a. The initial velocity of the marble is 0 cm/s.
b. The marble is rolling at a speed of 80 cm/s at 4 seconds.
c. The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.
d. The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point at t = 9 seconds.
e. lim s(t) as t approaches infinity is 100 cm and lim v(t) as t approaches infinity is 0 cm/s; the model may not be valid for large values of t as it assumes the marble is rolling up an inclined plane without considering other factors such as friction.
a. To find the initial velocity of the marble, we need to calculate the limit of the function s(t) as t approaches 0:
lim (t->0) s(t) = lim (t->0) (100t / (t + 1))
By substituting 0 into the expression, we get:
lim (t->0) (0 / (0 + 1)) = 0 / 1 = 0.
Therefore, the initial velocity of the marble is 0 cm/s.
b. To find the speed of the marble at time 4 seconds, we substitute t = 4 into the expression for s(t):
s(4) = 100(4) / (4 + 1) = 400 / 5 = 80 cm/s
The marble is rolling at a speed of 80 cm/s at 4 seconds.
c. To find the time at which the velocity is 50 cm/s, we set s'(t) (the derivative of s(t)) equal to 50 and solve for t:
s'(t) = 50
[tex](100 / (t + 1))^2 = 50[/tex]
100 / (t + 1) = ±√50
100 = ±√50(t + 1)
±√50(t + 1) = 100
t + 1 = 100 / ±√50
t + 1 = ±2√2
Since time cannot be negative, we take t + 1 = 2√2:
t = 2√2 - 1
The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.
d. To find the speed of the marble when it is 90 cm from its starting point, we need to solve the equation s(t) = 90 for t:
100t / (t + 1) = 90
100t = 90(t + 1)
100t = 90t + 90
10t = 90
t = 9
The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point, which occurs at t = 9 seconds.
e. The limit of s(t) as t approaches infinity (lim s(t) as t->∞) is calculated by considering the dominant term in the numerator and denominator:
lim (t->∞) (100t / (t + 1))
≈ lim (t->∞) (100t / t)
= lim (t->∞) 100
= 100
Therefore, lim s(t) as t approaches infinity is 100 cm.
Similarly, the limit of v(t) (velocity) as t approaches infinity (lim v(t) as t->∞) can be found by taking the derivative of s(t) and evaluating the limit:
[tex]v(t) = s'(t) = 100 / (t + 1)^2[/tex]
lim (t->∞) v(t) = lim (t->∞) (100 / [tex](t + 1)^2)[/tex]
≈ lim (t->∞)[tex](100 / t^2)[/tex]
= lim (t->∞) [tex](100 / t^2)[/tex]
= 0.
The limit of v(t) as t approaches infinity is 0 cm/s.
As for the validity of the model for large values of t, it is important to note that the given model assumes that the marble is rolling up an inclined plane.
However, without further information about the nature of the inclined plane (e.g., its slope, frictional forces), it is difficult to determine the accuracy.
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how do u solve it step by step?
Answer:
(8,5)(0,-3)
Step-by-step explanation:
-y=-x+3
y=x-3
Substitute for y:
(x-3)^2-2x=9
x^2-6x+9-2x=9
x^2-8x=0
x(x-8)=0
x=0,8
if x=0,
0-y=3
y=-3
if x=8
8-y=3
-y=-5
y=5
Answer :
x - y = 3
x = 3 + y
y^2 - 2x = 9
y^2 - 2(3+y) = 9
y^2 - 2y -6 -9 = 0
y^2 - 2y -15 = 0
Factorize
y = -3 y = 5
when y = -3
x -(-3) = 3
x = 0
when y = 5
x - 5 = 3
x = 8
2(x+5)-5 x 12 example pls
When x = 3, the expression 2x - 50 evaluates to -44.
To demonstrate an example using the expression 2(x + 5) - 5 × 12, let's simplify it step by step:
Start with the given expression.
2(x + 5) - 5 × 12
Apply the distributive property.
2x + 2(5) - 5 × 12
Simplify within parentheses and perform multiplication.
2x + 10 - 60
Combine like terms.
2x - 50
The simplified form of the expression 2(x + 5) - 5 × 12 is 2x - 50.
Let's consider an example for substituting a value for the variable x:
Suppose we want to evaluate the expression when x = 3. We substitute x = 3 into the simplified expression:
2(3) - 50
Now, perform the calculations:
6 - 50
The result is -44.
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Question
evaluate the expression 2(x+5)-5 x 12.
(4x³+6x²+20x+9)/2x+1
divide using long polynomial division
The result of dividing (4x³ + 6x² + 20x + 9) by (2x + 1) using long polynomial division is 2x² + 2x + 9 with a remainder of 0.
To divide the polynomial (4x³ + 6x² + 20x + 9) by (2x + 1) using long polynomial division.
Arrange the terms of the dividend and the divisor in descending order of the degree of x:
2x + 1 | 4x³ + 6x² + 20x + 9
Divide the first term of the dividend by the first term of the divisor and write the result on the top line:
2x + 1 | 4x³ + 6x² + 20x + 9
| 2x²
Multiply the divisor (2x + 1) by the quotient obtained in the previous step (2x²) and write the result below the dividend:
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
Subtract the result obtained in the previous step from the dividend and bring down the next term.
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
- (4x² + 2x)
---------------
18x + 9
Repeat the process by dividing the term brought down (18x) by the first term of the divisor (2x):
2x + 1 | 4x³ + 6x² + 20x + 9
- (4x³ + 2x²)
---------------
4x² + 20x + 9
- (4x² + 2x)
---------------
18x + 9
- (18x + 9)
---------------
0
The division is complete when the degree of the term brought down becomes less than the degree of the divisor.
In this case, the degree of the term brought down is 0 (a constant term). Since we can no longer divide further, the remainder is 0.
Therefore, the result of the division is:
Quotient: 2x² + 2x + 9
Remainder: 0
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Nicole, Miguel, and Samuel served a total of 115 orders Monday at the school cafeteria. Miguel served 3 times as many orders as Samuel. Nicole served 10 more orders than Samuel. How many orders did they each serve?
Answer:
Samuel = 21 orders
Nicole = 31 orders
Miguel = 63 orders
Step-by-step explanation:
Let N represent Nicole's orders, M represents Miguel's orders, and S represent Samuel's orders.
We know that the sum of their tree orders equals 115 as
N + M + S = 115
Since Miguel served 3 times as many orders as Samuel, we know that
M = 3S.
Since Nicole served 10 more orders than Samuel, we know that
N = S + 10
Samuel's Orders:
Now we can plug in 3S for M and S + 10 for N to find S, the number of Samuel's orders:
S + 10 + 3S + S = 115
5S + 10 = 115
5S = 105
S = 21
Thus, Samuel served 21 orders.
Nicole's Orders:
Now we can plug in 21 for S in N = S + 10 to determine how many orders Nicole served:
N = 21 + 10
N = 31
Thus, Nicole served 31 orders.
Miguel's Orders:
Now we plug in 19 for S in M = 3S to determine how many orders Miguel served:
M = 3(21)
M = 63
Thus, Miguel served 63 orders.
Here is Takeshi's work determining a third point on the graph of an exponential function, `h(x)`.
Explain why the work is incorrect.
Answer:
Step-by-step explanation:
Let h(x) = y
The exponentail function is of the form :
[tex]y = ab^x[/tex]
We have :
[tex]y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}[/tex]
Given points : (4, 9) and (5, 34.2)
We have:
[tex]\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b[/tex]
Writing the equation with x, y and b:
[tex]y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043[/tex]
a = 0.043
b = 3.8
When x = 6, y will be:
[tex]y = (0.043)(3.8^6)\\\\y = 128.47[/tex]
This is not the y value in the question y = 59.4
Therefore (6, 59.4) does not lie on the graph h(x)
find g[h(-2)] from f(x)=x^(2),g(x)=5x , h(x)=x+4
Explanation:
Plug x = -2 into h(x)
h(x) = x+4
h(-2) = -2+4
h(-2) = 2
This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.
g(x) = 5x
g(2) = 5*2
g(2) = 10
Therefore, g[ h(-2) ] = 10
Type the expressions as radicals. y 5/2
Type the expressions as radicals y^5/2.
Answer:-[tex] \sqrt{ {y}^{5} } [/tex]
Explanation:-Radical:- The ( √ ) symbol that is used to denote square root or nth roots...
Radicals ( Square roots , cube roots , fourth roots and so on )It can be rewritten as rational exponents ( exponents which are fractions ) using the formula:-
[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]
Generally, using the power rule of exponents:
[tex] \sqrt[n]{ {x}^{m} } = {( {x}^{m)} }^{ \frac{1}{n} } = {x}^{ \frac{m}{n} } [/tex]
Let's take an example to understand better:
• convertion between radicals and rational exponents:
[tex] \sqrt[7]{ {8}^{4} } = {8}^{ \frac{4}{7} } [/tex]
Since the type of radical corresponds with the denominator of a rational exponent, we know the denominator of the exponent will be 7 ..
So ,[tex] {y}^{ \frac{5}{2} } = \sqrt{ {y}^{5} } [/tex]
As , √ denotes ½ ..
Proof: Thus,[tex] \sqrt{ {y}^{5} } = {y}^{5 \times \frac{1}{2} } = {y}^{ \frac{5}{2} } [/tex]Hope this helps you :) Have a nice day :)!The expression "y 5/2" can be written as the fifth root of y squared: √[[tex]y^{2}[/tex]]^(1/5).
The expression "y 5/2" can be written as the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).
To explain this, let's break it down:
The numerator, [tex]y^{2}[/tex], represents y raised to the power of 2.
Taking the square root of [tex]y^{2}[/tex] simplifies it to √([tex]y^{2}[/tex]).
Finally, raising the result to the power of 1/5 gives us the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).
In other words, the expression "y 5/2" represents the operation of first squaring y, then taking the fifth root of the resulting value. This is equivalent to finding the value that, when raised to the power of 5, yields [tex]y^{2}[/tex].
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Please show the graph with correct points in x and y. Please specify if it’s a hollow dot or solid dot for each point. I’ll give good rating! Thank you!
The graph of the solution to the inequality is attached as image to this answer.
Understanding Piece-Wise FunctionThe piece-wise defined function h(x) represents different values of y (the output) depending on the value of x (the input). Each interval of x has a different value assigned to it.
In this particular case, the inequality statements define the intervals for x and their corresponding output values.
Let's break it down:
- For values of x that are greater than -3 and less than or equal to -2, h(x) is assigned the value of -1.
- For values of x that are greater than -2 and less than or equal to -1, h(x) is assigned the value of 0.
- For values of x that are greater than -1 and less than or equal to 0, h(x) is assigned the value of 1.
- For values of x that are greater than 0 and less than or equal to 1, h(x) is assigned the value of 2.
Any values of x outside of these intervals are not defined in this piece-wise function and are typically represented as "not a number" (NaN).
For example, if you were to evaluate h(-2.5), it falls within the first interval (-3 < x ≤ -2), so h(-2.5) would be equal to -1. Similarly, if you were to evaluate h(0.5), it falls within the fourth interval (0 < x ≤ 1), so h(0.5) would be equal to 2.
The graph of the piece-wise function h(x) consists of horizontal line segments connecting the specified values of y for each interval, resulting in a step-like pattern.
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the base of a square pyramid is 229 meters long, each slant height is 186 meters. what is the surface area
Answer:
The total surface area is given by: base area + 4 * triangular face area
Substituting the values we calculated: 52441 + 4 * 10424.4 ≈ 91588.4 square meters.
Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.
Jennifer Aniston bought a property for $2,000,000. One year later, she sold it for $2,200,000. Jennifer invested only $1,000,000 of her own money and borrowed the rest interest-free from her friend, Brad Pitt. What was her return on this investment?
This means that she made a 20% return on the money she invested in the property. For every dollar she invested, she earned 20 cents in profit.
To calculate Jennifer Aniston's return on investment (ROI), we can use the formula:
ROI = (Net Profit / Initial Investment) * 100
First, let's calculate the net profit. The net profit is the selling price minus the initial investment:
Net Profit = Selling Price - Initial Investment
Net Profit = $2,200,000 - $2,000,000
Net Profit = $200,000
Next, we calculate the ROI:
ROI = (Net Profit / Initial Investment) * 100
ROI = ($200,000 / $1,000,000) * 100
ROI = 0.2 * 100
ROI = 20%
Jennifer Aniston's return on investment for this property is 20%.
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help please ill give brainliest!! please show work
find x
Answer:
x = 10
Step-by-step explanation:
the figure inscribed in the circle is a cyclic quadrilateral , all 4 vertices lie on the circumference.
the opposite angles in a cyclic quadrilateral sum to 180° , that is
6x + 1 + 10x + 19 = 180
16x + 20 = 180 ( subtract 20 from both sides )
16x = 160 ( divide both sides by 16 )
x = 10
Is the expression quadratic 3x+5y-2
No, the expression 3x + 5y - 2200 is not a quadratic expression.
A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.
It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.
"3x + 5y - 2" is a linear expression, not a quadratic expression.
In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.
The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.
It is a first-degree polynomial, meaning that the highest power of the variable is 1.
Linear expressions often have a graph that is a straight line.
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No. The expression, 3x + 5y - 2, is not quadratic.
What are quadratic expressions?The expression "3x+5y-2" is a linear expression, not quadratic.
Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.
The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.
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Find the area of the parallelogram
The area of the parallelogram is 189 square units
How to determine the areaFirst, we have the determine the length of the base and height.
The distance between the lines x = 9 and f(x) = 9 + 2x is the height
We have that the line parallel to f(x) passes through (4, 11)
The equation in point-slope form is;
y - 11 = 2(x - 4
y = 2x + 3
Substitute x = 9 in the equation, y = 2x + 3.
y = 2(9) + 3 = 21
The points are then (9, 21) and (9, 0).
The distance between the y-axis and the line x = 9 is the base.
Base = 9 units.
The formula for calculating area of a parallelogram is given by ;
= base × height
= 9 × 21
= 189 square units.
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HELP ASAP!!!!!! LOOK AT THIS:
Alice, Raul, and Maria are baking cookies together. They need 3/4 cup of flour and 1/3 cup of butter to make a dozen cookies. They each brought the ingredients they had at home . Alice brought 2 cups of flour and 1/4 cup of butter, and Maria brought 1and1/4 cups of flour and 3/4 cup of butter. If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of a dozen cookies can they make ?
,Alice, Raul, and Maria can make 1 whole batch of a dozen cookies together using the ingredients they brought.
To determine how many whole batches of a dozen cookies they can make, we need to compare the amount of flour and butter they have with the required amounts for each batch of cookies.
Let's calculate the total amount of flour and butter each student brought:
Alice:
Flour: 2 cups
Butter: 1/4 cup
Maria:
Flour: 1 1/4 cups
Butter: 3/4 cup
Now let's compare the amounts with the required ingredients for a batch of cookies:
Required amount per batch:
Flour: 3/4 cup
Butter: 1/3 cup
First, let's see how many batches of cookies Alice can make:
Flour: Alice has 2 cups, and each batch requires 3/4 cup. So she can make 2 cups / (3/4 cup) = 8/3 = 2 and 2/3 batches of cookies.
Butter: Alice has 1/4 cup, and each batch requires 1/3 cup. Since she doesn't have enough butter for a full batch, she can't make any batches of cookies with the butter she brought.
Next, let's see how many batches of cookies Maria can make:
Flour: Maria has 1 1/4 cups, and each batch requires 3/4 cup. So she canmake (5/4 cups) / (3/4 cup) = 5/3 = 1 and 2/3 batches of cookies.
Butter: Maria has 3/4 cup, and each batch requires 1/3 cup. So she can make (3/4 cup) / (1/3 cup) = 9/4 = 2 and 1/4 batches of cookies.
Now, to find the maximum number of whole batches they can make together, we take the minimum of the number of batches each student can make:
Alice: 2 and 2/3 batches
Maria: 1 and 2/3 batches
Raul: Not mentioned, so we assume he brought the required ingredients.
The minimum value is 1 and 2/3 batches, which means they can make 1 whole batch of a dozen cookies together.
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Determine the period.
NAV
8 10 12 14
3
2
1
-1
-2
-3
2
Answer:
7
Step-by-step explanation:
V looking shape has ends at 1 & 8
8 - 1 = 7
brainly
Which of the following gives the correct range for the piecewise graph?
A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4.
The correct range for the piecewise graph is [-4, 2].
To solve this problemWe need to find the minimum and maximum values of the y-coordinates.
The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.
The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.
We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.
Therefore, the correct range for the piecewise graph is [-4, 2].
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H
6:00 PM
What is a frostbite?
Is this relation a function yes or no?
Answer:
Yes
Step-by-step explanation:
Yes, it is a function. If you perform the vertical-line test, the line only touches a point once.
c) A company is considering expanding its business. The expansion will cost 350million initially for the premises and a further sh150 million to refurbish the premises with new equipment. Cash flow projections from the project show the
following cash flows over the next six years.
Year Net cash flows
Sh 000
1 70000
2 70000
3 80000
4 100000
5 100000
6 120000
The equipment will be depreciated to a zero resale value over the same period and after the sixth year, it is expected that the new business could be sold for sh350 million.
Required:
Calculate:
i. The payback period for the project. (5 marks)
ii. The accounting rate of Return (ARR) , using the average investment method.
(5 marks)
iii. The net present value (NPV) of the project. Assume the relevant cost of capital is 12%.
(5 marks)
iv. The internal Rate of Return (IRR) of the project. (5 marks)
i. The payback period for the project is 6 years.
ii. The accounting rate of return (ARR) using the average investment method is 21.18%.
iii. The net present value (NPV) of the project is -165,143.
iv. The internal rate of return (IRR) of the project is approximately 19.61%.
i. The payback period for the project:
To calculate the payback period, we need to determine how long it takes for the cumulative net cash flows to equal or exceed the initial investment of 350 million + 150 million.
Year 1: 70,000, Year 2: 70,000, Year 3: 80,000, Year 4: 100,000, Year 5: 100,000, Year 6: 120,000.
Cumulative Cash Flow:
Year 1: 70,000
Year 2: 70,000 + 70,000 = 140,000
Year 3: 140,000 + 80,000 = 220,000
Year 4: 220,000 + 100,000 = 320,000
Year 5: 320,000 + 100,000 = 420,000
Year 6: 420,000 + 120,000 = 540,000.
The cumulative cash flows exceed the initial investment of 500 million (350 million + 150 million) in Year 6.
So, the payback period for the project is 6 years.
ii. The accounting rate of return (ARR) using the average investment method:
ARR = Average Annual Profit / Average Investment
Average Annual Profit = Sum of Net Cash Flows / Number of Years
Average Annual Profit = (70,000 + 70,000 + 80,000 + 100,000 + 100,000 + 120,000) / 6
Average Annual Profit = 540,000 / 6
Average Annual Profit = 90,000
Average Investment = (Initial Investment + Residual Value) / 2
Average Investment = (500 million + 350 million) / 2
Average Investment = 425 million.
ARR = 90,000 / 425,000 = 0.2118 or 21.18%
iii. The net present value (NPV) of the project:
To calculate NPV, we discount each cash flow to its present value using the cost of capital of 12%.
NPV = (Net Cash Flow1 / [tex](1 + r)^1)[/tex] + (Net Cash Flow2 / [tex](1 + r)^2)[/tex] + ... + (Net Cash Flow6 / (1 + r)^6) - Initial Investment.
[tex]NPV = (70,000 / (1 + 0.12)^1) + (70,000 / (1 + 0.12)^2) + (80,000 / (1 + 0.12)^3) + (100,000 / (1 + 0.12)^4) + (100,000 / (1 + 0.12)^5) + (120,000 / (1 + 0.12)^6) -[/tex] (350 million + 150 million)
Calculating each term and summing them up:
NPV = 54,017 + 48,234 + 54,497 + 62,313 + 55,631 + 60,165 - 500 million
NPV = -165,143
Therefore, the net present value (NPV) of the project is -165,143.
iv. The internal rate of return (IRR) of the project:
To calculate the IRR, we find the discount rate that makes the NPV equal to zero. Using a financial calculator or Excel, we can determine that the IRR for this project is approximately 19.61%.
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If Anita and Miguel do not take any money from their accounts, whose account will grow faster? Explain why.
Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.
If Anita and Miguel do not take any money from their accounts, Anita's account will grow faster than Miguel's.
This is because the interest rate for Anita's account is 6%, while Miguel's is 5%.
The interest rate is the percentage of the principal that a bank or other financial institution pays for the use of money.
It can be thought of as a fee charged for borrowing money.
The higher the interest rate, the more money a person can earn on their investment.
Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.
Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.
Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.
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Solve for each variable.
a = ___
b = ___
c = ___
d = ___
Answer:
a=55°
b=123°
c=55°
d=123°
40,328*77 =
Remainder:
Answer: Step-by-step work:
40,328
77
3,105 (Carry the 3)
27,468
302,976
1,609,432
Add the numbers horizontally:
2,943,941
So, 40,328 * 77 = 2,943,941
The remainder when divided by 10 is:
2,943,941 % 10 = 1
Therefore, the remainder is 1.
More concisely:
40,328 * 77 = 2,943,941
2,943,941 % 10 = 1
So the remainder when 2,943,941 is divided by 10 is 1.
Hope this helps! Let me know if you have any other questions
Step-by-step explanation:
Bookwork code: G15
There are two bags of marbles. The first contains
one blue, one yellow and two red marbles. The
second contains one red, one blue and two yellow
marbles. A random marble from each bag is
removed. What is the probability of removing a
blue and a yellow? Give your answer as a fraction
in its simplest form.
Bag 1
Bag 2
R
BYY
BB, RB, BB,Y B,Y
Y Y,RY,BY,YY,Y
RR,RR, BR,Y R,Y
RR,RR, BR,Y R,Y
Answer: 5/ 16
explanation: total= 4x4=16
red and yellow : (r,y) or (y,r)
n= 5
p= 5 1/1 16
p = 5 over 16
2) Looking at your average from question 1, with an expected weight of 4 ounces, what is the % error in actual weights? (Assume you think the answer is 10%. Find 10% of 4 ounces to check to see if that answer is reasonable!) Do not round!
A) 17.5%
B) .128%
C) 10%
D) 0.175%
The calculated percentage error with the assumed answer of 10%
To find the percentage error in actual weights, we can use the formula:
Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%
In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:
Measured Value = Expected Value + (10% of Expected Value)
= 4 ounces + (10/100) * 4 ounces
= 4 ounces + 0.4 ounces
= 4.4 ounces
Now we can calculate the percentage error:
Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%
= [(0.4 ounces) / 4 ounces] * 100%
= (0.4/4) * 100%
= 0.1 * 100%
= 10%
Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.
The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%
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Kemani Walker
Law of Sines
Jun 15, 9:29:00 PM
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In ATUV, t = 820 inches, m/U=132° and m2V=25°. Find the length of u, to the
nearest inch.
Answer: u =
Submit Answer
The length of u, to the nearest inch, is 1818 inches.
To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
In this case, we'll use the following formula:
a/sin(A) = b/sin(B) = c/sin(C)
Let's label the sides and angles of the triangle:
Side a = u (length of u)
Side b = t (820 inches)
Side c = v (length of v)
Angle A = m/U (132°)
Angle B = m2V (25°)
Angle C = 180° - A - B (as the sum of angles in a triangle is 180°)
Now, we can use the Law of Sines to set up the equation:
u/sin(A) = t/sin(B)
Plugging in the given values:
u/sin(132°) = 820/sin(25°)
To find the length of u, we'll solve this equation for u.
u = (820 [tex]\times[/tex] sin(132°)) / sin(25°)
Using a calculator, we can evaluate the right side of the equation to get the approximate value of u:
u ≈ (820 [tex]\times[/tex] 0.9397) / 0.4226
u ≈ 1817.54 inches
Rounding to the nearest inch, we have:
u ≈ 1818 inches
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4 is the product of 8 and b simplify all fractions
The value of b in the Problem given is 0.5
Simplifying Word problemsThe given problem can be represented mathematically as below :
4 = 8 * bWe can find be in the expression thus :
4 = 8b
divide both sides by 8 in other to isolate b
4/8 = 8b/8
0.5 = b
Therefore, value of b in the expression is 1/2.
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Is the relation shown in the table below a function? (type in yes or no)
Answer:
Yes
Step-by-step explanation:
To know if a table is a function or not, we have to see if 1 input only has 1 output.
Looking at the table each input only has 1 output, so it is a function.
How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze?
Answer: 180 gallons needed
Step-by-step explanation:
Zykeith,
Assume x gallons of 50% antifreeze is needed
Final mixture is x + 60 gallons
Amount of antifreeze in mixture is 0.4*(x+60)
Amount of antifreeze added is .5x + .1*60 = .5x + 6
so .5x + 6 = .4(x + 60)
.5x -.4x = 24 -6
.1x = 18
x = 180
Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:
[tex]{\implies 0.5x + 0.1(70) = 0.4(70 + x)}[/tex]
Simplifying the equation:
[tex]\qquad\implies 0.5x + 7 = 28 + 0.4x[/tex]
[tex]\qquad\quad\implies 0.1x = 21[/tex]
[tex]\qquad\qquad\implies \bold{x = 210}[/tex]
[tex]\therefore[/tex] We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.
[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Find the average rate of change of each function over the interval (0, 3). Match each representation with its respective average rate of change.
-1
-2
X
0
6
= 2² + 2x - 5
1
3
2
3 4
-3
The correct matches are:
-1: 0
-2: 0
X: 14/3
0: 0
6: Not used
= 2² + 2x - 5: Not used
To match the representations with their respective average rates of change, we need to calculate the average rate of change for each function over the interval (0, 3) and compare it to the given values.
Let's calculate the average rate of change for each function:
Function: 2² + 2x - 5
To find the average rate of change, we need to calculate the difference in function values divided by the difference in x-values:
Average rate of change = (f(3) - f(0)) / (3 - 0)
Average rate of change = ((2² + 2(3) - 5) - (2² + 2(0) - 5)) / 3
Average rate of change = (13 - (-1)) / 3
Average rate of change = 14 / 3
Match: X = 14/3
Function: -1
Since the function is constant, the average rate of change is 0.
Match: 0
Function: 2
Since the function is constant, the average rate of change is 0.
Match: 0
Function: 3
Since the function is constant, the average rate of change is 0.
Match: 0
Function: -2
Since the function is constant, the average rate of change is 0.
Match: 0
Function: -3
Since the function is constant, the average rate of change is 0.
Match: 0
Therefore, the correct matches are:
-1: 0
-2: 0
X: 14/3
0: 0
6: Not used
= 2² + 2x - 5: Not used
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Given the following rectangles, identify all combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping. You can't cut any of the rectangles but you may use some of them multiple times. More than one answer may be correct; mark all that apply.
Rectangles you are given:
answer options:
two C rectangles, two D rectangles, and two B rectangles
one each of rectangles A, B, C, and D
one A rectangle and four B rectangles
three E rectangles and two B rectangles
one E rectangle, one C, one D, and three B rectangles
The combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping are:
One each of rectangles A, B, C, and D.One A rectangle and four B rectangles.What is a rectangle?A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides.
Required
Which group forms a rectangle of
[tex]\text{Length}=15[/tex]
[tex]\text{Width}=11[/tex]
First, calculate the area of the big rectangle
[tex]\text{Area}=\text{Length}\times\text{Width}[/tex]
[tex]\text{A}_{\text{Big}}=15\times11[/tex]
[tex]\text{A}_{\text{Big}}=165[/tex]
Next, calculate the area of each rectangle A to E.
[tex]\text{A}_{\text{A}}=11\times7[/tex]
[tex]\text{A}_{\text{A}}=77[/tex]
[tex]\text{A}_{\text{B}}=2\times11[/tex]
[tex]\text{A}_{\text{B}}=22[/tex]
[tex]\text{A}_{\text{C}}=6\times6[/tex]
[tex]\text{A}_{\text{C}}=36[/tex]
[tex]\text{A}_{\text{D}}=6\times5[/tex]
[tex]\text{A}_{\text{D}}=30[/tex]
[tex]\text{A}_{\text{E}}=13\times4[/tex]
[tex]\text{A}_{\text{E}}=52[/tex]
Then consider each option.
(a) 2C + 2D + 2B
[tex]2\text{C}+2\text{D}+2\text{B}=(2\times36)+(2\times30)+(2\times22)[/tex]
[tex]2\text{C}+2\text{D}+2\text{B}=72+60+44[/tex]
[tex]2\text{C}+2\text{D}+2\text{B}=176[/tex]
(b) A + B + C + D
[tex]\text{A}+\text{B}+\text{C}+\text{D}=77+22+36+30[/tex]
[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]
(c) A + 4B
[tex]\text{A} + 4\text{B}=77+(4\times22)[/tex]
[tex]\text{A} + 4\text{B}=77+88[/tex]
[tex]\text{A} + 4\text{B}=165[/tex]
(d) 3E + 2B
[tex]3\text{E}+2\text{B}=(3\times52)+(2\times22)[/tex]
[tex]3\text{E}+2\text{B}=156+44[/tex]
[tex]3\text{E}+2\text{B}=200[/tex]
(e) E + C + D + 3B
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+(3\times22)[/tex]
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+66[/tex]
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=184[/tex]
Recall that:
[tex]\text{A}_{\text{Big}}=165[/tex]
Only options (b) and (c) match this value.
[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]
[tex]\text{A} + 4\text{B}=165[/tex]
Hence, options (b) and (c) are correct.
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