Answer:
40% probability that the package was weighed by Employee C
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: Incorrect package.
Event B: Weighed by Employee C.
A supermarket has three employees who equally packages and weighs produce.
This means that [tex]P(B) = \frac{1}{3}[/tex]
Employee C records the correct weight 94% of the time
So incorrectly 6% of the time, which means that [tex]P(A|B) = 0.06[/tex]
Probability of an incorrect package:
4% of 1/3(A)
5% of 1/3(B)
6% of 1/3(C)
So
[tex]P(A) = \frac{0.04 + 0.05 + 0.06}{3} = 0.05[/tex]
What is the probability that the package was weighed by Employee C?
[tex]P(B|A) = \frac{\frac{1}{3}*0.06}{0.05} = 0.4[/tex]
40% probability that the package was weighed by Employee C
Which is the graph |3x-6|=21
Answer:
it should look like this
A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 22 is made, and it is found that they have a mean of 2045.0 millimeters with a standard deviation of 13.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
Step-by-step explanation:
Information given
[tex]\bar X=2045[/tex] represent the sample mean
[tex]s=13[/tex] represent the standard deviation
[tex]n=22[/tex] sample size
[tex]\mu_o =2058[/tex] represent the value to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to cehck if the true mean for this case is equal to 2058 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2058[/tex]
Alternative hypothesis:[tex]\mu \neq 2058[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
ABCD is rhombus. DC = 5cm, AC = 6cm. Find the length of BD
Answer:
BD = 8Cm
Step-by-step explanation:
Given:
DC = 5cm
AC = 6cm.
Find;
BD = ?
Computation:
Rhombus's diagonal bisect each other at 90°
Using Pythagoras theorem
OD = [tex]\sqrt{AD^2-OA^2}[/tex]
OD = [tex]\sqrt{5^2-3^2}[/tex]
OD = 4 CM
So, BD = 2(OD)
BD = 2(4)
BD = 8Cm
Joe wants to saw a wooden plank into 3/4 -meter pieces. The length of the wooden plank is 15/4meters. How many 3/4 -meter pieces can Joe saw from the wooden plank?
Answer:
3 wooden plank he can saw
Answer:
he can saw 3 wooden planks
Step-by-step explanation:
The time a student sleeps per night has a distribution with mean 6.3 hours and a standard deviation of 0.6 hours. Find the probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night. Answer: (round to 4 decimal places)
Answer:
0.0154 = 1.54% probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
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.
In this question, we have that:
[tex]\mu = 6.3, \sigma = 0.6, n = 42, s = \frac{0.6}{\sqrt{42}} = 0.0926[/tex]
Find the probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
This is 1 subtracted by the pvalue of Z when X = 6.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{6.5 - 6.3}{0.0926}[/tex]
[tex]Z = 2.16[/tex]
[tex]Z = 2.16[/tex] has a pvalue of 0.9846
1 - 0.9846 = 0.0154
So
0.0154 = 1.54% probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year. If you had purchased a house in Midvale, UT for $ 172000 in 2004 in what year would the home be worth $ 249000 ?
Answer:
The home would be worth $249000 during the year of 2012.
Step-by-step explanation:
The price of the home in t years after 2004 can be modeled by the following equation:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the price of the house in 2004 and r is the growth rate.
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.
This means that [tex]r = 0.047[/tex]
$172000 in 2004
This means that [tex]P(0) = 172000[/tex]
What year would the home be worth $ 249000 ?
t years after 2004.
t is found when P(t) = 249000. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]249000 = 172000(1.047)^{t}[/tex]
[tex](1.047)^{t} = \frac{249000}{172000}[/tex]
[tex]\log{(1.047)^{t}} = \log{\frac{249000}{172000}}[/tex]
[tex]t\log(1.047) = \log{\frac{249000}{172000}}[/tex]
[tex]t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}[/tex]
[tex]t = 8.05[/tex]
2004 + 8.05 = 2012
The home would be worth $249000 during the year of 2012.
