Answers
Answer:
B
Step-by-step explanation:
(f-g)(x) just means f(x)-g(x)
so let's do that
make sure you distribute the minus in front of g to it's terms
-12x^3+19x^2-5-7x^2-15
-12x^3+12x^2-20
B.
Related Questions
Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2
Answers
Answer:
(a) [tex]f'(x)=-\frac{2}{x^3}[/tex]
(b) [tex]y=-0.25x+0.75[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1}{x^2}[/tex] .... (1)
According to the first principle of the derivative,
[tex]f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}[/tex]
Cancel out common factors.
[tex]f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}[/tex]
By applying limit, we get
[tex]f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}[/tex]
[tex]f'(x)=\frac{-2x)}{x^4}[/tex]
[tex]f'(x)=\frac{-2)}{x^3}[/tex] .... (2)
Therefore [tex]f'(x)=-\frac{2}{x^3}[/tex].
(b)
Put x=2, to find the y-coordinate of point of tangency.
[tex]f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25[/tex]
The coordinates of point of tangency are (2,0.25).
The slope of tangent at x=2 is
[tex]m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}[/tex]
Substitute x=2 in equation 2.
[tex]f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25[/tex]
The slope of the tangent line at x=2 is -0.25.
The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).
Using point slope form the equation of tangent is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-0.25=-0.25(x-2)[/tex]
[tex]y-0.25=-0.25x+0.5[/tex]
[tex]y=-0.25x+0.5+0.25[/tex]
[tex]y=-0.25x+0.75[/tex]
Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.
What would the value of an asset have to be now in order that it will grow to a value of $50,000 in 10 years if the value of the asset grows at 8% compounded continuously?
Answers
Answer: $ 22,466.45
Step-by-step explanation:
Given : Future value : [tex]FV= \$50,000[/tex]
The number of time period : [tex]t=10\text{ years}[/tex]
The rate of interest : [tex]r=8\ %=0.08[/tex]
Let P be the present value.
The formula to calculate the future value is given by :-
[tex]FV=Pe^{rt}[/tex]
[tex]50000=Pe^{0.08\times10}\\\\\Rightarrow\ 50000=P\times2.22554092849\\\\\Rightarrow\ P=\dfrac{50000}{2.22554092849}\\\\\Rightarrow\ P=22466.4482059\approx22,466.45[/tex]
Hence, the present value of asset would be $ 22,466.45.
The present value needed to obtain $50,000 in 10 years at an 8% continuously compounded interest rate is $22,466.48.
To determine the present value of an asset that grows to $50,000 in 10 years with an 8% annual compound interest rate, continuously compounded, we can use the formula for continuous compounding, which is:
A = Pe^rt
where:
A is the future value of the investment/loan, including interest,
P is the principal investment amount (the initial deposit or loan amount),
r is the annual interest rate (decimal),
t is the number of years the money is invested or borrowed for,
e is the base of the natural logarithm (approximately equal to 2.71828).
In this problem, we have A = $50,000, r = 0.08 (8% expressed as a decimal), and t = 10 years. We are solving for P, the present value.
Rearranging the formula to solve for P gives:
P = A / e^rt
P = 50000 / e^(0.08)(10)
Now calculate the value:
P = 50000 / e^0.8
P = 50000 / 2.22554... (using a calculator for e0.8)
P = $22,466.48 (rounded to two decimal places)
Thus, you would need to invest $22,466.48 now to have $50,000 in 10 years at an 8% annual compounded continuously interest rate.
Last year, Scott had 10,000 to invest. He invested some of it in an account that paid 7%
simple interest per year, and he invested the rest in an account that paid 9% simple interest per year. After one year, he received a total of $740 in interest. How much did he invest in each account?
Answers
Answer:
$8000 is invested for 7% interest and $2000 is invested for 9% interest
Step-by-step explanation:
Points to remember
Simple interest formula
I = PNR/100
P - Principle amount
N - Number of years
R - Rate of interest
To find the amount of investment
It is given that total amount = 10,000 and total interest = $740
Let 'x' be the amount invested at the rate of 7%
10,000 - x be the amount invested at the rate of 9%
I = PNR/100
740 = (x*1*7)/100 + (10000 - x)*1*9/100
740 = 7x/100 + 90000/100 - 9x/100
740 = 7x/100 + 900 - 9x/100
740-900 = -2x/100
-160 = -2x/100
x = 16000/2 = 8000
10000-8000 = 2000
Therefore $8000 is invested for 7% interest and $2000 is invested for 9% interest
Answer:
$8000 is invested for 7% interest and $2000 is invested for 9% interest
Step-by-step explanation:
Points to remember
Simple interest formula
I = PNR/100
P - Principle amount
N - Number of years
R - Rate of interest
To find the amount of investment
It is given that total amount = 10,000 and total interest = $740
Let 'x' be the amount invested at the rate of 7%
10,000 - x be the amount invested at the rate of 9%
I = PNR/100
740 = (x*1*7)/100 + (10000 - x)*1*9/100
740 = 7x/100 + 90000/100 - 9x/100
740 = 7x/100 + 900 - 9x/100
740-900 = -2x/100
-160 = -2x/100
x = 16000/2 = 8000
10000-8000 = 2000
Therefore $8000 is invested for 7% interest and $2000 is invested for 9% interest
I really hope it helped idiot noob die
If San Francisco accounts for 1.24 percent of total U.S. population, and has 1.43 percent of total U.S. laundry detergent sales, what is the CDI for this market? Also, what does this index mean? Remember the convention for CDIs and BDIs—they are expressed as whole numbers.
Answers
Answer:
CDI: 1.43/1.24x100= 115 What does this index mean? Good market potential.
Step-by-step explanation:
Answer: CDI: 1.43/1.24x100= 115 What does this index mean? Good market potential.
Step-by-step explanation:
Use partial fraction expansion to evaluate: LaTeX: \int\frac{x-1}{x^2+3x+2}dx ∫ x − 1 x 2 + 3 x + 2 d x a. LaTeX: -2\ln\left|x+1\right|+3\ln\left|x+2\right|+C − 2 ln | x + 1 | + 3 ln | x + 2 | + C b. LaTeX: \frac{-2}{x+1}+\frac{3}{x+2}+C − 2 x + 1 + 3 x + 2 + C c. LaTeX: \frac{2}{\left(x+1\right)^2}+\frac{-3}{\left(x+2\right)^2}+C 2 ( x + 1 ) 2 + − 3 ( x + 2 ) 2 + C d. LaTeX: \frac{1}{\left(x+3+\frac{2}{x}\right)^2}+C 1 ( x + 3 + 2 x ) 2 + C
Answers
The correct answer is -2 ln|x + 1| + 3 ln|x + 2| + C which corresponds to option (a).
We are asked to evaluate the integral:
∫ (x - 1) ÷ (x² + 3x + 2) dx
First, factor the denominator:
x² + 3x + 2 = (x + 1)(x + 2)
This allows us to use partial fraction decomposition to rewrite the integral :
(x - 1) ÷ [(x + 1)(x + 2)] = A ÷ (x + 1) + B ÷ (x + 2)
Next, solve for A and B:
Multiply both sides by the denominator (x + 1)(x + 2):x - 1 = A(x + 2) + B(x + 1)Set up equations by plugging in values for x to solve for A and B:When x = -1 : -1 - 1 = A(-1 + 2) + B(-1 + 1)-2 = A(1) + B(0) , so A = -2When x = -2 : -2 - 1 = A(-2 + 2) + B(-2 + 1)-3 = -B, so B = 3So, we can write :
(x - 1) ÷ [(x + 1)(x + 2)] = -2 ÷ (x + 1) + 3 ÷ (x + 2)
Integrate both terms separately :
∫ (-2 ÷ (x + 1)) dx + ∫ (3 ÷ (x + 2)) dx
This gives us :
-2 ln|x + 1| + 3 ln|x + 2| + C
Hence, the solution is :
-2 ln|x + 1| + 3 ln|x + 2| + C
The correct answer is option (a).
Complete Question :
Use Partial fraction expansion to evaluate : ∫ (x - 1) ÷ (x² + 3x + 2) dx
a. -2 ln|x + 1| + 3 ln|x + 2| + C b. [tex]\frac{-2}{x+1}+\frac{3}{x+2}+C - 2 x + 1 + 3 x + 2 + C[/tex]
c. [tex]\frac{2}{\left(x+1\right)^2}+\frac{-3}{\left(x+2\right)^2}+C 2 ( x + 1 ) 2 + - 3 ( x + 2 ) 2 + C[/tex]
d. [tex]\frac{1}{\left(x+3+\frac{2}{x}\right)^2}+C 1 ( x + 3 + 2 x ) 2 + C[/tex]
Solve |z| > (1/2)
{-1/2, 1/2}
{z|(-1/2) < z < (1/2)}
{z|z < (-1/2) ∪ z > (1/2)}
Answers
Answer:
{[tex]z|z<-\frac{1}{2}[/tex]}U{[tex]z|z>\frac{1}{2}[/tex]}
Step-by-step explanation:
Given the inequality [tex]|z| > \frac{1}{2}[/tex] you need to set up two posibilities:
FIRST POSIBILITY : [tex]z>\frac{1}{2}[/tex]
SECOND POSIBILTY: [tex]z<-\frac{1}{2}[/tex]
Therefore, you got that:
[tex]z<-\frac{1}{2}\ or\ z>\frac{1}{2}[/tex]
Knowing this, you can write the solution obtained in Set notation. This is:
Solution: {[tex]z|z<-\frac{1}{2}[/tex]}U{[tex]z|z>\frac{1}{2}[/tex]}
Answer:
{z|z < (-1/2) ∪ z > (1/2)}
Step-by-step explanation:
I got it right. I would explain if I were better at making sense lol
How many liters of a 80% acid solution must be mixed with a 15% acid solution to get 585 L of a 70% acid solution?
Answers
Answer:
573 L is im sure the correct answer
1. Use Excel to answer the following. In each question, find the blank to make the statement true. Note that Z represents we are using the standard normal distribution. Note: Round your answers to two decimal places. A) P(Z < -0.69) = B) P(Z > 1.84) = C) P(Z > )= 0.921 D) P(Z < ) = 0.61 2. Use Excel to answer the following. In each question, find the blank to make the statement true. In this example assume we have a variable X that is distributed normally with mean 30 and standard deviation 6. Note: Round your answers to two decimal places. A) P(X < 28.40) = B) P(X > 39.30) = C) P(X > )= 0.043 D) P(X < ) = 0.086
Answers
Answer:
1. A: 0.25; B: 0.03; C: 1.41; D: -0.28
2. A: 0.39; B: 0.06; C: 40.30; D: 21.81
Step-by-step explanation:
For CDF lookups, we used the Excel NORMDIST(x, mean, stdev, TRUE) function. For inverse CDF lookups, we used the NORMINV(x, mean, stdev) function.
Each of these functions works with the area under the curve from -∞ to x, so for cases where we're interested in the upper tail, we subtract the probability from 1, or subtract the x value from twice the mean.
For question 1, we computed the Z values in each case. The NORMDIST function works directly with x, mean, and standard deviation, so does not need the z value.
Answer for number 12
Answers
Answer:
12 a. 4605 feet 12 b. 1,459,063 square feet
Step-by-step explanation:
For the perimeter, we simply add the lengths of each of the 5 sides together (or multiply 5 times one side length).
P = 5(921)
P = 4605 feet
For the area, we will use composition...add the area of the triangle to the area of the trapezoid.
For the area of the triangle, the formula is
[tex]A=\frac{1}{2}bh[/tex].
Filling in our values gives us
[tex]A=\frac{1}{2}(1490)(541)[/tex] and
A = 403,045 square feet.
Now for the trapezoid. The formula for a trapezoid is
[tex]A=\frac{1}{2}(b_{1}+b_{2})(h)[/tex]
where the b's represent the bases and the h represents the height. Filling in our values gives us
[tex]A=\frac{1}{2}(921+1490)(876)[/tex]
Work inside the parenthesis first:
[tex]A=\frac{1}{2}(2411)(876)[/tex] and
A = 1,056,018
Now we add those together to get that area of the Pentagon is 1,459,063 square feet
Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. Find the probability that a randomly selected adult has an IQ less than 132. The probability that a randomly selected adult has an IQ less than 132 is?
Answers
Answer:
There is a 94.52% probability that a randomly selected adult has an IQ less than 132.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 20. This means that [tex]\mu = 100, \sigma = 20[/tex].
The probability that a randomly selected adult has an IQ less than 132 is?
This probability is the pvalue of Z when [tex]X = 132[/tex]. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{132 - 100}{20}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a pvalue of 0.9452.
This means that there is a 94.52% probability that a randomly selected adult has an IQ less than 132.
Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. The probability that a randomly selected adult has an IQ less than 132 is 0.9452 or 94.52%.
What is the probability?Let standardize the IQ value of 132 using the formula for standardization:
Z = (X - μ) / σ
Where:
Z= standardized value (Z-score)
X = IQ value
μ = mean= 100
σ = standard deviation =20
Let's calculate the Z-score for an IQ of 132:
Z = (132 - 100) / 20
Z = 32 / 20
Z = 1.6
Using a standard normal distribution table, the probability is 0.9452.
Therefore, the probability that a randomly selected adult has an IQ less than 132 is 0.9452 or 94.52%.
Learn more about probability here:https://brainly.com/question/13604758
#SPJ6
please help asap!!!!!!
Answers
Answer:
103.62 cm
Step-by-step explanation:
Given : Diameter, D = 33 cm
circumference = πD = 3.14 x 33 = 103.62 cm
Hello, I believe your answer is C.
You can find your answer by plugging in the diameter into the circumference formula: 2πr² (You must divide your diameter in half to get the radius).
52 POINTS, WILL GIVE BRAINLIEST!
Use the Polygon tool to draw a rectangle with a length of 6 units and a height of 4 units. One of the sides of the rectangle falls on line CD , and the rectangle has a vertex of C.
Each segment on the grid represents 1 unit.
Answers
Answer:
The answer is in the attachment.
Step-by-step explanation:
Look at the picture.
The rectangle that has a vertex of C and has one of it's sides on line CD, with the stated lengths is constructed as shown in the image attached below (see attachment).
What is a Rectangle?A rectangle can be described as a 4-sided polygon having all its four interior angles measuring 90 degrees each and has two pairs of opposite equal sides.
Thus, the rectangle that has a vertex of C and has one of it's sides on line CD, with the stated lengths is constructed as shown in the image attached below (see attachment).
Learn more about a rectangle on:
https://brainly.com/question/4141979
The table below shows the approximate height of an object x seconds after the object was dropped. The function h(x)= -16x^2 +100 models the data in the table. For which value of x would this model make it the least sense to use?
A. -2.75
B. 0.25
C. 1.75
D. 2.25
Answers
Answer:
the awnser is a -2.75
Step-by-step explanation:
Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining Bismuth-210 transforms into another atom (polonium-210 in this case) each day. If you begin with 233 mg of Bismuth-210, how much remains after 8 days?
Answers
Approximately 85.87 mg of Bismuth-210 would remain after 8 days.
Explanation:To calculate the amount of Bismuth-210 remaining after 8 days, we need to apply the concept of radioactive decay. Bismuth-210 decays by about 13% each day, meaning that 13% of the remaining Bismuth-210 transforms into another atom (Polonium-210) each day.
Let's calculate the amount remaining:
Start with 233 mg of Bismuth-210.After the first day, 13% of the remaining Bismuth-210 will decay, leaving 87% of the original amount: 0.87 * 233 mg = 202.71 mg.Repeat this process for each subsequent day.After 8 days, the amount remaining would be: (0.87)^8 * 233 mg = 85.87 mg.Therefore, after 8 days, approximately 85.87 mg of Bismuth-210 would remain.
Learn more about radioactive decay here:https://brainly.com/question/1770619
#SPJ3
After 8 days, approximately 76.69 mg of Bismuth-210 remains out of the initial 233 mg.
To calculate the amount of Bismuth-210 remaining after 8 days of radioactive decay, follow these steps:
Step 1:
Understand the decay rate.
Each day, 13% of the remaining Bismuth-210 decays into Polonium-210. This means that 87% of the Bismuth-210 remains each day.
Step 2:
Calculate the remaining amount each day.
Start with the initial amount of 233 mg of Bismuth-210.
After the first day: [tex]\( 233 \text{ mg} \times 0.87 = 202.71 \text{ mg} \)[/tex]
After the second day: [tex]\( 202.71 \text{ mg} \times 0.87 = 176.43 \text{ mg} \)[/tex]
Continue this process for 8 days.
Step 3:
Perform the calculations for 8 days.
[tex]\[ \text{Day 1: } 233 \text{ mg} \times 0.87 = 202.71 \text{ mg} \][/tex]
[tex]\[ \text{Day 2: } 202.71 \text{ mg} \times 0.87 = 176.43 \text{ mg} \][/tex]
[tex]\[ \text{Day 3: } 176.43 \text{ mg} \times 0.87 = 153.62 \text{ mg} \][/tex]
[tex]\[ \text{Day 4: } 153.62 \text{ mg} \times 0.87 = 133.67 \text{ mg} \][/tex]
[tex]\[ \text{Day 5: } 133.67 \text{ mg} \times 0.87 = 116.33 \text{ mg} \][/tex]
[tex]\[ \text{Day 6: } 116.33 \text{ mg} \times 0.87 = 101.28 \text{ mg} \][/tex]
[tex]\[ \text{Day 7: } 101.28 \text{ mg} \times 0.87 = 88.10 \text{ mg} \][/tex]
[tex]\[ \text{Day 8: } 88.10 \text{ mg} \times 0.87 = 76.69 \text{ mg} \][/tex]
Step 4:
Interpret the result.
After 8 days, approximately 76.69 mg of Bismuth-210 remains.
So, after 8 days, approximately 76.69 mg of Bismuth-210 remains.
Find the two geometric means between 20 and 5. 7. Solve: 44-32-3 8. Develop the identity for sin 2.4 using the identity for sin(A+ B).
Answers
Answer with explanation:
1.
Let a, and b be two numbers between 20 and 5 , which is in geometric progression.
So,the series is as Follows =20 , a, b, 5
Common ratio
[tex]=\frac{\text{Second term}}{\text{First term}}[/tex]
[tex]\frac{20}{a}=\frac{a}{b}=\frac{b}{5}\\\\b^2=5 a---(1)\\\\a^2=20 b\\\\\frac{b^4}{25}=20 b-----\text{Using 1}\\\\b^3=500\\\\b=(500)^{\frac{1}{3}}\\\\b=5\times (4)^{\frac{1}{3}}\\\\5a=25\times (4)^{\frac{2}{3}}\\\\a=5\times (4)^{\frac{2}{3}}[/tex]
2.
44 -32-3
=12-3
=9
3.
⇒Sin (2.4)=Sin(2+0.4)
⇒Sin 2 ×Cos (0.4)+Cos 2 × Sin (0.4)
⇒Sin (A+B)=Sin A×Cos B+Cos A×Sin B
Forty dash one percent of people in a certain country like to cook and 68% of people in the country like to shop, while 14% enjoy both activities. What is the probability that a randomly selected person in the country enjoys cooking or shopping or both?
Answers
Answer:
0.86 or 86%
Step-by-step explanation:
The data given represent 41% of people in a certain country like to cook and 68% of people in the country like to shop, while 14% enjoy both activities.
The probability that a randomly selected person in the country enjoys cooking or shopping or both.
People who like to cook P(C) = 41% = 0.40
People who like to shopping P(S) = 68% = 0.60
People who like cooking and shopping both P(C∩S) = 14% = 0.14
People who like cooking or shopping or both = P(C∪S)
= P(C) + P(S) - P(C∩S)
= 0.40 + 0.60 - 0.14
= 0.86
The probability that a randomly selected person in the country enjoys cooking or shopping or both is 0.86 or 86%
To calculate the probability that a selected person likes cooking or shopping or both, we add the probabilities of each individual event and subtract the overlapping probability. In this case, it's 94.1%.
Explanation:You want to find the probability that a randomly selected person in the country enjoys cooking, shopping, or both. To calculate this probability, you can use the principle of inclusion-exclusion for two sets A and B, where:
A is the event that someone enjoys cooking.B is the event that someone enjoys shopping.The formula for the probability that a randomly selected person enjoys either cooking or shopping (or both) is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Given:
P(A) = 40.1%P(B) = 68%P(A ∩ B) = 14%Plug in the values:
P(A ∪ B) = 40.1% + 68% - 14%
= 94.1%
So, the probability that a randomly selected person enjoys cooking or shopping or both is 94.1%.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
An Access Ramp to a freeway extends horizontally a distance of 80 feet while it rises a total of 15 feet . Find the Slope of the Access Ramp. A) 16/3 B) 19/16 C) 65 D) 3/16 E) 95
Answers
Answer:
D.
Step-by-step explanation:
Slope is rise over run by definition, and we are given the values for each in the problem. The run is 80 and the rise is 15 so
[tex]m=\frac{15}{80}=\frac{3}{16}[/tex]
what is the measurement of angle p? Round your answer to the nearest degree.
A. 29°
B.42°
C.65°
D.78°
Answers
You can use the law sines, which states that in a triangle the ratio between one side length and the sine of the opposite angle is constant.
So, we have
[tex]\dfrac{PR}{\sin(Q)}=\dfrac{QR}{\sin(P)}=\dfrac{PQ}{\sin(R)}[/tex]
In particular, we can use
[tex]\dfrac{PR}{\sin(Q)}=\dfrac{QR}{\sin(P)}[/tex]
to write
[tex]\dfrac{68}{\sin(73)}=\dfrac{47.6}{\sin(P)} \iff \sin(P) = \dfrac{47.6\sin(73)}{68}\approx 0.66[/tex]
Which means
[tex]P\approx \arcsin(0.66)\approx 42[/tex]
Suppose that 3% of all athletes are using the endurance-enhancing hormone EPO (you should be able to simply compute the percentage of all athletes that are not using EPO). For our purposes, a “positive” test result is one that indicates presence of EPO in an athlete’s bloodstream. The probability of a positive result, given the presence of EPO is .99. The probability of a negative result, when EPO is not present, is .90. What is the probability that a randomly selected athlete tests positive for EPO? 0.0297
Answers
Answer:
Step-by-step explanation:
So there is a 3% probability that an athlete is using EPO .
The probability of showing positive on a test when you've used it is 0.99.
3% x 0.99= 2.97%
The probability of a positive result without EPO is 0.1
97% x 0,1 = 9,7 %
My guess is that 2.97% + 9,7% = 12.67% or 0.1267.
