Answer:
Because you are recounting people several times. Say for example, let us number those people
{1,2,3,4} for the four girls and {1,2…7} for the boys.
One possible combination by your way is to fix one boy and girl each, say
{1,1} and then choose the remaining people. Let this combination be, for the sake of the example, {1,1,2,2,3}. This is a valid combination.
Now, when you fix another combination of a boy and a girl, say {1,2}, you could get the same combination as before because one the combinations while choosing the three remaining people would be {1,2,3}.
A correct way would be to choose girls and then choose 5− boys for 1≤≤4
So we get ∑4=1(4)(75−)=441
Answer:
We need group of 4 out of group of 5 + 6 = 11 people.
Part A
i)
2 boys and 2 girls:
5C2 * 6C2 = (5*4/2) * (6*5/2) = 150 waysii)
4 boys or 4 girls:
5C4 + 6C4 = 5 + 15 = 20 waysiii)
No restrictions:
11C4 = (11*10*9*8)/(4*3*2) = 330 waysPart B
Combination of 3 boys and 1 girl:
5C3*6C1 = (5*4/2)*6 = 60Total number of ways is 330 (found above)
Required probability:
P(3 boys and 1 girl) = 60/330 ≈ 0.1818 = 18.18%
Please help I this sum...It’s prove that...
Went with explanation...
Will give Brainliest...
Step-by-step explanation:
[tex](1) \: \: \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } [/tex]
Note that the 1st two factors can be combined:
[tex] \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } = \sqrt[3]{5 \times \frac{2}{5} } = \sqrt[3]{2} [/tex]
We also know that the numerator in the 3rd factor can be rewritten as
[tex] \sqrt[3]{64} = 4[/tex]
And the numerator in the 4th term can be rewritten as
[tex] \sqrt[6]{9} =({( {3})^{2} })^{ \frac{1}{6} } = \sqrt[3]{3} [/tex]
So let's rewrite expression #1
[tex] \sqrt[3]{2} \times \frac{4}{ \sqrt[3]{3} } \times \frac{ \sqrt[3]{3} }{ \sqrt[3]{2} } [/tex]
Notice that all the radical terms cancel out except for 4 therefore,
[tex]\sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } = 4[/tex]
A number, one-fourth of that number, and one-third of that number are added. The result is 38. What was the oringnal number?
Answer:
24
Step-by-step explanation:
x + (1/4)x + (1/3)x = 38
multiply both sides by 12 to clear the fractions
12x + 3x + 4x = 456
19x = 456
Divide both sides by 19
x = 24
Answer:
24
Step-by-step explanation:
x+1/4x+1/3x=38
x+7/12x=38
19/12x=38
x=38*12/19=24
Match each system to the number the first equation can be multiplied by to eliminate the
x-terms when adding to the second equation.
10x - 4y = -8
2
-5x + 6y = 10
역
-2x + 6y = 3
4x + 3y = 9
1/2
3x - By = 1
6x + 5y = 12
-1/2
- 8x + 10y = 16
- 4x - 5y = 13
-2
Answer/Step-by-step explanation:
✔️10x - 4y = -8
-5x + 6y = 10
Multiply the first equation by ½ to eliminate the x-term
Thus:
½ × 10x - 4y = -8 (eqn 1)
5x - 2y = -4
✔️-2x + 6y = 3 (eqn 1)
4x + 3y = 9
To eliminate the x-terms when adding to the second equation, multiply the first equation by 2
Thus:
2 × -2x + 6y = 3
-4x + 12y = 6
✔️3x - 8y = 1 (eqn 1)
6x + 5y = 12
To eliminate the x-terms when adding to the second equation, multiply the first equation by -2
Thus:
-2 × 3x - 8y = 1 (eqn 1)
-6x + 16y = -2
✔️-8x + 10y = 16 (eqn 1)
-4x - 5y = 13
To eliminate the x-terms when adding to the second equation, multiply the first equation by -½
Thus:
-½ × -8x + 10y = 16 (eqn 1)
4x - 5y = -8
Answer:
Match each system to the number the first equation can be multiplied by to eliminate the x-terms when adding to the second equation.
