Solution:
The probability of a particular event A occurring from an experiment is obtained from the number of ways that A can occur divided by the total number of possible outcomes. That is;
\(\begin{gathered} P(A)=\frac{n(A)}{n(T)} \\ \text{Where;} \\ P(A)=\text{ probability of event A} \\ n(A)=\text{ number of possible ways event A can occur} \\ n(T)=\text{ total number of possible outcomes} \end{gathered}\)In a stack of 8 cards with different numbers;
The probability that the first card is an odd number and the second card is greater than 6 is the product of the probability of odd number and the probability of greater than 6. That is;
\(P(\text{Odd and greater than 6)}=P(odd)\times P(greater\text{ than 6)}\)We have;
\(\begin{gathered} P(\text{odd)}=\frac{n(\text{odd)}}{n(T)} \\ P(\text{odd)}=\frac{4}{8} \\ P(\text{odd)}=\frac{1}{2} \end{gathered}\)Also,
\(\begin{gathered} P(\text{greater than 6)=}\frac{\text{n(greater than 6)}}{n(T)} \\ P(\text{greater than 6)=}\frac{\text{2}}{8} \\ P(\text{greater than 6)=}\frac{1}{4} \end{gathered}\)So, the probability that the first card is an odd number and the second is greater than 6 is;
\(\begin{gathered} P(\text{Odd and greater than 6)}=\frac{1}{2}\times\frac{1}{4} \\ P(\text{Odd and greater than 6)}=\frac{1}{8} \end{gathered}\)FINAL ANSWER:
\(\frac{1}{8}\)Please help I need this will give 100 points please help
The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:
-∞ < x < 1 or 1 < x < 6 or 6 < x < 2
Solving Inequality in a given domainGiven the inequality,
f(x²-2) < f(7x-8) over D₁ = (-∞, 2)
We need to find the values of x that satisfy this inequality.
Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.
First, we can find the values of x that make the expressions inside the function equal:
x² - 2 = 7x - 8
Simplifying, we get:
x² - 7x + 6 = 0
Factoring, we get:
(x - 6)(x - 1) = 0
So the values of x that make the expressions inside the function equal are x = 6 and x = 1.
We can use these values to divide the domain (-∞, 2) into three intervals:
-∞ < x < 1, 1 < x < 6, and 6 < x < 2.
We can choose a test point in each interval and evaluate
f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.
Let's choose -1, 3, and 7 as our test points.
When x = -1, we have:
f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)
Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.
When x = 3, we have:
f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)
Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.
When x = 7, we have:
f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)
Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.
Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:
-∞ < x < 1 or 1 < x < 6 or 6 < x < 2
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A soda factory makes 9 flavors of soda. Each case of soda has 5 cans of each flavor. They produce enough soda to fill 7 cases per hour, 14 hours a day. How many cans of soda does the factory produce in 6 days?
26,460 cans of soda
Step-by-step explanation:
First times 9 and 5 together then times 7 with it then times 14 then times 6 and you should end up with 26,460
-4 is greater than of equal to x - 11
Using the inequality rule we know that 11 is greater than -11, (11 > -11).
What is an Inequality Equation?Mathematical expressions with inequalities are those in which the two sides are not equal.
Contrary to equations, we compare two values in inequality.
Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.
So, let's say the inequality equation looks like this: A
Right now, A is valued at
Let p be used to representing the initial number.
P equals 11, so
Let q be used to representing the second number.
Q has a value of -11.
-11 and 11 are both numbers that are greater than zero.
Then, 11 > -11 ... (1)
A has a value of 11 > -11.
Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).
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Correct question:
Is 11 greater than, equal to, or less than -11?
identify each function as linear or exponential. explain. prompt 1f(x) equals the number of boxes in row x of a stack in which each row increases by 2 boxes answer for prompt 1 f(x) equals the number of boxes in row x of a stack in which each row increases by 2 boxes prompt 2f(x) equals the number of branches at level x in a tree diagram, where at each level each branch extends into 4 branches.
\(f(x) = 2x is linear.f(x) = 4^x is exponential.\) This is where at each level, each branch extends into 4 branches.
