The exponential function that represents the population r years after 1993 is A(t) = 2600(1.021)^t
How to find the exponential function that represents the populationFrom the question, we have the following parameters that can be used in our computation:
Initial population = 2600
Rate of growth = 2.1 percent per year
The above parameters can be represented as
Initial population, a = 2600
Rate of growth, r = 2.1% per year
The exponential function that represents the population r years after 1993 can then be represented as
A(t) = a * (1 + r)^t
Substitute the known values in the above equation, so, we have the following representation
A(t) = 2600 * (1 + 2.1%)^t
Evaluate the sum
A(t) = 2600 * (1.021)^t
So, we have
A(t) = 2600(1.021)^t
Hence, the expression is A(t) = 2600(1.021)^t
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The price of 2 items in P and Q come to a ratio of 4:5. When the price of P is increased of $12 and the price of Q is reduced by $6,the items have the same price. Find the original price of P
Answer:
p = 72
Step-by-step explanation:
If we know that the ratio from P to Q is 4:5, we can multiply both sides by y (y = amount multiplied) to get our numbers.
4 × y =?
5 × y =?
We need to put a value in for y.
Let's use 9.
4 × 9 = 36 (P)
5 × 9 = 45 (Q)
Now let's add 12 to P, and take away 6 from Q.
36 + 12 = 48
45 - 6 = 39
The numbers aren't the same yet.
Let's use a different value for y.
y = 18
The equations will now look like this:
4 × 18 = 72 (P)
5 × 18 = 90 (Q)
Let's add 12 and 6 to the numbers again.
72 + 12 = 84
90 - 6 = 84
The numbers match up!
Therefore, the original price of p = 72
93 is what percent of 124
Answer: 75%
Step-by-step explanation:
93 is 75 percent of 124.
Explained in the picture attached...
Hope that helps...
A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 1 mile per hour and walk at 3 miles per hour. Toward what point on the coast should he row in order to reach point Q in the least time? (Round your answer to two decimal places.) 0.84 mile(s) down the coast
Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.
As given in the question,
Nearest point on the coast is 2 miles far away
rate of the row = 1mile per hour
Walk at the rate of 3 miles per hour
Let 'x' hours be the least time to reach point Q.
Time = distance / speed
Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3
Time taken to reach the coast = (√ 4 + x² ) / 1
Total time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
To find least time dt/dx = 0
t = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )
⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )
Squaring both the side we get,
x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )
⇒3x² -24x +36 =0
⇒ x² -8x + 12 = 0
⇒ x = 2 or 6 hours
Therefore , the least time taken to reach the point Q is equal to 2 hours.
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Can I get some help with this?
The equations that represent given problem is
P + S = 384 and 2.50P + 1.25S = 696.25.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given that the cost of 1 slice pizza is $2.50.
The cost of 1 bottle can of soda is $1.25.
In total sell for a day is 384.
Assume that you sell P slice of pizza and S number of soda bottle.
Thus your total sell is P + S.
Therefore, P + S = 384.
The cost 1 slice pizza is $2.50
Then the cost P slice of pizza is $2.50P.
The unit rate of soda bottle is $1.25.
Then the cost S bottles of soda is $1.25S.
Therefore the total sell for that day is 2.50P + 1.25S
2.50P + 1.25S = 696.25
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Find the area of a rectangle with the sides of x+7 and 3x-4
The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.
Define area of rectangle.Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.
Given
Sides = x+7 and 3x-4
Area of rectangle
Length ×Breadth
(x + 7) (3x - 4)
Multiplying,
x(3x - 4) + 7(3x - 4)
3x² - 4x + 21x - 28
3x² + 17x - 28
The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.
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Which quantity is multiplied by pi in the formula for the area of a circle?
The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius
How to determine the multiplied quantity?From the question, we have the following parameters that can be used in our computation:
Area of a circle
The formula for the area of a circle is represented as
A = πr²
Express the formula as a product
So, we have the following representation
A = π * r²
In the above formula, we can see that the square of r is multiplied by pi
Hence, the required quantity is the square of the radius of the circle
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Roll one-8 sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by .
The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.
Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.
Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:
P(k successes in n trials) = [tex]C(n , k) * p^k * (1 - p)^{(n - k)}[/tex]
where:
C (n , k) represents the number of combinations of "n" things taken "k" at a time, and p is the probability of success in a single trial.Step1
Calculate the probability of rolling a seven on an 8-sided die (p).
Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),
p = 1/8.
