Answer:
Step-by-step explanation:
To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.
Step 1: Heating ice from -10.0°C to 0°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the temperature in Kelvin.
ΔS = 20.8 J / 263.15 K = 0.079 J/K
Step 2: Melting ice at 0°C
The heat required for this step can be calculated using the formula:
q = n * ΔHfus
where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the melting point of water in Kelvin (273.15 K).
ΔS = 3330 J / 273.15 K = 12.2 J/K
Step 3: Heating water from 0°C to 100°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the average temperature during the heating process (which is 50°C).
ΔS = 415.9 J / 323.15 K = 1.29 J/K
Step 4: Vaporizing water at 100°C
The heat required for this step can be calculated using the formula:
q = n * ΔHvap
where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the boiling point of water in Kelvin (373.15 K).
ΔS = 22600 J / 373.15 K = 60.5 J/K
Step 5: Heating steam from 100°C to 115°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat
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The probability that Mr Smith will have coffee with his breakfast is 0. 35. Find the probability that in the next 25 mornings, Mr Smith will have coffee on exactly 8 mornings
The probability that Mr Smith will have coffee on exactly 8 mornings out of the next 25 is 0.142, or 14.2%.
This scenario can be modeled by a binomial distribution, where:
The probability of success (having coffee) on any given morning is p = 0.35
The number of trials (mornings) is n = 25
The number of successes (mornings with coffee) we want to find the probability for is k = 8.
The probability mass function for a binomial distribution is given by:
[tex]P(X = k) = (n \: choose \: k) \times p^k \times (1-p)^{(n-k)},[/tex]
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n. It can be calculated as:
(n choose k) = n! / (k! × (n-k)!)
Using this formula and putting in the values we have,
[tex]P(X = 8) = (25 \: choose \: 8) \times 0.35^8 \times (1-0.35)^{(25-8)} [/tex]
[tex]P(X = 8) ≈ 0.142[/tex]
Therefore, the probability that Mr Smith will have coffee on exactly 8 mornings out of the next 25 is approximately 0.142, or 14.2%.
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Consider the vector field F(x, y, z) = (yz, -5xz, –4xy). Find the divergence and curl of F. div(F) = V.F= = curl(F) = V XF =( ). B) Consider the vector field F(x, y, z) = (-x?, -(x + y)
a) The divergence of F is -4x - 2y,
b) The curl of F is (-2(x+y), 0, -2x).
A) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:
div(F) = ∇ · F = ∂(yz)/∂x + ∂(-5xz)/∂y + ∂(-4xy)/∂z
= 0 - 5z - 4x
= -5z - 4x
To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:
curl(F) = ∇ × F = ( ∂(-4xy)/∂y - ∂(-5xz)/∂z, ∂(yz)/∂z - ∂(4xy)/∂x, ∂(-yz)/∂x - ∂(-5xz)/∂y )
= (-5z, y, -5x)
B) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:
div(F) = ∇ · F = ∂(-x²)/∂x + ∂(-(x+y)²)/∂y + ∂(0)/∂z
= -2x - 2(x+y)
= -4x - 2y
To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:
curl(F) = ∇ × F = ( ∂(0)/∂y - ∂(-(x+y)²)/∂z, ∂(0)/∂z - ∂(-x²)/∂x, ∂(-(x+y))/∂x - ∂(-x²)/∂y )
= (-2(x+y), 0, -2x)
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Elena has an empty mini fish tank. She drops her pencil in the tank and notices that it fits
just diagonally. (See the diagram.) She knows the tank has a length of 4 inches, a width of
5 inches, and a volume of 140 cubic inches. Use this information to find the length of
Elena's pencil. Explain or show your reasoning.
The length of Elena's pencil is approximately 9.49 inches.
Let's break down the problem :
We are given that Elena's mini fish tank has a length of 4 inches, a width of 5 inches, and a volume of 140 cubic inches.
To find the height of the tank, we can use the formula for the volume of a rectangular prism: volume = length * width * height.
Plugging in the given values, we have[tex]140 =4 \times 5 \times height.[/tex]
Solving for height, we get height [tex]= 140 / (4 \times 5) = 7[/tex] inches.
Now, let's move on to finding the length of Elena's pencil.
We are told that the pencil fits diagonally in the tank.
