Using the normal distribution and the central limit theorem, it is found that there is a 0.0571 = 5.71% probability of selecting a sample of 40 two-bedroom apartments and finding the mean to be at least $275 per month.
In a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of $250, hence [tex]\mu = 250[/tex].The standard deviation is of $100, hence [tex]\sigma = 100[/tex].The sample is of 40 apartments, hence [tex]n = 40, s = \frac{100}{\sqrt{40}}[/tex].The probability of selecting a sample of 40 two-bedroom apartments and finding the mean to be at least $275 per month is the p-value of Z when X = 275, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{275 - 250}{\frac{100}{\sqrt{40}}}[/tex]
[tex]Z = 1.58[/tex]
[tex]Z = 1.58[/tex] has a p-value of 0.9429.
1 - 0.9429 = 0.0571
0.0571 = 5.71% probability of selecting a sample of 40 two-bedroom apartments and finding the mean to be at least $275 per month.
You can learn more about the normal distribution and the central limit theorem at https://brainly.com/question/24663213
Which equation best matches the scenario below?
The total cost t is proportional to the number n of items purchased at a constant price of $4.
A) 4t = n
B) t = 4n
C) t = n ÷ 4
D) 4t = 4n
Answer:
Definetly t = 4n
The set-up cost for a machine that attaches snaps on clothing is $1,100. After set-up,
it costs $0.12 for each snap to be attached. A newer machine has come out that has
a set-up cost of $1,520. With the new machine, it only costs $0.09 for each snap to
be attached. How many snaps would the company have to attach to make the
purchase of the newer machine worthwhile?
Answer:
14,001
Step-by-step explanation:
old machine: 1,100+.12x
new machine: 1,520+.09x
if you plug in 14,000 for x, you get
old machine: 2,780
new machine: 2,780
therefore, you need 1 over 14,000 for it to be worth it because
if you plug in 14,001 for x, you get
old machine: 2,780.12
new machine: 2,780.09
which makes the new machine $.03 cheaper at this point (and the more snaps attached, the more the new machine will be worth it)
hope this helps!
16. Write an equation for the line that is parallel to the given line and passes through the given
(1 point)
point
y = 3x+7; (2, 10)
A. Y=3x + 11
B. y = 3x + 4
C. y=-3x+4
D. y=(-1/3)x+ 4
Answer:
Step-by-step explanation:
Parallel lines have identical slopes
y = 3x + b
add in the desired point
10 = 3(2) + b
b = 4
B. y = 3x + 4
What is the GCF of 9y and 12y?
comparing freezers
Maria compares two freezers.
Freezer A is 8 feet long, 4 feet wide, and 2 feet high.
Freezer B is 6 feet long, 4 feet wide, and 3 feet high.
correctly complete the statement : Freezer _ has _ more cubic feet than Freezer _ .
Answer:
Freezer B has 8 more cubic feet than Freezer A.
Step-by-step explanation:
Volume of Freezer A = 8 * 4 * 2 = 64 ft^3.
Volume of Freezer B = 6 * 4 * 3 = 72 ft^3.
72 - 64 = 8 ft^3.
Answer:
Freezer B has 8 more cubic feet than Freezer A.
Step-by-step explanation:
Solve the system of equations -6x-y=-16 and -6x-5y=-8 by combining equations
Answer:
[tex]\left \{ {{y=-2} \atop {x=3}} \right.[/tex]
Step-by-step explanation:
[tex]\left \{ {{-6x - y = -16} \atop {-6x - 5y = -8}} \right. <=> \left \{ {{4y= -8} \atop {-6x-5y =-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5y=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5*(-2)=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x=-18}} \right. <=> \left \{ {{y=-2} \atop {x=3}} \right.[/tex]
Which expression is NOT equivalent to the others?
14^2 x 12^2 x 12^1
14^2 x 12^3
14 x 14 x 12 x 12 x 12
14^1 x 14^1x 12^2 + 12^1
please help tysm ill mark brainliest
Answer:
use pemdas(order of the operations)and you'll get the answer 27!!
