In a typing class, the average number of words per minute N typed after t weeks of lessons was found to be
N =157/1 + 5.4e^-0.12t
Find the time necessary to type (a) 50 words per minute and (b) 75 words per minute
Answers
Answer:
i hope this helpes
Step-by-step explanation:
(a) To find the time necessary to type 50 words per minute, we need to solve the equation:
157/1 + 5.4e^-0.12t = 50
Rearranging the equation to isolate e^-0.12t and using the natural logarithm, we can find t:
ln(N - 157) = ln(5.4) - 0.12t
-ln(N - 157) = 0.12t - ln(5.4)
0.12t = ln(5.4) + ln(N - 157)
t = (ln(5.4) + ln(N - 157)) / 0.12
Plugging in N = 50, we get:
t ≈ 11.52 weeks
(b) To find the time necessary to type 75 words per minute, we follow the same steps as above:
157/1 + 5.4e^-0.12t = 75
ln(N - 157) = ln(5.4) - 0.12t
-ln(N - 157) = 0.12t - ln(5.4)
0.12t = ln(5.4) + ln(N - 157)
t = (ln(5.4) + ln(N - 157)) / 0.12
Plugging in N = 75, we get:
t ≈ 9.32 weeks
Answer:
For 50 wpm : 7.7 weeks approximately
For 75 wpm : 13.3 weeks approximately
Step-by-step explanation:
Given the relationship between N, the typing speed and t, the number of weeks of lessons as:
[tex]\mbox{\large N= \dfrac{157}{1+5.4e^{-0.12t}}}[/tex]
To solve for t for a particular N
cross-multiply the left side with the right side denominator to get
[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{N}}[/tex]
For N= 50 this works out to
[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{50}}[/tex]
[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157}{50} - 1}\\[/tex]
[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157-50}{50} } = \dfrac{107}{5} = 2.14[/tex]
Divide by 5.4 both sides:
[tex]\mbox{\large e^{-0.12t } = \dfrac{2.14}{5.4}} = 0.3963\\[/tex]
Take natural logs on both sides
[tex]\mbox{\large \ln(e^{-0.12t}) = \ln(0.3963)\\}[/tex]
[tex]\mbox{\large \ln(e^{-0.12t}) = -0.12 \;\textrm{since $ln(e^x)$ = x}}[/tex] since ln(eˣ) = x
ln(0.3963) = -0.9256
Therefore
[tex]t = \dfrac{-0.9256}{-0.12} = \dfrac{0.9256}{0.12} = {7.7133 \;weeks\approx \mbox{\large \boxed{7.7 \;weeks}}[/tex]
For N = 75, follow the same strategy and you will end up with
[tex]1+5.4e^{-0.12t}=\dfrac{157}{75} \\\\\\1+5.4e^{-0.12t}= 2.0933\\\\5.4e^{-0.12t} = 2.0933 - 1 = 1.0933\\\\e^{-0.12t} = \dfrac{1.0933}{5.4} = 0.2025\\\\[/tex]
Taking logs on both sides
[tex]-0.12t =-1.5971[/tex]
[tex]t = \dfrac{-1.5971}{-0.12} = 13.3097 \;weeks \approx \boxed{\mbox{\large 13.3 \;weeks}}[/tex]
Related Questions
suppose your mp3 player contains 100 songs. 10 of those songs are by your favorite group (say pink floyd one of my favorite bands). suppose the shuffle feature is used to play the songs in random order. note that after a shuffle all the 100 songs are played before the next shuffle.
1. What is the probability that the first U2 song heard is the 5th song played? 2. What is the probability that one of the first five songs played is a U2 song?
Answers
Probability is a measure of how likely something is to occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. For example, if there is a 20% chance of rain, the probability of rain is 0.2. Probability is often used to calculate the likelihood of different outcomes in a situation.
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You can drive 150 miles on 3/4 of a tank of gas in 3 hours. How far can you drive on one tank of gas
Answers
Answer: 200 miles
Step-by-step explanation: First divide 150 by 3 = 50, then multiply by 4 = 200 miles.
You can drive 200 miles with one tank of gas.
Step-by-step explanation:1. Identify the data.3/4 of a tank ---> 150 miles
1 full tank ---> x amount of miles
2. Solve the rule of 3.x = (1 full tank * 150 miles) / 3/4 of a tank
x = (1 * 150) / 3/4= 200 miles.
Check the attached image to better understand how a rule of 3 is solved. Beware that this procedure only applied when there is direct proportionality between the variables.
