Answer: V(W) = (1/3)*(*W^2*800ft - 8W^3) and the domain is 0 < W < 100ft.
Step-by-step explanation:
The dimensions of the box are:
L = length
W = width
H = heigth.
We know that:
L = 4*W
And the girth of a box is equal to: G = 2*W + 2*H
then we have:
2*W + 2*H + H = 200ft
2W + 3*H = 200ft
Then we have two equations:
L = 4*W
2W + 3*H = 200ft
We want to find the volume of the box, which is V = W*L*H
and we want in on terms of W.
Then, first we can replace L by 4*W (for the first equation)
and:
2*W + 3*H = 200ft
3*H = 200ft - 2*W
H = (200ft - 2*W)/3.
then the volume is:
V(W) = W*(4*W)*(200ft - 2*W)/3
V(W) = (1/3)*(*W^2*800ft - 8W^3)
The domain of this is the set of W such that the volume is positive, then we must have that:
W^2*800ft > 8W^3
To find the maximum W we can see the equality (the minimum extreme is 0 < W, because the width can only be a positive number)
W^2*800ft = 8W^3
800ft = 8*W
100ft = W.
This means that if W is equal or larger than 100ft, the equation gives a negative volume.
Then the domain is 0 < W < 100ft.
Which expression correctly represents “six more than the product of five and a number, decreased by one”?
Answer:
Step-by-step explanation:
Product of 5 and a number: 5n
Six more than that would be 5n + 6
Finally, "six more than the product of 5 and a number, decreased by one" would be
5n + 6 - 1, or 5n + 5
Answer: A) 6 + 5n - 1
Step-by-step explanation: edge. 2022
A director of the library calculates that 10% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 899 books would be less than 11%? Round your answer to four decimal places.
Answer:
0.8413
Step-by-step explanation:
p = 0.10
σ = √(pq/n) = 0.01
z = (x − μ) / σ
z = (0.11 − 0.10) / 0.01
z = 1
P(Z < 1) = 0.8413
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
We have,
We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.
First, we need to calculate the mean and standard deviation of the binomial distribution:
Mean:
np = 899 × 0.1 = 89.9
Standard deviation:
√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427
Next, we need to standardize the sample proportion of 11% using the formula:
z = (x - μ) / σ
where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Substituting the values we have, we get:
z = (0.11 - 0.1) / 0.9427 = 0.1059
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.
Therefore,
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
Rounded to four decimal places, the answer is 0.5425.
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Please answer this correctly
Answer:
60%
Step-by-step explanation:
Total Cards = 5
Even Numbers = 3
P(even) = 3/5
In %age:
=> 60%
Answer:
60%
Step-by-step explanation:
The numbers that are even from the list are 2, 4, and 6.
3 numbers are even out of 5 total numbers.
3/5 = 0.6
P(even) = 60%
A farmer is enclosing a rectangular area for a pigpen. He wants the length of the pen to be 20 ft longer than the width. The farmer can use no more than 100 ft of fencing. What is the pen’s greatest possible length? Let w represent the width of the pen. What expression represents the length?
Answer:
Width is 15, length is 35.We can check our answer by multiplying the length by 2 and the width by two in order for the perimeter to be equal to 200.15 times 2 is 30 and 35 times two equals 70.70+30=100 so our solution satisfies our problem.
Step-by-step explanation:
Let the width be x.Then the length should be x+20.The farmer can’t use more than 100 ft of fencing and by mentioning enclosing a rectangle area for a pigpen, we can tell that 100 is the perimeter.So 2(x+20) + 2(x)=100.2x+ 40 + 2x=100.4x+40=100.4x=60.X is 15 which is the width so then the length is 35.
Solve by completing the square: 5x2 + 20x + 32 = 0
Pls cam someone help me
Extremely confused with both if poss xxxx
Answer:
1. Red red blue blue
2. Red blue red blue
Step-by-step explanation:
A 50 percent chance
PLEASE HELP I’LL MARK BRAINLIEST If 1 equals 1 2/3 how much does 1 1/2 equal?
Answer:
0.9 (9/10)
Step-by-step explanation:
(see picture)
1. The graph of yf(x) is translated 3 units right and 4 units down. What is the equation of the translation
image in terms of the function ?
A. Y-3 = f(x+4)
B. y + 4 = f(x-3)
C. y + 3 = f(x-4)
D. y - 4 = f(x + 3)
Answer:
D.y-4=f(x+3)
Step-by-step explanation:
The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
The equation of the translation image of the function is y - 4 = f(x + 3).
which is the correct answer would be an option (D).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to the function
If shift down by 4 units, subtract 4 from the function
To determine the graph of y (x) is translated as 3 units right and 4 units down.
