Answer: [tex]17.5t[/tex]
Step-by-step explanation:
Given
Speed of boat A is [tex]v_a=9\ mi/hr[/tex]
Speed of boat B is [tex]v_b=15\ mi/hr[/tex]
Both are moving perpendicular to each other
Distance traveled by Boat A [tex]x_a=9t[/tex]
Distance traveled by Boat B [tex]x_b=15t[/tex]
Distance between them is given by Pythagoras theorem
[tex]\Rightarrow d^2=(x_a)^2+(x_b)^2\\\\\Rightarrow d^2=(9t)^2+(15t)^2\\\\\Rightarrow d=\sqrt{(9t)^2+(15t)^2}\\\\\Rightarrow d=\sqrt{81t^2+225t^2}\\\\\Rightarrow d=\sqrt{306t^2}\\\\\Rightarrow d=17.49t\approx 17.5t\ \text{miles}[/tex]
Distance between them is [tex]17.5t[/tex]
degree and classification of 4x^2+32x+63?
nvm its quadratic trinomial
Answer:
Pertaining to the mathematical expression conveyed, the answer to such proposed interrogate is acknowledged as the following:
Degree: 2nd degree term.
Classification: Quadratic trionomial.
Step-by-step explanation:
Evaluating the Degree:
The degree is acknowledged as the predominating term adjacent to a base of a peculiar value that denotes the particular allocation within a polynomial.
4x^2 has the highest degree of 2.
32x has the degree of one, being that x individually is x^1.
Since polynomials are defined by the term in which obtains the greatest degree, ^2 is referred to as quadratic, whereas ^3 is cubic, ^4…
Classification Evaluation:
Such could be determined by evaluating for the quantity of terms present within the mathematical expression or statement.
4x^2 is the first term.
32x is the second term.
63 is the third term (considered a constant).
Thus, the correct answer is a quadratic trinomial.
*I hope this helps.
Denver's elevation is 5280 feet above sea level. Death Valley is -282 feet. Is Death Valley located above sea level or below sea level???
(plz answer, due date is semtemper)
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Answer:
below
Step-by-step explanation:
When signed numbers are used to represent elevation with respect to sea level, positive signs are used for values above sea level, and negative signs are used for values below sea level. The given elevation of Death Valley indicates it is 282 feet below sea level.
Charles spent 1/4 of his allowance on a shirt, and 2/5 of the remainder on a book. A.What fraction of his allowance did he have left? B.If he spent $18 on the book, how much did he have at first?
Answer:
18.65
Step-by-step explanation:
1/4+2/5+18=18.65
18.65
hope it helps you good luck
Please Help me and don't report this
8 < x < 8.5 is your answer
other sides has to always be less than the hypotenuse
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Answer:
0.5 < x < 16.5
Step-by-step explanation:
The sum of the two shortest sides of a triangle must always exceed the length of the longest side.
If x and 8.0 are the short sides, then ...
x + 8.0 > 8.5
x > 0.5
If 8.0 and 8.5 are the short sides, then ...
8.0 +8.5 > x
16.5 > x
So, for the given triangle to exist, we must have ...
0.5 < x < 16.5
_____
Additional comment
You will notice that the value 0.5 is the difference of the given sides, and 16.5 is their sum. This will always be the case for a problem like this. The third side length always lies between the difference and the sum of the other two sides.
Can someone help me on 6?
Answer:
66600 ft
Step-by-step explanation:
First draw a rectangle and draw a diagonal line in the middle. The line makes two triangles, and the line itself is the hypotenuse. So, to find hypotenuse, the formula is:
a^2 + b^2 = c^2
The variable c defines the hypotenuse. Therefore:
a = 150
b = 210
Let's solve:
150^2 + 210^2 = c^2
22500 + 44100 = c^2
66600 = c^2
Therefore, in conclusion, the result we are getting is 66600 ft.
Hope This Helps!
Answer:
30√74 ft or 258.070 ft rounded to three decimal places.
Step-by-step explanation:
To find the length of a diagonal, add the square of the width and the square of the length together and find the square root of the sum.
d = √210² + 150²
d = √44100 + 22500
d = √66600
d = 258.069758 ft (This is the answer I got in six decimal places. Rounding it to three, as it says in the question, would be 258.07 ft, as 7 is greater than 5 (the third digit was 9 by the way).)
