Answer:
1246 teams
Step-by-step explanation:
We are told there are 7women & 6men.
If 5 people are selected and there must be more women than men in the team.
This means there must be a minimum of 3 women.
Thus;
For 3 women;
7C3 × 6C2 = 525
For 4 women;
7C4 × 6C3 = 700
For 5 women;
7C5 × 6C0 = 21
Thus;
Total = 525 + 700 + 21 = 1246 teams
How many L of a 10% alcohol solution must be mixed with 9l of a 80% alcohol solution to make a 55% solution
Answer:
Step-by-step explanation:
The best thing to do for these solution/mixture problems is to make a table:
#L * %alcohol = L alcohol
10% sol.
+ 80% sol.
55% sol.
In this way, we can keep track of our information AND figure out the equation we need to use to solve it. Notice first, the equation along the top of the table:
#L * %alcohol = L alcohol This tells us that we are multiplying the #L column times the %alcohol column to get the L alcohol column. Notice second, that there is a + sign to the far left, indicating that we are ADDING rows 1 and 2 together to get the mix. Let's start filling this in. The easy part is the % alcohol column. 10% alcohol has .10 alcohol as a decimal, likewise for the 80% and 55%:
#L * %alcohol = L alcohol
10% sol. .10
+ 80% sol. .80 =
55% sol. .55
Now to fill in the first column. We know that our unknown, from the problem, is the number of Liters, #L in the 10% solution, so that is x, and we also know that we have 9 L of the 80% alcohol. Filling that in:
#L * %alcohol = L alcohol
10% sol. x * .10
+ 80% sol. 9 * .80
55% .55
Now look back at the + sign. We are told that we are mixing the 10% with the 80%, so we are adding them together. So let's do that. We will also follow the rule for the table and multiply the first column times the second column to fill in the last column to complete the table:
#L * %alcohol = L alcohol
10% sol. x * .10 = .10x
+ 80% sol. 9 * .80 = 7.2
55% sol. (9 + x) * .55 = .55x + 4.95
If we add the 2 solutions together to get the new solution in the first column, we will also add the L alcohol in the last column to get our equation:
.10x + 7.2 = .55x + 4.95 and
- .45x = - 2.25 so
x = 5L
We need 5 Liters of the 10% solution if we want to mix that with 9L of 80% solution to get 14 L of 55% solution.
A block is being dragged along a horizontal surface by a constant horizontal force of size 45 N. It covers 8 m in the first 2 s and 8.5 m in the next 1 s. Find the mass of the block.
Answer: 15kg
Can anyone please explain this sum with proper working?
Answer:
Solution: To determine mass of the block we can use second Newton' law \vec F=m\vec a
F
=m
a
. The force and acceleration according the problem is directed along a horizontal surface, and we can omit the vector sign in Newton's law. The force we know F=45NF=45N, thus we should deduce the acceleration. The problem does not specify the initial speed at which time began to count, so for the first time interval, we may write the kinematics equation in the form
(1) S_1=v_1\cdot t_1+a\frac {t_1^2}{2}S
1
=v
1
⋅t
1
+a
2
t
1
2
, where S_1=8m, t_1=2s S
1
=8m,t
1
=2s , other quantities we don't know. The similar equation we can write for next time interval
(2) S_2=v_2\cdot t_2+ a\frac{t_2^2}{2}S
2
=v
2
⋅t
2
+a
2
t
2
2
. where S_2=8.5m, t_2=1s S
2
=8.5m,t
2
=1s
Note that during the first time interval, the speed of the block increased in accordance with the law of equidistant motion and it became the initial speed of the second interval, i.e.
(3) v_2=v_1+a\cdot t_1v
2
=v
1
+a⋅t
1
Substitute (3) to (2) we get
(4) S_2=(v_1+a\cdot t_1)\cdot t_2+ a\frac{t_2^2}{2}=v_1\cdot t_2+a\cdot t_1\cdot t_2+a\frac{t_2^2}{2}S
2
=(v
1
+a⋅t
1
)⋅t
2
+a
2
t
2
2
=v
1
⋅t
2
+a⋅t
1
⋅t
2
+a
2
t
2
2
From equation (1) and (4) we can exclude unknown quantity v_1v
1
, then remain only one unknown aa. For determine aa we dived (1) by t_1t
1
, (4) by t_2t
2
to find the average speed at time intervals and subtract (1) from (4).