The diagonal of a rectangular prism can be found using the formula: diagonal [tex]= \sqrt{(length^2 + width^2 + height^2) }[/tex]
Plugging in the values, we have diagonal [tex]= \sqrt{(4^2 + 5^2 + 7^2) }[/tex]
[tex]= \sqrt{(16 + 25 + 49) }[/tex]
= √90
= 9.49 inches (rounded to two decimal places).
Therefore, the length of Elena's pencil is approximately 9.49 inches.
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Find the value of this expression if x=8. x^2-8/x+1
The value of the expression when x=8 is 56/9.
To find the value of an expression, follow these steps:
Replace any variables in the expression with the given values. For example, if the expression is "3x + 5" and x = 2, replace x with 2 to get "3(2) + 5".Simplify the expression using the order of operations (PEMDAS/BODMAS). Evaluate any operations inside parentheses first, then perform any multiplications or divisions from left to right, and finally perform any additions or subtractions from left to right.Continue simplifying the expression until you reach a single value.To find the value of the expression when x=8, we substitute 8 for x in the expression:
(8^2 - 8) / (8+1)
= (64 - 8) / 9
= 56/9
Therefore, the value of the expression when x=8 is 56/9.
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PLEASE HELP!! Find the area of the figure.
The area of the trapezoid in this problem is given as follows:
15 square feet.
How to obtain the height of the trapezoid?The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:
A = 0.5 x h x (b1 + b2).
The dimensions for this problem are given as follows:
h = 3 ft, b1 = 4 ft and b2 = 6 ft.
Hence the area is given as follows:
A = 0.5 x 3 x (4 + 6)
A = 1.5 x 10
A = 15 square feet.
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7. Membership at the local Sky Zone costs $189 per year and an hour costs $15 each.
Write an expression (make sure it looks like an expression, not an equation) to
represent the total cost of going to Sky Zone for the year. Evaluate the expression
(make it an equation) if you jump for 19 hours in a year. Write a "therefore"
statement. (4 marks)
189*365=68985
68985/15= $4599
Step-by-step explanation:
or $5000 if you round up
This question is kinda confusing :(
Orlando wants to borrow $3,000 for the purchase of a used car. He has to pay back the loan after 4 years. The two loan options are simple interest at a rate of 5. 8% each year, or interest compounded annually at a rate of 5. 2% each year. Which method should he choose , simple or compound , and how much less will he owe using that method?
Orlando should consider using simple interest and the amount he will have to pay is $696, under the condition that he wants to borrow $3,000 for the purchase of a used car. He needs to clear the loan after 4 years.
Orlando should apply the simple interest method.
The amount of interest he will pay using simple interest is evaluated
I = P × r × t
Here
I = interest paid
P = borrowed principal amount
r = rate of annual interest
t = time
In this case,
P = $3,000
r = 5.8%
t = 4 years
Therefore,
I = $3,000 × 0.058 × 4
= $696
So Orlando will pay $696 in interest using simple interest.
The amount of interest he will pay using compound interest is calculated as follows:
[tex]A = P * (1 + r/n)^{(n*t)}[/tex]
I = A - P
Here,
A = end term amount
n = count of interest that is compounded each year
In this case,
P = $3,000
r = 5.2%
t = 4 years
Interest is compounded annually so n=1
Therefore,
A = $3,000 × (1 + 0.052/1)⁴
= $3,697.47
I = $3,697.47 - $3,000
= $697.47
So Orlando will pay $697.47 in interest using compound interest.
Therefore, Orlando should choose simple interest method and he will owe $1.47 less using that method.
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The original price of a skateboard, not including tax, was $96. Charlie bought the skateboard on sale, and he saved 30% off of the original price. What was the sale price of the skateboard?
A. 66. 00
B. 68. 80
C. 67. 20
D. 28. 80
The answer is (C) 67.20.
Charlie saved 30% off of the original price, which means he paid 70% of the original price.
Let x be the sale price of the skateboard.
We have:
0.7 * 96 = x
x = 67.20
Therefore, the sale price of the skateboard was $67.20.
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() Jamison works as a server at a local restaurant. He made $42.80 in tips on
Thursday night. He made 2 1/4 times that amount in tips on Friday night. How much
in tips did he earn on Friday?
Therefore, Jamison made $96.30 in tips on Friday night.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.