In the first prompt, the number of boxes in each row is increasing by a constant amount, so the function is linear. In the second prompt, the number of branches is increasing by a factor of 4 with each level, so the function is exponential.
A linear function is defined as one where the output increases by a constant amount for each increase in the input. An exponential function is defined as one where the output increases by a constant factor for each increase in the input. The first prompt corresponds to a linear function, while the second prompt corresponds to an exponential function.
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The complete question is-
Is the function f(x) = 4^x, where x is the number of branches at level x in a tree diagram, linear or exponential? Explain your answer.
The function F is given in 3 equivalent forms.
Which form most quickly reveals the y intercept?
Look at image below
Part 2: what is the y intercept?
The form that most quickly reveals the y intercept is
B f(x) = 1/2 x² - 5x + 21/2The y intercept is (0, 21/2)
What is y-intercept?The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.
In the form, f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept
hence we can easily say that the y intercept is (0, 21/2)
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Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.
Answer:
\(\huge\boxed{\sf Yes.}\)
Step-by-step explanation:
In a right angled triangle, the longest side is called hypotenuse.
So,
Hypotenuse = 13 m
The rest are:
Base = 5 m
Perpendicular = 12 m
Using Pythagoras Theorem to verify:
\((Hypotenuse)^2=(Base)^2+(Perpendicular)^2\)
Put the given data
(13)² = (12)² + (5)²
169 = 144 + 25
169 = 169Since, both left hand side and right hand side are equal, this means the triangle is a right-angled triangle.
\(\rule[225]{225}{2}\)
Solve f(-4) for f(x) = 7x - 4x
f(-4)= [?]
Enter
ternational Academy of Science. All Rights Reserved.
Answer:
-12
Step-by-step explanation:
What you have to do is plug -4 into the function as a puzzle. So, replace all x with -4.
f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12
f (-4) = 7x ( 1-4 ) - 4 (-4)
= -28 + 16
= -12
What is a equation example?
An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.
A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.
Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.
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Given DEF= WXY, use the Hypotenuse- Leg Congruence Theorem to find x.
A. 30
B. 45
C. 60
D. 90
E. 15
The correct option is A. 30° for the value of x in the similar triangles right triangles DEF and WXY.
What is the hypotenuse-leg congruent theorem for triangles?The hypotenuse-leg congruent theorem states that if two right-angled triangles have congruent legs, then their hypotenuses are also congruent.
it also implies that angle D is equal to angle W and angle F is equal angle Y
so;
x + 2x + 90 = 180° {sum of interior angles of a triangle}
3x + 90° = 180°
3x = 180° - 90° {subtract 90° from both sides}
3x = 90°
x = 90°/3 {divide through by 3}
x = 30°
Therefore, the value of x in the similar triangles right triangles DEF and WXY is equal to 30°
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Choose the function whose graph is given by:
IN
OA. y = sec(x) +2
B. y = sec (2x)
OC. y = 2sec(-x)
OD. y = 2csc(-x)
12s
J
35+
Answer:
C
Step-by-step explanation:
If you start by picking a point to plug in you can check easily to see what works.
Lets start with x=pi. If we plug that into all the answer choices,
A. sec(pi/2)+2 = does not exist
B. 1/2sec(2pi) = 1/2
C. 2sec(pi/2) = does not exist
D. 2csc(pi/2) = 1
So, since at pi there is a vertical asymptote it should not exist. So, A or C.
Then pick x = 0, y must be 2.
A. sec(0) +2 = 1+2 = 3
C. 2sec(0) = 2
So, C must be the answer.
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
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Determine whether the system
has no, one, or infinitely many
solutions.
2x + 3y = -17
y = x - 4
A. infinitely many solutions
B. one solution
C. no solutions
On studing about the nature of system of linear equation the correct option is B.
How to determine the nature of system of linear equations of two variables?
Consider the following two linear equations:
\(a_1x + b_1y + c_1 = 0a_2x + b_2y + c_2 = 0\)
(1) If \(\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\) them the system of equations have unique solution.
(2) If \(\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}\) them the system of equations have infinitely many solutions.
(3) If \(\frac{a_1}{a_2}= \frac{b_1}{b_2}\ne \frac{c_1}{c_2}\) them the system of equations have no solution.