An exact answer to that, in radical form, is 30√74 ft.
total number of chocolate boxes that can be produced: x+y (<,<=,>,>=) ___
restrictions based on demand of each: y(<,<=,>,>=) ___x
maximum amount of white chocolate production: y(<,<=,>,>=) ____
minimum amount of milk chocolate production: x(<,<=,>,>=) ____
minimum amount of white chocolate production: y(<,<=,>,>=) ____
vertices of feasible region : (0,0)(400,___)(____,___)(___,0)
optimization equation: profit = ____x+____y
your maximum profit is $____ .you should produce ____ boxes of milk chocolate and ____ boxes of white chocolate .
Answer:
Step-by-step explanation:
The idea here is to create lines according to the constraints we were given, graph the lines (which are actually inequalities), and then shade in the region that satisfies the inequality. Let's start at the beginning of the problem and we'll get our lines (inequalities) written.
The total number of boxes that can be produced according to the constraints is 800, so the inequality for that is
x + y ≤ 800 and solving for y:
y ≤ 800 - x
Another constraint on the white chocolate is that it has to be less than or equal to 200 boxes, so:
y ≤ 200
The max number of white chocolate boxes is half the number of milk chocolate, so:
y ≤ (1/2)x
The min number of milk chocolate boxes produced is:
x ≥ 0 and
The min number of white chocolate boxes produced is:
y ≥ 0 (This means that it is a possibility of making 0 milk chocolate boxes and all white chocolate boxes OR there is a possibility of making 0 white chocolate boxes and all milk chocolate boxes)
The production equation (which is used later) is:
2.25x + 2.50y (you make a profit of $2.25 on every milk chocolate box you sell and profit of $2.50 on every white chocolate box you sell).
The bold equations are the ones that need to be graphed (see graph below). Where those 3 lines intersect are the vertices of feasible region:
(0, 0), (400, 200), (600, 200), (800, 0).
Then take each x and y value from a coordinate and plug it into the profit equation (we don't need to use (0, 0)) starting with x = 400 and y = 200:
2.25(400) + 2.5(200) = $1400
Now using x = 600 and y = 200:
2.25(600) + 2.5(200) = $1850
Now using x = 800 and y = 0:
2.25(800) + 2.5(0) = $1800
So our max profit as seen by the evaluations is $1850, and that occurs when we sell 600 boxes of milk chocolate and 200 boxes of white chocolate.
6/5 times 17/18 in lowest terms
Answer:
17/15
Step-by-step explanation:
6/5 * 17/18
1/5 * 17/3
17/15
A die is rolled five times and a 5 or 6 is considered a success. Find the probability of
(i) at least 2 successes,
(ii) at least one but no more than 3 successes.
Answer:
(i) The probability of at least 2 successes is 0.2093.
(ii) The probability of at least one but no more than 3 successes is 0.9548.
Step-by-step explanation:
Now the total number of cases = {1, 2, 3, 4, 5, 6} = 6.
Favourable cases = {1, 6} = 2.
[tex]p = \frac{2} {3} = \frac{1} {3} \\\\q = 1- p\\\\q = \frac{2}{3} \\\\n=5[/tex]
i) at least 2 successes,
[tex]P(X\geq 2) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\geq 2) = 0.2093[/tex]
ii) at least one but no more than 3 successes,
[tex]P(X\leq 3) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\leq 3)= 0.9548[/tex]
Given the similarity statement ΔJKL∼ΔNOP , what’s the corresponding angle of ∠J
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Answer:
∠N
Step-by-step explanation:
J is the first letter listed in the left side of the similarity statement. The corresponding angle is the first letter listed in the right side of the similarity statement: ∠N.
__
Corresponding angles are listed in the same order. The similarity statement means ...
∠J≅∠N
∠K≅∠O
∠L≅∠P
Answer:
<J = <N
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
Question 4 of 10
What else would need to be congruent to show that ABC= AXYZ by SAS?
Answer:
D
Step-by-step explanation:
The correct answer is D. Answered by Gauthmath
In a certain town, 22% of voters favor the construction of a new hospital. For groups of 21 voters, find the variance for the number who did not favor the new hospital.
a. 1.9 voters
b. 4.6 voters
c. none of the given answers is correct
d. 3.6 voters
e. 13 voters
Answer:
Variance = 3.6 voteres
Step-by-step explanation:
Probability of favour voters, P = 0.22
Total number of voters, n = 21
The probability of voters who are in not favour of new hospital construction = 1 - P
The probability of voters who are in not favour of new hospital construction = 1 - 0.22
The probability of voters who are in not favour of new hospital construction, P* = 0.78
Variance = n x p* x (1 - p*)
Variance = 21 x 0.78 x 0.22
Variance = 3.6 voters
How many millitiers are in 4.55 liters?
Answer:
v nnv vb n
Step-by-step explanation:
b ng chfxhc.jx.gc,fhxfgfdkhgvn gghcjfuoctykfd mmyegfiuegfypgerukf khergfuoegrfyurgfirge jgreuyofrgiregvoifgr riygfepiygfreu;k frugfyrfbhrevf rrgfbreuobghfre rgeuherhbgerui freurehuregh ruogysfhurgiugwhlerghre rgiuyrge97grukbgr ker ruipuhrgeugregariyarga ;rskfglfsglgsfuifgryrgljs kjger;ugiergs hope this was helpful good luck!
x=cos(2t), y=sin(2t) find a rectangular coordinate equation for the curve by eliminating the parameter
Answer:
x^2+y^2=1
Step-by-step explanation:
Since cos^2(x)+sin^2(x)=1, x^2+y^2=1
1/2 + 4 5/8 please help
Answer:
[tex]5 \frac{1}{8}[/tex]
Step-by-step explanation:
Remember that [tex]\frac{1}{2} = \frac{4}{8}[/tex], so we want to find [tex]\frac{4}{8} + 4 + \frac{5}{8} = 4 + \frac{9}{8}[/tex]. However, this is not in it's simplest form because [tex]\frac{9}{8}[/tex] should be [tex]1 \frac{1}{8}[/tex]. Therefore, the final answer is [tex]4+1+\frac{1}{8} = 5 \frac{1}{8}[/tex].
Answer:
5 1/8 correct answer to question
The perimeter of the triangle below is .A 54 B 66. C 44. D 74. E 36.
Answer:
54
Step-by-step explanation:
This is an isosceles triangle since the base angles are the same. That means the unlabeled side must be 12
P = s1 + s2+s3 where s is the side
P = 12+12+30
P = 54
The two bottom angles are the same which means the two sides are also the same..
Perimeter = 12 + 12 + 30 = 54
Answer: A.54
Please help , write your answer I will be giving 10 points
Answer:
yes it represents the graph accurately
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5. Calculate the probability of getting at least 4 calls between eight and nine in the morning.
Answer:
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
Step-by-step explanation:
We have the mean during a time interval, which means that the Poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5.
This means that [tex]\mu = 5[/tex]
Calculate the probability of getting at least 4 calls between eight and nine in the morning.
This is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5}*5^{0}}{(0)!} = 0.0067[/tex]
[tex]P(X = 1) = \frac{e^{-5}*5^{1}}{(1)!} = 0.0337[/tex]
[tex]P(X = 2) = \frac{e^{-5}*5^{2}}{(2)!} = 0.0842[/tex]
[tex]P(X = 3) = \frac{e^{-5}*5^{3}}{(3)!} = 0.1404[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.265 = 0.735[/tex]
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
what is 32⋅(12)x+1=2x−14?
Answer:
[tex]x=-\frac{15}{382}[/tex]
Step-by-step explanation:
32 × 12x + 1 = 2x - 14
384x + 1 = 2x - 14
384x + 1 - 1 = 2x - 14 - 1
384x = 2x - 15
384x - 2x = 2x - 2x - 15
382x = - 15
382x ÷ 382 = - 15 ÷ 382
[tex]x=-\frac{15}{382}[/tex]
Write a polynomial equation of degree 4 that has the following roots: -1 repeated three times and 4
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Answer:
0 = x⁴ -x³ -9x² -11x -4
Step-by-step explanation:
Each root r contributes a factor of (x-r). The factored form of the polynomial of interest is ...
0 = (x +1)³(x -4)
0 = (x³ +3x² +3x +1)(x -4)
0 = x⁴ -x³ -9x² -11x -4
Please help, I’m not sure about this question.
How do i solve this quesiton 6(x − 2) > 15
Answer:
Step-by-step explanation:
[tex]\displaystyle\ \!\!6(x-2)>15 \\\\6x-12>15 \\\\6x>27\\\\ \boldsymbol{x>4,5 \ \ or \ \ x\in(4,5\ ; \infty)}[/tex]
Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation. What is the 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.
Answer:
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation.
This means that [tex]n = 3923, \pi = \frac{3196}{3923} = 0.8147[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 - 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.7987[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 + 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.8307[/tex]
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).
Please help I really don’t understand anything at all !
Answer:
see explanation
Step-by-step explanation:
1
2(3x + 1) = 4(x + 2) ← distribute parenthesis on both sides
6x + 2 = 4x + 8 ( subtract 4x from both sides )
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
------------------------------------------------------------
2
6x = 4(x - 3) ← distribute parenthesis
6x = 4x - 12 ( subtract 4x from both sides )
2x = - 12 ( divide both sides by 2 )
x = - 6
-----------------------------------------------------------
3
2(4x + 7) = 4x + 30 ← distribute parenthesis on left side
8x + 14 = 4x + 30 (subtract 4x from both sides )
4x + 14 = 30 ( subtract 14 from both sides )
4x = 16 ( divide both sides by 4 )
x = 4
---------------------------------------------------------------------
4
50 = - (y + 22) ← distribute parenthesis by - 1
50 = - y - 22 ( add 22 to both sides )
72 = - y ( multiply both sides by - 1 )
- 72 = y , that is
y = - 72
Write an equation of the line through each pair of points in slope-intercept form.
a(– 3,–2) and (–3,4)
b(3,2)and (–4,–5)
Answer and I will give you brainiliest
Answer:
see below
Step-by-step explanation:
a) (– 3, –2) and (–3, 4)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(4 - (-2) / (-3 - (-3))
Simplify the parentheses.
= (4 + 2) / (-3 + 3)
Simplify the fraction.
(6) / (0)
= undefined
If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.
In this case, the x-coordinate for both points is -3.
Therefore, your equation is x = -3.
b) (3, 2) and (–4, –5)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-5 - 2) / (-4 - 3)
Simplify the parentheses.
= (-7) / (-7)
Simplify the fraction.
-7/-7
= 1
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = 1x + b or y = x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.
2 = 1(3) + b
To find b, multiply the slope and the input of x(3)
2 = 3 + b
Now, subtract 3 from both sides to isolate b.
-1 = b
Plug this into your standard equation.
y = x - 1
This is your equation.
Check this by plugging in the other point you have not checked yet (-4, -5).
y = 1x - 1
-5 = 1(-4) - 1
-5 = -4 - 1
-5 = -5
Your equation is correct.
Hope this helps!
Which graph shows data that would allow the most accurate prediction for the number of water bottles a vendor sells based on the daily high temperature?
Graph A
Daily High Temperatures and Bottled Water Sales
On a graph, points are scattered all over the graph.
Graph B
Daily High Temperatures and Bottled Water Sales
On a graph, points are scattered all over the graph.
Graph C
Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Graph D
Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and increase.
PLS HELP ILL GIVE BRAINLIEST FAST
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Answer:
Graph C: Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Step-by-step explanation:
Apparently, Graph C shows data with the greatest degree of correlation. This suggests that any model of the data is likely to have less error than if the data were less well correlated.
Answer:
Graph C: Daily High Temperatures and Bottled Water Sales
On a graph, points are grouped together and form a line with positive slope.
Step-by-step explanation:
My class consists of 8 men and 7 women. I want to pick a group of 6 people for research.
Write each answer using fraction as needed.
a. In how many different ways can I pick this group?
b. What is the probability of having exactly 3 men in the group?
c. What is the probability of all the selected people in group are women?
d. What is the probability of having at least one man in the group?
Answer:
a.5005
b.[tex]\frac{1960}{5005}[/tex]
c.1/715
d.714/715
Step-by-step explanation:
We are given that
Total men=8
Total women=7
Total people, n=8+7=15
r=6
a.
