Split up the interval [1, 9] into n subintervals of equal length (9 - 1)/n = 8/n :
[1, 1 + 8/n], [1 + 8/n, 1 + 16/n], [1 + 16/n, 1 + 24/n], …, [1 + 8 (n - 1)/n, 9]
It should be clear that the left endpoint of each subinterval make up an arithmetic sequence, so that the i-th subinterval has left endpoint
1 + 8/n (i - 1)
Then we approximate the definite integral by the sum of the areas of n rectangles with length 8/n and height [tex]f(x_i)[/tex] :
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx \approx \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right)[/tex]
Take the limit as n approaches infinity and the approximation becomes exact. So we have
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx = \lim_{n\to\infty} \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right) \\\\ = \lim_{n\to\infty} \frac8n \sum_{i=1}^n \left(1+\frac{16}n(i-1)+\frac{64}{n^2}(i-1)^2-4-\frac{32}n(i-1)+6\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=1}^n \left(64(i-1)^2-16n(i-1)+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=0}^{n-1} \left(64i^2-16ni+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(64\sum_{i=0}^{n-1}i^2 - 16n\sum_{i=0}^{n-1}i + 3n^2\sum{i=0}^{n-1}1\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{64(2n-1)n(n-1)}{6} - \frac{16n^2(n-1)}{2} + 3n^3\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{49n^3}3-24n^2+\frac{32n}3\right) \\\\= \lim_{n\to\infty} \frac{8\left(49n^2-72n+32\right)}{3n^2} = \boxed{\frac{392}3}[/tex]
In the graph above, which vertical line (V) and horizontal line (H) can be used to graph point A?
A)
V: x = 1; H: y = 4
B)
V: x = 4; H: y = 1
C)
V: y = 4; H: x = 1
D)
V: x = 1; H: y = –4
Answer:
V: x = 1; H: y = 4
Step-by-step explanation:
Point A is at x = 1 and y = 4
A vertical line at x=1 and a horizontal line at y = 4
6. If gallon A has 8L of water and gallon B has 800 ml of water, calculate the total volume of water in both the gallons.
Answer:
send me again I can't understand question
Solve the inequality (help pls)
Answer:
B
Step-by-step explanation:
(-2/3x)-10<1/3
(-2/3x)<1/3+10
(-2/3x)<31/3
x>-31/2, -31/2=-15 (1/2), x> - 15 (1/2)
Help!!
A.) find f^-1 and use it to evaluate: f^-1(12)
B.) write a formula for the function g(x) that results when the parent function: f(x) = x^3 is vertically stretched by a factor of three, shifted to the left by 4 units and shifted down by 5 units
Answer:
Step-by-step explanation:
y = x³
x = ∛y
Switch x and y:
y = ∛x
f⁻¹(x) = ∛x
f⁻¹(12) = ∛12 ≅ 2.29
check:
x = 2.29
f(x) = 2.29³ ≅ 12
Four- sevenths of the children in class earned A's on the last math test. 18 children did not earn an A. How many earned A's? SHOW ALL WORK!!!
Answer: 24 people earnt As
Step-by-step explanation:
1. We know that 18 people are the other 3/7 of the class
2. We first find out 1/7, which is calculated by dividing 3/7 by 3, which is 18 / 3 so 6
3. We can then find 4/7 by multiplying the amount of 1/7 by 4, so 6 x 4 = 24
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 5 hours of burning, a candle has a height of 21.5 centimeters. After 24 hours of burning, its height is 19.6 centimeters. What is the height of the candle after 11 hours?
YEsStep-by-step explanation:
what fraction of 1 day is 48 minutes
Answer:
48 ÷ 60 = 4/5
Step-by-step explanation:
4/5 is the answer
Answer:
[tex]\frac{1}{30}[/tex]
Step-by-step explanation:
We require the number of minutes in a day.
i hour = 60 minutes
24 hours = 24 × 60 = 1440 minutes ( 24 hours in 1 day )
Then
fraction = [tex]\frac{48}{1440}[/tex] ( divide numerator/ denominator by 12 )
= [tex]\frac{4}{120}[/tex] ( divide numerator/ denominator by 4 )
= [tex]\frac{1}{30}[/tex]
The table and the Circle Chart shown display the percentage of dogs in seven different groups of dog breeds in a dog competition.
How does the Circle Graph misrepresent the data in the table?
A. The percentages do not add up to 100.
B. The size of the section representing the Non-Sporting group is smaller than the section that represents Herding group.
C. The number of regions in the graph is not correct for the data.
D. One of the breeds in the table is not represented in the Circle Chart.
Answer:
a
Step-by-step explanation:
Answer:
Incorrect, it's actually B.
Step-by-step explanation:
Look at the Non-Sporting Group and Herding Group. The sizes of the slices are different (NSG being smaller than HG)
through: (3, - 3); slope = 2/3
Answer:
y=2/3x - 5
Step-by-step explanation:
Since we have the slope and a point, we can make an equation in point intercept form (y=mc+b) by using the point slope form formula (y-y1)=m(x-x1), where (x1,y1) is the point you plug in.
(y-y1)=m(x-x1)
m=2/3
y1=-3
x1=3
y- -3=2/3(x-3)
y+3=2/3(x-3)
Distribute 2/3 with (x-3) by multiplying
y+3=2/3x - 2
Subtract 3 from both sides
y=2/3x - 5
1. Find the value of the unknown angles in the following diagram.
Answer:
z= 40
y=140
x= 115
Step-by-step explanation:
look at the pics
How to solve this question. I need to show my work for this question.
A cookie recipe calls for 3 eggs and makes 4 dozen cookies.
a). How many cookies could you make with a dozen eggs?
b). How many eggs would you need to make 18 dozen cookies?
Step-by-step explanation:
Recall that 1 dozen = 12 so 4 dozen cookies has a total of 48 cookies. We are going to use the following ratios to solve the problem:
[tex]\left(\dfrac{3\:\text{eggs}}{48\:\text{cookies}}\right)[/tex] and [tex]\left(\dfrac{48\:\text{cookies}}{3\:\text{eggs}}\right)[/tex]
a) [tex]12\:\text{eggs}×\left(\dfrac{48\:\text{cookies}}{3\:\text{eggs}}\right) = 192\:\text{cookies}[/tex]
b) 18 dozen cookies = 216 cookies
[tex]216\:\text{cookies}×\left(\dfrac{3\:\text{eggs}}{48\:\text{cookies}}\right) = 13.5\:\text{eggs}[/tex]
given that the following two are geometric series are convergent: 1+x+x^2+x^3+...and 1-x+x^2-x^3+... determine the value(s) of x for which the sum of the two series is equal to 8
Let S and T denote the two finite sums,
S = 1 + x + x ² + x ³ + … + x ᴺ
T = 1 - x + x ² - x ³ + … + (-x) ᴺ
• If both S = 8 and T = 8 as N goes to infinity:
Then
xS = x + x ² + x ³ + x ⁴ + … + x ᴺ⁺¹
-xT = -x + x ² - x ³ + x ⁴ + … + (-x) ᴺ⁺¹
so that
S - xS = 1 - x ᴺ⁺¹ ==> S = (1 - x ᴺ⁺¹)/(1 - x)
and similarly,
T = (1 - (-x) ᴺ⁺¹)/(1 + x)
For both sums, so long as |x| < 1, we have
lim [N → ∞] S = 1/(1 - x)
lim [N → ∞] T = 1/(1 + x)
Then if both sums converge to 8, this happens for
S : 1/(1 - x) = 8 ==> x = 7/8
T : 1/(1 + x) = 8 ==> x = -7/8
• If the sum S + T = 8 as N goes to infinity:
From the previous results, we have
1/(1 - x) + 1/(1 + x) = 8 ==> x = ±√3/2
Data was collected on reaction time of both hands for an experiment. 14 out of 27 students had a faster reaction time with their right hand than with their left hand. Using this information, we wish to construct a confidence interval for the proportion of all WCU students that have a faster reaction time with their right hand than with their left hand.
Calculate the lower boundary of a 99% confidence interval.
Give your answer as a decimal rounded to 3 places after the decimal.
Answer:
0.3902
Step-by-step explanation:
The question meets the criteria for the calculation of the confidence interval of a one sample proportion ;
Sample size, n = 27
Number of students with faster reaction time = 14
Phat = x / n = 14 / 27 = 0.6296
The confidence interval is calculated thus :
C. I = Phat ± Zcritical * √[p(1 - p)/n]
Zcritical at 99% = 2.576
C. I = 0.6296 ± 2.576 * √[0.6296(0.3704)/27]
C.I = 0.6296 ± 0.2394042
The lower boundary of C.I = 0.6296 - 0.2394042
Lower boundary = 0.3902
IF A= -35 , B = 10 , C= -5 verify that:-
a x (b+c) = a x b + a x c
Plz tell
Answer:
see below
Step-by-step explanation:
a x (b+c) = a x b + a x c
Let A= -35 , B = 10 , C= -5
-35 * ( 10 -5) = -35 *10 + -35 * -5
-35 *(5) = -350 + 175
-175 = -175
look at the image below plz helppppppppppppp
Answer:
150.
Step-by-step explanation
Four friends bought books at a bookstore. The person who got the best deal has the lowest ratio of cost to number of books purchased. Book Purchases Name Total Cost Number of Books Jo $9 4 Kei $12 8 Kate $30 16 Bryn $8 4
Answer:
Kei got the best deal.
Explanation:
The ratio of cost to number of books purchased for all of four friends will be.....
Jo ⇒ [tex]\frac{9}{4}[/tex], Kei ⇒ [tex]\frac{12}{8}[/tex] , Kate ⇒ [tex]\frac{30}{16}[/tex], Bryn ⇒ [tex]\frac{8}{4}[/tex]
From here you have to find the common denominator in this case is 16.
[tex]\frac{9}{4} =\frac{9*4}{4*4} =\frac{36}{16}[/tex]
[tex]\frac{12}{8} =\frac{12*2}{8*2} =\frac{24}{16}[/tex]
[tex]\frac{30}{16} =\frac{30*1}{16*1} =\frac{30}{16}[/tex]
[tex]\frac{8}{4} =\frac{8*4}{4*4} =\frac{32}{16}[/tex]
As you could tell the lowest is [tex]\frac{24}{16}[/tex] so the lowest is Kei.
You spend $7.00 at the store. The sales tax is 6%. How much is your total bill?
Please explain how you got the answer if you can.
Answer:
7.42
Step-by-step explanation:
First determine the amount of tax
7 * 6%
7 *.06
.42
Add this to the original bill
7 + .42
7.42
The total cost is 7.42
A triangle has side lengths of (4.6x-4.4y)(4.6x−4.4y) centimeters, (7.5x-8.8z)(7.5x−8.8z) centimeters, and (7.7z-9.2y)(7.7z−9.2y) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
The expression that represents the perimeter, in centimeters, of the triangle is [tex]77.41x^{2}+104y^{2}+ 136.73z^{2} -40.48xy - 132xz - 141.64yz[/tex] cm OR 77.41x²+104y²+136.73z²-40.48xy-132xz-141.64yz centimeters
From the question, the side lengths are
(4.6x-4.4y)(4.6x−4.4y) cm, (7.5x-8.8z)(7.5x−8.8z) cm, and (7.7z-9.2y)(7.7z−9.2y) cm.
First, we will clear the brackets one after the other
For (4.6x-4.4y)(4.6x−4.4y) cm
[tex]4.6x(4.6x-4.4y) -4.4y(4.6x-4.4y)[/tex]
[tex]21.16x^{2} -20.24xy -20.24xy+19.36y^{2}[/tex]
[tex]21.16x^{2} -40.48xy+19.36y^{2}[/tex]
∴ (4.6x-4.4y)(4.6x−4.4y) cm = [tex]21.16x^{2} -40.48xy+19.36y^{2}[/tex] cm
For (7.5x-8.8z)(7.5x−8.8z) cm
[tex]7.5x(7.5x-8.8z) -8.8z(7.5x-8.8z)[/tex]
[tex]56.25x^{2} - 66xz -66xz + 77.44z^{2}[/tex]
[tex]56.25x^{2} - 132xz + 77.44z^{2}[/tex]
∴ (7.5x-8.8z)(7.5x−8.8z) cm = [tex]56.25x^{2} - 132xz + 77.44z^{2}[/tex] cm
For (7.7z-9.2y)(7.7z−9.2y) cm
[tex]7.7z(7.7z-9.2y)-9.2y(7.7z-9.2y)[/tex]
[tex]59.29z^{2} - 70.84yz-70.84yz+84.64y^{2}[/tex]
[tex]59.29z^{2} - 141.64yz+84.64y^{2}[/tex]
∴ (7.7z-9.2y)(7.7z−9.2y) cm = [tex]59.29z^{2} - 141.64yz+84.64y^{2}[/tex] cm
Now, for the expression that represents the perimeter of the triangle,
Perimeter of a triangle can be calculated by determining the sum of all its sides
That is,
Perimeter of the triangle = [tex]21.16x^{2} -40.48xy+19.36y^{2}[/tex] cm + [tex]56.25x^{2} - 132xz + 77.44z^{2}[/tex] cm + [tex]59.29z^{2} - 141.64yz+84.64y^{2}[/tex] cm
[tex]=21.16x^{2} -40.48xy+19.36y^{2} + 56.25x^{2} - 132xz + 77.44z^{2} + 59.29z^{2} - 141.64yz+84.64y^{2}[/tex]
Collect like terms
[tex]= 21.16x^{2}+ 56.25x^{2} -40.48xy+19.36y^{2}+84.64y^{2} - 132xz + 77.44z^{2} + 59.29z^{2} - 141.64yz[/tex]
[tex]= 77.41x^{2} -40.48xy+104y^{2} - 132xz + 136.73z^{2} - 141.64yz[/tex]
[tex]= 77.41x^{2}+104y^{2}+ 136.73z^{2} -40.48xy - 132xz - 141.64yz[/tex] cm
Hence, the expression that represents the perimeter, in centimeters, of the triangle is [tex]77.41x^{2}+104y^{2}+ 136.73z^{2} -40.48xy - 132xz - 141.64yz[/tex] cm OR 77.41x²+104y²+136.73z²-40.48xy-132xz-141.64yz centimeters
Learn more here : https://brainly.com/question/19761201
find the slope of the line
answer choices: 4, 5, 20, 25
Answer: Third Choice. 20
Concept:
Here, we need to know the idea of a slope.
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Slope = Rise / Run = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)
Solve:
STEP ONE: Select two points on the line that intersects with the grids
A (0, 5)
B (1, 25)
STEP TWO: Apply the formula
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (25 - 5) / (1 - 0)
Slope = 20 / 1
Slope = 20
Hope this helps!! :)
Please let me know if you have any questions
Answer:
20
Step-by-step explanation:
We can find the slope of the line by using the slope formula
Slope = (y2 - y1)/(x2-x1)
Where the x and y values are derived from points chosen on the line
The points chosen may vary but I have chosen (1,25) and (2,45)
Now that we have chosen the points let's define our variables ( our variables are x1 x2 y1 and y2 )
x1 is the x value of the first point chosen.The x value of the first point chosen is 1 so x1 = 1
x2 is the x value of the second point chosen. The x value of the second point chosen is 2 so x2 = 2
y1 is the y value of the second point chosen. The y value of the first point chosen is 25 so y1 = 25
y2 is the y value of the second point chosen. The y value of the second point chosen is 45 so y2 = 45
Now to find the slope we simply plug in the values of the variables into the formula
Formula: (y2 - y1)/(x2-x1)
Variables: x1 = 1, x2 = 2, y1 = 25, y2 = 45
Plug in values
(45-25)/(2-1)
Subtract top numbers
(20)/(2-1)
Subtract bottom numbers
20/1
Simplify
The slope is 20
PLEASE HELPPPPPP!!!!! THIS IS DUE ASAP PLEASEEE
Answer:
1
Step-by-step explanation:
list the numbers that are odd or greater than 2
1,2,3,4,5,6
aka every single outcome
therefore the answer is just 1
Answer:
5/6
Step-by-step explanation:
The possible outcomes are 1,2,3,4,5,6
Odd numbers are 1,3,5
Greater than 2 are 3,4,5,6
Good solutions are 1,3,4,5,6 = 5 outcomes
P( odd or greater than 2) = good solutions / total
= 5/6
2. What is the number 643,581 rounded off
to the thousands place?
(1) 640,000
(2) 643,000
(3) 643,600
(4) 644,000
(5) 644,600
Answer:
(4) 644,000
Step-by-step explanation:
643,581
The 3 is in the thousands place
We look at the hundreds place
5
It is 5 or greater so we round the thousands place up 1
644000
A chef is going to use a mixture two different brands of Italian dressing the first spring and days 5% vinegar the second brain contains 15% vinegar the sheriff wants to make 390$ ml addressing that is 9% vinegar how much of each brand should she use
I guess the chef is making the mixture for the sheriff... Let x be the amount of dressing with 5% vinegar that is required, and y the amount of 15% vinegar dressing (both amounts in mL).
The sheriff wants 390 mL of the mixed dressing, so that
x + y = 390
x mL of the 5% dressing contains 0.05x mL of vinegar, while y mL of the 15% dressing contains 0.15y mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means
0.05x + 0.15y = 35.1
Solve for x and y :
y = 390 - x
0.05x + 0.15 (390 - x) = 35.1
0.05x + 58.5 - 0.15x = 35.1
23.4 = 0.10x
x = 234
y = 156
An organization consists of 8,684 employees. They decided to conduct a survey about their new vacation policies. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. Assuming a 95% confidence level, which of the following statements holds true?
Answer:
A. As the sample size is appropriately large, the margin of error is ±0.032.
Step-by-step explanation:
The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.
What is the distance from point Yto wx in the figure below?
W 16 Z
30
X
1612
34
O A. 4
O B. 162
O C. 16
O D. Cannot be determined
E. 16/3
F. 8
The length of YZ in the similar triangle given is calculated using Pythagoras theorem which gave us 16√3
What are Similar TriangleSimilar triangles are two or more triangles that have the same shape but may be different sizes. They have the same angles and corresponding sides that are proportional.
In this problem, we need to use the concept of ratio and proportions to find the length of YZ
However, we can simply use Pythagoras theorem to determine the length.
According to Pythagoras' Theorem, the square of the hypotenuse, or side opposite the right angle, in a right-angled triangle, is equal to the sum of the squares of the other two sides.
It is expressed as the equation a² + b² = c².
This is because the triangles forms a right angled triangle and we can easily apply that here.
YZ² = 16² + (16√2)²
YZ² = 768
YZ = √768
YZ = 16√3
The length or distance from point Y to WX which is the same as the length of YZ is calculated as 16√3.
Learn more on similar triangle here;
https://brainly.com/question/14285697
#SPJ1
Answer:
C. 16
Step-by-step explanation:
I hope this helps :)
brainliest to correct
Answer:
27
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
-9 × -3
= 27
Note: When you multiply two integers with same sign, then their product is positive.
Malika is 1.45 meters tall. At 10 a.m., she measures the length of a tree's shadow to be 32.25 meters. She stands 27.5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
Step-by-step explanation:
If the length of a tree's shadow is 32.25 meters. The height of the tree to the nearest hundredth of a meter will be : 9.84m
Given:
Malika height=1.45 meters
Length =32.25 meters
Width =27.5 meters
Height of the tree=x
Proportion:
1.45 : 32.25 :: x : 27.5
Now let determine the height of the tree
32.25-27.5/1.45=32.25/x
4.75/1.45=32.25/x
Cross multiply
4.75x=32.25×1.45
4.75x=46.7625
Divide both side
x=46.7625/4.75
x=9.84m
Inconclusion if the length of a tree's shadow is 32.25 meters. The height of the tree to the nearest hundredth of a meter will be : 9.84m
Learn more here:
https://brainly.com/question/23966984
d(v)=45, d(v)=1.1v+0.6v^2
Step-by-step explanation:
d(v)=1.1(45)+0.6(45)²
=1.1(45)+0.6(2025)
=49.5+1215
=1264.5
Which inequality represents all values of x which the product below is defined Square root 4x Square root x+2
Answer:
Option (D) x≥ 0 is absolutely correct
Step-by-step explanation:
The reason is that the square root function is defined for only non negative numbers.
Answer: x is greater than or equal to 0
Step-by-step explanation:
What are the odds IN FAVOR of picking a red marble from a bag of 10 green marbles, 10 yellow marbles, and 5 red marbles?
Answer:
there is a 20% chance of getting a red marble
Step-by-step explanation:
Answer:
there is a 1/5 percent chance or 20%
Step-by-step explanation:
Hope this helps!
There is a circle with a center of 0,0 on a coordinate plane. There is one point on the circle's circumference in which the x:y ratio is 3:1. What is a possible coordinate?
Answer:
(3, 1)
Step-by-step explanation:
A circle with radius √10 and centre at (0, 0) will have a point (3, 1) on its circumference.
