Answer:
4.6%.
Step-by-step explanation:
The probability that a can of paint contains contamination(C) is 3.23%
P(C)=3.23%
The probability of a mixing(M) error is 2.4%.
P(M)=2.4%
The probability of both is 1.03%.
[tex]P(C \cap M)=1.03\%[/tex]
We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e. [tex]P(C \cup M)[/tex]
In probability theory:
[tex]P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%[/tex]
The probability that a randomly selected can has contamination or a mixing error is 4.6%.
The equation h = 7m + 8 models the growth of a plant after it was put into a flowerbed. If
m is the number of months since it was planted and h is the plant's height in
centimeters, which statement is valid?
The vertical axis on a graph would
represent the number of months the plant
has been in the flowerbed.
The height of the plant is the dependent
variable.
The domain of the function represents the
height of the plant.
The variable m could be represented as
f(h).
Answer:
2
Step-by-step explanation:
the vertical axis would be h, the plant's height, and the horizontal axis would be m, the number of months. This would make statement 2 the only valid statement.
statement 1: Incorrect, as the vertical axis is the height
statement 2: correct, as h depends on m
statement 3: incorrect, as the domain is the horizontal and represents the number of months
statement 4: incorrect, as h = f(m)
Vlad tried to solve an equation step by step.
-8p 14 = 42
-8p = 28 step 1
p= -3.5 step 2
Find Vlad's mistake.
Choose 1 answer:
A)Step 1
B)Step 2
C)Vlad did not make a mistake
Answer:
C
Step-by-step explanation:
-8 14 = 42 (He subtracted 14 from 42)
-8p = 28 (Which is how he got 28)
p = -3.5 (He took 28 divide by -8 which got him -3.5)
Answer:
C
Step-by-step explanation:
C
If you have changed the tires on your car, the original diameter is 24.5 inches. to a new diameter of 26 inches, how fast are you actually going if your speedometer is reading 53 mph? A. 50.5 mph B. 53 mph C. 56.2 mph D. 62.8 mph
Answer: c) 56.2
Step-by-step explanation:
Compare the original rate to the the new rate:
[tex]\dfrac{diameter}{mph}:\dfrac{24.5\ in}{53\ mph}=\dfrac{26\ in}{x}\\\\\\24.5x=53(26)\\\\\\x=\dfrac{53(26)}{24.5}\\\\\\x=\large\boxed{56.2\ mph}[/tex]
Homework: Section 1.2 Applications Linear
Score: 0 of 1 pt
8 of 10 (7 complete)
1.2.31
How many quarts of pure antifreeze must be added to 4 quarts of a 10% antifreeze solution to obtain a 20% antifreeze solution?
quart(s) of pure antifreeze must be added.
(Round to the nearest tenth as needed)
Answer:
q = 0.5 quarts of 100% antifreeze
Step-by-step explanation:
q = quarts of pure antifreeze
Set this up as a weighted combination of the mixtures.
(100%)(q) + (10%)(4) = (20%)(q + 4)
100q + 40 = 20(q + 4)
5q + 2 = q + 4
4q = 2
q = 0.5 quarts of 100% antifreeze
A commuter uses a bus and a train to get to work. The train is more than 5 minutes late 1/6 of the times they use it The bus is more than 5 minutes late 3/5 of the times they use it. What is the probability that both the bus and train will be more than 5 minutes late?
Answer:
10% probability that both the bus and train will be more than 5 minutes late
Step-by-step explanation:
Independent events:
If two events, A and B, are independent, we have that:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
What is the probability that both the bus and train will be more than 5 minutes late?
The bus being more than 5 minutes late is independent of the train, and vice versa. So
Event A: Bus more than 5 minutes late
Event B: Train more than 5 minutes late
The train is more than 5 minutes late 1/6 of the times they use it
This means that [tex]P(B) = \frac{1}{6}[/tex]
The bus is more than 5 minutes late 3/5 of the times they use it.
