Answer:
a) 896 ways
c) 910 ways
Step-by-step explanation:
The question is a combination problem since it has to do with selection. In combination, if r object is selected from a pool of n objects, this can be done in nCr ways.
nCr = n!/(n-r)!r!
If from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed, we need to first calculate the total committee formed without any condition.
8C3 × 6C3
= 8!/5!3! × 6!/3!3!
= 8×7×6×5!/5!×6 × 6×5×4×3!/3!×6
= 56×20
= 1120ways
Now if;
a) two of the men refuse to serve together.
Since two men refuse to serve together, we will select 1 man from remaining 4 men since two has already been selected then select 3 from 8 women as shown.
4C1×8C3
= 4×56
= 224ways
Number of ways this can be done will be 1120-224 = 896ways
b) 1 man and 1 woman refuse to serve together
We need to choose 2 men from remaining 5 and 2 women from the rest of the men which is 7 as shown:
= (8-1)C(3-1) × (6-1)C(3-1)
= 7C2 × 5C2
= 7!/5!2! × 5!/3!2!
= 7×6×5!/5!×2 × 5×4×3!/3!×2
= 21×10
= 210ways
The number of ways this can be done will be 1120-210 = 910ways
Evaluate: [tex]3-2^2+4*3+5[/tex]
Answer:
16
Step-by-step explanation:
Apply PEMDAS:
Solve the exponent, multiply from left to right, and then subtract and add from left to right.
[tex]3-2^2+4*3+5\\\\3-4+4*3+5\\\\3-4+12+5\\\\-1+12+5\\\\11+5\\\\\boxed{16}[/tex]
Answer: 16
Step-by-step explanation:
The important thing to remember here is the Order of Operations
The Order of Operations states that first solve Parentheses, then Exponents, then Multiplication and Division, then Addition and Subtraction.
There are no parentheses.
Exponents: 3 - 4+4*3+5
Multiplication and Division: 3 - 4 + 12 + 5
Addition and Subtraction:
-1+12+5
11+5
16
Hope it helps <3
plz help !! write two real world situations that you can model using the exponential function f(x)=2 to the power of x
Answer:
Two real world situations are shown below.
Step-by-step explanation:
Initial population of a certain bacteria is 1 thousand and the population doubles in each hour. So, population of bacteria (in thousands) after x hours is
[tex]f(x)=1(2)^x[/tex]
[tex]f(x)=(2)^x[/tex]
A person invests 1 lakh rupees in shares and the amount is twice at the end of each year. So, total amount (in lakhs) after x years is
[tex]f(x)=1(2)^x[/tex]
[tex]f(x)=(2)^x[/tex]
A kite is flying at an angle of elevation of about 55°. Ignoring the sag in the string, find the height of the kite if 85 m of string has been let out.
Answer: 69.6 m
Step-by-step explanation:
Sin 55 deg = opposite side/hypotenuse
0.819 = height/string length
0.819 * 85= height
height = 69.6 m
how to do this question plz
Answer:
Step-by-step explanation:
surface area of two trapezoids=2[(12+8)/2×3]=2[30]=60 cm²
surface area of side rectangles=10×8+10×12=10(8+12)=200 cm²
surface area of top=10×5=50 cm²
surface area of bottom=10×3=30 cm²
Total surface area=60+200+50+30=340 cm²
Answer:
Step-by-step explanation:
to find the surface area , you need to find the area of each side(face)
top: 5*10=50
the bottom of the shape: 3*10=30
the front face:10*8=80
the sides are trapezoid shapes with:different dimensions:
side :8,12 and eight of 3 ( the shape has 3 faces the same)
area=((12+8)/2)*3= 30 (30*3 faces or sides)
add the numbers: 50+30+80+(30*3)=250 cm^2
I hope it is right and good luck
It would take an hour for plane A to meet plane B. If the distance between them will be 200 miles in 45 minutes, how far are they now?
Answer: 125 miles
if you do the math you will get the same answer.
Answer:
800 miles
Step-by-step explanation:
PLZZZZZ HLPPPPP MEEEEEEEEEE NOW <3
Answer:
[tex]g(x) = x^{2} + 6\cdot x + 7[/tex]
Step-by-step explanation:
The blue parabola is only a translated version of the red parabola. The standard form of a vertical parabola centered at (h,k), that is, a parabola whose axis of symmetry is parallel to y-axis, is of the form:
[tex]y - k = C\cdot (x-h)^{2}[/tex]
Where:
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex with respect to origin, dimensionless.
[tex]C[/tex] - Vertex constant, dimensionless. (If C > 0, then vertex is an absolute minimum, but if C < 0, then vertex is an absolute maximum).
Since both parabolas have absolute minima and it is told that have the same shape, the vertex constant of the blue parabola is:
[tex]C = 1[/tex]
After a quick glance, the location of the vertex of the blue parabola with respect to the origin is:
[tex]V(x,y) = (-3,-2)[/tex]
The standard form of the blue parabola is [tex]y+2 = (x+3)^{2}[/tex]. Its expanded form is obtained after expanding the algebraic expression and clearing the independent variable (y):
[tex]y + 2 = x^{2} +6\cdot x + 9[/tex]
[tex]y = x^{2} + 6\cdot x + 7[/tex]
Then, the blue parabola is represented by the following equations:
[tex]g(x) = x^{2} + 6\cdot x + 7[/tex]
HELPPPP Enter the ratio as a fraction in lowest terms (2 ft to 24 in.)Enter the ratio as a fraction in lowest terms
(27 minutes to 24 minutes) Enter the ratio as a fraction in lowest terms (no decimals).
(8.0 calories to 5.6 calories)
Answer:
I think the answers are 1 to 1 ,9 to 8 , 10 to7
Find the x- and y-intercept of the line.
5x – 4y = 40
A x-intercept is -4; y-intercept is 5.
B x-intercept is - 10; y-intercept is 8.
Cx-intercept is 5; y-intercept is -4.
D x-intercept is 8; y-intercept is -10.
Answer:
D
Step-by-step explanation:
you can put the function in your graphing calculator & the x-intercept is where the line crosses threw the line that goes left & right vise versa for the y-intercept.
Consider the following expression and the simplified expression. Expression Simplified Expression 3 x squared + 5 y squared box + 3 box + 4 y squared + 6 9 x squared minus y squared + 9 Which terms could be in the boxes to make the expressions equivalent? Positive 6 x squared and Negative 6 y squared Positive 6 x squared and Negative 10 y squared Positive 9 x squared and Negative 10 y squared Positive 9 x squared and Negative 6 y squared
Answer:
The correct answer is:
[tex]+6x^{2}\\-9y^2[/tex]
Step-by-step explanation:
We are given the term:
[tex]3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6 = 9x^{2} -y^{2} +9[/tex]
We have to fill in to the empty spaces such that the above equation gets satisfied.
First of all, let us simplify the LHS (Left Hand Side):
[tex]3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6\\\Rightarrow 3x^{2} +5y^{2} +4y^{2} [\text{ \ }] [\text{ \ }] +6 +3\\\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9[/tex]
Now, let us equate the LHS and RHS (Right Hand Side):
[tex]\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9 = 9x^{2} -y^{2} +9[/tex]
Equating the coefficients of [tex]x^{2}\ and\ y^{2}[/tex] in LHS and RHS:
One box will have value = [tex]9x^{2} -3x^{2} =+6x^{2}[/tex]
Other box will have value = [tex]-y^{2} -9y^{2} =-10y^{2}[/tex]
The correct answer is:
[tex]+6x^{2}\\-9y^2[/tex]
So, if we fill the boxes with above values, the expression will be simplified as given.
Answer:
The correct answer is B. Positive 6 x squared and Negative 10 y squared
Step-by-step explanation:
The perimeter of a triangle is 7 a − 11 b . If two of its sides are 2 a + b and a − 9 b , what is the third side?
Answer:
To find the missing side we need to calculate the sum of the two given sides and then subtract that from the perimeter.
7a - 11b - (2a + b + a - 9b)
= 7a - 11b - (3a - 8b)
= 7a - 3a - 11b + 8b
= 4a - 3b
sketch the graph for the following quadratic function.
[tex] - x ^{2} + 4x + 12[/tex]
it's ok if it's wrong.i just wanna see how the work done to do this
Answer:
Please refer to the attached image for the graph of given function.
Step-by-step explanation:
Given the equation:
[tex]-x^{2} +4x+12[/tex]
Let us rewrite by letting it equal to [tex]y[/tex].
[tex]y=-x^{2} +4x+12[/tex]
Now, we can see that it is a quadratic equation and it is known that a quadratic equation has a graph of parabola.
Let us compare the given equation with standard quadratic equation:
[tex]y=ax^{2} +bx+c[/tex]
we get:
[tex]a = -1\\b = 4\\c = 12[/tex]
Coefficient of [tex]x^{2}[/tex] is negative 1, so the parabola will open downwards.
Axis of symmetry: It is the line which will divide the parabola in two equal congruent halves.
Formula for axis of symmetry is:
[tex]x = -\dfrac{b}{2a}[/tex]
[tex]x = -\dfrac{4}{2(-1)}\\\Rightarrow x=2[/tex]
It is shown as dotted line in the image attached in the answer area.
Axis of symmetry will also contain the vertex of the parabola.
It is a downward parabola so vertex will be the highest point on this parabola.
Putting x = 2 in the equation of parabola:
[tex]y=-2^{2} +4\times 2+12\\\Rightarrow y =16[/tex]
So, vertex will be at P(2, 16).
Now, let us find points of parabola to sketch graph:
put x = 0, [tex]y=-0^{2} +4\times 0+12=12[/tex]
Another point is Y(0,12)
Now, let us put y = 0, it will give us two points because the equation is quadratic in x.
[tex]0=-x^{2} +4x+12\\\Rightarrow -x^{2} +6x-2x+12=0\\\Rightarrow -x(x -6)-2(x-6)=0\\\Rightarrow (-x-2)(x-6)=0\\\Rightarrow x = -2, 6[/tex]
So, other two points are X1(-2, 0) and X2(6,0).
If we plot the points P, Y, X1 and X2 we get a graph as attached in the image in answer area.
What is the y-intercept of the graph of the function f(x) = x^2 + 3x + 5?
Answer:
(0,5)
Step-by-step explanation:
To find the y-intercept, substitute in 0 for x and solve for y.
y=x^2 + 3x + 5
y=(0)^2 + 3(0) +5
y=0+0+5
y=5
Since there is no x coordinate for a y-intercept, the answer is (0,5)
Answer:
A. (0, -5) is the right answer on edge 2021
Yo tenía $ 2.00. Mi mamá me dio $ 10.00. Mi papá me dio $ 30.00. Mi tía y mi tío me dieron $ 100.00. Yo tenía otros $ 5.00. Cuánto tenía? La respuesta correcta será eliminada. Gané contra: Vero verito
Answer:
$147
Step-by-step explanation:
$2.00+$10.00+$30.00+$100.00+$5.00
=$147
El dinero total que tenía será de $ 147.00
Dado lo siguiente
La cantidad tenía inicialmente = $ 2.00
La cantidad dada por mamá = $ 10.00
La cantidad recibida de papá = $ 30.00
La cantidad recibida del tío y la tía = $ 100.00
Si tuviera otros $ 5,00
La cantidad total que tenía será la suma de todo el dinero que tenía y los recaudados como se muestra:
Dinero total que tenía = $ 2,00 + $ 10,00 + $ 30,00 + $ 100,00 + $ 5,00
Dinero total que tenía = $ 147.00
Por lo tanto, el dinero total que tenía será de $ 147.00.
Obtenga más información aquí: https://brainly.com/question/22309443
Which of the following is not a function?
A. {(4,5), (4,2), (5,4), (2,4)}
B. {(1,2), (2,3), (3,4), (4,5)}
C. {(1,2), (2,3), (3,3), (4,5)}
D. {(4,1), (5,1), (6,1), (7,1)}
Answer:
A
Step-by-step explanation:
it is A for for two outgoing (y)there is one in going(x)
Answer:
The answer is (A)
Step-by-step explanation:
Please help me!
30g of cornflakes contain 2.5g of fat
How many grams of fat are there in 566g of cornflakes?
Give your answer to 1 dp
Answer:
47 .2 Grams 0f FatStep-by-step explanation:
[tex]30g ----> 2.5g -fat\\566g ----> xg -fat\\30x = 1415\\\frac{30x}{30} =\frac{1415}{30} \\\\x = 47.1666\\\\x = 47.2g of Fat[/tex]
Please help find the measure of the arc
Answer: 214
Step-by-step explanation:
The circumference of a circle measures 360 degrees, and since minor arc EF measures 146 degrees, this means arc EDF measures [tex]360-146=214^{\circ}[/tex]
arc EDF measures is 214°
What is arc?The arc is a portion of the circumference of a circle
The circumference of a circle measures 360°,
Since minor arc EF measures 146°,
arc EDF measures = 360°-146° = 214°
Hence, arc EDF measures is 214°
learn more about arc of circle
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If an apple has a mass of 25 kg and a momentum of 50 kg-m/s
south, what is its velocity?
O 5 m/s south
O 125 m/s north
0 0.2 m/s south
2 m/s south
Answer:
2m/s south
Step-by-step explanation:
p = mv
Where p is the momentum, m is the mass, while v is the velocity.
Given that
m = 25kg
v = ?
p = 50kgm/s
Substituting the values into the formula.
50kgm/s = 25×v
50kgm/s = 25v
Divide both sides by 25
v = 50/25
v = 2m/s
From the option list, the answer is
2m/s south
Please please help!!! Study the diagram of circle Z. Points P, O, Q, and R lie on circle Z in such a way that OP¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯. If m∠QZR=(2x+9)∘ and m∠PZO=(4x−11)∘, what is the value of x?
x=3.3
x=15.3
x=10
x=12
Answer:
The correct option is
x = 10
Step-by-step explanation:
in a circle Given that chord [tex]\overline {OP}[/tex] is congruent to [tex]\overline {QR}[/tex], we have;
Measured angle m∠RZQ is congruent to measured angle m∠PZO
Congruent chords are subtended by congruent angles at the center of the circle
Therefore we have;
4·x - 11 is equal to 2·x + 9
4·x - 2·x = 9 + 11
2·x = 20
x = 10
The value of the measured angles are;
4·x - 11 = 4×10 - 11 = 40 - 11 = 29°
The value of x is 10°.
Answer:
x=10
Step-by-step explanation:
4·x - 11 is equal to 2·x + 9
4·x - 2·x = 9 + 11
2·x = 20
x = 10
The value of the measured angles are;
4·x - 11 = 4×10 - 11 = 40 - 11 = 29°
The value of x is 10°
jane will run less than 32 miles this week. So far she has run 19 miles. what are the possible numbers of additional miles she will run ?use t for the number of additional miles she will run.
Answer:
Jane will run more than 30 miles this week, as thus far she ran 22.
Step-by-step explanation:
X + 22>30
X>8
She runs more than 8 miles.
Answer:
Well, it depends.
Step-by-step explanation:
In the problem, it doesn't specify if the miles she runs is a positive integer or not, but I will assume that it is.
There are number of miles: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and 31.
So t = 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and 31
if anybody can answer atleast 1 of the 2 questions that would be great! Thank you:) *Grade 9 work*
Answer:
perimeter=[tex]2(l+b)[/tex]
2(3b+5+2b-1)=
2(5b+4)=0
5b+4=o
b=-4/5
but be can't be -ve
therefore,b=4/5 or 0.8
Answer:
6) The perimeter of the triangle is 3(3x - 1)
7) The perimeter of the rectangle is 2(5b + 4)
Step-by-step explanation:
The perimeter of a triangle and a rectangle is found by adding up all the sides.
6) Perimeter of triangle = 3x - 3 + 4x - 1 + 2x + 1 = 3x + 4x + 2x - 3 - 1 + 1 = 9x - 3 = 3(3x - 1)
7) Perimeter of rectangle = 2(L + B) = 2(3b +5 + 2b - 1) = 2(5b + 4)
The sum of the digits of a two-digit number is 7 .When the digits are interchanged the reversed number is five times the tens digit of the original number find the original number .
frnds pls help me
I want answer with full process pls help me
pls frnds do it fast pls help me
Answer:
Original number is 52.
Step-by-step explanation:
1) Two digit number xy,
it can be written as 10x + y.
2) The sum of the digits of a two-digit number is 7.
x + y = 7
3) The digits are interchanged the reversed number is yx,
the new number can be written as 10y + x.
4) The original number is 10x + y, so the tens digit of the original number is x.
5) Five times the tens digit of the original number is 5*x.
6) The reversed number is five times the tens digit of the original number:
10y + x = 5*x
7) We have system of two equations
x + y = 7 ----> x = 7 - y
10y + x = 5*x ---> 10y - 4x = 0
10y - 4x = 0
10y - 4(7 - y) =0
10y - 28 + 4y = 0
14y = 28
y = 2
x = 7 - y = 7 - 2 = 5
x = 5
Original number is 52.
New number 25.
Check:
Original number is 52, the tens digit is 5.
The reversed number (25) is five times the tens digit of the original number find the original number .
25 = 5*5 True
Which number is the opposite of -3? Starting at -3, how many steps does it take to get to the opposite of -3? What does this number of steps represent?
Answer:
3
Step-by-step explanation:
The Absolute value of -3 is 3 because it's the distance away from 0. Both have the same distance away from 0.
The opposite number of the integer number negative 3 will be 3.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The number that produces zero when multiplied by an is known as the additive inverse of a number, or a, in arithmetic. The opposite, a shift in the sign, and negation are other names for this number.
The number is given below.