Step 2
Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:
P(3 sevens in 10 rolls) = [tex]C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}[/tex]
On subtracting gives:
=C(10, 3) * (1/8)^3 * (7/8)^{7}
Plugging the value of C(10,3) = 120 in the above equation:
= 120 * (1/8)^3 * (7/8)^{7}
Step 3:
Calculate the final answer using the formula:
P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)
≈ 0.0142
Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.
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Mean Value Theorem. Hot water is dripping through a coffeemaker, filling a large cup with coffee. The amount of coffee in the cup at time t is given by a differentiable function C, where t is measured in minutes. Selected values of C(t) are given in the table below. Based on this information, is there a time t, 2 <= t <= 4, such that C'(t) = 2? Explain. t ( m i n u t e s ) 0 1 2 3 4 5 6 C ( t ) ( o u n c e s ) 0 5.3 8.8 11.2 12.8 13.8 14.5
Based on the information, there is a t, 2≤ t ≤ 4. using the Mean value theorem and t=2
To determine whether there is t or not?The given parameters are
t: 2≤t≤4
t is a continuous function between 2≤t≤4
We should equally know that the amount of coffee at the cup at a time y=C
Using the formula for t
t=C(4) -C(2)/4-2
Inputting the values of t at the extremes values
t=C(4) -C(2)/4-2 = (12.8-8.8)/4-2
Simplifying this to get
4/2
=2
⇒ C(2) is continuous on the coordinates (2,4) and this can be differentiated in the coordinates (2,4)
If we apply the intermediate value theorem, the is t in (2,4)
Therefore, C(t) = [C(4)- C(2)]/ 4-2
This implies that C(t) = 2
In conclusion, based on the information, there is a t, 2≤ t ≤ 4. using the Mean value theorem. and t=2
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Give expressions for the following:-
1) x is multiplied by -10 and then 5 is added to the result
2) 5 is multiplied by p and the result is subtracted from 26
3)y is multiplied by -5 and the result is added to 6
Answer:
1) -10x + 5
2) 5p - 26
3) -5y + 6
MULTIPLE CHOICE Question 2 Look at the drawing below. Which of the following statements, if true, would alone prove pllq? Select all that apply. There are at least two correct answers.
Answer:
no c is right answer
Step-by-step explanation:
angle b and e should be supplementary
Answer:
A, B and C
Step-by-step explanation:
Statement A
According to the Alternate Exterior Angles Theorem, when a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.
Given ∠c ≅ ∠f, and as ∠c and ∠f are alternate exterior angles, then p ║ q.
Statement B
According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
GIven ∠d ≅ ∠g, and as ∠d and ∠g are corresponding angles, then p ║ q.
Statement C
According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.
Given ∠b and ∠e are supplementary, and as ∠b and ∠e are the interior angles on the same side of the transversal [tex]\ell[/tex], then p ║ q.
Statement D
∠f and ∠g are a linear pair, therefore ∠f and ∠g are supplementary. However, this does not given enough information to prove p ║ q.
A simple random sample of 36 observations is derived from a normally distributed population with a known standard deviation of 9.8. [You may find it useful to reference the z table.] a. Is the condition that X is normally distributed satisfied? O Yes O No
Yes, the condition that X is normally distributed is satisfied. When a simple random sample is drawn from a population that is normally distributed, the sample will also be normally distributed, as long as the sample size is large enough (generally considered to be at least 30 observations). In this case, the sample size of 36 observations is sufficient to ensure that the sample is normally distributed.
The standard deviation is a useful measure because it allows you to compare the spread of different data sets, even if they have different means. For example, if two data sets have the same mean but one has a larger standard deviation, this suggests that the values in the data set with the larger standard deviation are more spread out or variable.
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A cell phone company’s average cost for producing cell phones is modeled by the equation y= 30,000+120x/x where y is the average cost per cell phone. For how many cell phones, x, will the average cost per cell phone be $150?
For x = 1000 cell phones, the average cost per cell phone will be $150.
What is a linear equation in two variables?
An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
To solve for x, we can rearrange the equation to solve for x:
y = 30000 + 120x/x
Isolating x on one side of the equation gives:
x = 30000/(y - 120)
Substituting y = 150 into this equation gives:
x = 30000/(150 - 120)
This simplifies to:
x = 30000/30
Which simplifies to:
x = 1000
Hence, for x = 1000 cell phones, the average cost per cell phone will be $150.