The x-coordinate will increase by 3 if we move it to the right.
If we shift it downward, it will become negative and read as y - 4.
So y - 4 = f(x + 3)
Therefore, the equation of the translation image of the function is y - 4 = f(x + 3).
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The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is given in seconds and d is measured in meters. Find an expression for the instantaneous velocity v(t) of the particle at any given point in time. Question 1 options: 6t3 – 5 5t3 + 6 6t2 + 5 5t2 – 6
Answer:
(C)[tex]6t^2+5[/tex]
Step-by-step explanation:
Given the distance, d(t) of a particle moving in a straight line at any time t is:
[tex]d(t) = 2t^3 + 5t - 2, $ where t is given in seconds and d is measured in meters.[/tex]
To find an expression for the instantaneous velocity v(t) of the particle at any given point in time, we take the derivative of d(t).
[tex]v(t)=\dfrac{d}{dt}\\\\v(t) =\dfrac{d}{dt}(2t^3 + 5t - 2) =3(2)t^{3-1}+5t^{1-1}\\\\v(t)=6t^2+5[/tex]
The correct option is C.
Answer:
6t2+5
Step-by-step explanation:
PLEASE HELP!! 2. Helen and Stephen both simplify the exponential expression .
Helen:
Stephen:
Unfortunately, they both made an error. Identify where each person made his or her error and explain in words what he or she did wrong. Then, correctly simplify the expression.
Answer:
We start with the expression:
exp( (4/3)*ln(2) - 1)
Here we can use that:
exp(ln(x)) = x.
and e^(a + b) = e^a*e^b.
the first step here is:
e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)
So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.
now, we have that:
a*ln(x) = ln(x^a)
then we can write:
(4/3)*ln(2) = ln(2^(4/3))
and e^(ln(2^(4/3)) = 2^(4/3)
then we have:
e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e
now we can write this as:
∛(2^4)/e
here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.
so the expression actually is:
∛(16)/e
PLEASE ANSWER FAST!! THANK YOU :)
Answer:
option 1 both statements are true
Step-by-step explanation:
Prove by PMI -- Principle of Mathematical Induction
1) n³ + 2n
n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1 ---->divisible by 3
n = 2 ; 2³ + 2*2 = 8+4 = 12 = 3*4 ----> is divisible by 3
Assume that It is valid for n = k ;
[tex]k^{3}+2k[/tex] = 3*m -----(I) , for all m ∈ N
We have to prove for n =k +1 , the statement is true.
n = k+1, [tex](k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2[/tex]
= k³ + 3k² + 3k + 3 + 2k
= k³ + 2k + 3k² + 3k + 3
= 3m + 3 (k² + k + 1)
= 3(3 + [k² + k + 1] ) is divisible by 3
Therefore, this statement is true
2) [tex]5^{2n}-1\\[/tex]
[tex]n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24[/tex]
This statement is also true
The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How many different teams made up of two girls and two boys could be chosen?
Answer:
30 ways
Step-by-step explanation:
Given the following :
Number of boys in school (n1) = 5
Number of girls in school (n2) = 3
Total number of team members to be selected = 4
Number of boys required in team(r1) = 2
Number of girls required in team(r2) = 2
How many different teams made up of two girls and two boys could be chosen?
= (2 boys from 5) * (2 girls from 3)
Using combination :
5C2 * 3C2
Recall :
nCr = n! ÷ (n-r)! r!
5C2 = 5! ÷ (5-2)! 2!
5C2 = 5! ÷ 3!2!
5C2 = (5*4) / 2 * 1 = 10ways
3C2 = 3! ÷ (3-2)! 2!
3C2 = 3! ÷ 1!2!
3C2 = (3) / 1 = 3ways
3C2 = 3/1 = 3ways
10 * 3 = 30 ways
choose the function that has domain x ≠ -3 range y ≠ 2.
The function is f(x)= 2x+1/x+3.
How to find the domain of a function?A work domain is a set of all possible inputs for a job. For example, the domain f (x) = x² is all real numbers, and the domain g (x) = 1 / x is all real numbers except x = 0. And we can define the special functions of its most limited domains.
Which function has the domain and range?The function domain f (x) is a set of all values defined by the function, and the scope of the function is a set of all values taken by f. (In grammar school, you probably call the domain a set of substitutes and a set of solutions.
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Answer:
B
Step-by-step explanation:
i got it right! :)
please simplfy this equation
Answer:
0
Step-by-step explanation:
√12 can be rewritten as √2²·3 = 2√3
√75 can be rewritten as √5²·3 = 5√3
2/5 * 5 = 2
so
2√3 - 2/5 * 5√3 = 2√3 - 2√3 = 0
Answer:
0
Step-by-step explanation:
PLEASE HELP!!! How many 2-digit numbers are among the terms of the arithmetic sequence 2, 7, 12, 17, ...?
Step-by-step explanation:
The difference between. Each numbers is 5 so, it's answer is 22 and 27
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)∫414√lnxdx,n=6
Answer:
trapezoidal rule: 14.559027midpoint rule: 14.587831Simpson's rule: 14.577542Step-by-step explanation:
We assume you want the integral ...
[tex]\displaystyle\int_4^{14}{\sqrt{\ln{x}}}\,dx[/tex]
The width of each interval is 1/6 of the difference between the limits, so is ...
interval width = (14 -4)/6 = 10/6 = 5/3
Then the point p[n] at the left end of each interval is ...
p[n] = 4 +(5/3)n
__
Trapezoidal Rule
The area of a trapezoid is the product of its average base length multiplied by the width of the trapezoid. Here, the "bases" are the function values at each end of the interval. The integral according to the trapezoidal rule can be figured as ...
[tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}\left(\dfrac{f(p[n])+f(p[n+1])}{2}\right)[/tex]
integral ≈ 14.559027
If you're doing this on a spreadsheet, you can avoid evaluating the function twice at the same point by using a weighted sum. Weights are 1, 2, 2, ..., 2, 1.
__
Midpoint Rule
This rule uses the area of the rectangle whose height is the function value at the midpoint of the interval.
[tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}{f(p[n+\frac{1}{2}])}[/tex]
integral ≈ 14.587831
__
Simpson's Rule
This rule gives the result of approximating the function over each double-interval by a parabola. It is like the trapezoidal rule in that the sum is a weighted sum of function values. However, the weights are different. Again, multiple evaluations of the function can be avoided by using a weighted sum in a spreadsheet. Weights for 6 intervals are 1, 4, 2, 4, 2, 4, 1. The sum of areas is ...
[tex]\dfrac{10}{3}\sum\limits_{n=0}^{2}{\left(\dfrac{f(p[2n])+4f(p[2n+1])+f(p[2n+2])}{6}\right)}[/tex]
integral ≈ 14.577542
Write the function whose graph is the graph of y= Vx, but is translated 5 units downward.
Answer:
y = Vx - 5
Step-by-step explanation:
shift down is -5
y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The function y = Vx represents the square root function, which is a graph of a half of a parabola opening upwards and passing through the point (0, 0).
To translate this function 5 units downward, we need to subtract 5 from the function. Therefore, the function we need is:
y = Vx - 5
This is the square root function shifted downward by 5 units.
The graph of this function will be the same as the graph of y = Vx, but shifted 5 units downward.
Hence, y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.
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Help me find volume for this given radius please
Answer:
see below
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
= 4/3 pi ( 7)^3
= 1372/3 pi in^3
Using 3.14 for pi
V =1436.0266666 in^3
Using the pi button
1436.75504 in^3
Discuss Mason's notion that you are to be an engineer first and a statistician second. What does that mean to you in terms of how you think about the career you are studying to begin, and how do you think this class might impact a job interview you might ultimately go on later in your studies
Answer:
The answer is explained below
Step-by-step explanation:
What use are statistics if there is no engineer to use them? In other words, a statistician corrects, improves, reinforces, and supports an engineer in building / designing / developing a new product and / or improving an existing product.
The statistician provides a special kind of vision through which I see the same problem in a completely different vision. So you can see the strengths, weaknesses of my product and the promise of improvements that can be made.
Each class of statistics is essential for a student to see and understand a problem in a whole new way where it is much easier to understand information.
Vickie buys a pack of 30 folders. She keeps 15 for herself and divides the rest between three of her friends. Which equation will help us find the number of folders each friend gets? *
Answer: 30 folders - 15 folders which she keeps = 15 folders; 15 folders / 3 friends = 5 folders per firend.
Step-by-step explanation:
Answer:
x= (30 -15)/3
Step-by-step explanation:
Number of folders = 30Kept for herself = 15 foldersDivided = the reminderNumber of friends= 3Each friend gets= ?If we call x the number each friend gets, then the equation is:
x= (30 -15)/3Solving this we get:
x= 5Each friend gets 5 folders
Do 2b+ b and 3b have the same value for all values of b? explain your reason
Answer:
Yes
Step-by-step explanation:
b is as in 1b so. . .
2 + 1 = 3
We can plug in b or as "b"
2b + b = 3b
So yes in whatever case 2b + b's value will always equal 3b's value
Answer:
yes
Step-by-step explanation:
because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9
Which of the following is parallel to
2Y = 6X + 4?
