If [tex]f(x)=x^2e^{-x^3}[/tex], then the area between the graph of [tex]f(x)[/tex] and the x-axis for non-negative x is given by the integral,
[tex]\displaystyle\int_0^\infty x^2e^{-x^3}\,\mathrm dx[/tex]
Let [tex]u=-x^3[/tex] and [tex]\mathrm du=-3x^2\,\mathrm dx[/tex]; then the integral is equivalent to
[tex]\displaystyle-\frac13\int_0^{-\infty}e^u\,\mathrm du=\frac13\int_{-\infty}^0e^u\,\mathrm du=\frac13\left(1-\lim_{u\to-\infty}e^u\right)=\boxed{\frac13}[/tex]
what is the solution to the system of equations?
y = 4x-10
y=2
A) (3,2)
B) (2,3)
C) (-2,2)
D) (2,-2)
Answer:
A) (3, 2)
Step-by-step explanation:
y = 4x - 10
y = 2
Substitute y with 2 in the first equation and solve for x.
y = 4x - 10
2 = 4x - 10
12 = 4x
3 = x
Solution: x = 3, y = 2
Answer: A) (3, 2)
A storage basin is 1240 ft by 637 ft. It’s 15.63 ft deep. How many gallons of water is in the basin
Answer:
12345824.4
Step-by-step explanation:
I'm not really sure. I just did 1240x637x15.63=12345824.4
answer:
53,445.1 gallons of water
Step-by-step explanation:
im not exactly sure but i looked up how to calculate gallons in a container and the website i went to told me to measure the interior length, width, and height which was already done, then it told me to multiply the length by width by height to get the volume of the container then it told me to divide the volume by 231 to get the number of gallons in the container, so 1,240* 637= 789,880* 15.63= 12,345,824.4÷231= 53,445.127272727272727272727272727 which rounded to the nearest tenth is 53,445.1, i honestly hope that this is right and that it helps
Which equation shows function g in factored form?
g(x) = 2x^2 – 6x – 56
O A. g(x) = 2(x-4)(x + 7)
OB.g(x) = 2(x2-3x-28)
OC. g(x) = (2x + 7)(x-8)
OD. g(x) = 2(x + 4)(x - 7)
Answer:
[tex]\boxed{\sf Option \ D}[/tex]
Step-by-step explanation:
[tex]\sf g(x) = 2x^2-6x-56\\[/tex]
Factorizing using mid term break formula
[tex]\sf g(x) = 2x^2-14x+8x-56\\g(x) = 2x(x-7)+8(x-7)\\g(x) = (2x+8)(x-7)\\g(x) = 2(x+4)(x-7)[/tex]
Of the following points, name all that lie on the same horizontal line? (1,-2) (-1,2) (-2,1) (2,-1)
Answer:
None
Step-by-step explanation:
Let’s graph the points first.
Look at the image below.
And by looking at the image we can tell that none of the points lay on the same horizontal line.
Thus,
none of the points lay on the same horizontal line.
Hope this helps :)
Andreas wants to estimate how many fish there are in a lake. One day he catches 20 fish,marks them,and returns them to the lake. The next day he catches 10 fish of which four are marked. Estimate the number of fish in the lake.
Answer:
50
Step-by-step explanation:
The ratio of marked fish to caught fish is 4:10, we need to solve for x in 20:x, since 4 * 5 = 20, 10 * 5 = x so x = 50 fish.
Two types of survey questions are open questions and closed questions. An open question allows for any kind of response; a closed question allows for only a fixed response. An open question and a closed question with its possible choices are given below. List the advantages and disadvantages of each question.
Open question: What can be done to get students to eat healthier foods?
Closed question: How would you get students to eat healthier foods?
1. Mandatory nutrition course
2. Offer only healthy foods in the cafeteria and remove unhealthy foods
3. Offer more healthy foods in the cafeteria and raise the prices on unhealthy foods
What are the advantag?
A. It is easy to compare the results of surveys with open questions.
B. An open question allows for new solutions to be introduced.
C. It is easy to quantify the responses of open questions.
D. An open question allows the respondent to go in-depth with their answer.
What are the disadvantages of an open question?