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134. In radian mode, graph both y = sin-' x and y = I - sin' x on the same coordinate-axis system. What do you notice?
Answer:
Step-by-step explanation:
To graph the functions y = sin^(-1) x and y = π - sin^(-1) x on the same coordinate-axis system, we can use the properties of the inverse sine function and the unit circle.
The inverse sine function, denoted as sin^(-1) x or arcsin x, is the inverse of the sine function. This means that if we input a value x into the inverse sine function, it will output the angle θ in radians that satisfies the equation sin θ = x.
The unit circle is a circle with radius 1 centered at the origin of a coordinate plane. The angles in the unit circle are measured in radians. On the unit circle, the x-coordinate of a point is equal to the cosine of the angle formed by the point and the positive x-axis, and the y-coordinate is equal to the sine of the angle.
Given this information, we can graph the functions y = sin^(-1) x and y = π - sin^(-1) x as follows:
For y = sin^(-1) x, we can input values of x into the inverse sine function and plot the resulting values of y on the coordinate plane. Since the range of the inverse sine function is -π/2 ≤ y ≤ π/2, we can start by plotting the points (-1, -π/2), (1, π/2), and (0, 0).
For y = π - sin^(-1) x, we can input values of x into the inverse sine function, subtract the resulting values from π, and plot the resulting values of y on the coordinate plane. Since the range of the inverse sine function is -π/2 ≤ y ≤ π/2, we can start by plotting the points (-1, π/2), (1, -π/2), and (0, π).
On the same coordinate-axis system, the graph of y = sin^(-1) x will be a curve that starts at (-1, -π/2), goes through (0, 0), and ends at (1, π/2). The graph of y = π - sin^(-1) x will be a curve that starts at (-1, π/2), goes through (0, π), and ends at (1, -π/2).
If we connect the points on the two curves, we will see that they intersect at (0, π/2) and (0, -π/2). This means that the two functions are reflections of each other about the x-axis.
find the generating function for the number of ways to distribute blank scratch paper to alice, bob, carlos, and dave so that alice gets at least two sheets, bob gets at most three sheets, the number of sheets carlos receives is a multiple of three, and dave gets at least one sheet but no more than six sheets of scratch paper. without finding the power series expansion for this generating function (or using a computer algebra system!), determine the coefficients on and in this generating function.
The generating function for the number of ways the coefficients on and in this generating function .
Given :
the generating function for the number of ways to distribute blank scratch paper to alice, bob, carlos, and dave so that alice gets at least two sheets, bob gets at most three sheets, the number of sheets carlos receives is a multiple of three, and dave gets at least one sheet but no more than six sheets of scratch paper.
Alice = x^2 + x^3 + ...... so on
Bob = 1 + x + x^2 + x^3
Carlos = 1 + x^3 + x^6+ ..... ... so on
Dave = x + x^2 + x^3 + x^4 + x^5 + x^6
The product of these could be a generating function that may be one idea to explore though if you need separate variables to know who got how many sheets or not.
The minimum term in the product will be x^3 as Alice gets 2 sheets and Dave gets 1 sheet is the minimal solution.
Then i wonder if the x^2 is x^2 or x^2 as there are a couple of ways to see where a 2 could go here.
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whats the domain,range, and y-intercept and tell me if its exponential or linear.
k(x)=50(1.3)^x
0.3% is the percentage rate of increase in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 50( 1.3)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.3
r = 0.3 ⇒ 0.3%
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What is the equation in point-slope form of the line that passes through the points (7, 5) and (-4, -1)
50pts
For the written question: [tex]y-5 =\frac{6}{11}(x-7 )[/tex].
For the question displayed on the image: [tex]y+6=-\frac{3}{4}(x-2)[/tex].
Step-by-step explanation:1. Point-slope form.[tex]y-y_{1} =m(x-x_{1} )[/tex]
In this equation, y1 is the "y" coordinate of the given point, Then, x1 is the "x" coordinate of the given point. Lastly, "m" represent the slope of the linear equation.
2. Calculate the slope.Formula: [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
x1: 7
x2: -4
y1: 5
y2: -1
Substitute into the formula and calculate.
[tex]\frac{(-1) -(5) }{(-4)- (7) }\\ \\\frac{-1 -5 }{-4- 7 }\\ \\\frac{-6}{-11}\\ \\\frac{6}{11}[/tex]
3. Substitute the values into the point-slope formula.m= 6/11
x1: "7" or "-4"
y1: "5" or "-1"
Note: If you use 7 as an "x" you can only use "5" for the "y" value. Same rule applies if you choose "-4". The idea is that the formula contains "x" and "y" values from a single ordered pair, not 2.