Find two consecutive even integers whose sum is -50. Which of the following equations could be used to solve the problem? A) 2 x + 2 = -50 B) 2 x = -50 C) 2 x + 1 = -50 D) x^2 + 1= -50
Answer:
[tex]2x+2=-50[/tex]
Step-by-step explanation:
[tex]x+2=y\\x+y=-50\\x+x+2=-50\\2x+2=-50[/tex]
The equation that can be used to find out [tex]x[/tex] and [tex]y[/tex] is [tex]2x+2=-50[/tex]
Answer:
[tex]\mathrm{A}[/tex]
Step-by-step explanation:
Two consecutive even integers.
The first integer is even and can be as [tex]x[/tex]
The second integer is also even and can be as [tex]x+2[/tex]
Their sum is [tex]-50[/tex]
[tex]x+x+2=-50[/tex]
[tex]2x+2=-50[/tex]
A courier service claims that 5% of all of its deliveries arrive late. Assuming the claim is true and deliveries are independent, a sample of 10 deliveries is randomly selected. What is the probability that more than 2 of the sample deliveries arrive late
Answer:
The probability that more than 2 of the sample deliveries arrive late = 0.0115
Step-by-step explanation:
This is a binomial distribution problem
A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.
It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.
The probability of each delivery arriving late = 5% = 0.05
- Each delivery is independent from the other.
- There is a fixed number of deliveries to investigate.
- Each delivery has only two possible outcomes, a success or a failure of arriving late.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of deliveries we're considering = 10
x = Number of successes required = number of deliveries that we expect to arrive late = more than 2 = > 2
p = probability of success = probability of a delivery arriving late = 0.05
q = probability of failure = probability of a delivery NOT arriving late = 0.95
P(X > 2) = 1 - P(X ≤ 2)
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.59873693924 + 0.31512470486 + 0.07463479852
= 0.98849644262
P(X > 2) = 1 - P(X ≤ 2)
= 1 - 0.98849644262
= 0.01150355738
= 0.0115
Hope this Helps!!!
Please answer this correctly
Description:
As we that that 3 of the students voted for counting .
4 Students voted for sorting
6 Students voted for shapes
7 Students voted for addition
Answer:
Counting - 3%
Sorting - 4%
Shapes- 6%
Addition- 7%
Please mark brainliest
Hope this helps.
Answer:
Counting: 15%
Sorting: 20%
Shapes: 30%
Addition: 35%
Step-by-step explanation:
Counting: [tex]\frac{3}{3+4+6+7} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%
Sorting: [tex]\frac{4}{3+4+6+7} =\frac{4}{20} =\frac{20}{100} =[/tex] 20%
Shapes: [tex]\frac{6}{3+4+6+7} =\frac{6}{20} =\frac{30}{100} =[/tex] 30%
Addition: [tex]\frac{7}{3+4+6+7} =\frac{7}{20} =\frac{35}{100} =[/tex]35%
There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. How many of these sets contain any 2 numbers? PLS HELP I'M REALLY STUCK AND DON'T JUST STEAL THE POINTS PLEASE
Answer:
90
Step-by-step explanation:
it is 90 because in the first slot there can be any 10 numbers and in the second slot the set can contain any of the remaining 9 numbers and then we can multiply these two numbers together to find the total amount of sets.
hope this helps :)
Answer:
45 different sets
Step-by-step explanation:
There are 10 numbers in {0,1,2,3,4,5,6,7,8,9}.
We are looking for a combination since order doesn't mater
There are 10 options for the first number
We have chosen 1
Now there are 9 numbers
10*9
But since order doesn't matter, we divide by 2
The set {1,2} is the same as the set {2,1}
90/2 = 45
The height of the triangle is 10 cm. It is decreased by 25%. Calculate the new height.
Decreased height = 10 x [tex]\frac{100 - 25}{100}[/tex]
= 10 x [tex]\frac{75}{100}[/tex]
= [tex]\frac{750}{100}[/tex]
= 7.5 cm
Answer:
7.5 cm
Step-by-step explanation:
Decreased height = 25% of 10
[tex]=\frac{25}{100}*10\\\\=0.25*10\\=2.5[/tex]
New height = 10 - 2.5 = 7.5 cm
11) At a certain company, an HR benefits meeting and shareholders meeting happen at the same time, so it is impossible for an employee to be at both. If the probability that an employee goes to the HR benefits meeting is 0.33, and the probability that an employee goes to the shareholders meeting is 0.66, what is the probability that an employee
Answer:
0.99
Step-by-step explanation:
The computation of the probability for employee goes for shareholder meeting or HR benefits meeting is
= Probability of HR benefits meeting + Probability of shareholder meeting
= 0.33 + 0.66
= 0.99
We simply added the both meeting probability i.e HR benefits and shareholder meeting so that the given probability could come
The waiting time in line at an ice cream shop has a uniform distribution between 3 and 14 minutes. What is the 75th percentile of this distribution? (Recall: The 75th percentile divides the distribution into 2 parts so that 75% of area is to the left of 75th percentile) _______ minutes Answer: (Round answer to two decimal places.)
Answer:
The 75th percentile of this distribution is 11 .25 minutes.
Step-by-step explanation:
The random variable X is defined as the waiting time in line at an ice cream shop.
The random variable X follows a Uniform distribution with parameters a = 3 minutes and b = 14 minutes.
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b;\ a<b[/tex]
The pth percentile is a data value such that at least p% of the data-set is less than or equal to this data value and at least (100-p)% of the data-set are more than or equal to this data value.
Then the 75th percentile of this distribution is:
[tex]P (X < x) = 0.75[/tex]
[tex]\int\limits^{x}_{3} {\frac{1}{14-3}} \, dx=0.75\\\\ \frac{1}{11}\ \cdot\ \int\limits^{x}_{3} {1} \, dx=0.75\\\\\frac{x-3}{11}=0.75\\\\x-3=8.25\\\\x=11.25[/tex]
Thus, the 75th percentile of this distribution is 11 .25 minutes.
Solve 2cos3x=0.9.
Pls help me with this trigonometric equations with multiple angles.
Answer:
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
Step-by-step explanation:
Given: [tex]2 cos(3x)=0.9[/tex]
To find: solutions of the given equation
Solution:
Triangle is a polygon that has three sides, three angles and three vertices.
Trigonometry explains relationship between the sides and the angles of the triangle.
Use the fact: [tex]cos x=a[/tex]⇒[tex]x=cos^{-1}(a)+2n\pi,x=2\pi-cos^{-1}(a)+2n\pi[/tex]
[tex]2 cos(3x)=0.9[/tex]
Divide both sides by 2
[tex]cos(3x)=\frac{0.9}{2}=0.45[/tex]
[tex]3x=cos^{-1}(0.45)+2n\pi,3x=2\pi- cos^{-1}(0.45)+2n\pi[/tex]
So,
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
100 pts. This is an assignment because multiple people asked this question. Find the sum of the digits of the number 6+66+666+6666 + ... +666...66, where the last number contains 100 digits.
The answer is attached.
Answer:
(20/27)(10^100 - 1) -200/3
log 3=.4771 log 5=.6990 find the value of log 150
Answer:
2.17609
Step-by-step explanation:
Easiest and fastest way is to just directly plug log base 10 of 150 into the calc, as it is a nasty decimal.
What type of angle is angle M?
c.
L
in
Practice
с
s in
- Space of
M
P.
nes and
O A. obtuse
and Proofs
O Bright
of
rap-Up
O C. acute
OD. straight
Answer:
B
Step-by-step explanation:
right
have a good day, hope this helps
Luke and skylar work at furniture store. Luke is paid $180 per week plus 5% of his total sales in dollars ,x,which can be represented by g(x)=180+0.05x. Skylar is paid $104 per week plus 7% of her total sales in dollars which can be represented by f(x)=104+0.07x. Determine the value of x in dollars that will make their weekly pay the same
Answer:
The total sales in dollars to make their pay equal is: $ 3800
Step-by-step explanation:
Since we need to find the number of sales that make both function equal in value, we equal both expressions, and solve for 'x":
[tex]180+0.05 \,x=104+0.07 \,x\\180-104=0.07\,x-0.05\,x\\76=0.02x\\x=\frac{76}{0.02} \\x=3800[/tex]
In a sample of 1200 U.S.​ adults, 191 dine out at a resaurant more than once per week. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​ adults, complete parts​ (a) through​ (d). ​Required:a. Find the probability that both adults dine out more than once per week. b. Find the probability that neither adult dines out more than once per week. c. Find the probability that at least one of the two adults dines out more than once per week. d. Which of the events can be considered unusual? Explain.
Answer:
a) The probability that both adults dine out more than once per week = 0.0253
b) The probability that neither adult dines out more than once per week = 0.7069
c) The probability that at least one of the two adults dines out more than once per week = 0.2931
d) Of the three events described, the event that can be considered unusual because of its low probability of occurring, 0.0253 (2.53%), is the event that the two randomly selected adults both dine out more than once per week.
Step-by-step explanation:
In a sample of 1200 U.S. adults, 191 dine out at a restaurant more than once per week.
Assuming this sample.is a random sample and is representative of the proportion of all U.S. adults, the probability of a randomly picked U.S. adult dining out at a restaurant more than once per week = (191/1200) = 0.1591666667 = 0.1592
Now, assuming this probability per person is independent of each other.
Two adults are picked at random from the entire population of U.S. adults, with no replacement, thereby making sure these two are picked at absolute random.
a) The probability that both adults dine out more than once per week.
Probability that adult A dines out more than once per week = P(A) = 0.1592
Probability that adult B dines out more than once per week = P(B) = 0.1592
Probability that adult A and adult B dine out more than once per week = P(A n B)
= P(A) × P(B) (since the probability for each person is independent of the other person)
= 0.1592 × 0.1592
= 0.02534464 = 0.0253 to 4 d.p.
b) The probability that neither adult dines out more than once per week.
Probability that adult A dines out more than once per week = P(A) = 0.1592
Probability that adult A does NOT dine out more than once per week = P(A') = 1 - P(A) = 1 - 0.1592 = 0.8408
Probability that adult B dines out more than once per week = P(B) = 0.1592
Probability that adult B does NOT dine out more than once per week = P(B') = 1 - P(B) = 1 - 0.1592 = 0.8408
Probability that neither adult dines out more than once per week = P(A' n B')
= P(A') × P(B')
= 0.8408 × 0.8408
= 0.70694464 = 0.7069 to 4 d.p.
c) The probability that at least one of the two adults dines out more than once per week.
Probability that adult A dines out more than once per week = P(A) = 0.1592
Probability that adult A does NOT dine out more than once per week = P(A') = 1 - P(A) = 1 - 0.1592 = 0.8408
Probability that adult B dines out more than once per week = P(B) = 0.1592
Probability that adult B does NOT dine out more than once per week = P(B') = 1 - P(B) = 1 - 0.1592 = 0.8408
The probability that at least one of the two adults dines out more than once per week
= P(A n B') + P(A' n B) + P(A n B)
= [P(A) × P(B')] + [P(A') × P(B)] + [P(A) × P(B)]
= (0.1592 × 0.8408) + (0.8408 × 0.1592) + (0.1592 × 0.1592)
= 0.13385536 + 0.13385536 + 0.02534464
= 0.29305536 = 0.2931 to 4 d.p.
d) Which of the events can be considered unusual? Explain.
The event that can be considered as unusual is the event that has very low probabilities of occurring, probabilities of values less than 5% (0.05).
And of the three events described, the event that can be considered unusual because of its low probability of occurring, 0.0253 (2.53%), is the event that the two randomly selected adults both dine out more than once per week.
Hope this Helps!!!
Expand 2x(5x-2)
Help please ?