A. Y = -3X + 3
B. Y = 3X + 4
C. Y = x + 3
D. Y = -2X - 3
E. Y= 1/2 X + 3
Answer:
B. y = 3x + 4
Step-by-step explanation:
Step 1: Find slope-intercept form of 1st equation
2y = 6x + 4
2y/2 = 6x/2 + 4/2
y = 3x + 2
A parallel line has the same slope but different y-intercept:
y = -3x + 3 (No, different slope)
y = 3x + 4 (Yes, same slope, different y-int)
y = x + 3 (No, different slope)
y = -2x - 3 (No, different slope)
y = 1/2x + 3 (No, different slope)
A flagpole is casting a 20 feet shadow. the flagpole measures 16 feet find the angle of elevation of the sun
Answer:
39°
Step-by-step explanation:
==>Given:
Shadow length = 20ft
Flag height = 16ft
==>Required:
Angle of elevation of sun (θ)
==>Solution:
To calculate the angle of elevation of the sun, recall the trigonometry formula SOHCAHTOA.
We are given adjacent side = 20ft, and opposite side = 16ft
Therefore, we would use TOA, which is:
tan θ = Opposite/Adjacent
tan θ = 16/20
tan θ = 0.8
θ = 38.6598083 ≈ 39°
Angle of elevation of the sun = 39°
7. Factor by grouping.
6p2 - 17p - 45
A (2p - 9)(3p + 5)
B (2p + 9)(3p + 5)
7096
Oc
C (2p - 9)(3p - 5)
90%
D (2p + 9)(3p - 5)
ping
Answer:
Step-by-step explanation: 4
1/4 ÷ 3/8 simplest form
Answer:
2/3
Step-by-step explanation:
divide by a fraction = multiply by reciprocal
1/4 * 8/3
2/3
Answer:
⅔
Step-by-step explanation:
= ¼ ÷ ⅜
= ¼ × ⁸/3
= ⅔
Have a great day !
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The non-even numbers are 1, 3, and 5 on the dice.
3 numbers out of 6.
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
Total sides of 6-sided die = 6
Numbers not even = 3
Probability of not getting an even = 3/6
=> 1/2
Try it
Evaluate the function g(x) = -2x² + 3x – 5 for the input values -2, 0, and 3.
g(-2) = -2(-2)2 + 3(-2) - 5
g(-2) = -2(4) - 6-5
g(-2) = ?
g(0) =?
g(3) =?
Answer:
g(-2) = -19g(0) = -5g(3) = -14Step-by-step explanation:
When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.
__
If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":
g(x) = (-2x +3)x -5
Then we have ...
g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19
g(0) = (-2(0) +3)(0) -5 = -5
g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14
A human resources specialist is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 61 people are unemployed. The following is the setup for this hypothesis test:
H0:p=0.05
Ha:p<0.05
Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
The following table can be utilized which provides areas under the Standard Normal Curve:
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029
-1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037
-1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046
-1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056
-1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068
Answer:
P-value =0.062
At a signficance level of 0.05, there is not enough evidence to support the claim that the unemployment rate is less than 5%.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the unemployment rate is less than 5%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]
The significance level is 0.05.
The sample has a size n=1500.
The sample proportion is p=0.041.
[tex]p=X/n=61/1500=0.041[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.041-0.05+0.5/1500}{0.0056}=\dfrac{-0.0087}{0.0056}=-1.5401[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.5401)=0.062[/tex]
As the P-value (0.062) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the unemployment rate is less than 5%.
What is the answer? ACB ~ EFD
Answer:
y=4solution,
[tex] \frac{ac}{ef} = \frac{cb}{fd} \\ or \: \: \frac{12}{y} = \frac{15}{5} \\ or \: 15 \times y = 12 \times 5( \: cross \: multiplication) \\ or \: 15y = 60 \\ or \: y = \frac{60}{15} \\ y = 4[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
The value of y is 4
Step-by-step explanation:
What is similarity ?
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
Given,
ΔACB~ΔEFD
The proportional sides are equal.
[tex]\frac{AC}{EF}=\frac{CB}{FD}=\frac{AB}{DE} \\\frac{12}{y}=\frac{15}{5} \\y=12*\frac{5}{15}\\\\ y=4[/tex]
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What is the area of the triangle?
9 4 12
Answer:
13.636
Step-by-step explanation:
The area can be found using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2.
For the given triangle, ...
a=9, b=4, c=12, s=(9+4+12)/2 = 12.5
A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636
The area of the triangle is about 13.636 square units.
Answer:
24 units\
Step-by-step explanation: