Answer:
mean of the sample μ₁ = $0.27
Standard deviation of the sample σ₁ = $0.83
Step-by-step explanation:
Step(i):-
given mean of the population 'μ' = $19.67
Mean of the sample
[tex]= \frac{mean}{n} = \frac{19.67}{72} = 0.27[/tex]
Mean of the sample μ₁ = 0.27
Step(ii):-
Given standard deviation of the population (σ) = $7.02
Standard deviation of sample
[tex]= \frac{mean}{\sqrt{n} } = \frac{7.02}{\sqrt{72} } = 0.827[/tex]
Standard deviation of sample = 0.827≅ 0.83
Final answer:-
mean of the sample μ₁ = $0.27
Standard deviation of the sample σ₁ = $0.83
Find one positive angle and one negative angle that is coterminal with the given angle of 300 degrees
Step-by-step explanation:
positive angle =300+180=480.
negative angle = 300 -180=120
Margaret needs to put a new gutter on one side of her roof. The shape of her roof is made up of two right triangles that are on each side of a square. If the area of the square is 6400ft2 and the base of each of the triangles is 70ft, what is the total length of the gutter she’ll need to replace?
Answer:
Step-by-step explanation:
If the area of the square is 6400ft², it means that the length of each side of the square is √6400 = 80ft
It means that the opposite side of each triangle is 80ft. Since each triangle is a right angle triangle, we would find the length of the hypotenuse, L by applying Pythagorean theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
L² = 80² + 70²
L² = 11300
L = √11300
L = 106.3 ft
The total length of the gutter would be the sum of the sides of the square and the two triangles.
Total length = 106.3 + 106.3 + 70 + 70 + 80 + 80 = 512.6 ft
The length of the gutter = 2(70) + 80 = 220 ft
Recall:
Area of a square = [tex]s^2[/tex]; where, s is the length of a side (all its side are equal.)Thus, the length of the gutter in the image shown below (see attachment) is:
2(base length of triangle) + side length of square
Area of square = 6400 ft² = s²
Side length = s = √6400
s = 80 ft
Base of triangle = 70 ft
The length of the gutter = 2(70) + 80 = 220 ftLearn more here:
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Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation of the sampling distribution of the sample means are:___________.
A) 8.7 and 1.94
B) 36 and 1.94
C) 36 and 1.86
The mean and the standard deviation of the sampling distribution of the sample means are 36 and 1.94 respectively.
Hence option B is correct.
Given Data
Population Mean, μ = 36.0
Population Standard Deviation, σ = 8
Sample size n = 17
Mean standard deviation, μ = 36.0
[tex]\sigma_\bar x[/tex] = [tex]\sigma/\sqrt{n}[/tex]
= [tex]8/\sqrt{17}[/tex]
= 1.94
The mean and the standard σ/√n of the sampling distribution of the sample means are 36 and 1.94 respectively.
Therefore correct option is B .
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6÷7 ? 7÷8 A. > B. < C. =
Answer:
B:<
Step-by-step explanation:
You can solve this question with fractions. The way I did it was by changing both equations into fractions like this: 6÷7=6/1x1/7=6/7 and 7÷8=7/1x1/8=7/8. Since they don't have a common denomintor and you still dont know which fraction is bigger/smaller, we are going to find a common denominator which is 56. After converting both fractions, (6/7=48/56 and 7/8=49/56) Now you can see that 7/8 is bigger than 6/7, which shows that 6÷7<7÷8.
Need help with this . The picture is enclosed
Answer: (fоg)(24)=5
Step-by-step explanation:
(fоg)(24) is f of g of 24. This means you plug in g(24) into f(x).
[tex]g(24)=\sqrt{24-8}[/tex]
[tex]g(24)=\sqrt{16}[/tex]
[tex]g(24)=4[/tex]
Now that we know g(24), we can plug it into f(x).
f(4)=2(4)-3
f(4)=8-3
f(4)=5
When planning a more strenuous hike, Nadine figures that she will need at least 0.6 liters of water for each hour on the trail. She also plans to always have at least 1.25 liters of water as a general reserve. If x represents the duration of the hike (in hours) and y represents the amount of water needed (in liters) for a hike, the following inequality describes this relation: y greater or equal than 0.6 x plus 1.25 Which of the following would be a solution to this situation?
Answer:
The solution for this is:
y = (0.6 * x) + 1.25
Hope it helps! :)
Answer:
Having 3.2 liters of water for 3 hours of hiking
Step-by-step explanation:
If x represents the number of hours and y represents the number of liters of water, then we can plug the possible solutions into our inequality to see which solution(s) work.
The first option is having 3 liters of water for 3.5 hours of hiking. We will plug 3 in for y and 3.5 in for x:
y > 0.6x + 1.25
3 > 0.6(3.5) + 1.25
3 > 3.35
But since 3 is not greater than 3.35, this does not work.
The next option is having 2 liters of water for 2.5 hours of hiking:
2 > 0.6(2.5) + 1.25
2 > 2.75
But 2 is not greater than 2.75, so this does not work.
Option c is having 2.3 liters of water for 2 hours of hiking:
2.3 > 0.6(2) + 1.25
2.3 > 2.45
Since 2.3 is not greater than 2.45, this solution does not work.
The last option is having 3.2 liters of water for 3 hours of hiking:
3.2 > 0.6(3) + 1.25
3.2 > 3.05
3.2 IS greater than 3.05, so this solution works!
28-171/3 equals what in lowest terms
Answer:
81
Step-by-step explanation:
let the terms be a,ar,ar²
r=2/3
a+a(2/3)+a(2/3)²=171
multiply by 9
9a+6a+4a=171×9
19 a=171×9
a=(171×9)/(19)
a=9×9=81
NCAA stated that of the nearly 8,000,000 high school students participating in high school athletics, only 460,000 of those students will compete at an NCAA college. For the sport of baseball in particular, there are 482,629 high school players. Of these, 6.9% will play in an NCAA college and 8.6% of the college players will go on to be drafted by the MLB. What is the probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB?
Answer:
0.5934% probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Playing at an NCAA college.
Event B: Being drafted by the MLB.
6.9% will play in an NCAA college
This means that [tex]P(A) = 0.069[/tex]
8.6% of the college players will go on to be drafted by the MLB.
This means that [tex]P(B|A) = 0.086[/tex]
What is the probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A) \times P(B|A)[/tex]
[tex]P(A \cap B) = 0.069*0.086 = 0.005934[/tex]
0.5934% probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB
2) A bike racer completed a 20.0 kilometer race. She pedaled the first 5.0 kilometers with an average speed of 20.0 km/hr. She pedaled the next 5.0 kilometers (which were uphill) at an average speed of 10.0 km/hr. She completed the next 5.0 kilometers (which were downhill) at an average speed of 25.0 km/hr and the final 5.0 kilometers she covered at an average speed of 20.0 km/houra) (2point) How long did it take the biker to complete the race
Answer:
Step-by-step explanation:
Time = distance/speed
Considering the first stage,
Speed = 20km/hr
Distance = 5km
Time = 5/20 = 0.25 hour
Considering the second stage,
Speed = 10km/hr
Distance = 5km
Time = 5/10 = 0.5 hour
Considering the third stage,
Speed = 25km/hr
Distance = 5km
Time = 5/25 = 0.2 hour
Considering the third stage,
Speed = 20km/hr
Distance = 5km
Time = 5/20 = 0.25 hour
Therefore, the time it took the biker to complete the race is
0.25 + 0.5 + 0.2 + 0.25 = 1.2 hours
A girl is x years old and her brother is 5 years older than her. (1) Find the sum of their ages. (2) If their father is 25 years older than the girl, what is the difference between the zum of yhe children's age and their fathers age
1) Sum = x + (x+5) = 2x + 5 years
2) Difference = 2x + 5 - (x + 25) = 2x + 5 - x - 25 = x -20
Write the equation of the line that is parallel to the x-axis and goes through the point (1, 4).
Answer:
y=4
Step-by-step explanation:
A line that is parallel to the x-axis would have an equation of y= ______.
This is because a horizontal graph has a gradient of zero, thus the value of m in y=mx+c is zero.
y=0x +c
y= c
Since it passed through the point (1,4):
When x=1, y=4,
4= 0(1) +c
c= 4
Thus, the equation of the line is y=4.