Answer: 10x^2 - 4x
Step-by-step explanation:
To expand, you are not simplifying, so multiplying out is the answer here. To do this, use the distributive property. The distributive property in this case means that if you are multiplying one number by a whole expression inside parenthesis, multiply the one number by each term in the expression:
2x(5x - 2)
= 2x(5x) + 2x(-2)
= 10x^2 - 4x
The product of the expression is equivalent to -
10x² - 4x.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as follows -
2x(5x - 2)
The given expression is -
2x(5x - 2)
10x² - 4x
Therefore, the product of the expression is equivalent to -
10x² - 4x.
To solve more questions on expression evaluation, visit the link below -
brainly.com/question/1041084
#SPJ5
Which of the following is the solution to 9|x-1|=-45
Answer:
No solutions.
Step-by-step explanation:
9|x-1|=-45
Divide 9 into both sides.
|x-1| = -45/9
|x-1| = -5
Absolute value cannot be less than 0.
Answer:
No solution
Step-by-step explanation:
=> 9|x-1| = -45
Dividing both sides by 9
=> |x-1| = -5
Since, this is less than zero, hence the equation has no solutions
Pleassseee hhheeelllppp
Answer/Step-by-step explanation:
When solving problems like this, remember the following:
1. + × + = +
2. + × - = -
3. - × + = -
4. - × - = +
Let's solve:
a. (-4) + (+10) + (+4) + (-2)
Open the bracket
- 4 + 10 + 4 - 2
= - 4 - 2 + 10 + 4
= - 6 + 14 = 8
b. (+5) + (-8) + (+3) + (-7)
= + 5 - 8 + 3 - 7
= 5 + 3 - 8 - 7
= 8 - 15
= - 7
c. (-19) + (+14) + (+21) + (-23)
= - 19 + 14 + 21 - 23
= - 19 - 23 + 14 + 21
= - 42 + 35
= - 7
d. (+5) - (-10) - (+4)
= + 5 + 10 - 4
= 15 - 4 = 11
e. (-3) - (-3) - (-3)
= - 3 + 3 + 3
= - 3 + 9
= 6
f. (+26) - (-32) - (+15) - (-8)
= 26 + 32 - 15 + 8
= 26 + 32 + 8 - 15
= 66 - 15
= 51
Please help mehhh please!!
Answer:
1
Step-by-step explanation:
The mean is the average of the sum of all integers in a data set.
Caroline has 2 pieces of cheese, Samuel has 4 pieces of cheese, Abby has 4 pieces of cheese, and Jason has 2 pieces of cheese
2 + 4 + 4 + 2 = 12
12 divides by 4, since there are 4 people, to equal the mean
12 / 4 = 3
Now since we have the mean, find the distance from the mean to each number
3 - 2 = 1
4 - 3 = 1
4 - 3 = 1
3 - 2 = 1
1 + 1 + 1 + 1 = 4
4 / 4 = 1
A graph has points (3, 9), (4, 13.5), and (5, 18). Given the graph of a linear function, identify the steps used to find the initial value. Check all that apply. Find the rate of change using rise over run. Find corresponding y values when x = 6, x = 7, and x = 8. Then plot the points to finish the line. Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line. The initial value corresponds to the y value when x = 1. The initial value corresponds to the y value when x = 0.
Answer:
its A, C, E on edg
Step-by-step explanation:
Answer:
a c e
Step-by-step explanation:
LU 1
- 2x + 3 < 5 and - 4x – 3 > 9
Answer: x>-1
x<-3
Step-by-step explanation:
[tex]-2x+3<5[/tex]
subtract 3 on both sides
[tex]-2x<2[/tex]
divide -2 on both sides
[tex]x>-1[/tex]
The sign changed because I divided by a negative.
[tex]-4x-3>9[/tex]
add 3 on both sides
[tex]-4x>12[/tex]
multiply -1 on both sides
[tex]4x<-12[/tex]
divide 4 on both sides
[tex]x<-3[/tex]
Brainlist please
Answer:
x > -1
x < -3
Step-by-step explanation:
-2x + 3 < 5
Subtract 3 on both sides.
