Step-by-step explanation:
If you look care fully from that number -11 he plused 3 to every number .
-11+3=-8
-8+3=-5
-5+3=-2
From the topic of sequence and series
What is the range of f(x) = (3/4)^x -4
{yly>-4}
{yly>3/4}
{yly<-4}
{vly<3/4}
Answer:
the range for this problem is the first one
The range of f(x) =(3/4)ˣ- 4 function is {yly>-4}, Option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
The function f(x) = (3/4)ˣ- 4 is an exponential function with a base of 3/4. The base is between 0 and 1, which means that the function is decreasing as x increases.
The function has a vertical asymptote at x = infinity, since the base is between 0 and 1, and the function approaches 0 as x approaches negative infinity.
As the exponential function (3/4)ˣ approaches 0 as x approaches infinity, we have:
lim((3/4)ˣ) = 0 as x -> infinity
So, the range of the given function is all real numbers greater than -4.
Hence, the range of function f(x) =(3/4)ˣ- 4 is {yly>-4}, Option A is correct.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ7
The study ran for several weeks during the semester. About a week after it started, the university announced that they would be holding training sessions for faculty and staff about how to handle situations involving a gunman on campus. This shut down the study for several days as the university needed the lab building for training. The study then resumed according to script after the training. The researchers found that those in the experimental group did not differ in their memories regarding the presence of a gun compared to those in the control condition. That is, the mean score that a gun was present was similar for the experimental group (M = 65%, SD = 11.4%) and the control group (M = 63%, SD = 13.26%). a. Maturation b. Regression to the mean c. Selection d. Mortality e. Instrumentation f. Testing g. History h. Interactions i. Diffusion j. No Threa
Answer: option (g)
Step-by-step explanation:
So the question says :
The study ran for several weeks during the semester. About a week after it started, the university announced that they would be holding training sessions for faculty and staff about how to handle situations involving a gunman on campus. This shut down the study for several days as the university needed the lab building for training. The study then resumed according to script after the training. The researchers found that those in the experimental group did not differ in their memories regarding the presence of a gun compared to those in the control condition. That is, the mean score that a gun was present was similar for the experimental group (M = 65%, SD = 11.4%) and the control group (M = 63%, SD = 13.26%). a. Maturation b. Regression to the mean c. Selection d. Mortality e. Instrumentation f. Testing g. History h. Interactions i. Diffusion j. No Threat
ANS ⇒ The correct answer to this question is option G.
We can confirm here that History is the biggest threat to internal validity in the study as a significant period of time was allowed to pass between the testing conditions.
cheers i hope this helped !!!
The equation for the trend line for the scatterplot shown below is y = 5x + 24. What does the slope mean in the context of this problem?
A). The total amount of dollars earned is about $64
B). If no hours are worked, $24 is made
C). For each hour worked the dollars earned increases by $5
D). A total of $80 was earned
Please help
Answer:
C) For each hour worked the dollars earned increases by $5
Step-by-step explanation:
I don't have the context of the problem.
However, we do know that in math, when we have an equation of the form [tex]y=mx+b[/tex], the slope m represents the rate of change. This means, how much one quantity changes in regards to other quantity (from the options I can assume that we are talking about amount earned and hours worked).
Thus, in this case we have [tex]m=5[/tex] and this tells us how much the payment increase in terms of hours worked. Thus, we can say that for each work we work the payment increases by $5.
Thus, the correct answer is c) For each hour worked the dollars earned increases by $5
The speed of an object in space is shown in the graph.
What is the slope of the line?
(picture) please and thank you
Answer:
1 / 15
Step-by-step explanation:
The vertical change (rise) is 6 - 3, or just 3. The horizontal change (run) is 0.4 - 0.2, or 0.2. Thus the slope of this line is m = rise / run = 0.2 / 3 = 2 / 30 = 1 / 15
The size of a slow-growing bacteria strain increases continuously over time. This equation describes the predicted size of the bacteria strain, in square millimeters, after t minutes: y = 112(1.58)t. According to the equation, what will the approximate size of the bacteria strain be after 5 minutes?
Answer:
1102.8 mm^2
Step-by-step explanation:
We presume your equation is intended to be ...
y = 112(1.58)^t
Since t is in minutes, fill in the given value and do the arithmetic:
y = 112(1.58)^5 = 112(9.84658) ≈ 1102.8
The approximate size of the bacteria strain will be 1102.8 mm^2 after 5 minutes.
Answer:
Explanation:
To find the size of bacteria in five minutes, substitute 5 for t in the equation and simplify:
y = 112(1.58)5
= 112 ∙ 9.85
= 1,103.2.
Round the answer to the closest integer to get 1,103.
Step-by-step explanation:
Independent random samples from two regions in the same area gave the following chemical measurements (ppm). Assume the population distributions of the chemical are mound-shaped and symmetric for these two regions.
Region I: ; 438 1013 1127 737 491 840 306 402 1155 1075 500 340
Region II: ; 778 464 563 610 827 894 476 394 824 387 816 767 479 710 389 826
Required:
Find a 90% confidence interval.
Answer:
The 90% confidence interval for the difference between means is (-161.18, 205.18).
Step-by-step explanation:
Sample mean and standard deviation for Region I:
[tex]M=\dfrac{1}{12}\sum_{i=1}^{12}(438+1013+1127+737+...+1075+500+340)\\\\\\ M=\dfrac{8424}{12}=702[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{12}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{11}\cdot [(438-(702))^2+(1013-(702))^2+...+(500-(702))^2+(340-(702))^2]}\\\\\\[/tex]
[tex]s=\sqrt{\dfrac{1}{11}\cdot [(69696)+(96721)+...+(131044)]}\\\\\\s=\sqrt{\dfrac{1174834}{11}}=\sqrt{106803.1}\\\\\\s=326.8[/tex]
Sample mean and standard deviation for Region II:
[tex]M=\dfrac{1}{15}\sum_{i=1}^{15}(778+464+563+...+479+710+389+826)\\\\\\ M=\dfrac{10204}{15}=680[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{15}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{14}\cdot [(778-(680))^2+(464-(680))^2+...+(389-(680))^2+(826-(680))^2]}\\\\\\[/tex]
[tex]s=\sqrt{\dfrac{1}{14}\cdot [(9551.804)+(46771.271)+...+(84836.27)+(21238.2)]}\\\\\\ s=\sqrt{\dfrac{545975.7}{14}}=\sqrt{38998}\\\\\\s=197.5[/tex]
Now, we have to calculate a 90% confidence level for the difference of means.
The degrees of freedom are:
[tex]df=n1+n2-2=12+15-2=25[/tex]
The critical value for 25 degrees of freedom and a confidence level of 90% is t=1.708
The difference between sample means is Md=22.
[tex]M_d=M_1-M_2=702-680=22[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{326.8^2}{12}+\dfrac{197.5^2}{15}}\\\\\\s_{M_d}=\sqrt{8899.853+2600.417}=\sqrt{11500.27}=107.24[/tex]
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=1.708 \cdot 107.24=183.18[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 22-183.18=-161.18\\\\UL=M_d+t \cdot s_{M_d} = 22+183.18=205.18[/tex]
The 90% confidence interval for the difference between means is (-161.18, 205.18).
A team of 5 IT specialists is to be selected to attend a lecture from 16 IT specialists. In how
many different ways can the team be formed?
124
4368
480
2880
Answer:
[tex] 16C5= \frac{16!}{5! (16-5)!}= \frac{16!}{5! 11!}= \frac{16*15*14*13*12*11!}{5! 11!}[/tex]
If we simplify we got:
[tex] 16C5 = \frac{16*15*14*13*12}{5*4*3*2*1}=4368[/tex]
And the best option would be:
4368
Step-by-step explanation:
For this case we have a total of 16 IT specialists and we want to select 5 IT specialists from the total of 16 so we can use the combination formula given by:
[tex] nC x= \frac{n!}{x! (n-x)!}[/tex]
And replacing we got:
[tex] 16C5= \frac{16!}{5! (16-5)!}= \frac{16!}{5! 11!}= \frac{16*15*14*13*12*11!}{5! 11!}[/tex]
If we simplify we got:
[tex] 16C5 = \frac{16*15*14*13*12}{5*4*3*2*1}=4368[/tex]
And the best option would be:
4368
the cost is 284 the operating expenses are 43 the reduced price is 299 what is the operating loss
Answer:
28
Step-by-step explanation:
operating loss is loss when value of operating loss is more than gross profit.
In the given problem
cost: 284
price : 299
profit = 299 - 284 = 15
but given that there is operating expense as well.
operating expenses = 43
as expense is greater than profit there is loss which is called operating loss.
operating loss = operating expense - profit = 43 - 15 = 28
Thus, operating loss is 28.
The profit a company makes from producing x tabletops is modeled by the equation p(x) = 480x minus 2x squared. For what number of tabletops does the company need to make a profit of zero dollars?
Answer:
240 table tops or none
Step-by-step explanation:
p(x) = 480x- 2x^2
For profit to be 0, it means;
p(x)= 0
Therefore 480x- 2x^2 = 0
Dividing through by 2 we have ;
240x - x^2 = 0
By factorisation of x we have ;
(240-x) x = 0
x = 0 or 240-x= 0; x= 240( by moving x to the right of the expression:240-x= 0; we have 240=x => x=240).
So the company needs to produce 240 table tops or none in order not to make a profit.
The company need to make a profit of zero dollars will be 240.
What is a profit?A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running or creating anything.
The profit a company makes from producing x tabletops is modeled by the equation is given as,
p(x) = 480x – 2x²
Then the company need to make a profit of zero dollars will be
p(x) = 0
480x – 2x² = 0
2x(240 – x) = 0
x = 0, 240
More about the profit is given below.
https://brainly.com/question/15036999
#SPJ2
Data on a sample of 100 customers of Alibaba, a direct marketing company, for the current year. The variables are defined as follows: Customer = a code for the customer Own Home = 1 if customer owns home, o if renting Close = 1 if lives close to stores (with similar merchandise), O if not Salary = annual household salary in $ Catalogs = number of catalogs this customer was sent this year Amount Spent = Amount spent total on purchases this year You are given the result of the multiple regression with dependent variable = Amount Spent. Use this output to answer the questions
(a) - (g) below the output. SUMMARY OUTPUT Regression Statistics Multiple R 0.8366 R Square 0.6999 Adjusted R Squ 0.6873 Standard Error 512.72 Observations 100 ANOVA df f ignificance F 55.39 0 .000 Regression Residual Total 4 95 99 SS 58241400.88 24974011.87 83215412.75 M S 14560350.22 262884.34 Intercept Own Home Close Salary Catalogs Coefficients Standard Error -91.67 185.917 -229.47 121.800 -604.90 114.229 0.02216 0.002 42.62 8.451 t Stat -0.493 -1.884 -5.295 9.836 5.043 P-value Lower 95% Upper 95% 0.623 -460.76 277.42 0.063 -471.27 12.34 0.000 -831.67 -378.12 0.000 0.02 0.03 0.000 25.84 59.40
(b) Using the regression model in (a), predict the mean amount spent by Amy, a customer who has the following characteristics: does not own a home, but lives close to stores that have similar merchandise, salary is $60,000 and is sent 12 catalogs this year. Give the value rounded to the nearest cent.
(c) Suppose Brenda has the same characteristics as Amy but does not live close to store with similar merchandise. How much would you expect Brenda to spend? Give the value rounded to the nearest cent.
Answer:
a. [tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)[/tex]
b. the expected amount spent by Amy is $1144.47
c. the expected amount that Brenda is going to spend is $1749.37
Step-by-step explanation:
(a)
From the regression output; the equation for the regression model can be written as:
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)[/tex]
From the information given in the question;
(b)
Amy does not own a home but rent; the variables given also stated that ;
Own Home = 1 if customer owns home, 0 if renting
So for Amy ; Own Home = 0 (since it is rented)
Close = Yes(1)
Salary = $60,000
Catalogs = 12
Therefore;
the mean amount spent by Amy is by using the regression model is ;
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 1) +(0.02216 * 60000) + (42.62 * 12)[/tex]
[tex]\hat{amount} \ \hat{ spent} = -91.67 -0-604.90 +1329.6 + 511.44[/tex]
[tex]\hat{amount} \ \hat{ spent} =1144.47[/tex]
Thus; the expected amount spent by Amy is $1144.47
(c)
If Brenda has the same characteristics as Amy but does not live close to store with similar merchandise.
Then the Close for Brenda will be = No (0)
Thus; the amount spent by Brenda will be:
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 0) +(0.02216 * 60000) + (42.62 * 12)[/tex]
[tex]\hat{amount} \ \hat{ spent} = -91.67 -0-0 +1329.6 + 511.44[/tex]
[tex]\hat{amount} \ \hat{ spent} = 1749.37[/tex]
Thus, the expected amount that Brenda is going to spend is $1749.37
What’s the surface area of this shape?
Answer:
210 in²
Step-by-step explanation:
6*2.5+6*6*2+(8+6)*2.5+10*2.5+1/2*6*8*2+6*2.5= 210 in²
Does anyone know how to solve this?
Find the distance between the points (1,7) and ( 5, 10).
Answer:
Step-by-step explanation:
[tex]\sqrt{(5-1)^{2} +(10-7)^{2}\\\\\sqrt{4^{2} + 3^{2} \\\\\sqrt{16+9} = \sqrt{25} = 5[/tex]
In the equation 52y = 104, what is the next step in the equation solving sequence?
Solve for the variable.
Isolate the variable using inverse operations.
Combine like terms.
Move all numbers without a variable.
Answer:
Isolate the variable using inverse operations.
You would divide each side by 52.
00:00
Use the Distributive Property to find the product of 6 x 3,584. Enter your answer in the box.
Answer:
21,504
Step-by-step explanation:
This is the usual method multiplication is done "by hand."
6 × 3584 = 6 × (3000 +500 +80 +4)
= 6×3000 +6×500 +6×80 +6×4
= 18000 +3000 +480 +24
= 21000 +504
= 21,504
_____
Many of us are taught in grade school to do the multiplication right to left:
= 6×4 +6×80 +6×500 +6×3000
... writing down the digit corresponding to the place value of the product, and "carrying" any more significant digits to add to the next product.
Here, that looks like 6×4 = 24, write down 4, carry 2. 6×8 = 48, add 2 to get 50, write down 0, carry 5. 6×5 = 30, add 5 to get 35, write down 5, carry 3. 6×3 = 18, add 3 to get 21, write down 21. Then the product is 21504.
__
When doing mental calculation, or using an abacus or soroban, it often works better to do the multiplication left to right, as shown in the answer above.
need asap to get the points plz
the problaty of getting Gray tile is 6 time
The percentage charged each month on purchases charged to the credit card
account is called the__?
A) periodic rate
B) new balance
C) unpaid balance
D) minimum payment
Answer:
A) periodic rate
Step-by-step explanation:
Because a percentage that is charged or added to the credit card we assume that it is an interest rate, they also tell us that it is charged every month, that is, it has a known collection frequency, which means that it is Newspaper.
therefore, the answer in this case is A) periodic rate since it complies with the premise of the statement
Question: I had $5.00 My Mom gave me $10.00 while my Dad gave me $30.00. My Aunt and Uncle gave me 100.00. I had another $5.00 How much money did I really have?
Answer:
I had $10
I have $150
Step-by-step explanation:
This is a riddle and not a math question
So
I had $5I received $10+$30+$100= $140I had another $5The answer to the question how much I had is:
$5 + $5 = $10The answer to the question how much I have is:
$5+ $10 + $30 + $100 + $5 = $150Here we need to perform an addition of several numbers.
We will find that the total amount of money that you have is $150.
We know that:
You had $5.00
Your mom gave you $10.00
Your dad gave you $30.00
Your aunt and uncle gave you $100.00
You had another $5.00
Now you want to find how much money do you have, so you just need to add these numbers.
We can add it as:
$5 + $10 + $30 + $100 + $5
We can perform the addition in any order we want, for example:
($5 + $5) + $10 + $30 + $100
$10 + $10 + $30 + $100
($10 + $10) + $30 + $100
$20 + $30 + $100
($20 + $30) + $100
$50 + $100 = $150
You have $150.
If you want to learn more, you can read:
https://brainly.com/question/19245500
Q1.
Diaries are sold in boxes of 12
Pencils are sold in boxes of 10
Rulers are sold in boxes of 6
A teacher wants to buy the same number of diaries, pencils and rulers.
Work out the smallest number of boxes of each item he could buy.
boxes of diaries
boxes of pencils
boxes of rulers
Tebal
Answer:
5 boxes of diaries
6 boxes of pencils
10 boxes of rulers
Step-by-step explanation:
In order to find the smallest number of units that would be possible to buy, find the least common multiple between the number of units in each box:
[tex]12\ \ 10\ \ 6\ |2\\6\ \ \ \ 5\ \ \ 3\ |2\\3\ \ \ \ 5\ \ \ 3\ |3\\1\ \ \ \ 5\ \ \ 1\ |5\\1\ \ \ \ 1\ \ \ 1\ | = 2*2*3*5=60[/tex]
The number of boxes required for each item to get 60 units is:
[tex]d=\frac{60}{12} = 5\ boxes \\p=\frac{60}{10} = 6\ boxes \\r=\frac{60}{6} = 10\ boxes[/tex]
the smallest number of boxes of each item he could buy is:
5 boxes of diaries
6 boxes of pencils
10 boxes of rulers
A company employs six women and eight men. The company randomly selects one employee to receive additional vacation time. Using the classical approach, what is the probability that the selected employee will be a woman
Answer: 6/14 or 3/7
Step-by-step explanation:
There are a total of 14 employees hired so it would like like this: 1/14 if you were to chose one of all 6 women and 8 men hired.
There are 6 women that may be chosen out of all 14 employees of which 8 are men, now what this would look like is : 6?14 or simplified, (3/7).
This means there is a 6/14 chance of choosing a woman instead of a man in these 14 hired employees. just because the question asks, "what is the chance of a woman getting chosen", of the other 5 women and 8 men hired, so the answer is 6/14 or 3/7 to chosen as a women instead of men in all the 14 employees that may/might be chosen. hope this helps love yawl!!
STAY SAFE !!! LOVE YOU !!! <3 <3 <3 <3
..... <3 <3 <3 <3 <3 <3 <3 .....
How do I solve this?
Answer:
h(x-11)=-5
Step-by-step explanation:
just put the equetion from the top
h(x-11)=-5
What are the coordinates of the pre-image of B'?
O (2, -8)
O (-8, -2)
O (-2, 8)
O (8,2)
Answer:
b. (-8, -2)
Step-by-step explanation:
Reflection across the x-axis
(x, y) ---> (x, -y)
B'(- 8, 2) ---> B( - 8, -2)
The coordinates of the pre image of B is (-8,-2) by studying the given graph.
How to find reflected coordinates of B'The given figure ABCD is reflected across the x-axis to create the figure A'B'C'D'.
By referring the graph we can say that the coordinate of B' is (-8,2)
The reflected point will have y coordinate's sign changed as the figure is reflected across x-axis.
Thus the pre image of B' will be (-8,-2)
Hence the coordinates of the pre image of B' is (-8,-2)
Learn more about coordinate system here:
brainly.com/question/84289
#SPJ2
The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 15 cm and the width is 12 cm, how fast is the area of the rectangle increasing?
Answer:
105 cm ^ 2 / s
Step-by-step explanation:
We have that the area of a rectangle is given by the following equation:
A = l * w
being the length and w the width, if we derive with respect to time we have:
dA / dt = dl / dt * w + dw / dt * l
We all know these data, l = 15; w = 12; dl / dt = 5; dw / dt = 3, replacing we have:
dA / dt = 5 * 12 + 3 * 15
dA / dt = 105
Which means that the area of the rectangle increases by 105 cm ^ 2 / s
Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 the job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this. 30 + 15 x greater-than-or-equal-to 90 Which best describes the restrictions on the jobs Deepak will accept? He only accepts jobs that last 4 or more hours. He only accepts jobs that last 5 or more hours. He only accepts jobs that last 8 or more hours. He only accepts jobs that last 9 or more hours.
Answer:
(A)He only accepts jobs that last 4 or more hours.
Step-by-step explanation:
Deepak charges $30 for each job plus an additional $15 for each hour he works.
Let the number of hours =x
Deepak's Total Income for x hours =30+15x
Since he only accepts jobs if he will earn at least $90 the job.
[tex]\text{Total Income}\geq 90[/tex]
[tex]30+15x\geq 90[/tex]
We then solve the inequality for x
[tex]30+15x\geq 90\\$Subtract 30 from both sides\\30-30+15x\geq 90-30\\15x\geq 60\\$Divide both sides by 15\\15x\div 15\geq 60 \div 15\\x\geq 4[/tex]
We therefore conclude that Deepak only accepts jobs that last 4 or more hours.
The correct option is A.
Answer:
A) He only accepts jobs that last 4 or more hours.
Step-by-step explanation:
Correct me if i'm wrong sorry if i am :)
Which expressions are equivalent to StartFraction 1 Over 36 EndFraction? Check all that apply. 3 Superscript negative 6 6 Superscript negative 2 StartFraction 6 cubed Over 6 Superscript 5 EndFraction StartFraction 6 squared Over 6 Superscript negative 1 EndFraction 6 times 6 Superscript negative 2 6 Superscript negative 9 Baseline times 6 Superscript 7
Answer:
6^-2
6^3/6^5
6^-9 *6^ 7
Step-by-step explanation:
We want the fractions equal to 1/36
We know that a^-b = 1/a^b
We also know that a^b / a^c = a^(b-c)
We also know that a^b * a^c = a^(b+c)
3^ -6 = 1/3^6 = 1/729
6^-2 = 1/6^2 = 1/36
6^3/6^5 = 6^(3-5) = 6^-2 = 1/6^2 = 1/36
6^2 / 6^-1 = 6^(2- -1) = 6^3 = 216
6*6^-2 = 6^(1-2) = 6^-1 = 1/6
6^-9 *6^ 7 = 6^(-9+7) = 6^ -2 = 1/6^2 = 1/36
Answer:
B C and F
Step-by-step explanation:
An NCAA study reported that the average salary of the 300 major college football coaches is $1.47 million. Using a random sample of 30 coaches and a population standard deviation of $300,000, what is the probability that the sample mean is between $1.4 million and $1.5 million per year?
Answer:
60.85% probability that the sample mean is between $1.4 million and $1.5 million per year
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:
In millions of dollars.
[tex]\mu = 1.47, \sigma = 0.3, n = 30, s = \frac{0.3}{\sqrt{30}} = 0.0548[/tex]
What is the probability that the sample mean is between $1.4 million and $1.5 million per year?
This is the pvalue of Z when X = 1.5 subtracted by the pvalue of Z when X = 1.4. So
X = 1.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.5 - 1.47}{0.0548}[/tex]
[tex]Z = 0.55[/tex]
[tex]Z = 0.55[/tex] has a pvalue of 0.7088
X = 1.4
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.4 - 1.47}{0.0548}[/tex]
[tex]Z = -1.28[/tex]
[tex]Z = -1.28[/tex] has a pvalue of 0.1003
0.7088 - 0.1003 = 0.6085
60.85% probability that the sample mean is between $1.4 million and $1.5 million per year
Answer:
[tex] z= \frac{1.4-1.47}{\frac{0.3}{\sqrt{30}}}= -1.278[/tex]
[tex] z= \frac{1.5-1.47}{\frac{0.3}{\sqrt{30}}}= 0.548[/tex]
And we can find the probability with this difference:
[tex] P(-1.278<z<0.548) = P(z<0.548) -P(z<-1.278) =0.708-0.101= 0.607[/tex]
So then the probability that the sample mean is between $1.4 million and $1.5 million per year is 0.607
Step-by-step explanation:
For this case we have the following info given:
[tex] \mu = 1.47[/tex] the true mean for the problem
n =30 represent the sample size
[tex] \sigma = 0.3 millions[/tex] represent the population deviation
And we want to find this probability
[tex] P(1.4< \bar X <1.5)[/tex]
And we can use the z score given by:
[tex] z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z scores for the limits we got:
[tex] z= \frac{1.4-1.47}{\frac{0.3}{\sqrt{30}}}= -1.278[/tex]
[tex] z= \frac{1.5-1.47}{\frac{0.3}{\sqrt{30}}}= 0.548[/tex]
And we can find the probability with this difference:
[tex] P(-1.278<z<0.548) = P(z<0.548) -P(z<-1.278) =0.708-0.101= 0.607[/tex]
So then the probability that the sample mean is between $1.4 million and $1.5 million per year is 0.607
Write the given second order equation as its equivalent system of first order equations. u′′−5u′−4u=1.5sin(3t),u(1)=1,u′(1)=2.5 Use v to represent the "velocity function", i.e. v=u′(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.)
Answer:
hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to
Answer: v = 5v + 4u + 1.5sin(3t),
0 1 4 5 0 1.5sin(3t) 1 2.5Step-by-step explanation:
u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1
v represents the "velocity function" i.e v = u'(t)
As v = u'(t)
u' = v
since u' = v
v' = u"
v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )
= 5v + 4u + 1.5sin(3t) ( noting that v = u' )
so v' = 5v + 4u + 1.5sin(3t)
d/dt [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex]= [tex]\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex] + [tex]\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right][/tex]
Given that u(1) = 1 and u'(1) = 2.5
since v = u'
v(1) = 2.5
note: the initial value for the vector valued function is given as
[tex]\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1\\2.5\\\end{array}\right][/tex]
ive been struggling with cones so pls halp me TwT i appreciate it a lot
lateral area
surface area
volume
Answer:
Volume = PI * radius^2 * height / 3
Volume = 4,712.39 cubic feet
Lateral Area = PI * radius * slant height
slant height^2 = 20^2 + 15^2
slant height ^2 = 625 slant height = 25
Lateral Area = PI * 15 * 25 = 1,178.1 square feet
Surface Area = PI * radius^2 = 706.86 square feet
Step-by-step explanation:
A pyrotechnician plans for two fireworks to explode together at the same height in the air. They travel at speeds shown below. Firework B is launched 0.25 s before Firework A. How many seconds after Firework B launches will both fireworks
explode?
Firework A
360 ft/s
Firework B
340 ft/s
Answer:
both fireworks will explode 4.5 seconds after Firework B launches
Step-by-step explanation:
Given;
speed of firework A, [tex]V_A[/tex]= 360 ft/s
speed of firework B, [tex]V_B[/tex] = 340 ft/s
If the two fireworks explodes at the same height, then the height attained by the two fireworks are equal.
let the distance traveled by each firework before explosion = d
Distance = speed x time
Distance A = Distance B
speed A x time = speed B x time
let the time both fireworks explodes after Firework B launches = t
([tex]V_A[/tex]) t = ([tex]V_B[/tex] ) t
360t = 340t
if firework B is launched 0.25 s before Firework A, for the time of the two fireworks to be equal since we are considering time (t) after 0.25 seconds, we will have;
360(t-0.25) = 340t
360t - 90 = 340t
360 t - 340 t = 90
20 t = 90
t = 90/20
t = 4.5 seconds
Therefore, both fireworks will explode 4.5 seconds after Firework B launches
Solve the inequality 7x ≥ –7
Answer:
x ≥ -1
Step-by-step explanation:
Divide everything by 7 to isolate x and you have your answer!
Answer:
x ≥ –1
Step-by-step explanation:
7x ≥ –7
Divide by 7
7x /7≥ –7/7
x ≥ –1