Answer:
11
Step-by-step explanation:
I'm assuming that [.] fldenote absolute value even tho the absolute value function is represented by (|.|)
value of [-7] will be positive that us 7.
= 7 + 4
= 11
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. If the operator is accurate, what is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Answer:
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.
This means that [tex]p = 0.07[/tex]
Sample of 459 phone calls:
This means that [tex]n = 459[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.07[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\sqrt{\frac{0.07*0.93}{459}}} = 0.0119[/tex]
What is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%?
Proportion below 0.07 - 0.03 = 0.04 or above 0.07 + 0.03 = 0.1. Since the normal distribution is symmetric, these probabilities are the same, which means that we find one of them and multiply by 2.
Probability the proportion is below 0.04.
p-value of Z when X = 0.04. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.04 - 0.07}{0.0119}[/tex]
[tex]Z = -2.52[/tex]
[tex]Z = -2.52[/tex] has a p-value of 0.0059
2*0.0059 = 0.0118
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Life Expectancies In a study of the life expectancy of people in a certain geographic region, the mean age at death was years and the standard deviation was years. If a sample of people from this region is selected, find the probability that the mean life expectancy will be less than years. Round intermediate -value calculations to decimal places and round the final answer to at least decimal places.
Answer:
The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
We have:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].
Sample of size n:
This means that the z-score is now, by the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Find the probability that the mean life expectancy will be less than years.
The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
A game increased in price by 1/2 After the increase it was priced at £72. What was the original
price of the game?
Answer:
£48
Step-by-step explanation:
£72 / 3 = £24
£24 x 2 = £48
Hope this helps c:
What is the true solution to the equation below?
l n e Superscript l n x Baseline + l n e Superscript l n x squared Baseline = 2 l n 8
x = 2
Given:
The equation is:
[tex]\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8[/tex]
To find:
The solution for the given equation.
Solution:
We have,
[tex]\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8[/tex]
It can be written as:
[tex]\ln x+\ln x^2=2\ln 8[/tex] [tex][\because \ln e^x=x][/tex]
[tex]\ln (x\cdot x^2)=2\ln 8[/tex] [tex][\because \ln a+\ln b=\ln (ab)][/tex]
[tex]\ln (x^3)=\ln 8^2[/tex] [tex][\because \ln x^n=n\ln x ][/tex]
On comparing both sides, we get
[tex]x^3=8^2[/tex]
[tex]x^3=64[/tex]
Taking cube root, we get
[tex]x=\sqrt[3]{64}[/tex]
[tex]x=4[/tex]
Therefore, the required solution is [tex]x=4[/tex].
Answer:
x=4
Step-by-step explanation:
What is the true solution to the equation below?
ln e Superscript ln x Baseline + ln e Superscript ln x squared Baseline = 2 ln 8
x = 2
x = 4
x = 8
3 folders cost \$2.91, 2, point, 91. Which equation would help determine the cost of 22 folders? Choose 1 answer:
Answer:
Step-by-step explanation:
3=$2.91
22=x
3x=64.02
x=21.34
Identify the domain of the function shown in the graph.
(-3).(+9)-(-24)-(+6).(+2)
Find the equation of the line.
(It's a Khan Academy Algebra 1 Course Challenge Question if that helps)
Hello,
2 points of the line: (2,0) and (0,3)
[tex]\Delta\ y=3-0=3\\\Delta\ x=0-2=-2\\\dfrac{\Delta\ y}{\Delta\ x} =\dfrac{-3}{2} \\\\y-0=\dfrac{-3}{2}*(x-2)\\\\\boxed{y=-\dfrac{3x}{2}+3}\\[/tex]
Choose all that apply:
1.Circle A and circle A', have the same circumference.
2.The radii of circle A and circle A', have the same lengths.
