The probabilities in each of the given categories are; A) 51.33%; B) 51.33% C) 30.33% D) 30.33%
How to find the Probability of Selection?The number of ways to select 2 out of 25 is; 25C2 = 25! / (23! * 2!)
= 25*24/2
= 300
(A) Probability of selecting 1 male and 1 female:
[(11C1) * (14C1)]/300 = [11!/(10! * 1!)] * [(14!/(12! * 2!))
= 51.33%
(B) Probability of selecting 1 female and 1 male:
[(14C1) * (11C1)]/300 = 51.33%
(C) Probability that 2 females are selected is;
(14C2)/300 = 30.33%
D) Probability that no males are selected is;
P(no males) = (11C0 * 14C2 )/300 = 30.33%
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Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y 2x+122x + y ≤5
The solution of the inequalities is (0.375, 4.25)
How to graph the inequalities?The system of inequalities is given as:
3y > 2x + 12
2x + y ≤ 5
Next, we plot the inequalities on a graph (see attachment)
From the graph, both inequalities intersect at
(x, y) = (0.375, 4.25)
This represents the solution of the inequalities
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solve the following portion for x/11=8/3. round to nearest tenth
Match the expressions to their solutions or equivalents. (-3/8) + (-1/8)
Answer:
-1/2
Step-by-step explanation:
-3/8+-1/8=-4/8 which is equal to -1/2
Answer:
1/4
Step-by-step explanation:
(3/8)+(-1/8)
= (3/8) - (1/8)
= 2/8
= 1/4
This is multiple choice pls help
Answer: b and e
Step-by-step explanation:
b - the slope is positive
the slope is 8 not negative 8 because, 4+4/2-1 = 8/1 = 8 since subtracting 4 and -4 makes it 4+4
e - it is possible for x to be positive and for y to be negative
Number 8 is the answer 90*
Answer:
E
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
Consider the triangle on the left
3rd angle = 180° - 60° - 90° = 180° - 150° = 30°
the 3rd angle of the triangle on the left = 30° ( vertically opposite angle ), so
∠ 1 = 180° - 30° - 65° = 180° - 95° = 85°
Given: 3x+12=8x−18 algebraic proofs
Step Reason
3x+12=8x−18
12=5x−18
30=5x
6=x
x=6
The value of x comes out to be 6 from the algebraic equation.
Solving the Given Algebraic Equation for x:
Given algebraic equation is,
3x + 12 = 8x - 18
⇒ 12 = 8x - 3x -18
8x - 3x - 18 = 12
5x - 18 = 12
5x = 12 + 18
5x = 30
x = 30 / 5
x = 6
What is an algebraic equation?
A mathematical statement in which two expressions are put equal to one another is known as an algebraic equation. One or more variables, coefficients, and constants make up an algebraic equation in most cases. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y 2x+122x + y ≤5
The plotting of the inequalities was done using geogebra online graphing calculator. The graph is attached.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. It should be noted that in inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Inequality is an expression used to show the nonequal comparison of numbers and variables.
Given the system of inequalities:
3y > 2x + 12
3y - 2x > 12 (1)
2x + y < -5 (2)
Plotting the inequalities using GeoGebra online graphing calculator. The graph is attached
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ил
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10: Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1
Solution :
Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1
Answer: The given equation is
f(x) = x^{4} - 1
x- and y-intercept of the graph of the function f(x) = x^4 - 1 is
x-intercept(s): (1,0), (−1,0)
y-intercept(s): (0, −1)
A graph of the above point is attached
Step-by-step explanation:
Given equation, f(x) = x^{4} - 1
let's assume the above equation with respect to y to find intercept i.e
y = x^{4} - 1 .........................(i)
Now, for the x-intercept put y = 0 in eq.(i)
So, we get,
0 = x^4 - 1
x^4 = 1
x = -1, +1
from above we get the x-intercept (1,0), (−1,0)
Now, for the y-intercept put x = 0 in eq.(i)
So, we get
y = 0^4 - 1
y = -1
from above we get the y-intercept (0, -1)
Therefore, from all above
x- and y-intercept of the given equation f(x) = x^4 - 1 isx-intercept(s): (1,0), (−1,0)
y-intercept(s): (0, −1)
Graph of the given equation f(x) = x^4 - 1 with intercept is
if a person invested half of her money at 11% and half at 10% and received $420 interest. find the total amount
The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the total amount of money invested, hence:
(0.5* x * 0.11) + (0.5 * x * 0.1) = 420
x = 4000
The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.
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Given the coordinates below, what is the midpoint of AB?
