Using the normal distribution and the central limit theorem, it is found that the probability is of 0.1368 = 13.68%.
Normal Probability DistributionIn 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.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
47% of its customers are looking to buy a sport utility vehicle (SUV), hence p = 0.47.A sample of 61 customers is taken, hence n = 61.The mean and the standard error are given by:
[tex]\mu = p = 0.47[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.47(0.53)}{61}} = 0.0639[/tex]
The probability that less than 40% of the sample are looking to buy an SUV is the p-value of Z when X = 0.4, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.4 - 0.47}{0.0639}[/tex]
Z = -1.095
Z = -1.095 has a p-value of 0.1368.
0.1368 = 13.68% probability that less than 40% of the sample are looking to buy an SUV.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
Can someone help me with these please
Answer:
1a. 210 m^2 1b. 14 ft^2 1c. 199.5 in^2
2a. 270 cm^2 2b. 162 m^2 2c. 272 cm^2
3a. 348 ft^2 3b. 230 in^2 3c. 312.5
Step-by-step explanation:
The area of a triangle can be calculated with one equation...
A = 1/2bh
b stands for base, h stands for height
1a. A = 1/2(21)(20)
One half divides 20 easily..
A = 21(10)
A = 210
1b. A = 1/2(7)(4)
One half divides 4 easily..
A = 2(7)
A = 14
1c. A = 1/2(19)(21)
A = 1/2(399)
A = 199.5
2a. A = 1/2(36)(15)
One half divides 36 easily..
A = 18(15)
A = 270
2b. A = 1/2(18)(18)
One half divides 9 easily..
A = 9(18)
A = 162
2c. A = 1/2(32)(17)
One half divides 32 easily..
A = 16(17)
A = 272
3a. A = 1/2(29)(24)
One half divides 24 easily..
A = 12(29)
A = 348
3b. A = 1/2(23)(20)
One half divides 20 easily..
A = 10(23)
A = 230
3c. A = 1/2(25)(25)
A = 1/2(625)
A = 312.5
Finding area of triangle --> [tex]\frac{1}{2}*b*h[/tex]
b --> length of base of triangleh --> length of height of triangleQuestion 1:
a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2}*20*21 = 210 m^2[/tex]
b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2}*4*7 = 14 ft^2[/tex]
c. [tex]Area = \frac{1}{2}*b*h= \frac{1}{2} *21*19=199.5in^2[/tex]
Question 2:
a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *36*15 = 270cm^2[/tex]
b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *18*18 = 162m^2[/tex]
b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *17*32 = 272cm^2[/tex]
Question 3:
a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *24*29 = 348ft^2[/tex]
b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *20*23 = 230in^2[/tex]
c. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *25*25 = 312.5cm^2[/tex]
Finding Area of Parallelogram --> b * h
b: length of base of parallelogramh: length of height of parallelogramQuestion 1
a. [tex]Area = b * h = 24 * 26 = 624cm^2[/tex]
b. [tex]Area = b * h = 15 * 30 = 450in^2[/tex]
c. [tex]Area = b * h = 21 * 31 = 651 mm^2[/tex]
Question 2
a. [tex]Area = b * h = 18 * 17 = 306 in^2[/tex]
b. [tex]Area = b * h = 10.5 * 15 = 157.5m^2[/tex]
c. [tex]Area = b * h = 12.5*11=137.5cm^2[/tex]
Question 3:
a. [tex]Area = b * h = 5.7*11.5=65.55in^2[/tex]
b. [tex]Area = b * h = 8 * 12.5 = 100ft^2[/tex]
c. [tex]Area = b * h = 1.7 * 3.6 = 6.12m^2[/tex]
Hope that helps!
Find the minimum distance from the parabola x-y^2=0
to the point (0,3).
Answer:
√5
Step-by-step explanation:
The distance from the given point to the curve can be found using the distance formula. The resulting expression can be minimized to find the minimum distance.
d = √((x2 -x1)² +(y2 -y1)²)
__
Point on the ParabolaA point on the parabola can be described by ...
x -y² = 0
x = y² . . . . . add y²
Then a point on this curve is ...
(y², y)
Distance to Given PointThe distance to it from (0, 3) is ...
d = √((0 -y²)² +(3 -y)²) = √(y⁴ +y² -6y +9)
Find the MinimumThe distance will be minimized when the derivative of the radical expression is zero:
d(y⁴ +y² -6y +9)/dy = 0 = 4y³ +2y -6
0 = 2y³ +y -3 . . . . . . . . remove a factor of 2
This will have a rational root in the set {±1, ±3}.
