Answer:
probability of getting both are unripe
= 0.15
probability of getting both are ripe
= 0.375
Probability of one ripe and one unripe
=0.234375
Probability of at least one unripe
=0.625
Step-by-step explanation:
50 mangoes 20 of which are unriped in the first basket .
Riped = 50-20= 30
Probability of unripe = 20/50
Probability of unripe= 0.4
Probability of ripe = 30/50
Probability of ripe = 0.6
40 mangoes of which 15 are unripe In the second basket
Number of riped= 40-15= 25
Probability of unriped= 15/40
Probability of unriped= 0.375
Probability of riped= 25/40
Probability of riped= 0.625
probability of getting both are unripe
= 0.4*0.375
probability of getting both are unripe
= 0.15
probability of getting both are ripe
= 0.6*0.625
= 0.375
Probability of one ripe and one unripe
= 0.625*0375
= 0.234375
Probability of at least one unripe
= 1- probability of no unripe
= 1 - probability of both ripe
= 1-0.375
= 0.625
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x) 2. If we multiply a polynomial by a constant, is the result a polynomial? 3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Answer:
1. k=0
2. yes, result is still a polynomial.
3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)
Step-by-step explanation:
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)
for k=0 any polynomial f(x) will reduce f(k) to the constant term.
2. If we multiply a polynomial by a constant, is the result a polynomial?
Yes, If we multiply a polynomial by a constant, the result is always a polynomial.
3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Yes.
If
deg(f+g) < deg(f) and
deg(f+g) < deg(g)
then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.
Write these numbers in standard form 906000000
Answer:
9.06×10 to the power of 8(8 is superscript above 10)
Answer:
9.06 x 10^8
Step-by-step explanation:
906000000 = 9.06 x 10^8
8 decimal places in
Find the total area of the prism.
Answer:
A=1,728
Step-by-step explanation:
To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.
The width is 12, the hight is 12, and the depth is 12 so you can write
A=12*12*12
Multiply 12 by 12
A=144*12
Multiply 12 by 144 to get your final total area
A=1,728
Hope this helps, feel free to ask follow-up questions if confused.
Have a good day! :)
Please answer in the form of an angle or degree
Step-by-step explanation:
angle A = angle B( Corresponding angles)
so,
5x - 5 = 3x + 13
=> 5x - 3x = 13 + 5
=> 2x = 18
=> x = 9
angle B = 3x + 13 = (3×9) + 13 = 27 + 13 = 40
Answer:
x=9, ∠B=40
Step-by-step explanation:
In this case, ∠A≅∠B, as they are corresponding angles. Therefore, if you set up the equation to be 5x-5=3x+13,
2x=18, x=9
∠B=3(9)+13=27+13=40
h
e
l
p
m
e
o
u
t
:)
Answer:
First answer.
Step-by-step explanation:
Multiply everything by 10, to get rid of the decimals.
Just trying to finish this so I can get my stanceboy racecar back
Answer:
x ≥ 4 AND x + y ≤ 10
Step-by-step explanation:
If you need up to 10 volunteers, then you can take 10 or less. If we add y and x, we'll get the total amount of people, therefore making the inequality:
x + y ≤ 10.
Now, he needs no fewer than 4 females, so he can take 4 or greater. This means that x should be greater than or equal to 4.
x ≥ 4.
Nothing was mentioned about how many males he needed (y) so these two inequalities match the situation.
Hope this helped!
How many even 3 digit positive integers can be written using the numbers 3,4,5,6,and 7?
Answer:
I got 45, but I may be wrong.
Step-by-step explanation:
When a number is even, the number must end in an even number. Here, the even numbers are 4 and 6, so the numbers we are going to create are all going to end in 4 and 6.
To answer this question, we just have to find as many possible combinations following the guidelines provided.
334
344
354
364
374
434
444
454
464
474
534
544
554
564
574
634
644
654
664
674
336
346
356
366
376
436
446
456
466
476
536
546
556
566
576
636
646
656
666
676
736
746
756
766
776
x =x=x, equals ^\circ ∘
Answer:
x = 64
Step-by-step explanation:
A circle equal 360 degrees
180 + 90 + x + 26 = 360
Combine like terms
296+x = 360
Subtract 296 from each side
296+x-296 = 360-296
x = 64
A landscaping company charges $50 per cubic yard of mulch plus a delivery charge of $24. Find a
linear function which computes the total cost C(in dollars) to deliver a cubic yards of mulch.
