Consider the integral 8 (x2+1) dx 0 (a) Estimate the area under the curve using a left-hand sum with n = 4. Is this sum an overestimate or an underestimate of the true value? overestimate underestimate (b) Estimate the area under the curve using a right-hand sum with n = 4. Is this sum an overestimate or an underestimate of the true value? overestimate underestimate
Answers
Answer:
(a) 120 square units, underestimate
(b) 248 square units, overestimate
Step-by-step explanation:
(a) left sum
The left sum is the sum of the areas of the rectangles whose width is the total interval width (8-0) divided by the number of divisions (n=4). The height of each rectangle is the function value at its left edge.
We can compute the sum by adding the function values and multiplying that total by the width of the rectangles:
left sum = (1 + 5 + 17 + 37)×2 = 60×2 = 120 . . . square units
The curve is increasing throughout the interval of interest, so the left sum underestimates the area under the curve.
__
(b) right sum
The rectangles whose area is the right sum are shown in the attachment, along with the table of function values. The right sum is computed the same way as the left sum, but using the function value on the right side of each subinterval.
right sum = (5 + 17 + 37 + 65)×2 = 124×2 = 248 . . . square units
The curve is increasing throughout the interval of interest, so the right sum overestimates the area under the curve.
_____
The actual area under the curve on the interval [0, 8] is 178 2/3, just slightly less than the average of the left- and right- sums.
The left-hand and right-hand sums are common methods to estimate the area under a curve. Using n=4, the left-hand sum tends to be an underestimate, while the right-hand sum is usually an overestimate of the actual area.
Explanation:The integral 8(x²+1)dx from 0 to a is the area under the curve defined by the function 8(x²+1). A common way to approximate this area is by using left-hand and right-hand sums.
(a) Left-Hand Sum: Using n=4, we divide the interval [0, a] into 4 equal subintervals. For each subinterval, we find the left endpoint and plug it into our function, then multiply by the length of the subinterval. Sum these values to get the left-hand sum. This sum is usually an underestimate of the true area as it leaves out the area under the curve that lies to the right of the left-hand rectangle in each subinterval.
(b) Right-Hand Sum: The process is similar to the left-hand sum, but we use the right endpoint of each subinterval. The right-hand sum tends to be an overestimate of the true area as it includes the area above the curve that lies to the right of the rectangle in each subinterval.
Learn more about Area Under the Curve here:https://brainly.com/question/31603257
#SPJ11
Related Questions
let f(x) = -2x/(x^2-x-5) There are 2 numbers that are not in the domain of f. Give the larger value to 2 decimal places.
Answers
Answer:
Step-by-step explanation:
The 2 numbers that are not in the domain of the function are the 2 numbers that cause the denominator of the function to equal 0. In order to find those 2 numbers, we have to factor the quadratic that is in the denominator. When you factor, you get x = 2.79 and x = -1.79
Those are the values of x that cause the denominator to equal 0, which of course is NEVER allowed in math!
Tangent lines-someone please help explain
Answers
The angle between radius and tangent to circle is 90 degrees.
The quadrilateral formed by the two tangents and the two rays has two angles of 90 degrees, an angle of 40 degrees and an unknown angle.
The sum of the angles of a quadrilateral is 360 degrees.
⇒ x = 360° - 90 - 90 - 40 = 140°
x = 140°
if cos θ = -0.6, and 180° < θ < 270°, find the exact value of sin 2θ.
Answers
Answer:
sin(2θ) = 0.96
Step-by-step explanation:
In the third quadrant, both sin(θ) and cos(θ) are negative. Then the double-angle trig identity tells us ...
sin(2θ) = 2·sin(θ)·cos(θ) = -2cos(θ)√(1 -cos(θ)²) . . . . using the negative root
Filling in the given value, we have
sin(2θ) = -2·(-0.6)(√(1-(-0.6)²) = 2·0.6·0.8 = 0.96
PLEASE ANSWER WITH AN EXPLANATION! THANK YOU
Answers
Answer:
[tex]\large\boxed{A=153\ cm^2}[/tex]
Step-by-step explanation:
Look at the picture.
