Answer: The mean and standard deviation of the sampling distribution of the sample mean for samples of size n=64 is
[tex]113.9\text{ and }4.0[/tex] respectively.
Step-by-step explanation:
Given : The mean of sampled population : [tex]\mu = 113.9[/tex]
The standard deviation of sampled population : [tex]\sigma = 32.1[/tex]
We know that the mean and standard deviation of the sampling distribution of the sample mean for samples of size n is given by :_
[tex]\mu_s=\mu\\\\\sigma_s=\dfrac{\sigma}{\sqrt{n}}[/tex]
Now, the mean and standard deviation of the sampling distribution of the sample mean for samples of size n=64 will be :-
[tex]\mu_s=113.9\\\\\sigma_s=\dfrac{32.1}{\sqrt{64}}=4.0125\approx4.0[/tex]
The mean of the sample is 113.9, and the standard deviation of the sample is 4.0
The given parameters are:
[tex]\mu = 113.9[/tex] --- the population mean
[tex]\sigma = 32.1[/tex] --- the population standard deviation
[tex]n = 64[/tex] --- the sample size
The sample mean is calculated as:
[tex]\bar x = \mu[/tex]
So, we have:
[tex]\bar x = 113.9[/tex]
The sample standard deviation is calculated as:
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
This gives
[tex]\sigma_x = \frac{32.1}{\sqrt {64}}[/tex]
[tex]\sigma_x \approx 4.0[/tex]
Hence, the mean of the sample is 113.9, and the standard deviation of the sample is 4.0
Read more about mean and standard deviation at:
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A red car is driving along the road in the direction of the police car and is 100 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 85 feet per second. How fast is the red car actually traveling along the road?
I think to solve this question, subtract the rate of feet per second disappearing from the distance of feet between the 2 cars.
100-85=15fps
The car is traveling at 15 feet per second.
Hope this helps!
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 6.5% and the tax in the second city was 4.5% The total hotel tax paid for the two cities was $582.50
. How much was the hotel charge in each city before tax?
Answer:
First city: $5,500
Second city: $5,000
Step-by-step explanation:
Let's define x as the hotel price in the first city and y the hotel price in the second city. We can start with this equation:
y = x - 500 (The hotel before tax in the 2nd city was $500 lower than in the 1st.)
Then we can say
0.065x + 0.045y = 582.50 (the sum of the tax amounts were $582.50)
We place the value of y from the first equation in the second equation:
0.065x + 0.045 (x - 500) = 582.50
0.065x + 0.045x - 22.50 = 582.50 (simplifying and adding 22.5 on each side)...
0.11x = 605
x = 5,500
The cost of the first hotel was $5,500
Thus, the cost of the second hotel was $5,000 (x - 500)
g. How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once? a. 6 b. 36 c. 720 d. 46,656
Answer:
720
Step-by-step explanation:
Given : The word ABSENT
To Find: How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once?
Solution:
Number of letters in ABSENT = 6
So, No. of arrangements can be formed using the letters in the word ABSENT, if each letter is used only once = 6!
= [tex]6 \times 5 \times 4\times 3 \times 2 \times 1[/tex]
= [tex]720[/tex]
So, Option C is true
Hence there are 720 different 6-letter arrangements can be formed using the letters in the word ABSENT.
Final answer:
There are 720 different 6-letter arrangements that can be formed from the word ABSENT, by applying the permutation formula 6! = 720. The correct option is c.
Explanation:
The question asks: How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once? To answer this, we need to calculate the number of permutations of 6 letters taken from 6. This is a simple permutation problem where we use the formula for permutations which is n!, where n is the total number of items to choose from and ! denotes a factorial, meaning the product of all positive integers up to n.
Given that the word ABSENT has 6 letters and we are arranging all 6, we have 6! = 6×5×4×3×2×1 = 720. Therefore, there are 720 different 6-letter arrangements that can be formed using the letters in ABSENT, with each letter used only once.
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.
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.Solve the following using the crossing-graphs method. (Round your answer to two decimal places.) 5 + 69 × 0.96t = 32
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
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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?
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.
Angle measures and segment lengths. Someone please explain
ooops, i made a mistake. deleted. Give the other guy brainly
sorry
Check the picture below.
PLEASE ANSWER
factor the polynomial using the pattern
x^2+9x+8
x^2(a+b)x+ab=(x+a)(x+b)
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)
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!!! :(
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
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 \
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]
........Help Please.......
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
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?
Answer:
Step-by-step explanation:
The answer above this answer is correct
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.
