Answer:
3 - x =-9
3+ 9 =x
x = 12
so, correct answer
x =12
The lifetimes of a certain brand of light bulbs are known to be normally dsitributed with a mean of 1700 hours and standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. The probability is 0.20 that the sample mean lifetime is more than how many hours?
A. 1652.
B. 1725.
C. 1752.
D. 1670.
Answer:
1742 hours
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.
Single light:
Mean of 1700 hours and standard deviation of 400 hours, which means that [tex]\mu = 1700, \sigma = 400[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{400}{\sqrt{64}} = 50[/tex]
The probability is 0.20 that the sample mean lifetime is more than how many hours?
This is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]0.84 = \frac{X - 1700}{50}[/tex]
[tex]X - 1700 = 50*0.84[/tex]
[tex]X = 1700 + 50*0.84[/tex]
[tex]X = 1742[/tex]
3(2x - 1) + 7 = -44 solve for x
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
answer is x =-8
hope that helps^^
Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in 12 hours. Beatrice and Charlie can build the ant hill in 15 hours. How long, in hours, will it take to build the ant hill if Aran, Beatrice, and Charlie work together?
Answer:
They complete the hill in 8 hours
Step-by-step explanation:
Equations:
Let's call the variables:
Aran can make build the ant hill in A hours
Beatrice can make build the ant hill in B hours
Charlie can make build the ant hill in C hours
In one hour, Aran makes 1/A of the ant hill.
In one hour, Beatrice makes 1/B of the ant hill.
In one hour, Charlie makes 1/C of the ant hill.
Aran and Beatrice build it in 10 hours, thus:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}=\frac{1}{10}\qquad\qquad[1][/tex]
Similarly:
[tex]\displaystyle \frac{1}{A}+\frac{1}{C}=\frac{1}{12}\qquad\qquad[2][/tex]
[tex]\displaystyle \frac{1}{B}+\frac{1}{C}=\frac{1}{15}\qquad\qquad[3][/tex]
We need to find the time taken for the three ants to build the anthill:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=[/tex]
Adding [1], [2], and [3]:
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}[/tex]
Adding the fractions (LCM=60):
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6}{60}+\frac{5}{60}+\frac{4}{60}[/tex]
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6+5+4}{60}=\frac{15}{60}=\frac{1}{4}[/tex]
Dividing by 2:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{8}[/tex]
All ants together make 1/8 of the hill, thus they complete the hill in 8 hours
In 1 week, Kim jogged 5.6 miles. She increased the distance she jogged each week by
3
4
3
4
mile. At the end of 5 weeks, how many total miles had Kim jogged?
Answer:
19.6 miles
Step-by-step explanation:
All you have to do is add up by each number for example 5.6+3 miles is 8.6 miles so just keep adding up the miles to get this answer
Last year, Tim rode his bike a total of 50 3/8 miles. This year, he rode his bike a total of 258 3/4 miles. Which of the following explains about how much farther Tim rode his bike this year than last year? A. About 200 times farther; Subtract last year's distance from this year's distance to get 208 3/8.
Then round to the nearest hundred to get 200.
B. About 50 times farther; Round each distance to the nearest whole number.
Then multiply last year's distance by 50 to see that 259 is close to 50 × 5.
C. About 10 times farther; 258 is about 5 times 50, and 34 is 2 times 38, so multiply 5 × 2 to get 10.
D. About 5 times farther; Round each distance to the nearest whole number.
Then multiply last year's distance by 5 to see that 259 is close to 50 × 5.
Answer:
D
Step-by-step explanation:
Ron sells bananas for $0.60 each. How many bananas did Ron sell if he made $150.00, after taking off $39.00 for his banana stand rental?
The number of bananas that Ron sold is 315.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that,
Cost for a banana = $0.60
Also given, he made $150.00, after taking off $39.00 for his banana stand rental.
Total amount of money that Ron made by selling the bananas = $150 + $39 = $189
Number of bananas sold = 189 / 0.6
= 315
Hence Ron sold 315 bananas.
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Let f(x) = 4x - 1, h(x) = - X-3.
Find (f o h)(-5).
Answer:
(f o h)(-5)=-33
Step-by-step explanation:
Let f(x) = 4x - 1, h(x) = - X-3.
(f o h)=4(-x-3)-1
(f o h)=-4x-12-1
(f o h)=-4x-13
(f o h)(-5)=-4(-(-5))-13
(f o h)(-5)=-20-13
(f o h)(-5)=-33
Which of the following could be the lengths of the sides of a 30-60-90 triangle?
Answer: D. 15 square root with 3 inside
Step-by-step explanation:
Just try it
Answer:
c
Step-by-step explanation:
Suppose X has an exponential distribution with mean equal to 11. Determine the following: (a) (Round your answer to 3 decimal places.) (b) (Round your answer to 3 decimal places.) (c) (Round your answer to 3 decimal places.) (d) Find the value of x such that . (Round your answer to 2 decimal places.)
Answer:
[tex]P(X > 11) = 0.368[/tex]
[tex]P(X > 22) = 0.135[/tex]
[tex]P(X > 33) = 0.050[/tex]
[tex]x = 33[/tex]
Step-by-step explanation:
Given
[tex]E(x) = 11[/tex] --- Mean
Required (Missing from the question)
[tex](a)\ P(X>11)[/tex]
[tex](b)\ P(X>22)[/tex]
[tex](c)\ P(X>33)[/tex]
(d) x such that [tex]P(X <x)=0.95[/tex]
In an exponential distribution:
[tex]f(x) = \lambda e^{-\lambda x}, x \ge 0[/tex] --- the pdf
[tex]F(x) = 1 - e^{-\lambda x}, x \ge 0[/tex] --- the cdf
[tex]P(X > x) = 1 - F(x)[/tex]
In the above equations:
[tex]\lambda = \frac{1}{E(x)}[/tex]
Substitute 11 for E(x)
[tex]\lambda = \frac{1}{11}[/tex]
Now, we solve (a) to (d) as follows:
Solving (a): P(X>11)
[tex]P(X > 11) = 1 - F(11)[/tex]
Substitute 11 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{1}{11}* 11})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{11}{11}})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-1})[/tex]
Remove bracket
[tex]P(X > 11) = 1 - 1 + e^{-1}[/tex]
[tex]P(X > 11) = e^{-1}[/tex]
[tex]P(X > 11) = 0.368[/tex]
Solving (b): P(X>22)
[tex]P(X > 22) = 1 - F(22)[/tex]
Substitute 22 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{1}{11}* 22})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{22}{11}})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-2})[/tex]
Remove bracket
[tex]P(X > 22) = 1 - 1 + e^{-2}[/tex]
[tex]P(X > 22) = e^{-2}[/tex]
[tex]P(X > 22) = 0.135[/tex]
Solving (c): P(X>33)
[tex]P(X > 33) = 1 - F(33)[/tex]
Substitute 33 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{1}{11}* 33})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{33}{11}})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-3})[/tex]
Remove bracket
[tex]P(X > 33) = 1 - 1 + e^{-3}[/tex]
[tex]P(X > 33) = e^{-3}[/tex]
[tex]P(X > 33) = 0.050[/tex]
Solving (d): x when [tex]P(X <x)=0.95[/tex]
Here, we make use of:
[tex]P(X<x) = F(x)[/tex]
Substitute [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X<x) = 1 - e^{-\lambda x}[/tex]
So, we have:
[tex]0.95 = 1 - e^{-\lambda x}[/tex]
Subtract 1 from both sides
[tex]0.95 -1= 1-1 - e^{-\lambda x}[/tex]
[tex]-0.05=- e^{-\lambda x}[/tex]
Reorder the equation
[tex]e^{-\lambda x} = 0.05[/tex]
Substitute 1/11 for [tex]\lambda[/tex]
[tex]e^{-\frac{1}{11} x} = 0.05[/tex]
Solve for x:
[tex]x = -\frac{1}{1/11}\ ln(0.05)[/tex]
[tex]x = -11\ ln(0.05)[/tex]
[tex]x = 32.9530550091[/tex]
[tex]x = 33[/tex] --- approximated
4/5 ÷ 1/5 = ?????????
Answer:
4
Step-by-step explanation:keep change flip 4/5 x 5/1 = 20/5= 4
Answer for 5 stars answer and a heart with a comment. Please hurry!
Here is a diagram of a person standing next to a lorry.
The diagram shows two centimetre rulers.
The person and the lorry are drawn to the same scale.
The lorry is approximately 9.5 m in length.
Using the scale diagram, estimate the height of the person in metres.
Answer:
Length of the person = 1.9 m
Step-by-step explanation:
Actual length of the lorry = 9.5 m
Length of the lorry as per scale = 10 cm
Scale factor used to get the actual length of the lorry = [tex]\frac{\text{Actual length}}{\text{Length on scale}}[/tex]
= [tex]\frac{9.5}{10}[/tex]
= 0.95 : 1
Let the actual length of the person = x meters
Length of the person as per scale = 2 cm
Scale factor used to get the length of person is same.
Therefore, relation between the actual length of the person and scale length will be,
[tex]\frac{x}{2}= \frac{0.95}{1}[/tex]
x = 2 × 0.95
x = 1.9 meters
A zoo worker works 189.25 hours in 23 days. If she works the exact same number of hours per day, how many hours does she work each day?
How many nineths does it take to make the same as 1/3
Answer:
3
Step-by-step explanation:
Answer:
3/9ths
Step-by-step explanation:
I'm so confused what is the answer plz?
Answer:
option b .
yes, by SAS.
.............
find the logarism of 6395
Answer:
this is clear that answer
I need some homework help please.
Answer:
x^2-5x=6
x^2-5x-6=0
x^2+x-6x-6=0
x(x+1)-6(x+1)=0
(x-6)(x+1)=0
x=6, -1
-5x= -30, 5
Step-by-step explanation:
Which value for p makes the expressions 9p - 5 and (3 + p) 5 equivalent?
7
6
4
5
1
10
Answer:
numbers dont do into math please move this to englash
Step-by-step explanation:
it posted Wong
An electronics retailer is developing a model for insurance on new cell phone purchases. It estimates that 60% of customers never make a claim25% require a small repair costing an average of $50and 15% require a full refund costing $200. What is the average cost the retailer should expect to pay to each customer?
Answer:
$42.50
Step-by-step explanation:
$42.50 will cover the costs of all people who request full refunds, while still allowing the company to profit.
The average cost the retailer should expect to pay to each customer if It estimates that 60% of customers never make a claim is $4250.
What is average?The average is a numeric figure that represents a big amount of data in a single way. The average mark of the class is calculated by averaging the students' grades in a given subject.
It is more important to understand how the class as a whole performed than how each individual student performed.
Given:
It estimates that 60% of customers never make a claim, 25% require a small repair costing an average of $50 and 15% require a full refund costing $200,
Calculate the average cost as shown below,
Assume there are 100 customers, then,
The average cost = 25% of 100 × 50 + 15% of 100 × 200
The average cost = 25 × 50 + 15 × 200
The average cost = 1250 + 3000
The average cost = 4250
Thus, the average cost the retailer should expect to pay to each customer is $4250.
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Identify all sets to which the number -7 belongs.
Answer:
Step-by-step explanation:
-7 which set of number belongs, betwen
Natural
Whole
Intergers
Rational
Irrational
Real
Please help me!!!!!!!!!!
what is 473.2608 rounded to the nearest tenth
Answer:
473.2608 rounded to the nearest tenth Is 473.3
Step-by-step explanation:
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
$56.10
Step-by-step explanation:
Answer:
$8.50
Step-by-step explanation:
What is the fraction shown above?
Solve the equation.
-6p=48
Answer:
p=-8
Step-by-step explanation:
A negative multiplied by a negative is a positive.
The medical practice you are working at has seen an average of 22.4 patients a day for the past 3 months. 3/4ths of those patients have insurance in one form or another.
A homeowner is building a flower bed in the backyard. He plans to put a layer of fertilizer over the entire flower bed.The diagram shows the flower bed and its dimensions in feet.
4w2 + 3w - 1
5w - 2.
Which expression represents the area in square feet that the homeowner will cover with fertilizer?
Answer:
The answer is 4w^2 + 8w - 3
Step-by-step explanation:
Umm I hope it's right
ILL GIVE BRAINLEST !!!!
Enter an equation for the function that includes the points. Give your answer in the form a(b*). In the
event that a = 1, give your answer in the form b*.
(1, 12) and (2, 144)
The equation is f(x)=
Please help with my question
Graphing linear equation using a table [ x = - 1 ]
• • • • • • • • • • • • • • • • • • • • • • • • • • • •
(I only need help in filling the table, aswell as the slope and y-intercept, thanks! ^u^)
0
1
2
3
4
5
take x 1 so 1-1
2-1..........
PLS HELP ASAP Which equation models this situation?
28 more than a number is 33.
A. X+ 33 = 28
B. X- 28 = 33
C. X = 28 + 33
D. X + 28 = 33
Answer:
d
Step-by-step explanation:
Answer:
more than a number = addition
so it is D because the end result has to be 33.
Step-by-step explanation:
Hope this helped!