Trial and error shows that y=1 is the only real solution to this equation.
__
Then the minimum distance is ...
d = √(1⁴ +1² -6·1 +9) = √5
_____
Additional comment
The attached graph shows that a circle with radius √5 centered at (0, 3) will intersect the parabola at exactly one point. That confirms our solution.
What is the area of the trapezoid?
7 cm
10 cm
6 cm
7 cm
1
13 cm
O A. 43 cm?
O B. 60 cm?
O C. 70 cm?
Answer:
B. 60 cm²
Step-by-step explanation:
The formula for the area of a trapezoid is: [tex]\frac{1}{2}(b_{1} + b_{2} )h[/tex]
Plugging in the given values, we can solve:
[tex]\frac{1}{2} (13+7)(6)\\\\\frac{1}{2}(20)(6)\\\\10(6)\\\\= 60[/tex]
hope this helps!
sebuah Mobil memerlukan Benson sebanyak 45 liter until menempuh jarak 480 km, jika Mobil tersebut menempuh jarak 320 km, maka banyak bensin Yang diperlukan adalah...
jelaskan ya..
Answer:
what??? I can't understand you sorry
John was at the store and he saw his favorite video game
Answer:
That's cool
Step-by-step explanation:
Answer:
Thats cool and all but whats the wuestion
Step-by-step explanation:
hii i need help, helppp thank you
Answer:
i think c
Step-by-step explanation:
i hope this helped
Answer:
c
Step-by-step explanation:
Pls help! ASAP [tex] [/tex]
Answer:
BC
Seg AC
Ray KM
Approximate square root of 35 using an appropriate linear approximation.
Answer:
5.91
Step-by-step explanation:
35 is between the perfect squares 25 and 36.
√25 = 5
√36 = 6
/ 5 25 \
| d 10 |
1 < x 35 > 11
| 1 |
\ 6 36 /
11/1 = 10/d
11d = 10
d = 0.909
√35 = 5 + d = 5.909
√35 = 5.91
Find the missing side of the right triangle. Leave answer in
simplest radical form.
If the legs of a right triangle are 6 and 8, then the hypotenuse
is
a 40
b 30
C 20
d 10
Altitude (AB) = 6cm
Base (BC) = 8cm
To FindHypotenuse (AC) = ?
[tex] \fbox \text{According To Pythagoras Theorem = }[/tex]
[tex] \text{(Hypotenuse)² = (Altitude)² + (Base)²}[/tex]
Inserting The Values
[tex] \text{(Hypotenuse)²} =( {6})^{2} + (8) {}^{2} [/tex]
[tex] (\text{AC}) {}^{2} = (6) {}^{2} + (8) {}^{2} \\ \implies \text{(AC)} {}^{2} = 36 + 64 \\ \implies\text{AC} = \sqrt{100} \\ \implies\text{AC} = 10 \\ \\ \therefore \text{Hypotenuse (AC)} = 10 \text{cm}[/tex]
Correct Option D= 10cm
Hope this helpsSimplify using the order of operations.
9−4 ·5+6
we know that the multiplication comes first in the family then we start from left to right
4 x 5= 20
9-20 = -11
-11 + 6 = -5
there you go!
[tex]9 - 4 \times 5 + 6[/tex]
[tex]9 - 20 + 6[/tex]
[tex] - 11 + 6[/tex]
[tex] - 5[/tex]
27. To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a
randomized block design in which the subjects were blocked by age-group (under 40 years and 40 years or
older). Which of the following must be true about the randomized block design of the experiment?
(A) The number of subjects in each block is different.
88 Treatments are randomly assigned to subjects within each block.
(C) The design cannot have a control group because subjects are blocked by age-group.
fo) The experiment uses a matched-pairs design, where subjects from one block are paired with subjects from
the other block.
E) The subjects in one block receive one treatment, and the subjects in the other block receive the other
treatment
In a randomized block design, it is expected treatments are randomly assigned within each block.
What does a randomized block design imply?Subjects are divided into blocks based on a specific features such as age, gender, education, etc.Within each block subjects that receive treatment and does who do not are randomly assigned.The treatment in all blocks is the same. For example, if the purpose is to study the effect of medicine all treatment subjects should receive the same medicine and dose.What is the purpose of this design?The purpose is to minimize the effect of certain factors such as age.
Based on the above, it is expected in this experiment the treatment is randomly assigned to a specific number of subjects within each block.
Learn more about experiment in: https://brainly.com/question/11256472
The equation x2 + 4y2 = 36 represents which conic section?
ellipse
circle
hyperbola
parabola
Answer: The answer is ellipse
What is the next number in the sequence? 9….16….24….33…
Answer:
43
Step-by-step explanation:
The first increase from 9 to 16 is 7
The second increase from 16 to 24 is 8
The third from 24 to 33 is 9
Following the pattern the next increase must be by 10. 33+10=43
6. Find the volume of the given figures. Compute and solve
Hi! I'm giving 35 points for this question! No scams or anything unrelated or you will get reported, thanks!
How could the relationship of the data be classified?
A fairly strong positive correlation
A fairly weak positive correlation
A fairly strong negative correlation
A fairly weak negative correlation
Answer:
A fairly weak positive correlation
Step-by-step explanation:
Answer:
B; A fairly weak positive correlation.
Step-by-step explanation:
Tip: You will know it's a negative if the line in the graph can be part of an N.
what is the mean of these number 8 40 50 85 1 5 46 65 41 13 34 67 53 71 44
Answer:
41.53
Step-by-step explanation:
add all the numbers and divide by how much there is
623 /15
41.53
hope this helps!!
help me please
I couldn't solve it
[tex]\text{L.H.S}\\\\=\dfrac{\sin^4 A - \cos^4 A}{ \sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A)^2-(\cos^2 A)^2}{\sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A + \cos^2 A)(\sin^2 A-\cos^2 A)}{\sin A + \cos A}\\\\\\=\dfrac{1\cdot(\sin A+\cos A)(\sin A - \cos A)}{\sin A +\cos A}\\\\\\=\sin A - \cos A\\\\\\=\text{R.H.S}~~~ \\\\\text{Proved.}[/tex]
Answer:
heya! ^^
[tex] \\ \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } = ( \: sin \: A\: - \: cos \: A \: )\\[/tex]
[tex] \\LHS = \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } \\ \\ \frac{( \sin {}^{2} \: A + \cos {}^{2} \: A)( \sin {}^{2} A - \cos {}^{2} A) }{ (\sin \: A + \cos \: A) } \\ \\ we \: know \: that \: - \: sin {}^{2} A + cos {}^{2} A = 1 \\ \\ \therefore \: \frac{(1)(\sin {}^{2} \: A - \cos {}^{2} \: A)}{(\sin \: A + \cos \: A)} [/tex]
now , we're well aware of the algebraic identity -
[tex]a {}^{2} - b {}^{2} = (a + b)(a - b)[/tex]
using the identity in the equation above ,
[tex]\dashrightarrow \: \frac{(sin \:A - \: cos \: A)\cancel{(sin \:A + \: cos \: A )}}{\cancel{(sin \: A\: + \: cos \: A)}} \\ \\ \dashrightarrow \: (sin \: A \: - \: cos \: A) = RHS[/tex]
hence , proved ~
hope helpful :D
Find the value of the given trigonometric function.
cos 420°
Recall that cos(x + y) = cos(x) cos(y) - sin(x) sin(y). So
cos(420°) = cos(360° + 60°)
cos(420°) = cos(360°) cos(60°) - sin(360°) sin(60°)
cos(420°) = cos(60°)
since cos(360°) = 1 and sin(360°) = 0. Then
cos(420°) = cos(60°) = 1/2
What is equivalent to24.02
Answer:
Fraction 24 2/100 which equals 24 1/50 OR in decimal form 24.020
Step-by-step explanation:
Hope this helps! :)
Danielle needs to walk three miles, if she wants to reach her destination in 45 minutes (3/4 hour), how fast does she need to walk?
1 mile per every 15 minutes
or 4 mph
If f (x)=
(3 + x)/
(x-3)
what is f(a + 2)?
[tex]f(x) = \frac{3 + x}{x - 3} [/tex]
[tex]f(a + 2) = \frac{3 + a + 2}{a + 2 - 3} = \frac{a + 5}{a - 1} [/tex]
Find the value of xxx in the isosceles triangle shown below. Choose 1 answer: Choose 1 answer: (Choice A) A x = 20x=20x, equals, 20 (Choice B) B x = 7x=7x, equals, 7 (Choice C) C x=\sqrt{52}x= 52 x, equals, square root of, 52, end square root (Choice D) D x = \sqrt{40}x= 40 x, equals, square root of, 40, end square root
Answer:
look at pic
Step-by-step explanation:
In the given case, the value of "x" in the given isosceles triangle is 18 degrees.
The given triangle is an isosceles triangle, which means that it has two equal sides. Let's denote the length of each equal side as "x".
