Answer:
The probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds is P(X<368)=0.011.
Step-by-step explanation:
We have a normal distribution with mean 460 and standard deviation 40 to describe the time for the mile run in its secondary-school fitness test.
We have to calculate the probabiltiy that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
To calculate this, we have to calculate the z-score for X=368:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{368-460}{40}=\dfrac{-92}{40}=-2.3[/tex]
Then, we can calculate the probability:
[tex]P(X<368)=P(z<-2.3)=0.011[/tex]
Use the mathematical induction to prove that 7^n -1 is divisible by 6 whenever n is a positive integer
Answer:
Step-by-step explanation:
1) first of all, let s check for n = 1
[tex]7^1 -1=7-1=6[/tex]
that s true
2) We assume that this is true for n
[tex]7^n-1[/tex] is divisible by 6
what about [tex]7^{n+1}-1[/tex] ?
we know that there is a k natural so that [tex]7^n-1=6k[/tex]
so [tex]7^n = 1+6k[/tex]
then [tex]7^{n+1} = 7*7^n = 7(1+6k)\\[/tex]
so [tex]7^{n+1}-1 = 7(1+6k)-1 = 6+7*6k = 6(1+7k)[/tex]
so it means that [tex]7^{n+1}-1[/tex] is divisible by 6
3) finally as this is true for n=1 and if this is true for n then it is true for n+1 we can conclude that [tex]7^n-1[/tex] is divisible by 6 for n positive integer
Given the function g(x)=2∙3x+1, Find g−1 (x)
Answer:
[tex]g^{-1}(x)=\frac{x-1}{6}[/tex]
What’s the correct answer for this question?
Answer: Choice C
Step-by-step explanation:
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.
3/10≠3/5*1/4
so event A and B are not independent.
Please answer this correctly
Answer: 1-20=2 and 60-80=4
Step-by-step explanation:
the first is 2 number of building
and the third one is 4 number of buldings
Hope this helps :)
NEED HELP ASP Find the common difference of the arithmetic sequence -8, -15, -22, ...
Answer:
-7
Step-by-step explanation:
To find the differences in a sequence, subtract the term before:
-15 -(-8) = -7
-22 -(-15) = -7
These differences are the same, so constitute the "common" difference.
The common difference of the sequence is -7.
Removing which point from the coordinate plane would make the graph a function of x? On a coordinate plane, points are at (negative 2, negative 3), (negative 2, 1), (negative 4, 3), (0, 4), (1, 1), and (2, 3). (–4, 3) (–2, 1) (0, 4) (1, 1)
Answer:
(-2, 1)
Step-by-step explanation:
For a relation consisting of (x, y) pairs to be a function, all of the x-values must be unique. In the given relation, points (-2, -3) and (-2, 1) have the same x-value. Removing either point will make the relation a function.
Of these, the only one listed among answer choices is (-2, 1).
Answer:
-2 , 1
Step-by-step explanation:
good luck love
ADDITIONAL 100 POINTS PLS HELP ASAP follow up question ( first question on log )
Answer:
Hello!
I believe this is what you are looking for:
x=3
33=27
32=9
S=Surface area
V=Volume
L=Length
R=Radius
I hope this helped. If not, please let me know. I will try my best again. :)
Step-by-step explanation:
A hospital needs 0.100 gg of 133 54Xe 54133Xe for a lung-imaging test. If it takes 10 daysdays to receive the shipment, what is the minimal amount mXemXem_Xe of xenon that the hospital should order? Express your answer numerically in grams
Answer:
The correct answer will be "0.400 gm".
Step-by-step explanation:
The give values are:
Needs of hospital, N = 0.100 gm
Time, t = 10 days
Minimum amount of Xenon, N₀ = ?
As we know,
⇒ [tex]N(t)=N_{0} \ e^{-\lambda t}[/tex]
∴ Decay constant, λ = [tex]\frac{ln2}{t_{1/2}}[/tex]
λ = [tex]\frac{ln2}{5}[/tex]
On putting values, we get
⇒ [tex]0.100=N_{0} \ e^{-\frac{ln2}{5}}\times 10[/tex]
⇒ [tex]0.1=N_{0} \ e^{-2ln2} = N_{0} \ e^{-ln4}[/tex]
⇒ [tex]0.1=N_{0} \ e^{ln\frac{1}{4}}[/tex]
⇒ [tex]0.1=\frac{N_{0}}{4}[/tex]
⇒ [tex]N_{0}=0.1\times 4[/tex]
⇒ [tex]MX_{e}=0.400 \ gm[/tex]
The probability of teenager owning a game system is .72 and the probability of teenager owning a cell phone is .93.
the probability of a teenager owning both gaming system and cell phone is .68
what is the probability of a teenager owning a gaming system or a cell phone? round to the nearest thousandth
Answer: 0.97
Step-by-step explanation:
Formula : For events A and B
P(A or B) = P(A) + P(B) - P(A and B)
Given : The probability of teenager owning a game system is .72.
i.e. P(game system) =0.72
The probability of teenager owning a cell phone is .93.
i.e. P(cell phone) = 0.93
The probability of a teenager owning both gaming system and cell phone is .68
i.e. P( game system and cell phone) = 0.68
Now , the probability of a teenager owning a gaming system or a cell phone is given by :_
P(game system or cell phone) = P(game system) +P(cell phone)- P( game system and cell phone)
= 0.72+0.93-0.68
= 0.97
Hence, the probability of a teenager owning a gaming system or a cell phone is 0.97.
6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives: y = x – 5
Answer:
x =6y =13Step-by-step explanation:
This is the method I am familiar with.
I Hope It helps :)
[tex]METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\[/tex]
[tex]Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6[/tex]
Answer:
Correct answers is
Step-by-step explanation:
1. 3
2. B
3. 6
4. (6,13)
Which is true about the polynomial-8m3+11m
Answer:
“It is a binomial with a degree of 3”
Step-by-step explanation:
Since it has just two different coefficients, it would be considered “binomial” for that reason. As you can notice, the highest degree is 3. So match those up and the correct answer would be the second choice “It is a binomial with a degree of 3”
Answer:
B
Step-by-step explanation:
Can someone solve this?
Answer:
32°CDAStep-by-step explanation:
1. The angle facing the given arcs is half their sum, so is (180 +116)/2 = 148°. Angle 1 is the supplement of this, ...
angle 1 = 180° -148° = 32°
__
2. Short arc WY is the supplement of 70°, Long arc WVY is the difference of that and 360°:
arc WVY = 360° -(180° -70°) = 180°+70°
arc WVY = 250° . . . . . matches choice C
__
3. Call the point of intersection of the secants X. The rule for secants is ...
(XA)(XC) = (XB)(XD)
So, the length XC is ...
XC = (XB)(XD)/(XA) = 2.4
and ...
AC = XA +XC = 3.2 +2.4 = 5.6 . . . . . matches choice D
__
4. As in problem 3, the product of lengths from the point of secant intersection to the points of circle intersection is the same for both secants.
(NQ)(NR) = (NP)(NS)
Substituting segment sums where necessary, we have ...
NQ(NQ +QR) = NP(NP +PS)
Solving for PS, we have ...
PS = NQ(NQ +QR)/NP - NP . . . . . matches choice A
Which of the following is an example of theoretical probability?
O A. Lisa attempted 25 basketball free throws and made 14 of them.
The probability Lisa will make a free throw is
14
25
O B. Mike invited 10 friends to a party, and 7 of them said yes. The
probability that a friend will say yes is
7
10
O C. Kelli put 6 red marbles and 5 blue marbles in a bag. The probability
of selecting a red marble is
6
11
O D. Tony listened to 40 songs on the radio and liked 29 of them. The
probability he will like a song is
29
40
The correct answer is C. Kelli put 6 red marbles and 5 blue marbles in a bag. The probability of selecting a red marble is 6 /11
Explanation:
Theoretical probability occurs as you calculate the probability of a specific outcome in a situation, without experimenting or observing it. Because of this, the probability is theoretical rather than experimental. Also, you can know this, if you divide the number of specific favorable outcomes by the total of possible outcomes.
Option C shows a theoretical probability because this is the only case the probability has not been observed or experimented. Also, expressing the probability as 6/11 is completely correct because 6 is the total of red marbles(possible desired outcomes), while 11 is the total marbles (possible outcomes).
Score: 4 of 8 pts
TA
23.1.59
A ball is thrown upward and outward from a height of 5 feet. The height of the ball, f(x), in feet, can be mo
f(x) = -0.2x² +2.1x+5
where x is the ball's horizontal distance, in feet from where it was thrown. Use this model to solve parts (
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
The maximum height is feet, which occurs feet from the point of release
(Round to the nearest tenth as needed.)
Answer:
10.5 ft high
5.3 ft horizontally
Step-by-step explanation:
The equation can be written in vertex form to answer these questions.
f(x) = -0.2(x² -10.5x) +5
f(x) = -0.2(x² -10.5x +5.25²) +5 +0.2(5.25²)
f(x) = -0.2(x -5.25)² +10.5125
The vertex of the travel path is (5.25, 10.5125).
The maximum height is 10.5 feet, which occurs 5.3 feet (horizontally) from the point of release.
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?
Answer:
55% probability that a randomly selected depth is between 2.25 m and 5.00 m
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X between c and d is given by the following formula.
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.
This means that [tex]a = 2, b = 7[/tex]
What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?
[tex]P(2.25 \leq X \leq 5) = \frac{5 - 2.25}{7 - 2} = 0.55[/tex]
55% probability that a randomly selected depth is between 2.25 m and 5.00 m
A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles). The fitted regression is Time = −7.126 + .0214 Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the critical value for a right-tailed test to see if the slope is positive, using α = .05.
Answer:
Thus; the slope is positive
Step-by-step explanation:
Given that :
the sample size = 20
for the slope; the degree of freedom df = n - 2
= 20 -2
= 18
Using ∝ = 0.05
From t -table , one tailed, at df =18)
[tex]t_{\alpha , df}}= t_{0.05, df = 18} = 1.734[/tex]
Thus the t- critical for the right tailed test is 1.734. This simply refers to the fact that the critical region is test statistics.
Incorporating the Excel Formula [ T.INV (1 - 0.05).18) = 1.734063607
≅ 1.734
Find coordinates of the mid point AS if A is (-4,7) and 5,3
The right answer is (1/2 , 5)
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
What Ln(z) is answer????!!
Write z in exponential form:
[tex]z=1-i=\sqrt2 e^{-i\frac\pi4}[/tex]
Then taking the logarithm, we get
[tex]\mathrm{Ln}(z)=\ln(\sqrt2) + \ln e^{-i\frac\pi4} = \boxed{\ln(\sqrt2)-\dfrac\pi4i}[/tex]
so a is the correct answer.
Based on your understanding of the ideas of external consistency and fruitfulness, which of the following statements best describes the relevance of these ideas to the acceptance of hypotheses?a. A fruitful hypothesis is considered stronger because fruitful hypotheses are always externally consistent with previously held theories. b. A fruitful hypothesis is considered stronger because fruitful hypotheses promote scientific progress by revealing new avenues of research and analysis.c. An adequate theory is always a fruitful theory. d. All internally coherent theories are fruitful.
Answer:
b
Step-by-step explanation:
externally consistent ideas are the ideas that are consistent with other well-confirmed hypothesis.
Fruitfulness of a hypothesis can be measured from the fact it it suggests something other than what it was originally suppose to explain.
Solve for y
A)4
B)5
C)20
D)100
Ayo help meee I need helpppppp please I’m so nice and funnyyyyy
Answer: nice and funnyyyyy y=4
Step-by-step explanation:
subtract 2 16/21 - (-8 5/21). reduce if possible
Answer:
11
Step-by-step explanation:
The radius of a circular disk is given as 21 cm with a maximum error in measurement of 0.2 cm.
A) Use differentials to estimate the maximum error in the calculated area of the disk.
B) What is the relative error?
C) What is the percentage error?
Answer:
a) [tex]\Delta A \approx 26.389\,cm^{2}[/tex], b) [tex]r_{A} \approx 0.019[/tex], c) [tex]\delta = 1.9\,\%[/tex]
Step-by-step explanation:
a) The area of the circular disk is modelled after this expression:
[tex]A = \pi \cdot r^{2}[/tex]
The total differential is given by the following formula:
[tex]\Delta A = 2\pi r \cdot \Delta r[/tex]
The maximum absolute error in the calculated area of the disk is:
[tex]\Delta A = 2\pi \cdot (21\,cm)\cdot (0.2\,cm)[/tex]
[tex]\Delta A \approx 26.389\,cm^{2}[/tex]
b) The relative error is given by:
[tex]r_{A} = \frac{\Delta A}{A}[/tex]
[tex]r_{A} = \frac{26.389\,cm^{2}}{\pi \cdot (21\,cm)^{2}}[/tex]
[tex]r_{A} \approx 0.019[/tex]
c) The percentage error is:
[tex]\delta = r_{A}\times 100\,\%[/tex]
[tex]\delta = 0.019 \times 100\,\%[/tex]
[tex]\delta = 1.9\,\%[/tex]
A small child has 6 more quarters than nickels. If the total amount of the coins is $3.00, find the number of nickels and quarters the child has.
Answer:
nickels- 5, quarters- 11
Step-by-step explanation:
nickel= 5 p, quarter= 25 p
5x+25(x+6)= 300
30x+150=300
30x=150
x=150/30
x=5 nickels
x+6= 11 quarters
g It is known that 20% of products on a production line are defective. Products are inspected until first defective is encountered. a) What is the probability that the experimenter must inspect six products
Question:
It is known that 20% of products on a production line are defective. Products are inspected until first defective is encountered. a) What is the probability that the experimenter must inspect six products to find a defective product?
Answer:
P(x = 6) = 0.0655
P(x = 6) = 6.55%
Step-by-step explanation:
It is given that 20% of products on a production line are defective.
p = 0.20
Then
q = 1 - p = 1 - 0.20 = 0.80
Which means that 80% of products on the production line are not defective.
We want to find out the probability that the experimenter must inspect six products to find a defective product.
Let x is the number of inspections to get a defective product.
P(x = 6) = ?
If out of 6 inspections 1 is defective then it means 5 are not defective
so the probability is
P(x = 6) = p¹ × q⁵
P(x = 6) = 0.20¹ × 0.80⁵
P(x = 6) = 0.20 × 0.32768
P(x = 6) = 0.0655
P(x = 6) = 6.55%
Therefore, there is 6.55% chance that the experimenter finds a defetive product in 6 inspections.
Identify the predictor variable and the response variable. A farmer has data on the amount of precipitation crops received and the harvest of the crops. The farmer wants to determine the harvest of his crop based on the amount of precipitation his crop received.
Answer:
The Predictor variable is the amount of precipitation received while the Response variable is the crop harvest.
Step-by-step explanation:
The Response variable in an experiment is the factor being measured or studied. They are also known as the dependent variables. Predictor variables are those values that explain the changes in the Response variable. They are also known as the independent variables.
In the question above, the amount of precipitation provides an explanation for the harvest of his crops. Therefore, the amount of precipitation can be rightly described as the predictor or independent variable, while the harvest of his crops is described as the response or dependent variable.
Please answer this correctly
Answer:
41-60 => 5
Step-by-step explanation:
41-50 => 2
51-60 => 3
So 2+3 =5
Answer:
5
Step-by-step explanation:
Add up the number of children between 41 and 60
41-50: 2
51-60: 3
------------
total 5
A motorboat can maintain a constant speed of 28 miles
per hour relative to the water. The boat makes a trip
upstream to a certain point in 35 minutes; the return trip
takes 21 minutes. What is the speed of the current?
Answer:
7mph
Step-by-step explanation:
Given
Time Taken to go upstream Tup = 35 min
Time Taken to go downstream Tdown=21 min.
Let the absolute speed (i.e speed relative to the stationary riverbed) be :
Vup : going upstream
Vdown: going downstream.
We know that the distance traveled upstream = distance traveled downstream, hence we can equate both distances, i.e. :
Distance Traveled Upstream = Distance Traveled Downstream
Vup · Tup = Vdown · Tdown (substituting the values for time above)
35Vup = 21Vdown
Vup = (21/35) Vdown ------------(eq 1)
We are also given that the motorboat can travel at V = 28 mph relative to the water.
Since going upstream, we are going AGAINST the current, relative to the riverbed, we expect to be travelling slower. In fact, the absolute difference between the speed relative to the water (i.e V = 28 mph) and the speed relative to the seabed (i.e Vup), is equal to the speed of the current.
The same can be said for going downstream WITH the current, that the absolute difference between V = 28mph and Vdown is also equal to the speed of the current.
Hence we can equate the two:
28 - Vup = Vdown - 28
Vup + Vdown = 2(28)
Vup + Vdown = 56 ---------------------(eq 2)
If we solve the system of equations (eq 1) and (eq2), we will get
Vup = 21 mph and Vdown = 35 mph
(sanity check tells us that this makes sense because we expect to be going slower upstream because we are going against the current)
Hence current speed
= 28-Vup
= 28 - 21
= 7 mph. (answer)
Sanity Check:
Current speed can also be written:
= Vdown-28
= 35 - 28
= 7 mph (same as what we found above, so this checks out)
The speed of the current motorboat = 7 mph
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Speed of boat in still water = 28 mph
Let the speed of stream = w
Here, The upstream time is 35 min = 35/60 h = 7/12 h
downstream time is 21 min = 21/60 h = 7/20 hours
Since, The distance (d = vt) traveled either way is the same, but at different speeds and times.
Hence, Set upstream and downstream distances (vt) equal and solve for w as;
⇒ (28 - w)(7/12) = (28 + w)(7/20)
⇒ 20 (28 - w) = 12 (28 + w)
⇒ 5(28 - w) = 3(28 + w)
⇒ 140 - 5w = 84 + 3w
⇒ 140 - 84 = 5w + 3w
⇒ 56 = 8w
⇒ w = 7
Thus, The speed of the current = 7 mph
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
A recent national survey found that parents read an average (mean) of 10 books per month to their children under five years old. The population standard deviation is 5. The distribution of books read per month follows the normal distribution. A random sample of 25 households revealed that the mean number of books read last month was 12. At the .01 significance level, can we conclude that parents read more than the average number of books to their children
Answer:
Step-by-step explanation:
Null hypothesis: u = 10
Alternative hypothesis: u =/ 10
Using the formula: t = (x - u) / (s /√n)
Where x = 12, u = 10, s = 5 and n = 25
t= (12-10) / (5/√25)
t = (2)/(5/5)
t = 2/1= 2
t = 2.0
At a 0.01 level of significance with a degree of freedom of 24, the p-value is 0.0569, which is greater than 0.01 we will fail to reject the null and conclude that parents do not read more than the average number of books to their children
Which graph show the line y-4=3(x+1)
Answer:
x or slope: 3
y-intercept: 7
x y
0 7
1 10
Explanation:
which expression is equivalent to (5x^3)(4x)^3?
A. 20x^6
B. 320x^6
C. 500x^6
D. 8,000x^6
Answer:
320 x^6
Step-by-step explanation:
(5x^3)(4x)^3
5 x^3 * 4^3 * x*3
5x^3 *64x^3
320 x^6
Answer:
B
Step-by-step explanation:
= 5x^3 * 4^3 * x^3
= 5x^3 *64x^3
= 320x^6
Hope this helps!
