The values of 12C4 and 11P4 are 495 and 7920, respectively
The expressions are illustrations of permutation and combination, and they are calculated using:
[tex]^nC_r = \frac{n!}{(n -r)!r!}[/tex]
and
[tex]^nP_r = \frac{n!}{(n -r)!}[/tex]
So, we have:
[tex]^{12}C_4 = \frac{12!}{(12 -4)!4!}[/tex]
Evaluate the difference
[tex]^{12}C_4 = \frac{12!}{8!4!}[/tex]
Evaluate the factorials
[tex]^{12}C_4 = \frac{479001600}{967680}[/tex]
Divide
[tex]^{12}C_4 = 495[/tex]
Also, we have:
[tex]^{11}P_4 = \frac{11!}{(11 -4)!}[/tex]
Evaluate the difference
[tex]^{11}P_4 = \frac{11!}{7!}[/tex]
Evaluate the quotient
[tex]^{11}P_4 = 7920[/tex]
Hence, the values of 12C4 and 11P4 are 495 and 7920, respectively
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In the swimming pool design explain how to find the area of the pool surface
Answer:
Sample Response: Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.
Step-by-step explanation:
i did it.
Answer:
Sample Response: Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.
Step-by-step explanation:
make sure to inlcued
- area of rectangle
- half the diameter for the radius
- half the area of the circle
- subtract the area of the half circle from the area of the rectangle
i need help please ill give you 20 points
Answer: x < -1
Remember:
A white dot indicates > or <, not ≥ or ≤.In this case, the arrow is pointing to the left, so x must be < -1.Answer: D, or x<-1
Step-by-step explanation:
The arrow on the number line indicates the direction in which the set of numbers represented is going. In this case, the arrow is pointing in the negative direction from -1; so we know that it will be either x < -1 or x ≤ -1
The circle represents whether the set of points is inclusive or exclusive. This is an exclusive case, which means that the point x = -1 is not included in the set of points.
That's how we know the inequality represented by the graph is x < -1
What is the volume of a rectangular prism with l = 4 1/2 cm, w = 3 1/2 cm, and h = 6 cm?
Step-by-step explanation:
Volume of a rectangular prism is:
V = lwh
Given that l = 4½, w = 3½, and h = 6:
V = (4½)(3½)(6)
V = 94.5
The volume is 94½ cm³.
The formula for the volume of a rectangular prism is:
V = length x width x height
OR
V = l x w x h
You must plug in the values given in the equation
4[tex]\frac{1}{2}[/tex] x 3[tex]\frac{1}{2}[/tex] x 6
94 1/2 cm^3
Hope this helped!
~Just a girl in love with Shawn Mendes
Larry’s checkbook has a balance of $922.63. What is most likely the reason that Larry’s balance is different from the banks balance
Answer:
Check 318 was not cashed or deposited.
Step-by-step explanation:
If you look at the check numbers, check number 318 was not used. Therefore that is why Larry's balance is different from the banks balance.
Answer:
Step-by-step explanation:
Option D. check 318 was not cashed or deposited.
There were m visitors in an exhibition on the first day and 1,200 fewer vistors on the second day. On the third day, the number of vistors was 30% greator than the number of vistors on the second day. What was the average number of vistors over the three days?
Answer:
Step-by-step explanation:
The average number is given by :
[m + (m - 1200) + (m - 1200)(1.30 ] / 3 =
[ 2m + 1.30m - 1200 - 1560] / 3 =
[3.3m - 2760] / 3 =
[1.1 m - 920 ]
What is the range of 19, 12, 13, 3, 0, 0, 0, 0, 0, 0, 2, 13
Answer:
The answer is 19.
Step-by-step explanation:
To find the range you have to subtract the lowest number and highest number in the data set.
19-0=19
Hope this helps.
The range of the given set {19, 12, 13, 3, 0, 0, 0, 0, 0, 0, 2, 13} is 19, which is the difference between the largest (19) and smallest (0) values in the set.
