Answer:
1/6
Step-by-step explanation:
Use conditional probability:
P(A given B) = P(A and B) / P(B)
P(4 given 3) = P(4 and 3) / P(3)
P(4 given 3) = (1/36) / (1/6)
P(4 given 3) = 1/6
Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large
rectangles of thick cardboard with a length of 12 inches and width of 8 inches to make the boxes.
She is interested in maximizing the volume of the boxes and wants to know what size squares to
cut out at each corner of the cardboard (which will allow the corners to be folded up to form the
box) to do this. What is the maximum volume?
Answer:
x = 1,6 in ( the side of the corner squares )
V(max) = 67,58 in³
Step-by-step explanation:
The cardboard is:
L = 12 in w = 8 in
Let´s call "x" the side of the square from the corner:
Then the sides of the base of the open box are:
( L - 2*x ) and ( w - 2*x ) and x is the height
( 12 - 2*x ) and ( w - 2*x )
V(ob) = (L - 2*x ) * ( - 2*x ) * x
Wich is a function of x
V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x
V(x) = ( 96 - 24*x - 16*x + 4*x²) * x
V(x) = 96*x - 40*x² + 4*x³
Tacking derivatives on both sides of the equation
V´(x) = 12*x² - 80*x + 96
V´(x) = 0 12*x² - 80*x + 96 = 0
Solving for x
x₁,₂ = 80 ± √ 6400 - 4608 / 24
x₁,₂ = 80 ± 42,33 / 24
x₁ = 5,10 We dismiss this solution since 2*x becomes 2*5,10 = 10,20
ant this value is bigger than 8 inches
x₂ = 1,60 in
Therefore dimensions of the box
a = 12 - 2*x ; a = 12 - 3,20 ; a = 8,8 in
b = 8 - 2*x ; b = 8 - 3,20 ; b = 4,80 in
And the volume of the open box is:
V(max) = 8,8*4,8*1,6
V(max) = 67,58 in³
How do we Know that is the maximun value for V?
We find V´´(x) = 24*x - 80 for x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has a local maximun for a value of x = 1,6
What is the quotient between 215÷9
215/9
= 23.888888........
It is written as shown in the picture
5+5 is what i can not even get it is hard
Answer:
Step-by-step explanation:
10 plzz give me brainliest see ya
find the missing value for each of the following 3 questions
1. 5% of 60 is _____
2. 40% of 500 is _____
3. 75% of 60 is ______
Answer:
1. 3
2. 200
3. 45
Step-by-step explanation:
what is the value of the digit in the tens place? 6,423
Answer: 20 :)
Step-by-step explanation:
I didn't grasp this topic too well. can someone help me?
Answer:
2 hours
Step-by-step explanation:
I'm pretty sure its 2 hrs. If she did not take any breaks, she would have made it in 2 hrs due to her taking a 2 hr break. If its not 2 hours, its 3. But I am 99% sure its 2 hrs.
The equations y = tan^2 (x) and y = 1 are graphed below. According to the graphwhich of the following is part the solution to the trigonometric inequality tan^2 (x) < 1 over the interval 0 <= x <= 2pi radians?
Answer: a
Step-by-step explanation:
just took test edg2020
The part of the solution of the equation that lies in the solution region of the inequality is x = π/6, the correct option is A.
What is an Inequality?An Inequality is a statement that is formed when two expressions are joined using an inequality operator.
The equation is
y = tan²x
y = 1
the inequalities are
tan²x < 1 ( 0≤ x ≤ 2π)
The graph of the system of equations and the inequality is plotted, and attached with the answer.
The answer can be seen as x = π/6.
To know more about Inequality
https://brainly.com/question/20383699
#SPJ5
y=x+5 and y=3x-3 I need to get this in a ordered pair
9514 1404 393
Answer:
(x, y) = (4, 9)
Step-by-step explanation:
Perhaps the ordered pair you want is the one that satisfies both equations.
We can find that by equating the expressions for y:
x +5 = 3x -3
8 = 2x . . . . . . . . add 3-x to both sides
4 = x . . . . . . . . . divide by 2
y = 4+5 = 9
The ordered pair is (x, y) = (4, 9).
help:) Factor f(x) = 4x^3+ 23x^2- 70x + 16 into linear factors given that - 8 is a zero of f(x).
Answer:
(x + 8)(x - 2)(4x - 1)
Step-by-step explanation:
Given that x = - 8 is a zero then (x + 8) is a factor
Divide f(x) by (x + 8) using Synthetic division
- 8 | 4 23 - 70 16
↓ - 32 72 - 16
---------------------------------
4 - 9 2 0
Quotient = 4x² - 9x + 2 = (x - 2)(4x - 1)
Thus
f(x) = (x + 8)(x - 2)(4x - 1)
Please answer this correctly without making mistakes
Answer:
4 dollars per pound
Step-by-step explanation:
3 x 4 =12
I WILL MARK BRAINLIST
Answer:
The answer is D
Step-by-step explanation:
The Jones family has a monthly income of $6,500. The budgeted the following: Retirement savings $700, Emergency savings $550, and Housing expenses $1,300. Which of the following shows the percentage of income used for housing expenses
Answer:
1867
Step-by-step explanation:
took the test
I NEED ANSWER ASAP PLEASE
NEED HELP
Look at the shaded products. All of the products are the same number. What is true about the pattern?
One of the factors is always 1. When you multiply a number by 1, the product is that number.
One of the factors is always 1. When you multiply a number by 1, the answer is always 1.
One of the factors is always 0. When you multiply a number by 0, the product is that number.
One of the factors is always 0. When you multiply a number by 0, the product is always 0.
Answer:
The Answer is One of the factors is always 0. When you multiply a number by 0, the product is always 0.
Saleh can jog 2 3/7 miles in 6/11 hour. Find his average speed in miles per hour.
Answer:
3.73
Step-by-step explanation:
Nancy invested $750 per month in a 401k that earned 6% annual return for 30 years. Alex
invested $1,500 per month in a 401k that also earned 6% annual return, but for 15 years. Which
of the following would be true?
Nancy's balance would be greater than Alex's in the end.
O Nancy's balance is $4,308 and Alex's balance is $3,595.
O Alex's balance would be greater than Nancy's in the end.
The investment and balance would be the same in the end.
Answer:
A and BStep-by-step explanation:
Nancy's balance:
750*(1 + 0.06)^30 = $4308 rounded to whole numberAlex's balance:
1500*(1 + 0.06)^15 = $3595 rounded to whole numberOptions:
A. Nancy's balance would be greater than Alex's in the end.
CorrectB. Nancy's balance is $4,308 and Alex's balance is $3,595.
CorrectC. Alex's balance would be greater than Nancy's in the end.
IncorrectD. The investment and balance would be the same in the end.
Incorrect∠10 and angle _____ are complementary angles.?
a.) ∠9 I
b.)∠11 O
Answer:
9
Step-by-step explanation:
they add up to 90 degrees
Answer: B
Step-by-step explanation:
HAVE A BLESSED DAY!!!!!!
What is the chance of rolling two dice and the dice add up to six?
around 13% chance
Step-by-step explanation:
2. Which relation below is NOT a function?
A. {(-2, 4), (1,3), (0,4)}
B. {(5,5), (4,4), (3,3) }
C. {(-4,0), (-7,0), (11, 0)}
D. {(1,4), (2,5) (1,7)}
C is the answer to that question i think
Answer:
b
Step-by-step explanation:
The answer is B because different X values cannot have the same y values. For example in A the x values, -2 and 0, have the same y value 4. That's not possible.
Although C also has a similar problem ALL of the X values have the same y value meaning that the function is an undefined function which is still a type of function. Its basically a function where all the y values are the same.
Divide 7560 in the ratio 4 : 5
Answer:
3360 4200
Step-by-step explanation:
8,900 incoming freshman to a university take an entrance exam, with the top 10% being offered admission to the university's honors program. The average test score is 78%, with a standard deviation of 11%. Use a calculator to find what the student must score to be invited to join the honors program if only 65 scores are looked at to determine the honors admissions requirement.
Answer:
The student must score 79.75% to be invited to join the honors program.
Step-by-step explanation:
Let X denote the score of a freshman in the entrance exam.
It is provided that the average test score is 78%, with a standard deviation of 11%.
It is provided that the top 10% being offered admission to the university's honors program.
Let x denote the score eligible for being offered admission to the university's honors program.
Then, P (X ≤ x) = 0.90.
Then P (Z < z) = 0.90.
The corresponding z-score is, 1.28.
*Use a z-table.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n}}\\\\1.28=\frac{x-78}{11/\sqrt{65}}\\\\x=78+(1.28\times \frac{11}{\sqrt{65}})\\\\x=79.75\%[/tex]
Thus, the student must score 79.75% to be invited to join the honors program.
Graph a line with a slope of 4 that contains the point (3,0).
Hi there!
Recall that slope-intercept form is:
y = mx + b
Where m = slope
In this instance, we are given a slope of 4, therefore:
y = 4x + b
Substitute in the x and y coordinates of the point given:
0 = 4(3) + b
0 = 12 + b
Subtract 12 from both sides:
-12 = b
Therefore, the equation would be:
y = 4x - 12
Graph the equation by finding x and y values or using a calculator:
x = 0, y = 4(0) - 12 = 12 (0, 12)
x = 1, y = 4(1) - 12 = -8 (1, -8)
x = 2, y = 4(2) - 12 = -4 (2, -4)
x = 3, y = 4(3) - 12 = 0 (3, 0)
And so forth:
To graph a line passing through a point (3, 0) and slope 4, we will find the equation of the line first.
Since, equation of a line passing through a point (h, k) and slope 'm' is given by,
y - k = m(x - h)
Therefore, equation of a line passing through (3, 0) and slope 4 will be,
y - 0 = 4(x - 3)
y = 4x - 12
For y-intercept put x = 0 in the equation,
y = 4(0) - 12
y = -12
For x-intercept put y = 0 in the equation,
0 = 4x - 12
x = 3
Therefore, line will intersect x-axis at (3, 0) and y-axis at (0, -12).
By joining these points we can find the graph of the line passing through (3, 0) and having slope = 4.
Learn more,
https://brainly.com/question/18817730
Solve the word problem using a proportion. Danny, who was 6 ft tall, cast a 15 ft shadow. The building he was standing next to cast a 35 ft shadow. How tall was the building? 30 ft, 70 ft, or 14 ft?
Answer: 14 feet
Step-by-step explanation:
Answer:
14 feet
Step-by-step explanation:
Lisa and Rachel want to determine their muscular endurance, but they don't have access to a gym or any weight-lifting equipment. What can they use?
A.
maxing out method
B.
percent of 1 RM method
C.
calisthenic method
D.
absolute method
Answer:
C- calisthenic method
Step-by-step explanation:
In the absence of the weight-lifting equipment, it is also possible to measure the muscular endurance by the use of the calisthenic method.
What is muscular endurance?The term muscular endurance has to do with the ability of a muscle to undergo a strenous activity repeatedly without being fatigued. It is common to measure muscular endurance by the use of weight-lifting equipments.
In the absence of the weight-lifting equipment, it is also possible to measure the muscular endurance by the use of the calisthenic method.
Learn more about calisthenic method: https://brainly.com/question/13037898
#SPJ2
Find the equation of the line parallel to y=3x+5 that passes through (0,4) y=3x+4
HELP ME!!
The number of tiktoks celia can make varies directly with the numbers of hours she spends making them. She can make 8 tiktoks in 1/2 an hour. How many tiktoks can she make in 3 hours?
Answer:
She can make 48 in 3 hours.
Step-by-step explanation:
Step-by-step explanation:
3*1/2=equivalent to an hour and 5 minutes which she would do would be about 48
Determine whether the two lines are parallel, perpendicular, coinciding, or only intersecting. y = - 2x + 7 6x + 3y = 1 Choose the correct answer below. coinciding O only intersecting O parallel O perpendicular
Answer:
Intersecting
Step-by-step explanation:
$6,000 is invested in an account at interest rate r, compounded continuously. Find the time (in years) required for the amount to double when r= 9.5% and when r=2.5%.
Answer: When r= 9.5% , time = 7.3 years
When r= 2.5% , time = 27.7 years
Step-by-step explanation:
Exponential equation for compounded continuously:
[tex]A=Pe^{rx}[/tex] , where P= Principal value invested , r= rate of interest, x= time
Given : P= $6,000
A = 2P= 2 ($6,000) = $12,000 (i)
When r= 9.5%= 0.095
[tex]A= 6000e^{0.095x}[/tex] (ii)
From (i) and (ii)
[tex]6000e^{0.095x}=12000\\\\\Rightarrow\ e^{0.095x}=2\\\\\Rightarrow\ \ln e^{0.095x} =\ln 2\\\\\Rightarrow\ 0.095x=0.693147\\\\\Rightarrow\ x=\dfrac{0.693147}{0.095}=7.296284210\approx7.3 \text{ years}[/tex]
For r= 2.5% = 0.025
[tex]6000e^{0.025x}=12000\\\\\Rightarrow\ e^{0.025}=2\\\\\Rightarrow\ \ln e^{0.025x} =\ln 2\\\\\Rightarrow\ 0.025x=0.693147\\\\\Rightarrow\ x=\dfrac{0.693147}{0.025}=27.72588\approx27.7 \text{ years}[/tex]
find if the series converges conditionally, converges absolutely, or diverges ∑k=1 ∞ (k^2k 3^k)/k!
Answer:
Diverges
Step-by-step explanation:
Using the ratio test to test the series:
Given f(x)=2x+5 find f(3)
answer choices are:
1. ) 28
2.) -28
3.) 11
4.) 6x+5
5.) 5
Answer:
3.) 11
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
f(x) = 2x + 5
f(3) is x = 3
Step 2: Solve
Substitute: f(3) = 2(3) + 5Multiply: f(3) = 6 + 5Add: f(3) = 11