A(-6, -10)
B(2,5)
Given :
[tex] \: [/tex]
A(-6, -10)B( 2, 5)
[tex] \: [/tex]
[tex] \gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}[/tex]
[tex] \: [/tex]
Let's solve by using midpoint formula :
[tex] \: [/tex]
[tex] \bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}[/tex]
[tex] \: [/tex]
[tex] \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}[/tex]
[tex] \: [/tex]
[tex] \: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}[/tex]
[tex] \: [/tex]
[tex]\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}[/tex]
[tex] \: \: [/tex]
[tex] \underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓[/tex]
Hope Helps! :)
Which graph shows the solution to the inequality lx+3l≥2 ?
The difference of the square of a number and 8 is equal to 8 times that number. Find the positive solution.
Answer:
[tex]2\sqrt{6} +4[/tex]
Step-by-step explanation:
Let x be that unknown number.
From the information given from the question, we can deduce:
[tex]x^{2} -8=8x[/tex]
From here, we can solve for x to find what is the number.
[tex]x^{2} -8=8x\\x^{2} -8x-8=0[/tex] (Quadratic Equation)
From here we can use the Quadratic Formula to solve for x.
[tex]x=\frac{-b+/-\sqrt{b^{2} -4ac} }{2a}[/tex]
In this case,
a = 1, b = -8 , c = -8
We substitute a, b and c to find x.
[tex]x=\frac{-(-8)+/-\sqrt{(-8)^{2}-4(1)(-8) } }{2(1)} \\= 2\sqrt{6} +4[/tex]
(Reject the negative solution)
(06.03 HC)
Solve the following system of equations. Show all work and solutions.
y = 3x2 + 6x + 4
y = -3x2 + 4
Answer: [tex](x,y)=\{(-1,1), (0,4) \}[/tex]
Step-by-step explanation:
[tex]3x^2 +6x+4=-3x^2 +4\\\\6x^2 +6x=0\\\\x^2 +x=0\\\\x(x+1)=0\\\\x=-1, 0\\\\x=-1 \longrightarrow y=1\\\\x=0 \longrightarrow y=4\\\\\therefore (x,y)=\{(-1,1), (0,4) \}[/tex]
The solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given quadratic equations are given as below:-
y = 3x² + 6x + 4
y = -3x² + 4
Equate the equations and solve for the value of x.
3x² + 6x + 4 = -3x² + 4
6x² + 6x = 0
x² + x = 0
x ( x + 1 ) = 0
x = 0 and x = -1
At x=0 and x=-1 the values of y are calculated as below:-
y = -3x² + 4
y = 0+ 4 = 4
y = -3 + 4 = 1
Therefore, the solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).
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Write the equation of the line.
(Check image)
Options:
a. y = -2/3x + 4
b. y = 2/3x + 4
c. y = 3/2x + 4
d. y = -3/2x + 4
please show step by step
Continue preparing to analyze the data (step 3): Choose an appropriate numerical summary.
An appropriate numerical summary is descriptive statistics.
What is a numerical summary?It should be noted that a numerical summary means a number used to describe specific characteristics of a data set.
In this case, descriptive statistics can be used. This is used to describe the data set.
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cual es la mitad de 980
Al aplicar operaciones de aritmética básica, tenemos que la mitad de 980 es igual a 490.
¿Cuál es la mitad de un número par?
En esta pregunta tenemos un número par de tres dígitos que termina en cero. De acuerdo con la teoría numérica, un número de base 10 de más de un dígito que tenga un número par relacionado con números impares como último dígito, tendrá un número impar si es dividido por 2.
Ahora bien, si tenemos un número par con más de un dígito que termina en cero, entonces tendrá un número par que termina en 0 si es dividido por 2.
Si dividimos 980 por 2, entonces tenemos 490 como resultado:
980/2 = 98/2 × 10 = 49 × 10 = 490
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A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One student used the inequality 90 greater-than 2.50 (x + 5) to find x, the number of students that the field trip budget could accommodate. Which best describes the error in the student’s inequality?
Answer:
Step-by-step explanation:
x is the number of students
(x+5) is the number of students and chaperons
$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have
2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)
The inequality "90 greater-than 2.50 (x + 5) "
90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign
90 ≥ 2.50(x+5)
Which rules define the function graphed below?