3. Conclude.You can drive 200 miles with one tank of gas.
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Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren't present in legitimate records. Some patterns, like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford's law. Call the first digit of a randomly chosen legitimate record ????X for short. The histogram of the probability distribution for ????X is shown here.
What is the shape of this histogram?
Answers
The shape of the histogram for the first digit of a randomly chosen legitimate record following Benford's law is a logarithmic curve, with the first digit "1" appearing most frequently, followed by "2," and so on, with the frequency of each digit decreasing as the digit increases.
What is tax return?A tax return is a document filed with a tax authority (such as the IRS) that reports an individual's or a business's taxable income, expenses, and other information for a given tax year. The purpose of a tax return is to determine how much tax an individual or business owes or to claim a refund if they overpaid their taxes during the year.
Benford's law is a mathematical principle that predicts the frequency of occurrence of digits in many real-life sets of data. According to the law, in such datasets, the first digit is likely to be a "1" more often than any other digit, followed by "2", and so on, with "9" being the least likely first digit. The law has been shown to hold true for many types of data, including population sizes, stock prices, and physical constants.
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6. Sally would like to lease a car worth $48,000 for a three-year period. The leasing company told Sally that after three years, the car would have a
will Sally have to pay off during her three-year lease?
a.
b.
C.
d.
$1,133
$7,200
$11,210
$36,790
Answers
The will Sally have to pay off during her three-year lease is d. $36,790.
How much Sally have to pay off during her three-year lease?To determine the amount Sally will have to pay off during her three-year lease, we need to understand the concept of depreciation.Depreciation is the decrease in value of an asset over time due to factors such as age, wear and tear, and market changes.For example, if a car is worth $48,000 and depreciates by 10% per year, its value after one year would be $48,000 * (1 - 0.1) = $43,200.After two years, its value would be $43,200 * (1 - 0.1) = $38,880. After three years, its value would be $38,880 * (1 - 0.1) = $34,992.So, the amount Sally would have to pay off during her three-year lease is $48,000 - $34,992 = $13,008.In conclusion, the answer is d. $36,790.
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expand the logarithm as much as possible. rewrite the expression as a sum, difference, or product of logs. ln (1/g^k) Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, ln(1/gk)
Answers
The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).
In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :
Product Rule : logₐ MN = logₐ M + logₐ N , with the same base, multiply two numbers result add the exponents.Quotient Rule : logₐ M/N = logₐ M – logₐ N, with the same base, divide two numbers result add the exponents.Power Rule : Raise an exponential expression to power and multiply the exponents. Logₐ Mᵖ = p logₐ MZero Exponent Rule, logₐ 1 = 0.We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)
applying quotient rule,
=> f(x) = ln(1) - ln( gᵏ)
Appling power rule,
=> f(x) = ln(1) - k ln( g)
Applying Zero Exponent Rule,
=> f(x) = 0 - k × ln( g)
Hence, the required expansion is f(x) = - k × ln( g).
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additional Vocabulary Support 3-1 help please I need this rn
Answers
Answer:
Step-by-step explanation:
this set of ordered pairs is a relation but it is not a function
each value in the right oval of the arrow diagram is an output
each value in the left oval of the arrow diagram is an input
this set of ordered pairs is a relation and a function
y=3(x+3)−4 using the given table of values and following the instructions below
Answers
Answer:
y = 3x + 5
Step-by-step explanation:
y = 3x + 5
y = 3x + 9 - 4
y = 3x + 5
If you need more help, comment on my answer. K? feel free to comment. lol.
Identify the solid formed by a given net.
A: Cylinder
B: Triangular prism
C: Square pyramid
D: Rectangular prymid
[60 points]
Answers
The solid formed by a given net is option D. Rectangular pryramid
What is a Rectangular Pyramid?A rectangular pyramid is a three-dimensional shape that has a square base and four triangular sides that meet at a single point at the top. It is a type of polyhedron
Also rectangular pyramid is a polyhedron with a rectangular base and four triangular faces that meet at a common point called the apex.
Therefore, the correct answer is as given above. It can be concluded that the solider formed is option D. rectangular pyramid
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a car wash uses 50 gallons of water every 40 sec. how much water does it use per sec?
Answers
Answer:
1.25 gallons per second
Step-by-step explanation:
To find out the amount of water per second, we must divide the gallons by the time.
50/40 = 1.25
Answer: 1.25
Step-by-step explanation: If they use 50 gallons of water every 40 seconds you just divide 50 and 40 which equals 1.25
The Hurricane Hunters took the following measurements from a hurricane over several days as it developed. Using the graph, what would be the wind speed of a hurricane with an air pressure
of 937 kPa?
