d-Denis
e-Earl
d+e=42
e+8=d
e+8+e=42
2e+8=42
2e=34
e=17
d=17+8=25
Denis is 25 and Earl is 17
Answer
Earl is 17 years old.
Denis is 25 years old.
See? Easy!
Step-by-step explanation:
Which expression is equivalent to log Subscript 8 Baseline 4 a (StartFraction b minus 4 Over c Superscript 4 Baseline EndFraction)?
Answer:
[tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex].
Step-by-step explanation:
The given expression is
[tex]\log_84a\left(\dfrac{b-4}{c^4}\right)[/tex]
Using the properties of logarithm, we get
[tex]\log_84+\log_8a+\log_8\left(\dfrac{b-4}{c^4}\right)[/tex] [tex][\because \log_a mn=\log_a m+\log_a n][/tex]
[tex]\log_84+\log_8a+\log_8(b-4)-\log_8c^4[/tex] [tex][\because \log_a \frac{m}{n}=\log_a m-\log_a n][/tex]
[tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex] [tex][\because \log_a x^n =n\log_a x][/tex]
Therefore, the required expression is [tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex].
Answer:
B on edge
Step-by-step explanation:
Which of these levelers will make it easier to lift the object
Answer:
C
Step-by-step explanation:
Because it would have less weight to carry
(like Ross 6.28) The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L.M.) brings his car in at time 0 and Sally Carrera (S.C) brings her car in at time t, what is the probability that S.C.’s car is ready before L.M.’s car? Assume that service times are independent and service begins upon arrival of the car.
Answer: provided in the explanation section
Step-by-step explanation:
The complete question says:
The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L.M.) brings his car in at time 0 and Sally Carrera (S.C) brings her car in at time t, what is the probability that S.C.'s car is ready before L.M.'s car? Assume that service times are independent and service begins upon arrival of the car Be sure to: 1) define all random variables used, 2) explain how independence of service times plays a part in your solution, 3) show all integration steps. (b) If both cars are brought in at time 0, with work starting on S.C. 's car only when L.M.'s car has been completely serviced, what is the probability that S.C.'s car is ready before time 2?
Ans to this is provided in the images uploaded as it is not possible to put the symbols here...
i hope you find this helpful.
cheers !!
Triangle ABC is a right triangle whose right angle is ZABC.
Find the measure of ZEBF.
ZABC and DBF are vertical angles, so they have the same
measure. Because IZABC is 90°, the sum of m2. DBE and
m2 EBF must also be 90°
Solve for x in this equation.
x + (x - 12) = 90
2x - 12 = 90
2x = 102
X51
m2 EBF = 51°
1.What is m
2.What is m
3.Explain how to find m
Answer: m is 13
m is 6
you find m by calculating!
Step-by-step explanation:
Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. Select all that apply.
{f(x) = 2(3)^x
{g(x) = 10log(x+3)
(-1.9, 15.9)
(-2, 0.2)
(1.9, -15.9)
(2, -0.2) (1.9, 15.9)
Answer:
closest choice: (-2, 0.2)
Step-by-step explanation:
The attached image from a graphing calculator shows the solutions (to the nearest tenth) to be ...
(-1.9, 0.2)
(1.0, 6.0)
The closest of the offered choices is (-2, 0.2). None are actually correct.
For 120 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degree.Round your answer to 4 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.Sample size is .Number of samples is .When constructing a x-bar chart:The center line should be .ESD(x-bar) equals .The upper control limit (UCL) should be .The lower control limit (LCL) should be .
Answer:
Center line = 46
UCL = 46.84852
LCL = 45.15148
Step-by-step explanation:
Given:
Standard deviation = 0.8
Mean, u = 46
Sample size, n= 8
First calculate the estimated standard deviation:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{0.8}{\sqrt{8}} = 0.282843[/tex]
a) The center line, X', would be the average across all components. Here the average across all 960 bottles is 46
Therefore,
[tex] X' = 46 [/tex]
b) The upper control limit, UCL:
UCL = u + 3s
= 46 + 3(0.28284)
= 46 + 0.84852
= 46.84852
c) The upper control limit, LCL:
LCL = u + 3s
= 46 - 3(0.28284)
= 46 - 0.84853
= 45.15148
Will mark brainliest! Thanks ! and like if you can please explain it cuz I want to understand it to :)
Answer: F.) 7 triangles
Step-by-step explanation:
Congruent means completely equal in side lengths and angles. Think of this weird figure like 4 triangles that are see through and are covering a diamond underneath
Of those 4 "see through triangles", there are 3 equal to ΔABC
Now on the diamond underneath, there is another 4. Its hard to actually explain what I mean, but take two triangles from that dimaond. Theyre gonna be congruent to ΔABC.