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.
Consider the following matrix A={{1,-1,0,0},{2,-1,0,0},{0,0,1,0},{-1,-1,0,1}}Which of the following statements is true? Check the correct answer(s) below.A. The homogeneous system Ax=0 has infinitely many solutionsB. The matrix A has determinant −1C. The matrix A is not invertibleD. The matrix A is singular.E. None of the above
The correct answer is:
Option: E
E. None of the above
Step-by-step explanation:We know that a system of equation i.e.[tex]Ax=0[/tex] has infinite many solutions if det(A)=0
Also, the matrix is singular if det(A)=0and is non-singular or invertible otherwise i.e. when det(A)≠0
We know that when a homogeneous system has i.e. [tex]Ax=0[/tex] is such that: |A|≠0 then the system has a unique solution.The matrix that will be formed by the given set of vectors is:
[tex]A=\begin{bmatrix}-1 &2 &0 &-1 \\ -1&-1 &0 &-1 \\ 0 &0 &1 &0 \\ 0 &0 &0 &1 \end{bmatrix}[/tex]
Also, determinant i.e. det of matrix A is calculated by:
[tex]\begin{vmatrix}-1 &-2 &0 &-1 \\ -1&-1 &0 &-1 \\ 0 &0 &1 &0 \\ 0 &0 &0 &1 \end{vmatrix}=1(1(1+2))=3[/tex]
Hence, determinant is not equal to zero.
This means that the matrix is invertible and non-singular.
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.
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.
The half-life of a certain radioactive element is 200 years. How will it take for a 100 pound chunk of this element to decay to a chunk that is 50 pounds?
It would take 200 years (by definition of half-life). 50 is 1/2 of 100.
if cos θ = -0.6, and 180° < θ < 270°, find the exact value of sin 2θ.
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
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?
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 for x in the equation
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]
Solve the following system of equations
3x - 2y =5
-2x - 3y = 14
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]
.......Help Please......
Answer:
largest: Rsmallest: KStep-by-step explanation:
The slope of the graph at x=0 is related to the value of b. It is also proportional to the value of a, which is the same for all but curve B. The red curve R has the largest slope at x=0, (much larger than 3/4 the slope of curve B), so curve R has the greatest value of b.
Similarly, the smallest value of b will correspond to the curve with the smallest (most negative) slope. That would be curve K. Curve K has the smallest value of b.
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?
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]
PLEASE ANSWER WITH AN EXPLANATION! THANK YOU
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]
Tangent lines-someone please help explain
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°
(a) Suppose you borrowed $400,000 for a home mortgage on January 1, 2010 with an annual interest rate of 3.5% per year compounded monthly. If you didn't make any payments and were only charged the interest (and no late fees), how much would you owe on the mortgage on January 1, 2030?
Answer:
$804,680.814 ( approx )
Step-by-step explanation:
The amount formula in compound interest is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where, P is the principal amount,
r is the annual rate of interest,
n is the compounding periods in a year,
t is the time in years,
Given, P = $ 400,000,
r = 3.5 %=0.035,
n = 12, ( 1 year = 12 months )
t = 20 years,
Thus, the amount would be,
[tex]A=400000(1+\frac{0.035}{12})^{240}[/tex]
[tex]=400000(\frac{12.035}{12})^{240}[/tex]
[tex]=\$ 804680.813963[/tex]
[tex]\approx \$ 804680.814[/tex]
The amount owed on the mortgage on January 1, 2030, would be approximately [tex]\$765,320.99.[/tex]
To solve this problem, we need to calculate the compound interest on the mortgage over a period of 20 years (from January 1, 2010, to January 1, 2030). The formula for compound interest is given by:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Given:
- [tex]\( P = \$400,000 \)[/tex]
-[tex]\( r = 3.5\% = 0.035 \)[/tex] (as a decimal)
- n = 12 (since the interest is compounded monthly)
- t = 20 years
Plugging these values into the compound interest formula, we get:
[tex]\[ A = 400,000 \left(1 + \frac{0.035}{12}\right)^{12 \times 20} \][/tex]
[tex]\[ A = 400,000 \left(1 + \frac{0.035}{12}\right)^{240} \][/tex]
[tex]\[ A = 400,000 \left(1 + 0.002916667\right)^{240} \][/tex]
[tex]\[ A = 400,000 \left(1.002916667\right)^{240} \][/tex]
Now, we calculate the value inside the parentheses:
[tex]\[ 1.002916667^{240} \ = 1.913209802 \][/tex]
Finally, we multiply this by the principal amount to find out how much would be owed:
[tex]\[ A \ = 400,000 \times 1.913209802 \][/tex]
[tex]\[ A \ = \$765,320.99 \][/tex]
A runner runs around a circular track. He completes one lap at a time of t = 269 s at a constant speed of v = 4.6 m/s. What is the radius, r in meters, of the track?