A. It is difficult to compare the results of surveys with open questions.
B. It is difficult to quantify the responses of open questions.
C. The form of the question may influence the opinion of the respondent.
D. An open question limits the possible responses of the respondent.
Answer and explanation:
Advantages of open questions:
B. An open question allows for new solutions to be introduced.
D. An open question allows the respondent to go in-depth with their answer.
Disadvantages of open questions:
A. It is difficult to compare the results of surveys with open questions.
B. It is difficult to quantify the responses of open questions.
Advantages of closed questions:
- It is easy to compare the results of surveys with closed questions.
- It is easy to quantify the responses of closed questions.
Disadvantages of closed questions:
- A closed question limits the possible responses of the respondent.
-The researcher must spend time to generate a satisfactory list of possible responses from the respondent.
- possible answers may also be insufficient to be useful.
Open questions and closed questions in research questionnaires are two popular methods of getting data from respondents. They both have advantages and disadvantages and can be used interchangeably or together in questionnaires.
Closed Questions have defined answer alternatives or answer categories. Eg: Which is your favourite time of the day? (Morning or Evening etc)
Open Questions have free answers, not clear defined alternatives or categories. Eg : Why do you like morning/ evening time the most ?
Closed Questions give brief concrete answers, Open Questions have more essence of subjective & personal elaboration.
Advantages of Open Questions
Open questions allows for new solutions to be introduced. Open questions allows the respondent to go in-depth with their answer.Disadvantages of Open Questions
It is difficult to compare the results of surveys with open questions.It is difficult to quantify the responses of open questions.Advantages of Closed Questions
It is easy to quantify the responses, with these questions. It is easy to compare the results, with these questionsDisadvantages of Closed Questions
The form of question may influence potential of respondent. It limits the possible responses of respondentTo learn more, refer https://brainly.com/question/2855510?referrer=searchResults
Nigel is going from London, UK, to Moscow, Russia, by train. He goes 517 kilometers
on a train from London to Paris, France. He takes another train 837 kilometer to Munich
Germany, and switches trains in Munich to ride 399 kilometers on a train to Vienna,
Austria. His last train ride carries him 2,088 kilometers from Vienna to Moscow
Find his total distance by first rounding each distance to the nearest hundred kilometers
before adding
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
1) List out all distances singly, before rounding off.
i) From London to Paris → 517Km
ii) From Paris to Munich → 837Km
iii) From Munich to Vienna → 399Km
iv) From Vienna to Moscow → 2,088Km
2) Estimating the distances singly on the basis of rounding off to the nearest 100.
i) 517Km ≈ 500Km to the nearest 100
ii) 837Km ≈ 800Km to the nearest 100
iii) 399Km ≈ 400Km to the nearest 100
iv) 2,088Km ≈ 2,100Km to the nearest 100
3) Summing all estimated distances.
500 + 800 + 400 + 2100
= 3,800Km.
NB: when a number is equal or above 50, you are to round it off as 100; when the number is below 50, you are to round off as zero (0).
Which of the following is equivalent to4−(−5∗9−1)÷2+(5)2−7?
Answer:
-20
Step-by-step explanation:
Follow the PEDMAS order (from top to bottom):
Parentheses
Exponents
Division and Multiplication
Addition and Subtraction
(-5 × 9 - 1) ÷ 2 + (5)2 - 7
(-45 - 1) ÷ 2 + 10 - 7
-46 ÷ 2 + 10 - 7
-23 + 10 - 7
-13 - 7
-20
Answer:
-20
Step-by-step explanation:
=> [tex](-5 * 9-1)/2+(5)2-7[/tex]
Expanding parenthesis
=> [tex](-45-1)/2+10-7[/tex]
=> [tex]-46/2 + 3[/tex]
=> -23 + 3
=> -20
20 points please help!!!
Answer:
a = 16
b = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Length of the design 16 inches is represented by the point (0, 16) and length of 12 inches by (1, 12).
That means these points lie on the graph of the function 'f' represented by,
f(x) = a(b)ˣ
For the point (0, 16),
f(0) = a(b)⁰
16 = a(1)
a = 16
For another point (1, 12),
f(1) = a(b)¹
12 = ab
12 = 16(b) [Since a = 16]
b = [tex]\frac{12}{16}[/tex]
b = [tex]\frac{3}{4}[/tex]
Therefore, values of a and b are 16 and [tex]\frac{3}{4}[/tex] respectively.
What is the sum of the reciprocal of 1/-13 and the reciprocal of -1/2
Answer:
-15
Step-by-step explanation:
1/-13
The reciprocal is
[tex]1/ 1/-13[/tex]
Because of the law of indices,
We'll have [tex] 1 * -13 [/tex]
= -13.