Substitution:
[tex]y-(5) =(\frac{6}{11})(x-(7) )\\ \\y-5 =\frac{6}{11}(x-7 )[/tex]
4. Write the final equation.[tex]y-5 =\frac{6}{11}(x-7 )[/tex].
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Using this same logic and applying it to the aditional question posted as a picture, correct answer should be [tex]y+6=-\frac{3}{4}(x-2)[/tex].
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The diameter of a circle is 2 meters. What is the circle's circumference?
Answer:
the circumference of the circle is 6.28metres
Step-by-step explanation:
diameter=2m
circumference=2πr or πd
it is a diameter so use the formula πd
take π=22/7 or 3.14
c=22/7×2m=44/7=6.28m
In a recent year, the total sales at Restaurant A were $475,000 more than at Restaurant B. Total sales at the two stores were $550,000,000. What were the
sales for the year at each store?
Sales of one store is $274762500 and sales of other store is $275237500.
Define equation.A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Given
In a recent year, the total sales at Restaurant A were $475,000 more than at Restaurant B. Total sales at the two stores were $550,000,000.
Let sales of one store be x
Equation,
475000 + x + x = 550,000,000
2x = 550,000,000 - 475000
2x = 549525000
x = 274762500
Sales of one store = $274762500
Sales of other store
= $274762500 + $475000
= $275237500
Sales of one store is $274762500 and Sales of other store is $275237500.
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Point B is located at
(-3,0)
(3,0)
(0,3)
(0,-3)
Answer:
(3,0)
have a nice day.(I needed 20 charecters so yeah i needed to say this)
Answer:
(3,0)
Step-by-step explanation:
The first number in the ordered pair tells us how far we are from the orgina (0,0) (the middle of the graph). We are 3 units to the right. The second number in the ordered pair tells us how far up or down from (0,0) we are. You do not go up for down so that number should be zero.
Amy and three friends are renting a house near the campas for $2400 per month. She plays 1/4 of the rent. What is her monthly rent?
Answer:
Amy has to pay $600 every month for rent.
Step-by-step explanation:
To take 1/4 of a number is to multiply 1/4 and said number.
So you can do 0.25*number
or number/4.
For this problem, the number is 2400 because Amy is going to pay 1/4 of 2400 for rent.
[tex]rent = 2400/4\\rent = 600[/tex]
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0. Mardo ordered 2 reclining chairs for $230 each and a coffee table for $350. The shipping cost is $100. Marco is going to pay off his bill in 5 equal payments. How much is each of Marco's payments?
The amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.
Explain the division operation?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people belong to each group after a fair distribution is the basic objective of division.The data for the given question-
Mardo placed an order for a coffee table and two recliners for a total of $230 each. The price of shipping is $100. Marco will settle his debt in five equal payments.Thus, the total cost becomes-
Total cost = 2 x reclining chairs + coffee table + shipping cost
Total cost = 2 x 230 + 350 + 100
Total cost = $910
For the amount of each payment when there are 5 equal payments.
Total cost = 910/5
Total cost = $182
Thus, the amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.
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Question (Leo has an allowance of $80 from doing chores. He puts $22 into his
savings account. Leo plans to buy 4 new shirts this month. How much
money can Leo spend on each shirt?)
Answer:
Leo can spend $18 on each shirt.
Step-by-step explanation:
Boris feeds his dog 3/5 pounds of dog food for each meal. Boris has just bought 30 pounds of dog food. For how many meals will the food last?
The number of meals that Boris can feed his dog will be 50 meals.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Boris takes care of his canine with 3/5 pounds of canine nourishment for every dinner. Boris has quite recently purchased 30 pounds of canine food.
The number of meals that Boris can feed his dog will be calculated as,
⇒ 30 ÷ (3/5)
Simplify the expression, then we have
⇒ 30 ÷ (3/5)
⇒ 30 / (3/5)
⇒ 30 x 5 / 3
⇒ 10 x 5
⇒ 50
The number of feasts that Boris can take care of his canine will be 50 dinners.
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PLEASE HELP ME ITS TIMED!!!
Answer: The coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.