8x + 10y = 16
-2
4x-5y = 13
2× + бу = 3
4x + 3у = 9
3x - 8y = 1
6x + 5y = 12
10x - 4y =-8
-5x + бу = 10
1/2
2
-1/2Step-by-step explanation:
Lanu draws a rectangle that is 10 inches wide and 20 inches long. Which rectangle described down below has the same area
Answer:
b. 8 inches wide and 25 inches long
Step-by-step explanation:
Here are the options
5 inches wide and 25 inches long
b. 8 inches wide and 25 inches long
c. 15 inches wide and 15 inches long
d 15 inches wide and 25 inches long
Area of a rectangle = length x width
10 x 20 = 200
first option
5 x 25 = 125 does not have the same area as the one lanu drew
second option
8 x 25 = 200 has the same area as the one lanu drew
third option
15 x 15 = 225 does not have the same area as the one lanu drew
fourth option
15 x 25 = 375 does not have the same area as the one lanu drew
What is an equation of the line that is perpendicular to 3z +y=-5 and passes through the point (3, – 7)?
Enter your equation in the box
What is the area of the circle in terms of pi?
Answer:
[tex]4.2025\pi\:\mathrm{m^2}[/tex]
Step-by-step explanation:
The area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]. In the figure, we're given a diameter of 4.1. All diameters of a circle are exactly 2 times the length of all radii of the circle. Therefore, the radius of the circle is [tex]4.1\cdot \frac{1}{2}=2.05[/tex].
Thus, the area of the circle is [tex]2.05^2\pi=\boxed{4.2025\pi\:\mathrm{m^2}}[/tex]
Please help meeeee ASAP
What is the value of h in the figure below? In this diagram,
BAD - CBD
Answer:
Option D
Step-by-step explanation:
By using geometric mean theorem in the given right triangle ABC,
[tex]\frac{AD}{BD}= \frac{BD}{DC}[/tex]
BD² = AD × DC
h² = (AC - CD) × DC
h² = (25 - 16) × 16
h² = 9 × 16
h = [tex]\sqrt{144}[/tex]
h = 12
Therefore, measure of side h = 12 units.
Option D will be the correct option.
Answer:
12 is correct via a p e x
A country's population in 1994 was 21 million.
In 2001 it was 22 million. Estimate
the population in 2011 using the exponential
growth formula. Round your answer to the
nearest million.
P= Aekt
Enter the correct answer.
DONE
DOO
+1?
Answer:
Step-by-step explanation:
22 = 21 [tex]e^{7k\\}[/tex]
(22/21) = [tex]e^{7k}[/tex]
ln(22/21) = 7k ln(e)
ln(22/21) = 7k
0.046520016 = 7k
k=0.006645717
~~~~~~~~~~~~~~~~
P = 21 [tex]e^{0.006645717*17\\}[/tex]
P = 23.51
Write the equation of the line that passes through the point (4,−1) that is parallel to the line 2x−3y=9
First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:
2x−3y+8=0
⇒−3y=−2x−8
⇒3y=2x+8
⇒y=
3
2
x+
3
8
Therefore, the slope of the line is m=
3
2
.
Now since the equation of the line with slope m passing through a point (x
1
,y
1
) is
y−y
1
=m(x−x
1
)
Here the point is (2,3) and slope is m=
3
2
, therefore, the equation of the line is:
y−3=
3
2
(x−2)
⇒3(y−3)=2(x−2)
⇒3y−9=2x−4
⇒2x−3y=−9+4
⇒2x−3y=−5
Hence, the equation of the line is 2x−3y=−5.
Answer:
y=2/3x-11/3
Step-by-step explanation:
Hi there!