-1/2
The reciprocal is
1 ÷ -1/2
Because of the law of indices,
We'll have [tex] 1 * -2 [/tex]
= -2
Therefore, the sum would be -13 + (-2) which would be equals to -15.
-15
Step-by-step explanation:
1/-13
The reciprocal is
Because of the law of indices,
We'll have
= -13.
-1/2
The reciprocal is
1 ÷ -1/2
Because of the law of indices,
We'll have
= -2
Therefore, the sum would be -13 + (-2) which would be equals to -15.
A pharmacist wants to mix a 30% saline solution with a 10% saline solution to get 200 mL of a 12% saline solution. How much of each solution should she use
Answer:
30% constituents=20 mL
10% constituents=180 mL
Step-by-step explanation:
x= 30% volume
y=10% volume
For our first equation, we know the total volume is 200 mL and is the sum
x+y=200
y=200-x (1)
For our second equation, we do a mass balance for 200 mL of final solution.
12% w/v = 0.12 g/mL
This means that in 1 mL of solution, we have 0.12 g of NaCl.
For any solution, concentration multiplied by volume will give the mass of NaCl:
Mass in x mL= C*V (g/mL) (mL)
So in 200 mL, we have
0.12*200 (g/mL) (mL)
=24g of NaCl
Cx*Vx + Cy*Vy=24
0.3x+0.1y=24 (2)
Substitute y=200-x into (2)
0.3x+0.1(200-x)=24
0.3x+20-0.1x=24
0.2x=24-20
0.2x=4
Divide both sides by 0.2
0.2x/0.2=4/0.2
x=20
Substitute x=20 into (1)
y=200-x
y=200-20
y=180
30% constituents=20 mL
10% constituents=180 mL
An open box is to be made from a 5 ft by 9 ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.
Answer: 21 ft³
Step-by-step explanation:
Let x represent the height of the box.
Then the 5 ft width of cardboard is (5 - 2x) when creating the box
and the 9 ft length of cardboard is (9 - 2x) when creating the box.
Volume = length x width x height
= (9 - 2x)(5 - 2x)(x)
= 45x - 28x² + 4x³
Using Calculus to solve for x, set the derivative equal to zero and use the quadratic formula to solve for x:
V' = 45 - 56x + 12x²
0 = 12x² - 56x + 45
x = 3.6, x = 1.0
Use those values to find the width, length, and volume:
height(x) × width (5 - 2x) × length (9 - 2x) = Volume
3.63 × -2.26*
1 × 3 × 7 = 21
*width cannot be negative so the height cannot be 3.63
The smaller of two numbers is one-half the larger, and their sum is 27. Find the numbers. Answer: The numbers are ___ ___ ___
Answer:
the smaller is 9 while the digger is 18
A population is increasing according to the exponential function defined by y = 3e^.04x, where y is in millions and x is the number of years. Which of the following should be done in order to answer the question "When will the population reach 4 million?"
A. Solve 3e^.04x=12
B. Evaluate y = 3e^.04x(4).
C. Evaluate y = 3e^.04x(1/4)
D. Solve 3e^.04x= 4.
Answer:
D. Solve 3e^0.04x= 4.Step-by-step explanation:
Given the population increasing according to the exponential function defined by y = 3e^0.04x, where y is in millions and x is the number of years, to determine when the population will reach 4 million, the following steps must be carried out.
Since y is in millions, we will first substitute y = 4 into the modeled equation as shown;
4 = 3e^0.04x
Therefore to calculate x, we need to solve the expression 3e^0.04x = 4 for the value of x and this is arrived at by simply substituting y = 4 into the given equation.
To get x;
3e^0.04x = 4
e^0.04x = 4/3
taking the ln of both sides
lne^0.04x = ln1.333
0.04x = 0.287
x = 0.287/0.04
x≈ 3.59 years
If the sum of the first n terms of an AP is 1/2 (3n^2+7n),then find its nth term.Hence write its 20th term.
Answer:
62
Step-by-step explanation:
Sn=1/2(3n^2+7n)
S1=1/2(3+7)=5
S2=1/2(3*4+7*2)=26/2=13
We know
S1=a1=5
S2=a1+a2=13
S2-s1=a1+a2-a1
13-5=a2
a2=8
We know d=a2-a1
d=8-5=3
nth term of AP =an=5+(n-1)3
an= 2+3n
Therefore 20th term =
a20= 2+3(20)=62
Hence 20th term of AP is 62
I hope this helps
The line passing through points
(4,0) and (-2, 1) has a slope of?
A. -6
B. -1/6
C. 1/2
D. 2
E. 1/6
Answer:
b. -1/6
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (1 - 0)/(-2 - 4) = 1/(-6) = -1/6
Answer:
m = -1/6 = B
Step-by-step explanation:
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\ x_1=4\\ y_1=0\\ x_2=-2\\y_2=1.\\m = \frac{1-0}{-2-4} \\m = \frac{1}{-6}[/tex]
Solve application problems using radical equations. Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 378 square feet. How long can a side of his patio be?
Answer:
3(sqrt42) ft
Step-by-step explanation:
If l is side length of square patio, then area of patio would be l^2.
l^2 = 378
l = sqrt378 = 3(sqrt42)
Which point satisfies the system of equations y = 3x − 2 and y = -2x + 3? PLEASE I NEED IT NOW
Answer:
(1,1)
Step-by-step explanation:
y = 3x − 2
y = -2x + 3
the point that satisfies the system:
when the two functions are equal
3x-2=-2x+3
3x+2x=3+2
5x=5
x=5/5=1
when x=1
y=-2x+3
y=-2(1)+3
y=1
Answer:
(1,1) or x=1 and y=1
Step-by-step explanation:
Since both equations are equal to y you can use substitution, replacing he y in y=3x-2 with -2x+3, giving you the equation -2x+3=3x-2. We can use this to solve for x. To isolate the variable you first need to add 2 to both sides, giving you -2x+5=3x, then add 2x to both sides. This gives you 5=5x, lastly you need to divide both sides by 5 to get x=1. Now you can plug x(1) into 1 of the 2 given equations to find y, I'll use y=3x-2. When x is plugged in as 1 you get the equation y=3(1)-2, after multiplying you get y=3-2, then you subtract to get y=1. In order to make sure this is the correct solution you can also plug in x as 1 and now y as 1 into the other equation, y=-2x+3. We can plug 1 in for x and solve for -2(1)+3 to get -2+3, or 1, so y is 1 for both equations, therefore the solution we got was correct, x=1 and y=1, or (1,1).
2.35=11x Equals What
Answer:
x=0.2136
Step-by-step explanation:
Answer:
x=0.214 rounded to the thousandths
Step-by-step explanation:
2.35=11x
divide each side by 11 to isolate the x
x=0.214 rounded to the thousandths
Rent for a 3 bedroom apartment is regularly $936 per month. Apartment management is now offering one month free for a 12 month lease. If you sign a one year lease and apply the free month equally across months, how much is your monthly lease amount?
Answer:
$858
Step-by-step explanation:
Monthly lease amount is ⇒ $936
Considering one moth free, yearly rental would be
⇒ 11*$936= $10296The monthly lease amount :
⇒ $10296 / 12 = $858if 176 dollars can be exchanged for the 140pounds and 1 pound is exchanged for RS 130 how many dollars can be exchanged for RS 2925
Answer:
Number of dollar = 28.28 (Approx)
Step-by-step explanation:
Given:
176 dollar = 140 pound
1 pound = Rs.130
Find:
Number of dollars in Rs 2925
Computation:
1 pound = Rs.130
Number of pound = 2925 / 130
Number of pound = 22.5 pound
1 pound = 176 / 140
Number of dollar = [176 / 140]22.5
Number of dollar = 28.28 (Approx)
What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8?
Step-by-step explanation:
the common ratio is -4
Gn=2 (-4)^n-1
Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent x values? Select both in the
list.
In any coordinate pair, the first number is the x-value and the second number is the y-value.
To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.
The slope of the line that passes through (1, 14) and (4,9) is -5/3.
It is find the slope of the line.
what is slope?The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:
m = Rise/Run
If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex] So, the equation would be:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
In any coordinate pair, the first number is the x-value and the second number is the y-value.
The difference of the y values and divide by the difference in the x values:
m=(14-9)/(1-4) is equal to -5/3.
The slope of the line that passes through (1, 14) and (4,9) is -5/3.
Learn more about slope here:
https://brainly.com/question/17114095
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A manufacturing process that produces electron tubes is known to have a 10% defective rate. Suppose a random sample of 15 tubes is selected from the manufacturing process. a) Find the probability that no more than two defectives are found?
