The approximation of the area of the region R under the graph of the function is 18.625 square units.
In this question we must calculate the approximate area ([tex]A[/tex]) below the curve by means of Riemann sums with left endpoints, whose expression is described below:
[tex]A = \Delta x \cdot \Sigma\limits^{n-1}_{i=0} f(a + i\cdot \Delta x)[/tex], for [tex]x \in [a,b][/tex] (1)
[tex]\Delta x = \frac{b-a}{n}[/tex] (2)
Where:
[tex]a[/tex] - Lower bound[tex]b[/tex] - Upper bound[tex]n[/tex] - Number of subintervals[tex]i[/tex] - IndexIf we know that [tex]a = -1[/tex], [tex]b = 2[/tex], [tex]n = 6[/tex] and [tex]f(x) = 7 - x^{2}[/tex], then the approximate area is:
[tex]\Delta x = \frac{2-(-1)}{6}[/tex]
[tex]\Delta x = 0.5[/tex]
[tex]A = 0.5\cdot [f(-1) + f(-0.5)+f(0)+f(0.5)+f(1)+f(1.5)][/tex]
[tex]A = 0.5\cdot (6+6.75+7+6.75+6+4.75)[/tex]
[tex]A = 18.625[/tex]
The approximation of the area of the region R under the graph of the function is 18.625 square units.
To learn more on Riemann sums, we kindly invite to check this verified question: https://brainly.com/question/21847158
$10,000 is invested at two different rates. $2,500 is invested at 4%, and the rest is invested at 5%. How much interest is earned at the end of one year? Show all work for full credit.
8.76× 10 6 is times than 8.76× 10 2 .
10^6 = 10 *10*10*10*10*10 = 1,000,000
10^2 = 10*10 = 100
1000000/100 = 10,000 times larger
Find the value of ab
The casino la bella fortuna is for sale and you think you might want to buy it, but you wantto know how much money you are going to make. all the present owner can tell you is thatthe roulette game red or black is played about 1000 times a night, 365 days a year. eachtime it is played you have probability 19/37 of winning the player’s bet of $10 and probability18/37 of having to pay the player $10.
The expected value of the roulette game red or black is -$0.62 per game, indicating an expected average loss.
Explanation:The expected value of the roulette game red or black can be calculated by multiplying the probabilities of winning and losing by their corresponding outcomes. In this case, the probability of winning ($10) is 19/37, and the probability of losing ($-10) is 18/37. Multiply these probabilities by their corresponding outcomes and subtract to get the expected value:
Expected value = (19/37 * $10) + (18/37 * -$10) = -$0.54 + (-$0.54) = -$0.62
This means that if you play this game repeatedly, over a long string of games, you would expect to lose an average of 62 cents per game.
Learn more about Expected value here:https://brainly.com/question/37190983
#SPJ12
(03.03 HC)
The table shows the outputs, y, for different inputs, x:
Input (x) 6 12 15 25
Output (y) 14 15 15 16
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 7x − 15. Which relation has a greater value when x = 6? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 6? (5 points)
Ignoring color, what kind of symmetry does the pinwheel have? A. rotational symmetry B. line symmetry C. both rotational and line symmetry D. neither
Which of the following is closest to 27.8 times 9.6? A. 280. B 300. C 2,800. D 3,000
A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points) Like football Do not like football Total Like baseball A D G Do not like baseball B E H Total C F I Part B: What percentage of the survey respondents did not like either football or baseball? (3 points) Part C: Do the survey results reveal a greater dislike for football or baseball? Justify your answer. (2 points)
Two people are traveling and need to exchange the currency of their native country for the currency of the country they are visiting. drag each exchange to match the ratio of currency to currency in each category.
Answer:
The solution is shown in attached figure.
Step-by-step explanation:
In table 1,
US currency (Dollars) Foreign currency
50.00 31.50
The foreign currency per US dollar is
[tex]\frac{31.50}{50}=0.63[/tex]
Therefore 0.63 is not equal to the exchange rate of Mexican peso and euro.
In table 2,
US currency (Dollars) Foreign currency
20.00 14.60
The foreign currency per US dollar is
[tex]\frac{14.60}{20}=0.73[/tex]
Therefore 0.73 is equal to the exchange rate of euro.
In table 3,
US currency (Dollars) Foreign currency
25.00 18.25
The foreign currency per US dollar is
[tex]\frac{18.25}{25}=0.73[/tex]
Therefore 0.73 is equal to the exchange rate of euro.
In table 4,
US currency (Dollars) Foreign currency
40.00 724.80
The foreign currency per US dollar is
[tex]\frac{724.80}{40}=18.12[/tex]
Therefore 18.12 is equal to the exchange rate of Mexican peso.
In table 5,
US currency (Dollars) Foreign currency
15.00 271.80
The foreign currency per US dollar is
[tex]\frac{271.80}{15}=18.12[/tex]
Therefore 18.12 is equal to the exchange rate of Mexican peso.
The equation d=13/v shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?
Answer: the density approaches infinity
Step-by-step explanation:
a garden table and a bench cost 817 dollars combined. The garden table costs 83 less than the bench. what is the cost of the bench
The scatter plot below shows the relationship between the length (x) in meters and mass f(x) in kg of a marine animal
(1,0)(2,10)(3,20)(4,30)(5,40)(6,50)(7,65)(8,70)(9,80)(10,90)
Which of the following fuction is best represented by the scatter plot?
F(x)=9-10.3x
F(x)=-10.3+9x
F(x)=-9+10.3x
F(x)=10.3-9x
Answer:
F(x)=-9+10.3x
Step-by-step explanation:
Given:
(1,0)
(2,10)
(3,20)
(4,30)
(5,40)
(6,50)
(7,65)
(8,70)
(9,80)
(10,90)
F(x)=9-10.3x and F(x)=10.3-9x cannot be the function of given scatter plot since the slope in these functions are negative
So, The equation of line can be F(x)=-10.3+9x or F(x)=-9+10.3x
Refer the attached figure.
Using desmos calculator
We conclude that the function is best represented by the scatter plot is [tex]F(x)=-9+10.3x[/tex]
A bag contains 40 marbles, 4 of which are blue, 10 are red, 25 are green, and 1 is purple. Shawna takes a marble out of the bag, records the color, and returns it to the bag. How many green marbles should she expect after 400 trials? (5 points)
What is 18a and 12ab's GCF
Answer:
6a
Step-by-step explanation:
18a = 2 · 3² · a
12ab = 2² · 3 · a · b
Factors common to both lists are 2, 3, a, so the GCF is 2·3·a = 6a.
How do you interpret algebraic expressions in terms of their context
find the volume of a sphere with a diameter of 25 cm. approximate pi as 3.14 and round your answer to the nearest hundredth
a rectangle has a width of 17 ft and a lenghth of 8ft....PLEASE HELP ME SOS!!! ASAP!!!
perimeter is 17 +17 +8 + 8 = 50 feet
area = 17 x 8 = 136 square feet
cost = 136 x $3.50 = $476.00
A journal entry for the sale of $10 par common stock for $18 per share would include
a. a credit to Cash
b. a debit to common stock
c. a credit to Paid in Capital in Excess of Par-Common Stock
d. a debit to Paid in Capital n Excess of Par-Common Stock
Jim drove 204 miles in 4 hours. If he can keep the same pace how long will it take him to drive 918 miles
A certain species of tree grows an average of 4.2 cm per week. write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.
Average growth rate = 4.2 cm/week.
So, common difference d = 4.2
The height of the tree a0 = 200 centimeters.
The height of the tree after end of the first week a₁ = 200 + 4.2 = 200 + 4.2(1)
The height of the tree after end of the second week a₂ = 200 + 4.2 + 4.2 = 200 + 4.2(2).
The height of the tree after end of the third week a3 = 200 + 4.2 + 4.2 + 4.2 = 200 + 4.2(3).
The height of the tree after the end of the nth week an = 200 + 4.2(n).
The equation is a_n = 200 + 4.2(n).
Text me the answer please
A = h/2 * (a + b ); for h
Find a nonzero vector normal to the plane
Suppose a least-squares regression line is given by modifyingabove y with caret equals 4.302 x minus 3.293y=4.302x−3.293. what is the mean value of the response variable if x equals 20x=20
The mean value of the response variable y when x equals 20 in the least-squares regression line equation y = 4.302x - 3.293 is 82.041.
Explanation:The given equation is y = 4.302x - 3.293, which is a least-squares regression line. In this formula, x is the independent variable and y is the resulting dependent variable or response. The goal is to find the mean value of the response variable when x is 20. This can be achieved simply by plugging 20 in place of x in our equation and calculating the resulting value for y.
We will substitute x = 20 into the equation y = 4.302x - 3.293. Therefore, the value of y when x is 20 is:
y = 4.302(20) - 3.293 = 82.041
So, when x = 20, the mean value of the response variable y or the predicted y value is 82.041.
Learn more about Least-Squares Regression Line here:https://brainly.com/question/30403468
#SPJ12
Kurt wants to have $25,000 in an investment account four years from now. the account will pay 0.2 percent interest per month. if he saves money every month, starting one month from now, how much will he have to save each month to reach his goal
Kurt will have to save an amount of $496.75 each month.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
Final amount of the account, A = $25,000
Interest rate, r = 0.2% = 0.002
Number of years, t = 4 years
Interest compounded monthly, so n = 12
Annuity can be found using the formula,
Annuity = 25,000 ÷ {[(1 + 0.002)^(12×4) - 1] / 0.002}
= 25,000 ÷ {[(1.002)⁴⁸ - 1] / 0.002}
= 496.75
Hence the amount Kurt needs to save each month is $496.75.
To learn more about Annuities, click on the link :
https://brainly.com/question/29759069
#SPJ6
If the measure of angle A is 40* and the length of side b is 15 inches, which can be the length of side a if it is possible to form two triangles
An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground? (s= 16t^2)
Answer:
After 3 seconds the object hit the ground.
Step-by-step explanation:
An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground.
Given that displacement, s = 16t²
To reach ground displacement should be 144 feet.
That is
s = 16t² = 144
t² = 9
t = 3 seconds.
After 3 seconds the object hit the ground.
G study find the exact value of each of the remaining trigonometric functions cos theta=4/5 270< theta
Given that cos theta is 4/5 within the 270 to 360-degree range, sin(theta) is -3/5, tan(theta) is -3/4, sec(theta) is 5/4, csc(theta) is -5/3, and cot(theta) is -4/3.
Explanation:The question indicates that we are dealing with trigonometry and specifically asks for the remaining trigonometric functions given that cos theta = 4/5 and theta is in the range of 270o to 360o.
This implies that theta is in the fourth quadrant where cosine is positive, and the other trigonometric functions can have different signs.
Since we have the cosine of theta, we can use the Pythagorean identity to find the sine of theta. The identity states that in2(theta) + cos2(theta) = 1.
Plugging in the given cosine value, we have:
sin2(theta) + (4/5)2 = 1
sin2(theta) = 1 - 16/25
sin2(theta) = 9/25
sin(theta) = ±√(9/25) = ±3/5
However, since theta is in the fourth quadrant, the sine is negative, and therefore we find:
sin(theta) = -3/5
For the tangent of theta, we use the definition tan(theta) = sin(theta)/cos(theta), which yields:
tan(theta) = (-3/5) / (4/5) = -3/4
The values of the other three trigonometric functions (secant, cosecant, and cotangent) are the reciprocals of the three we just calculated:
sec(theta) = 1/cos(theta) = 5/4
csc(theta) = 1/sin(theta) = -5/3
cot(theta) = 1/tan(theta) = -4/3
WILL GIVE BRAINLIEST...
You have 45 ft of the fence you enclose your yard, you are going to use the side of your house as one of the sides and put a fence down the width of the yard so your dog as a place to play, the length is three less than the width. What is the area of your yard?
An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many cats are at the shelter?
To find the number of cats at the animal shelter, we can set up and solve a system of equations using the given information. In this case, the number of dogs is 126 and the number of cats is 146.
Explanation:To solve this problem, let's assign variables to represent the number of cats, dogs, and rabbits at the shelter. Let's say the number of cats is 'c', the number of dogs is 'd', and the number of rabbits is 'r'.
From the given information, we can form three equations:
The total number of animals is 350: c + d + r = 350The number of rabbits is 5 less than one-half the number of cats: r = (1/2)c - 5There are 20 more cats than dogs: c = d + 20Using these equations, we can solve for the value of 'c' (the number of cats).
By substituting the value of 'c' from equation 3 into equation 2, we get:
r = (1/2)(d + 20) - 5
Now, we substitute the values of 'c' and 'r' from equations 3 and 1 into equation 1:
(d + 20) + d + ((1/2)(d + 20) - 5) = 350
Simplifying this equation, we get:
2d + (1/2)d + 35 = 350
Combining like terms, we have:
4d + d + 70 = 700
Simplifying further, we find:
5d + 70 = 700
Subtracting 70 from both sides of the equation, we get:
5d = 630
Dividing both sides by 5, we find that d = 126. Therefore, there are 126 dogs at the shelter.
Finally, by substituting the value of d back into equation 3, we find:
c = 126 + 20 = 146. Thus, there are 146 cats at the shelter.
Learn more about Solving Systems of Equations here:
https://brainly.com/question/29050831
#SPJ11