We are given the equation 2x-3y=9 and we want to write an equation that is parallel to it and that passes through (4,-1)
Parallel lines have the same slopes
So we need to first find the slope of 2x-3y=9
We can do this by converting the equation of the line from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
To do this, we need to isolate y on one side
2x-3y=9
subtract 2x from both sides
-3y=-2x+9
divide both sides by -3
y=2/3x-3
as 2/3 is in the place where m is, 2/3 is the slope of the line
It's also the slope of the line parallel to it that passes through (4,-1).
Here's the equation of that line so far:
y=2/3x+b
now we need to find b
as the line will pass through the point (4,-1), we can 4 as x and -1 as y in order to solve for b
-1=2/3(4)+b
multiply
-1=8/3+b
subtract 8/3 to both sides
-11/3=b
Substitute -11/3 as b into the equation
y=2/3x-11/3
There's the equation
Hope this helps!
Juan works at a retail store. He earns $6 an hour plus 1 $5 bonus each time he gets someone to sign up for the stores credit card.
Write a formula that will help Juan determine how much he will earn in one week.
a= total amount earned
h= hours worked in one week
b= number of cards sold in one week
Answer:
6h + 5b = a
Step-by-step explanation:
Please help ill appreciate it
Answer:
B
Step-by-step explanation:
the area of the triangle is 18 square units
Please help I’ll give brainliest
answer:
ans:
0.03 km³ = 0.03 × 10⁹ m³ = 3×10⁷ m³6052 mL³ =6052×10^(-9) L³ = 6.052×10^(-6) L³5.43 cg³ = 5.43 × 10^(-6) g³ 2100m³ = 2100 × 10^(-9) km³ = 2.1 × 10^(-6) km³Step-by-step explanation:
1000 m = 1 km
1000 mL = 1 L
100 cg = 1 g
What is the y-intercept of function f?
Answer:
B
Step-by-step explanation:
When x=1, we will use the second equation
-(1)+1 = 0
In parallelogram GHJK if m∡GHJ=140˚ find m ∡KGH.
Answer: m∠x = 40°
Step-by-step explanation:
This works the exact same way as the other one
Being adjacent angles in a parallelogram, the two angles would be supplementary (add up to 180°).
140° + x° = 180°
x = 40°
f(4) =
If g(x) = 2, x =
<
In the triangles, GK PN and HG 2MP.
Which statement correctly compares the angles?
H
M
Angle G is congruent to angle P.
O Angle G is smaller than angle P.
O Angle G is larger than angle P.
O Angle G is congruent to angle N.
32 cm
40 cm
G
K
P
N
Answer:
G is smaller than P. Visually comparing G to P you are doing a rough comparison to a 90° (or right) angle. Angle G is a little bit tilted to the right making it just under 90°
The statement which correctly compares the angles is Angle G is smaller than angle P.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given are two triangles.
Given that,
GK is congruent to PN.
HG is congruent to MP.
Also, given that,
HK = 32 cm and MN = 40 cm
Angle G is opposite to the side HK.
Angle P is opposite to the side MN.
Angles opposite to the greater side will be greater.
So angle P is greater than angle G
Or, angle G is smaller than angle P.
Hence, Angle G is smaller than angle P.
Learn more about Angles here :
https://brainly.com/question/11846909
#SPJ7
Which tiles should be added to the model below to make zero?
- - - - - -
O 6 negative tiles
O 6 positive tiles
O 3 negative tiles and 3 positive tiles
O 6 negative tiles and 6 positive tiles
Answer:
3 positive tiles hope.helps
what does it mean when someone tells you on a post “extra swag”
Answer:
Swag actually means stylish and confident
Anthony worked to earn $25.00. Joyce worked for $8.00 per hour. If he earns $5.00 per hour, how many hours did Anthony work?
Answer:
5 hours
divide 25 by 5 you get 5
can someone please help for brainlest
Answer:
The area will be 2 times the old area.
Step-by-step explanation:
When you double something, that means you multiply it by 2, therefor it will be 2 times the old area.