Now, consider the given equation.
2x+3y = -17
y = x - 4
Rearrange the above equation as follows:
2x+3y +17 = 0
x - y - 4 = 0
Now, on comparing,
\(a_1=2, a_2=1, b_1=3, b_2=-1, c_1=17, c_2=-4\)
Now, take ratio as follows:
\(\frac{a_1}{a_2}=\frac{2}{1}\\\frac{b_1}{b_2}=\frac{3}{-1}\\\frac{c_1}{c_2}=\frac{17}{-4}\)
It satisfies the first condition hence, there is one solution for the system of equations.
Hence, the correct option is B.
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Find the value of m if 2y³+my²+11y+m+3 is exadly divisible by (2y-1)
\(\large\underline{\sf{Solution-}}\)
Given that:
\(\sf p(y) = 2y^3+my^2+11y+m+3 \)
We are also given that, p(y) is divisible by 2y - 1.
So, 2y - 1 is a factor of p(y).
\(\sf\longmapsto 2y-1=0\)
\(\sf\longmapsto y=\dfrac{1}{2}\)
So, 1/2 is a zero of p(y).
\(\sf\longmapsto p(1/2) =0 \)
\(\sf\longmapsto p(y) = 2y^3+my^2+11y+m+3 \)
\(\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right)^3+m\left(\dfrac{1}{2}\right)^2+11\left(\dfrac{1}{2}\right)+m+3 \)
So,
\(\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{8}\right)+m\left(\dfrac{1}{4}\right)+11\left(\dfrac{1}{2}\right)+m+3 \)
\(\sf\longmapsto p\left(\dfrac{1}{2}\right) = \dfrac{1}{4}+\dfrac{m}{4}+\dfrac{11}{2}+m+3 \)
\(\sf\longmapsto p\left(\dfrac{1}{2}\right) =\dfrac{1}{4}+\dfrac{m}{4}+\dfrac{22}{4}+\dfrac{4m}{4}+\dfrac{12}{4} \)
\(\sf\longmapsto 0 =\dfrac{1+m+22+4m+12}{4} \)
\(\sf\longmapsto 0 =\dfrac{5m+35}{4}\)
\(\sf\longmapsto 5(m+7)=4\times0\)
\(\sf\longmapsto 5(m+7)=0\)
\(\sf\longmapsto m+7=0\)
\(\longmapsto\bf m=-7\)
Therefore, the value of m is -7.
12 and a half percent of 48.40
Answer:
6.05
Step-by-step explanation:
12 and a half percent of 48.4 = 6.05 because you can put .125 in your calculator and it is the same at 12.5% so you do .125 * 48.40 and you get 6.05
Movie tickets cost $6 for adults and $2 for children under the age of 12. If 175 movie tickets were sold with cash receipts of $750, how many children’s tickets were sold?
Answer:
75 child tickets and 100 adult tickets were sold.
Step-by-step explanation:
Given that adult tickets cost $ 6 and children's tickets cost $ 2, knowing that 175 tickets were sold for $ 750, to determine how many child tickets were sold the following calculation must be performed:
2 x 175 = 350
750 - 350 = 400
6 - 2 = 4
400/4 = 100
175 - 100 = 75
100 x 6 = 600
75 x 2 = 150
Therefore, 75 child tickets and 100 adult tickets were sold.
please answer this. i’ve asked 3 questions of this same thing bc people don’t even answer them, i’ll give brainliest to whoever answers correctly. i’m failing and really need this answered
1. A wave has a wavelength of 5 m and a frequency of 2 Hz. At what speed/velocity does the
wave travel?
2. The speed/velocity of a wave on a guitar string is 100m/s and the frequency is 1,000 Hz. What
is the wavelength of the wave?
3. If the speed/velocity of a wave is 25 m/s and the wavelength is 5 m, what is the frequency of
this wave?
We will be using the formula: Speed = Wavelength * Frequency
1. Given: Wavelength = 5 m and Frequency = 2 Hz
Speed of the wave = Wavelength * Frequency
Speed of the wave = 5 * 2
Speed of the wave = 10 m/s
__________________________________________________________
2. Given: Speed of the wave = 100 m/s and Frequency= 1000 Hz
Wavelength = Speed / Frequency
Wavelength = 100 / 1000
Wavelength = 0.1 m
__________________________________________________________
3. Given: Speed of the Wave = 25 m/s Wavelength = 5 m
Frequency = Speed / Wavelength
Frequency = 25 / 5
Frequency = 5 Hz
m over 8 minus 5 equal 12
Answer:
m = 136
Step-by-step explanation:
m/8 - 5 = 12
1. Add 5 on both sides
m/8 - 5 + 5 = 12 + 5
m/8 = 17
Multiply 8 on both sides since u are trying to isolate the variable
m/8 * 8 = 17*8
m = 136
Check
136/8 - 5 = 12
17 - 5 = 12
12 = 12
Hope it helped!
Step-by-step explanation:
\(\frac{m}{8}\) - 5 = 12 : Original Problem
\(\frac{m}{8}\) -5 +5 = 12 + 5 : Bringing the constants to one side
\(\frac{m}{8}\) = 17 : Simplification
\(\frac{m}{8}\)×8 = 17×8: Isolating the variable
m = 136 : The answer!!!
Checking the answer
\(\frac{136}{8}\) -5 = 12 : Substitution
\(\frac{136}{8}\) = 17 : Bringing constants to one side and simplification
136 = 17 × 8 : Isolating the answer
136 = 136 : Success!!!
I hope this is what you wanted and I hope this helps!!!
Find the equation of the parabola by short cut.Focus (0,2) and directrix: y=6
Given:
\(undefined\)In a random sample of 1500 Arts majors who are graduating from the University of Western Cape this summer (2021), we observe that 1380 have already found a job.
What is the proportion of students that have already NOT found a job (rounded off to two decimals)? [3]
The proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places.
To find the proportion of Arts majors who have not found a job, we first need to calculate the total number of students who have not found a job.
The total number of students who have not found a job would be 1500 - 1380 = 120.
To calculate the proportion of students who have not found a job, we can divide the number of students who have not found a job by the total sample size:
The proportion of students who have not found a job = 120 / 1500 = 0.08 or 8%.
Therefore, the proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places. This suggests that a majority of the graduating Arts majors from the University of Western Cape have found employment before their graduation.
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What number has 5 hundred thousands, 2 fewer ten thousands than hundred thousands, 2 more thousands than hundred thousands, 2 more hundreds than ten thousands, 2 fewer tens than hundred thousands, and the same number of ones as hundreds?
Answer:
537,535
Step-by-step explanation:
To solve this, we can first insert the 5 hundred thousands.
5 _ _, _ _ _
To solve for 2 fewer ten thousands than hundred thousands, we can use this equation:
5 - 2 = 3Inserting 3 into the equation:
5 3 _, _ _ _
To solve for 2 more thousands than hundred thousands, we can use this equation:
5 + 2 = 7Inserting 7 into the equation:
5 3 7, _ _ _
To solve for 2 more hundreds than ten thousands, we can use this equation:
3 + 2 = 5Inserting 5 into the equation:
5 3 7, 5 _ _
To solve for 2 fewer tens than hundred thousands, we can use this equation:
5 - 2 = 3Inserting 3 into the equation:
5 3 7, 5 3 _
To solve for the final one, the same number of ones as hundreds, we can just insert 5 into the equation.
5 3 7, 5 3 5
Therefore, the number is 537,535.
Charls invested $140. She earned a simple interest of 3% pee year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charls received at the ned of two years?
Answer:
$148.4
Step-by-step explanation:
140 times 0.03=4.2
4.2=8.4
140+8.4=148.4
Question:
Given the demand equation p=190/q+10 where 10<0<85, for what value of q is | n | a maximum? For what value is it minimum?
The maximum and minimum value of η at q = 10 and q = 85 respectively.
The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.
η is the elasticity of demand.