-2x < 5 - 3
-2x < 2
Divide -2 into both sides.
x < 2/-2
x > -1
-4x - 3 > 9
Add 3 on both sides.
-4x > 9+3
-4x > 12
Divide -4 into both sides.
x > 12/-4
x < -3
Write 7^4 as a multiplication expression
Answer:
Exponents are simply repeated multiplication so the answer is 7 * 7 * 7 * 7.
A portfolio has average return of 13.2 percent and standard deviation of returns of 18.9 percent. Assuming that the portfolioi's returns are normally distributed, what is the probability that the portfolio's return in any given year is between -43.5 percent and 32.1 percent?
A. 0.950
B. 0.835
C. 0.815
D. 0.970
Answer:
B. 0.835
Step-by-step explanation:
We can use the z-scores and the standard normal distribution to calculate this probability.
We have a normal distribution for the portfolio return, with mean 13.2 and standard deviation 18.9.
We have to calculate the probability that the portfolio's return in any given year is between -43.5 and 32.1.
Then, the z-scores for X=-43.5 and 32.1 are:
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{(-43.5)-13.2}{18.9}=\dfrac{-56.7}{18.9}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{32.1-13.2}{18.9}=\dfrac{18.9}{18.9}=1\\\\\\[/tex]
Then, the probability that the portfolio's return in any given year is between -43.5 and 32.1 is:
[tex]P(-43.5<X<32.1)=P(z<1)-P(z<-3)\\\\P(-43.5<X<32.1)=0.841-0.001=0.840[/tex]
what is the Y intercept of the quadratic function f(x)=(x-6)(x+3)
Answer:
(0,-24)Option C is the correct option.
Solution,
Given that,
[tex]f(x) = (x - 8)(x + 3)[/tex]
put f(x)=y
[tex]y(x - 8)(x + 3) - - > equation \: (i)[/tex]
For finding y- intercept
put x=0
We get,
[tex]y = (0 - 8)(0 + 3) - - > from \: {eq}^{n} \: (i)[/tex]
[tex]y = ( - 8) \times 3 \\ y = - 24 \\ y - intercept = (0 ,- 24)[/tex]
hope this helps...
Good luck on your assignment..
HELP ME PWEASEE
Fifteen grams of chemical A is used to produce 3 grams of chemical B. Write an
equation for the amount of chemical B, measured in grams of chemical A, b = f(a), as a function of the amount of chemical, a.
Answer:
[tex]b=\dfrac{1}{5}a[/tex].
Step-by-step explanation:
We need to write an equation for the amount of chemical B as a function of the amount of chemical A.
[tex]b=f(a)[/tex]
[tex]b\propto a[/tex]
[tex]b=ka[/tex] ...(1)
where, k is constant of proportionality.
It is given that fifteen grams of chemical A is used to produce 3 grams of chemical B. It means a=15 and b=3.
Substitute a=15 and b=3 in (1).
[tex]3=k(15)[/tex]
[tex]k=\dfrac{3}{15}=\dfrac{1}{5}[/tex]
Substitute [tex]k=\dfrac{1}{5}[/tex] in (1).
[tex]b=\dfrac{1}{5}a[/tex]
Therefore, the required function is [tex]b=\dfrac{1}{5}a[/tex].
I need help please ASAPPP!
Answer:
16
Step-by-step explanation:
Please see attached photo for diagrammatic explanation.
Note: r is the radius
Using pythagoras theory, we can obtain the value of 'x' in the attached photo as shown:
|EB|= x
|FB| = 10
|EF| = 6
|EB|² = |FB|² – |EF|²
x² = 10² – 6²
x² = 100 – 36
x² = 64
Take the square root of both side.
x = √64
x = 8
Now, we can obtain line AB as follow:
|AB|= x + x
|AB|= 8 + 8
|AB|= 16
Therefore, line AB is 16