Answer:
[tex]\boxed{\text{197 m}}[/tex]
Step-by-step explanation:
The formula relating distance (d), speed (s), and time (t) is
d = st
1. Calculate the distance
d = 269 s × 4.6 m·s⁻¹ = 1240 m
2.Calculate the track radius
The distance travelled is the circumference of a circle
[tex]\begin{array}{rcl}C & = & 2 \pi r\\1240 & = & 2 \pi r\\\\r & = & \dfrac{1240}{2 \pi }\\\\& = & 197\\\end{array}\\\text{The radius of the track is }\boxed{\textbf{197 m}}[/tex]
The radius in meters is 196.9 meters.
The runner ran around the track in 269 seconds at a speed of 4.6 m/s. This will enable us to find the distance around the track which is the circumference of the track.
Distance = Speed × time
= 4.6 × 269
= 1,237.4 meters
The distance here is the circumference which can also be found by the formula:
Circumference = π × diameter
1,237.4 = 22/7 × Diameter
Diameter = 1,237.4 ÷ 22/7
= 393.7 meters
Now that we have the diameter, the radius is:
= Diameter / 2
= 196.9 meters
In conclusion, the radius is 196.3 meters
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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:
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.
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Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = ∞ e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. Find ℒ{f(t)}. (Write your answer as a function of s.)
The Laplace Transform of a function f(t) is a tool used to solve differential equations by converting them into simpler algebraic equations. The transform itself is given by the integral ℒ{f(t)} = ∫∞₀ e−stf(t) dt, but without knowing the specific form of f(t), the exact transformation cannot be computed.
Explanation:The Laplace Transform, as defined by Definition 7.1.1, is a mathematical tool often used to handle differential equations, especially in the fields of Physics and Engineering. The main idea behind the transform is to convert the differential equations, which are difficult to solve, into simple algebraic equations. These simple equations are relatively easy to solve. Once solved, the inverse Laplace Transform is employed to obtain the solution to the original differential equation.
The question asks to compute the Laplace Transform ℒ{f(t)} of a function. By definition, the Laplace transform of a function f(t), defined for t ≥ 0 is given by the integral ℒ{f(t)} = ∫∞₀ e−stf(t) dt. The question doesn't give an explicit form of the function f(t). In general, if f(t) = e^(-αt), where α is a constant, then its Laplace Transform is given by ℒ{e^(-αt)} = 1/(s + α) for s > α.
If you could kindly provide me with the specific function f(t), I can better determine the Laplace Transform ℒ{f(t)}
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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?
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%
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A Membership to the Gym Costs $ 25 Per Person in 1995 .The Membership Cost has Increased by an average of $ 6 per Person for each Year Since 1995 .Write a Linear Equation for the Cost of a GYM Membership For One Person Since 1995. So , What is the Cost of A GYM Membership in 2009 ????
Step-by-step explanation:
Let n = number of years since 1995
Let C = cost of gym membership in any particular year
Initial cost in 1995 = $25
Additional cost each year = $6
We can say the following:
Cost at any given year = cost in 1995 + ($6 x number of years after 1995)
Or expressed as the following : C = 25 + 6n (Ans)
In 2009, the number of years since 1995,
= 2009 - 1995
= 14 years
Hence, cost in 2009,
= $25 + ($6 x 14 years)
= $109 (Ans)
$109 is the Cost of A GYM Membership in 2009.
What does "cost" mean to you?
The cost is the sum of money that a business spends on the development or manufacturing of goods or services. It excludes the profit margin markup. The sum of money spent to create a good or product, as seen from the seller's perspective, is the cost.given,
Let n = number of years since 1995
Let C = cost of gym membership in any particular year
Initial cost in 1995 = $25
Additional cost each year = $6
formula ,
Cost at any given year = cost in 1995 + ($6 x number of years after 1995)
put value in formula
C = 25 + 6n
now,
In 2009, the no of member in years since 1995,
= 2009 - 1995
= 14 years
Hence, cost of gym membership in 2009,
= $25 + ($6 x 14 years)
= $109
Therefore, cost of gym membership in 2009 = $109
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