Answer:
y =4
Step-by-step explanation:
Parallel to x axis means a horizontal line
Horizontal lines are of the form
y =
Since it goes through the point (1,4)
y =4
Please answer this correctly
Answer:
3| 4 4 7
4| 0 3 4
5| 5 5 5
6| 0 1 3 8 9
7| 9
8| 1 4 6 8
hope it helps!
Step-by-step explanation:
Check the numbers and list out the tens digit in stem (that is 3-8) and then write the corresponding leaf values
(First picture)How do u turn this algebraic expression into a verbal expression(PLEASE I NEED HELP ASAP)(Second picture)How do you turn this verbal expression into a algebraic expression(I WILL GIVE YOU A THANK U PLEASE HELP ME)
Answer:
for the first picture,
5(x-4)+2
= Five multiply the difference between a number x and four more than two.
[tex] - 2( {x + 4)}^{2} - 1[/tex]
= Negative two multiply the number x increased by four to the power of two less than one
second picture,
4 times the quantity x =4x
A number y cubed plus x squared decreased by 7
[tex]7 - ( {y}^{3} + {x}^{2} )[/tex]
5 times the difference of a number x and 4 plus 2=
5(x-4)+2
the difference of x and y is divided by 3 and added by 8 =
[tex]( \frac{x - y}{3} ) + 8[/tex]
Which of the following are point-slope equations of the line going through (3,
6) and (1,-2)? Check all that apply:
Answer:
y+2=4(x-1)
y-6=4(x-3)
Step-by-step explanation:
Slope between (3, 6) and (1, -2)
6-(-2)/3-1
8/2
4
y+2=4(x-1)
y-6=4(x-3)
Find an equation for the plane that is tangent to the surface z equals ln (x plus y )at the point Upper P (1 comma 0 comma 0 ).
Let [tex]f(x,y,z)=z-\ln(x+y)[/tex]. The gradient of [tex]f[/tex] at the point (1, 0, 0) is the normal vector to the surface, which is also orthogonal to the tangent plane at this point.
So the tangent plane has equation
[tex]\nabla f(1,0,0)\cdot(x-1,y,z)=0[/tex]
Compute the gradient:
[tex]\nabla f(x,y,z)=\left(\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y},\dfrac{\partial f}{\partial z}\right)=\left(-\dfrac1{x+y},-\dfrac1{x+y},1\right)[/tex]
Evaluate the gradient at the given point:
[tex]\nabla f(1,0,0)=(-1,-1,1)[/tex]
Then the equation of the tangent plane is
[tex](-1,-1,1)\cdot(x-1,y,z)=0\implies-(x-1)-y+z=0\implies\boxed{z=x+y-1}[/tex]
128 to 1 significant number
Answer:
The answer is 100.
Step-by-step explanation:
The original figure has 3 significant figures
Rounded to 1 significant figure is 100
The function h(t) = –16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot.
What does h(3.2) represent?
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
Answer:
h(3.2) represents the height of the rock 3.2 seconds after it is propelled. Remember, h(t) represents the height of a rock t seconds after it is propelled.
Answer:
D
Step-by-step explanation:
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
A company rents water tanks shaped like cylinders. Each tank has a radius of 5 feet and a height of 3 feet the cost is 3$ per cubic foot how much does it cost to rent one water tank? Use 3.14 for pie, and do not round your answer.
Answer:
$706.50 to rent one water tank.
Step-by-step explanation:
The volume of the tank can be calculated by taking the area of the base times the height.
The area of the base is found by taking the radius²×pi: 5²×3.14=78.5.
The multiply that by the height to find the volume: 78.5×3=235.5.
To find the cost of renting the tank, multiply the volume of the tank by the price per cubic foot : 235.5×3=$706.50
A taxi company charges based on the function rule P(t) = 0.5t + 2.5, where t is the
time taken for a trip (in minutes) and P(t) is the amount in dollars. If a trip takes 30 minutes, how much will it cost the client?
Answer:
$17.5
Step-by-step explanation:
hello,
we need to compute P(30)
P(30) = 0.5*30 + 2.5 = 15 + 2.5 = 17.5
hope this helps
Divide up the number 480 in a ratio of 3:5.