A. 235
B. 182
C. 203
D. 222
Answers
The wind speed of a hurricane with an air pressure of 937 kPa is 203, hence option C is correct answer.
What is point - slope form?A straight line is represented using its slope and a point on the line using point slope form. This indicates that the point slope form is used to get the equation of a line whose slope is'm' and which passes through a point. The equation of a straight line can be expressed in several ways. Point slope shape is one of them. The point slope form's equation is as follows: y - y1 = m (x - x1)
From the given graph we can observe that the two coordinates of the wind and pressure are:
(x1, y1) = (934, 206)
(x2, y2) = (922, 218)
The slope of the line is given by:
m = (y2 - y1) / (x2 - x1)
m = (218 - 206) / (922 - 934)
m = - 12/ 12
m = - 1
Using the point-slope form we have:
y - y1 = m (x - x1)
Substituting the values:
y - 206 = -1 (x - 934)
y - 206 = -x + 934
y = -x + 934 + 206
y = -x + 1140
Substitute the value of x = 937kPa:
y = -x + 1140
y = -937 + 1140
y = 203
Hence, the wind speed of a hurricane with an air pressure
of 937 kPa is 203, hence option C is correct answer.
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A particle is moving on the perimeter of a circle with radius r=5 with angular speed of π/8 radians per second. After completing 4 full rotations, the particle traveled for 7 more seconds and stopped. What is the length of the total distance the particle traveled?
Answers
The length of the total distance the particle traveled is, 327π/8.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
A particle is moving on the perimeter of a circle with radius r=5 with angular speed of π/8 radians per second.
Now, First of all, let's calculate the the circumference. This is found by this equation:
⇒ P = 2πr
Here, r = 5
⇒ P = 2π × 5
⇒ P = 10π
And, The distance of completing 4 full rotations is,
⇒ D = 4P
⇒ D = 4 × 10π
⇒ D = 40π
Since, In one second the particle traveled π/8 radians.
Here, the particle traveled for 7 more seconds and stopped, this distance is,
⇒ 7 (π/8)
⇒ 7π/8
Thus, the length of the total distance the particle traveled is;
⇒ 40π + 7π/8
⇒ 327π/8
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Complete the expression so that it is equivalent to 2 (x+6)
Answers
The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.
What is an expression?
A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
Given expression is
2 (x+6)
Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.
The mathematical representation is a(b+c) = ab + ac.
Apply the Distributive property in the given expression:
(2×x) + (2×6)
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the population density of city A is 6,000 people per square mile l. city B is a dilation of city A with scale factor 1.2 if city B has 3/5 of the population of city A what is the population density of city B
Answers
The population density in city B is 6000 people per square mile considering it has 3/5 of the population in city A.
What is the population density in city A?The population density in city A is 6,000.
What is the population density in city B?It is known that city B, is bigger than city 1.2 times bigger than city A, so this means:
1 mile in city A = 1.2 miles in city B
Using this, and knowing that the population in city B is 0.6 times that of the one in city A, let's calculate the density:
0.6 x 6000 / 1.2 = 3,000 people per square mile
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player A had 653 less than twice the number of home runs player b had, r
Answers
You can represent the problem with an equation. Let x be the number of home runs player B had.
According to the statement, player A had 653 less than twice the number of home runs player B had.
so you can write the equation:
Player A = 2x - 653
This equation shows the relationship between the number of home runs player B had (x) and the number of home runs player A had (2x - 653). To find the number of home runs player B had, you can solve for x by adding 653 to both sides of the equation:
x = (Player A + 653) / 2
So if you know the number of home runs player A had, you can use this equation to find the number of home runs player B had.
a rectangular residential lot with the area 7475 is 50m longer then it is wide find the dimensions of the lot
Answers
The Area of path is 400cm of a rectangular residential lot with the area 7475 is 50m longer then it is wide.
What is area of the path?The difference between the areas of the two rectangles represents the path's area. To calculate the two areas, we shall utilize the rectangle's area formula. To get the necessary size of the path, first calculate the area of the larger rectangle by subtracting the area of the smaller rectangle.
In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle. In contrast, when we talk about a rectangle's perimeter, we mean the total of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.
Area of park = l × b = 40 × 35 = 1350
Area of park with path is = 45 + 2.5 + 2.5 x 30 + 2.5 + 2.5 = 1750 cm
Therefore,
Area of path = Area of park with path - Area of rectangular park
= 1750 - 1350 = 400cm
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complete question:
A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path.
A car consumes fuel at a rate of 8litres/100 km.
(1) How many litres is needed to travel 400 km? (2)How far you can travel with 50 /?
Answers
For one litre the cars travels
=400/400
=10
therefore it can travel 10 km in 1 lit
so, the distance travelled by car in 50 litres is
=50×10
Please help me solve this
Extra points
Answers
Answer:
X + 9
Step-by-step explanation:
sum is addition
What is 1 1/2 x 1/2.
Answers
Answer:
3/4 or 0.75
Step-by-step explanation:
1 1/2 is 3/2
so 3/2*1/2
then you multiply the numerators and then the denominators so you get 3/4 and that's you answer
 Need help will reward
Answers
When investing, the principal is the money that is kept in an investment account.
What is meant by principal investment?
Cash held in an investment account serves as the principal while investing. The amount you really borrow when you take out a loan—before interest is applied—is known as the principle.
Senior employees at venture capital firms, principals are ranked above associates and analysts. They are less senior than partners, but they could be on the partner track. Principals can assist the company in sourcing and carrying out deals, much like an associate.
When you sell an investment, you normally only need to pay taxes if you make a profit. To determine whether you made a profit or loss, you must deduct the cost basis of your investment—typically, the price you paid—from the sale price.
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The principal for amount $2496.76 at 1% compound interest annually for 3 years is $ 2420.03.
What does the term "primary investment" mean?When investing, the principal is the money that is kept in an investment account. The principle of a loan is the amount that you actually borrow when you apply for one, before interest is added.
Principals are the most senior personnel in venture capital firms, ahead of associates and analysts. They are not as senior as partners, but they might be moving toward becoming partners. Similar to an associate, principals can help the business find and close deals.
You typically only have to pay taxes on an investment sale if you make a profit. You must subtract the cost basis of your investment, which is often the price you bought, from the sale price to establish if you made a profit or a loss.
Using the formula,
Amount = P(1 + R/100)ⁿ
Where P = principle amount,
R = rate of interest,
n = time period,
It is given that
Amount = $2496.79
Rate of interest (R ) = 1%
(n) time period = 3,
Putting the above values in the formula,
2496.76 = P (1 + 1/100)³
⇒ 2496.76 = P (101/100)³
⇒ 2496.76 / (101/100)³ = P
⇒ P = 2496.76 / 1.03
⇒ P = $ 2420.03
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if f(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and "f '(6) = 6", find f '(1).
Answers
If function F(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6, the value of an F'(1) is 114.
We know that the chain rule of differentiation (derivative)
The derivative of composite function f(g(x)) is: f'(g(x))⋅g'(x)
Consider function F(x) = f(xf(xf(x)))
We need to differentiate above function with respect to x.
F'(x) = f'(xf(xf(x))) × d/dx[x f(xf(x))]
We use product rule of derivative to find d/dx[x f(xf(x))]
d/dx[x f(xf(x))] = f(xf(x)) d/dx(x) + x d/dx(f(xf(x)))
After simplifying these expressions we get.
F'(x) = f'(xf(xf(x))) [f(xf(x)) + xf'(xf(x)) + x(f(x) + xf'(x))]
For x = 1 above expression would be,
F'(1) = f'(1 f(1 f(1))) [f(1 f(1)) + 1 f'(1 f(1)) + 1 (f(1) + 1 f'(1))]
F'(1) = f'(f(4)) [f(4) + f'(4) + (4 + 4)]
F'(1) = f'(6) [6 + 5 + 8]
F'(1) = 6 × 19
F'(1) = 114
Therefore, the value of F'(1) = 114.
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The complete question is:
If F(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6, find F '(1).
Nathan made a mistake while solving an equation. His work is shown.
Where did Nathan make a mistake?
In Step 1, Nathan did not multiply
both terms in parentheses by 3.
In Step 2, Nathan did not simplify
52-3x correctly.
In Step 3, Nathan did not divide
by the correct number.
In Step 4, Nathan did not simplify
-24
correctly.
8
Step t
Step 2:
Step 3.
Step 4.
3(x - 8) = 5x
3x - 24
5x
- 3x
-24 = 8x
8x
-24
8
8
- 3x
"
-3 = x
Answers
The solution to the equation is x = -12 and Nathan made a mistake while simplifying in Step 2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
3 ( x - 8 ) = 5x
On simplifying the equation , we get
3x - 24 = 5x
Adding 24 on both sides , we get
3x = 5x + 24
Subtracting 3x on both sides , we get
3x - 5x = 24
-2x = 24
Divide by 2 on both sides , we get
-x = 12
So , x = -12
Hence , the solution is x = -12
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what is the mean of the sampling distribution equal to, what is the symbol for it, and how is it calculated? give the equation for the mean of the sampling distribution and show the number(s) that is/are used in the calculation
Answers
The mean of the sampling distribution is the average value of the mean of a large number of samples of the same size, taken from the same population. The symbol for the mean of the sampling distribution is usually represented by the Greek letter "mu" (μ). It is calculated as the sum of all the sample means divided by the number of samples.
The equation for the mean of the sampling distribution is given as:
μ = (1/n) * Σ x
where:
μ = mean of the sampling distribution
n = number of samples
Σ x = sum of the sample means
x = mean of each individual sample
The mean of the sampling distribution represents the center of the distribution and provides an estimate of the population mean. In this equation, the mean of each individual sample (x) is calculated first, and then those sample means are summed and divided by the number of samples (n) to find the mean of the sampling distribution (μ).
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What is the equation of the curve that passes through the point (1,8) if the slope of the curve at any point X is given by dy/dx= 3x^2+2
Answers
Refer to the attached images.
find the indefinite integral by using the appropriate formula. (use c for the constant of integration.) x2 cos(x) dx
Answers
Solve for the value of A
(Can someone help me please)
Answers
A=22
y intercept of f(x) = -2/9 x + 1/3
Answers
Answer:
Y-intercept: 1/3
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
In this case, the y-intercept is 1/3
A bag is filled with green and blue marbles. There are 68 marbles in the bag. If there are 40 more green marbles that blue marbles, find the number of green marbles and the number of blue marbles in the bag.
Answers
Answer:
There are 40 green marbles and 28 blue marbles.
Step-by-step explanation:
There are 68 marbles in the bag. At LEAST 40 are green, therefore 68-40=28. So we have 28 blue marbles
Shakil and Omar both walk to the same shop from different starting points.
The distance-time graphs show information about their journeys.
How much shorter in km was the distance Omar had to walk?
Answers
Distance is the number of units between two points.
Shakil's distance was 15 km shorter than Omar's
How to interpret the graphs
From Shakil's graph, the highest distance from home is 10 kmFrom Omar's graph, the highest distance from home is 25 kmCalculate the difference between these distances
d=25km-10km
Evaluate the differences
d=15km
Hence, Shakil's distance was 15 km shorter than Omar's
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Let (Y1, Y2) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin. That is, Y1 and Y2 have a joint density function given by
f (y1, y2) = 1/ π , y^2 1 + y^2 2 ≤ 1, 0, elsewhere.
Find P(Y1 ≤ Y2).
Solve using polar coordinates.
Answers
To solve this problem using polar coordinates, we need to change from rectangular coordinates to polar coordinates, which represent points in the plane as pairs of polar coordinates (r,θ).
Given that Y1 = rcos(θ) and Y2 = rsin(θ), the condition Y1 ≤ Y2 is equivalent to 0 ≤ θ ≤ π/2. Hence, the required probability can be expressed as:
P(Y1 ≤ Y2) = ∫∫_{0<=θ<=π/2, 0<=r<=1} f(r,θ) dr dθ
where f(r,θ) = 1/π, 0 <= r <= 1.
The integration yields P(Y1 ≤ Y2) = 1/2.
Therefore, the probability that Y1 is less than or equal to Y2 for a point chosen randomly inside the unit circle is 1/2.
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in each of the following scenarios, select the appropriate scale of measurement.
1. an investor collects data on the weekly closing price of gold throughout the year.
a. Ratio b. Nominal c. Interval d. Ordinal
Answers
The appropriate scale of measurement for an investor collecting data on the weekly closing price of gold throughout the year is:
a. Ratio
A ratio scale of measurement allows for meaningful comparisons of absolute differences between two values and the computation of ratios.
In the scenario of collecting weekly closing price data of gold, values such as "$1,000 per ounce" or "$2,000 per ounce" can be meaningfully compared to determine the ratio of change.
Using the ratio scale of measurement, it is possible to perform various statistical operations, such as mean, median, and standard deviation, which are meaningful and give us insights into the data.
For example, you can calculate the mean closing price for gold over a given period.
Additionally, the ratio scale allows for meaningful comparisons of magnitudes, such as "twice the value" or "half the value." Thus, a ratio scale is the most appropriate measurement scale in this scenario.
To learn more about ratio scale, click on the link below:
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