We have
square with side length a = 9
trapezoid with base lengths b₁ = 9 and b₂ = 6 and the height length h = 6
right triangle with legs lengths l₁ = 3 + 6 = 9 and l₂ = 6
The formula of an area of a square
[tex]A=a^2[/tex]
Substitute:
[tex]A_I=9^2=81\ cm^2[/tex]
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
Substitute:
[tex]A_{II}=\dfrac{9+6}{2}\cdot6=\dfrac{15}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3=(15)(3)=45\ cm^2[/tex]
The formula of an area of a right triangle:
[tex]A=\dfrac{l_1l_2}{2}[/tex]
Substitute:
[tex]A_{III}=\dfrac{(9)(6)}{2}=\dfrac{54}{2}=27\ cm^2[/tex]
The area of the shape:
[tex]A=A_I+A_{II}+A_{III}\\\\A=81+45+27=153\ cm^2[/tex]
Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of the sample mean are
Answers
Answer: The mean and the standard error of the distribution of the sample mean are 200 and 2.
Step-by-step explanation:
Given: Sample size : n= 81
Mean of infinite population : [tex]\mu=200[/tex]
We know that the mean of the distribution of the sample mean is same as the mean of the population.
i.e. [tex]\mu_x=\mu=200[/tex]
The standard error of the distribution of the sample mean is given by :-
[tex]S.E.=\dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\Rightarrow\ S.E.=\dfrac{18}{\sqrt{81}}=\dfrac{18}{9}=2[/tex]
Hence, the mean and the standard error of the distribution of the sample mean are 200 and 2.
The mean of the sample mean distribution for a random sample of size 81 from a population with a mean of 200 and a standard deviation of 18 is 200, and the standard error is 2.
Explanation:The question is about determining the mean and the standard error of the distribution of the sample mean. According to the Central Limit Theorem, regardless of the distribution of the original population, the distribution of the sample mean tends to form a normal distribution as the sample size increases. In this case, the mean of the sample mean distribution is the same as the population mean, which is 200.
The standard error of the mean is calculated as the population standard deviation divided by the square root of the sample size. So, the standard error in this scenario would be 18/√81 = 2.
Therefore, in a random sample of size 81 taken from an infinite population with a mean of 200 and a standard deviation of 18, the mean of the sample mean distribution is 200, and the standard error is 2.
Learn more about Sample Mean Distribution here:https://brainly.com/question/31520808
#SPJ3
If 2000 dollars is invested in a bank account at an interest rate of 8 per cent per year,
Find the amount in the bank after 12 years if interest is compounded annually:
Answers
Answer:
$5036.34
Step-by-step explanation:
Each year, 8% of the existing balance is added to the existing balance, effectively multiplying the amount by 1.08. If that is done for 12 years, the effective multiplier is 1.08^12 ≈ 2.51817. The the amount in the bank at the end of that time is ...
$2000×2.51817 = $5036.34
The amount in the bank after 12 years with an annual interest rate of 8% on a principal amount of 2000 dollars, compounded annually, will be approximately $5025.90.
Explanation:This is a compound interest problem. The formula used to solve this type of problem is A = P(1 + r/n)^(nt), where:
P is the principal amount (initial money),r is the annual interest rate,t is the number of years,n is the number of times that interest is compounded per year.In this case, P = $2000, r = 8% or 0.08, t = 12 years and n = 1 (as interest is compounded annually). Substituting these values in the equation, we get:
A = 2000(1 + 0.08/1)^(1*12)
.
The resulting Amount A after 12 years will be approximately $5025.90.
Learn more about Compound Interest here:https://brainly.com/question/34614903
#SPJ3
A bag contains 2 steel balls and 5 brass balls. The total weight is 13 pounds. If 2 steel balls are added and 2 brass balls are removed, the weight decreases to 12 pounds. How much does each kind of ball weigh?
Answers
s=number of steel balls
b=number of brass balls
2s+5b=13
4s+3b=12
Multiply first equation by -2 to get -4s-10b=-26
add the two equations
-7b=-14
Simplify
b=2 now substitute 2 for b in any equation to get s=1.5
Answer:
Step-by-step explanation:
The answer above this answer is correct
The conversion factor relating feet to meters is 1 ft=0.305 m. Keep in mind that when using conversion factors, you want to make sure that like units cancel leaving you with the units you need. You have been told that a certain house is 164 m2 in area. How much is this in square feet?
Answers
Answer:
1763 ft²
Step-by-step explanation:
Using the given conversion factor, ...
(164 m²)(1 ft/(.305 m))² = 165/.093025 ft² ≈ 1763 ft²
_____
The exact conversion factor is 1/0.3048, so the area is closer to 1765 ft². For a 4-significant digit answer, you need to use a conversion factor accurate to 4 significant digits.
To convert square meters to square feet, you must square the feet to meter conversion factor, resulting in approximately 10.764 sq ft/sq m. You then multiply this by the square meter measurement to get the equivalent in square feet. Therefore, the house's area, which was provided as 164 square meters, translates to approximately 1765.736 square feet.
Explanation:The measure of the area in square feet can be derived using the conversion factor for feet to meters, 1 ft = 0.305 m. However, when you deal with areas, you must square the conversion factor. We then apply the conversion factor to the known area in reference, which in our case is 164 square meters.
So our conversion factor becomes (1/0.305)² sq ft/sq m = 10.764 sq ft/sq m.
To use the conversion factor, we multiply it by the metric unit measurement, like this: 164 m²*(10.764 ft²/m²) = 1765.736 square feet.
So, the house's area is approximately 1765.736 square feet.
Learn more about Unit Conversion here:https://brainly.com/question/32030244
#SPJ2
x^2+y^2=25 Find the distance of point (x,y) from origin.
Answers
Answer:
5 units
Step-by-step explanation:
This is a circle with a center of (0, 0). The square root of 25 represents the radius of the circle which is 5. The radius represents the distance that the outside of the circle is from the center.
Solve for x in the equation
Answers
Answer:
[tex]\large\boxed{x=6\pm3\sqrt{10}}[/tex]
Step-by-step explanation:
[tex]x^2-12x+36=90\\\\x^2-2(x)(6)+6^2=90\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-6)^2=90\iff x-6=\pm\sqrt{90}\\\\x-6=\pm\sqrt{9\cdot10}\\\\x-6=\pm\sqrt9\cdot\sqrt{10}\\\\x-6=\pm3\sqrt{10}\qquad\text{add 6 to both sides}\\\\x=6\pm3\sqrt{10}[/tex]
Angle measures and segment lengths. Someone please explain
Answers
ooops, i made a mistake. deleted. Give the other guy brainly
sorry
Check the picture below.
Find the point, P, at which the line intersects the plane. x equals 7 plus 9 t, y equals 3 minus 7 t, z equals 7 minus 5 t; 5 x minus 6 y minus 9 z equals negative 1 \
Answers
Answer:
The point of intersection [tex]P\left(\dfrac{1133}{122},\dfrac{149}{122},\dfrac{699}{122}\right)[/tex]
Step-by-step explanation:
Equation of line:
[tex]x=7+9t[/tex]
[tex]y=3-7t[/tex]
[tex]z=7-5t[/tex]
Equation of plane:
[tex]5x-6y-7z=-1[/tex]
We need to find the point of intersection of line and plane.
Point of intersection: When both line and plane meet at single point.
So, put the value of x, y and z into plane.
[tex]5(7+9t)-6(3-7t)-7(7-5t)=-1[/tex]
[tex]35+45t-18+42t-49+35t=-1[/tex]
[tex]122t=-1+32[/tex]
[tex]t=\dfrac{31}{122}[/tex]
Substitute the value of t into x, y and z
[tex]x=7+9\cdot \dfrac{31}{122}=\dfrac{1133}{122}[/tex]
[tex]y=3-7\cdot \dfrac{31}{122}=\dfrac{149}{122}[/tex]
[tex]z=7-5\cdot \dfrac{31}{122}=\dfrac{699}{122}[/tex]
Point of intersection:
[tex]\left(\dfrac{1133}{122},\dfrac{149}{122},\dfrac{699}{122}\right)[/tex]
Hence, The point of intersection [tex]P\left(\dfrac{1133}{122},\dfrac{149}{122},\dfrac{699}{122}\right)[/tex]
The volume of water flowing through a pipe varies directly wlth the square of the radius of the pipe. If the water flows at a rate of 80 liters per minute through a pipe with a radlus of 4 cm, at what rate would water flow through a pipe with a radius of 3 cm? (Rigorous) (Competency 007) 11. A) 45 liters per minute B) 6.67 liters per minute C) 60 liters per minute D) 4.5 liters per minute
Answers
Answer:
A
Step-by-step explanation:
Volume varies directly with the square of the radius, so:
V = k r²
When V = 80, r = 4.
80 = k (4)²
k = 5
V = 5r²
When r = 3:
V = 5 (3)²
V = 45
The flow is 45 L/min.
The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of The Thomas Supply Company Inc. invoices. 13 13 13 20 26 27 31 34 34 34 35 35 36 37 38 41 41 41 45 46 47 47 48 52 53 56 56 62 67 82
Determine the first and third quartiles, determine the seconds decile and the eighth decile,determine the 67th percentile.
