How do you calculate a definite integral from a graph?
Answers
, dy or dt to name a few. The thing we integrating with respect to, is dependent upon the graph.
Here’s an example: (Picture at the bottom)
If I take my bounds from 0 to 2 on the X-axis, that would give me an area underneath the curve that is exactly like a triangle. You can solve it with half base times height if you wanted.
If I were to take my bounds to be 2 to 6 on the X-axis then that’s an area in the shape of a trapezoid. Remember that you’re integrating the function so that means that your integrand will be the function.
So, for the first one it would be the integral sign, 2 on the top, 0 on the bottom, the integrand would be f(x), and it’s in respect to dt.
For the second one it would be exactly the same except your bounds would just be from 2 to 6
(2 on the bottom 6 on top).
I hope that helps.
Related Questions
Jonas is buying a three-day supply of camping snacks. An energy bar costs $1.50, and a bag of dried
mangoes costs $3.00. Jonas plans to have 7 snacks per day and can spend up to $45.00.
If p is the number of energy bars he can buy, and m is the number of bags of mangoes he can buy,
which system of equations and inequalities can be used to represent the possible number of each
snack he can buy?
p+m
21
=
21
p+m = 45
1.5p + 3m
p> 0
m >0
1.5p + 3m < 45
p> 0
m 2 0
1.5p + 3m
3p + 1.5m
p20
m 20
p+m = 21
8p + 1.5m
p> 0
m >0
Answers
Answer:
P+m=21
1.5p + 3m < 45
p > 0
m > 0
Step-by-step explanation:
what are three segments from this figure?
Answers
Answer:
AD, DA, ED, DE
Step-by-step explanation:
A sculpture sits on a pedestal in the shape of a square prism. The side lengths of a base of the prism are 3 feet. The height of the prism is 4 feet. The museum director wants to cover all but the underside of the pedestal with foil that costs $0.22 per square foot. How much will the foil cost?
Answers
Answer:
Total cost of covering the pedestal is $12.54.
Step-by-step explanation:
The pedestal is a square prism so top and bottom are of square shape.
Hence, we have here length = width
We know that the Total Surface Area of a Prism is:
[tex]\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)[/tex]
Where l is length,
w is width and
h is height of prism
We know that here w = l = 3 feet
and h = 4 feet
Also, underside of pedestal is not to be covered.
The underside of pedestal is square type.
So,
[tex]\text{Required Total Surface Area = } l\times w+ 2\times w \times h+2\times h \times l[/tex]
[tex]\Rightarrow 3 \times 3 + 2 \times 3 \times 4 + 2 \times 3 \times 4\\\Rightarrow 9 + 24 + 24\\\Rightarrow 57\ ft^{2}[/tex]
Cost of cover per square foot = $ 0.22
Total cost of [tex]57\ ft^{2}[/tex] [tex]\Rightarrow 0.22 \times 0.57 = \$12.54[/tex]
In a class of 35 students, 15 are seniors, 20 are females, and 7 are both a senior and a female. If I choose a student at random, what is the probability I choose a female or a senior?
Answers
Answer:
1Step-by-step explanation:
15 + 20 / 35
35/35 = 1 (certain)
The probability of choosing a female or senior is 1, because these are the only two groups represented in the class.
I'm always happy to help :)
Answer:
1.
Step-by-step explanation:
Prob ( Choosing a female) = 20/35
Prob ( Choosing a senior) = (15)/ 35 = 15/35
Requires probability = 20/35 + 15/35
= 35/35
= 1.
A shoe manufacturer was investigating the weights of men's soccer cleats. He felt that the weight of these cleats was less than the average weight of 10 ounces. After a random sample of 13 pairs of cleats, he found that sample mean was 9.63 and the standard deviation was .585. At a significance level of .05, can it be concluded that the researcher was correct?
Show work
Answers
Answer:
The conclusion is that the researcher was correct
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 13[/tex]
The sample mean is [tex]\= x = 9.63[/tex]
The standard deviation is [tex]s = 0.585[/tex]
The significance level is [tex]\alpha = 0.05[/tex]
The Null Hypothesis is [tex]H_o : \mu = 0[/tex]
The Alternative Hypothesis is [tex]H_a = \mu < 10[/tex]
The test statistic is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{s}{\sqrt{n} } }[/tex]
Substituting values
[tex]t = \frac{9.63 - 10 }{\frac{0.585}{\sqrt{13} } }[/tex]
[tex]t = - 2.280[/tex]
Now the critical value for [tex]\alpha[/tex] is
[tex]t_{\alpha } = 1.645[/tex]
This obtained from the critical value table
So comparing the critical value of alpha and the test value we see that the test value is less than the critical value so the Null Hypothesis is rejected
The conclusion is that the researcher was correct
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answers
Answer:D
Step-by-step explanation:
(4/5)^0
(4^0)/(5^0)=1/1=1
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply
Answers
Using tan(A+B), find the exact value of tan(105).
Answers
Answer:
-2-√3
Step-by-step explanation:
The sum of angles formula for tangent is ...
tan(A+B) = (tan(A) +tan(B))/(1 -tan(A)tan(B))
For the desired angle, we can use A=45°, B=60°. Then we have ...
tan(105°) = (tan(45°) +tan(60°))/(1 -tan(45°)tan(60°))
The tangent values we need are ...
tan(45°) = 1
tan(60°) = √3
Then our tangent is ...
tan(105°) = (1 +√3)/(1 -1·√3) = (1 +√3)²/((1 -√3)(1 +√3)) = (4+2√3)/(-2)
tan(105°) = -(2+√3)
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A1 be the event that the receiver functions properly throughout the warranty period, A2 be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A1)= .95, P(A2) = .98, and P(A3) = .80.a. What is the probability that all three components function properly throughout the warranty period?b. What is the probability that at least one component needs service during the warranty period?c. What is the probability that all three components need service during the warranty period?
Answers
Answer:
that is alot the prob. is 20
Step-by-step explanation:
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing!
Answers
Answer:
Step-by-step explanation:
B or c
Please help ASAP! I will mark Brainliest! Please READ the question THEN answer CORRECTLY! No guessing!
Answers
Answer:
its C
Step-by-step explanation:
Hope this helps!!
Answer:
B. Week 6
Step-by-step explanation:
[tex]f(x) = 2^{x}[/tex]
We know that f(x) represents number of subscribers, x represents week number. So plug in 64 for f(x).
[tex]64 = 2^{x}[/tex]
Uh-oh, how do we solve this? We need to go from exponential form to logarithmic form.
[tex]64 = 2^{x}[/tex]
log₂(64) = x
We're basically asking the question: 2 to the what equals 64? And we can plug this into the calculator as log₂(64) (on TI-84, it's MATH->logBASE(). Or you can just think about it:
2 x 2 x 2 x 2 x 2 x 2 = 64.
There are 6 2s, so 6 is the answer.
Find the sum of the interior angle measures of a convex octagon (an eight-sided polygon).
Answers
Answer:
1080
Step-by-step explanation:
:)
what is the area of a circle with the equation (x − 6)² + (y + 2)² = 17 ?
Answers
Answer:
17π
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
Area of a circle is:
A = πr²
r² = 17, so A = 17π.
After flooding damaged much of the crop, the cost of a head of lettuce jumped from $0.92 to $2.26. What percent of increase is this? Round to the nearest one percent.
Answers
Answer:
146%
Step-by-step explanation:
[tex] percent~change = \dfrac{new~price - old~price}{old~price} \times 100% [/tex]
If the percent change is positive, it is a percent increase.
If the percent change is negative, it is a percent decrease.
Your numbers are
old price = $0.92
new price = $2.26
Plug in the numbers in the formula above and evaluate the expression.
percent change = ($2.26 - $0.92)/($0.92) * 100%
percent change = ($1.34)/($0.92) * 100%
percent change = 1.4565 * 100%
percent change = 146%
Since the percent change is a positive number, it is a percent increase.
Answer: The percent increase is 146%.
CAN SOME HELP ME PLEASE IT'S DUE IN 10 MINS
Answers
Answer:
Step-by-step explanation:the first one
A store display shows two red shirts, one blue shirt, and three shirts with red and white stripes. The display also shows two pairs of blue jeans, one pair of white pants, and one pair of white shorts. What is the probability of randomly selecting an item with white or red on it?
A) 1/4 B) 3/10 C)1/2 D) 7/10
Answers
Answer:
its 7/10
Step-by-step explanation:
The probability of randomly selecting an item with white or red on it is 3/10.
What is the probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
A store display shows two red shirts, one blue shirt, and three shirts with red and white stripes.
The display also shows two pairs of blue jeans, one pair of white pants, and one pair of white shorts.
The probability of randomly selecting an item with white or red on it is given by;
[tex]\rm Probability=\dfrac{Total \ number \ of \ items}{Total \ red \ or \ white \ items}\\[/tex]
Total items = 2 + 1 + 3 + 2 + 1 + 1 = 10 itens.
Substitute all the values in the formula
[tex]\rm Probability=\dfrac{Total \ number \ of \ items}{Total \ red \ or \ white \ items}\\\\\rm Probability=\dfrac{3}{10}\\\\[/tex]
Hence, the probability of randomly selecting an item with white or red on it is 3/10.
Learn more about probability here;
https://brainly.com/question/20849420
#SPJ2
(-3x + 15) + (-3x + 2)
Answers
Answer:
If you are looking for a simplified equation, then the answer is -6x + 17
Step-by-step explanation:
(-3x + 15) + (-3x + 2)
Because you are only adding and subtracting here, you can take out the parentheses.
-3x + 15 -3x + 2
= -6x + 17
The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.12 kWh. A previous study found that for an average family the standard deviation is 1.2 kWh and the mean is 17.9 kWh per day. If they are using a 90% level of confidence, how large of a sample is required to estimate the mean usage of electricity? Round your answer up to the next integer.
Answers
Answer:
A sample size of at least 271 is required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Maxium error of 0.12.
How large of a sample is required to estimate the mean usage of electricity?
We need a sample size of at least n.
n is found when [tex]M = 0.12, \sigma = 1.2[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.12 = 1.645*\frac{1.2}{\sqrt{n}}[/tex]
[tex]0.12\sqrt{n} = 1.645*1.2[/tex]
[tex]\sqrt{n} = \frac{1.645*1.2}{0.12}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645*1.2}{0.12})^{2}[/tex]
[tex]n = 270.6[/tex]
Rounding up
A sample size of at least 271 is required.
Alice and Bob share some money in the
ratio 7:5. Alice got £4 more than Bob. How
much did Alice get?
Answers
Answer:
14
Step-by-step explanation:
7-5 = 2
4/2 = 2
2 x 7 = 14
Giving brainliest for CORRECT awnser.
Answers
Answer:
B.
Step-by-step explanation:
So, first off, the quadratic formula is -b plus or minus sqrt(b^2-4ac)/2a. Plug the equation given, and you get B.
subtract 6066 from 294
Answers
Answer:
-5772
Step-by-step explanation:
294-6066=-5772
Answer:
The answer would be 2,772
Step-by-step explanation:
6,066 - 294 = 2,272
I hope that helps!!:)
Describe how to graph point K at (5, 4) the steps
Answers
Answer:
here is ur answer
Today a shoe store it’s at 20% of the price of a pair shoes and for the next three days it will take 20% of the previous days price if the price of a pair of shoes yesterday was $200 what will be the price of the pair of shoes three days from now
A.160.00
B.128.00
C.102.40
D.81.92
Answers
If the price of the shoe yesterday was $200 and on this day 20 percent has been taken thus it will have $160. In the next 3 days if another 20 percent will be taken out from the previous $160 then the final answer is $128.
ps.. can u give brainly pls :3
£48 is divided between Alf and Ted in the ratio of 7:9. How much does Alf receive?
Answers
Now you do 48 divided by 16 which is 3 to get one price. Since Alf is divided by 7 you multiply 3 with 7. So the answer would be £21
7:9=7+9=16
Alf is 7 which means 7/16*£48=6.125
y varies directly as x.y = 52 when x=4. Find y when x= 10.
y=
(Simplify your answer.)
Answers
Answer:
9ha
shhsi a sa.anjwkw a zkaq
Peter rolls a fair dice 114 times. How many times would Peter expect to roll a number greater than 1?
Answers
Answer:
A dice of six faces has 5 numbers bigger than 1 (from 2 to 6).
Then, the number Peter is expecting is : 114 x (5/6) = 95 (times)
Hope this helps!
:)
A tennis ball machine shoots 21 forehands 25 backhands and 9 lobs if a player missed 6 forehands 17 backhands and 2 lobs how many balls were hit
Answers
Answer:
30
Step-by-step explanation:
55 - 25 = 30
the price increase of a set of golf clubs is from $250 to $750. What is the percent increase?
Answers
Answer:
300%
Step-by-step explanation:
3 times 250 is 750
What is 4/12 x 70.please help me
Answers
Answer:
70/3
Step-by-step explanation:
Your welcome :)
Step-by-step explanation:
4 / 12 = 1/3 = 0.33
0.33 x 70 = 23. 33
Every year, census researchers collect data from 850 public and private hospitals across the United States. Which issue will invalidate the conclusion of the hypothesis test? Group of answer choices The data comes from only 850 hospitals in the U.S. when there are 5,700 hospitals in the U.S. Researchers received more data from public hospitals than from private hospitals. The data is selected by choosing the first 850 hospitals from an alphabetized list.
Answers
Answer:
Option C
Step-by-step explanation:
For a better, clear and unbiased sampling, choosing randomly might not allow for a biased sampling. Choosing in an alphabetical order might not give a representative of the whole hospitals both private and public, thus invigilator the conclusion of our hypothesis test.