The range of a set of numbers is the difference between the largest and smallest values in the set. To find the range of the given numbers {19, 12, 13, 3, 0, 0, 0, 0, 0, 0, 2, 13}, follow these steps
Step 1: Arrange the numbers in ascending order: {0, 0, 0, 0, 0, 0, 2, 3, 12, 13, 13, 19}.
Step 2: Find the smallest value: 0.
Step 3: Find the largest value: 19.
Step 4: Calculate the range: Largest value - Smallest value = 19 - 0 = 19.
The range of the given numbers is 19.
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line segment AB has endpoints A(1,-3) and B(-2,1). What is the midpoint of line segment AB
Answer:
[tex]\large\boxed{\left(-\dfrac{1}{2},\ -1\right)}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)\\\\================================\\\\A(1,\ -3),\ B(-2,\ 1)\\\\\text{Substitute:}\\\\x=\dfrac{1+(-2)}{2}=\dfrac{-1}{2}=-\dfrac{1}{2}\\\\y=\dfrac{-3+1}{2}=\dfrac{-2}{2}=-1[/tex]
Answer:
[tex](\frac{-1}{2} ,-1)[/tex]
Step-by-step explanation:
line segment AB has endpoints A(1,-3) and B(-2,1).
To find the midpoint of AB we use formula
[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
A(1,-3) is (x1,y1) , B(-2,1) is (x2,y2)
Plug in the values in the formula
[tex](\frac{1-2}{2} ,\frac{-3+1}{2} )[/tex]
[tex](\frac{-1}{2} ,\frac{-2}{2} )[/tex]
[tex](\frac{-1}{2} ,-1)[/tex]
Can someone please help me
Answer:
Let's solve your system by substitution.
x=5;y=−7
Step: Solve x=5 for x:
x=5
Step: Substitute 5 for x in y=−7:
y=−7
y=−7
Answer:
x=5 and y=−7
x=3;y=2x−1
Step: Solve x=3 for x:
x=3
Step: Substitute 3 for x in y=2x−1:
y=2x−1
y=(2)(3)−1
y=5(Simplify both sides of the equation)
Answer:
x=3 and y=5
Let's solve your system by substitution.
y=6x+3;y=5x+4
Step: Solve y=6x+3 for y:
y=6x+3
Step: Substitute 6x+3 for y in y=5x+4:
y=5x+4
6x+3=5x+4
6x+3+−5x=5x+4+−5x(Add -5x to both sides)
x+3=4
x+3+−3=4+−3(Add -3 to both sides)
x=1
Step: Substitute 1 for x in y=6x+3:
y=6x+3
y=(6)(1)+3
y=9(Simplify both sides of the equation)
Answer:
x=1 and y=9
2x+3y=2;y=x−6
Step: Solve y=x−6 for y:
y=x−6
Step: Substitute x−6 for y in 2x+3y=2:
2x+3y=2
2x+3(x−6)=2
5x−18=2(Simplify both sides of the equation)
5x−18+18=2+18(Add 18 to both sides)
5x=20
divide both sides by 5
5x/5 and 20/5
x=4
Step: Substitute 4 for x in y=x−6:
y=x−6
y=4−6
y=−2(Simplify both sides of the equation)
Answer:
x=4 and y=−2
Lines LM and QR are graphed on this coordinate plane. Which point is the intersection of lines LM and QR?
na
A. (-3,1)
B. (-3.-3)
c. (1.-3)
D. (1.3)
The first number is the X coordinate and the second number is the Y coordinate.
Looking left to right the lines intersect at X = 1
Looking up and down they intersect at Y = -3
The answer is C. (1,-3)
Find the height of a triangle that has an area of 30 square units and a bas measuring 12 units
That answer is 180. The formula is a=bh1/2
PLEASE HELP
find the vertex of f(x)=x^2+2x+3 (make sure you show your work)
ANSWER
(-1,2)
EXPLANATION
The given quadratic expression is:
[tex]f(x) = {x}^{2} + 2x + 3[/tex]
The coefficient of the quadratic term is already 1.