Answer:
180:300
Step-by-step explanation:
You first divide 480 by 8 because 3+5= 8 and then you multiply that answer (60) by 3 to get 180 and then you multiply it by 5 to get 300. So you get the ratio of 180:300.
IF UR CLEVER PLEAZE HELP ME OUT I AM ON A LIVE LESSON . NEEDS TO BE ANSWERED STAT!!!!
Answer:
384cm2
Step-by-step explanation:
surface area
12×12=144
10×12/2=60
60×4=240
240+144=384cm2
In the diagram below, $RT:TS = 1:2$ and $SR = PQ = 20$. Find $UV$.
It's pretty easy not college levlel just some simple high school geomerty.
Answer: 12
Step-by-step explanation: Because $\overline{PQ}$, $\overline{UV}$, and $\overline{SR}$ are all perpendicular to $\overline{QR}$, we have $\overline{PQ} \parallel \overline{UV} \parallel \overline{SR}$. Therefore, we have $\angle UPQ = \angle UTS$ and $\angle UQP = \angle UST$, which means that $\triangle UPQ \sim \triangle UTS$. So, we have $UQ/US = PQ/ST$.
Because $ST/SR = 2/3$ and $PQ = SR$, we have
\[\frac{UQ}{US} = \frac{PQ}{ST} = \frac{SR}{ST} = \frac{3}{2}.\]Since $UQ/US = 3/2$, we have $UQ/QS = 3/5$.
We have $\triangle UQV \sim \triangle SQR$ by AA Similarity, so $UV/SR = UQ/QS = 3/5$. Therefore, we have $UV = (3/5)SR = \boxed{12}$.
In October , Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than ounces, it was about lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of hours (The Wall Street Journal, October , ). Assume that battery life of the iPad Mini is uniformly distributed between and hours.a. Give a mathematical expression for the probability density function of battery life.A.B.C.The correct answer is:- Select your answer -b. What is the probability that the battery life for an iPad Mini will be hours or less (to 4 decimals)
Answer:
a. Probability density function for the battery life
[tex]f(x)={\begin{cases}{\dfrac {1}{12-8.5}}=\dfrac{1}{3.5}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}[/tex]
b. P(x<11) = 0.7143
Step-by-step explanation:
The question is incomplete
In October, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a. Give a mathematical expression for the probability density function of battery life.
b. What is the probability that the battery life for an iPad Mini will be 11 hours or less (to 4 decimals).
a. We model the battery life as random variable with an uniform distribution with parameters a (min. value)=8.5 hours and b (max. value)=12 hours.
The probability that the battery life takes any value between 8.5 and 12 is constant. Also, the probability that takes any value outside the interval (8.5, 12) is 0.
We can express that as:
[tex]f(x)={\begin{cases}{\dfrac {1}{12-8.5}}=\dfrac{1}{3.5}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}[/tex]
The last is the probability density function for the battery life.
b. We can calculate P(x<11) using the cumulative density function or integrating the density function between x=0 (or x=a=8.5) and x=11.
[tex]P(x<11)=\int\limits^{11}_{8.5} \dfrac{1}{3.5} \, dx=\dfrac{1}{3.5}(x_2-x_1)=\dfrac{1}{3.5}(11-8.5)=\dfrac{2.5}{3.5}= 0.7143[/tex]
What is the scale factor of the two triangles below ?
Answer:
none of the choices are correct
Step-by-step explanation:
it's 4/3
20/15=4.3333333333333
4/3=4.333333333333333
8/6=4.33333333333
The scale factor of the two triangles is [tex]\frac{3}{4}[/tex].
What is scale factor of the two triangles?
When two triangles are similar, the reduced ratio of any corresponding sides is called the scale factor of the similar triangles.
What is similar triangle?Similar triangles are triangles that have the same shape, but their sizes may vary.
According to the given question
We have two triangles NGK and ALH
In which
NG = 15, GK = 6, NK = 3
And, AL = 20, LH = 8 and AH = 4
Since, we have to find the scale factor of these two triangles so the two triangles must be similar.
As, ΔNGK is similar to ΔALH
⇒ [tex]\frac{NG}{AL} = \frac{GK}{LH} = \frac{NK}{AH}[/tex]
⇒ [tex]\frac{15}{20} = \frac{6}{8} =\frac{3}{4}[/tex]
⇒ [tex]\frac{3}{4} = \frac{3}{4} =\frac{3}{4}[/tex]
Hence, the scale factor of the two triangles is [tex]\frac{3}{4}[/tex].
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A truck starts off 180 miles directly east from the city of Hartville. It travels due south at a speed of 45 miles per hour. After travelling 49 miles, how fast is the distance between the truck and Hartville changing
Answer:
11.82 mph
Step-by-step explanation:
The angle between the direction of travel and the direction to the city of Hartville is ...
arctan(180/49) ≈ 74.77°
The speed from the direction of Hartville is the the actual speed multiplied by the cosine of this angle:
speed from Hartville = (45 mph)×cos(74.77°) ≈ 11.82 mph
_____
Comment on the solution
There are other approaches you can use to solve this. One is to compute the change in distance over a small period of time, such as 0.02 hours.
0.01 hours before the time of interest, the distance to the city is ...
d1 = √(180² +(49-.01(45))²) ≈ 186.4326 . . . miles
0.01 hours after the time of interest, the distance to the city is ...
d2 = √(180² +(49+.01(45))²) ≈ 186.6690 . . . miles
Then the rate of change of distance is ...
(d2 -d1)/(t2 -t1) = (186.6690 -186.4326)/0.02 = 11.82 . . . mi/h
__
Another is to write the distance equation and differentiate it. (You will find the solution looks very much like the trig solution above.)
d = √(180² +(45t)²)
dd/dt = 45²t/√(180² +(45t)²) . . . . . to be evaluated at t=49/45
rate of change = 45(49/√(180²+49²)) ≈ 11.82 . . . mi/h
In a bag there are 2 red, 3 yellow, 4 green, and 6 blue marbles.
What is the probability of P (yellow or green)?
Answer:
7/15
Step-by-step explanation:
There are 15 marbles total. -->
3 of them are yellow => 4 of them are green
3 + 4 = 7
7/15
Hope This Helps!
Answer: 7/15=46%
Step-by-step explanation:
There is in total of 15 marbles
but 3 of them are yellow and 4 are green.
4+3=7
7/15=0.466...
7/15≈0.46
0.46=46%
A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 340 found that 60% of the readers owned a laptop. State the null and alternative hypotheses. Answer
Answer:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
Step-by-step explanation:
Information given
n=340 represent the random sample taken
[tex]\hat p=0.60[/tex] estimated proportion of readers owned a laptop
[tex]p_o=0.65[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v{/tex} represent the p value
Hypothesis to test
We want to check if the true proportion of readers owned a laptop if different from 0.65
Null hypothesis:[tex]p=0.65[/tex]
Alternative hypothesis:[tex]p \neq 0.65[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
Write an equation for a polynomial function that has the given roots
-2. 3i , and 5
Answer:
x^4 - 3x^3 - x^2 - 27x - 90 = 0.
Step-by-step explanation:
If 3i is one root then another is -3i.
In factor form we have:
(x + 2)(x - 5)(x - 3i)(x + 3i) = 0
(x^2 - 3x - 10)(x^2 -9i^2) = 0
(x^2 - 3x - 10)(x^2 + 9) = 0
x^4 + 9x^2 - 3x^3 - 27x - 10x^2 - 90 = 0
x^4 - 3x^3 - x^2 - 27x - 90 = 0.
in a triangle ABC shown below, side AB is 8 and side AC is 4
Answer: c) AD = 4 and AE = 2
Step-by-step explanation:
To prove that DE = (1/2) BC, we need to use a proportion that shows that AB = (1/2)AC and AE = (1/2)AD
We are given that AB = 8 and AC = 4 so we need AE = (1/2)AD
a) AD = 4, AE = 8
8 = (1/2)4
8 = 2 FALSE
b) AD = 2, AE = 4
4 = (1/2)2
4 = 1 FALSE
c) AD = 4, AE = 2
2 = (1/2)4
2 = 2 TRUE!
d) AD = 2, AE = 2
2 = (1/2)2
2 = 1 FALSE
PLEASE HELP MEH RN!!!
Answer:
its 4x
Step-by-step explanation:
Answer:
4x
Step-by-step explanation:
