Complete question :
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people
Answer:
486,200
Step-by-step explanation:
Given that the rate of change in population is represented by the function:
f(t) = 5,700√t + 11,000
To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation
f(t) = 5,700t^1/2 + 11,000
Taking the integral of f with respect to t:
∫(5,700t^1/2 + 11,000)
[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C
[(5700t^3/2)/ 3/2] + 11000t + C
Where C = constant
If population before construction = 67000
Then C = 67000
t = time = 16 years
Substitute values into the original change equation:
[(5700(16)^3/2)/ 3/2] + 11000t + 67000
[(5700 * 64) / 1.5] + 11000(16) + 67000
243200 + 176000 + 67000
= 486,200
Find f(x) and g(x) so the function can be expressed as y = f(g(x) y = [tex]\frac{8}{x^2}[/tex]+4
Answer:
Step-by-step explanation:
Hello,
[tex]f(g(x))=\dfrac{8}{x^2}+4[/tex]
So if we take
[tex]f(x)=\dfrac{8}{x}+4 \ \ and \\\\g(x)=x^2\\ \\f(g(x))=\dfrac{8}{g(x)}+4=\dfrac{8}{x^2}+4[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The margin of error ________ (increases or decreases) with an increased sample size and ________ (increases or decreases) with an increase in confidence level.
With such a larger sample size, the margin of error lowers (grows or decreases), whereas, at a higher confidence level, it increases (increases or declines).
The margin of error:
A margin of error increases as the confidence level rises, resulting in a larger interval. A margin of error is reduced as confidence is increased, resulting in a narrower interval.By increasing sample size and confidence level, the margin of error lowers and grows.
Margin of error [tex](E) = Z_c * {\frac{\sigma}{\sqrt{n}}}[/tex]
Here [tex]Z_c[/tex] denotes the confidence level's critical value.Whenever it comes to sample size, n is the number of people who take part in the study.As a result, the margin of error lowers as the sample size grows, and the margin of error increases as the confidence level grows.Find out more about the margin of error here:
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Find the value of x.
x=2.86
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {24}^{2} + {32}^{2} = 40[/tex]
[tex]c = 40[/tex]
[tex]6x + 6 + 9x - 9 = 40[/tex]
[tex](6x + 9x) + (6 - 9) = 40[/tex]
[tex]15x - 3 = 40[/tex]
[tex]15x = 43[/tex]
[tex]x = 2.866[/tex]
[tex]23.16 + 16.74 = 39.9[/tex]
the
[tex]6(2.86) + 6 = 23.16[/tex]
[tex]9(2.86) - 9 = 16.74[/tex]
Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the distribution of the population is normally distributed. 150 150 180 170
a. State the null and alternative hypotheses.
b. Using a critical value, test the hypothesis at the 10% level of significance.
c. Using a p-value, test the hypothesis at the 10% level of significance.
d. Using a confidence interval, test the hypothesis at the 10% level of significance.
e. Could a Type II error have been committed in this hypothesis test?
Answer:
a; H0: u= 140 Ha: u ≠ 140 two tailed test.
b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or
3 > t ( ∝/2) (n-1) =2.353
c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05 therefore reject H0.
d. Again reject H0 as 140 < 150.163
e. A type II error has not been committed as H0 is rejected.
Step-by-step explanation:
We formulate the null and alternative hypotheses as
a; H0: u= 140 Ha: u ≠ 140 two tailed test.
For a two tailed test the significance level ∝= 0.1 the critical region is given by
t ≤ t ( ∝/2) (n-1) and t > t ( ∝/2) (n-1)
So the critical region will be
t≤ t ( ∝/2) (n-1) =2.353
where
t= x` - u / s/ √n
Sr. No X X²
1 150 22500
2 150 22500
3 180 32400
4 170 28900
∑ 650 106,300
X`= ∑x/n = 650/4= 162.5
s²= 1/n-1 (x-x`)²= 1/n-1 [ ∑x² -(∑x)²/n ]
= 1/3[106,300 -650²/4] = 225
s= 15
Putting the values in the above equation
t= 162.5- 140/ 15/ √4
t= 3
So calculated value of t= 3
b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or
3 > t ( ∝/2) (n-1) =2.353
c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05 therefore reject H0.
d. a 90% confidence interval based on the calculated values will be
x`± 1.645 (s)/ √n
Putting the values
162.5 ±1.645 ( 15/2)
162.5 ±12.3375
174.84 , 150.163
d. Again reject H0 as 140 < 150.163
e. A type II error has not been committed as H0 is rejected.
