Answer:
100
Step-by-step explanation:
The population is changing linearly. This means that the population is increasing by a particular value n every year.
From 2009 to 2017, there are 8 increases and so, the population increases by 8n.
The population increased from 1700 to 2500. Therefore, the population increase is:
2500 - 1700 = 800
This implies that:
8n = 800
=> n = 800/8 = 100
The average population growth per year is 100.
What is the quadratic regression equation that fits these data
Answer:
Rounded to two decimals the regression curve is:
[tex]y=-0.70\,x^2+2.37\,x+11.96[/tex]
Step-by-step explanation:
The objective of this problem is to have you use a calculator and enter the data in to separate lists: one containing the x-values, and the other the correspondent y-values (following the same order).
Once the data is entered, you need to access the regression tool and request a quadratic form of regression.
You should get and image and resulting function as shown in the attached image.
Answer:
Rounded to two decimals the regression curve is:
Step-by-step explanation:
A concert promoter sells tickets and has a marginal-profit function given below, where Upper P prime (x )is in dollars per ticket. This means that the rate of change of total profit with respect to the number of tickets sold, x, is Upper P prime (x ). Find the total profit from the sale of the first 480 tickets, disregarding any fixed costs.
Answer:
09
Step-by-step explanation:
There are 60 people at the subway station 12 of them jumped the
turnstile. What percentage of people jumped the turnstile? What
percentage of people paid?
Answer:
20% jumped the turnstile
80% paid
Step-by-step explanation:
We can calculate the percent of people that jumped it by dividing the number that did by the total:
12/60 = 0.2, which is 20%
If 20% jumped it, then this means 80% paid.
Answer:
jumped= 20%
paid= 80%
Step-by-step explanation:
[tex]\frac{12}{60}[/tex]×100 = 20%
[tex]\frac{48}{60}[/tex]×100 = 80%
Find the number for which: 25% is a lb
Answer:
1.25 lbs
Step-by-step explanation:
Since we are given 25% of a number is equal to 1 pound, we simply add 25% to 1 to get our number:
1(1 + 0.25)
1(1.25)
1.25 lbs
Answer:
4a lb
Step-by-step explanation:
If 25% is 1 a lb, then just multiply by 4 to get 4 a lb
You are given that sin(A)=−20/29, with A in Quadrant III, and cos(B)=12/13, with B in Quadrant I. Find sin(A+B). Give your answer as a fraction.
Answer:
[tex]sin(A+B)=-\dfrac{345}{377}[/tex]
Step-by-step explanation:
Given that:
[tex]sin(A)=-\dfrac{20}{29}\\cos(B)=\dfrac{12}{13}[/tex]
A is in 3rd quadrant and B is in 1st quadrant.
To find: sin(A+B)
Solution:
We know the Formula:
1. [tex]sin(A+B) = sinAcosB+cosAsinB[/tex]
2. [tex]sin^{2} \theta+cos^{2} \theta=1[/tex]
Now, let us find the values of cosA and sinB.
[tex]sin^{2} A+cos^{2} A=1\\\Rightarrow (\frac{-20}{29})^2+cos^{2} A=1\\\Rightarrow cos^{2} A=1- \dfrac{400}{941}\\\Rightarrow cos^{2} A=\dfrac{941-400}{941}\\\Rightarrow cos^{2} A=\dfrac{441}{941}\\\Rightarrow cos A=\pm \dfrac{21}{29}[/tex]
A is in 3rd quadrant, so cosA will be negative,
[tex]\therefore cos A=-\dfrac{21}{29}[/tex]
[tex]sin^{2} B+cos^{2} B=1\\\Rightarrow sin^{2} A+(\frac{12}{13})^2=1\\\Rightarrow sin^{2} B=1- \dfrac{144}{169}\\\Rightarrow sin^{2} B=\dfrac{169-144}{169}\\\Rightarrow sin^{2} B=\dfrac{25}{169}\\\Rightarrow sinB=\pm \dfrac{5}{13}[/tex]
B is in 1st quadrant, sin B will be positive.
[tex]sinB =\dfrac{5}{13}[/tex]
Now, using the formula:
[tex]sin(A+B) = sinAcosB+cosAsinB\\\Rightarrow -\dfrac{20}{29} \times \dfrac{12}{13}-\dfrac{21}{29}\times \dfrac{5}{13}\\\Rightarrow -\dfrac{20\times 12+21\times 5}{29\times 13} \\\Rightarrow -\dfrac{240+105}{29\times 13} \\\Rightarrow -\dfrac{345}{377}[/tex]
[tex]sin(A+B)=-\dfrac{345}{377}[/tex]
From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 265. A thermostat used in an electrical device is to be checked for accuracy of its design setting of 200◦F. Ten thermostats were tested to determine their actual settings, resulting in the following data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0 Perform the t-test to determine if the mean setting is different from 200◦F. Use α = 0.05
Answer:
[tex]t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =2*P(t_{(9)}>2.32)=0.0455[/tex]
For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.
Step-by-step explanation:
Information given
data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0
We can calculate the sample mean and deviation with the following formulas:
[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=201.77[/tex] represent the sample mean
[tex]s=2.41[/tex] represent the sample standard deviation
[tex]n=10[/tex] sample size
[tex]\mu_o =200[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to test
We want to determine if the true mean is equal to 200, the system of hypothesis are :
Null hypothesis:[tex]\mu = 200[/tex]
Alternative hypothesis:[tex]\mu = 200[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
The statistic is given by:
[tex]t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =2*P(t_{(9)}>2.32)=0.0455[/tex]
For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.
Not sure how to solve this
Answer:
Step-by-step explanation:
x-y=3
-y=3-x
y=x-3
when x=3 y=0
when x=1 y=-2
when x=2 y=-1
Use the counting principle to determine the number of elements in the sample space. Two digits are selected without replacement from the digits 1, 2, 3, and 4.
Answer:
if the order of the digit matters, we have:
options: 1, 2, 3, 4.
We want to select two digits.
First selection: we have 4 options
Second selection: we have 3 options (because we already selected one in the first selection)
The total number of elements in the sample space, or the total number of combinations, is equal to the product of the number of options in each selection, this is:
P = 4*3 = 12
how large of a sample of state employee should be taken if we want to estimate with 98% confidence the mean salary to within 2000 g
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
How large of a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to be within $2,000? The population standard deviation is assumed to be $10,500. z-value for 98% confidence level is 2.326.
Answer:
Sample size = n = 150
Step-by-step explanation:
Recall that the margin of error is given by
[tex]$ MoE = z \cdot (\frac{\sigma}{\sqrt{n} } ) $\\\\[/tex]
Re-arranging for the sample size (n)
[tex]$ n = (\frac{z \cdot \sigma }{MoE})^{2} $[/tex]
Where z is the value of z-score corresponding to the 98% confidence level.
Since we want mean salary to be within $2,000, therefore, the margin of error is 2,000.
The z-score for a 98% confidence level is 2.326
So the required sample size is
[tex]n = (\frac{2.326 \cdot 10,500 }{2,000})^{2}\\\\n = (12.212)^{2}\\\\n = 149.13\\\\n = 150[/tex]
Therefore, we need to take a sample size of at least 150 state employees to estimate with 98% confidence the mean salary to be within $2,000.
Rearrange to form a shape name S,E,P,C,M,A,S
Answer:
ESCAPES
Step-by-step explanation:
John and Robyn promised their three sons that they will each get to pick one spot within 500 miles of their home in City A to visit on their vacation. Scott chooses to visit City B so that he can visit some of the popular attractions there. Jacob chooses City C so he can visit a museum. Jevon chooses City D so that he can visit his grandparents. The approximate distances between these cities are as follows, City A to City B is 296 miles, City A to City C is 206 miles, City A to City D is 79 miles, City B to City C is 497 miles, City B to City D is 241 miles, and City C to City D is 281 miles.
Requried:
a. Represent this traveling salesman problem with a complete, weighted graph showing the distances on the appropriate edges. Lot Arepresent City A, B represent City B, C represent City C, and represent City D.
b. Use the brute force method to determine the shortest route for the family to complete their vacation.
Answer:
A) Weighted graph is attached
B) Shortest routes are;
1. A → C → B → D → A
2. A → D → B → C → A
Step-by-step explanation:
A) We are told their home is in City A. So that's where any journey will begin from.
Furthermore we are told that;
City A to City B = 296 miles
City A to City C = 206 miles
City A to City D = 79 miles
City B to City C = 497 miles
City B to City D = 241 miles
City C to City D = 281 miles.
I have attached an image of the weighted graph showing the distances on the appropriate edges.
B) We want to find the shortest route using Brute force method. The brute force method is by solving a particular problem by checking all the possible cases/routes to get the desired result we are looking for.
In this case, the desired result is the shortest route for the family to complete their vacation. So, i have attached a diagram showing the different routes via brute force method.
From the brute force method, the shortest length route is 1023 miles and this routes are from Cities;
1. A → C → B → D → A
2. A → D → B → C → A
2.4.16
Let:
U= {a,b,c,d,e,f,g,h}
A = {b,d,e}
B = {a,d,e}
C={a,c,f,g,h}
Find the set (AnB) U (Anc).
Select the correct choice below and if necessary fi
Answer:
(A⋂B) U (A⋂C) = {d, e}
Step-by-step explanation:
U= {a,b,c,d,e,f,g,h}
A = {b,d,e}
B = {a,d,e}
C={a,c,f,g,h}
=> A⋂B = {d,e}
=> A⋂C = ∅
=> (A⋂B) U (A⋂C) = {d, e}
The regular price of a baseball cleats is $80. If the cleats are on sale for 45% off. then: (how to solve this two questions?) a) What is the value of the discount, in dollars? b) What is the final selling price of the cleats, before tax?
Answer:
The discount is 36 dollars
The sale price is 44 dollars
Step-by-step explanation:
First find the discount by multiplying the original price by the discount rate
80*45%
Change to decimal form
80*.45
36
The discount is 36 dollars
The sale price is the original price minus the discount
80-36
44
The sale price is 44 dollars
the graph below has the same shape as the graph g(x)=x^2 but it is shifted down 3 units and to the left 2 units what is this equation
Answer:
Option (C)
Step-by-step explanation:
Parent function g(x) = x² [Vertex at the origin (0, 0)]
When this function is shifted 3 units down,
Rule to be followed,
g(x) → g(x) - 3
So, g'(x) = x² - 3
Followed by 2 units shift to the left,
Rule to be followed,
g'(x) → g'(x + 2)
F(x) = (x + 2)² - 3
Therefore, Option (C) will be the answer.
what is 3 + 3 × 3 + 3 =
Answer:
15
Step-by-step explanation:
PEMDAS
3x3 = 9
3+3 = 6
9+6 = 15
By the BODMAS rule we get, 3 + 3 × 3 + 3 = 15
The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).
3 + 3 × 3 + 3 =
3 × 3 = 9
3 + 9 + 3 = 15.
Therefore, the correct answer is 15.
Learn more about BODMAS rule here:
https://brainly.com/question/16738857
#SPJ4
Entertainment Software Association would like to test if the average age of "gamers" (those that routinely play video games) is more than 30 years old. A Type I error would occur if Entertainment Software Association concludes that the average age of gamers is: _______.
A. Equal to 30 years when, in reality, the average age is not equal to 30 years
B. Not equal to 30 years when, in reality, the average age is equal to 30 years
C. Greater than 30 years when, in reality, the average age is 30 years or less
D. 30 years or less when, in reality, the average age is more than 30 years
Answer:
"30 years or less when, in reality, the average age is more than 30 years"
Step-by-step explanation:
Type I error is produced when conclusion rejects a true null hypothesis.
The null hypothesis is
"The average gamer is more than 30 years old"
(deduced from the wording, not explicitly stated).
Then if the conclusion is "the average gamer is less than or equal to 30 years old" when in reality the average age is more than 30 years, then there is a type I error, since the null hypothesis is rejected.
Answer is D:
"30 years or less when, in reality, the average age is more than 30 years"
Write a pair of integers whose sum is- -8
Answer:
-3+(-5)
Checking our answer:
Adding this does indeed give -8
Given X= 5+ V16 select the value(s) of x. Check
all of the boxes that apply.
-11
1
9
21
Answer:
[tex]x = 9\ or\ x = 1[/tex]
Step-by-step explanation:
Given
[tex]x = 5 + \sqrt{16}[/tex]
Required
Find the value of x
[tex]x = 5 + \sqrt{16}[/tex]
We start by taking the square root of 16; Square root of 16 is +4 or -4; So, we have:-
[tex]x = 5 \±4[/tex]
The expression above can be split into two; This is as follows
[tex]x = 5 + 4\ or\ x = 5 - 4[/tex]
[tex]x = 9\ or\ x = 1[/tex]
Hence, the solution to [tex]x = 5 + \sqrt{16}[/tex] is B. 1 and C. 9
Answer:
its b and c
Step-by-step explanation:
the guy who answered first said so
also i just did it
Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. 27% of the possible Z values are greater than _____________.
Answer:
27% of the possible Z values are greater than 0.613
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 0, \sigma = 1[/tex]
27% of the possible Z values are greater than
The 100 - 27 = 73rd percentile, which is X when Z has a pvalue of 0.73. So X when the z-score is 0.613.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.613 = \frac{X - 0}{1}[/tex]
[tex]X = 0.613[/tex]
27% of the possible Z values are greater than 0.613
write the standard form of line that passes through (1,5) and (-2,3)
Answer:
2/3x - y = -13/3
Step-by-step explanation:
Step 1: Find slope m
m = (3 - 5)/(-2 - 1)
m = -2/-3
m = 2/3
y = 2/3x + b
Step 2: Find b
5 = 2/3(1) + b
5 = 2/3 + b
b = 13/3
Step 3: Write equation in slope-intercept form
y = 2/3x + 13/3
Step 4: Move 2/3x over
-2/3x + y = 13/3
Step 5: Factor out -1
-1(2/3x - y) = 13/3
Step 6: Divide both sides by -1
2/3x - y = -13/3
Jane is collecting data for a ball rolling down a hill. She measures out a set of different distances and then proceeds to use a stop watch to find the time it takes the ball to roll. What are the independent, dependent, and control variables in this experiment?
Answer:
Step-by-step explanation:
The independent variables are the input values which are not dependent on the other value.
The dependent variables are the output values whose values depends on the value of some other number.
The independent variable in this case is the data on the set of distances she measured out.
The dependent variable in this case is the the time (measured by the stopwatch) it takes for the ball to roll.
The control variable in this case study is the size of ball, slope of hill, weight of ball etc.
BÉ is an angle bisector of ZABC.
If mŁABE = 2x + 20 and mZEBC = 4x - 6,
determine the value of x.
B.
x = [? ]
find the value of x that makes abcd a parallelogram
The 4 angles need to add to 360.
2 of them are 70
The other two need to equal 360-140 = 220
They are both the same so one angle needs to equal 220/2 = 110
Now find x:
X + 60 = 110
Subtract 60 from both sides:
X = 50. The answer is D
Suppose Gabe, an elementary school student, has just finished dinner with his mother, Judy. Eyeing the nearby cookie jar, Gabe asks his mother if he can have a cookie for dessert. She tells Gabe that she needs to check his backpack to make sure k. Gabe cannot remember where he left his backpack, but he knows for sure that he did not complete his bomework and will not be alowed to cat a cookie. Gabe believes his only option is to quickly steal a cookie while his mother is out of the room. Judy then leanves the room to look for Gabe's backpack. Assome that Judy could return at any time in the next 90 seconds with equal probability, For the first 40 seconds, Gabe sheepishly wonders if he will get caught rying to grab a nearby cookie. After waiting and not secing his mother, Gabe decides that he needs a cookie and begins to take one from the jar Assuming it takes Gabe 30 seconds to grab a cookie from the jar and devour it without a trace, what is the probability that his mother returns in time to catch Gabe stealing a cookie?
Answer:
0.56
Step-by-step explanation:
What is the probability that his mother returns just in time to catch Gabe stealing a cookie?
The probability of this is the same as 1 minus the probability that Gabe is NOT caught.
- Judy could return at anytime in the next 90 seconds
- Gabe spends the first 40 seconds pondering... time wasted=40secs
- It takes 30 seconds (out of the remaining 50secs) to finish eating a cookie without a trace
- The question says that Gabe was going to do it, so he probably did
Now we're looking for the probability that he gets caught. That is, probability that he does not "successfully" complete the 30secs task within the remaining 50secs.
Remember that each second has an equal probability of being the second that Judy comes back in. The latter of the 90 seconds does not carry a higher probability!
So the probability of catching Gabe (despite the 30secs it takes to complete his task) is 50/90 which is equal to 0.56
The rule of 70 states that if yt grows at a rate of g percent per year, then the number of years it takes yt to:
Answer:
с.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g
Step-by-step explanation:
The given options
a.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to g 70
b. if yt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/1
с.i fyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g
d. if yt grows at a rate of g percent per year, then the number of years it takes yt to triple is approximately equal to 70/g
е.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is exactly equal to 70/g
The rule of 70 refers to the time period in which the investment you make is doubled. It analyzed that in how many years it took for doubling the amount by considering the specific rate of return
Now we go through the options and as we can see that the option c meets the requirement as the g represents the growth rate and it fits to the above explanation
I need help asap solving this!
Answer:
See Explanation
Step-by-step explanation:
[tex]f(x) = 4 - 6x + 3 {x}^{2}...(1) \\ plug \: x = a \: in \: (1) \\ f(a) = \boxed{ 4 - 6a + 3 {a}^{2} } \\ \\ next \: plug \: x = (a + h) \: in \: (1) \\ f(a + h) = 4 - 6(a + h) + 3 {(a + h)}^{2} \\ = 4 - 6a - 6h + 3( {a}^{2} + {h}^{2} + 2ah) \\ = 4 - 6a - 6h + 3 {a}^{2} + 3{h}^{2} + 6ah \\ f(a + h) = \boxed{3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4} \\ \\ now \\ \\ \frac{f(a + h) - f(a)}{h} \\ \\ = \frac{(3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4) -(4 - 6a + 3 {a}^{2} ) }{h} \\ \\ = \frac{3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4 -4 + 6a - 3 {a}^{2} }{h} \\ \\ = \frac{ 3{h}^{2} + 6ah - 6h }{h} \\ \\ = \frac{3h( {h} + 2a - 2) }{h} \\ \\ \frac{f(a + h) - f(a)}{h} = \boxed{ 3( 2a + h - 2)}[/tex]
Patty buys a new car and gets it appraised every few years. After owning the car for 3 years, its value is $15,000. After owning the car for 5 years, its value is $9,000. What is the constant of proportionality in this inverse variation?
Answer: 45,000.
Step-by-step explanation:
The equation of inverse variation is given by:-
[tex]k=xy[/tex]
, where k is the constant of proportionality.
Given: After owning the car for 3 years, its value is $15,000. After owning the car for 5 years, its value is $9,000.
Here,
[tex]x_1=3,\ y_1=15000\\\\x_2=5,\ y_2=9000[/tex]
Then, [tex]k=x_1y_1=3\times15000=45,000[/tex]
or [tex]k=x_2y_2=5\times9000=45,000[/tex] [answer is same in both cases.]
Hence, the constant of proportionality in this inverse variation is 45,000.
4. A rectangle-shaped picture frame has a length of 4b cm and an area of 12ab² square cm. Find the width. *
Answer:
3ab
Step-by-step explanation:
area = length * width
width = area/length
width = (12ab^2)/(4b)
width = 3ab
What is the justification for step 2 in the solution process?
Answer:
Answer C
Step-by-step explanation:
You are balancing this equation out by subtracting 7x from both sides. This means you are using the subtraction property of equality.
Pat bounces a basketball 25 times in 30 seconds. At that rate, approxiaetely how many times will Pat bounce the ball in 150 seconds?
Answer:
125 times
Step-by-step explanation:
30x5=150
25x5=125