This means that [tex]P(A) = \frac{3}{5}[/tex]
Then
[tex]P(A \cap B) = \frac{3}{5}*\frac{1}{6} = \frac{3}{30} = 0.1[/tex]
10% probability that both the bus and train will be more than 5 minutes late
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
V=
Answer: V=4778.4 cm³
Step-by-step explanation:
[tex]V=\pi r^2\frac{h}{3}[/tex] is the formula for volume. Since we are given the height and radius, we can directly plug it into the equation
[tex]V=\pi (13)^2(\frac{27}{3})[/tex]
[tex]V=169\pi (9)[/tex]
[tex]V=1521\pi[/tex]
[tex]V=4778.4cm^3[/tex]
Plastic knives are sold in packs of 15 for 32p. Plastic forks are sold in packs of 12 for 43p. Sam wants to buy the same number of forks as knives. What is the least amount of money Sam will be able to spend?
Step-by-step explanation:
Find the lowest common multiple of 15 and 12.
Which is 60.
15×4=60 so 32x4=£1.28
12x5=60 so 43x5=£2.15
2.15+1.28= £3.43
A random sample of math majors taking an introductory statistics course were surveyed after completing the final exam. They were asked, "How many times did you review your final exam before handing it in to the professor?" The results are displayed in a probability density function for the random variable X, the number of times students reviewed their exam before handing it in. Find the standard deviation of X. Round the final answer to two decimal places. x P(X = x) 1 1/5 2 2/5 7 2/5
Answer:
[tex] E(X) =1 *\frac{1}{5} +2 *\frac{2}{5} +7*\frac{2}{5}= 3.8[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) =1^2 *\frac{1}{5} +2^2 *\frac{2}{5} +7^2*\frac{2}{5}= 21.4[/tex]
The variance would be given by:
[tex] Var(X) =E(X^2) -[E(X)]^2 = 21.4 -[3.8]^2 = 6.96[/tex]
And the deviation would be:
[tex] Sd(X) =\sqrt{6.96}= 2.638[/tex]
Step-by-step explanation:
For this case we have the following distribution given:
X 1 2 7
P(X) 1/5 2/5 2/5
We need to begin finding the mean with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(X) =1 *\frac{1}{5} +2 *\frac{2}{5} +7*\frac{2}{5}= 3.8[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) =1^2 *\frac{1}{5} +2^2 *\frac{2}{5} +7^2*\frac{2}{5}= 21.4[/tex]
The variance would be given by:
[tex] Var(X) =E(X^2) -[E(X)]^2 = 21.4 -[3.8]^2 = 6.96[/tex]
And the deviation would be:
[tex] Sd(X) =\sqrt{6.96}= 2.638[/tex]
Multiply or divide as indicated.
10x^5 divide 2x^2
Answer:
5x^3(to the power of 3)
Step-by-step explanation:
10x^5/2x^2
divide the 10/2 like normal to get 5
x^5/x^2 (subtract the powers 5-2 when dividing powers)
you would get 5x^3
In monitoring lead in the air after the explosion at the battery factory, it is found that the amounts of lead over a 6 day period had a standard error of 1.93. Find the margin of error that corresponds to a 95% confidence interval. (Round to 2 decimal places) 4.56
Answer:
1.54
Margin of error M.E = 1.54
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-M.E
Where M.E = margin of error
M.E = zr/√n
Given that
Standard deviation r = 1.93
Number of samples n = 6
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
M.E = (1.96×1.93/√6) = 1.544321633166
M.E = 1.54 (to 2 decimal place)
Margin of error M.E = 1.54
Please show how the following equasion Square root of 64+6/-2*-2 I cannot arrive at the answer of 9.5
Answer:
[tex]9.5[/tex]
Step-by-step explanation:
[tex]\sqrt{64}+\frac{6}{-2\left(-2\right)}[/tex]
[tex]\sqrt{64}+\frac{6}{2 \times 2}[/tex]
[tex]8+\frac{6}{4}[/tex]
[tex]\frac{19}{2}[/tex]
[tex]=9.5[/tex]
Answer:
Hello!