6. If x + 2 is the only factor of the polynomial P(x),then P(2) is:
Options:
A. Cannot be determined
B. Not Zero
C. R(2)
D. Zero
Answer:
P(x) = x + 2p(2) = 2 + 2 p(2) = 4So option B is the answer.
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) is Not Zero. Therefore, the option B is the correct answer.
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
Given information;
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) :
P(x) = x + 2
p(2) = 2 + 2
p(2) = 4
The P(2) is Not Zero.
Therefore, the option B is the correct answer.
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Consider the distribution of exam scores graded 0 from 100, for 79 students. When 37 students got an A, 24 students got a B and 18 students got a C. How many peaks would you expect for distribution?
Answer:
Three
Step-by-step explanation:
Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores
-36 4/9 - (-10 2/9) -(18 2/9)
Answer: [tex]-44\dfrac{4}{9}[/tex]
Step-by-step explanation:
The given expression: [tex]-36\dfrac{4}{9}-(-10\dfrac{2}{9})-(18\dfrac{2}{9})[/tex]
Here, [tex]36\dfrac{4}{9}=\dfrac{36\times9+4}{9}=\dfrac{328}{9}[/tex]
[tex](10\dfrac{2}{9})=\dfrac{92}{9}\\\\(18\dfrac{2}{9})=\dfrac{9\times18+2}{9}=\dfrac{164}{9}[/tex]
That is
[tex]-36(\dfrac{4}{9})-(-10\dfrac{2}{9})-(18\dfrac{2}{9}) = -\dfrac{328}{9}-(-\dfrac{92}{9})-\dfrac{164}{9}\\\\=-\dfrac{328}{9}+\dfrac{92}{9}-\dfrac{164}{9}\\\\=\dfrac{-328+92-164}{9}\\\\=\dfrac{-400}{9}\\\\=-44\dfrac{4}{9}[/tex]
What is the common difference in the arithmetic sequence 1,1.25,1.5,1.75,… ?
Answer:
0.25.
Step-by-step explanation:
To find the common difference, you need to find the number that each value increases by.
1.75 - 1.5 = 0.25.
1.5 - 1.25 = 0.25.
1.25 - 1 = 0.25.
All values apparently increase by 0.25. So, that is your common difference.
Hope this helps!
Answer:
0.25
Step-by-step explanation:
The common difference is the value added to the first term to get the second term, then added to the second to get the third and so on.
To find the common difference, subtract the first term from the second. Then check by subtracting the second term from the third.
The sequence is: 1,1.25,1.5,1.75
second term - first term
1.25- 1= 0.25
third term- second term
1.5 -1.25= 0.25
The common difference in the arithmetic sequence is 0.25
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 72 58 62 38 44 66 42 49 76 52 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
Mean: 55.9
Median: 55
Mode: None
Step-by-step explanation:
First, find the mean by dividing the sum by the number of elements:
(72 + 58 + 62 + 38 + 44 + 66 + 42 + 49 + 76 + 52) / 10
= 55.9
Next, find the median by putting the numbers in order and finding the middle one:
38, 42, 44, 49, 52, 58, 62, 66, 72, 76
There is no middle number, so we will take the average of 52 and 58, which is 55.
Lastly, to find the mode, we have to find the number that occurs the most.
All of the numbers occur one time, so there is no mode.
Which of the following is a solution for 5 - 2x ≤ -3?
Answer:
x≥4
Step-by-step explanation:
The required solution for the inequality 5 - 2x ≤ -3 is x ≥ 4 or x ∈ [4, ∞).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
5 - 2x ≤ -3.
Solve the inequality,
Add 3 to both the sides,
5 - 2x + 3 ≤ -3 + 3
8 - 2x ≤ 0
-2x ≤ -8
Multiply -1 both the sides,
2x ≥ 8
x ≥ 4
The solution for the inequality is x ≥ 4 or x ∈ [4, ∞).
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Which is an infinite arithmetic sequence? a{10, 30, 90, 270, …} b{100, 200, 300, 400} c{150, 300, 450, 600, …} d{1, 2, 4, 8}
Answer:
C
Step-by-step explanation:
An arithmetic sequence has a common difference d between consecutive terms.
Sequence a
30 - 10 = 20
90 - 30 = 60
270 - 90 = 180
This sequence is not arithmetic
Sequence b
200 - 100 = 100
300 - 200 = 100
400 - 300 = 100
This sequence is arithmetic but is finite, that is last term is 400
Sequence c
300 - 150 = 150
450 - 300 = 150
600 - 450 = 150
This sequence is arithmetic and infinite, indicated by ........ within set
Sequence d
2 - 1 = 1
4 - 2 = 2
8 - 4 = 4
This sequence is not arithmetic
Thus the infinite arithmetic sequence is sequence c
What is the area of the regular polygon shown below?
Answer:
shown below..I can't see..
Answer:
93.5 for area
Step-by-step explanation:
there is no picture so that's a simple guess
There are 13 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommittees are possible?
Answer:
9
Step-by-step explanation:
13-4=9
If an adult male is told that his height is 3 standard deviation above the mean of the normal distribution of heights of adult males, what can he assume?
Answer:
He can be on either the lower end of that 95%, or on the higher end. this guy is not a too short, nor is he extremely tall.
Sry if it's nor right, It was a little confusing.
Hope this helps!（づ￣3￣）づ╭❤～
He can be on either the lower end of that 95%, or on the higher end.
This guy is not too short, nor is he extremely tall.
We have given that
Height =2
Everything on the normal model is within 2 standard deviations away from the mean.
What is the standard deviation?The standard deviation is a measure of the amount of variation or dispersion of a set of values.
So He can be on either the lower end of that 95%, or on the higher end.
This guy is not too short, nor is he extremely tall.
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At a baby shower, 15 guests are in attendance and 4 of them are randomly selected to receive a door prize. If all 4 prizes are identical, in how many ways can the prizes be awarded?
Answer:
1365
Step-by-step explanation:
We figure out combinations using this formula: n!
r!(n-r)!
n=15
r=4
So n!= 15x14x13x12x11x0x9x8x7x6x5x4x3x2x1
r! = 4x3x2x1 times 15-4!, which is 11! = 11x10x9x8x7x6x5x4x3x2x1
Put this together and you have 15x14x13x12/4x3x2x1=
There are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
What are the Combinations?Combinations are the procedures used in mathematics to pick k things from n different items without replacement.
The following formula computes the combinations of k items from n:
(n, k) = n! / k!×(n-k)!
The number of ways to award the 4 door prizes to 4 guests out of a group of 15 guests is a combinatorial problem that can be calculated using the formula.
Here, n = 15 (the total number of guests) and k = 4 (the number of prizes to be awarded).
So, the number of ways to award the prizes is:
C(15, 4) = 15! / (4! (15 - 4)!)
= 15! / (4! 11!)
= 15 x 14 x 13 x 12 / (4 x 3 x 2 x 1)
= 1365.
Therefore, there are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
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what would be the answer for f(0) = -3x+7?
Answer: 7
Step-by-step explanation:
f(0) means that x is equal to zero and so you substitute all the x's for zeros which means -3 times 0 plus 7 is equal to 7
Answer:
[tex]x=\frac{7}{3}[/tex]
Step-by-step explanation:
Since any number multiplied by zero equals zero, our equation is really:
0 = -3x+7
First, we'd have to subtract the 7 from both sides:
-7 = -3x
Now we need to divide the negative three from both sides to isolate the x.
7/3 = x
So, our answer is x=7/3
Hope this helps!! <3 :)
An individual is teaching a class on Excel Macros. The individual plans to break the class up into groups of 4 and wants each group to have 2 exercises to practice on, with no group doing the same exercise. The individual wants to know how many exercises he will need. Solve for the dependent variable (y) if the independent variable is 16.
