
2500 * 0.3048 = 762
Answer:762.5 meters
Step-by-step explanation:
1 foot =0.305 m
Hence,0.305×2500=762.5 metres as the answer.
gordon types 1,972 words in 29 minutes
Gordon types _______ words per minute
PLSSS HELPP ME
Answer:
68 words
Step-by-step explanation:
To find how many words Gordon types per minute :
1972 ÷ 29 = 68 #