Answer:
option 3
Step-by-step explanation:
Length = 5 m, Base = 3 m
Area = Length x Base
= 5 x 3
= 15 m²
Base is double = 2 x 3 = 6 m
Length remains same = 5m
New Area = Length x Base
= 5 x 6
= 30 m²
The new Area is increase by 2 times the old Area .
SOMEBODY PLEASE HELP I DON’T HAVE MUCH TIME
Find the volume of this sphere.
Use 3 for TT.
V
V [?]cm
V = 713
12cm
Answer:
904.78
Step-by-step explanation:
I hope this is correct, if it isn't please feel free to let me know and I can fix it. I'm sorry in advance if it is incorrect.
20 POINTS!!!!!! Answer 1-16 Hurry no work just answer needed
1. Alternate angle
2. Alternate exterior angle
3. Corresponding angle
4. Vertical angle
5. Consecutive angle
6. Alternate exterior angle
7. x = 110°
8. x = 70°
9. x = 60°
10. x = 130°
11. x = 53°
12. x = 60°
13. x = 30°
14. x = 65°
15. x = 24°
16. x = 174°
hope this helps....
Please helppppppppp meeeeeee
Answer:
m∠B = 94º
Step-by-step explanation:
Supplementary angles total 180
(8x + 6) + ( 7x + 24) = 180
Combine like terms
15x + 30 = 180
15x = 150
x = 10
m∠B = 7x + 24
m∠B = 7(10) + 24
m∠B = 94º
Which sequence is arithmetic?
O 6, 12, 15, 21, ..
o 7, 14, 21, 36, ..
O 8, 16, 32, 64, ...
9, 18, 27, 36, ...
! Task 1. Bookwork code: G24 Calculator X not allowed Anthony has three number cards, as shown below. The minimum of the three cards is 6. The range of the three cards is 5. What is the mean of Anthony's three cards? Cards are 6, 7 and unknown
Answer:
8
Step-by-step explanation:
In order to find the range you need to subtract maximum card number from the minimum card number. We know that the range is 5 and that the minimum card is 6 so we can set up the equation like this to find the maximum shown as x.
[tex]5=x-6[/tex]
Add 6 to both sides
[tex]11=x[/tex]
Now we know all the the numbers of the three cards Anthony has since we were given the minimum = 6, 7, and solved for the last card which was the maximum = 11. In order to find the mean we have to add all of the numbers then divide by how many numbers there are (in this case it will be 3):
[tex]mean=\frac{6+7+11}{3}[/tex]
Add 6+7+11
[tex]mean=\frac{24}{3}[/tex]
Divide by 3
[tex]mean=8[/tex]
Hi can anyone pls help me with this problem I would really appreciate it !
Answer:
A
Step-by-step explanation:
The scale factor k is the ratio of corresponding sides, image to original.
k = [tex]\frac{CP'}{CP}[/tex] = [tex]\frac{15}{75}[/tex] = 0.2
Since k < 1 this represents a reduction.
P is in the shape of a circle. Q is in the shape of a quarter circle of radius 20 cm. P Q 20 cm The area of Q is 4 times the area of P. Work out the radius of P. You must show all your working.
El perímetro de un rectángulo es 58 y su base excede en 10 a su ancho, ¿Cuánto mide la base? AYUDAAAA
Answer:
The base is 19.5.
Step-by-step explanation:
The given question is, "The perimeter of a rectangle is 58 and its base exceeds its width by 10, how long is the base?"
Perimeter = 58
Base, l = 10+b
The perimeter of a rectangle is :
P = 2(l+b)
58 = 2(10+b+b)
29 = (10+2b)
29-10 = 2b
19 = 2b
b = 9.5
Base, l = 10 + 9.5
= 19.5
Hence, the base is 19.5.
All swimming equipment is on sale with a 30% discount. A snorkeling set regularly sells
for $50. Find the discount.
Answer:
15
Step-by-step explanation:
50 * .30=15