Answer:
0.873 = 87.3% probability that an athlete tests negative and is not a user of an illegal drug
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Not a user of an illegal drug.
Event B: Tests negative.
The test for this drug is 90% accurate for non-drug users (this means there is a 90% chance the test comes back negative if the person is a non-user)
This means that [tex]P(B|A) = 0.9[/tex]
It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance.
So 100 - 3 = 97% probability that the athlete does not use the drug, so [tex]P(A) = 0.97[/tex]
What is the probability that an athlete tests negative and is not a user of an illegal drug
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = 0.9*0.97 = 0.873[/tex]
0.873 = 87.3% probability that an athlete tests negative and is not a user of an illegal drug
how Do you graph an
absolute valve function
Answer:
To graph the absolute value, you need to know where the vertex is, so the numbers will be going down, then turn and start going back up, or going up and then turn and start going down, the middle point will be the vertex and should be the center point of the table.
Amanda ate 1/3 of her mom's pie. she gave the remaining 2/3 to 4 friends, What fraction did each friend get.
Are the following ratios equivalent
16:48 and 112:336
Answer:
Yes
Step-by-step explanation:
what's the answer to this
Ratio 7/11 two other ways
Answer:
Isn't it 7:11 and 7 to 11
Step-by-step explanation:
One gallon is approximately 3.79 liters. Write a direct variation equation that relates 2 gallons to y liters.
370
Answer:
2 gallons x 3.79 = 7.58 liters
Step-by-step explanation:
1 gallon = 3.79 liters
so
2 gallons x 3.79 liters = 7.58 liters
2 x 3.79 = y liters
Which of the following is the equation for the line of symmetry in this figure?
Can someone help please!
Answer:
X=3
Step-by-step explanation:
3 is in the middle of the figure.
I hope this helps!
Five times a number decreased by 8 is less than 37. Write an algebraic inequality to represent this situation.
Answer:
5x - 8 < 37
Step-by-step explanation:
I'm so sorry if this is wrong
simplify x^2-9x+14/x^2+5x-14
Round 342.296269789 to 2 decimal places.
Answer:
342.29
Step-by-step explanation:
You take away the other decimal places.
The round-up to 2 decimal places of 342.296269789 will be 342.30.
How do round any digit?To round up or down of tens place then we need to look at the unit place if it is less than 5 then we need to round down and if it is greater than 5 then we need to round up of tens digit.
In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we round down and if it is 5 or greater than 5 then we will round up.
For example round of 346 will, be350 and round of 344 will be 340
Given the digit,
342.296269789
Now,
The 3rd decimal digit is 6 which is greater than 5
So,
2nd digit will round up since it is 9 so it will round as 10 and gives 1 to the first decimal place.
So,
342.296269789 ⇒ 342.30.
Hence "The round-up to 2 decimal places of 342.296269789 will be 342.30".
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10) Jacolby can score 30 goals in 6 minutes. Khamari can score 42 goals in 7 minutes. How many more goals can Khamari make per minute? a) 3 goals b) 2 goals c) 1 goal d) 4 goals
Answer:
c)1 goal
Step-by-step explanation:
Since Jacolby can make 30 goals in 6 minutes, that makes (30/6) 5 goals per minute. Khamari can make 42 goals in 7 minutes, that makes (42/7) 6 goals per minute. So Jalcolby is 5 and Khamari is 6, and the question is asking how many MORE. 6-5 is 1, so Khamari can make 1 more goal per minute than Jacolby.
Hope this helps.
WILL MARK BRAINLYIST
Bashir deposits money into a savings account every year. In his first year of saving money, he deposited $1,500.
Each year after that, he deposited $2,250. Write an explicit expression to represent the total amount of money, in
dollars, Bashir has deposited into his account, where n represents the number of years he has been contributing
money to the account.
Answer:
[tex]y = 2250x + 1500[/tex]
Step-by-step explanation:
How much more money does it cost to burn trash than to send it to a landfill? Sanitation Costs (per pound) Recycling $30 Landfilling $50 Burning $75 2,000 pounds = 1 ton/ $25 per ton / $25 per pound / $45 per ton / $45 per pound
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. y
Answer:
[tex]Volume = \frac{384}{7}\pi[/tex]
Step-by-step explanation:
Given (Missing Information):
[tex]y = x^\frac{3}{2}[/tex]; [tex]y = 8[/tex]; [tex]x=0[/tex]
Required
Determine the volume
Using Shell Method:
[tex]V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy[/tex]
First solve for a and b.
[tex]y = x^\frac{3}{2}[/tex] and [tex]y = 8[/tex]
Substitute 8 for y
[tex]8 = x^\frac{3}{2}[/tex]
Take 2/3 root of both sides
[tex]8^\frac{2}{3} = x^{\frac{3}{2}*\frac{2}{3}}[/tex]
[tex]8^\frac{2}{3} = x[/tex]
[tex]2^{3*\frac{2}{3}} = x[/tex]
[tex]2^2 = x[/tex]
[tex]4 =x[/tex]
[tex]x = 4[/tex]
This implies that:
[tex]a = 4[/tex]
For [tex]x=0[/tex]
This implies that:
[tex]b=0[/tex]
So, we have:
[tex]V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy[/tex]
[tex]V = 2\pi \int\limits^4_0 {p(y)h(y)} \, dy[/tex]
The volume of the solid becomes:
[tex]V = 2\pi \int\limits^4_0 {x(8 - x^{\frac{3}{2}}}) \, dx[/tex]
Open bracket
[tex]V = 2\pi \int\limits^4_0 {8x - x.x^{\frac{3}{2}}} \, dx[/tex]
[tex]V = 2\pi \int\limits^4_0 {8x - x^{\frac{2+3}{2}}} \, dx[/tex]
[tex]V = 2\pi \int\limits^4_0 {8x - x^{\frac{5}{2}}} \, dx[/tex]
Integrate
[tex]V = 2\pi * [{\frac{8x^2}{2} - \frac{x^{1+\frac{5}{2}}}{1+\frac{5}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{x^{\frac{2+5}{2}}}{\frac{2+5}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{x^{\frac{7}{2}}}{\frac{7}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{2}{7}x^{\frac{7}{2}}]\vert^4_0[/tex]
Substitute 4 and 0 for x
[tex]V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [{4*0^2 - \frac{2}{7}*0^{\frac{7}{2}}])[/tex]
[tex]V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [0])[/tex]
[tex]V = 2\pi * [{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*2^2^{*\frac{7}{2}}][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*2^7][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*128][/tex]
[tex]V = 2\pi * [{64 - \frac{2*128}{7}][/tex]
[tex]V = 2\pi * [{64 - \frac{256}{7}][/tex]
Take LCM
[tex]V = 2\pi * [\frac{64*7-256}{7}][/tex]
[tex]V = 2\pi * [\frac{448-256}{7}][/tex]
[tex]V = 2\pi * [\frac{192}{7}][/tex]
[tex]V = [\frac{2\pi * 192}{7}][/tex]
[tex]V = \frac{\pi * 384}{7}[/tex]
[tex]V = \frac{384}{7}\pi[/tex]
Hence, the required volume is:
[tex]Volume = \frac{384}{7}\pi[/tex]
The volume of the solid of revolution generated by revolving the plane region about the y-axis is [tex]\frac{10240\pi}{3}[/tex] cubic units.
How to calculate the volume of a solid of revolution by shell method
Let be [tex]f(x) = x^{5/2}[/tex] and [tex]g(x) = 32[/tex], whose point of intersection is [tex](x,y) = (4, 32)[/tex]. Solid of revolution generated by revolving the plane region about the y-axis is defined by the following formula:
[tex]V = 2\pi\int\limits^{32}_0 {y\cdot g(y)} \, dy[/tex] (1)
If we know that [tex]g(y) = y^{2/5}[/tex], then the volume of the solid of revolution is:
[tex]V = 2\pi\int\limits^{32}_{0} {y^{7/5}} \, dy[/tex]
[tex]V = 2\pi\cdot \left(\frac{5}{12}\cdot y^{12/5}\right)\left|_{0}^{32}[/tex]
[tex]V = \frac{5\pi}{6} \cdot y^{12/5}|\limit_{0}^{32}[/tex]
[tex]V = \frac{5\pi}{6}\cdot 32^{12/5}[/tex]
[tex]V = \frac{10240\pi}{3}[/tex]
The volume of the solid of revolution generated by revolving the plane region about the y-axis is [tex]\frac{10240\pi}{3}[/tex] cubic units. [tex]\blacksquare[/tex]
Remark
The statement is incomplete. Complete form is shown below:
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. [tex]y = x^{5/2}[/tex], [tex]y = 32[/tex], [tex]x = 0[/tex].
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identify the function of the transformation
mega has 3 weter botels and wants to give each of her friends 4 how many will she need
Answer:
12
Step-by-step explanation:
3 times 4 is 12
Robin braided g inches of a friendship bracelet. Olivia braided 12 less than 1/3 the number of inches robin braided. Select all of the expressions that represent the total number of inches braided by robin and Olivia
I NEED DONE ASAP PLEASEEE
Answer:
Step-by-step explanation:
The correct expressions that represent the total number of inches braided by robin and Olivia is,
⇒ 4 (1/3g - 3)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Robin braided g inches of a friendship bracelet.
And, Olivia braided 12 less than 1/3 the number of inches robin braided.
Now, The total number of inches braided by Robin and Olivia = Number of inches braided by Robin + Number of inches braided by Olivia
Hence, We get;
⇒ g + 1/3g - 12
⇒ 4/3g - 12
⇒ 4 (1/3g - 3)
Thus, The correct expressions that represent the total number of inches braided by robin and Olivia is,
⇒ 4 (1/3g - 3)
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Write your answer with no spaces and any fraction with “/“
Answer:
The slope is 1/2
Step-by-step explanation:
Hi!
Disclaimer: Just for this response, I'm going to write it the same way you write a fraction out on paper just so it's easier to see.
First, you plot the two coordinates on the graph:
(0,0) and (2,1)
The formula for slope is [tex]\frac{y1 - y2}{x1 - x2}[/tex]
Now we plug in numbers accordingly:
[tex]\frac{0 - 1}{0 - 2}[/tex]
Simplify:
[tex]\frac{-1}{-2} \\[/tex]
Simplify:
[tex]\frac{1}{2}[/tex]
Let me know if you have any questions
PLEASE HELP ASAP
How many hours will it take a culture of bacteria to increase from 20 to 2000 if the growth rate per hour is 50%
Answer:
200 hours
Step-by-step explanation:
if it increases by 50% of 20 an hour, so it increases 10 and hour. 2000÷10=200
Enter range of values for x
Answer:
42=3x+15
42-15+3x
27/3 = 9
Step-by-step explanation:
Can someone please solve number 6 for me it’s urgent
Answer:
Value of blank = 1 / (-5x)
Step-by-step explanation:
Given:
__ × (-5x) = 1
Find:
Value of blank
Computation:
Assume;
Blank = y
So,
y × (-5x) = 1
y = 1 / (-5x)
Value of blank = 1 / (-5x)
can i get a OHHHHHH YEAHHHH
Answer:
AW YEAHHHHHHHHHHHHHHHHHHHHHHHHHHH
Step-by-step explanation:
Answer:
OH YEAHHHH
Step-by-step explanation:
lol
A blue whale is swimming at an average rate of 3 miles per hour.
Write a linear equation that gives the distance y in miles that the whale swims in x hours.
Answer:
y = 3x
Step-by-step explanation:
you can use the equation to determine how many miles the whale swims in any desired hour
example, if you want to know how far it swims in 5 1/2 hours then just plug 5 1/2 in for 'x' and solve for 'y'
y = 3(5.5)
y = 16.5
whale travels 16.5 miles when going at a rate of 3 mph
What are two ways to say the time 3.7 minutes out loud? points)
Answer:
1.) three-point seven minutes
2.) three and seven-tenths minutes
Step-by-step explanation:
I hope I helped!!!
Given the rectangle ABCD, find measure of angle EFH, measure of angle FEH. Also find, HI and GE.
HF= 36
measure of angle HFG = 30
Help needed for this Que’s please.!
Step-by-step explanation:
step 1. the sale is 20% off; that means times 0.8.
step 2. the additional coupon is 10% off of the sale price; that means times 0.9.
step 3. so the final price is (0.8)(0.9) times the retail price
step 4. (0.8)(0.9) = 0.72 or a 28% discount and not 30%.
The Franklins inherited $3,500, which they want to invest for their child's future college expenses. They use the following formula to calculate the value of their investment over time, where
A = value of the investment after years, P = principal invested, r = annual interest rate, and n = number of times compounded per year.
A = P(1 +
you
71
If they invest the inherited money at an annual rate of 8.25% with interest compounded monthly, what is the value of the account to the nearest dollar, after 5 years?
Answer:
1443.75 i think
Step-by-step explanation:
Thus, Franklin has $5011 after 5 years for an annual rate of 8.25% with interest compounded monthly.
The Franklins inherited $3,500, which they want to invest for their child's future college expenses. Using formula [tex]A = p(1+r/n)^{nt}[/tex]
where A is the value of the investment after t years, P is the principal invested, r is the annual interest rate and n is the number of times compounded per year.
an annual rate of 8.25% with interest compounded monthly, what is the value of the account to the nearest dollar, after 5 years is to be determined.
Statistic is the study of mathematics which deal with relations between comprehensive data.
Using formula [tex]A = p(1+r/n)^{nt}[/tex]
[tex]A = 3500*(1+0.0825/12)^{12*5}\\A = 3500*(1+0.006)^{60}\\A = 3500*(1.006)^{60}\\A = 5011.25\\[/tex]
A ≈ 5011
Thus, Franklin has $5011 after 5 years for an annual rate of 8.25% with interest compounded monthly.
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(PLEASE ANSWER ASAP ITS ALREADY LATE I WILL MARK BRAINLYIEST) Mohammad makes and sells jewelry. His monthly goal is to make a profit over $2,500. He sells each piece of jewelry for $25. He has a monthly fixed cost of $1,725. The inequality 25x+1,725>2,500 models this situation. which best describes the meaning of x in the inequality? A.) the number of pieces of new Mohammad must sell to reach his goal
B.) the profit made from 1 month of sales
C.) the profit made from selling 25 pieces of jewelry
D.) the number of pieces of jewelry that Mohammad must sell to recover his monthly fixed costs
Answer:
A
Step-by-step explanation:
It must be the amount he sells since each piece costs $25 and he must reach his goal
what is B? b-1/4=3 1/2
Answer:
hello! :) have a good day!
Exact Form:
b =15/4
Decimal Form:
b =3.75
Mixed Number Form:
b =3 3/4
If $5.000 is invested at a rate of 8%, compounded weekly, find the value of the investment after 7 years.