65
4
3
32
(0.2)
-2
-3-
(3,5)
--3--2--11 1 2 3 4
O y=x; y = 5
O y = x + 2; y = 5
O y=x; x = 5
O y=x+2; x = 5
The rules that define the piecewise function graphed are as follows:
y = x + 2, y = 5.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
In this problem, for x between 0 and 3, a linear function is given, with slope given as follows:
m = (5 - 2)/(3 - 0) = 1.
The y-intercept is of 2, as y = 2 when x = 0, hence the definition is:
[tex]y = x + 2, 0 \leq x \leq 3[/tex]
For x greater than 3, the function is constant at y = 5, hence the definition is:
y = 5, x > 3.
Hence, the rules that are used to define the piecewise function graphed are as follows:
y = x + 2, y = 5.
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which of the following regression equation best fits the data graphed below?
Answer:
D
Step-by-step explanation:
if the area of the figure below is 400m. find x
Answer:
it's answer came 20000o
could anyone help me with this?
Answer:
Step-by-step explanation:
A=6x²
[tex]\frac{dA}{dt} =6\times 2x \times \frac{dx}{dt} \\\frac{dA}{dt}=12x \frac{dx}{dt}[/tex]
In a certain chemical, a ratio of zinc to copper is 4 to 11 . A jar of the chemicals contains 319 copper. How many grams of zinc does it contain?
Answer:
116
Step-by-step explanation:
zinc : copper
4 : 11
11 = 319
zinc = 4 / 11 * 319
Zinc = 116
Find the reminder when 3x² + 2x -7 is divided by x - 1
Answer:
-2
Step-by-step explanation:
When x = 1, 3x² + 2x - 7 = -2.
HELP PLS!!! I GIVE BRAINLIEST
Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).
What is the Multiplication Property of Equality?The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.
In step 5 where the multiplication property of equality is applied, we would have:
sin(A) = CD/b
Multiply both sides by b
sin(A) × b = CD/b × b
b(sin A) = CD
CD = b(sin A)
This same property is applied to sin B = CD/a to get CD = a(sin B).
Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).
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His wife makes a final test of Odysseus' identity by getting him to tell
about the building of his bed
the name or his favorite dog
about the day he went away
how he got a scar on his arm
Answer: About the building of his bed
Use the Associative Property to find the value of the variable.
(8 x 15) x s = 8 x (15 x 11)
Answer:
hey its me again so the answer is 11.
I'm sure because I did this.
Which figure is described below?
The locus of points in a plane 1 unit from the point (0,0).
ray
circle
plane
line
Answer:
CIRCLE
Step-by-step explanation:
Kite A B C D is shown. Lines are drawn from point A to point C and from point B to point D and intersect.
Figure ABCD is a kite. The area of ABCD is 48 square units. The length of line segment BD is 8 units.
What is the length of AC?
5 units
6 units
10 units
12 units
The length of AC is 12 units . Option D
How to determine the length
The formula for area of a kite is given thus;
Area = [tex]\frac{p * q}{2}[/tex]
Where p and q are the lengths
Area of kite = 48 square units
BD, q = 8 units
AC , p = unknown
Substitute the values
[tex]48 = \frac{AC * 8}{2}[/tex]
Cross multiply
[tex]AC * 8 = 48 * 2[/tex]
[tex]8AC = 96[/tex]
[tex]AC = \frac{96}{8}[/tex]
[tex]AC = 12[/tex] units
Thus, the length of AC is 12 units . Option D
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Answer:option 4
Step-by-step explanation:
What is the value of p
Answer:
2
Step-by-step explanation:
You have the correct answer selected: 2.
The reason for this is that when there are exponents inside and outside of the parenthesis like this, they are multiplied.
2 times 2 is 4. That's why (8^2)^2 = 8^4
Answer:
p = 2
Step-by-step explanation:
[tex](8^{2}) ^{p}[/tex] = [tex]8^{4}[/tex]
[tex]8^{2p}[/tex] = [tex]8^{4}[/tex]
[tex]8^{p}[/tex] = [tex]8^{\frac{4}{2}[/tex]
p = 2
Find all the solutions to 3x^3 - 6x^2 + 30x - 20 = -20
Answer: Option (1)
Step-by-step explanation:
[tex]3x^3 - 6x^2 + 30x-20=-20\\\\3x^3 - 6x^2 + 30x=0\\\\3x(x^2 - 2x+10)=0\\\\[/tex]
So, either [tex]x=0[/tex] or [tex]x^2 -2x +10=0[/tex]
For the second case, we know x=0.
For the second case, we can use the quadratic formula.
[tex]x=\frac{2 \pm \sqrt{(-2)^2 - 4(1)(10)}}{2}\\\\x=1 \pm 3i[/tex]