Then, the elasticity of demand is given as:
η = ( dq/ dp) × ( p / q )
Now, we have p = 190/ (q + 10)
Therefore,
p ( q + 10 ) = 190
pq + 10p = 190
q = ( 190 - 10p ) / p
Now,
dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )
dq / dp = ( -190/ p² )
Substituting these values in the elasticity demand,
η = ( dq/ dp) × ( p / q )
η = ( -190/ p² ) × ( p / q )
η = ( -190/ pq )
η = ( -190/ [190 / (q + 10 ) ]q )
η = [ - ( q + 10 ) / q ]
| η | = | - ( q + 10 ) / q |
η = ( q + 10 ) / q = 1 + 10/q
The critical point is when | η' | = 0.
η' = ( d / dq ) ( 1 + 10/q )
η' = - 10/ q²
- 10/ q² = 0
Hence, - 10/ q² is not defined.
Therefore, the function is not defined at q = 0.
Therefore, q = 0 is not a solution.
We have 10 ≤ q ≤ 85
The value of functions at the endpoint,
At q = 10,
η = ( 1 + 10/q )
η = ( 1 + 10/10 )
η = 1 + 1 = 2
At q = 85,
η = ( 1 + 10/q )
η = ( 1 + 10/85 )
η = 1.11764
Therefore, the absolute value of the elasticity of demand is maximum at q = 10.
The absolute value of the elasticity of demand is minimum at q = 85.
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lcm of 40,36,126
a)2520
b)2568
Answer:
The correct choice is option a. 2520
Step-by-step explanation:
LCM of 40, 30, and 126 is as followed:
= 2 × 2 × 2 × 3 × 3 × 5 × 7
= 2520
Answer:
a)2520 is correct
Compare with using >, =, or <
answer for 100 points
:D
The numbers are compared with the inequality symbols as follows:
a. 3 > -3.
b. 12 < 24.
c. -12 > -24.
d. 5 = - (-5).
e. 7.2 > 7.
f. -7.2 < 7.
g. -1.5 = -3/2.
h. -4/5 > -5/4.
i. -3/5 = -6/10.
j. -2/3 < 1/3.
What are the inequalities?The inequality symbols used in this problem are defined as follows:
>: greater than.=: equals to.<: less than.The observations to some items are given as follows:
c. -12 > -24 -> for negative numbers, the lower the absolute value of the number, the greater it is.d. 5 = - (-5) -> applying the parenthesis, we have that: - (-5) = 5, as the negative before the parenthesis changes the sign inside the parenthesis.g. -1.5 = -3/2. -> the fraction is converted to decimal dividing the numerator of -3 by the denominator of 2.More can be learned about inequalities at https://brainly.com/question/25275758
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pls solve this thanks
the equation below represents the total price of Michigan State University per semester where c represents the number of classes and t represents the total cost for the semester including a one time fee for room and board
The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).
The equation captures the relationship between these variables and calculates the overall cost for a student attending the university. It is important to note that the equation provides a quantitative representation and does not take into account other factors such as scholarships, financial aid, or additional expenses. Therefore, the equation serves as a useful tool for estimating the total cost of attending Michigan State University, allowing students and their families to plan and budget accordingly for their education.For such more question on equation
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The distance around a triangle is 40 centimeters. If two sides are equal and the length of the third side is 10 centimeters, what is the length of each of the other two sides?
Answer:
15 centimeters each = the two other sides of the triangle is 30 cm.
Step-by-step explanation:
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Which of the following is an EXPLICIT formula for the sequence 12, 15, 18, 2 points
21...
Help please!!
Answer:
An=12+3(n-1) это просто
In the trapezoid, find the measure of yº
(6x + 20°? Can y’all help?
Answer:
y=64°
Step-by-step explanation:
Within a trapezoid, the angles on the same side of a leg add up to 180:
(6x+20)+(4x)=180
6x+4x=180-20
10x=160
x=16
Since the base lines are parallel, and the leg lines are equal in length, y=4x
y=4(16)
y=64°
Can some please explain how to solve this? Thank you. 1/2(3/2y+1/3)=-1/2(y-5/2)
Answer:
Step-by-step explanation:
52y−13=−12 5 2 y - 1 3 = - 1 2. Combine 52 5 2 and y y . 5y2−13=−12 5 y 2 - 1 3 = - 1 2. Move all terms not containing y y to the right side of the equation.