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
The following data points represent the number of classes that each teacher at Broxin High School teaches.
Sort the data from least to greatest.
Find the interquartile range (IQR) of the data set.
57511945346
Answers
Answer:
IQR= 3
Step-by-step explanation:
Hello!
The data represents the number of classes taught by each teacher at Broxin High School.
To calculate the IQR you have to do the following steps:
1) Arrange the data from least to greatest:
Raw data: 5, 7, 5, 1, 1, 9, 4, 5, 3, 4, 6
Arranged: 1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
2) Calculate the 1st Quartile (Q₁):
The first quartile divides the bottom 25% of the data from the top 75%, to know which value of the data set corresponds to it you have to calculate its position:
PosQ₁= (n+1)/4= (11+1)/4= 3
This means that the 1st quartile corresponds to the 3rth observation:
1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
Q₁= 3
3) Calculate the 3rd Quartile (Q₃)
The third quartile divides the bottom 75% of the data from the top 25%, as before, you have to calculate its position and then identify the value in the data set.
PosQ₃= (n+1)*(3/4)= (11+1)*(3/4)= 9
The third quartile corresponds to the 9th observation:
1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
Q₃= 6
4) Interquartile range (IQR)
The IQR shows you the distance where the middle 50% of the data set is.
IQR= Q₃-Q₁= 6-3 = 3
I hope this helps!
ivana has 5.50 luc has 1.4 times as much as ivana, how many indian rupees would ivana get if the value of rupees are 61.92 per dollar rate
Answers
If f(x) = 3x + 7, find f(a - 1)
Answers
Answer:
3a+4
Step-by-step explanation:
f(x) = 3x + 7,
Let x = a-1
f(a - 1) = 3(a-1) +7
Distribute
=3a -3 +7
= 3a +4
Deena wants to buy a 2200 laptop, but she doesn't have the money. She decides to finance the purchase and will pay montly payments of 231.55 for a year. How much extra will Deena end up paying for the laptop becuase she financed it rather than paying for it all once.
Answers
Answer:
$578.6
Step-by-step explanation:
231.55 multiplied by 12 is 2778.6.
Subtract that by the amount that she could've paid in a whole you would get 578.6.
A bag of colored marbles contains 16 blue marbles, 12 red marbles, and 8 yellow marbles.
What is the theoretical probability of drawing a red marble?
Enter your answer as a reduced fraction, like this: 3/14
Answers
Answer:
The theoretical probability of drawing a red marble is 1/3.
Step-by-step explanation:
1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.
2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.
3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.
A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 34 minutes. The owner has randomly selected 23 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 34 minutes. Suppose the P-value for the test was found to be 0.0290. State the correct conclusion
Answers
Answer:
We conclude that the mean delivery time actually exceeds 34 minutes.
Step-by-step explanation:
We are given that the owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 34 minutes.
The owner has randomly selected 23 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 34 minutes. Suppose the P-value for the test was found to be 0.0290.
Let [tex]\mu[/tex] = average time spent on the deliveries.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 34 minutes {means that the mean delivery time is less than or equal to 34 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 34 minutes {means that the mean delivery time actually exceeds 34 minutes}
Now, the decision rule based on the P-value to whether null hypothesis should be accepted or rejected is given by;
If the P-value of test statistics is less than the level of significance, then we will reject our null hypothesis.If the P-value of test statistics is more than the level of significance, then we will not reject our null hypothesis.Here, we assume that the level of significance is 5%.
Since, the P-value of test statistics is less than the level of significance as 0.029 < 0.05, so we have sufficient evidence to reject our null hypothesis.
Therefore, we conclude that the mean delivery time actually exceeds 34 minutes.
Two squares are similar. The first square has sides that measure 4 inches, and the second squares has sides that measure 12 inches. The scar factor used to get from the first square to the second one is
Answers
Answer:
3
Step-by-step explanation:
Well, first off I'm assuming that by "scar factor" you mean scale factor. So if the two squares are similar then that means the sides are also similar, that means that they are equivalent. So all you have to do is 12/4 to get 3. So then to check it, you do 4 times 3 which gets you to 12.
So the final answer is 3
help me plss to find the area
Answers
Answer:
A=88 square units
Step-by-step explanation:
A=B x H
A= 11 x 8
A=88 square units
Graph f(x) = 3x and g(x) = 3x – 5.
Which describes the transformation from
the graph of f(x) to the graph of g(x)?
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Answer:
g(x) is translated 5 units down of that from f(x)
What’s the correct answer for this?
Answers
Answer:
D.
Step-by-step explanation:
Rotation by 180 about O will map QSU onto itself.
Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters which measurement does 17 meters represent
Answers
The answer in length
The length is used to measure the distance between to end points or edges. so 17 meters measurement represent the length.
What is perimeter?Its the sum of length of the sides used to made the given figure.
Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters.
Area is what is on the inside.
The perimeter is the outside of the hole thing.
Hence, the length is used to measure the distance between to end points or edges.
so 17 meters measurement represent the length.
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Sara goes on a slingshot ride in an amusement park. She is strapped into a spherical ball that has a radius of centimeters. What is the volume of air in the spherical ball? Use this formula: , where r is the sphere’s radius.
A.
B.
C.
D.
Answers
Answer:
A. 4×π×3²×[tex]10^{6}[/tex]
Step-by-step explanation:
r = 3×10² = 3×100 = 300
[tex]\frac{4}{3}[/tex]×π×300³=
[tex]\frac{4}{3}[/tex]×π×27,000,000=
[tex]\frac{108,000,000}{3}[/tex]×π=
36,000,000π
Answers solved:
A. 36,000,000π
B. 108,000,000π
C. 3,600,000π
D. 32,400,000π
The solution is Option A.
The volume of the air in the spherical ball is given by the equation
V = 4π ( 3 )² ( 10 )⁶ cm³
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the volume of the sphere be represented as V
Now , the radius of the spherical ball be r
The value of r = 3 ( 10 )² cm
So , the volume of the spherical ball = ( 4/3 ) πr³
Substituting the values in the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x [ 3 ( 10 )² ]³
On simplifying the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x ( 3 )³ ( 10 )⁶
Volume of the spherical ball V = 4 x π x ( 3 )² ( 10 )⁶
Therefore , the value of V is 4π ( 3 )² ( 10 )⁶
Hence , the volume of the spherical ball is 4π ( 3 )² ( 10 )⁶
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Using the information below, Solve for x. Show Your Work with your answer.
X + 2y = 5
2x + y = 12
-2(x + 2y = 5)
-2x - 4y = - 10
-2x - 4y = -10
2x + 6y = 12
_____________
2y = 2
————————
2 2
y=1
Answers
[insert answer here]
Step-by-step explanation:
what happens to the value of the expression 5/x + 5 as x decreases froma large positive number to a small positive number
Answers
Answer:
The value increases
Step-by-step explanation:
the smaller the divisor, the larger the quotient.
What type of triangle is shown in the image?
Acute triangle
Right triangle
Equilateral triangle
Obtuse triangle
Answers
The type of triangle shown in the image is the Obtuse triangle.
What is an obtuse triangle?
A triangle is said to be an obtuse triangle if one of its angles measures more than 90 degrees.
In the given diagram, one of the angles measures more than 90 degrees.
So, the given triangle is an obtuse triangle.
Hence, the type of triangle shown in the image is the Obtuse triangle.
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If a 3 ft tall globe casts a 1 ft long shadow, then how tall is an adult giraffe that casts a 6 ft shadow?
Answers
Answer:
it has to be 18
Step-by-step explanation:
because 3 to 1 so 6 just multiply 3 by 6
Connor is 4 2/3 feet tall. How many inches is that?
Answers
Answer:
hes
56 inches
hope it helps
What is the right answer!???????
Answers
Answer:
dont know need points
Step-by-step explanation:
Answer:
What points are needed?
There are 14 math teachers and 26 science teachers at
school today. What is the ratio of math teachers to math
and science teachers at school?
Answers
Answer: 2.86
Step-by-step explanation:
14+26=40
40/14
Answer:
2.86
Step-by-step explanation:
Which number line represents the solution set for the inequality 2x24?
+
-10
-8
-6
4
- 2
0
2
4
6
8
10
+
+
+
+
+
-4
-10
-8
-6
-2
0
+
6
+
10
2
4
8
+
+
-10
-8
--6
-4
O
-2
2
4
6
8
10
-10
-8
--6
-4
-2
0
2
4
6
8
10
Answers
Answer:
the answer is what I think 46
The solution of the inequality - 1/2x ≥ 4 is shown in Option 2.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
Inequality is,
⇒ - 1/2x ≥ 4
Now, We can simplify as;
⇒ - 1/2x ≥ 4
⇒ 1/2x ≤ - 4
⇒ x ≤ - 8
When we plot this inequality on a number line,
An arrow starting with a solid point from x = -8 and arrow directing towards negative numbers will represent the given inequality.
Hence, Option (2) will be the answer.
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you roll a cube find the probability of rolling an even number?
Answers
Answer: 1/2
Step-by-step explanation: Note that to roll an even number, we can roll a 2, 4, or 6.
So there are three ways to roll an even number.
Now let's use our ratio for the probability of an event.
P(event) = number of favorable outcomes/total number of outcomes
Since we want to find the probability of rolling a 3, the number of favorable outcomes for rolling a 3 will go on top in the ratio.
Also, remember that a number cube has six total outcomes.
So 6 will go in the bottom of our ratio
So the probability of rolling an even number is 3/6.
However, we can reduced 3/6 to 1/2.
Always reduce when finding probability.
So the probability or likelihood of rolling an even number is 1/2.
Suppose we want to explore if there is significant evidence of difference among Category A, B, and C in the proportion of Level 1 for certain characteristic.
A B C Total
Level 1 50 90 225 365
Level 2 150 210 275 635
Total 200 300 500 1000
At significant level 0.05, test the equality of proportion of Level 1 for category A, B and C. If needed, perform the Marascuilo procedure for pairwise comparisons. Show your work.
Answers
Answer:
Kindly check explanation (since we need to show how the work is done) but what can be noticed is that there is a proportional difference between the 3.
Step-by-step explanation:
Know that Vo :ht = 1//3, where t = 1,2,3.
(1). The expected values for levels A, B and C = 0.33 which is a total of 100%.
The observed values = 50, 90, and 225 with a total of 365.
The expected values = 121.67 for the three categories which gives us a total of 365.
For the three categories, the differences between the observed values and the expected values are -71.67, -31.67 and 103.33.
(2). Thus, the value for the test statistics is = (observed values - expected values)^2/ expected values.
So, for the three categories (A,B and C) we have; 42.217, 8.244 and 87.754. The total = 138.215.
Therefore the critical value = 5.991.
(3). We have to reject the null hypothesis Because 138.215 is greater than 5.991.
(4). For Marascuilo, we have;
Proportion
Group 1 - group 2 = 0.05(absolute difference) and 0.099050609( critical range) which is insignificant.
Group 1 - group 3 = 0.2( absolute difference) and 0.092643256(critical range) which is significant.
Group 2 - group 3 = 0.15(absolute difference) and 0.084615602(critical range) which is also significant.
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 2x − 4x3, a = −1 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 10(x + 1) + 12(x + 1)2 − 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 10(x + 1) + 4(x + 1)2 − 12(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 + 10(x + 1) + 12(x + 1)2 + 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 12(x + 1) + 10(x + 1)2 − 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 + 10(x + 1) + 4(x + 1)2 + 12(x + 1)3
Answers
Answer:
f(x) = 2 - 10 (1 + x) + 12 (1 + x)^2 - 4 (1 + x)^3
Step-by-step explanation:
The general form of the series is shown in the attachment. For the purpose here, we need to evaluate f(-1), f'(-1), f''(-1) and so on.
f(x) = 2x -4x^3; f(-1) = 2(-1)(1 -2(-1)^2) = (-2)(-1) = 2
f'(x) = 2 -12x^2; f'(-1) = 2 -12(-1)^2 = -10
f''(x) = -24x; f''(-1) = -24(-1) = 24
f'''(x) = -24; f'''(-1) = -24
So, the series is ...
f(x) = 2 -10(x +1)/1! +24(x +1)^2/2! -24(x +1)^3/3!
f(x) = 2 -10(x +1) +12(x +1)^2 -4(x +1)^3 . . . . . . . matches the first choice
Ana has a rectangular garden with a width of 2.3 meters and a length of 2.8 meters. She makes the model below to help her determine the area of her garden. What is the area of Ana's garden?
Answers
Answer:
6.44 m2
Step-by-step explanation:
My sister went QUaCk and my heart QuaKeD
Answers
Answer:
That's nice
But it should've YEETED
Step-by-step explanation:
Answer:
haha
Step-by-step explanation:
Help !!! I got -15 & it’s wrong !
Answers
Answer:
-11
Step-by-step explanation:
I substitute x in ( put parenthesis around x so it makes it clear)
-9-6-18+9+4+9
simplify
-33+22
-11
Answer: -11
Step-by-step explanation:
That polynomial simplifies to -2x^2-x+4
If we plug in -3 for x, we get -2(-3)^2-(-3)+4 and thats -11
Two Variable Statistics
Scatter Plots and Function Models AND PLEASE ANSWER ALL OF THE PART IF
Answers
Answer:
see step by step
Step-by-step explanation:
sorry rough sketch.
Answer:
idk
Step-by-step explanation:
Does it take more
inches or feet to equal a given
length? Explain.
Answers
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answers
Answer:
A) 26
E) 12
Step-by-step explanation:
11x ≥ 132
x ≥ 12
The solution set would include numbers greater than or equal to 12
Which function models this variation:
a varies directly with b and inversely with c, and when b=10 and c=20, a=14. Using your function, what is the value of a when b=18 and c=9 ?
A. a=b2c;a=1
B. a=b2c;a=2
C. a=2bc;a=1
D. a=2bc;a=2