(5) \frac {S_2}{t_2}-\frac {S_1}{t_1}=v_1+a\cdot t_1 +a\frac {t_2}{2}-(v_1+a\frac{t_1}{2})=a\frac{t_1+t_2}{2}-
t
2
S
2
−
t
1
S
1
=v
1
+a⋅t
1
+a
2
t
2
−(v
1
+a
2
t
1
)=a
2
t
1
+t
2
− For acceleration we get
(6) a=2\cdot ( {\frac{S_2}{t_2}-\frac{S_1}{t_1})/(t_1+t_2)}=2\cdot \frac{(8.5m/s-4m/s)}{3s}=3ms^{-2}a=2⋅(
t
2
S
2
−
t
1
S
1
)/(t
1
+t
2
)=2⋅
3s
(8.5m/s−4m/s)
=3ms
−2
For mass from second Newton's law we get
(7) m=\frac{F}{a}=\frac{45N}{3ms^{-2}}=15kgm=
a
F
=
3ms
−2
45N
=15kg
Answer: The mass of the block is 15 kg
What type of line is PQ?
A. side bisector
B. altitude
C. median
D. angle bisector
Answer:
D
Step-by-step explanation:
Since ∠ RPQ = ∠ SPQ = 60° , then
PQ bisects ∠ RPS and is an angle bisector
PQ exists the angle bisector of angle RPS. It means PQ divides the angle RPS in two equivalent parts.
What is angle bisector?
Angle bisector in geometry directs to a line that divides an angle into two equivalent angles. A bisector represents the thing that bisects a shape or an object into two equivalent regions. If we draw a ray that bisects an angle into two equivalent parts of the exact measurement, then it exists named an angle bisector.
It is given that ray PQ is the angle bisector of angle RPS. It means PQ divides the angle RPS in two equivalent parts.
[tex]$m \angle R P Q=m \angle QP S=60^{\circ}$[/tex]
Now, [tex]&m \angle R P S=m \angle R P Q+m \angle Q P S \\[/tex]
[tex]&m \angle R P S=60^{\circ}+60^{\circ} \\[/tex]
[tex]&m \angle R P S=120^{\circ}[/tex]
Therefore, the measure of angle RPS is [tex]$60^{\circ}$[/tex].
Therefore, the correct answer is option D. angle bisector.
To learn more about angle bisector
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Anyone? Ive tried and its not clicking
Answer:
Hello Bro How Are You....?
En un triángulo ABC, se traza la mediana BM, si AM = 5x - 4 y MC = 3x + 6. Calcula AC.
A) 5 B) 7 C) 14 D) 21 E) 42
Answer:
A) 5
Step-by-step explanation:
If triangle LMQ is similar to triangle LNP, calculate the length of segment LP.
Answer:
LP = 15
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{LM}{LN}[/tex] = [tex]\frac{LQ}{LP}[/tex] , substitute values
[tex]\frac{4}{10}[/tex] = [tex]\frac{LQ}{LQ+QP}[/tex]
[tex]\frac{2}{5}[/tex] = [tex]\frac{LQ}{LQ+9 }[/tex] ( cross- multiply )
5LQ = 2(LQ + 9) = 2LQ + 18 ( subtract 2LQ from both sides )
3LQ = 18 ( divide both sides by 3 )
LQ = 6
Then
LP = LQ + QP = 6 + 9 = 15
find the least square number which is exactly divisible by 8,12,15&20
Answer:
first we need to find the LCM of the given numbers i.e. 8, 12, 15 and 20
2*2*2*5*3=120
Then
as 2, 3, 5 are not in pairs, we need to multiply the LCM with 2*5*3=30
so,
least perfect square number which is divisible by each of numbers 8 12 15 and 20
=120*30=3600
Step-by-step explanation:
Hello can we be friends.....
1. What is the sum of 3/4 and 4/5?
Grade improvement and study motivation
Answer:
yes because we are leraning new things
Complete the sentence. The amount of time it takes to drive from your house to the library is most likely to be a function of the _____.
Answer:
D. distance
Step-by-step explanation:
really ? given the choices you needed help with that ?
only D makes sense. the rest is completely ridiculous and has nothing to do with driving from the house to the library.
Evaluate the following expression using the values given: (1 point)
Find 3x − y − 3z if x = −2, y = 1, and z = −2.
A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below.
Which equation can be used to determine the amount of cherry juice in each mixture?
5q + 3(8 – q) = 36
5q + 3(8 – q) = 8
q + (8 – q) = 8
q + 5 = 5q
Answer:
I think 5q+3(8-q) =36 is the answer for this question
Based on the amount the restaurant manager spends on the juice mixture, the amount of cherry juice can be found as 5q + 3(8 – q) = 8.