I don't know i may be wrong because you've put as an answer 0.0297 but if you like you may take only the first part of the answer.
There is a 0.1267 = 12.67% probability that a randomly selected athlete tests positive for EPO.
A positive test can happen in two cases:
When EPO is present(3% of the time), with 0.99 probability.When EPO is not present(100 - 3 = 97% of the time), with 1 - 0.9 = 0.1 probability.Then, adding these probabilities:
[tex]p = 0.03(0.99) + 0.97(0.1) = 0.1267[/tex]
0.1267 = 12.67% probability that a randomly selected athlete tests positive for EPO.
A similar problem is given at https://brainly.com/question/24161830
For Mexican American infants born in Arizona in 1986 and 1987, the probability that a child's gestational age is less than 37 weeks is 0.142 and the probability that his or her birth weight is less than 2500 grams is 0.051. Furthermore, the probability that these two events occur simultaneously is 0.031. Please show work!a. are A and B independent?b. For a randomly selected Mexican American newborn, what is the probability that A or B or both occur?c.What is the probability that event A occurs given that event B occurs?
Answers
Answer: Hence, a) No, they are not independent
b) 0.193
c) 0.60
Step-by-step explanation:
Since we have given that
Probability that a child's gestational age is less than 37 weeks say P(A)= 0.142
Probability that his or her birth weight is less than 2500 grams say P(B) = 0.051
P(A∩B) = 0.031
We need to check whether it is independent or not.
Since ,
[tex]P(A).P(B)=0.142\times 0.051=0.0072[/tex]
and
[tex]P(A\cap B)=0.051[/tex]
So, we can see that
[tex]P(A).P(B)\neq P(A\cap B)[/tex]
So, it is not independent.
a) Hence, A and B are not independent.
b) P(A∪B) is given by
[tex]P(A\ or B\ or\ both)=P(A)+P(B)\\\\P(A\ or\ B\ or\ both)=0.142+0.051=0.193[/tex]
c) P(A|B) is given by
[tex]P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.031}{0.051}=0.60[/tex]
Hence, a) No,
b) 0.193
c) 0.60
A market researcher obtains a list of all streets in a town. She randomly samples 10 street names from the list, and then administers survey questions to every family living on those 10 streets. What type of sampling is this?
Answers
Answer: Simple random sampling
Step-by-step explanation:
Given: A market researcher obtains a list of all streets in a town. She randomly samples 10 street names from the list, and then administers survey questions to every family living on those 10 streets.
Since she randomly samples street names , therefore the type of sampling is simple random sampling.
A simple random sample is a sample that is a subset of the population the researcher surveyed selected in a way such that all the individuals in the population has an equal chance to be selected.
Consider the vector field F=(x2+y2,4xy). Compute the line integrals ∫c1F⋅ds and ∫c2F⋅ds, where c1(t)=(t,t2) and c2(t)=(t,t) for 0≤t≤1. Can you decide from your answers whether or not F is a gradient vector field? Why or why not?
Answers
[tex]\displaystyle\int_{C_1}\vec F\cdot\mathrm d\vec s=\int_0^1(t^2+t^4,4t^3)\cdot(1,2t)\,\mathrm dt=\int_0^1(t^2+9t^4)\,\mathrm dt=\boxed{\frac{32}{15}}[/tex]
Integral over [tex]C_2[/tex]:[tex]\displaystyle\int_{C_2}\vec F\cdot\mathrm d\vec s=\int_0^1(2t^2,4t^2)\cdot(1,1)\,\mathrm dt=\int_0^16t^2\,\mathrm dt=\boxed{2}[/tex]
The value of the line integral depends on the path, so [tex]\vec F[/tex] is not a gradient vector field.
The line integrals ∫c1F⋅ds and ∫c2F⋅ds are computed by replacing x and y with the parametric representations, calculating ds, completing the dot product, and conducting the integration. If the results are identical, F is a gradient vector field.
Explanation:To compute the line integrals, ∫c1F⋅ds and ∫c2F⋅ds, where c1(t)=(t, t2) and c2(t)=(t,t) for 0≤t≤1 of the vector field F=(x2+y2,4xy), we can reduce each of them to an integral over t, the parameter of the path. In the case of c1(t), replace x and y by t and t² correspondingly, for calculation. Similarly, in the case of c2(t), replace x and y by t in calculations.
Let's consider ∫c1F⋅ds. Here, F = (t²+t⁴,4t³) and ds can be calculated using the Pythagorean theorem leading to sqr(1+4t²). The dot product F.ds is then calculated and integrated from 0 to 1. Repeat the process for ∫c2F⋅ds.
A vector field F is said to be a gradient vector field if integral from one point to another remains the same regardless of the path chosen to get from one point to the other. Comparing the obtained results will determine the truth of this statement.
Learn more about Vector Field Line Integrals here:https://brainly.com/question/31477889
#SPJ3
Suppose that you believe that the probability you will get a grade of B or better in Introduction to Finance is .6 and the probability that you will get a grade of B or better in Introduction to Accounting is .5. If these events are independent, what is the probability that you will receive a grade of B or better in both courses?
Answers
Answer: Probability that he will receive a grade of B or better in both courses is 0.30.
Step-by-step explanation:
Since we have given that
Probability that he will get a grade of B or better in introduction to Finance say P(A) = 0.6
Probability that he will get a grade of B or better in introduction to Accounting say P(B) = 0.5
Since A and B are independent events.
We need to find the probability that he will receive a grade of B or better in both the courses.
So, it becomes,
[tex]P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.6\times 0.5\\\\P(A\cap B)=0.30[/tex]
Hence, Probability that he will receive a grade of B or better in both courses is 0.30.
The probability that you will receive a grade of B or better in both courses is 0.3.
The probability that you will receive a grade of B or better in both Introduction to Finance and Introduction to Accounting, given that the events are independent, is calculated by multiplying the individual probabilities of each event.
[tex]\( P(F) = 0.6 \) \( P(A) = 0.5 \)[/tex]
Since the events are independent, the probability of both events occurring is given by the product of their individual probabilities:
[tex]\( P(F \text{ and } A) = P(F) \times P(A) \)[/tex]
Substituting the given probabilities:
[tex]\( P(F \text{ and } A) = 0.6 \times 0.5 \) \( P(F \text{ and } A) = 0.3 \)[/tex]
The final answer is [tex]\(\boxed{0.3}\).[/tex]
HELP URGENT - put 27 points on question please help!
Write a quadratic function in standard form whose graph passes through (-5,0), (9,0), and (8, -39).
f(x) =
Answers
Answer:
f(x) = 3x² - 12x -135
Step-by-step explanation:
standard form of a quadratic equation is
y = Ax² + Bx + C
You are given 3 solutions for X and Y, i.e( x=-5, y = 0), (x = 9,y = 0) and (x = 8,y = -39)
Substitute each of this equations into the quadratic equation to obtain a system of 3 equations
For ( x=-5, y = 0), 25A - 5B + C = 0 ---------- eq (1)
For ( x= 9, y = 0), 81A + 9B + C = 0 ---------- eq (2)
For ( x= 8, y = -39), 64A + 8B + C = -39 ---------- eq (3)
You have 3 equations and 3 unknowns. Solving this system of 3 equations will give:
A = 3, B = -12, c = -135
Hence the quadratic equation is
y = 3x² - 12x -135
or in function form:
f(x) = 3x² - 12x -135
Travel: One Cyclist drives at Six miles per hour faster then another Cyclist. Express the speed of the faster Cyclist in terms of the speed of the lowest Cyclist .....
Answers
Answer:
Faster cyclist: 6x
Slower: x
Step-by-step explanation:
x = mph
The speed of the faster cyclist is expressed as v + 6 mph, where v represents the speed of the slower cyclist.
To express the speed of the faster cyclist in terms of the speed of the slower cyclist, let's denote the speed of the slower cyclist as v mph. The problem states that the faster cyclist travels at a speed that is six miles per hour faster than the slower cyclist. Therefore, the speed of the faster cyclist can be expressed as v + 6 mph.
For example, if the slower cyclist is travelling at a speed of 9 mph, the faster cyclist would be traveling at 9 mph + 6 mph = 15 mph.
Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = 4 + ln (t), y = t^2 + 6, (4, 7)
Answers
Answer:
y = 2x − 1
Step-by-step explanation:
By eliminating the parameter, first solve for t:
x = 4 + ln(t)
x − 4 = ln(t)
e^(x − 4) = t
Substitute:
y = t² + 6
y = (e^(x − 4))² + 6
y = e^(2x − 8) + 6
Taking derivative using chain rule:
dy/dx = e^(2x − 8) (2)
dy/dx = 2 e^(2x − 8)
Evaluating at x = 4:
dy/dx = 2 e^(8 − 8)
dy/dx = 2
Writing equation of line using point-slope form:
y − 7 = 2 (x − 4)
y = 2x − 1
Now, without eliminating the parameter, take derivative with respect to t:
x = 4 + ln(t)
dx/dt = 1/t
y = t² + 6
dy/dt = 2t
Finding dy/dx:
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (2t) / (1/t)
dy/dx = 2t²
At the point (4, 7), t = 1. Evaluating the derivative:
dy/dx = 2(1)²
dy/dx = 2
Writing equation of line using point-slope form:
y − 7 = 2 (x − 4)
y = 2x − 1
To find the tangent to the curve represented by the parametric equations x = 4 + ln(t), y = t² + 6, both methods, eliminating and not eliminating the parameter t, yield the same result. The slope of the tangent line at the point (4, 7) is determined to be 2, thus the equation of the tangent is y - 7 = 2(x - 4).
To find the equation of the tangent to the given curve at the point (4, 7) with the parametric equations x = 4 + ln(t) and y = t² + 6, we can approach the problem in two ways: with and without eliminating the parameter t.
Firstly, without eliminating the parameter, we need to find the derivatives dx/dt and dy/dt, and then use them to find dy/dx which is the slope of the tangent at the given point. Since dx/dt = 1/t and dy/dt = 2t, at the point (4, 7), we have t = 1, making the slope dy/dx = (dy/dt)/(dx/dt) = 2 × 1 / (1/1) = 2. The equation of the tangent line can thus be written as y - y₁ = m(x - x₁), where m is the slope, and (x₁, y₁) is the point of tangency.
This gives us the equation y - 7 = 2(x - 4).
Use the definition of the Laplace transform to find L(f(t) if f(t)=t^5
Answers
Answer:
120/s^6
Step-by-step explanation:
There is an easy formula for this...
L(t^n)=n!/(s^(n+1))
Your n=5 here
L(t^5)=5!/(s^6)
L(t^5)=120/s^6
[tex]\mathcal{L}\{t^n\}=\dfrac{n!}{s^{n+1}}[/tex]
So
[tex]\mathcal{L}\{f(t)\}=\dfrac{5!}{s^{5+1}}=\dfrac{120}{s^6}[/tex]
Consider the given function and the given interval. f\(x\) = 2 sin\(x\) - sin\(2 x\) text(, ) [0 text(, ) pi] (a) Find the average value fave of f on the given interval. fave = Correct: Your answer is correct. (b) Find c such that fave = f(c). (Enter solutions from smallest to largest. If there are any unused answer boxes, enter NONE in the last boxes. Round the answers to three decimal places.)
Answers
a. The average value of [tex]f[/tex] on the given interval is
[tex]\displaystyle f_{\rm ave}=\frac1{\pi-0}\int_0^\pi(2\sin x-\sin2x)\,\mathrm dx=\boxed{\frac4\pi}[/tex]
b. Solve for [tex]c[/tex]:
[tex]\dfrac4\pi=2\sin c-\sin2c\implies\boxed{c\approx1.238\text{ or }c\approx2.808}[/tex]
Which will result in a difference of squares?
(-7x+4)(-7x+4)
(-7x + 4)(4-7x)
(-7x+4)(-7x-4)
(-7x + 4)(7x-4)
Answers
Answer:
[tex]\large\boxed{(-7x+4)(-7x-4)}[/tex]
Step-by-step explanation:
[tex]\text{The difference of squares:}\ a^2-b^2=(a-b)(a+b)\\\\(-7x+4)(-7x-4)=(-7x)^2-4^2=49x^2-16[/tex]
(-7x + 4) (-7x - 4) can be written as a difference of squares.
Option C is the correct answer.
What is an expression?
An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The difference of squares is a special algebraic form that occurs when we multiply two binomials of the form (a + b)(a - b).
This results in the product of two terms:
The square of the first term minus the square of the second term.
In other words, we have (a + b)(a - b) = a² - b².
In the given options, only (-7x + 4) (-7x - 4) can be written as a difference of squares, by applying the above formula.
We can rewrite it as:
(-7x + 4) (-7x - 4) = (-7x)² - 4² = 49x² - 16
The other options do not follow this pattern and cannot be written as a difference of squares.
Thus,
(-7x + 4)(-7x - 4) = 49x² - 16
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ5
How many different three-digit numbers can be formed using the digits 1 comma 2 comma 9 comma 6 comma 4 comma 3 comma and 8 without repetition? For example, 664 is not allowed.
Answers
Answer:
129 468
Step-by-step explanation:
I'm not sure if you're supposed to reuse the same numbers just in a different Three digit number. Or if you're supposed to use the number one time and one time only. But if not here's there's some numbers that you could use
He basically all You have to do Is take the numbers and turning them into three digit numbers Without repetition.
Hope this helps you!
Also it's saying that 664 is not allowed Because it they are reusing the six When there's no Extra six to use. So remind you not to use the same number twice!