C(x) =
Answer: c(x) = $50*x + $24
Step-by-step explanation:
First, this situation can be modeled with a linear equation like:
c(x) = s*x + b
where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)
Then we know that:
The company charges $50 per cubic yard, so the slope is $50
A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.
Then our equation is:
c(x) = $50*x + $24
This is:
"The cost of buying x cubic yards of mulch"
Find the distance between the points (–9, 0) and (2, 5). Find the distance between the points (–9, 0) and (2, 5).
Answer:
sqrt( 146)
Step-by-step explanation:
To find the distance, we use the following formula
d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)
sqrt( ( -9-2) ^2 + ( 0-5) ^2)
sqrt( ( -11) ^2 + ( -5) ^2)
sqrt( 121+25)
sqrt( 146)
Use Demoivres Theorem to find (-square root 3 +i)^6
Answer:
[tex]z=(-\sqrt{3}+i)^6[/tex] = -64
Step-by-step explanation:
You have the following complex number:
[tex]z=(-\sqrt{3}+i)^6[/tex] (1)
The Demoivres theorem stables the following:
[tex]z^n=r^n(cos(n\theta)+i sin(n\theta))[/tex] (2)
In this case you have n=6
In order to use the theorem you first find r and θ, as follow:
[tex]r=\sqrt{3+1}=2\\\\\theta=tan^{-1}(\frac{1}{\sqrt{3}})=30\°[/tex]
Next, you replace these values into the equation (2) with n=6:
[tex]z^6=(2)^6[cos(6*30\°)+isin(6*30\°)]\\\\z^6=64[-1+i0]=-64[/tex]
Then, the solution is -64
Answer:
A) -64
Step-by-step explanation:
Edge 2021
Find a formula for an for the arithmetic sequence.
Answer:
a(n)= a(n+1)+4
Step-by-step explanation:
The first terms of this sequence are: 4,0, -4, -8, -12
Let 4 be a0 and 0 a1.
● a1-a0 = 0-4
●a1-a0 = -4
●a1 = -4+a0
So this relation links the first term with the second one.
replace 1 in a1 with n.
0 in a0 will be n-1
● an = -4+a(n-1)
Add one in n
● a(n+1) = a(n)-4
● a(n) = a(n+1)+4
A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09 *Note: An increase in film speed would lower the value of the observation in microjoules per square inch. We may also assume the speeds of the film follow a normal distribution. Use this information to construct a 98% interval estimate for the difference in mean speed of the films. Does decreasing the thickness of the film increase the speed of the film?
Answer:
A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Step-by-step explanation:
We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.
For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.
Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;
P.Q. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15
[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06
[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11
[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09
[tex]n_1[/tex] = sample of 25-mil film = 8
[tex]n_2[/tex] = sample of 20-mil film = 8
[tex]\mu_1[/tex] = population mean speed for the 25-mil film
[tex]\mu_2[/tex] = population mean speed for the 20-mil film
Also, [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005
Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.
So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;
P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98 {As the critical value of t at 14 degrees of
freedom are -2.624 & 2.624 with P = 1%}
P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98
P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ) = 0.98
P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98
98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]
= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]
= [-0.042, 0.222]
Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F. A) Determine the cooling constant k.B) What is the differential equation satisfied by the temperature F(t) of the bar?C) What is the formula for F(t)?D) Determine the temperature of the bar at the moment it is submerged.