To find the value of "x", we need to use the properties of an isosceles triangle. In an isosceles triangle, the base angles (the angles opposite to the equal sides) are congruent (equal in measure).
Since the base angles are congruent, we can set up the following equation: 2x + 3x + 5x = 180 degrees
Combining like terms, we have: 10x = 180 degrees
To solve for "x", we divide both sides of the equation by 10: x = 18 degrees
Therefore, the value of "x" in the given isosceles triangle is 18 degrees.
To know more about isosceles here
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Give the equation of the line in point-
slope form that goes through the point
(-3,7) and is parallel to the line 4x-3y=7
Answer:
[tex]y-7=\frac{4}{3} (x+3)[/tex]
Step-by-step explanation:
Hi there!
We are given the point (-3, 7)
We want to write the equation of the line containing that point, in point slope-form, and that is also parallel to 4x-3y=7
Parallel lines contain the same slope
So first, let's find the slope of 4x-3y=7
To do that, we can convert the line from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope, and b is the y intercept)
To do that, we need to isolate y on one side
So start by subtracting 4x from both sides
4x-3y=7
-4x -4x
________________
-3y=-4x+7
Divide both sides by -3
y=[tex]\frac{4}{3}x[/tex]- [tex]\frac{7}{3}[/tex]
Since 4/3 is in the place of where m should be, the slope of the line is 4/3
It is also the slope of our new line, which we are trying to find
As stated earlier, we want to write this line in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
This is where the point we were given earlier comes in. We simply need to substitute our values (of the point and the slope) into the formula to find the equation.
First, with the slope; substitute 4/3 as m in the equation
[tex]y-y_1=\frac{4}{3} (x-x_1)[/tex]
Now substitute -3 as [tex]x_1[/tex] in the equation
[tex]y-y_1=\frac{4}{3} (x--3)[/tex]
We can simplify this to:
[tex]y-y_1=\frac{4}{3} (x+3)[/tex]
Now substitute 7 as [tex]y_1[/tex] into the equation
[tex]y-7=\frac{4}{3} (x+3)[/tex]
Hope this helps!
pls help me i really need help
Answer:
hey pls help me I urgently need help
please help the assignment is due today
Answer:
[tex]\tt B)\;93^o[/tex]
Step-by-step explanation:
[tex]\tt 2(19x+1)+(19x+1)+15x=360[/tex]
[tex]\tt 38x+2+19x-2+15x=360[/tex]
[tex]\tt 38x+19x+15x+2-2=360[/tex] (Add similar elements)
[tex]\tt 72x+2-2=360[/tex] (2-2=0)
[tex]\tt 72x=360[/tex]
[tex]\tt \cfrac{72x}{72}=\cfrac{360}{72}[/tex] ( Divide both sides by 72)
[tex]\tt x=5[/tex]
Now,
m∠km:-
[tex]\tt 19x-2[/tex]
[tex]\tt 19(5)-2[/tex] (Multiply 19*5= 95)
[tex]\tt =95-2[/tex] (Subtract)
[tex]\tt = 93[/tex]
Therefore, m∠km=93° is the answer.
_____
PLEASE HELP ME FIND THE SURFACE AREA OF THIS PRISM
Answer: i don't know
Step-by-step explanation: i don't know sorry
Using two or more complete sentences, describe how to find the general rule for the arithmetic sequence with a4=−1 and a6=−13. In your final answer, include all of your calculations
Answer:
-4 is your final answer in it
Find the area of the shape.
A boy has 380 prize tickets he wants to exchange for action figures at a prize booth. At
this prize booth 5 tickets can be exchanged for a large action figure, and 7 tickets can be
exchanged for 2 small action figures. The boy wants 4 times as many small action figures as
large action figures. Based on this information, can the boy get 80 small action figures?
Answer:
yes the boy can get 80 small action figures
Answer:
Yes
Step-by-step explanation:
Given
380 tickets in possession5 tickets → large action fig.7 tickets → 2 small action fig.Boy wants 4 times small action fig. as large action fig.Solving
We need to find if he can get 80 small fig.S = 805L + 7(2S) = 3805L + 280 = 3805L = 100L = 20Now, our condition was that : [number of small fig. = 4 x number of large fig.]80 (small) = 4 x 20 (large) [∴ verified]⇒ He can get 80 small action figuresWhat is 8 cm enlarged by a scale factor of 6.5
Answer:
8cm enlarged by a scale factor of 6.5 is 52cm I believe.
Step-by-step explanation:
8 times 6.5= 52cm