Here,
Jamison made $42.80 in tips on Thursday night.
To find out how much he made in tips on Friday night, we need to multiply the Thursday amount by 2 1/4, which is the same as multiplying it by 9/4.
$42.80 x 9/4 = $96.30
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I need help on this question, and please explain how you did it.
The expression for AB in terms of x and √3 is:
AB = x√3.
What is an expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
In a right triangle ABC, if sin B = 0.5, then we know that:
sin B = opposite / hypotenuse
So, we can write:
0.5 = AB / CB
We also know that:
CB² = AB² + AC²
Substituting the value of AC, we get:
CB² = AB² + (3x)²
CB² = AB² + 9x²
Now, we can substitute the value of CB² from the first equation:
(AB / 0.5)² = AB² + 9x²
4AB² = AB² + 9x²
3AB² = 9x²
AB² = 3x²
The expression for AB in terms of x and √3 is:
AB = x√3
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Casho signed up for a streaming music service that costs $7 per month. The service allows Casho to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1. 50 per song. How much total money would Casho have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded ss songs?
To find out how much Casho would have to pay in a month in which she downloaded 30 songs, we need to consider both the monthly subscription cost and the cost per song for offline listening.
Step 1: Determine the cost of the monthly subscription, which is $7.
Step 2: Calculate the cost of downloading 30 songs for offline listening. To do this, multiply the cost per song ($1.50) by the number of songs (30).
1.50 * 30 = $45
Step 3: Add the monthly subscription cost ($7) to the cost of downloading 30 songs ($45).
7 + 45 = $52
So, Casho would have to pay $52 a month in which she downloaded 30 songs.
Now, let's find out how much Casho would have to pay if she downloaded ss songs.
Step 1: The cost of the monthly subscription remains the same at $7.
Step 2: Calculate the cost of downloading ss songs for offline listening. Multiply the cost per song ($1.50) by the number of songs (ss).
1.50 * ss = 1.50ss
Step 3: Add the monthly subscription cost ($7) to the cost of downloading ss songs (1.50ss).
7 + 1.50ss = 7 + 1.50ss
The total amount Casho would have to pay if she downloaded ss songs is 7 + 1.50ss.
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Find the amount of tin needed to make a milk can that has a diameter of 4cm and height of 5cm
In the surface area, the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here we know that the tin is in the shape of cylinder.
Now to find the amount we need to determine the surface area of the cylinder.
Now Height h = 5 cm, Diameter = 4 cm then radius r = d/2 = 4/2 = 2 cm.
Now using formula then,
Surface Area = 2[tex]\pi\\[/tex]r(h+r) square unit.
=> Surface area = [tex]2\times3.14\times2(5+2)=2\times3.14\times2\times7[/tex] = 87.92 [tex]cm^2[/tex]
Hence the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].
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6. A certificate of deposit (CD) pays 2. 25% annual interest compounded biweekly. If you
deposit $500 into this CD, what will the balance be after 6 years?
The balance of the CD after 6 years will be $678.35.
To calculate the balance of the CD after 6 years, we need to use the formula:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A = the balance after 6 years
P = the initial deposit of $500
r = the annual interest rate of 2.25%
n = the number of times the interest is compounded per year (biweekly = 26 times per year)
t = the number of years (6)
Plugging in the values, we get:
A = [tex]500(1 + 0.0225/26)^{(26*6)[/tex]
A = 500(1.001727)¹⁵⁶
A = 500(1.3567)
A = $678.35
Therefore, the balance of the CD after 6 years will be $678.35.
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This is absolute value so if u dont know just leave if u steal points im reporting
Answer:
k = - 1/3------------------------
We know the property of an absolute value: it is never negative.
Hence the given inequality is equivalent to below equation:
(3k + 1)/74 = 03k + 1 = 03k = - 1k = - 1/3This is the only solution.
When we solve for K in the inequality, 0 ≥ |(3K + 1) / 74|, the result obtained is -1/3
How do i solve 0 ≥ |(3K + 1) / 74|?We can solve the expression 0 ≥ |(3K + 1) / 74| as illustrated below:
0 ≥ |(3K + 1) / 74|
Remove the absolute sign
0 ≥ (3K + 1) / 74
Cross multiply
0 ≥ (3K + 1) / 74
0 × 74 ≥ 3K + 1
0 ≥ 3K + 1
Collect like terms
0 - 1 ≥ 3K
-1 ≥ 3K
Divide both sides by 3
-1/3 ≥ K
K = -1/3
Thus, we can conclude from the above calculation that the value of K in the inequality, 0 ≥ |(3K + 1) / 74| is -1/3
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Two lines meet at a point that is also the vertex of an angle set up and solve an appropriate equation for x and y.