Answer:
Probability of obtaining no more than two defective tubes = 0.816
Step-by-step explanation:
The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).
Where n is number of samples;
r is maximum number of defective tubes, r ≤ 2;
p is probability of defective tubes = 10% or 0.1
q is probability of non-defective tubes, q = 1 - p
Further explanations and calculations are given in the attachment below:
The square below represents one whole.
Answer:
6 percent
Step-by-step explanation:
6/100 is shaded. This is the same thing as 0.06. Once I move the decimal two places to the right, I get 6. (I move the decimal place because percents are out of 100, so two decimal places.) This means 6 percent.
Find the slope of the line that passes through the points (3,6) and (5, 3).
-3/2
3/2
2/3
Answer:
-3/2.
Step-by-step explanation:
To find the slope, we find the rise over run.
In this case, the rise is 6 - 3 = 3.
The run is 3 - 5 = -2.
The slope is 3 / (-2) = -3/2.
Hope this helps!
Answer:
-3 / 2
Step-by-step explanation:
slope formula is: change in y / change in x , y2-y1 / x2-x1
let (3.6) is (x1 , y2) and (5 , 3) (x2 , y2)
3 - 6 / 5 - 3 = -3 / 2
the slope is -3 / 2
.. ..
Please answer this correctly without making mistakes
Answer:
ace hardware store
Step-by-step explanation:
Ace is the place with the helpful hardware folks!
Researchers at the Centers for Disease Control and Prevention have been studying the decay pattern of a new virus with a decay rate of 22% per hour. They start with 500 viruses that they want to check on in the next 8 hours. How many viruses will they find in 8 hours? Round your answer to the nearest whole number.
Answer:
They will find 69 viruses in 8 hours.
Step-by-step explanation:
The number of viruses after t hours is given by the following equation:
[tex]V(t) = V(0)(1-r)^{t}[/tex]
In which V(0) is the initial number of viruses and r is the decay rate, as a decimal.
They start with 500 viruses
This means that [tex]V(0) = 500[/tex]
Decay rate of 22% per hour.
This means that [tex]r = 0.22[/tex]
So
[tex]V(t) = V(0)(1-r)^{t}[/tex]
[tex]V(t) = 500(1-0.22)^{t}[/tex]
[tex]V(t) = 500(0.78)^{t}[/tex]
How many viruses will they find in 8 hours?
This is V(8).
[tex]V(t) = 500(0.78)^{t}[/tex]
[tex]V(8) = 500(0.78)^{8}[/tex]
[tex]V(8) = 68.51[/tex]
Rounding to the nearest whole number
They will find 69 viruses in 8 hours.
Answer:
The researchers will find 86 viruses.
Step-by-step explanation:
Identify the value of each variable in the formula. Be sure to put the percent in decimal form. Be sure the units match—the rate is per hour and the time is in hours.
A =?
A0 = 500
R= -0.22/hour
t= 8 hours
Substitute the values in the formula.
A= A0e^rt
A= 500e^-0.22x8
Compute the amount.
A ≈ 86.02
Round to the nearest whole number.
A ≈ 86
If John has pairs of red, orange, yellow, blue and green socks, how many can he wear them in over 5 days, repetition is allowed because hog is alright with wearing dirty socks. A)5! B)25 C)5^5 D)125
Answer:
Total ways = 5×5×5×5×5
Total ways = 5^5
Total ways = 3125
Therefore, the correct option is C) 5^5
Step-by-step explanation:
John has pairs of red, orange, yellow, blue and green socks.
Which means that John has 5 different colors pairs of socks.
We are asked to find out in how many ways can he wear them over 5 days.
1st Day:
On the first day John has 5 ways to choose from.
2nd Day:
On the second day John has 5×5 ways to choose from.
(Since repetition is allowed)
3rd Day:
On the third day John has 5×5×5 ways to choose from.
4th Day:
On the fourth day John has 5×5×5×5 ways to choose from.
5th Day:
On the fifth day John has 5×5×5×5×5 ways to choose from.
Total ways = 5×5×5×5×5
Total ways = 5^5
Total ways = 3125
Therefore, the correct option is C) 5^5
1). f(x) = 3x + 15 then what's f^-1(x)?
Answer:
Step-by-step explanation:
f(x)=3x+15
let f(x)=y
y=3x+15
flip x and y
x=3y+15
3y=x-15
y=1/3 x-5
or f^{-1}x=1/3 x-5