⇒ - 3
The opposite of the number negative 3 will be given as,
⇒ - (-3)
⇒ 3
The opposite number of the integer number negative 3 will be 3.
More about the Algebra link is given below.
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PLZ HELP!!! BRAINLIEST AND POINTS!!!
The answer is for this question is c
2(3x+2)+2(2x-1)
=10x+2
This is a polynomial
So the answer is c
Helppp!!!! please!!!
Answer:
F. cylinder
Step-by-step explanation:
A cylinder has a circle for its base, which has no vertices and is not a polygon. This, therefore, disqualifies a cylinder as a polyhedron.
Which inequality is represented by this graph?
Help please :’/
Answer:A
Step-by-step explanation:
It is a solid line and the area below is shaded so it has to be less than the slope, hope this helped!
<!> Brainliest is appreciated! <!>
Answer:
Its A because you find the slope, -1/3 which is followed by x. The x intercept is 1 so you do plus one. Because the line is solid and negative, it makes it a less-than equal to sign. Hope this helps at all!
Step-by-step explanation:
Seven lamps labeled A through G are arranged in a row. Each lamp has its own switch. Now lamps A, C, E, and G are on and other lamps are off. Ben starts to flip each switch from A to G the following way: if the lamp is on, he turns it off; if the lamp is off, he turns it on. He repeats the pattern until he flips the switches 2011 times. Which lamps are on finally? dont bully me im in 5th grade also this is due in 4 days
Answer:
O=on
X=off
OXXOXOX after 2011 flips.
Step-by-step explanation:
There are many ways to get the answer.
A. Actually flip them 2011 times.
One way is to put 7 cards on the table, and name them A to G, with A,E,C,G facing up, and the other facing down.
Now flip the cards in order A to G 2011 times and find the answer.
Since you have four days to find the answer, you only have to flip about 500 times a day.
B. Simplify procedure A above.
Do the same as above, actually flip the cards, but only 14 times.
You will find that the cards are restored to the original position after 14 flips.
If we divide 2011 by 14, we get a quotient of 143 with a remainder of 9.
We know we don't have to make 143 sets of 14 flips. We only need to make 9!
Then again, we know that after 7 flips, the lights will be all opposite.
If O=on, and X=off then the situations are
OXOXOXO initial
XOXOXOX after 7 flips
OXXOXOX after 9 flips, which is also after 2011 flips, and that is the final answer.
PLEASE HELP ! ! ! pleaseeeee ! ! ! ! ! :C
Answer:
5/2
Step-by-step explanation:
When you multiply exponents, you add the powers, and when you subtract exponents, you subtract the powers.
Step 1: Move negative exponents
[tex]\frac{2^25^6}{2^35^35^2}[/tex]
Step 2: Combine exponents
[tex]\frac{2^25^6}{2^35^5}[/tex]
Step 3: Remove like terms
[tex]\frac{5^1}{2^1}[/tex]
Step 4: Exponent
5/2
intro to geometric sequences (help pls)
Answer:
Option B
Step-by-step explanation:
The formula for geometric sequence is given by:
[tex]a_{n} = a_{1}r^{n-1}[/tex]
Where,
[tex]a_{n}[/tex] = nth term of sequence
[tex]a_{1}[/tex] = 1st term of the sequence
[tex]r[/tex] = common ratio (ration of the second term to the first term)
So,
Here:
[tex]a_{1}[/tex] = 12
[tex]r[/tex] = 6/12 = 1/2
Plugging in the values of [tex]a_{1}[/tex] and r in the above formula:
=> [tex]a_{n} = 12 * (\frac{1}{2}) ^ {n-1}[/tex]
Find the area of the triangle.
Answer:
80cm^2
Step-by-step explanation:
Answer:
80 ft^2
Step-by-step explanation:
To find the area of a triangle, multiply 1/2*base*height. When you plug in the numbers, the formula looks like this: 1/2*10*16. This will give you 80 ft^2
Evaluate. 8−2⋅3+7 Enter your answer in the box
Answer:
9
Step-by-step explanation:
8−2⋅3+7
PEMDAS
Multiply and divide first
8−6+7
Then add and subtract
2+7
9
Answer:
9
Step-by-step explanation:
Remember to follow the order of operations, PEMDAS. Note that PEMDAS =
Parenthesis
Exponent (& Roots)
Multiplication
Division
Addition
Subtraction
First, multiply -2 with 3:
-2 * 3 = -6
Next, follow the left -> right rule. First subtract, then add:
8 - 6 = 2
2 + 7 = 9
9 is your answer.
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