Step-by-step explanation: The coefficient of the term with a certain power of t and a certain power of q in the expansion of a binomial raised to a power can be found using the binomial formula. The formula is given by:
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(a + b)^n = sum_{k=0}^n choose(n, k) * a^(n-k) * b^k
In this case, we have a = 3t, b = -q, and n = 17. We want to find the coefficient of the term with t^3 and q^14, which means we need to find the coefficient of the term with a^(n-k) = t^3 and b^k = q^14. Plugging these values into the formula, we get:
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(3t - q)^17 = sum_{k=0}^17 choose(17, k) * 3^(17-k) * (-1)^k * t^(17-k) * q^k
To find the coefficient of the term with t^3 and q^14, we need to find the value of choose(17, k) for k = 3. The binomial coefficient choose(n, k) is equal to the number of ways to choose k items from a set of n items. It can be calculated using the formula:
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choose(n, k) = n! / (k! * (n-k)!)
where n! is the factorial of n, which is the product of all positive integers less than or equal to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
In our case, we have n = 17 and k = 3, so the coefficient we are looking for is:
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choose(17, 3) = 17! / (3! * (17-3)!) = 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (3 * 2 * 1 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 17 * 16 / 3 = 816 / 3
Therefore, the coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.
3. What type of angle is angle A?
obtuse
acute
right
straight
The angle A is an obtuse angle of the regular polygon.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The interior angle of a polygon is [(n-2)180°]/n.
Where n is the number of sides of the polygon.
The number of sides of the polygon is 8.
The measure of the interior of the polygon is [(8-2)180°]/8
= 135°
The obtuse angle is an angle that more than 90°.
Therefore angle is an obtuse angle.
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Check the binomial distribution to see whether it can be approximated by the normal distribution. Round p and q to 1 decimal place, as needed. n = 95 P = 0.96 9 -0.04 np - and ng Is a normal approximation appropriate ? Yes No
As per the binomial distribution, the value of the normal approximation is 0.6573
The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
Here we have given that n = 95 P = 0.96 and q = 0.04
Now, here we have to check the binomial distribution to see whether it can be approximated by the normal distribution.
While we looking into the given question we know that the value of n = 95 P = 0.96.
Then as per the binomial distribution formula, the normal distribution is calculated as,
=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴
When we simplify this one then we get the value as 0.6573
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A time-and-motion study measures the time required for an assembly-line worker to perform a repetitive task. The data show that the time required to bring a part from a bin to its position on an automobile chassis varies from car to car according to a Normal distribution with mean seconds and standard deviation seconds. The time required to attach the part to the chassis follows a Normal distribution with mean seconds and standard deviation seconds. The study finds that the times required for the two steps are independent. A part that takes a long time to position, for example, does not take more or less time to attach than other parts.
(a) Find the mean and standard deviation of the time required for the entire operation of positioning and attaching the part.
(b) Management’s goal is for the entire process to take less than seconds. Find the probability that this goal will be met. Show your work
The mean time of the entire operation is given by 31 seconds and standard deviation is approximately 4.47 seconds
mean time (μ₁) = 11 seconds
mean chassis time (μ₂) = 20 seconds
a)Total time taken = μ₁ + μ₂ = 11 +20 = 31 seconds
Now we will find the standard deviation:
standard deviation = √ (2²+4²) = √ 20 ≈ 4.47 seconds
b) The probability that the entire process will take less time:
Total time taken = 31 seconds
Less time taken will be 2 seconds for the entire time
P(T<30) = 30 - 31 / 4.47 = - 0.22
Now from the normal distribution table we get the p-value as :
p-value = 0.4129
Hence the required probability is 41.29 % .
The population or sample standard deviation and the standard error of a statistic are not the same thing, but they are related. The standard error of the sample mean is the standard deviation of the set of means computed by drawing an infinite number of repeated samples from the population and computing a mean for each sample.
The mean's standard error is estimated by dividing the sample standard deviation by the square root of the sample size, which matches the population standard deviation divided by the square root of the sample size.
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in the morning there were t people at the beach. later at noon, 2/7 of the people left the beach and there were 30 people left on the beach. find t
Answer:
42
Step-by-step explanation:
If 2/7 left that means that 5/7 are still there.