Step-by-step explanation:
LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answer:
See below
Step-by-step explanation:
Dilation of 4
Z (0, -1) Z' (0, -4)
X (1, -1) X' (4, -4)
If x + 2 and x - 3 are factors of the following polynomial, then find the values of a and b. F(x) = x^2 + ax^2- 7x + b
[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]
[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]
30=2y+16 simplify your answer as much as possible
Answer:
y=7
Step-by-step explanation:
A line that includes the point (0, -2) has a slope of 1. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=1x-2
Step-by-step explanation:
Well this one is already given
When x=0, it's the y intercept
and it gives the slope, so we got it :D
Answer:
y=x-2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=1(x-0)
y+2=1(x)
y+2=x
y=x-2
PrOblem 1: Find the slope of the line containing the points: (3,-5) and (-1, -2)
Problem 2: Find the x and y intercepts of the line: 2x – 3y = 12
Problem 3: Graph the line x-4y=8
Answer:
1) -3/4
2) (6, 0), (0, -4)
3) connect (0,-2) and (8,0) together
Step-by-step explanation:
1) (-2) - (-5) / (-1) - 3 = -3/4
2) x = 0 -3y=12 y = -4, y= 0 2x = 12 x = 6, x intercept = (6, 0) y intercept = (0, -4)
3) x - 4y = 8 this could be written as y = x/4 - 2 and y intercept is (0, -2) and x intercept is (8, 0) so connect these points together and make a line
#1
m=y2-y1/x2-x1m=-2+5/-1-3m=3/-4#2
Inetercept form x/a+y/b=1
2x-3y=122/12x-3/12y=12/12x/6-y/4=1x inetercept at 6 and y intercect at -4
#3
Graph attached
Which of the following equations has only one solution? A. x^2 -8 x + 16 = 0 B. x(x - 1) = 8 C. x^2 = 16
[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]
The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travelling at uniform speed. Which equation represents the distance (y) from the lighthouse, based on the number of hours (x)? Number of Hours Distance from Lighthouse (in oceanic miles) 2 53 4 95.5 6 138 8 180.5 10 223 12 265.5 14 308 16 350.5 A. y = 42.5x + 10.5 B. y = 10.5x + 32 C. y = 21.25x + 10.5 D. y = 12.25x + 28.5 E. y = 12.5x + 10.5
Answer:
ddd
Step-by-step explanation:
find the value of x {0<x<(π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2
In attachment I have answered this problem.
The value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 is x = π/4.
Since cos x /(cosec x + 1) + cos x /(cosec x - 1) = 2
Taking the L.C.M (cosecx + 1)(cosecx - 1), we have
[cosx(cosecx - 1) + cosx(cosecx + 1)]/(cosecx + 1)(cosecx - 1) = 2
[cosxcosecx - cosx + cosxcosecx + cosx]/(cosec²x - 1²) = 2
[cosx/sinx - cosx + cosx/sinx + cosx]/(cosec²x - 1²) = 2
[cotx - cosx + cotx + cosx]/(cosec²x - 1) = 2
collecting like terms, we have
[cotx + cotx + cosx - cosx ]/(cosec²x - 1) = 2
[2cotx + 0]/(cosec²x - 1) = 2
2cotx/(cosec²x - 1) = 2
cotx/(cosec²x - 1) = 1
Since cot²x + 1 = cosec²x ⇒ cot²x = cosec²x - 1
So, cotx/(cosec²x - 1) = 1
cotx/cot²x = 1
1/cotx = 1
tanx = 1
Taking inverse tan of both sides, we have
x = tan⁻¹(1)
x = 45°
x = 45 × π/180
x = π/4
So, the value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 is x = π/4.
Learn more about trigonometric equations here:
https://brainly.com/question/24371132
50 POINTS FOR EACH PERSON PLSSSSS HELP!!!!!
∫[tex]x^{\frac{3}{2} }[/tex]㏑(x) dx
Answer:
Look at images below ^^
Step-by-step explanation:
I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)
Answer:
Try this on for size
Step-by-step explanation:
What percent of 111 is 94?
Answer:
I’d say 84.68%
x+3x+3y+3z=21
Find the value of X.
Answer:
[tex] x = \frac{21 - 3y - 3z}{4} [/tex]Step-by-step explanation:
Question:-To find value of xEquation:-x + 3x + 3y + 3z = 21Solution:-=> x + 3x + 3y + 3z = 21
[On adding like terms x and 3x]=> 4x + 3y + 3z = 21
[On subtracting both sides with 3y]=> 4x + 3y + 3z - 3y = 21 - 3y
[On Simplification]=> 4x + 3z = 21 - 3y
[On subtracting both sides with 3z]=> 4x + 3z - 3z = 21 - 3y - 3z
[On Simplification]=> 4x = 21 - 3y - 3z
[On dividing both sides with 4][tex] = > \frac{4x}{4} = \frac{21 - 3y - 3z}{4} [/tex]
[On Simplification][tex] = > x = \frac{21 - 3y - 3z}{4} (ans)[/tex]
Given :
x + 3x + 3y + 3z = 21To Find :
The value of xSolution :
[tex]\qquad { \dashrightarrow \: { \sf{x + 3x + 3y + 3z = 21}}}[/tex]
Adding the like terms :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3y + 3z = 21}}}[/tex]
Transposing 3y to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3z = 21 - 3y}}}[/tex]
Now, Transposing 3z to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x = 21 - 3y - 3z}}}[/tex]
Dividing both sides by 4 :
[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{4x}{4} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{{x} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
Therefore, the value of x = 21 – 3y – 3z/4
The age melat five times older than the age of hana.In ten years time the ratio of the age of hana to melat is 5:9. find the present age of hana and melat?