What is the amount of cherry juice used?Assuming the cherry juice is q and the lime juice is r, the following formulas would be true:
q + r = 8
5q + 3r = 36
The first equation can be rewritten as:
q + r = 8
r = 8 - q
Using substitution into the second formula we get:
5q + 3r = 36
5q + 3(8 - q) = 36
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please me in the math
Find the H.C.F
[tex] {x}^{2} - 4 \\ {x}^{3} + 8 \\ {x}^{2} + 5x + 6[/tex]
it so simple
Step-by-step explanation:
Solution
First equation x ² - 4
= (x+2) (x-2)
Second equation = x ³ +8 + = x³+2^3
= (x-2) (x² + x₁2 +2²) = (x-2) (x² + 2x+4)
3 Third equation = x ² + 5x + 6
= x² + 6x= x +6 = x(x+6)-1(x+6)
(x-1) (x+6)
H.C. F= x-2
Karma was given some birthday money. She puts money in an account. Every month after that, she deposits the same amount of money. The equation that models this situation is y=75x+60, where y is the amount of money in the account and x is the number of deposits. What does the y-intercept mean in this situation
Answer:
y represents the amount in the bank account after 7 months.
Step-by-step explanation:
Let karma gets x money on his birthday.
He has 60 in his account initially
He deposits teh same money for the seven months
So, the money he has after the seven months is 7 x + 60
According to the question,
y =7 x + 60
It shows that the amount after seven months is y.
Plz someone do this for me I’ll give a lot of points
Answer:
RW is congruent to WX
Step-by-step explanation:
We know that PW and WV and Angle W is vertical angle so We need to include that RW congruent to WX.
Which number belongs to the solution set of the equation?
x + 3 = 45
A. 15
B. 48
C. 43
D. 42
Answer:
D
Step-by-step explana
[tex] \sf \: The \: value \: of \: x \: is \: the \: number \: that \: belongs \: to \: the \: solution \: \\ \sf \: set \: of \: the \: equation. \: So \: we \: need \: to \: find \: x.[/tex]
[tex] \sf \: x + 3 = 45 \\ \sf \: x = 45 - 3 \\ \sf \: x = \underline{42}[/tex]
Answer ⟶ [tex]\boxed{\bf{D.42}}[/tex]
10)
Ka
The longer base of a trapezoid has endpoints of (-2,- 4) and (4,0). The shorter base contains the point (3, 1).
(40)
(2)
We an equation of the line that contains the shorter base of the trapezoid. Provide valid mathematical reasoning and calculations to
you derived your equaiton.
of a trapezoid are parallel
Suation and explanation in the space provided.
Math symbols
Relations
Geometry
Answer:
y = 2·x/3 - 1
Step-by-step explanation:
The endpoints of the longer base of the trapezoid = (-2, -4), and (4, 0)
The point contained on the shorter base = (3, 1)
The slope of the line representing the longer base, m, is given as follows;
m = (0 - (-4))/(4 - (-2)) = 2/3
The slope of the shorter base = The slope of the longer base = m = 2/3
The equation of the line representing the shorter base in point and slope form is therefore;
y - 1 = (2/3)·(x - 3)
∴ y = 2·x/3 - 2 + 1 = 2·x/3 - 1
The equation of the shorter side of the trapezoid is y = 2·x/3 - 1
What’s 4 divided by $5.32
Answer:
0.752
Step-by-step explanation:
Solve for ppp. 16-3p=\dfrac23p+516−3p= 3 2 p+516, minus, 3, p, equals, start fraction, 2, divided by, 3, end fraction, p, plus, 5 p=p=p, equals
Given:
The given equation is:
[tex]16-3p=\dfrac{2}{3}p+5[/tex]
To find:
The value of p.
Solution:
We have,
[tex]16-3p=\dfrac{2}{3}p+5[/tex]
Multiply both sides by 3.
[tex]3(16-3p)=3\left(\dfrac{2}{3}p+5\right)[/tex]
[tex]48-9p=2p+15[/tex]
Isolating the variable terms, we get
[tex]48-15=2p+9p[/tex]
[tex]33=11p[/tex]
Divide both sides by 11, we get
[tex]\dfrac{33}{11}=p[/tex]
[tex]3=p[/tex]
Therefore, the required solution is [tex]p=3[/tex].
Answer:
p=3
Step-by-step explanation:
i got it right on khan
A box contains 6 red, 3 white, 2 green, and 1 black (in total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least two white balls?
Answer:
Pick at least 4 balls to be sure that you are getting balls with the same color.
Step-by-step explanation:
Here, you want to know the least number of balls to be taken out of the box to be sure that you have all the three colors represented.