3. Points A and A', are both on the xxx-axis.
4. None of the above
Answer:
Step-by-step explanation:
1. Circle A and circle A', have the same circumference. (Yes)
2. The radii of circle A and circle A', have the same lengths. (Yes)
3. .... (No)
4. ... (No)
Someone pls answer ? It’s 8,9,1,2
Answer:
Step-by-step explanation:
8.
any number ×0=0
so b
9.
additive identity
any number+0=same number
c
1.
[tex]\frac{(3+u)^2}{8} =\frac{(3+5)^2}{8} =\frac{8^2}{8} =\frac{64}{8} =8\\where ~u=5[/tex]
2.
-2(a-7)=-2×a-2×(-7)=-2a+14
Find the equivalent exponential expression.
(543
Answer:
(5) we have multiple the powers
PLEASE HELP!!! What is the domain of D(t) as it applies in this situation?!?!
Answer:
This Question Is From The Novel Of The Fantastic Mr.Fox
Q. Boggis , Bunce and Bean are Offering a reward for Mr.Fox , They are tired of Losing Chickens Geese and Cider , Create a Description And Drawing of Mr.Fox to allow him to be captured , use the word bank....
________________________________
Swift | Slay | Ginger | Rough | Fast
Thief. | Clever | Fur | Tail | Wife | Night
Cunning | Bushy | wiry | bush | Den | trick
________________________________
answer???????? with explanations, para lam ko di mga hula
Answer:
144
Step-by-step explanation:
To Find :-
Least Common denominator .Solution :-
We have ,
> 1/8 , 2/9 , 3/12 .
The denominator of the fractions are ,
> 8 , 9 , 12
The LCM of 8,9,12 will be ,
2 | 8 , 9 , 12
2 | 4 , 9 , 6
2 | 2 , 9 , 3
3 | 2 , 3 , 1
Therefore , LCM will be ,
> 2⁴ × 3² = 16 × 9 = 144
Jerome is cooking dinner. He needs 8 ounces of broccoli for each person.
Part A: Jerome is not sure how many people will come to dinner. Write an expression with a variable that represents the amount of broccoli Jerome needs for dinner. Identify what the variable represents.
Part B: If Jerome has 32 ounces of broccoli, how many people can he feed? Create an equation and show all work to solve it.
Answer:
Step-by-step explanation:
Part A.....let P be the number of people that will show up.....so....
The total amount of broccoli needed (in ounces) = 8P ounces
Part B
32 = 8P divide both sides by 8
4 = P so.....4 people can be fed.....!!!
Step-by-step explanation:
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week.
Answer:
0.9898 = 98.98% probability that there will not be more than one failure during a particular week.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
3 failures every twenty weeks
This means that for 1 week, [tex]\mu = \frac{3}{20} = 0.15[/tex]
Calculate the probability that there will not be more than one failure during a particular week.
Probability of at most one failure, so:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.15}*0.15^{0}}{(0)!} = 0.8607[/tex]
[tex]P(X = 1) = \frac{e^{-0.15}*0.15^{1}}{(1)!} = 0.1291[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.8607 + 0.1291 = 0.9898[/tex]
0.9898 = 98.98% probability that there will not be more than one failure during a particular week.
Round 790 to the nearest hundred? Hurry pls and please don't answer if you know you wrong
Answer:
HEY THERE!
Step-by-step explanation:
the answer is:800
hope it helps and have a great day!
Ans: 800
explanation:
Calculate the pH of a buffer solution made by mixing 300 mL of 0.2 M acetic acid, CH3COOH, and 200 mL of 0.3 M of its salt sodium acetate, CH3COONa, to make 500 mL of solution. Ka for CH3COOH = 1.76×10–5
Answer:
Approximately [tex]4.75[/tex].
Step-by-step explanation:
Remark: this approach make use of the fact that in the original solution, the concentration of [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] are equal.
[tex]{\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}[/tex]
Since [tex]\rm CH_3COONa[/tex] is a salt soluble in water. Once in water, it would readily ionize to give [tex]\rm CH_3COO^{-}[/tex] and [tex]\rm Na^{+}[/tex] ions.
Assume that the [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] ions in this solution did not disintegrate at all. The solution would contain:
[tex]0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COOH[/tex], and
[tex]0.06\; \rm mol[/tex] of [tex]\rm CH_3COO^{-}[/tex] from [tex]0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COONa[/tex].
Accordingly, the concentration of [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] would be:
[tex]\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].
[tex]\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].
In other words, in this buffer solution, the initial concentration of the weak acid [tex]\rm CH_3COOH[/tex] is the same as that of its conjugate base, [tex]\rm CH_3COO^{-}[/tex].
Hence, once in equilibrium, the [tex]\rm pH[/tex] of this buffer solution would be the same as the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex].
Calculate the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex] from its [tex]{\rm K}_{a}[/tex]:
[tex]\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}[/tex].
20 and 1/2 feet times 13 and 1/8 feet is what total
Answer:
269 and 1/16 feet total (or 269.0625 feet to be precise)
Step-by-step explanation:
20 and 1/2 = 20.5
13 and 1/8 = 13.125
20.5 * 13.125 = 269.0625 feet = 269 and 1/16 feet
The owner of a busy coffee shop wanted to see if it was worth keeping tea on the menu. She logged the number of cups of tea she sold each day for seven days.
6 12 5 7 7 3 9
Calculate the mean, median, range, and midrange of the number of cups of tea sold for the week.
Answer:
mean = 7
median = 7
range = 9
mid range = 7.5
Step-by-step explanation:
3, 5, 6, 7, 7, 9, 12
Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
12 - 3 = 9
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
3, 5, 6, 7, 7, 9, 12
median = 7
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
(6 + 12 + 5 + 7+ 7 + 3 + 9) / 7 = 7
Mid range = (highest value + lowest value) / 2
(12 + 3) / 2 = 7.5
prove this qns plzz
Answer:
L.H.S.
= (cos5a.sin2a-cos4a.sin3a)/ (sin5a.sin2a-cos4a.cos3a)
Multiply numerator and denominator by 2.
= 2(cos5a.sin2a - cos4a.sin3a) / 2(sin5a.sin2a - cos4a.cos3a)
= (2cos5a.sin2a - 2cos4a.sin3a)/
(2sin5a.sin2a - 2cos4a.cos3a) = [sin(5a+2a)-sin(5a-2a)-sin(4a+3a)
+sin(4a-3a)]/[cos(5a-2a)-cos(5a+2a)-sin(4a-3a) +cos(4a+3a)]
= (sina - sin3a)/(cso3a-cosa)
= (-2cos2a.sina)/(-2sin2a.sina)
= cos2a/sin2a
= cot2a
= R.H.S.
answer is in a picture have a look
The following table shows the distribution of people in a tennis tournament, and one
person is to be selected at random.
Find the probability that the selected person is a female.
Express your answer as a decimal, rounded to the nearest hundredth.
Under Age 35
Male 8 Female 18
35 years and older
Male 11 Female18
Answer:
36/55
Step-by-step explanation:
Total 55 persons, total females 36.
The probability that the selected person is a female from the given table is gotten as; 0.65
What is the Probability?
From the given table we see that;
Males under 35 years = 8
Females under 35 years = 18
Males 35 years and older = 11
Females 35 years and older = 18
Thus;
Total number of people = 8 + 18 + 11 + 18
Total people = 55
Thus, probability that the selected person is a female is;
P(female) = (18 + 18)/55
P(female) = 36/55
P(female) = 0.65
Read more about Probability at; https://brainly.com/question/251701
Write a rational function that meets the following criteria:
Vertical asymptote at x = 1
Horizontal asymptote at y = 2
and a hole at x = 3
Carin opened a money market account with a
deposit of $3,000. This account earns 2% simple
interest annually. How many years will it take for
her $3,000 deposit to earn $420 in interest, assum-
ing she does not withdraw any of the money?
Answer:
7
Step-by-step explanation:
For simple interest,
I = prt
where I = interest,
p = principal (amount deposited)
r = annual rate of interest
t = time in years
We have r = 2% = 0.02
p = $3,000
I = $420
We need to find t
I = prt
420 = 3000 * 0.02 * t
420 = 60t
t = 420/60
t = 7
Answer: 7 years
I need this to pass summer school
Answer: The answer is b
2(2x + 4) + 2(x - 7) = 78. Determine the side lengths of this rectangle.
[tex]2(2x + 4) + 2(x - 7) = 78[/tex]
[tex]4x + 8 + 2x - 14 = 78[/tex]
[tex](4x + 2x) + (8 - 14) = 78[/tex]
[tex]6x - 6 = 78[/tex]
[tex]6x = 78 + 6[/tex]
[tex]6x = 84[/tex]
[tex]x = \frac{84}{6} [/tex]
[tex]x = 14[/tex]
Is this a function? Yes or no?
Answer:
NO
Step-by-step explanation:
NO
please help will mark brainly. *personal finance*
Answer:
{B} travelling costs paid in connection with a temporary work assignment
The sum of 3 consecutive odd numbers is 183. What is the third number in this sequence?
Answer:
61
Step-by-step explanation:
3x + 6 = 183
3x = 177
x = 59
(x+2) = (59+2) = 61
It is correct on khan academy
Answer:
The third number in this sequence is 63.
Step-by-step explanation:
Let the first odd number be x.
Since our sequence are consecutive odd numbers, the second term must be (x + 2) and the third (x + 4). If we only add one, we will get even numbers.
Their sum is 183. Hence:
[tex]x+(x+2)+(x+4)=183[/tex]
Solve for x. Combine like terms:
[tex]3x+6=183[/tex]
Subtract six from both sides:
[tex]3x=177[/tex]
And divide both sides by three. Hence:
[tex]x=59[/tex]
Therefore, our sequence is 59, 61, and 63.
The third number in this sequence is 63.
Note: If we do not get an odd number or if we get a fraction for x, we can conclude that no three consecutive integers sum to 183.
Số táo của An, Bình, Chi là như nhau. An cho đi 17 quả , Chi cho đi 19 quả thì lúc này số táo của Chi gấp 5 lần tổng số táo còn lại của An và Bình. Hỏi lúc đầu mỗi bạn có bao nhiêu quả táo? ( Giải bài toán trên bằng phương trình hoặc hệ phương trình )
Answer:
So, the initial number of apples is 7.
Step-by-step explanation:
The number of apples of An, Binh, and Chi are the same. An gave away 17 apples, Chi gave away 19 apples, so now Chi's apples are 5 times higher than the total remaining apples of An and Binh. How many apples did each of you have at first? (Solve the above problem by equation or system of equations)
Let the initial numbers of apples is a.
An gave 17 apples
Chi gave 19 apples
So,
x - 19 = 5 (x - 17 + x)
x - 19 = 5 (2x - 17)
x - 19 = 10 x - 85
9 x = 66
x = 7
solve it
[tex]4 \frac{1}{3} \times (3 \frac{1}{3} \times 3 \frac{1}{2} ) \ {}^{7} \div 9 \frac{3}{4} [/tex]
solve it fast
Answer:
[tex]\frac{257357187500}{19683}[/tex]
Step-by-step explanation:
We can convert these mixed fractions to ordinary fractions.
[tex]4(1/3)=\frac{(4*3)+1}{3}=\frac{13}{3}[/tex]
[tex]3(1/3)=\frac{10}{3}[/tex]
[tex]3(1/2)=\frac{7}{2}[/tex]
[tex]9(3/4)=\frac{39}{4}[/tex]
Then we have:
[tex]\frac{13}{3}*(\frac{10}{3}*\frac{7}{2})^{7}*\frac{4}{39}[/tex]
[tex]\frac{257357187500}{19683}[/tex]
I hope it helps you!