Answer:
A) cooling constant = 0.0101365
B) [tex]\frac{df}{dt} = k ( 60 - F )[/tex]
c) F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]
D)137.46 ⁰
Step-by-step explanation:
water temperature = 60⁰F
temperature of Bar after 20 seconds = 120⁰F
temperature of Bar after 60 seconds = 100⁰F
A) Determine the cooling constant K
The newton's law of cooling is given as
= [tex]\frac{df}{dt} = k(60 - F)[/tex]
= ∫ [tex]\frac{df}{dt}[/tex] = ∫ k(60 - F)
= ∫ [tex]\frac{df}{60 - F}[/tex] = ∫ kdt
= In (60 -F) = -kt - c
60 - F = [tex]e^{-kt-c}[/tex]
60 - F = [tex]C_{1} e^{-kt}[/tex] ( note : [tex]e^{-c}[/tex] is a constant )
after 20 seconds
[tex]C_{1}e^{-k(20)}[/tex] = 60 - 120 = -60
therefore [tex]C_{1} = \frac{-60}{e^{-20k} }[/tex] ------- equation 1
after 60 seconds
[tex]C_{1} e^{-k(60)}[/tex] = 60 - 100 = - 40
therefore [tex]C_{1} = \frac{-40}{e^{-60k} }[/tex] -------- equation 2
solve equation 1 and equation 2 simultaneously
= [tex]\frac{-60}{e^{-20k} }[/tex] = [tex]\frac{-40}{e^{-60k} }[/tex]
= 6[tex]e^{20k}[/tex] = 4[tex]e^{60k}[/tex]
= [tex]\frac{6}{4} e^{40k}[/tex] = In(6/4) = 40k
cooling constant (k) = In(6/4) / 40 = 0.40546 / 40 = 0.0101365
B) what is the differential equation satisfied
substituting the value of k into the newtons law of cooling)
60 - F = [tex]C_{1} e^{0.0101365(t)}[/tex]
F(t) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]
The differential equation that the temperature F(t) of the bar
[tex]\frac{df}{dt} = k ( 60 - F )[/tex]
C) The formula for F(t)
t = 20 , F = 120
F(t ) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]
120 = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]
[tex]C_{1} e^{0.0101365(20)}[/tex] = 60
[tex]C_{1} = 60 * 1.291[/tex] = 77.46
C1 = - 77.46⁰ as the temperature is decreasing
The formula for f(t)
= F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]
D) Temperature of the bar at the moment it is submerged
F(0) = 60 + 77.46[tex]e^{0.01013659(0)}[/tex]
F(0) = 60 + 77.46(1)
= 137.46⁰
express 3.222......in p/q form
Answer:
3.22222...... = [tex]\frac{29}{9}[/tex]
Step-by-step explanation:
In this question we have to convert the number given in recurrent decimals into fraction.
Recurrent decimal number is 3.22222.......
Let x = 3.2222......... -------(1)
Multiply this expression by 10.
10x = 32.2222........... -------(2)
Now subtract the expression (1) from (2),
10x = 32.22222.....
x = 3.22222.......
9x = 29
x = [tex]\frac{29}{9}[/tex]
Therefore, recurrent decimal number can be written as [tex]\frac{29}{9}[/tex] which is in the form of [tex]\frac{p}{q}[/tex].
find the slope for (-4,-2)(-3,-6)
Answer:
The slope is -4.
Step-by-step explanation:
The values -2 and -6 are 4 values apart.
The values -4 and -3 are 1 value apart.
Since the second coordinate is lower than the first one, the slope of this is negative.
4 / 1 = 1
Negating 1 gets us -1.
Hope this helped!
Answer:
[tex] \frac{y}{x} = \frac{ - 4}{1} = - 4[/tex]
Step-by-step explanation:
[tex]x = ( - 3) - ( - 4) = 1[/tex]
[tex]y = ( - 6) - ( - 2) = - 4[/tex]
Select the correct answer. Consider the function f(x) = 3x and the function g, which is shown below. How will the graph of g differ from the graph of f? The graph of g is the graph of f shifted to the right by 3 units. The graph of g is the graph of f shifted down by 3 units. The graph of g is the graph of f shifted to the left by 3 units. The graph of g is the graph of f shifted up by 3 units.
Answer:
The graph of g is the graph of f shifted up by 3 units.
Step-by-step explanation:
Consider the graph of a function r with real numbers k and h.
Transformation Effect
r(x) + k shifts the graph up k units
r(x) - k shifts the graph down k units
r(x + h) shifts the graph to the left h units
r(x - h) shifts the graph to the right h units
It is given that g(x) = f(x) + 3. Therefore, the graph of g is the graph of f shifted up by 3 units.
Find the missing side of a triangle when one side is 3.16 and the other is 3
Answer:
0.992774 ≅ .993
Step-by-step explanation:
a²+b²=c²
a=x
b=3
c=3.16
x²+3²=3.16²
x²+9=9.9856
x²=.9856
x=0.992774
x≅0.993
-6+4q+(-6q)−6+4q+(−6q)minus, 6, plus, 4, q, plus, left parenthesis, minus, 6, q, right parenthesis ?
Answer:
-16-5q
Step-by-step explanation:
-6+4q-6q-6+4q-6q-6+4q-6q= -18-6q
Answer:C
Step-by-step explanation: 100% correct I did it on Khan Academy
A circle has a center at (4, -7) and a radius of 4 units. Write an equation of this circle.
Answer:
(x – 4)^2 + (y + 7)^2 = 16
Step-by-step explanation:
The formula of a circle is:
(x – h)^2 + (y – k)^2 = r^2
(h, k) represents the coordinates of the center of the circle
r represents the radius of the circle
If you plug in the given information, you get:
(x – 4)^2 + (y – (-7))^2 = 4^2
which simplifies into:
(x – 4)^2 + (y + 7)^2 = 16
Which point is a solution to the system of inequalities graphed here? y -5 x + 4 A. (1,6) B. (-6,0) C. (0,5) D. (5,0)
Answer:
D
Step-by-step explanation:
this is the only one inside the overlapping inequalitlies
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C
Write the equation of a line through the given point with the given slope (0,6);m undefined
Answer:
x=0
Step-by-step explanation:
If the slope is undefined, the line is vertical
vertical lines are of the form
x =
Since the point is (0,6)
x=0
Item 25
The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function.
0
1
2
3
4
5
6
7
8
9
10
Item 25
The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function.
0
1
2
3
4
5
6
7
8
9
10
Answer:
5
Step-by-step explanation:
please help me out with these questions. Its trigonometry.
Find the value of the lettered angles
In case the pic's not clear;
[tex] \cos \alpha = \sin(50 + \alpha ) [/tex]
Answer: i) θ = 30°, 60°, 210°, & 240°
ii) θ = 20° & 200°
Step-by-step explanation:
i) sin (2θ) = cos 30°
[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]
To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above. θ = 30°, 60°, 210°, 240°
If you need ALL of the solutions (more than one rotation), add 180n to the solutions. θ = 30° + 180n & 60° + 180n
*********************************************************************************************
ii) cos α = sin (50 + α)
Use the Identity: cos α = sin (90 - α)
Use Transitive Property to get: sin (50° + α) = sin (90° - α)
50° + α = 90° - α
50° + 2α = 90°
2α = 40°
α = 20°
To find all solutions for one rotation, add 360/2 = 180 to the solution above.
α = 20°, 200°
If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n
surface area of a equilateral by hand
surface area of a equilateral by hand a 140.4 cm and 9cm
What is 36/100 added with 4/10
Answer:
0.76 or 19/25
Step-by-step explanation:
Convert 4/10 so that it has a common denominator with 36/100.
4/10 x 10/10 = 40/100
Now that the denominator is the same, just add the top values.
40/100 + 36/100 = 76/100
We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.
Answer:
19/25Step-by-step explanation:
[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]
[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]
A publisher requires 2∕3 of a page of advertisements for every 5 pages in a magazine. If a magazine has 98 pages, to the nearest whole page, how many pages of the magazine are advertisements?
Answer:
[tex]\boxed{13}[/tex] pages
Step-by-step explanation:
Divide the total number of pages by 5 to get how many sets of every 5 pages will contain 2/3 of a page of advertisements.
[tex]\frac{98}{5} = 19.6[/tex]
Multiply this value by [tex]\frac{2}{3}[/tex] to get the total number of pages.
[tex]19.6 * \frac{2}{3} \approxeq 13[/tex] pages
A study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed. The sample average age was 24.2 with a standard deviation of 3.7. The p-value is
Answer:
The p-value is 2.1%.
Step-by-step explanation:
We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.
The sample average age was 24.2 with a standard deviation of 3.7.
Let [tex]\mu[/tex] = true average age a "child" moves permanently out of his parents' home in the United States.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average age = 24.2
s = sample standard deviation =3.7
n = sample of U.S. Adults = 43
So, the test statistics = [tex]\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }[/tex] ~ [tex]t_4_2[/tex]
= 2.127
The value of t-test statistics is 2.127.
Now, the p-value of the test statistics is given by;
P-value = P( [tex]t_4_2[/tex] > 2.127) = 0.021 or 2.1%
The population, p, in thousands of a resort community is given by P(t)=700t/4t[tex]x^{2}[/tex]+9
Answer:
Step-by-step explanation:
pt=700 is basically evaluate it form the bottom to the top and u must mark me as brainly