Answer:
carbon take x(1)+4(-2)=0
x(1)-8=0
x(1)=8
x=8
please help
meeeeeeeeeeeeeeee
Answer:
C 43
Step-by-step explanation:
happy holidays
Answer:
Since the two triangles are similar, the two medians AC and FH are in proportion. The proportionality rate is [tex]k=\frac{48}8=6[/tex]. That is the same ratio of the sides., so AD is k times the corresponding side FG, or [tex]\overline {AD} = k\overline{FG} = 6\times 9 = 63[/tex]
Write the percent as fraction or mixed number in simplest form 34%
Answer: 34/100
Step-by-step explanation:
it is 34% out of 100, so it is 34/100. Reduced is 17/50
if a + b equal to pi by 4 then prove that 1 + cot a into 1 + cot B equal to 2 into cot a into cot b
Answer:
(cotA − 1) (cotB − 1) = 2
Step-by-step explanation:
A+B= π/4 = 180°/4 = 45°
A+B=45°
∴ cot(A+B)=cot45°
∴ cotBcotA−1 / (cotB+cotA) = 1
⇒cotB + cotA = cotBcotA = 1
⇒cotB + cotA − cotBcotA + 1 = 0
⇒cotBcotA − cotB − cotA − 1 = 0
⇒cotBcotA − cotB − cotA − 1 + 2 = 0+2
⇒cotBcotA − cotB − cotA + 1 = 2
⇒cotB(cotA − 1) (cotA − 1) = 2
⇒(cotA − 1) (cotB − 1) = 2
Proved
Help me plzzzzzzzzzzzzz
Answer: It is D
Step-by-step explanation:
Please answer the file question.
Answer:
WT = 63
Step-by-step explanation:
Given Δ SDE is similar to Δ SWT then the ratio of corresponding sides are in proportion, that is
[tex]\frac{WT}{DE}[/tex] = [tex]\frac{ST}{SE}[/tex] , substitute values
[tex]\frac{5x+3}{56}[/tex] = [tex]\frac{4x-3}{40}[/tex] ( cross- multiply )
56(4x - 3) = 40(5x + 3) ← distribute parenthesis on both sides
224x - 168 = 200x + 120 ( subtract 200x from both sides )
24x - 168 = 120 ( add 168 to both sides )
24x = 288 ( divide both sides by 24 )
x = 12
Then
WT = 5x + 3 = 5(12) + 3 = 60 + 3 = 63
Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign. HELP MEEE ASAPPPP ILL GIVE BRAINLIEST!!!!!!
Answer:
y > - x - 4
Step-by-step explanation:
1) Find the equation of the line
2) The equation of the line is y = - x - 4
3) Identify where the graph is shaded
4) It is shaded above and to the right of the line
5) This means that it is more positive/ greater than the unshaded areas
6) Switch the = sign to > to signify the inequality
7) All done!
Step-by-step explanation:
the delimiter line is going through the points (-4, 0) and (0, -4).
the line function
y = mx + b
m is the slope of the line, b is the y-intercept (the y value when x = 0).
the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.
so, for the 2 found points :
x changes by +4 (from -4 to 0)
y changes by -4 (from 0 to -4).
the slope m is then
-4/+4 = -1
and the y-intercept is -4 (as explained).
so, the line is
y = -x - 4
and the graphic says that all values greater than our equal to the line values are valid, so
y >= -x - 4
Find the area and perimeter of a square whose side length is
2x+3
Answer:
Area = 4x^2 + 12x + 9
Perimeter = 8x + 12
Step-by-step explanation:
Jake has $120 to spend for a party. Juice costs $8. Pizza costs $12. Write the standard equ.
how much juice and pizza Jake can buy?
Answer:
$8x + $12y = $120
Step-by-step explanation:
x = amount of juice
y = amount of pizza
$120 = his total money
answer pls having problem in this
[tex]\dfrac{\sqrt[3]{343}}{\sqrt[3]{-343}}=\dfrac{\sqrt[3]{343}}{-\sqrt[3]{343}}=-1[/tex]