5/7x = 30 Multiple both sides by 7/5
x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]
x = 42
NO LINKS!! Please help me with this problem. Part 10ff
Answer:
[tex]\begin{array}{|c|c|}\cline{1-2} n& P\\\cline{1-2} 1& 0.5\\\cline{1-2} 2& 0.74\\\cline{1-2}3& 0.82\\\cline{1-2} 4 & 0.86\\\cline{1-2} 5& 0.89\\\cline{1-2} 6& 0.91\\\cline{1-2} 7& 0.92\\\cline{1-2} 8& 0.93\\\cline{1-2} 9& 0.94\\\cline{1-2} 10& 0.95\\\cline{1-2} \end{array}[/tex]
Step-by-step explanation:
Given function:
[tex]P=\dfrac{0.5+0.9(n-1)}{1+0.9(n-1)}[/tex]
To complete the table, substitute the given values of n into the given function.
[tex]\boxed{\begin{aligned}n=1 \implies P & =\dfrac{0.5+0.9(1-1)}{1+0.9(1-1)}\\\\P & =\dfrac{0.5+0.9(0)}{1+0.9(0)}\\\\P & =\dfrac{0.5+0}{1+0}\\\\P & =\dfrac{0.5}{1}\\\\P&=0.5\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=2 \implies P & =\dfrac{0.5+0.9(2-1)}{1+0.9(2-1)}\\\\P & =\dfrac{0.5+0.9(1)}{1+0.9(1)}\\\\P & =\dfrac{0.5+0.9}{1+0.9}\\\\P & =\dfrac{1.4}{1.9}\\\\P&=0.74 \; \sf (2 \; d.p.)\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=3 \implies P & =\dfrac{0.5+0.9(3-1)}{1+0.9(3-1)}\\\\P & =\dfrac{0.5+0.9(2)}{1+0.9(2)}\\\\P & =\dfrac{0.5+1.8}{1+1.8}\\\\P & =\dfrac{2.3}{2.8}\\\\P&= 0.82 \; \sf (2 \; d.p.)\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=4 \implies P & =\dfrac{0.5+0.9(4-1)}{1+0.9(4-1)}\\\\P & =\dfrac{0.5+0.9(3)}{1+0.9(3)}\\\\P & =\dfrac{0.5+2.7}{1+2.7}\\\\P & =\dfrac{3.2}{3.7}\\\\P&= 0.86 \; \sf (2 \; d.p.)\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=5 \implies P & =\dfrac{0.5+0.9(5-1)}{1+0.9(5-1)}\\\\P & =\dfrac{0.5+0.9(4)}{1+0.9(4)}\\\\P & =\dfrac{0.5+3.6}{1+3.6}\\\\P & =\dfrac{4.1}{4.6}\\\\P&= 0.89\; \sf (2 \; d.p.)\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=6 \implies P & =\dfrac{0.5+0.9(6-1)}{1+0.9(6-1)}\\\\P & =\dfrac{0.5+0.9(5)}{1+0.9(5)}\\\\P & =\dfrac{0.5+4.5}{1+4.5}\\\\P & =\dfrac{5}{5.5}\\\\P&= 0.91 \; \sf (2 \; d.p.)\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=7 \implies P & =\dfrac{0.5+0.9(7-1)}{1+0.9(7-1)}\\\\P & =\dfrac{0.5+0.9(6)}{1+0.9(6)}\\\\P & =\dfrac{0.5+5.4}{1+5.4}\\\\P & =\dfrac{5.9}{6.4}\\\\P&=0.92 \; \sf (2 \; d.p.)\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=8 \implies P & =\dfrac{0.5+0.9(8-1)}{1+0.9(8-1)}\\\\P & =\dfrac{0.5+0.9(7)}{1+0.9(7)}\\\\P & =\dfrac{0.5+6.3}{1+6.3}\\\\P & =\dfrac{6.8}{7.3}\\\\P&=0.93\; \sf (2 \; d.p.)\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=9 \implies P & =\dfrac{0.5+0.9(9-1)}{1+0.9(9-1)}\\\\P & =\dfrac{0.5+0.9(8)}{1+0.9(8)}\\\\P & =\dfrac{0.5+7.2}{1+7.2}\\\\P & =\dfrac{7.7}{8.2}\\\\P&=0.94 \; \sf (2 \; d.p.)\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}n=10 \implies P & =\dfrac{0.5+0.9(10-1)}{1+0.9(10-1)}\\\\P & =\dfrac{0.5+0.9(9)}{1+0.9(9)}\\\\P & =\dfrac{0.5+8.1}{1+8.1}\\\\P & =\dfrac{8.6}{9.1}\\\\P&=0.95 \; \sf (2 \; d.p.)\end{aligned}}[/tex]
Am I right or wrong on this question
Answer:u are right
Step-by-step explanation:
