The plans for a home renovation include a new window. The homeowner picked a window shaped like the one shown. Identify the polygon and classify it as regular or irregular.
Answers
Answer:
Octagon regular.
Step-by-step explanation:
This shape has 8 sides to it is an octagon. A octagon irregular doesn't have equal sides while this one does. The best way to tell is if it looks like a stop sign which are octagon regular.
Related Questions
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 14 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answers
Answer:
[tex]x=30\\y=68\\z=82[/tex]
Step-by-step explanation:
x = measure of the first angle
y = measure of the second angle
z = measure of the third angle
The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)
[tex]y+z=5x[/tex]
The third angle is 14 more than the second
[tex]z=y+14[/tex]
And remember that the sum of these three angles must be equal to 180.
[tex]x+y+z=180[/tex]
Let's take these equations
[tex]y+z=5x\\z=y+14\\x+y+z=180[/tex]
If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....
[tex]x+y+z=180\\x+(y+z)=180\\x+(5x)=180[/tex]
Distribute the + sign
[tex]x+5x=180[/tex]
Combine like terms;
[tex]6x=180[/tex]
Divide by 6.
[tex]x=\frac{180}{6}\\ x=30[/tex]
We have now defined that the measure of the first angle is 30º.
Let's take another equation... for example [tex]z=y+14[/tex]
I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.
[tex]x+y+z=180\\30+y+(y+14)=180[/tex]
Distribute the + sign and Combine like terms;
[tex]30+y+y+14=180\\44+2y=180\\[/tex]
Subtract 44 to isolate 2y.
[tex]2y=180-44\\2y=136[/tex]
Now divide by 2.
[tex]y=\frac{136}{2}\\ y=68[/tex]
We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.
[tex]x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82[/tex]
Points X( -6, -4), Y( -2, -8), Z( 2,-4) are the vertices of a right triangle. What is the area of XYZ? Round to the nearest tenth.
Answers
Answer:
16
Step-by-step explanation:
distance between point x and z is 8 units
distance between point z and y is 4 units
8 * 4 = 32
formula for area of a triangle (l * w)/2
plugin: (8 * 4)/2 = 16
A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The p-value is
Answers
Answer:
The p-value of the test is 0.023.
Step-by-step explanation:
In this case we need to determine whether the addition of several advertising campaigns increased the sales or not.
The hypothesis can be defined as follows:
H₀: The stores average sales is $8000 per day, i.e. μ = 8000.
Hₐ: The stores average sales is more than $8000 per day, i.e. μ > 8000.
The information provided is:
[tex]n=64\\\bar x=\$8300\\\sigma=\$1200[/tex]
As the population standard deviation is provided, we will use a z-test for single mean.
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{8300-8000}{1200/\sqrt{64}}=2[/tex]
The test statistic value is 2.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the two-tailed test as follows:
[tex]p-value=P(Z>2)\\=1-P(Z<2)\\=1-0.97725\\=0.02275\\\approx 0.023[/tex]
*Use a z-table for the probability.
The p-value of the test is 0.023.
The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tower. The height, h, of the penny is recorded after each second, t, in the table. Write an equation for the curve of best fit, then find the approximate height of the penny after 7 seconds.
Answers
Answer:
The equation for the height of the penny in function of time is:
[tex]h(t)=1451-16t^2[/tex]
After 7 seconds, the penny will be at a height of 667 feet.
Step-by-step explanation:
The penny will have a free fall.
The initial velocity is zero, and the initial height is h(0)=1,451.
The acceleration will be the gravity, that has a value g=32 ft/s^2.
Then, we can model this starting by the speed:
[tex]dv/dt=-g\\\\v(t)=v_0-gt=-gt[/tex]
Then, the height becomes:
[tex]dh/dt=v(t)=-gt\\\\h(t)=h_0-\dfrac{gt^2}{2}=1451-\dfrac{32}{2}t^2\\\\\\h(t)=1451-16t^2[/tex]
The approximate height of the penny after 7 seconds can be calculated as:
[tex]h(7)=1451-16(7^2)=1451-16*49=1451-784=667[/tex]
After 7 seconds, the penny will be at a height of 667 feet.
Priscilla’s grandmother’s fruit salad recipe calls for one part apple, one part orange, four parts strawberry, two parts cherry, and three parts grape. Priscilla uses the same measuring cup to measure all of the fruit, so one part is equal to one cup of diced fruit. In this exercise, you will compare the quantities in the recipe to understand ratios better.