That's 4 + 3 = 7 total triangles
16. Model with Math What must be the sum of
the two remaining numbers, x and y? Write an
equation to show how to find this sum.
Answer:
The sum of the two remaining numbers, x and y = 60
Question:
The question isn't clear enough as some information have been omitted. Let's consider the following:
Model with Math. The average of six numbers is 18. If the average of four numbers is 12. What must be the sum of the two remaining numbers, x and y?
Write an equation to show how to find this sum.
Step-by-step explanation:
Mathematical models are applied to represent things in the real world in order to solve problems.
The formula we would use to solve this problem is an example of a mathematical model.
Types of mathematical model we can use include equations and graphs.
Using equations:
Average of six numbers = 18
Average of four of the numbers = 12
Total sum of the four numbers = 4×12 = 48
the two unknown numbers are x and y
Average of six numbers = (Sum of all 6 numbers)/6
=(Total sum of four numbers + x + y)/6
(48 + x + y)/6 = 18
The equation that shows how to find the sum:
(1/6)(48 + x + y) = 18
48 + x + y = 18×6
48 + x + y = 108
x + y = 108-48
x+y = 60
The sum of the two remaining numbers, x and y = 60
What is the measure of
55°
The sum or measures of interior angle in a triangle is 180°.
Angle A, 35° + Angle C, 90° =125°
Angle B= 180°-125°=55°[angle B]
A car is discounted 10% and sells for $15,673. What was the discount amount?
Answer:
$1741.44
Step-by-step explanation:
The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:
10% = 90% × 1/9
The discount was ...
$15,673/9 = 1,741.44
_____
Check
The original is the sum of the discounted amount and the discount:
original price = $15,673.00 +1,741.44 = $17, 414.44
10% of that value is 1,741.44, as shown above.
If 4/3 * 3/4 = 5k, then k =
Answer:
1/5
Step-by-step explanation:
switch sides, delete both common factors and your stuck with 5k=1. then you put both in a fraction and it gets you 1/5
A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling the number 1, 3, or 4. If there is more than one element in the set, separate them with commas. Sample space: {} Event of rolling the number 1 3, or 4 :
Answer:
Sample space: [tex]\Omega=\{1,2,3,4,5,6\}[/tex]
Event of rolling the number 1 3, or 4 : A={1,3,4}
Step-by-step explanation:
When you roll a number cube with faces labeled from 1 to 6 once.
The possible outcomes are: 1,2,3,4,5 or 6.
Therefore, the sample space of this event is:
Sample space: [tex]\Omega=\{1,2,3,4,5,6\}[/tex]Given the event of rolling the numbers 1, 3, or 4.
Now we are required to give the outcomes for the event of rolling number 1,3 or 4. Let's call the event A. The set of possible outcomes for A has all the numbers 1, 3 and 4 as follows
Event of rolling the number 1 3, or 4 :A= {1,3,4}A researcher reports that the farther college students are from their parents, the more often they communicate with their parents (either by phone or by e-mail). Is this an example of a positive correlation or a negative correlation?
Answer:
Positive correlation
Step-by-step explanation:
A positive correlation exists between two variables, when both variables tend to move along the same direction. In order words, when one particular variable increases, there is also an increase in the other variable.
The case stated above is an example of positive correlation, because, the farther the students are from their parents, the more often they communicate with them. As distance increases, so does the number of, perhaps, phone calls increases as well.
Answer:
Positive correlation
Step-by-step explanation:
A positive correlation occurs whereby in a relationship between two variables, both variable move in the same direction meaning as one increases, the other also increases.
In this study, an increase in distance enforces an increase in communication with the parents.
Write this number in expanded notation:178.25
Answer:
100+70+8+0.2+0.05. is the answer
Answer:
178.25 as a fraction is 178 1/4 or 713 / 4
Step-by-step explanation:
hope it works out !!
If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest
Answer:
The age difference between the youngest and the oldest is 48
A fuel oil tank is an upright cylinder, buried so that its circular top is 8 feet beneath ground level. The tank has a radius of 6 feet and is 18 feet high, although the current oil level is only 12 feet deep. Calculate the work required to pump all of the oil to the surface. Oil weighs 50\, \hbox{lb/ft}^3.
Answer:
1.504×10⁶ ft·lb
Step-by-step explanation:
We understand the top of the oil in the tank is 12 ft below ground level, and the bottom of the tank is 8+18=26 ft below ground level. Then the average depth of the oil is (12+26)/2 = 19 ft below ground level.
The height of the oil in the tank is 26-12=14 ft, so the volume of it is ...
V = πr²h = π(6 ft)²(14 ft) = 504π ft³ ≈ 1583.36 ft³
__
So, the work required to raise that volume of oil to the surface is ...
(1538.36 ft³)(50 lb/ft³)(19 ft) = 1.504×10⁶ ft·lb
Find the area of the following square.
Write your answer in simplest form.
Be sure to include the correct unit in your answer.
4 1/2m
Answer:
[tex]20.25 \: m^2[/tex]
Step-by-step explanation:
Use the formula for the area of a square.
[tex]A=s^2[/tex]
Where [tex]s=4.5[/tex]
[tex]s^2\\(4.5)^2\\20.25[/tex]
The area of the square is 20.25 square meters as per the concept of the square.
To find the area of a square, we need to square the length of one of its sides. In this case, the side length is given as 4 1/2 meters.
First, we need to convert the mixed number 4 1/2 into an improper fraction. We can rewrite it as 9/2.
Next, we square the side length:
[tex]\frac{9}{2}^2 = \frac{81}{4}[/tex].
To simplify the fraction, we can divide the numerator by the denominator:
81 ÷ 4 = 20 remainders 1.
Therefore, the area of the square is 20 1/4 square meters.
However, we can simplify the mixed number further. Since 4 can be divided by 4 and 1 can be divided by 4, we have:
20 1/4
= 20 + 1/4
= 20 + 1/4
= 20 + 0.25
= 20.25.
Therefore, the area of the square is 20.25 square meters.
To learn more about the square;
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Please answer this correctly
Answer:
Bailey: 16%
Coco: 28%
Ginger: 32%
Ruby: 24%
I hope this helps!
Suppose U.S. consumers 21 years and older consumed 26.4 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:
H0: μ ≤ 26.4
Ha: μ > 26.4
(a) Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?
a) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence lower than throughout the United States.
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
c) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence higher than throughout the United States.
d) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence lower than throughout the United States.
(b) What is the Type I error in this situation? What are the consequences of making this error?
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
b) The type I error is not rejecting H0 when it is true. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually less than or equal to 26.4.
c) The type I error is not rejecting H0 when it is false. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually greater than 26.4.
d) The type I error is rejecting H0 when it is false. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually greater than 26.4.
(c) What is the Type II error in this situation? What are the consequences of making this error?
a) The type II error is accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is less than or equal to 26.4.
b) The type II error is not accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is not.
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
d) The type II error is not accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is greater than 26.4.
Answer:
Step-by-step explanation:
A. If the null hypothesis was rejected, the conclusion would be
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
B. The correct option is
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
C. The correct option is
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
Kortholts that fail to meet certain precise specifications must be reworked on the next day until they are within the desired specifications. A sample of one day's output of kortholts from the Melodic Kortholt Company showed the following frequencies: Plant A Plant B Row Total Specification Met 85 35 120 Specification Not Met 15 25 40 Column Total 100 60 160 Find the chi-square test statistic for a hypothesis of independence. Multiple Choice 7.22 14.22 -0.18 14.70
Answer:
The value of Chi-square test statistic for a hypothesis test of independence is 14.22.
Step-by-step explanation:
The data provided is for one day's output of Kortholt's from the Melodic Kortholt Company.
The formula to compute the chi-square test statistic for a hypothesis of independence is:
[tex]\chi^{2}=\sum {\frac{(O-E)^{2}}{E}}[/tex]
The formula to compute the expected frequencies (E) is:
[tex]E=\frac{\text{Row Total}\times \text{Column Total}}{N}[/tex]
Consider the Excel output attached.
Compute the value of Chi-square test statistic as follows:
[tex]\chi^{2}=\sum {\frac{(O-E)^{2}}{E}}[/tex]
[tex]=1.333+2.222+4.000+6.667\\=14.222\\\approx 14.22[/tex]
Thus, the value of Chi-square test statistic for a hypothesis test of independence is 14.22.
An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a random variable with variance = 5.
a) What is the probability that at most 3 cars per year will experience a catastrophe?
b) What is the probability that more than 1 car per year will experience a catastrophe?
Answer:
(a) Probability that at most 3 cars per year will experience a catastrophe is 0.2650.
(b) Probability that more than 1 car per year will experience a catastrophe is 0.9596.