Both vertical angles measure 90 degrees, and the adjacent angles each measure 90 degrees as well.
When two lines intersect at a point, we can use the properties of vertical and adjacent angles to set up and solve equations relating to their measures. This can help us find missing angles or verify that two angles are congruent.
When two lines intersect at a point, they form two angles. These angles are called vertical angles, and they are always congruent. In addition, the two lines also form two pairs of adjacent angles, each pair of which adds up to 180 degrees.
Let's consider an example to understand this concept better. Suppose we have two lines AB and CD that intersect at point P. If angle APD measures x degrees, then angle BPC also measures x degrees because they are vertical angles. Similarly, angle APB and angle CPD are adjacent angles, and their sum is 180 degrees. If angle APB measures y degrees, then angle CPD also measures y degrees.
Therefore, we can set up the following equation:
x + y = 180
This equation relates the measures of the adjacent angles formed by the two lines. We can solve for one variable in terms of the other by rearranging the equation:
y = 180 - x
This equation gives us the measure of one angle in terms of the measure of the other. We can substitute this expression into the equation for the vertical angles to get:
2x = 180
Solving for x, we find that x = 90.
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PLEASE HELP ME IMMEDIATELY!!!!!
The intervals where f is decreasing are given as follows:
None of the above.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented by y also increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.Hence the decreasing intervals of the function are given as follows:
-3.5 < x < -1.x > 2.5.Which are none of the options given in the problem.
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Explain how you can determine if (x + 3) is a factor of the given polynomial through factoring and polynomial division:
(A-APR. 2) (A1. 26. A, A1. 26. B)
x3-x2-12x
fast with step by step explanation if possible please!
To determine whether (x + 3) is a factor of the polynomial x^3 - x^2 - 12x, we can use polynomial division.
Step 1: Write the divisor, (x + 3), on the left side of a long division symbol and the dividend, x^3 - x^2 - 12x, on the right side.
x + 3 | x^3 - x^2 - 12x
Step 2: Divide the first term of the dividend, x^3, by the first term of the divisor, x, and write the result, x^2, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the dividend.
lua
x^2 - 4x
___________________
x + 3 | x^3 - x^2 - 12x
- (x^3 + 3x^2)
----------
-4x^2
Step 3: Bring down the next term of the dividend, -12x, and write it next to the remainder, -4x^2.
lua
Copy code
x^2 - 4x
___________________
x + 3 | x^3 - x^2 - 12x
- (x^3 + 3x^2)
----------
-4x^2 - 12x
Step 4: Divide the first term of the new dividend, -4x^2, by the first term of the divisor, x, and write the result, -4x, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the previous subtraction.
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PLEASE HELP ME ASAP
Can you please make a copy and put dots in eachone that goes where its supposed to go
Answer:
1
1
1
2
2
2
2
Step-by-step explanation:
A translation is applied to the square formed by the points A(−3, −4) , B(−3, 5) , C(6, 5) , and D(6, −4) . The image is the square that has vertices A′(−3, −6) , B′(−3, 3) , C′(6, 3) and D′(6, −6) . Select the phrase from the drop-down menu to correctly describe the translation. The square was translated Choose... .
The square was translated 2 units downwards.
Describing the transformationFrom the question, we have the following parameters that can be used in our computation:
Points A(−3, −4) , B(−3, 5) , C(6, 5) , and D(6, −4) . The image is the square that has vertices A′(−3, −6) , B′(−3, 3) , C′(6, 3) and D′(6, −6)The square was translated 2 units downward since all the y-coordinates of the vertices of the image square are 2 units less than the corresponding y-coordinates of the vertices of the pre-image square.
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Find the critical value t Subscript c for the confidence level c=0.90. and sample size n=26
The critical value t Subscript c for a confidence level of 0.90 and sample size of 26 is 1.708. A t-value greater than or less than 1.708 in absolute value would lead to rejection of the null hypothesis at the 0.10 level of significance.
To find the critical value t Subscript c for the confidence level c=0.90 and sample size n=26, we can use a t-distribution table or calculator.
Since we have a sample size of n=26, we have n-1 = 25 degrees of freedom. Using a t-distribution table or calculator with 25 degrees of freedom and a confidence level of 0.90, we get
t Subscript c = 1.708
Therefore, the critical value t Subscript c for the confidence level c=0.90 and sample size n=26 is 1.708. This means that if we calculate the t-value from our sample data and it is greater than or less than 1.708 in absolute value, we can reject the null hypothesis at the 0.10 level of significance.
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A skier can purchase a daily or season pass.
The daily pass costs $48 per day and included
the price of ski rentals. The season pass costs
$190 plus a daily fee of $10 to rent the skis.
How many days would a skier have to go skiing
in order for both options to cost the same?
A.
5 days
C. 240 days
D. 10 days
B.
3 days
We know that the skier would have to go skiing for 5 days in order for both options to cost the same.
To find out how many days a skier would have to go skiing for both options to cost the same, we need to set up an equation. Let's use "d" to represent the number of days the skier goes skiing.
For the daily pass option:
Total cost = $48 x d
For the season pass option:
Total cost = $190 + ($10 x d)
Now we can set up the equation:
$48 x d = $190 + ($10 x d)
Simplifying this equation, we get:
$38 x d = $190
Solving for "d", we get:
d = 5
Therefore, the skier would have to go skiing for 5 days in order for both options to cost the same.
So the answer is A. 5 days.
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Emir earned some money doing odd jobs last summer and put it in a savings account that earns 10% interest compounded monthly. After 9 years, there is $400. 00 in the account. How much did Emir earn doing odd jobs?
Round your answer to the nearest cent
Emir earned approximately $207.05 doing odd jobs.
Let x be the amount that Emir earned doing odd jobs. We can use the formula for compound interest, A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we have P = x, r = 0.1, n = 12 (since interest is compounded monthly), t = 9, and A = 400. Solving for x, we get:
x = A/(1+r/n)^(nt) = 400/(1+0.1/12)^(12*9) ≈ $207.05
Therefore, Emir earned approximately $207.05 doing odd jobs.
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The following table is based on 16 trials.
Х 15 16 17 18
frequency 2 4 8 2
Based on the table, how many 16's would you expect to get if there are 120 trials?
This means that there is a 50% chance that the outcome of a trial will be 17.
The given table represents the frequency distribution of a discrete random variable X, which has four possible outcomes: 15, 16, 17, and 18. The frequency of each outcome indicates the number of times that outcome occurs in 16 trials.
To calculate the probability of a specific outcome, we divide its frequency by the total number of trials. In this case, we want to find P(X=17), which is the probability that the outcome of a trial is 17. From the table, we see that the frequency of X=17 is 8, which means that 17 occurred 8 times out of 16 trials. Therefore,
P(X=17) = frequency of X=17 / total number of trials = 8 / 16 = 0.5
This means that there is a 50% chance that the outcome of a trial will be 17.
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Full Question: The Following Table Is Based On 16 Trials. X 15 16 17 18 Frequency 2 4 8 2 Based On The Table, What Is P(X=17)? Leave Your Answer In Decimal Form To Three Places.
The following table is based on 16 trials.
x 15 16 17 18
frequency 2 4 8 2
Based on the table, what is P(x=17)?
Leave your answer in decimal form to three places.
Tabitha bought a new SUV and obtained a loan for $29,000. The annual interest
rate is 4. 3% for 7 years. If Tabitha takes the loan for 5 years instead of 7, she will
save. 5% on the interest rate. How much less will Tabitha pay for her SUV if she
takes the loan for 5 years? *
Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.