Answers
Answer:
There are 11 parts of fruit: 4-strawberry, 3- grape, 2, cherry, 1- apple, 1-orange 4/11 from the entine quantity of fruits- strawberry
3/11-grapes
2/11- cherries
1/11- apples
1/11- oranges } ⇒ the quantity of oranges and apples are equal Hope it helps ;>
Which fraction equals a repeating decimal?
30/50
13/25
5/30
13/10
Answers
Answer:
5/30
Step-by-step explanation:
5/30 = 1/6 =0.166666666...
The fraction equals a repeating decimal is 5/30.
What are decimals?A decimal numeral system is the standard system for denoting integer and non-integer numbers. The way of denoting numbers in the decimal system is often referred to as decimal notation.
Now the given fractions are,
30/50
13/25
5/30
13/10
Converting them into decimals we get,
30/50 = 0.6
13/25 = 0.52
5/30 = 0.1666..
13/10 = 1.3
Thus the repeating decimal is 0.1666..
So, the fraction with repeating decimal is 5/30 = 0.1666..
Thus, the fraction equals a repeating decimal is 5/30.
To learn more about fraction :
brainly.com/question/1301963
#SPJ2
€1.4 m
1.9 m
Tim has to cover 3 tanks completely with paint.
Each tank is in the shape of a cylinder with a top and a bottom.
The tank has a diameter of 1.4 metres and a height of 1.9 m.
A tin of paint covers 5 m
Find the total surface area of the 3 tanks and state how
many tins of paint Tim will need to buy
You must show your working
Total marks 5
Answers
Answer:
Step-by-step explanation:
Since each tank is cylindrical, we would apply the formula for determining the total surface area of a cylinder which is expressed as
Total surface area = 2πr² + 2πrh
Where
r represents the height of the cylinder.
h represents the height of the cylinder.
π = 3.14
From the information given,
Height = 1.9
Diameter = 1.4
Radius = diameter/2 = 1.4/2 = 0.7
Total surface area = 2 × 3.14 × 0.7² + 2 × 3.14 × 0.7 × 1.9 = 3.0772 + 8.3524 = 11.4296 m²
Total surface area of the 3 cylinders = 11.4296 × 3 = 34.29 m²
Since a tin of paint covers 5 m², the number of tins paints that Tim will need to buy is
34.29/5 = 6.858
Since the tins of paint must be whole numbers, he needs to buy 7 tins of paints.
State if the two vectors are parallel, orthogonal, or neither.
u=18i+8j
v=9i+4j
Answers
Answer:
Parallel, since [tex]\vec u = 2\cdot \vec v[/tex].
Step-by-step explanation:
The relation between both vectors is determined by the use of the dot product, whose expression is:
[tex]\cos \theta = \frac{\vec u \bullet \vec v}{\|\vec u\| \|\vec v\|}[/tex]
Where:
[tex]\cos \theta = 1[/tex] if vectors are parallel to each other and [tex]\cos \theta = 0[/tex] if vectors are orthogonal. Then, norms and dot product are calculated hereafter:
[tex]\|\vec u\| = \sqrt{18^{2}+8^{2}}[/tex]
[tex]\|\vec u\| \approx 19.698[/tex]
[tex]\|\vec v \| = \sqrt{9^{2}+4^{2}}[/tex]
[tex]\|\vec v\| \approx 9.849[/tex]
[tex]\vec u \bullet \vec v = (18)\cdot (9) + (8)\cdot (4)[/tex]
[tex]\vec u \bullet \vec v = 194[/tex]
[tex]\cos \theta = \frac{194}{(19.698)\cdot (9.849)}[/tex]
[tex]\cos \theta = 1[/tex]
The two vectors are parallel to each other, which is also supported by the fact that one vector is multiply of the other one. That is,
[tex]18i + 8j = 2\cdot (9i + 4j)[/tex]
[tex]\vec u = 2\cdot \vec v[/tex]
What is the volume of a cylinder with a base radius of 4 and height 7?
Answers
Answer:
351.86
Step-by-step explanation:
4. The Gold family sold their house for $450,000. They paid a realty
company 6% for selling the house. How much money did they pay the
company? *
Answers
Answer:
27,000
Step-by-step explanation:
$450,000 x 0.06= $27,000
0.06 is the 6% that you multiply by the total amount they earned to see how much they paid the realty company.
what is the value of the rational expression below when x is equal to 4? x+20/x+4
Answers
Answer:
3
Step-by-step explanation:
All we need to do here is plug in the number 4 for the variable x. Wherever there's an x, kidnap it and replace it with a 4!
[tex]\frac{x + 20}{x + 4}[/tex]
x = 4
[tex]\frac{4 + 20}{4 + 4}[/tex]
Do the addition.
4 + 20 = 24
4 + 4 = 8
[tex]\frac{24}{8}[/tex]
We can simplify this! What is 24 divided by 8?
24/8 = 3
The answer is 3!
Round 299 to the nearest hundred. Enter your answer in the box below.
Answers
Answer:
300
Step-by-step explanation:
hundreds tens ones
2 9 9
We look at the tens
It is 5 or higher so we round up the hundreds place
2 becomes 3
300
Answer:
300
Step-by-step explanation:
its obv 300 because 299 is greater than 249 and if it is less than 249 it is rounded to 200.
What goes into the boxes
Answers
Answer:
See explanation
Step-by-step explanation:
[tex]6 {c}^{2} + 2 {c}^{4} - c \\ \\ standard \: form = \red{ \boxed{ \bold{2 {c}^{4} + 6 {c}^{2} - c}}} \\ \\ degree = \purple{ \boxed{ \bold{4}}} \\ \\ leading \: coefficient = \orange{ \boxed{ \bold{1}}}[/tex]
The circle graph shows how Spencer spent his money in the month of July.
A circle graph representing Spencers expenses. 27 percent is clothing, 11 percent is Gasoline, 44 percent is Food and 18 percent is Entertainment.
Part A
If Spencer spent a total of $704.00 in the month of July, which is the best estimate for the amount of money he spent on clothing?
$70.00
$140.00
$210.00
$280.00
00:00
Part B
Which is the best estimate for the amount of money he spent on entertainment?
$140.00
$35.00
$105.00
$160.00
Answers
Answer:
$190.08
Step-by-step explanation:
Take 27% of the total $704 spent in July:
0.27($704) = $190.08
He spent an estimated $190.08 on clothing in July.
Answer:
Step-by-step explanation:
I THINK 140
A sphere is inscribed in a cube. Explain the relationship between the surface areas of the two solid figures
Answers
Answer:
No one knows. Jk just go look at the other brainly links. the question has already been asked and answered so you can go see them there.
Step-by-step explanation:
:)
In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. (a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03? Use a 95% confidence level. (Round your answer up to the nearest whole number.)
Answers
Answer:
A sample size of 657 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent.
This means that [tex]\pi = 0.19[/tex]
(a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03?
A sample size of n is needed.
n is found when [tex]M = 0.03[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.19*0.81}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.19*0.81}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.19*0.81}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.19*0.81}}{0.03})^{2}[/tex]
[tex]n = 656.91[/tex]
Rounding up to the nearest whole number.
A sample size of 657 is needed.
Writing Percents as Fractions
a. Write 35% as a fraction in simplest form.
35% =
35
100
Write as a fraction with
a denominator of 100.
7
20
Simplity.
Answers
Answer:
Answers are below
Step-by-step explanation:
Percent means "out of 100" so 35% is 35/100. We can simplify this fraction by dividing the numerator and denominator by 5. 35/100 / 5 = 7/20.
7/20 multiply the numerator and denominator by 5.
7/20 x 5 = 35/100
If this answer is correct, please make me Brainliest!
Answer:
b and c
Step-by-step explanation:
If u(x)=-2x^2+3 and v(x)=1/x, what is the range of (uov)(x)
Answers
Answer:
Do my question i will do yours
Step-by-step explanation:
Answer:
The Answer is C
Step-by-step explanation:
How do I type in exponents
Answers
Answer:
on what
Step-by-step explanation: normaly you have a button that you can have certain characters
You roll two dice. How many ways can you
roll a sum of 8 or a sum of 10?
Answers
Answer:
5 different ways
Step-by-step explanation:
for the 8
2 and 6
3 and 5
4 and 4
for then tens
5 and 5
4 and 6
Shira packs 170 lemon bars in boxes for the bake sale. Each box holds 8 lemon bars. She takes home the lemon bars tha are leg over after she has filled as many boxes as possible. Ahora use partial quotients to find how many boxes of lemon bars she can fill to sell at the bake sale. She finds only two partial quotients when she divides. Use the numbers in the box to answer the questions
1 2 7 8 20 21 23 27 29
Answers
Question:
1. How many full boxes of lemon bars can Shira fill?
2. How many delicious lemon bars will she be taking home?
Answer:
1. Number of filled box = 21
2. Number of take home = 2
Step-by-step explanation:
Given
Number of lemon bars = 170
Each bar contains 8 lemon bars
Required
(1) & (2)
To calculate the number of boxes Shira can fill, we simply divide the total number of bars by constituents of each bar .
i.e.
Number of filled box = 170/8
Number of filled box = 21.25
But here, we only need the quotient of the division because it represents the filled boxed.
So,
Number of filled box = 21
Calculating the number of take home.
We'll follow the same steps as (1) above but here, we only need the remainder of the division.
When 170 is divided by 8, the remainder is 2.
So, number of boxes she'll take home is 2.
See calculation below
Number of take home = 170 % 8
Number of take home = 2
Consider the graph of the exponential function, y =3(2)^x. The x- intercept of the graph is
Answers
Answer:
the x intercept is 2
Step-by-step explanation:
I just went over this unit
Answer:
2
Step-by-step explanation:
The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded. Was there a significant increase in the typical salesperson’s weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the p-value, and interpret it
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is
The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.
Salesperson Before After
Sid Mahone $320 $340
Carol Quick 290 285
Tom Jackson 421 475
Andy Jones 510 510
Jean Sloan 210 210
Jack Walker 402 500
Peg Mancuso 625 631
Anita Loma 560 560
John Cuso 360 365
Carl Utz 431 431
A. S. Kushner 506 525
Fern Lawton 505 619
Solution:
Corresponding income of salespersons before and after form matched pairs.
The data for the test are the differences between the income is salespersons.
μd = the income before minus their income after.
Bedore after diff
320 340 -20
290 285 5
421 475 - 54
510 510 0
210 210 0
402 500 - 98
625 631 -6
569 560 0
360 365 - 5
431 431 0
506 525 - 19
505 619 - 114
Sample mean, xd
= (- 20 + 5 - 54 + 0 + 0 - 98 - 6 + 0 - 5 + 0 + - 19 - 114)/12 = - 25.92
xd = - 25.92
Standard deviation = √(summation(x - mean)²/n
n = 12
Summation(x - mean)² = (- 20 + 25.92)^2 + (5 - 25.92)^2 + (- 54 + 25.92)^2+ (0 + 25.92)^2 + (0 + 25.92)^2 + ( - 98 + 25.92)^2 + ( - 6 + 25.92)^2 + (0 + 25.92)^2 + (- 5 + 25.92)^2 + (0 + 25.92)^2 + (- 19 + 25.92)^2 + (- 114 + 25.92)^2 = 17784.5168
Standard deviation = √(17784.5168/12
sd = 38.5
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
1) The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 12 - 1 = 11
2) The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = ( - 25.92- 0)/(38.5/√12)
t = - 2.33
3) We would determine the probability value by using the t test calculator.
p = 0.02
4) Assume alpha = 0.05
Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. We can conclude that at 5% significance level, there is a significant increase in the typical salesperson’s weekly income due to the innovative incentive plan
what is this phrase in numerical expression
triple the sum of seventeen and ten
pls help
Answers
Answer: so you would do 17 plus ten which is 27 so triple 3 so your answer is 27^3
Step-by-step explanation:
sum so your adding plus you need the exponent which is times 3
Trisomy 18 (T18) is a rare genetic disorder that severely disrupts a baby's development prior to birth. Many die before birth and most die before their first birthday. T18 occurs in only 1 in 2500 pregnancies in the U.S. A genetic test on the mother's blood can be done to test for T18 in her baby. The overall probability of a positive test result is 0.010384. The probability of a positive test result for a baby with T18 is 0.97. The probability of a negative test result for a baby without T18 is 0.99. A mother's blood tests positive for T18. What is the probability that her baby has T18
Answers
Answer:
3.74% probability that her baby has T18
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test.
Event B: The baby having T18.
T18 occurs in only 1 in 2500 pregnancies in the U.S.
This means that [tex]P(B) = \frac{1}{2500} = 0.0004[/tex]
The probability of a positive test result for a baby with T18 is 0.97.
This means that [tex]P(A|B) = 0.97[/tex]
The overall probability of a positive test result is 0.010384.
This means that [tex]P(A) = 0.010384[/tex]
What is the probability that her baby has T18
[tex]P(B|A) = \frac{0.0004*0.97}{0.010384} = 0.0374[/tex]
3.74% probability that her baby has T18
2. Inflation is at a rate of 7% per year. Evan's favorite bread now costs $1.79. What did it cost 10 years ago? How long
before the cost of the bread doubles?
Answers
Answer:
It cost $0.91 10 years ago.
It takes 10.24 years for the cost of bread to double.
Step-by-step explanation:
The equation for the price of bread after t years has the following format:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the current price, and r is the inflation rate, as a decimal.
If we want to find the price for example, 10 years ago, we find P(-10).
Inflation is at a rate of 7% per year. Evan's favorite bread now costs $1.79.
This means that [tex]r = 0.07, P(0) = 1.79[/tex]. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]P(t) = 1.79(1+0.07)^{t}[/tex]
[tex]P(t) = 1.79(1.07)^{t}[/tex]
What did it cost 10 years ago?
[tex]P(-10) = 1.79(1.07)^{-10} = 0.91[/tex]
It cost $0.91 10 years ago.
How long before the cost of the bread doubles?
This is t for which P(t) = 2P(0) = 2*1.79. So
[tex]P(t) = 1.79(1.07)^{t}[/tex]
[tex]2*1.79 = 1.79(1.07)^{t}[/tex]
[tex](1.07)^{t} = 2[/tex]
[tex]\log{(1.07)^{t}} = \log{2}[/tex]
[tex]t\log{1.07} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.07}}[/tex]
[tex]t = 10.24[/tex]
It takes 10.24 years for the cost of bread to double.
Three methods, A, B and C, are available for teaching a certain industrial skill. The failure rate is 15% for A, 5% for B and 10% for C. The method A is used 30%, B is used 40% and C is used 30% of the time. A worker is taught the skill by one of the methods but fails to learn it correctly. a. (10 points) What is the probability that he was taught by method A? b. (5 points) What is the probability of B given A?
Answers
Answer:
a) so the correct answer is that the probability that method A has been taught is 0.4737
b) the probability that B receives A is 0.5
Step-by-step explanation:
With the previous data we know that 3 methods teach an industrial skill and when putting into practice a worker does not learn, we have the failure rates like this:
method A fails 15%
method B fails: 5%
method C fails: 10%
usage percentages:
A: 30%
B: 40%
C: 30%
a) the probability that method A has been taught is as follows:
P (failure rate) = P (A) * P (failure rate A) + P (B) * P (failure rate B) + P (C) * P (failure rate C)
we replace the data obtaining:
P = 0.3 * 0.15 + 0.4 * 0.05 + 0.3 * 0.1 = 0.095
P ( failure rate A) = P (A) * P (failure rate A) / P (failure rate)
we replace the data obtaining:
0.3 * 0.15 / 0.095 = 0.4737
so the correct answer is that the probability that method A has been taught is 0.4737
b) the probability that B receives A is as follows:
P (B | A) = P (B) = 0.50
Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
Answers
Answer:
93.25% probability that they have taken this steroid
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test
Event B: Taking the steroid.
Suppose the probability of an athlete taking a certain illegal steroid is 10%.
This means that [tex]P(B) = 0.1[/tex]
Given that the athlete has taken this steroid, the probability of a positive test result is 0.995.
This means that [tex]P(A|B) = 0.995[/tex]
Positive test:
99.5% of 10%(If the athlete has taken).
100-99.2 = 0.8% of 100-10 = 90%(Athlete has not taken)
Then
[tex]P(B) = 0.995*0.1 + 0.008*0.9 = 0.1067[/tex]
Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.1*0.995}{0.1067} = 0.9325[/tex]
93.25% probability that they have taken this steroid
John wants to invest P dollars at a 4% interest rate. After 5 years the investment will be worth 2000 dollars. How much will it be worth in 11 years?
Answers
Answer:
About $2530.63
Step-by-step explanation:
The formula for this kind of calculation is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where P is the initial investment, r is the interest rate, n is the number of times you compound your investment per year, and t is the number of years. Assuming that you compound yearly, plugging in the numbers that you have given, you are left with:
[tex]2000=P(1+\frac{0.04}{1})^{t}[/tex]
[tex]2000=P\cdot (1.04)^5\\P\approx 1643.85\\A=1643.85 \cdot (1.04)^{11}\approx $2530.63[/tex]
Hope this helps!
100 POINTS
PLEASE PROVIDE STEPS. FOR BOTH
FIND THE INTEGRALS
Answers
Answer:
8. -⅓ cos³x + C
9. sec x + eˣ + C
Step-by-step explanation:
8. ∫ sin x cos²x dx
If u = cos x, then du = -sin x dx.
∫ -u² du
-⅓ u³ + C
-⅓ cos³x + C
9. ∫ (sec x tan x + eˣ) dx
∫ sec x tan x dx + ∫ eˣ dx
These are both standard integrals:
sec x + eˣ + C
Question 8:
∫sinxcos²xdx
∫-u²du (let u = cos(x))
-∫u²du
-u(^2+1)/2+1
-cos^(2+1)(x)/2+1
-1/3cos³(x)
-1/3cos³(x) + C
Question 9:
∫(secxtanx + eˣ)dx
∫sec(x)tan(x)dx + ∫eˣdx (apply sum rule)
sec(x) + eˣ (sec(x)tan(x)dx = sec(x) and eˣdx = eˣ)
sec(x) + eˣ + C
Best of Luck!