Step-by-step explanation:
We are given that the distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with variance = 5.
Let X = the number of cars per year that will experience the catastrophe
SO, X ~ Poisson([tex]\lambda = 5[/tex])
The probability distribution for Poisson random variable is given by;
[tex]P(X=x) = \frac{e^{-\lambda} \times \lambda^{x} }{x!} ; \text{ where} \text{ x} = 0,1,2,3,...[/tex]
where, [tex]\lambda[/tex] = Poisson parameter = 5 {because variance of Poisson distribution is [tex]\lambda[/tex] only}
(a) Probability that at most 3 cars per year will experience a catastrophe is given by = P(X [tex]\leq[/tex] 3)
P(X [tex]\leq[/tex] 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= [tex]\frac{e^{-5} \times 5^{0} }{0!} +\frac{e^{-5} \times 5^{1} }{1!} +\frac{e^{-5} \times 5^{2} }{2!} +\frac{e^{-5} \times 5^{3} }{3!}[/tex]
= [tex]e^{-5} +(e^{-5} \times 5) +\frac{e^{-5} \times 25 }{2} +\frac{e^{-5} \times 125}{6}[/tex]
= 0.2650
(b) Probability that more than 1 car per year will experience a catastrophe is given by = P(X > 1)
P(X > 1) = 1 - P(X [tex]\leq[/tex] 1)
= 1 - P(X = 0) - P(X = 1)
= [tex]1-\frac{e^{-5} \times 5^{0} }{0!} -\frac{e^{-5} \times 5^{1} }{1!}[/tex]
= 1 - 0.00674 - 0.03369
= 0.9596
Calculate g(x)=f(x+1) when f(x) =4x-2
Answer:
g(x)= 2/5
Step-by-step explanation:
g(xl=f(4x-2)+1
5×-2
5x/5
x=2/5
The table represents a function. A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12. Which value is an output of the function? –6 –2 4 7The table represents a function. A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12. Which value is an output of the function? –6 –2 4 7
Answer:
-2 is an output of the function.
Step-by-step explanation:
The given table is as follows:
[tex]\left[\begin{array}{cc}{x}&f(x)\\-6&8\\7&3\\4&-5\\3&-2\\-5&12\end{array}\right][/tex]
Here, the values written on the left side of table i.e. values of [tex]x[/tex] are known as the domain values or input values to a function.
The values written on the right side of table i.e. values of [tex]f(x)[/tex] are known as the range values or output values of the function [tex]f(x)[/tex].
Let us consider the pairs of values:
(-6,8) then left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]
i.e. when [tex]x=-6[/tex], the output value [tex]f(x) =8[/tex].
The same thing applies for all the pairs of values.
similarly for the pair (3,-2):
Left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]
i.e. when [tex]x=3[/tex], the output value [tex]f(x) =-2[/tex].
So, the answer is:
-2 is an output of the function.
Answer:
-2
Step-by-step explanation:
What percentage of the total number of microstates are in one of the three most likely macro states of 100 coins being tossed (49 heads and 51 tails, 50 heads and 50 tails, or 51 heads and 49 tails)
Answer:
Step-by-step explanation:
Idk
Jake made a rectangular garden area as shown in the figure. He wants to add 3 inches of topsoil to the entire area.
36 in
15 in
How much topsoil does Jake need to get at the nursery?
540 in.
1,080 in.
1,386 in.
1,620 in.
Answer:
1,620in
Step-by-step explanation:
LxWxH
36 x 15 x 3 = 1,620 in
Answer:
1620
Step-by-step explanation:
Estimate the quotient 241 ÷ 5. A. 40 B. 250 C. 50 D. 60
Answer:
The quotient of 241 ÷ 5 is 48.
Step-by-step explanation:
Division is splitting into equal parts or groups.
The quotient is the answer after we divide one number by another.
To find the quotient 241 ÷ 5 you must:
Write the problem in long division format
[tex]5\overline{|\smallspace241}[/tex]
Divide 24 by 5 to get 4
Multiply the quotient digit 4 by the divisor 5
Subtract 20 from 24
Bring down the next number of the dividend
Divide 41 by 5 to get 8
Multiply the quotient digit 8 by the divisor 5
Subtract 40 from 41
[tex]\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{241}{5}\:\mathrm{is}\:48\:\mathrm{with\:remainder\:of}\:1\\\\48\quad \mathrm{Remainder}\quad \:1[/tex]
Alice studies the relationship between climate and heart disease around the world. H(t)H(t)H, left parenthesis, t, right parenthesis models the probability for the occurrence of heart disease (in percents relative to the global average) at an area where the temperature is ttt degrees Celsius. According to Alice's model, when the temperature is -5\degree\text{ C}−5° Cminus, 5, degree, start text, space, C, end text (which is the lowest temperature included in the model), the probability is 10\%10%10, percent above average. Then the probability decreases until the temperature reaches 30\degree\text{ C}30° C30, degree, start text, space, C, end text (which is the highest temperature included in the model), where the probability is 20\%20%20, percent below average. Which number type is more appropriate for the domain of HHH?
Answer:
The domain of the function H(t), is [-5, 30].
The range of the function H(t), is [(10% + average), (average - 20%)]
Step-by-step explanation:
The domain of a function is the complete set of possible values of the independent variable.
For this question, the function is H(t), with the temperature, t, serving as the independent variables and H(t) the evidently dependent variable.
The domain of a function refers to all the possible independent variable values that will give corresponding real dependent variable values.
For this question, Alice's model has the probability for the occurrence of heart disease (in percents relative to the global average) at an area, H(t) varying with the temperature of that area in degree Celsius.
At a temperature of -5°C (the lowest temperature in the model), the probability is 10% above the average.
Then, the probability decreases with increase in temperature, taking a value 20% lower than the average when the temperature is at its highest of 30°C in the model.
So, temperature ranges from -5°C to 30°C and the probability for the occurrence of heart disease ranges from 10% above the average to 20% below the average.
The domain of the function H(t), from the definition given above would therefore be [-5, 30]
And the range of the function H(t), is [(10% + average), (average - 20%)]
Hope this Helps!!!
The Real Number type is more appropriate fro the domain of H(t).
The domain of H(t) is given as [tex]-5 \leq t \leq 30[/tex]
Given that:
The lowest temperature included in the model is -5° C
The highest temperature included in the model is 30° C
The domain of H includes the values of the temperature. Since the temperature can be non integer too, sometimes rational too, thus we use Real Number type for the domain of H(t).
The domain of H(t) will be given by the following interval on real number line:
[tex]\begin{aligned} Domain(H(t)) = [-5, 30]\\\end{aligned}[/tex]
or [tex]-5 \leq t \leq 30[/tex].
Hence, the Real Number type is more appropriate fro the domain of H(t).
The domain of H(t) is given as [tex]-5 \leq t \leq 30[/tex].
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The mean annual salary for intermediate level executives is about $74000 per year with a standard deviation of $2500. A random sample of 36 intermediate level executives is selected. What is the probability that the mean annual salary of the sample is between $71000 and $73500?
Answer:
11.51% probability that the mean annual salary of the sample is between $71000 and $73500
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 normally distributed samples are 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.
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 = 74000, \sigma = 2500, n = 36, s = \frac{2500}{\sqrt{36}} = 416.67[/tex]
What is the probability that the mean annual salary of the sample is between $71000 and $73500?
This is the pvalue of Z when X = 73500 subtracted by the pvalue of Z when X = 71000. So
X = 73500
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{73500 - 74000}{416.67}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151
X = 71000
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{71000 - 74000}{416.67}[/tex]
[tex]Z = -7.2[/tex]
[tex]Z = -7.2[/tex] has a pvalue of 0.
0.1151 - 0 = 0.1151
11.51% probability that the mean annual salary of the sample is between $71000 and $73500
What is the solution to this equation?
10x - 3(x- 6) = x + 30
O A. x = 8
O B. x = 2
C. X= 4
[tex]answer \\ 2\\ solution \\ 10x - 3(x - 6) = x + 30 \\ or \: 10x - 3x + 18 = x + 30 \\ or \: 10x - 3x - x = 30 - 18 \\ or \: 7x - x = 12 \\ or \: 6x = 12 \\ or \: x = \frac{12}{6} \\ x = 2 \\ hope \: it \: helps[/tex]
Answer:
x=2
Step-by-step explanation:
10x - 3(x- 6) = x + 30
Distribute
10x -3x+18 = x+30
Combine like terms
7x + 18 = x+30
Subtract x from each side
6x+18 = 30
Subtract 18 from each side
6x = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x =2
What is the length of AC
Answer:
5.8
Step-by-step explanation:
The angle bisector makes the triangle sides on either side of it proportional.
AC/CD = AB/BD
AC = CD·AB/BD
AC = 2(8.1/2.8) = 8.1/1.4 ≈ 5.7857 . . . . substitute shown values, evaluate
AC ≈ 5.8