Answer:
32
Step-by-step explanation:
If there are 16 independent variables (groups) then there would need to be 2 unique exercises x 16 groups = 32 exercises. If the independent variable is the number of students, then they would only need 8.
The Total Exercises each group will do 2x/4
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Total exercises individual need is y = 4x/2
y - 4x/2
The No. of groups = 4
Each group has to do exercises = 2
Total no. of exercises individual need is y
Total Exercises each group will do 2x/4
Total exercises individual need
y = 2x/4 (4)
y - 4x/2
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Write a variable expression for a number w increased by 4 (A) 4 ÷ w (B) w + 5 (C) w + 4
Answer:
C) w+4
Step-by-step explanation:
w=the variable
+4= increased by 4
HOPE THIS HELPS!!!!!! :)
<33333333333
A train leaves the station traveling north at 75 mph 2 hours later a second train leaves on a parallel track and travels north at 125 mph how far from the station will they meet
Answer:
At 3 hours, the trains will be equidistant from the station.
Step-by-step explanation:
The first train leaves at 75 miles per hour and has a 2 hour head start. This will put the first train at mile marker 150 (75 * 2) when the second train leaves the station at 125 mph.
To solve when they will be near each other, we set up an equation to solve for t.
150 + 75t = 125t
150 = 50t
3 = t
So given this value, we know the trains will be equidistant from the train station on parallel tracks after 3 hours.
Cheers.
A hypothesis test is the following:
a. a descriptive technique that allows researchers to describe a population
b. an inferential technique that uses information about a population to make predictions about a sample
c. a descriptive technique that allows researchers to describe a sample
d. an inferential technique that uses the data from a sample to draw inferences about a population
Answer:
c
Step-by-step explanation:
c. a descriptive technique
a family size pizza is $24 and costs 3 times as much as a small pizza. peter buys two family size pizzas and 3 small pizzas. how much does he spend in all?
Answer: 72
Step-by-step explanation:
no. of family pizzas- 2
cost of one family pizza - 24 each
total cost for family pizza -48
one family pizza's cost equals to 3 small pizzas
which is cost of 3 small pizzas = 24
therefore, total cost= 24+48
=72
write the equation of a horizontal ellipse with a major axis of 18, and minor axis of 10, and a center at (-4, 5).
See the attached picture
[tex]\bold{\text{Answer:}\quad \dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1}[/tex]
Step-by-step explanation:
A "horizontal" ellipse means that the x-radius is bigger than the y-radius. Thus, x is the major axis and y is the minor axis.
The equation of an ellipse is: [tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] where
(h, k) is the center of the ellipsea is the radius on the x-axisb is the radius on the y-axisIt is given that the center is at (-4, 5) --> h = -4, k = 5
It is given that the major axis has a length of 18 --> x-radius = 9
It is given that the minor axis has a length of 10 --> y-radius = 5
Input those values into the equation of an ellipse to get:
[tex]\dfrac{(x-(-4))^2}{9^2}+\dfrac{(y-5)^2}{5^2}=1[/tex]
Simplify to get:
[tex]\dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1[/tex]
Renting a car costs $30 per day, or $600 per month. Renting daily is cheaper for a few days, but after how many days are the two options equal (after which renting monthly is cheaper)?
Answer:
20 days
Step-by-step explanation:
Renting a car costs $30 per day.
y = 30x
Renting a car costs $600 per month
y = 600
Set the two equations equal to each other.
30x = 600
(30x)/30 = (600)/30
x = 20
After 20 days, the two options have an equal cost.
A right triangle has vertices (−7,9),(3,9),(−7,−15). Find the perimeter of the triangle. please help. a simple formula will due. and an explanation
Answer:
60
Step-by-step explanation:
If the sides of the triangle have lengths a, b, c, the perimeter is their sum:
P = a + b + c
Any of the side lengths can be found using the distance formula. However, since two of the sides are aligned with the axes, their lengths are easily found by subtracting coordinates.
If the points are labeled A, B, C, in order, then the two right-angle sides are ...
c = AB = 3 -(-7) = 10
b = AC = 9 -(-15) = 24
The Pythagorean theorem tells you that you can find the third side from the relation ...
a² = b² +c²
a² = 10² +24² = 676
a = √676 = 26
Now, we can use these values in the formula for the perimeter:
P = a + b + c = 26 + 24 + 10
P = 60
The perimeter of the triangle is 60 units.
Subtract 2x^2 -9x - 7 from 8x^2 -5x + 9.
Answer:
-6x² -4x -16
Step-by-step explanation:
be watchful of signs to avoid making errors
Please help me out!! (the question and answer choices are all in the image). Please include all work!! <3
Answer:
bgd=cgd+cgb
agf=cgd
50=cgd
cgd=50
bgd=90
so cgd=50
bgc=40
bgd=90
Answer:
C 90-degrees
Step-by-step explanation:
Using alternate interior angles, you can say m<CGD = 50 degrees.
From here, using the fact that line BE is a bisector of line CF, we know that the sum of degrees of the line BE would be 180 degrees.
So we can say m<EGD + m<CGD + m<BGC = 180. Plug in our known values.
90 + 50 + m<BGC = 180
m<BGC = 40
And we can see that m<BGD = m<BGC + m<CGD
Thus, m<BGD = 40 + 50 = 90.
So the m<BGD = 90 degrees.
Cheers.
What is the slope of the line shown below?
A. -3/2
B. 3/2
C. 2/3
D. -2/3
Answer:
2/3
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= (1- -7)/(9 - -3)
= ( 1+7)/( 9+3)
= 8/12
Simplifying
= 2/3
Answer:
C. 2/3
Step-by-step explanation:
You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.
y2 is equal to the y coordinate of the second point: 1
y1 is equal to the y coordinate of the first point: -7
x2 is equal to the x coordinate of the second point: 9
x1 is equal to the x coordinate of the first point: -3
So if you plug these values into the equation, you will get:
1 - (-7)/ 9- (-3)
= 1 + 7/ 9 + 3
= 8/12
= 2/3
In the xy-coordinate system above, line / (not shown) does not contain point in either quadrant II or
quadrant IV. Which of the following could be the equation of line /?
•x=3
•y=3x
•y=3x+3
•y=-3x-3
Answer:
y=3x
Step-by-step explanation:
If the line cannot be in quadrants II or IV, it must pass through the origin(0,0) and be in quadrants I and III.
Substitute (0,0) for y and x to find the answer.
1) x=3, 0=3 NO
2) y=3x, 0=3(0), 0=0 YES
3) y=3x+3, 0=3(0)+3, 0=3 NO
4) y=-3x-3, 0=-3(0)-3, 0=-3 NO
So the answer must be 2) y=3x
the length of a mathematical text book the is approximately 18.34cm and its width is 11.75 calculate ?
the approximate perimeter of the front cover?
the approximate area of the front cover of the book?
Answer:
Perimeter=60.18cm
Area=215.495cm^2
Step-by-step explanation:
Given:
Length of book=18.34cm
Breadth=11.75cm
Solution:
Perimeter=2(l +b)
P=2(18.34+11.75)
P=2 x 30.09
P=60.18cm
Area=l x b
A=18.34 x 11.75
A=215.495 cm^2
Thank you!
A researcher was interested in whether a new sports drink could change people's running endurance. For one week, 6 participants continued with their normal routine and then their endurance was measured. The following week, the same participants were instructed to drink the new sports drink an hour before their endurance was measured. Below are your data.
Week I 90 100 110 110 85 95
Week 2 100 110 110 120 95 95
What type of analysis would be used on the above data?
a. Z-test
b. One sample t-test
c. Independent samples t-test
d. Dependent samples t-test
Answer:
The correct option is (d).
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
We use the paired t-test if we have 2 measurements on the same item, person or thing. We should also use this test if we have 2 items that are being measured with a unique condition.
For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.
In this case, the same participants are selected for both the trials.
And the difference between the endurance before and after the usage of the new sports drink are noted.
Thus, the analysis that would be used on the data is the Dependent samples t-test.