I hope that this is the answer you are looking for
=8.09320
That is the rounded answer.
I hope that helped you!
Step-by-step explanation:
On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Find the probability expressions: (Round your answers to 2 decimal places.)
a. P(X=50)P(X=50).
b. P(X≤75)P(X≤75).
c. P(X>50)P(X>50).
d. P(X<100)P(X<100).
Answer:
a. P(X=50)= 0.36
b. P(X≤75) = 0.9
c. P(X>50)= 0.48
d. P(X<100) = 0.9
Step-by-step explanation:
The given data is
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Where X is the variable and P(X) = probabililty of that variable.
From the above
a. P(X=50)= 0.36
We add the probabilities of the variable below and equal to 75
b. P(X≤75) = 0.16+ 0.36+ 0.38= 0.9
We find the probability of the variable greater than 50 and add it.
c. P(X>50)= 0.38+0.10= 0.48
It can be calculated in two ways. One is to subtract the probability of 100 from total probability of 1. And the other is to add the probabilities of all the variables less than 100 . Both would give the same answer.
d. P(X<100)= 1- P(X=100)= 1-0.1= 0.9
MY LAST 2 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
1. Molly is trying to find a relationship between the largest angle and largest side of a triangle. She has drawn dozens of triangles, and measured their parts. She’s ready to make a conjecture. What kind of reasoning was Molly using? Explain how you know it’s that kind of reasoning.
11. Which step in the proof has a flaw?
Given AB=BC prove B is the midpoint of AC
IMAGE BELOW
A) Step 1
B) Step 3
C) No Flaw.
D) Step 2
Answer:
C.
Step-by-step explanation:
11. There is no flaw since step 1 is given, and there is the right reason for step 2.
1. Molly is using inductive reasoning because she is collecting the data to make a conjecture.
11. There is no flaw.
Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Step-by-step explanation:
x and x+2 are the numbers
x(x+2)=143
x²+2x-143=0
x²+13x-11x-143=0
x(x+13)- 11(x+13)=0
(x+13). (x-11)=0
x+13=0. x=-13
x-11=0. x=11
3.
B
С
A
D
E
How many rays intersect at point o?
A classic counting problem is to determine the number of different ways that the letters of "misspell" can be arranged. Find that number.
Answer:
10,080 different ways that the letters of "misspell" can be arranged.
Step-by-step explanation:
Number of arrangents of the letters of a word:
A word has n letters.
The are m repeating letters, each of them repeating [tex]r_{0}, r_{1}, ..., r_{m}[/tex] times
So the number of distincts ways the letters can be arranged is:
[tex]N_{A} = \frac{n!}{r_{1}! \times r_{2}! \times ... \times r_{m}}[/tex]
In this question:
Misspell has 8 letters, with s and l repeating twice.
So
[tex]N_{A} = \frac{8!}{2!2!} = 10080[/tex]
10,080 different ways that the letters of "misspell" can be arranged.
To ______ a function, you need to stretch or compress it
Answer: It’s to change the shape of a function
Step-by-step explanation:
To change the shape of a function, you need to stretch or compress it.
How to stretch or compress a function?In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.
Is there a function for every shape?By definition, a function has one possible output for any given input. So if you want your function defined as some y=f(x), then not every shape can be written as a function. Any shape that has two points directly above each other (relative to the x-axis) cannot be written as a function, even a piecewise one.
Learn more about the shape of a function, here: https://brainly.com/question/1884491
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A recent national survey found that parents read an average (mean) of 10 books per month to their children under five years old. The population standard deviation is 5. The distribution of books read per month follows the normal distribution. A random sample of 25 households revealed that the mean number of books read last month was 12. At the .01 significance level, can we conclude that parents read more than the average number of books to their children
Answer:
Step-by-step explanation:
Null hypothesis: u = 10
Alternative hypothesis: u =/ 10
Using the formula: t = (x - u) / (s /√n)
Where x = 12, u = 10, s = 5 and n = 25
t= (12-10) / (5/√25)
t = (2)/(5/5)
t = 2/1= 2
t = 2.0
At a 0.01 level of significance with a degree of freedom of 24, the p-value is 0.0569, which is greater than 0.01 we will fail to reject the null and conclude that parents do not read more than the average number of books to their children
For what value of the variable will the value of 7y−2 be ten more than the value of 2y?