So we add and subtract the square of half the coefficient of x.
[tex]f(x) = {x}^{2} + 2x + 1 - 1+ 3[/tex]
We factor the first three terms to obtain
[tex]f(x) =(x + 1)^{2} + 2[/tex]
This is now in the form:
[tex]f(x) = a({x - h)}^{2} +k[/tex]
where (h,k) which is equal to (-1,2) is the vertex.
Please help..........
Answer:
C
Step-by-step explanation:
This is saying sum 5 and a number and multiply the result by 4
let n be the number then 5 + n is the sum, and
4(5 + n) is 4 times the resultant sum
how this 0=t2−t−2 become this 0=(t−2)(t+1)
In order to t² - t -2 = 0 become into this (t - 2)(t + 1) = 0, we have to know that a polynomial of the form ax² + bx + c = 0 can be factored as a(x + r1)(x + r2) = 0, where r1 and r2 are the roots of the equation ax² + bx + c = 0 and we can find them using the Quadratic Formula.
Let's solve the equation step-by-step.
t² - t -2 = 0 has the form at² + bt + c = 0, so can be factored as a(t + r1)(t + r2) = 0. With a = 1, b = -1, and c = -2
Step 1. Use the Quadratic Formula to find the roots r1 and r2.
t = −b ± √b²−4ac/2a
t = -(-1) ± √(-1)²−4(1)(-2)/2(1)
t = 1 ± √1+8/2
t = 1 ± √9/2 where r1 = 1 + √9/2 and r2 = 1 - √9/2
Step 2. Calculate the roots r1 and r2
r1 = 1 + √9/2 = 2
r2 = 1 - √9/2 = -1
Step 3. Write the factored equation a(t + r1)(t + r2) = 0, with a = 1 and the values of r1 and r2 with opposite signs.
1(t - 2)(t + 1) = 0
(t - 2)(t + 1) = 0
Patrica scored 80% on a math test. She missed 4 problems. How many problems were on the test?
Answer:
20
Step-by-step explanation:
Patrica got 80% correct. She missed 4 problems, so that must have been the remaining 20% of the test.
Therefore:
4 = 20% x
Percent means out of 100, so:
4 = (20/100) x
4 = 1/5 x
x = 20
There were 20 problems on the test.
what is the value of x to the nearest tenth
You will have to use trig to solve this:
The side you have is adjacent to the known angle
The side you are looking for is opposite the known angle
^^^This means you need to use tan:
tan(24) = [tex]\frac{x}{12}[/tex]
.445222 = [tex]\frac{x}{12}[/tex]
^^^input tan(24) into calculator, then multiply 12 to both sides to isolate and solve for x
5.3 ≈ x
Hope this helped!
Does anyone know this?
Answer:
h(1)= 1
h(4)=5
Step-by-step explanation:
Given
h(x)= x^3 for 1≤x≤3
and
h(x)=5 x>3
Now finding h(1), i.e when x=1
x=1 lies in the range 1≤x≤3 hence putting value x=1 in x^3
h(1)= 1^3
= 1
Now finding h(4), i.e when x=4
x=1 lies in the range x<3 hence putting value x=4 in h(x)=5
h(4)= 5 !
Jessica borrow $316 for 9 months he paid it off by paying $38.27 monthly what will she pay in finance charges
Answer:
my answer is 34 r 18 I am guessing
Answer:
answer is $28.43
Step-by-step explanation:
You take $38.27x9. Then minus that answer minus $316
Please answer quickly.
Answer:
3) 3a - 2 + 3 = -2
3a = -2 + 2 - 3 = -3
a = -3/3 = -1
4) m/-6 - 18 - 4 = -16
m/-6 = -16 + 18 + 4 = 6
m = 6 · (-6) = -36
5) x/-2 - 4 + 22 = -28
x/-2 = -28 + 4 - 22 = -46
x = -46 · (-2) = 92
6) -13 = 5 + 20m - 2m
-13 = 5 + 18m
-18 = 18m
m = -18/18 = -1
7) -2(2p - 1) = -14
-4p + 2 = -14
-4p = -14 - 2 = -16
p = -16/(-4) = 4
8) -1(8x + 20) = 12
-8x - 20 = 12
-8x = 12 + 20 = 32
x = 32/(-8) = -4
9) -49 = 7(2x + 3)
-49 = 14x + 21
-14x = 49 + 21 = 70
x = 70/-14 = -5
10) 3(8h - 4) + 17 = -19
24h - 12 + 17 = -19
24h = -19 + 12 - 17 = -24
h = -24/24 = -1
The length of the transverse axis is 11, and the length of the red line segment is 19. How long is the blue line segment?
Answer:
8
Step-by-step explanation:
Answer: 8
Step-by-step explanation:
Which line is the best model for the data in the scatter plot?
Answer:
the 1st one in the 2nd row
Step-by-step explanation:
Evaluate.
5 • [(14 + 3 • 30) + 120] + 103 – 10
Answer:
1213
Step-by-step explanation:
simplify
Answer:
1213
Step-by-step explanation:
5 • [(14 + 3 • 30) + 120] + 103 – 10
Evaluate 3*30 first
5 • [(14 + 90) + 120] + 103 – 10
Evaluate 14 + 90 = 104
5 * [104 + 120] + 103 - 10
5 * (224) + 103 - 10
5*(224) + 93
1120 + 93
1213
Let f(x) =Sqrt 9x and g(x) =x+7 whats the smallest number that's in the domain of f ° g
The smallest number that's in the domain of f ° g is x = 0.
Explanation:The function f(x) = √(9x) represents the square root of 9x.
The function g(x) = x + 7 represents adding 7 to x. To find the smallest number that is in the domain of f ° g, we need to determine the values of x that satisfy both f(x) and g(x).
We can start by looking at the domain of g(x), which includes all real numbers. So any value of x will work for g(x).
Next, we need to consider the domain of f(x). Since taking the square root of a negative number is not defined in the real number system, we must ensure that 9x is positive or zero.
So we set 9x ≥ 0 and solve for x: x ≥ 0. This means any non-negative value of x will work for f(x).
Now, to find the smallest number in the domain of f ° g, we need to find the intersection of the domains of f(x) and g(x).
Since any value of x will work for g(x) and only non-negative values of x will work for f(x), the smallest number that satisfies both functions is x = 0.
Which is the simplified form of the expression (6 to the power of -2 times 6 to the power of 5) to the -3rd power?
A)6 to the 30th power
B)1 over (6 to the power of 9)
C)6 to the power of 0
D)1 over (6 to the power of 16)
Answer:
B. 1/6^9
Step-by-step explanation:
6^-2 = 1/6^2
1/6^2 * 6^5 = 6^5/6^2 = 6^3
6^(3 * -3) = 6^-9= 1/6^9
Answer:
B) 1 over (6 to the power of 9)Step-by-step explanation:
[tex]\left(6^{-2}\cdot6^5\right)^{-3}\qquad\text{use}\ a^n\cdot a^n=a^{n+m}\\\\=(6^{-2+5})^{-3}=(6^3)^{-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=6^{(3)(-3)}=6^{-9}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{6^9}[/tex]
Which statement proves that quadrilateral JKLM is a kite?
∠M is a right angle and MK bisects ∠LMJ.
LM = JM = 3 and JK = LK = .
MK intersects LJ at its midpoint.
The slope of MK is –1 and the slope of LJ is 1.
Answer:
B) LM = JM = 3 and JK = LK = √17
Step-by-step explanation:
just took test, A is wrong, can i get brainliest please?
Answer:
B) LM = JM = 3 and JK = LK = √17
Find the value of x, rounded to the nearest tenth.
X multiplied by the side labeled 5 is equal to the line labeled 9 multiplied by the line labeled 5.1
9 x 5.1 = 45.9
x = 45.9 / 5
x = 9.18
x = 9.2
The probability of it snowing in Eastern Canada tomorrow is 0 . 4 0.40, point, 4. The probability of it snowing in Western Canada tomorrow is 2 5 5 2 start fraction, 2, divided by, 5, end fraction. Which of these events is more likely? Choose 1 answer: Choose 1 answer: (Choice A) A It snows in Eastern Canada tomorrow. (Choice B) B It snows in Western Canada tomorrow. (Choice C) C Neither. Both events are equally likely.
Answer:
c
Step-by-step explanation:
Both the events are equally likely so neither can be more likely.
The correct answer is: C Neither. Both events are equally likely.
Given that the probability of it snowing in Eastern Canada tomorrow is 0.4 and that of in Western Canada is 2/5,
We need to determine which of the given events is more likely,
To determine which event is more likely, we compare the probabilities provided for each event:
The probability of it snowing in Eastern Canada tomorrow is 0.4.
The probability of it snowing in Western Canada tomorrow is 2/5, which is equivalent to 0.4.
Since both probabilities are equal (0.4), we can conclude that both events, A (It snows in Eastern Canada tomorrow) and B (It snows in Western Canada tomorrow), are equally likely.
Therefore, the correct answer is: C Neither. Both events are equally likely.
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Write an equation for the vertical translation. y = 2/3x; 4 units down
Answer:
y = [tex]\frac{2}{3}[/tex] x - 4
Step-by-step explanation:
Given y = f(x), then
y = f(x) + c represents a vertical translation
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Here the translation is 4 units down ⇒ c = - 4, thus
y = [tex]\frac{2}{3}[/tex] x - 4
The equation of a line y = 2/3x moved 4 units down would be y = 2/3x - 4.
Explanation:In the case of a vertical translation, the equation of a line y = mx + b is altered by adding or subtracting a constant value, which moves the line up or down on the coordinate plane. For example, with the given equation of a line, y = 2/3x, to translate it 4 units down, we subtract 4 from y. Therefore, the equation for the vertical translation would be y = 2/3x - 4.
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How many solutions does this system of equations have?
Y=-3x+7
Y=-3x-6
A. Infinitely many
B. Two solutions
C. One solution
D. No solutions
System of equations helps us to compare two real-life problems. The system of equations will have no solution.
What is a System of equations?Inconsistent System
A system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
As the systems of two-equations are given, therefore, the two equations are:
Y=-3x+7Y=-3x-6Now, if we plot the two-equation on the graph, we will find that the lines of the two equations are parallel. therefore, the system of equations will have no real solution or will have no solution.
Hence, the system of equations will have no solution.
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PLEASE I NEED THIS TO PASS A TEST AND GRADUATE!!!
Function g is transformed to obtain function h as shown.
(x)=g(x+2)-5
Which statement describes how the graph of h is different from the graph of g?
A. The graph of h is the graph of g shifted 2 units to the right and 5 units up.
B. The graph of h is the graph of g shifted 5 units to the left and 2 units down.
C. The graph of h is the graph of g shifted 5 units to the right and 2 units up.
D. The graph of h is the graph of g shifted 2 units to the left and 5 units down.
Answer:
D. The graph of h is the graph of g shifted 2 units to the left and 5 units down.
Step-by-step explanation:
Graph: h(x) = g ( x + 2 ) - 5
x + 2 means the graph is shifted to left by 2 units.
-5 means to shift the graph down by -2 units
so, the graph of h is the graph of g shifted 2 units to the left and 5 units down.
A set of equations is given below:
Equation C: y = 3x + 7
Equation D: y = 3x + 2
Which of the following best describes the number of solutions to the given set of equations?
One solution
Two solutions
Many solutions
No solution