Answers
Final answer:
Explanation of quartiles, deciles, and percentiles in a dataset of gas-powered generator invoice payment times. Lastly, the 67th percentile in the data set is approximately 46 days.
Explanation:
The first quartile (Q1) is found by locating the median of the lower half of the data set, which results in a value of 34 days. The third quartile (Q3) is the median of the upper half of the data set, yielding a value of 47 days. The second decile corresponds to the 20th percentile, which is approximately 31 days. The eighth decile corresponds to the 80th percentile, which is approximately 47 days. Lastly, the 67th percentile in the data set is approximately 46 days.
State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A firm makes products A and B. Product A takes 2 hours each on machine M; product B takes 4 hours on L and 3 hours on M. Machine L can be used for 8 hours and M for 6 hours. Profit on product A is $9 and $7 on B. Maximize profit.
Answers
Final answer:
The problem requires formulating a linear programming model to maximize the profit function Z = 9x + 7y with constraints on machine time for product A and B (2x + 3y ≤ 6 for machine M and 4y ≤ 8 for machine L) and the non-negativity restrictions (x, y ≥ 0).
Explanation:
The linear programming problem can be stated in mathematical terms with an objective function and constraints for a firm making products A and B. The objective is to maximize profit, which is the sum of 9 dollars per unit of product A and 7 dollars per unit of product B. Let the number of products A and B produced be represented by variables x and y, respectively.
The objective function to maximize is Z = 9x + 7y.
Constraints:
Machine M's availability limits product A to 2 hours each, and product B to 3 hours each, with a total available time of 6 hours: 2x + 3y ≤ 6.Machine L can be used for 8 hours and is only required for product B, which takes 4 hours: 4y ≤ 8.Non-negativity constraints: x ≥ 0 and y ≥ 0, since the number of products cannot be negative.please help asap!!!!!
Answers
Answer:
The volume of the prism is 27√3/2
Step-by-step explanation:
* Lets revise the triangular prism properties
- The triangular prism has five faces
- Two bases and three side faces
- The two bases are triangles
- The three side faces are rectangles
- The rule of its volume is Area of its base × its height
* Lets solve the problem
- The triangular prism has two bases which are equilateral triangles
- The length of each side of the triangular base is 3"
- The height of the prism is 6"
∵ The volume of the prism = area of the base × its height
∵ The base is equilateral triangle of side length 3"
- The area of any equilateral triangle is √3/4 s²
∴ The area of the base of the prism = √3/4 × (3)² = 9√3/4
∵ The length of the height of the prism is 6"
∴ The volume of the prism = 9√3/4 × 6 = 27√3/2
* The volume of the prism is 27√3/2
Solve the following system of equations
3x - 2y =5
-2x - 3y = 14
Answers
Answer:
x = -1 and y = -4
Step-by-step explanation:
It is given that,
3x - 2y = 5 ----(1)
-2x - 3y = 14 ------(2)
To find the solution of equations
(1) * 2 ⇒
6x - 4y = 10 -----(3)
(2) * 3 ⇒
-6x - 9y = 42 ----(4)
eq(3) + eq(4) ⇒
6x - 4y = 10 -----(3)
-6x - 9y = 42 ----(4)
0 - 13y = 52
y = 52/(-13) = -4
Substitute the value of y in eq(1)
3x - 2y = 5 ----(1)
3x - (2 * -4) = 5
3x +8 = 5
3x = 5 - 8 = -3
x = -3/3 = -1
Therefore x = -1 and y = -4
Answer:
The solution is:
[tex](-1, -4)[/tex]
Step-by-step explanation:
We have the following equations
[tex]3x - 2y =5[/tex]
[tex]-2x - 3y = 14[/tex]
To solve the system multiply by [tex]\frac{3}{2}[/tex] the second equation and add it to the first equation
[tex]-2*\frac{3}{2}x - 3\frac{3}{2}y = 14\frac{3}{2}[/tex]
[tex]-3x - \frac{9}{2}y = 21[/tex]
[tex]3x - 2y =5[/tex]
---------------------------------------
[tex]-\frac{13}{2}y=26[/tex]
[tex]y=-26*\frac{2}{13}[/tex]
[tex]y=-4[/tex]
Now substitute the value of y in any of the two equations and solve for x
[tex]-2x - 3(-4) = 14[/tex]
[tex]-2x +12 = 14[/tex]
[tex]-2x= 14-12[/tex]
[tex]-2x=2[/tex]
[tex]x=-1[/tex]
The solution is:
[tex](-1, -4)[/tex]
A car was valued at $39,000 in the year 1995. The value depreciated to $11,000 by the year 2003.
A)What was the annual rate of change between 1995 and 2003? (Round to 4 decimal places)
B)What is the correct answer to part A written in percentage form?
C)Assume that the car value continues to drop by the same percentage. What will the value be in the year 2007?
Please help ASAP the homework is due Monday!!! :(
Answers
Answer:
14.6328% , $5836.03
Step-by-step explanation:
Here we are going to use the formula
[tex]A_{0}(1-r)^n = A_{n}[/tex]
[tex]A_{0}[/tex] = 39000
r=?
[tex]A_{8}[/tex] = 11000
n=8
Hence
[tex]39000(1-r)^8 = 11000[/tex]
[tex](1-r)^8 = \frac{11000}{39000}[/tex]
[tex](1-r)^8 = 0.2820[/tex]
[tex](1-r) = 0.2820^{\frac{1}{8}[/tex]
[tex](1-r) = 0.2820^{0.125}[/tex]
[tex](1-r) = 0.8536[/tex]
[tex](1-0.8536=r[/tex]
[tex]r = 0.1463[/tex]
Hence r= 0.1463
In percentage form r = 14.63%
Now let us see calculate the value of car in 2003 that is after 12 years
we use the main formula again
[tex]A_{0}(1-r)^n = A_{n}[/tex]
[tex]A_{0}[/tex] = 39000
r=0.1463
[tex]A_{12}[/tex] = ?
n=12
[tex]39000(1-0.14634)^{(12} = A_{12}[/tex]
[tex]39000(0.8536)^{12} = A_{12}[/tex]
[tex]39000*0.1497 = A_{12}[/tex]
[tex]A_{12}=5840.34[/tex]
Hence the car's value will be depreciated to $5840.34 (approx) by 2003.
The annual rate of change between 1995 and 2003 is -0.1463
The annual rate of change between 1995 and 2003 is -14.63%
The value of the car in 2007 would be $5,844.24
The value of the car decreases as the years go by. This is referred to as depreciation. Depreciation is the decline in value of an asset as a result of wear and tear.
In order to determine the annual rate of change, use this formula:
g = [tex](FV / PV) ^{\frac{1}{n} } - 1[/tex]
Where:
g = depreciation rate
FV = value of the car in 2003 = $11,000
PV = value of the car in 1995 = $39,000
n = number of years = 2003 - 1995 = 8
[tex](11,000 / 39,00)^{\frac{1}{8} } - 1[/tex] = -0.1463 = -14.63%
The value of car in 7 years can be determined using this formula:
FV = P (1 + g)^n
$39,000 x (1 - 0.1463)^12
$39,000 x 0.8537^12 = $5,844.24
A similar question was answered here: https://brainly.com/question/12980665?referrer=searchResults
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Answers
Answer: Hence, the probability that the whole shipment would be accepted is 0.371.
Many would be rejected.
Step-by-step explanation:
Since we have given that
Number of tablets to be tested = 42
Probability of getting a defect = 5% = 0.05
We need to find the probability that this whole shipment will be accepted.
As we have mentioned that if there is only one or none defect, then the whole shipment would be accepted.
P(accepted) = P(either none or one defect) = P(X=0)+P(X=1)
[tex]P(X=0)=(1-0.05)^{42}=(0.95)^{42}=0.115\\\\and\\\\P(X=1)=42\times (0.05)(0.95)^{41}=0.006\times 42=0.256[/tex]
So, P(Accepted) = 0.115+0.256=0.371
Hence, the probability that the whole shipment would be accepted is 0.371.
Many would be rejected.
Solve the following using the crossing-graphs method. (Round your answer to two decimal places.) 5 + 69 × 0.96t = 32
Answers
Answer:
The solution is 22.98.
Step-by-step explanation:
Here, the given equation,
[tex]5 + 69\times 0.96^t = 32[/tex],
Let [tex]f(t) = 5 + 69\times 0.96^t[/tex]
And, [tex]f(t) = 32[/tex]
Where, t represents x-axis and f(t) represents y-axis,
Since, [tex]f(t) = 5 + 69\times 0.96^t[/tex] is an exponential decay function having y-intercept (0,74).
Also, f(t) = 32 is the line, parallel to x-axis,
Thus, after plotting the graph of the above functions,
We found that they are intersecting at (22.984, 32)
Hence, the solution of the given equation = x-coordinate of the intersecting point = 22.984 ≈ 22.98
To solve the given equation, 5 + 69 × 0.96t = 32, you start by subtracting 5 from both sides, then divide by 69. Then, divide both sides by 0.96 to solve for t. The solution is t ≈ 0.41 (rounded to two decimal places).
Explanation:To solve the equation 5 + 69 × 0.96t = 32 using the crossing-graphs method, we first simplify the equation:
Start by subtracting 5 from both sides of the equation: 69 × 0.96t = 32 - 5.This results in: 69 × 0.96t = 27.Next, divide both sides by 69: 0.96t = 27/69.Which simplifies to 0.96t ≈ 0.391 (rounded to three decimal places).Finally, divide both sides by 0.96 to solve for t: t ≈ 0.391/0.96 ≈ 0.41 (rounded to two decimal places).Learn more about Crossing-graphs method here:https://brainly.com/question/34386833
#SPJ6
A coin is tossed 30 times it lands 12 times on heads and 18 times on tails what is experimental probability of the coin landing on tails?
Answers
Answer:
3/5
Step-by-step explanation:
Total tossed : 30
# of times landed on tails : 18
Experimental probability of tails = 18/30 = 3/5
A large school district in southern California asked all of its eighth-graders to measure the length of their right foot at the beginning of the school year, as part of a science project. The data show that foot length is approximately Normally distributed, with a mean of 23.4 cm and a standard deviation of 1.7 cm. Suppose that 25 eighth-graders from this population are randomly selected. Approximately what is probability that the sample mean foot length is less than 23 cm?
Answers
Answer:
The probability of the sample mean foot length less than 23 cm is 0.120
Step-by-step explanation:
* Lets explain the information in the problem
- The eighth-graders asked to measure the length of their right foot at
the beginning of the school year, as part of a science project
- The foot length is approximately Normally distributed, with a mean of
23.4 cm
∴ μ = 23.4 cm
- The standard deviation of 1.7
∴ σ = 1.7 cm
- 25 eighth-graders from this population are randomly selected
∴ n = 25
- To find the probability of the sample mean foot length less than 23
∴ The sample mean x = 23, find the standard deviation σx
- The rule to find σx is σx = σ/√n
∵ σ = 1.7 and n = 25
∴ σx = 1.7/√25 = 1.7/5 = 0.34
- Now lets find the z-score using the rule z-score = (x - μ)/σx
∵ x = 23 , μ = 23.4 , σx = 0.34
∴ z-score = (23 - 23.4)/0.34 = -1.17647 ≅ -1.18
- Use the table of the normal distribution to find P(x < 23)
- We will search in the raw of -1.1 and look to the column of 0.08
∴ P(X < 23) = 0.119 ≅ 0.120
* The probability of the sample mean foot length less than 23 cm is 0.120
A club has 50 members, 10 belonging to the ruling clique and 40 second-class members. Six members are randomly selected for free movie tickets. What is the probability that 3 or more belong to the ruling clique?
Answers
Answer: The probability that 3 or more belong to the ruling clique is 0.34.
Step-by-step explanation:
Since we have given that
Number of total members = 50
Number of belonging to ruling clique = 10
Number of belonging to second class member = 40
We need to find the probability that 3 or more belong to the ruling clique.
Let X be the number of outcomes belong to ruling clique.
So, it becomes,
P(X≥3)=1-P(X<3)
[tex]P(X\geq 3)=1-P(X=1)-P(X=2)\\\\P(X\geq 3)=1-\dfrac{^{10}C_1\times ^{40}C_5}{^{50}C_6}-\dfrac{^{10}C_2\times ^{40}C_4}{^{50}C_6}\\\\P(X\geq 3)=1-0.41-0.25\\\\P(X\geq 3)=0.34[/tex]
Hence, the probability that 3 or more belong to the ruling clique is 0.34.
The probability of selecting 3 or more members from the ruling clique when choosing 6 members randomly from a club of 50 members (10 in ruling clique, 40 second-class) is 8.56%.
Explanation:This probability problem can be solved using the concepts of Combinations and Binomial Theorem. You need to determine the number of ways to choose 3, 4, 5, or 6 members from the ruling clique (10 members) and the remaining from the second-class members (40 members). For each case, divide by the total number of ways to choose 6 members from all 50 members to get the probability. Sum up all the probabilities for each case to get the total probability of having 3 or more from the ruling clique.
Calculations:1. Number of ways of choosing 3 from the ruling clique and 3 from the second class: C(10,3)*C(40,3) = 120*9880 = 1,185,600 ways
2. Number of ways of choosing 4 from the ruling clique and 2 from the second class: C(10,4)*C(40,2) = 210*780 = 163,800 ways
3. Number of ways of choosing 5 from the ruling clique and 1 from the second class: C(10,5)*C(40,1) = 252*40 = 10,080 ways
4. Number of ways of choosing 6 from the ruling clique and 0 from the second class: C(10,6)*C(40,0) = 210*1 = 210 ways
Total ways to choose 3 or more from the ruling clique: 1,185,600 + 163,800 + 10,080 +210 = 1,359,690 ways
From 50 members, the total ways to choose 6: C(50,6) = 15,890,700 ways
The Probability of 3 or more from the ruling clique = 1,359,690 / 15,890,700 = 0.0856 or 8.56%
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
Two automobiles left simultaneously from cities A and B heading towards each other and met in 5 hours. The speed of the automobile that left city A was 10 km/hour less than the speed of the other automobile. If the first automobile had left city A 4 1/2 hours earlier than the other automobile left city B, then the two would have met 150 km away from B. Find the distance between A and B.
Answers
Answer:
450 km
Step-by-step explanation:
Equations
We can define 3 variables: a, b, d. Let "a" and "b" represent the speeds of the cars leaving cities A and B, respectively. Let "d" represent the distance between the two cities. We can write three equations in these three variables:
1. The relation between "a" and "b":
a = b -10 . . . . . . . the speed of car A is 10 kph less than that of car B
2. The relation between speed and distance when the cars leave at the same time:
d = (a +b)·5 . . . . . . distance = speed × time
3. Note that the time it takes car B to travel 150 km to the meeting point is (150/b). (time = distance/speed) The total distance covered is ...
distance covered by car A in 4 1/2 hours + distance covered by both cars (after car B leaves) = total distance
4.5a + (150/b)(a +b) = d
__
Solution
Substituting for d, we have ...
4.5a + 150/b(a +b) = 5(a +b)
4.5ab +150a +150b = 5ab +5b^2 . . . . . . multiply by b, eliminate parentheses
5b^2 +0.5ab -150(a +b) = 0 . . . . . . . . . . subtract the left side
Now, we can substitute for "a" and solve for b.
5b^2 + 0.5b(b-10) -150(b -10 +b) = 0
5.5b^2 -5b -300b +1500 = 0 . . . . . . . . eliminate parentheses
11b^2 -610b +3000 = 0 . . . . . . . . . . . . . multiply by 2
(11b -60)(b -50) = 0 . . . . . . . . . . . . . . . . factor
The solutions to this equation are ...
b = 60/11 = 5 5/11 . . . and . . . b = 50
Since b must be greater than 10, the first solution is extraneous, and the values of the variables are ...
b = 50a = b-10 = 40d = 5(a+b) = 5(90) = 450The distance between A and B is 450 km.
_____
Check
When the cars leave at the same time, their speed of closure is the sum of their speeds. They will cover 450 km in ...
(450 km)/(40 km/h +50 km/h) = 450/90 h = 5 h
__
When car A leaves 4 1/2 hours early, it covers a distance of ...
(4.5 h)(40 km/h) = 180 km
before car B leaves. The distance remaining to be covered is ...
450 km - 180 km = 270 km
When car B leaves, the two cars are closing at (40 +50) km/h = 90 km/h, so will cover that 270 km in ...
(270 km)/(90 km/h) = 3 h
In that time, car B has traveled (3 h)(50 km/h) = 150 km away from city B, as required.
Answer:
450km
Step-by-step explanation:
Take it that each automobile travels at 30 km an hour, for 150 km, meaning it will be 450 km apart.
........Help Please.......
Answers
Answer:
b = 1.098
Step-by-step explanation:
Each year, the GDP is 9.8% higher than the year before, so the multiplier each year is 1 + 9.8% = 1.098. This is the value of b.
b = 1.098
PLEASE ANSWER
factor the polynomial using the pattern
x^2+9x+8
x^2(a+b)x+ab=(x+a)(x+b)
Answers
Answer:
x² + 9x + 8 = (x + 1)(x + 8)
x² + 9x + 8 = (x + 8)(x + 1)
Step-by-step explanation:
* Lets explain how to factorize the polynomial using the pattern
- The form of the quadratic polynomial is x² + px + q, where p is the
coefficient of x and q is the numerical term
∵ x² + (a + b)x + (ab) = (x + a)(x + b)
- From the formula above the coefficient of x is the sum of the two
factors a and b
∴ p = a + b and q = ab
- That means p is the sum of two numbers and q is the product of
the same numbers
* Lets solve the problem
∵ x² + 9x + 8 is a quadratic polynomial
∵ x² + px + q is the form of quadratic polynomial
∴ p = 9 and q = 8
∵ p = a + b and q = ab
∴ a + b = 9 ⇒ (1)
∴ ab = 8 ⇒ (2)
- We must to find two numbers their product is 8 and their sum is 9
∵ The possibility of 8 as a product of two numbers is:
2 × 4 OR 1 × 8
∵ The sum of 1 + 8 = 9
∴ The value of a and b are 1 and 8
- It does't matter which of them = 1 or which of them = 8
∴ x² + (a + b)x + ab = x² + (1 + 8)x + (1)(9)
∵ x² + (a + b)x + (ab) = (x + a)(x + b)
∴ x² + (1 + 8)x + (1)(9) = (x + 1)(x + 8)
∴ x² + 9x + 8 = (x + 1)(x + 8)
- OR
∴ x² + 9x + 8 = (x + 8)(x + 1)
3 balls are randomly drawn from a box containing 4 yellow 2 blue and 5 red balls. Youwin a prize if all three are yellow. What is the probability of winning?
Answers
Answer: [tex]\dfrac{4}{165}[/tex]
Step-by-step explanation:
Given : The number of yellow balls in the box = 4
The total number of balls = [tex]4+2+5=11[/tex]
Since the given situation has dependent events.
Then, the probability of that all three balls are yellow is given by :-
[tex]\text{P(YYY)}==\dfrac{^4P_3}{^{11}P_3}=\dfrac{4\times3\times2}{11\times10\times9}\\\\\Rightarrow\ \text{P(YYY)}=\dfrac{4}{165}[/tex]
Hence, the probability of winning =[tex]\dfrac{4}{165}[/tex]
In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data it was noted that 95% of those who went to class on Fridays pass the course, while only 10% of those who did not go to class on Fridays passed the course. If a student passes the course, what is the probability that they did not attend on Fridays?
Answers
Answer: Probability that students who did not attend the class on Fridays given that they passed the course is 0.043.
Step-by-step explanation:
Since we have given that
Probability that students attend class on Fridays = 70% = 0.7
Probability that who went to class on Fridays would pass the course = 95% = 0.95
Probability that who did not go to class on Fridays would passed the course = 10% = 0.10
Let A be the event students passed the course.
Let E be the event that students attend the class on Fridays.
Let F be the event that students who did not attend the class on Fridays.
Here, P(E) = 0.70 and P(F) = 1-0.70 = 0.30
P(A|E) = 0.95, P(A|F) = 0.10
We need to find the probability that they did not attend on Fridays.
We would use "Bayes theorem":
[tex]P(F\mid A)=\dfrac{P(F).P(A\mid F)}{P(E).P(A\mid E)+P(F).P(A\mid F)}\\\\P(F\mid A)=\dfrac{0.30\times 0.10}{0.70\times 0.95+0.30\times 0.10}\\\\P(F\mid A)=\dfrac{0.03}{0.695}=0.043[/tex]
Hence, probability that students who did not attend the class on Fridays given that they passed the course is 0.043.
8. Write three other proportions for each given proportion. 35 miles/2 hours=87.5 miles/5 hours
Answers
Answer:
218.75 miles / 12.5 hours
437.5 miles / 25 hours
656.25 miles / 37.5 hours
Step-by-step explanation:
35 miles / 2 hours = 87.5 miles / 5 hours
This is the ratio of 2.5. So, the other proportions are
87.5 x 2.5 miles / 5 x 2.5 hours = 218.75 miles / 12.5 hours
87.5 x 5 miles / 5 x 5 hours = 437.5 miles / 25 hours
87.5 x 7.5 miles / 5 x 7.5 hours = 656.25 miles / 37.5 hours
a figure has a vertex at (-1,-3). if the figure has a line symmetry about x-axis , what are the coordinates of another vertex of the figure?
a. (3,1)
b. (-1,3)
c. (-3,-1)
d. (1,-3)
Answers
Answer:
b. (-1,3)
Step-by-step explanation:
the image of the point (x ; y) by symmetry about x-axis is : ( x ;- y)
so the answer "b" : (-1,3)