To calculate the total amount Tabitha might pay for the SUV with a 7-year loan, we are able to use the compound interest formula for calculating the total amount of a loan, that is:
[tex]total amount = principal x (1 + interest charge)^{time}[/tex]
Wherein:
principal is the amount of the loaninterest charge is the annual interest rate Time is the length of the loan in yearsWith a 7-year loan, the full amount Tabitha could pay is:
[tex]total amount = $29,000 x (1 + 0.043)^{7} = $37,501.76[/tex]
To calculate the overall amount she could pay with a 5-year loan and a 5% decrease interest rate, we first need to calculate the new interest price. A 5% discount inside the interest price of 4.3% is:
New interest price = 4.3% - 5% = 3.3%
Then we can use the equal formula as before to calculate the total amount with the 5-year mortgage:
[tex]total amount = $29,000 x (1 + 0.033)^{5} = $33,093.47[/tex]
The difference in the overall amount among the two loans is:
$37,501.76 - $33,093.47 = $4,408.29
Therefore, Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.
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Why does this limit evaluate to 0 instead of 2?
[tex]\lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right)[/tex]
You're partially correct, as if x approaches ∞ it would approach 2, as eˣ is exponentially growing if x is positive.
If x is negative, which it is in this case, eˣ would get exponentially smaller. For example, e⁻² = 1/e².
So, in this case [tex]\frac{5}{e^x}[/tex] would get exponentially larger, as it is a number over an increasingly small number, like how [tex]\frac{1}{0.001}[/tex] is larger than [tex]\frac{1}{0.1}[/tex].
Therefore the limit would be equivalent to [tex]\frac{2}{\infty}[/tex], which is equal to 0
[tex] \Large{\boxed{\sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = 0}} [/tex]
[tex] \\ [/tex]
Explanation:
We are trying the find the limit of [tex] \: \sf \dfrac{2}{1 - \dfrac{5}{ {e}^{x} } } \: [/tex] when x tends to -∞.
[tex] \\ [/tex]
Given expression:
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) [/tex]
[tex] \\ [/tex]
[tex]\blue{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Properties\text{:}}}} \\ \\ \sf{ \diamond \: \dfrac{c}{ + \infty} = 0^{ + } \: \: and \: \: \dfrac{c}{ - \infty} = 0^{ - } \: \: , \: where \: c \: is \: a \: positive \: number.} \\ \\ \\ \diamond \: \sf \dfrac{c}{ {0}^{ + } } = + \infty \: \: and \: \: \dfrac{c}{ {0}^{ - } } = - \infty \: \: , \: where \: c \: is \: a \: positive \: number.\\ \\ \\ \diamond \: \sf c - \infty = -\infty \: \: and \: \: c + \infty = \infty \: \: ,\: where \: c \: is \: a \: positive \: number. \\ \\ \\ \sf{ \diamond \: \green{e ^{ - \infty} = 0^{+} \: \: and \: \: e ^{ + \infty} = + \infty} } \\ \end{array}}\\\end{gathered} \end{gathered}}[/tex]
[tex] \\ [/tex]
Substitute -∞ for x[tex] \\ [/tex]
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \sf \left(\dfrac{2}{1-\frac{5}{e^{ - \infty}}}\right) [/tex]
[tex] \\ [/tex]
Simplify knowing that [tex] \sf e^{-\infty} \\ [/tex] approaches 0 but remains a positive number. This will be written as 0⁺.
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \left(\dfrac{2}{1-\frac{5}{e^{ - \infty}}}\right) = \left(\dfrac{2}{1-\frac{5 \: \: }{0^{ + } }}\right)[/tex]
[tex] \\ [/tex]
Simplify again knowing that 5/0⁺ = +∞.
[tex] \\ [/tex]
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \left(\dfrac{2}{1-\frac{5 \: \: }{0^{ + } }}\right) = \sf \left(\dfrac{2}{1 - \infty}\right) = \dfrac{2}{ - \infty} [/tex]
[tex] \\ [/tex]
Conclusion[tex] \\ [/tex]
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \dfrac{2}{ - \infty} = 0^{-} \\ \\ \\ \implies \boxed{ \boxed{ \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) =0}}[/tex]
[tex] \\ \\ \\ [/tex]
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3. John has a bag of marbles. The ratio
of red marbles to blue marbles is 3:7.
What percent of the marbles are red?
Answer:
Step-by-step explanation:
percentage is taken as out of 100 we have to do like this for finding any percentage for any given ratio.
add the given ration 7+3=10
now as ratio is given from red to blue so we have red=3 and blue=7.
now final step is that simply do this.....
if 10(total) is equal to 100 %
then 3(for red) is equal how many percentage?
so we know that it will be (3 x 100) / 10 = 30%
so 30 percent of marbles are red.
An object is launched vertically in the air at 41.65 meters per second from a 7-meter-tall platform. using the projectile motion model h(t)=-4.9t^2+v0t+h0, where h(t) is the height of the projectile t seconds after it’s departure, v0 is the initial velocity in meters per second, and h0 is the initial height in meters, determine how long it will take for the object to reach its maximum height. what is the maximum height?
To find the maximum height of the object, we need to first determine when the object reaches that height. We can use the projectile motion model h(t) = -4.9t^2 + v0t + h0 to solve for the time it takes for the object to reach its maximum height.
Since the object is launched vertically, we know that its initial velocity is 41.65 m/s and its initial height is 7 meters. We can substitute these values into the projectile motion model and solve for when the object reaches its maximum height by finding the vertex of the resulting quadratic function.
h(t) = -4.9t^2 + 41.65t + 7
To find the time it takes for the object to reach its maximum height, we can use the formula t = -b/2a, where a = -4.9 and b = 41.65.
t = -(41.65)/(2(-4.9))
t = 4.25 seconds
Therefore, it takes 4.25 seconds for the object to reach its maximum height.
To find the maximum height, we can plug in this time value into the projectile motion model and solve for h(t).
h(4.25) = -4.9(4.25)^2 + 41.65(4.25) + 7
h(4.25) = 89.57 meters
The maximum height of the object is 89.57 meters.
In summary, the object launched vertically from a 7-meter-tall platform with an initial velocity of 41.65 m/s takes 4.25 seconds to reach its maximum height of 89.57 meters. This is found by using the projectile motion model h(t) = -4.9t^2 + v0t + h0 and finding the time it takes for the object to reach its maximum height, and then plugging in that time value to find the maximum height.
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(1 point) Calculate T..T,, and n(u, v) for the parametrized surface at the given point. Then find the equation of the tangent plane to the surface at that point. (u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v) = . The tangent plane: = 92
Given points:
(u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v)
the equation of the tangent plane at the point (u, v) = (24, 9) is:-8x + z = -183T
Process of finding equation:
To start, let's find T..T,, which represents the magnitude of the tangent vector at the given point:
T..T, = ||n(u, v)|| = ||n(24, -31, 72)|| = ||<48, -62, 144>|| = sqrt(48^2 + (-62)^2 + 144^2) = sqrt(11668) ≈ 108.03
Next, let's find the normal vector n(u, v) at the given point:
n(u, v) =
where f_u and f_v are the partial derivatives of the surface equation with respect to u and v, respectively.
In this case, we have:
f(u, v) = (24 + 0,u - 40, 8u)
f_u = <0, 1, 8>
f_v = <1, 0, 0>
Therefore, at the point (u, v) = (24, 9), we have:
n(u, v) = <0, 1, 8> x <1, 0, 0> = <-8, 0, 1>
Finally, let's find the equation of the tangent plane at the point (u, v) = (24, 9). The equation of a plane can be written as:
Ax + By + Cz = D
where A, B, and C are the components of the normal vector, and D can be found by plugging in the coordinates of the point on the plane. In this case, we have:
A = -8
B = 0
C = 1
D = -8(24) + 1(9) = -183
Therefore, the equation of the tangent plane at the point (u, v) = (24, 9) is:
-8x + z = -183
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The sales director noticed that sales in the Midwest and Northeast regions were not as expected. Additional field training is necessary for the sales representatives in these regions. After conducting a one-month training program, the sales director wants to determine the effectiveness of the training. After all, the company invested a significant amount of money in this program! So the sales director collects the sales data for the first month after the training. The sales director wants to compare the number of orders secured by those who attended the training program and those who didn't attend. This study will help the company to determine the effectiveness of the training. Part A What type of study is the sales director conducting—a survey, an observational study, or an experiment? Justify your answer
The type of study the sales director is conducting is an experiment to compare the number of orders secured by those who attended the training program and those who didn't attend.
The sales director conducted an experimented
The experiment is to do a test to see if something works or to try to improve it
Here the objective of the experiment was to see the effectiveness of the training by providing a one-month training program for employees. After that, the sales director collects the sales data for the first month. The sales director compared the number of orders secured by those who attended the training program and those who didn't attend. This experiment will help the company to determine the effectiveness of the training. If the experiment is effective or not.
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