You know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know you have all the colors of balls represented, you will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that you have taken all the colors since you would have exhausted picking other balls at this point.
So you shall be needing at least 4 balls picked to ensure that you have all the colors represented
Question 6 of 10
How much would $500 invested at 6% interest compounded monthly be
worth after 5 years? Round your answer to the nearest cen
(0) - P(144
A $674,43
B. $886,41
C, 5669.11
D. $512,68
9514 1404 393
Answer:
A. $674.43
Step-by-step explanation:
The account balance is given by ...
A = P(1 +r/12)^(12t) . . . . . principal P invested at annual rate r for t years
A = $500(1 +0.06/12)^(12·5) = $500(1.005^60)
A ≈ $674.43
what's is 11 divided by 620
Answer:
0.017741
Step-by-step explanation:
state the dimensions of the matrix. identify the indicated element
Answer:
D; 2 * 3; -4
Step-by-step explanation:
The dimension of the matrix refers to the number of elements in a row multiplied by the number of elements is a column
In a row, we have 2 elements, in a column , we have 3 elements
So the matrix is of 2 * 3 dimension
a21, refers to the element in the matrix that is in the row 2 column 1 and that is -4
Determine whether ABC are functions:
A. (2,5) (3,7) (-1,4) (0, 6)
B.(-3, 1) (4, 2) (5,-2) (-3,-1)
C. (3,4) (-4, 6) (-1,0) (0,1)
A.
B.
C.
Answer:
A. Function
B. Not a function
C. function
Which shows a difference of squares?10 y squared minus 4 x squared16 y squared minus x squared8 x squared minus 40 x 2564 x squared minus 48 x 9
Answer:
16 y squared minus x squared
Step-by-step explanation:
The other all expressions except 16y²-x² doesn't complete the square and its difference. Then we can check 16y²-x²,
Now take the expression 16y²-x² and we can try to solve it.
We can simplify the terms separately to associate them as perfect squares,
→ 16y² = (4y)² --- (1)
→ x² = (1x)² --- (2)
Now we can take the difference of eq. (1) and eq. (2),
→ 16y²-x²
→ (4y)²-(1x)² --- (3)
Now eq. (3) shows a difference of squares.
Another representation is,
→ (4y - x) (4y + x)
→ 16y²- x²
→ (4y)²- (1x)²
Therefore, the expression 16y²-x² shows a correct difference of squares.
Answer:
its b trust
Step-by-step explanation:
someone please help me
Step-by-step explanation:
D) (A³/2)³ = A⁹/8
A³ whole to the power 3 is A⁹
2³ is 8
Angle ADB and CD are straight lines.
angle ADC = 5 x angle CDB
Work out the size of angle ADC.
Answer:
150 degrees
Step-by-step explanation:
5 + 1 = 6
180 : 6 = 30
30 x 5 = 150
Connor wants to represent 25 divided by the difference of 12 and seven he writes the expression of ( 25÷12) -7 is Connor expression correct explain
Step-by-step explanation:
Step 1: Check to see if Connor is right
25 divided by the difference of 12 and seven
25 / (12 - 7)
Since we have a 12 and seven, that means that we have them together. However, how Connor is presenting it, it would be 25 divided by 12 subtracted 7. Therefore, Connor is incorrect.
Answer:
No he's not correct.
Step-by-step explanation: Let's take a step back and look at the question, he wants to represent the difference of 12 and 7 ÷ by 25. Therefore in order to do that we need to figure out the difference 12 and 7 so the equation would look like this 12-7=5 after doing that we divide 5 by 25 so it would look like this 25÷5=5.
So the correct equation is (12-5) ÷25
Hope this helps!
7. La somme de deux multiples de 3 consécutifs est de 129. Quels sont ces deux nombres?
Answer:
Les deux nombres doivent avoir une différence de 3. Algébriquement, ce serait x + (x + 3) = 129. 2x est alors égal à 126. X est égal à 63 et x + 3 est à 66. Ces nombres sont des multiples consécutifs de 3 dont la somme est de 129.
Step-by-step explanation:
The two numbers must have a difference of 3. Algebraically, it would be x + (x + 3) = 129. 2x then is equal to 126. X equals 63 and x + 3 is 66. These numbers are consecutive multiples of 3 whose sum is 129.
In a fruit cocktail, for every 15 ml of orange juice you need 5 ml of apple juice and 50 ml of coconut milk. What is the ratio of apple juice to coconut milk to orange juice expressed in its simplest form?
Answer:
1:10:3
Step-by-step explanation:
