Cumulative probability is a random variable determined by adding the probability density functions altogether, and its calculation can be defined as follows:
Cumulative function calculation:Random variable distributions are described using the cumulative distribution function. It can be applied to a discrete, continuous, or mixed variable to describe the probability.Given:
[tex]\to f(x)= \sqrt{x^2-1} \\\\\to g(x) = \sqrt{x^2+1}[/tex]
Find:
[tex]\to f(g(x))[/tex] and [tex]g(f(x))[/tex]
[tex]\to f(g(x))[/tex]
[tex]\to f(\sqrt{x^2+1})\\\\\to \sqrt{\sqrt{(x^2-1)+1}} \\\\\to \sqrt{\sqrt{x^2-1+1}} \\\\\to \sqrt{\sqrt{x^2}} \\\\\to \sqrt{x}} \\\\[/tex]
[tex]\to g(f(x))\\\\\to g(\sqrt{x^2-1})\\\\\to \sqrt{\sqrt{(x^2+1)-1}} \\\\\to \sqrt{\sqrt{x^2+1-1}} \\\\\to \sqrt{\sqrt{x^2}} \\\\\to \sqrt{x} \\\\[/tex]
Find out more about the cumulative function here:
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Ca anyone answer this??
Answer:*
*Can
Step-by-step explanation:
Which word phrase represents the numerical expression? (7 - 3) ÷ 2 *
The sum of seven and three, divided by two.
The sum of seven and three, multiplied by two.
The difference of seven and three, divided by two.
The difference of seven and three, multiplied by two.
Answer:
The difference of seven and three divided by two
Step-by-step explanation:
You do the operations in the parentheses first, according to PEMDAS.
1. In each of the following expressions, c represents the original cost of an item.
10.900
TL 0.10c
C -0.10c
a. Circle the expression(s) that represents 10% of the original cost. If more than one is
correct explain why the expressions you chose are equivalent.
represents ® D
b. Put a box around the expression(s) that represent the final item after a 10% decrease.
If more than one is correct explain why the expressions you chose are equivalent.
2. An item that was selling for $72.00 is reduced to $60.00. Find the percent decrease in
price. Round your answer to the nearest tenth.
3. A baseball team had 80 players shows up for tryouts last year and this year 96 players
show up for tryouts. Find the percent increase in players from last year to this year.
4. The price of a bag of bagels rose from $2.80 in January to $3.50 in April. What was the
percent increase of the price of a bag of bagels?
A 20%
B. 25%
C. 70%
D. 80%
5. Joe's weekly pay increased from $80 to $100. What is the percent increase in pay?
A 40%
B. 25%
C. 20%
D. 80%
Plzzzzz help
Find the values of x and y
Answer:
2x-10=x+80
2x-x=80+10
X=90
3y-4=y+20
3y-y=20+4
2y=24
Y=24/2
Y=12
Im not sure man, but i hope it helps, good luck :)
Tamu ran 30 minutes and burned 170 calories. How many calories did Tamu burn per minute. Write your answer as a decimal.
Answer:
170/30= 5.6
Step-by-step explanation:
There should also be a line like - over the 6
During an experiment, Aika measured the time it took for a ball to roll down a ramp set at an angle. She measured that it took 1.010 seconds. The exact time it should take based on calculations is 0.904 seconds. What was her experimental error?
Answer:
11.725%
Step-by-step explanation:
Given that :
True value = 0.904 seconds
Measured time = 1.010 seconds
Experimental error :
(|measured value - True value | / true value) * 100%
(|1.010 - 0.904| ÷ 0.904) * 100%
= 0.106 / 0.904 * 100%
= 0.1172566 * 100%
= 11.725%
Answer:
11.725%
Step-by-step explanation:
The area A of a circle in square feet with a radius r in feet is given by the formula, A=πr2. What is the area of a circle with a radius of 3 feet? Round your answer to the nearest thousandths.
Answer:
28.29
Step-by-step explanation:
A=πr2
=3.14(3^2) (btw the ^2 is exponent)
=3.14(9)
=28.29
Quadrilateral ABCD was translated 4 units to the left and 2 units down to create Quadrilateral A'B'C'D', Which rule describes this transformation?
(xy) -> (x + 4. y + 2)
(x,y) -> (x - 4. y - 2)
(x,y) -> (x - 4y + 2)
(x,y) --> (x - 2. y + 4)
Answer:
(x,y) -> (x - 4. y - 2)
Last year, nine employees of an electronics company retired. Their ages at retirement are listed below.
56 65 62 53 68 58 65 52 56
Find the median retirement age. Round your answer to one more decimal place than is present in the original data values.
Answer:
58.0
Step-by-step explanation:
Given the data:
56 65 62 53 68 58 65 52 56
Reorderd data: 52, 53, 56, 56, 58, 62, 65, 65, 68
Median = 1/2(n + 1) th term
n = sample size = 9
Hence,
Median = 1/2(9 + 1)th term
Median = 1/2(10)th term
Median = 5th term
5th term in the reordered data = 58
Hence, median age is 58
There were five winning lottery tickets for a total jackpot of 40,000. 3 of the winners won twice as much as the other two. how much did each of the two that won the least get?
There are five prizes available on the 1000 lottery tickets that were sold, assuming Saket purchased one. Only 0.005% of participants will win something.
What does the term probability mean?Probability measures how likely an event is to occur. It's difficult to know everything that will happen in advance. We can only forecast how likely an event is to occur using it, or how likely it is to occur.The likelihood of an event occurring is determined by probability: P(A) = f / N. Probability and odds are related, but probability is necessary for odds to exist. Probability is required before calculating the likelihood of an event. Classical, empirical, subjective, and axiomatic viewpoints are the four most popular approaches to probability.Here is an easy use of probability in daily life that you probably already utilize. Before we organize a significant outing, we always consult the weather prediction. The forecaster will occasionally say that there is a 60% chance of rain.Given,
Total number of outcomes =1000
Favorable outcomes =5
Simplify, 5 ÷ 1000
Then we get,
∴ Required probability = 0.005.
The complete question is:
1000 tickets of a lottery were sold and there are 5 prizes on these tickets, if Saket has purchased one lottery ticket. What is the probability of wining a prize ?
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3
Simplify the expression below:
20 – 10y – 7y + 9
Answer:
y = 1.705882353
Step-by-step explanation:Combine like terms: 20 + 9 = 29
29 + -10y + -7y = 0
Combine like terms: -10y + -7y = -17y
29 + -17y = 0
Solving
29 + -17y = 0
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-29' to each side of the equation.
29 + -29 + -17y = 0 + -29
Combine like terms: 29 + -29 = 0
0 + -17y = 0 + -29
-17y = 0 + -29
Combine like terms: 0 + -29 = -29
-17y = -29
Divide each side by '-17'.
y = 1.705882353
Simplifying
y = 1.705882353
Pete dad usually deposits $25 into his bank account every week.for the next weeks he wants to deposit more than the usually $25 and he wants the extra amount deposited to be the same each week.Which inequality and solution show how much more he can deposit each week and keep the total of his deposit above $500 for those 8 weeks? Yo
Answer:
The answer is "8(25+x)>500;x>37.50".
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\to 8(25+x)>500\\\\\to 200 +8x>500\\\\\to 8x> 300\\\\\to x> \frac{300}{8}\\\\\to x> 37.50[/tex]
That's why above given choice is correct.
Help please ASAP giving brainly and giving 64 points please
the answer is three i think
x = 3 because the only equation to get five would be 3. 2 plus 3 is 5. 3 plus 2 is also five. So three is the answer.
tile model
X 1 1 1 = 1 1 1 1 1
X = 3
Answer:
for the first one x = 4
for the second one x = -8
Step-by-step explanation:
x − 7 + 7= −3 + 7 so x = 4
x + 3 − 3= −5 − 3 so x = -8
A pharmacist has 600 milliliters of a solution that is 30% active ingredient. How much pure water should she add to the solution to get a solution that is 15% active ingredient?
Answer:
600 ml of pure water.
Step-by-step explanation:
To determine how much pure water the pharmacist should add to a 600ml solution with 30% active ingredient, so that this solution becomes 15%, the following calculation must be performed:
600 x 0.3 = 180
15 = 180
100 = X
100 x 180/15 = X
18,000 / 15 = X
1,200 = X
1,200 - 600 = 600
Thus, 600 ml of pure water should be added to achieve a 15% solution.
The width of a rectangle is shown below:
A coordinate plane with a point A at negative 4, 4 and C at negative 4, negative 3.
If the area of the rectangle to be drawn is 42 square units, where should points B and D be located if they lie to the right of points A and C?
Answer:
D
Step-by-step explanation:
(2, 4) and D(2, −3)
Donovan is playing a word game with letter tiles. Players earn 10 points for every word they make with the tiles., plus 5 extra points if a word has 6 or more letters. At the end of the game, 3 points are taken away for each tile not used. Write an expression to represent Donovan's total score if one of his words contains 6 letters.
Answer:
10w-3t+5
Step-by-step explanation:
The expression represents Donovan's total score if one of his words contains 6 letters is 10w-3t+5.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
Let's say the number of words written is w and the number of tiles is t.
As per the given,
Players earn 10 points so 10w will be points through words.
3 points taken away thus -3t.
One word contains 6 letters thus +5 points.
Total score = 10w - 3t + 5.
Hence "The expression represents Donovan's total score if one of his words contains 6 letters is 10w-3t+5".
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Olive weights are classified according to a unique set of adjectives implying great size. For example, the mean weight of olives classified as "Colossal" is 7.7 grams. Suppose a particular company’s crop of "Colossal" olives is approximately Normally distributed with a mean of 7.7 grams and a standard deviation of 0.2 grams. Which of the following represents the probability that the mean weight of a random sample of 3 olives from this population is greater than 8 grams?
a. 0.0970
b. 0.9953
c. 0.0668
d. 0.0047
e. 0.1932
Answer:
d. 0.0047
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
We have that [tex]\mu = 7.7, \sigma = 0.2[/tex]
Sample of 3:
[tex]n = 3, s = \frac{0.2}{\sqrt{3}} = 0.1155[/tex]
Which of the following represents the probability that the mean weight of a random sample of 3 olives from this population is greater than 8 grams?
This is 1 subtracted by the pvalue of Z when X = 8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8 - 7.7}{0.1155}[/tex]
[tex]Z = 2.6[/tex]
[tex]Z = 2.6[/tex] has a pvalue of 0.9953
1 - 0.9953 = 0.0047
The probability is given by option d.
You can calculate the z score for the specified sample and then use the z tables to find the p value(probability) needed.
The probability that the mean weight of a random sample of 3 olives from this population is greater than 8 grams is given by
Option d : 0.0047
How to find the z score for a sample taken from a normal distribution holding random variate?Suppose that the sample is of size 'n', then we have the z score(we are converting random variable X to standard random variable Z) as:
[tex]Z = \dfrac{X - \overline{x}}{s} = \dfrac{X - \mu}{\sigma/\sqrt{n}}[/tex]
where [tex]\overline{x}[/tex] is mean of the sample
s is the standard deviation of the sample,
and we used the central limit theorem which says that a sample from a normally distributed population with [tex]mean = \mu[/tex] and standard deviation = [tex]\sigma[/tex] can have its mean approximated by population mean and its standard deviation approximated by [tex]s = \dfrac{\sigma}{\sqrt{n}}[/tex]
Using the data given to find the intended probabilityLet the weight of the the olives for the given crop of olives of a particular company for taken random sample is given by X (a random variable)
Then, we have:
[tex]X \sim N(7.7, 0.2)[/tex]
where
[tex]\mu = 7.7, \sigma = 0.2[/tex]
Thus, we have:
[tex]\overline{x} = \mu, s = \sigma/\sqrt{n} = 0.2/\sqrt{3}[/tex]
Using the given facts, we get the needed probability as:
[tex]P( X> 8)[/tex] sample size n = 3)
Then, using the z score, we get):
[tex]P(X > 8) = 1 - P(X \leq 8) = 1 - P(Z \leq \dfrac{8 - 7.7}{0.2/\sqrt{3}})\\\\P(X > 8)=1- P(Z \leq \dfrac{0.3\sqrt{3}}{0.2}) = 1- P(Z \leq 1.5 \times \sqrt{3} )\\\\P(X > 8) = 1 - P(Z \leq 2.59) = 1- 0.9952 \approx 0.0047[/tex]
Thus,
The probability that the mean weight of a random sample of 3 olives from this population is greater than 8 grams is given by
Option d : 0.0047
Learn more about standard normal distribution here:
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Korl spent $46.20 on 12 gallons. what was the price per gallon?
Answer:
3.85
Step-by-step explanation:
46.20/12
12 goes into 46.20
3.85
The area of rectangle RSTU is 36x2+25x−25. The length of the rectangle RSTU is 4x+5. Which expression describes the width of the rectangle RSTU?
Given:
The area of the rectangle RSTU = [tex]36x^2+25x-25[/tex]
Length of the rectangle RSTU = [tex]4x+5[/tex]
To find:
The width of the rectangle RSTU.
Step-by-step explanation:
We have,
[tex]36x^2+25x-25[/tex]
Splitting the middle term, we get
[tex]=36x^2+45x-20x-25[/tex]
[tex]=9x(4x+5)-5(4x+5)[/tex]
[tex]=(4x+5)(9x-5)[/tex]
We know that, the area of a rectangle is
[tex]Area=Length \times width[/tex]
Area of rectangle is product of (4x+5) and (9x-5).
Since (4x+5) is the length of the rectangle, therefore, (9x-5) is the width of the rectangle RSTU.
Find the domain and range of the relation.
please please help me
Answer:
The domain of the relation is [tex]D = [-2,\infty)[/tex]
The range of the relation is [tex]R = (-\infty, \infty)[/tex]
Step-by-step explanation:
Domain and range:
Domain is considered to be the input values, in a graph, the values of x.
Range is considered to be the output values, in a graph, the values of y.
In this graph:
x starts at -2 and goes to infty. So the domain is: [tex]D = [-2,\infty)[/tex]
As for y, the arrows indicates it goes to infinity. So [tex]R = (-\infty, \infty)[/tex]
HELP MIDDLE SCHOOL QUESTION
answer:
26.563 miles.
step-by-step explanation:
5.123 + 6.34 + 7.1 + 8 = 26.563
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Type using number words. (Remember to use a hyphen in your answer where needed.)
355
I need a answer Plss sombody help me
Answer:
add 4 and 2
because you always have to simplify numbers that are inside the parentheses.
HELPPPPPPPPPPPPPPPPPPpppp
Answer:
Step-by-step explanation:
Part A:
Add all the mass together so 1,105.5 grams
Complex Numbers I need help
Answer:
Answer is (4+3i)+(5-6i)=(9-3i)
Step-by-step explanation:
I hope it's helpful!
==============================================
Work Shown:
(4+3i) + (5-6i)
4+3i + 5-6i
(4+5) + (3i-6i)
9 + (3-6)i
9 + (-3)i
9 - 3i
As the steps above show, we treat the 'i' as a variable. So we could think of the expression as (4+3x)+(5-6x) and simplify to get 9-3x. Though we use ''i' instead of x.
f(n) = (2n – 2) + 2; 52 ( PLEASE ANSWER QUCIKLY WILL GIVE BRAINLIEST AND THANKS PLEASEEEEE!!!!!!) FIND THE POSITION FOR THE GIVEN TERM
Answer:
[tex]n =26[/tex]
Step-by-step explanation:
Given
[tex]f(n) = (2n - 2) + 2[/tex]
Required
Find n when [tex]f(n) = 52[/tex]
Substitute 52 for f(n) in [tex]f(n) = (2n - 2) + 2[/tex]
[tex]52 = (2n - 2) + 2[/tex]
Remove bracket
[tex]52 = 2n - 2 + 2[/tex]
[tex]52 = 2n[/tex]
Make n the subject
[tex]n = \frac{52}{2}[/tex]
[tex]n =26[/tex]
The position is 26
A builder is using the scale drawing below to build a house. If the owner decides to increase the living room dimensions by 25%,what is the new length and width of the living room floor? (1cm=5 feet)
Answer:
Step-by-step explanation:
Building scale is 1cm=5feet
This means 1 cm is equivalent to 5 feet
If 1 cm is equals to 5 feet and the owner wants a 25% increase in dimension, this means;
25/100 =0.25.
0.25 x the actual dimension
0.25 x 5 = 1.25
1.25 + actual dimension
1.25 + 5 = 6.25.
This means the scale of the room will be on 1cm =6.25feet.
If the length of the room is A, the width is B;
The new length will then be 1.25 x A =1.25A
1.25A + A
The length of the new room is 1.25A +A
While the width of the new room is 1.25B +B
What is the value of x?
Answer:
4
simplied=2
Step-by-step explanation:
10²=8²+x²
10²=8²-x²
20=16-x²
x²=4
Simplied=2
Skylar invested $8,900 in an account paying an interest rate of 2.6% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to
the nearest dollar, would be in the account after 11 years?
Answer:
11847
Step-by-step explanation:
8900e ^0.026(11)
8900e^0.286
11846.7228518
answer 11847
Answer: 11749
Step-by-step explanation:
A=Pe
rt
=
5500
=
0.069
=
11
P=5500r=0.069t=11
Given values
=
5500
0.069
(
11
)
A=5500e
0.069(11)
Plug in
=
5500
0.759
A=5500e
0.759
Multiply
=
11748.7645718
A=11748.7645718
Use calculator (with e button)
≈
11749
A≈11749
Round to nearest dollar
The two trapezoids below are similar. What is the length of EF
Answer:
answer is 6
Step-by-step explanation:
i know answer is 2 weeks late