Combination formula:
Selection of r out of n people by total number of ways
[tex]nC_r[/tex]
Using the formula
We have n=15
r=6
Total number of ways=[tex]15C_6[/tex]
Total number of ways=[tex]\frac{15!}{6!9!}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
Total number of ways=[tex]\frac{15\times 14\times 13\times 12\times 11\times 10\times 9!}{6\times 5\times 4\times 3\times 2\times 1\times 9!}[/tex]
Total number of ways=5005
b. The probability of having exactly 3 men in the group
=[tex]\frac{8C_3\times 7C_3}{15C_6}[/tex]
Using the formula
Probability,[tex]P(E)=\frac{favorable\;cases}{Total\;number\;of\;cases}[/tex]
The probability of having exactly 3 men in the group=[tex]\frac{\frac{8!}{3!5!}\times \frac{7!}{3!4!}}{5005}[/tex]
=[tex]\frac{\frac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\times \frac{ 7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}}{5005}[/tex]
=[tex]\frac{56\times 35}{5005}[/tex]
The probability of having exactly 3 men in the group
=[tex]\frac{1960}{5005}[/tex]
c. The probability of all the selected people in the group are women
=[tex]\frac{8C_0\times 7C_6}{5005}[/tex]
The probability of all the selected people in the group are women
[tex]=\frac{\frac{8!}{0!8!}\times \frac{7\times 6!}{6!1!}}{5005}[/tex]
The probability of all the selected people in the group are women
[tex]=\frac{7}{5005}=\frac{1}{715}[/tex]
d. The probability of having at least one man in the group
=1- probability of all the selected people in group are women
The probability of having at least one man in the group
[tex]=1-\frac{1}{715}[/tex]
[tex]=\frac{715-1}{715}[/tex]
[tex]=\frac{714}{715}[/tex]
The probability of having at least one man in the group [tex]=\frac{714}{715}[/tex]
Clear parentheses by applying the distributive property.
-(-4s + 9t + 7)
Answer:
4s-9t-7
Step-by-step explanation:
multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same
the sum of five consecutive number is 45
Answer:
7, 8, 9, 10, 11
Step-by-step explanation:
7+8+9+10+11
7 + 8 = 15
15 + 9 = 24
24 + 10 = 34
34 + 11 = 45
The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is 2630. Assume the standard deviation is$500 . A real estate firm samples 100 apartments. Use the TI-84 Plus calculator.a) What is the probability that the sample mean rent is greater than $27007?b) What is the probability that the sample mean rent is between $2450 and $2550? c) Find the 25th percentile of the sample mean. d) Would it be unusual if the sample mean were greater than $26457?e) Do you think it would be unusual for an individual to have a rent greater than $2645? Explain. Assume the variable is normally distributed.
Answer:
a) 0.0808 = 8.08% probability that the sample mean rent is greater than $2700.
b) 0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.
c) The 25th percentile of the sample mean is of $2596.
d) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
e) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
If |Z|>2, the measure X is considered unusual.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2630. Assume the standard deviation is $500.
This means that [tex]\mu = 2630, \sigma = 500[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{500}{\sqrt{100}} = 50[/tex]
a) What is the probability that the sample mean rent is greater than $2700?
This is the 1 subtracted by the p-value of Z when X = 2700. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2700 - 2630}{50}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a p-value 0.9192
1 - 0.9192 = 0.0808
0.0808 = 8.08% probability that the sample mean rent is greater than $2700.
b) What is the probability that the sample mean rent is between $2450 and $2550?
This is the p-value of Z when X = 2550 subtracted by the p-value of Z when X = 2450.
X = 2550
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2550 - 2630}{50}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a p-value 0.0548
X = 2450
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2450 - 2630}{50}[/tex]
[tex]Z = -3.6[/tex]
[tex]Z = -3.6[/tex] has a p-value 0.0002
0.0548 - 0.0002 = 0.0546.
0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.
c) Find the 25th percentile of the sample mean.
This is X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-0.675 = \frac{X - 2630}{50}[/tex]
[tex]X - 2630 = -0.675*50[/tex]
[tex]X = 2596[/tex]
The 25th percentile of the sample mean is of $2596.
Question d and e)
We have to find the z-score when X = 2645.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2645 - 2630}{50}[/tex]
[tex]Z = 0.3[/tex]
|Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
1/x-2/3=3/2x find x
Answer:
1/x-2/3=3/2x
-2/3=3/2x-1/x
-2/3=(3-2)/2x
-2/3=1/2x
by cross multiplication
-2(2x)=1(3)
-4x=3
x= -3/4
Step-by-step explanation:
I hope this will help
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