Answer:
y=2.4
Step-by-step explanation:
7y-2=2y+10
7y-2y=10+2
5y=12
y=12/5=2.4
According to a polling organization, 22% of adults in a large region consider themselves to be liberal. A survey asked 200 respondents to disclose their political philosophy: Conservative, Liberal, Moderate. Treat the results of the survey as a random sample of adults in this region. Do the survey results suggest the proportion is higher than that reported by the polling organization? Use an alphaequals0.01 level of significance.
Answer:
No. There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling organization (P-value = 0.0366).
Step-by-step explanation:
The question is incomplete: there is no information about the results of the survey. We will assume that 55 of the subjects answer "liberal", and test the claim.
This is a hypothesis test for a proportion.
The claim is that the proportion of liberals is higher than that reported by the polling organization.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.22\\\\H_a:\pi>0.22[/tex]
The significance level is 0.01.
The sample has a size n=200.
The sample proportion is p=0.275.
[tex]p=X/n=55/200=0.275[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{200}}\\\\\\ \sigma_p=\sqrt{0.000858}=0.029[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.275-0.22-0.5/200}{0.029}=\dfrac{0.053}{0.029}=1.792[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>1.792)=0.0366[/tex]
As the P-value (0.0366) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling organization.
A student works at an on- campus job Monday through Friday. The student also participates in intramural volleyball on Tuesdays and Thursdays. Given Events A and B, are the two events mutually exclusive? Explain your answer.
Event A: On a random day of the week, the student is working at their on-campus job.
Event B: On a random day of the week, the student is playing intramural volleyball.
Answer:
No, the events are not mutually exclusive because they share the common outcomes of the student working and playing volleyball on certain days.
Step-by-step explanation:
A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.
In this case, A and B have outcomes in common since the student both works and plays volleyball on Tuesdays and Thursdays. Thus, the events are not mutually exclusive.
Ms. Ironperson and Mr. Thoro are making
Avenger posters to give children when they
visit Avenger Academy. Ms. Ironperson has
completed 12 posters and will complete 6
more per day. Mr. Thoro has not started yet
but can make 12 per day. At some point Mr.
Thoro will catch up and both will have finished
the same number of posters. When this does
happen, how many posters will each Avenger
have completed?
If x denotes the number of days and y denotes
the number of posters, what are the equations
needed to solve this problem? (7 points)
Answer:
y = 12 + 6x
y = 12x
Step-by-step explanation:
From the information provided, the following equations are derived:
y = 12 + 6x ------- Eqn 1
y = 12x ------- Eqn 2
Since Eqns 1 and 2 have the same subject, we equate them to solve for x. We have:
12x = 12 + 6x
Putting like terms together, we have:
12x - 6x = 12 ⇒ (12 - 6)x = 12
6x = 12 ⇒ x = 2
x = 2
Substitute x into Eqn 1 or 2
Eqn 1
y = 12 + 6x
y = 12 + 6(2) = 12 + 12
y = 24
Eqn 2
y = 12x
y = 12(2)
y = 24
It means that it will take Ms. Ironperson and Mr. Thoro 2 days apiece to produce the same number of posters at the current rate (which is 24 posters). Both Ms. Ironperson and Mr. Thoro will individually take 2 days to produce 24 Avenger posters apiece.
Which expression is equivalent to 5^10 times 5^5. 5^2 5^5 5^15 5^50
Answer:
5^15
Step-by-step explanation:
(5^10)(5^5)= 5^10+5= 5^15
Use the zero product property to find the solutions to the equation x2 – 9 = 16.
x= -3 or x = 3
x= -6 or x = -3
Ox= -5 or x = 5
O x= 7 or x = 1
Answer:
x = ±5
Step-by-step explanation:
x^2 – 9 = 16
Add 9 to each side
x^2 – 9+9 = 16+9
x^2 = 25
Take the square root of each side
sqrt(x^2) = ±sqrt(25)
x = ±5
Answer:
[tex]x = 5 \: \: \: or \: \: x = - 5[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 9 = 16 \\ {x}^{2} = 16 + 9 \\ {x}^{2} = 25 \\ x = \sqrt{25} \\ x = 5 \\ x = - 5[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning at least 30 times. Group of answer choices Greater than 0.60 Between 0.20 and 0.40 Between 0.01 and 0.20 Between 0.40 and 0.60 Almost 0
Answer:
Between 0.01 and 0.20
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 500, p = 0.05[/tex]
So
[tex]\mu = E(X) = np = 500*0.05 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734/tex]
Find the probability of winning at least 30 times.
Using continuity correction, this is [tex]P(X \geq 30 - 0.5) = P(X \geq 29.5)[/tex]. So this is 1 subtracted by the pvalue of Z when X = 29.5. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29.5 - 25}{4.8734}[/tex]
[tex]Z = 0.92[/tex]
[tex]Z = 0.92[/tex] has a pvalue of 0.8212
1 - 0.8212 = 0.1788
So the correct option is:
Between 0.01 and 0.20
Design and complete a frequency table for Belinda.
Belinda ask 20 people, how many hours of TV did you watch last week?
Here is the results
3,17,4,4,6,11,14,14,1,20,9,8,9,6,12,7,8,13,13,9.
Belinda wants to show these result in a frequency table.
She will use 4 equal groups.
The first group will start with 1 hour and the last group will end with 20 hours.
Answer:
Step-by-step explanation:
Since she will use 4 groups or class intervals, the the class width would be 20/4 = 5 hours
The class groups would be
1 to 5
5 to 10
10 to 15
15 to 20
The class mark for each class is the average of the minimum and maximum value of each class. Therefore, the class marks are
(1 + 5)/2 = 3
(5 + 10)/2 = 7.5
(10 + 15)/2 = 12.5
(15 + 20)/2 = 17.5
The frequency table would be
Class group Frequency
1 - 5 4
5 - 10 8
10 - 15 6
15 - 20 2
The total frequency is 4 + 8 + 6 + 2 = 20
A jar of marbles contains the following: two purple marbles, four white marbles, three blue marbles, and two green marbles. What is the probability of selecting a white marble from a jar of marbles?
Answer:
4/11
Step-by-step explanation:
There are 11 marbles in total, if 4 of them are white, then you have a 4/11 chance of getting a white marble.
Find x
PLEASE HELP ME !! 11 POINTS !
Answer:
5
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp /hyp
sin 30 = x / 10
10 sin 30 = x
10 * 1/2 = x
5 =x
Arsha predicted that she would sell 225 magnets. She actually sold 240 magnets. What are the values of a and b in the table below? Percent Error Item Approximate value Exact value Error Absolute error Ratio Percent error Magnets 225 240 a b a = Negative StartFraction 15 over 225 EndFraction; b = negative 6.7 percent a = Negative StartFraction 15 over 240 EndFraction; b = negative 6.25 percent a = StartFraction 15 over 240 EndFraction; b = 6.25 percent a = StartFraction 15 over 225 EndFraction; b = 6.7 percent
Answer:
c
Step-by-step explanation:
Dorothy Kaatz, a computer programmer, earns a regular hourly rate of
$15.25 and earns double that when she works overtime. Kaatz usually works
40 regular hours and 12 hours overtime while she's trying to update the
company's systems before the month's end. What is her straight-time pay?
What is her overtime pay? What is her total pay?
Answer:
$976
Step-by-step explanation:
Straight time pay= $15.25(hourly rate) × 40(hours worked)= $610
Overtime Rate = 15.25×2= $30.50
Overtime Pay= $30.5 × 12 (Hours worked overtime)= $366
Total Pay= Basic wage + Overtime Wage = $976
