Answer:
We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:
[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]
[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]
And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria
Step-by-step explanation:
For this case we have the follwing info given:
[tex] \mu = 80.9[/tex] represent the mean
[tex]\sigma = 10.7[/tex] represent the deviation
We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:
[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]
[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]
And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria
Three populations have proportions 0.1, 0.3, and 0.5. We select random samples of the size n from these populations. Only two of the distributions of the sample proportions are normally distributed. Choose all possible values of n.
a. 10
b. 100
c. 50
d. 40
e. 20
Answer:
(1) A Normal approximation to binomial can be applied for population 1, if n = 100.
(2) A Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.
(3) A Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.
Step-by-step explanation:
Consider a random variable X following a Binomial distribution with parameters n and p.
If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
np ≥ 10 n(1 - p) ≥ 10The three populations has the following proportions:
p₁ = 0.10
p₂ = 0.30
p₃ = 0.50
(1)
Check the Normal approximation conditions for population 1, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.10=1<10\\\\n_{b}p_{1}=100\times 0.10=10=10\\\\n_{c}p_{1}=50\times 0.10=5<10\\\\n_{d}p_{1}=40\times 0.10=4<10\\\\n_{e}p_{1}=20\times 0.10=2<10[/tex]
Thus, a Normal approximation to binomial can be applied for population 1, if n = 100.
(2)
Check the Normal approximation conditions for population 2, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.30=3<10\\\\n_{b}p_{1}=100\times 0.30=30>10\\\\n_{c}p_{1}=50\times 0.30=15>10\\\\n_{d}p_{1}=40\times 0.10=12>10\\\\n_{e}p_{1}=20\times 0.10=6<10[/tex]
Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.
(3)
Check the Normal approximation conditions for population 3, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.50=5<10\\\\n_{b}p_{1}=100\times 0.50=50>10\\\\n_{c}p_{1}=50\times 0.50=25>10\\\\n_{d}p_{1}=40\times 0.50=20>10\\\\n_{e}p_{1}=20\times 0.10=10=10[/tex]
Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.
in triangle ABC shown below, Segment DE is parallel to Segment AC:
Answer:
Selected option is correct
Step-by-step explanation:
Triangle BDE and BAC are similar because of the two pairs of equal angles (AA)
1. angle B
2. angle BDE = angle BAC
1a. A deep-sea diver is at sea level. He submerges 15 feet per minute,
How many feet below sea level is he after submerging for 10 minutes? First question.
Second question,Then write an integer representing the deep-sea current location.
PLZZZ answer this correctly and i give you a brainliest!!!
Answer:
150, 15x
Step-by-step explanation:
After ten minutes he will be 15 * 10 = 150 feet below sea level.
We can call the number of minutes the diver has been underwater for as x so the integer is 15 * x = 15x.
5) BRAINLIEST + 10+ POINTS! A 60 foot tall radio tower r feet from an observer subtends an angle of 3.25°. Use the arc length formula to estimate r (the distance between the observer and the radio tower) to the nearest foot. r≈ ___ feet
Answer:
1057
Step-by-step explanation:
tower is 60 feet high.
angle of 3.25 degrees.
3.25/360 * 2 * pi * r = the arc length of this angle.
that would be equal to 0.0567232007* r
if we assume the arc length and the height of the tower are approximately equal, then 0.0567232007 * r = 60
solving for r, we get r = 60/0.0567232007 = 1057.768237 feet.
that's about how far the tower is from the observer.
since the arc length is going to be a little longer than the length of the chord formed by the flagpole, this means that the distance of 1057.768237 meters is going to be a little less than the actual distance.
Answer:
≈ 1058 ft
Step-by-step explanation:
Use of arc formula: s=rθ
Given:
s= 60 ftθ= 3.25°= 3.25*π/180°= 0.0567 radr= s/θ= 60/0.0567 ≈ 1058 ft
Find the missing length indicated. x=
Answer: x = 120
Step-by-step explanation:
Here we have 3 triangles, one big and two smaller ones, one at the left and other at the right.
Now, the right sides is shared by the right smaller triangle and the big triangle, if this length is Z, we have that (using the angle in top of it, A, such that 64 is adjacent to A.)
Cos(A) = 64/Z
Cos(A) = Z/(64 +225)
We can take the quotient of those two equations and get:
[tex]1 = \frac{64*(64 + 225)}{Z^2} = \frac{18496}{Z^2}[/tex]
Then:
Z = √(18,496) = 136.
now, we have that for the smaller triangle one cathetus is equal to 64 and the hypotenuse is equal to 136.
Then, using the Pythagorean theorem:
64^2 + x^2 = 136^2
x = √(136^2 - 64^2) = 120
Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer. 360 units2 586 units2 456 units2 552 units2
Answer:
Option (4)
Step-by-step explanation:
Surface area of a prism = 2B + P×h
where B = Area of the triangular base
P = perimeter of the triangular base
h = height of the prism
B = [tex]\frac{1}{2}(\text{leg 1})(\text{leg 2})[/tex]
Since, (Hypotenuse)² + (Leg 1)² + (Leg 2)² [Pythagoras theorem]
(20)² = (12)² + (Leg 2)²
Leg 2 = [tex]\sqrt{400-144}[/tex]
= 16 units
Therefore, B = [tex]\frac{1}{2}\times 12\times 16[/tex]
= 96 units²
P = 12 + 16 + 20
P = 48 units
h = 7.5 units
Surface area of the prism = 2(96) + (48×7.5)
= 192 + 360
= 552 units²
Therefore, surface area of the given triangular prism = 552 units²
Option (4) will be the answer.
A normally distributed population of package weights has a mean of 63.5 g and a standard deviation of 12.2 g. XN(63.5,12.2) a. What percentage of this population weighs 66 g or more
Answer:
The percentage is %z [tex]= 41.9[/tex]%
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 63.5 \ g[/tex]
The standard deviation is [tex]\sigma = 12.2 \ g[/tex]
The random number is x = 66 g
Given the the population is normally distributed
The probability is mathematically represented as
[tex]P(X > 66 ) = P(\frac{X - \mu }{\sigma} > \frac{x - \mu }{\sigma } )[/tex]
Generally the z-score for this population is mathematically represented as
[tex]Z = \frac{ X - \mu}{ \sigma}[/tex]
So
[tex]P(X > 66 ) = P(Z > \frac{66 - 63.5 }{12.2 } )[/tex]
[tex]P(X > 66 ) = P(Z > 0.2049 )[/tex]
Now the z-value for 0.2049 from the standardized normal distribution table is
[tex]z = 0.41883[/tex]
=> [tex]P(X > 66 ) = 0.41883[/tex]
The percentage is
% z [tex]= 0.41883 * 100[/tex]
%z [tex]= 41.9[/tex]%
A state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement. You choose 4 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x.Is the experiment binomial?A. Yes, there are a fixed number of trials and the trials are independent of each other.B. No, there are more than two outcomes for each trial.C. Yes, the probability of success is the same for each trial.D. No, because the probability of success is different for each trial.
Answer:
A) Yes, there are a fixed number of trials and the trials are independent of each other.
Sample size 'n' = 37
probability of success p = 0.1081
q = 0.8919
Step-by-step explanation:
Explanation:-
Given data we will observe that
There are a fixed number of trials and the trials are independent of each other.
Given a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.
Given size 'n' = 37
The probability that a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.
Proportion
[tex]p = \frac{x}{n} = \frac{4}{37} = 0.1081[/tex]
q = 1 - p = 1 - 0.1081 = 0.8919
Final answer:-
Sample size 'n' = 37
p = 0.1081
q = 0.8919
hurry helpppppppppp please guys
Answer: The box with three shaded squares and one non-shaded square
Step-by-step explanation:
You are trying to find the representation of the shaded region.
The scale shows point A at 0.75, and the scale can range from 0 to 1.
0.75 is equal to 3/4 of 1
3 of the 4 squares are shaded
So, the common ratio is 3:4 or 3/4
If tan A=2/3 and tan B= -3/5 what is the exact value of cot(A-B)?
Answer:
cot(A-B) = 3/19
Step-by-step explanation:
The formula for cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A)
we know that cot A = 1/ Tan A
Given
tan A=2/3
therefore cot A = 1/ tan A = 1/2/3 = 3/2
tan B= -3/5
cot B = 1/ tan B = 1/-3/5 = -5/3
Thus,
(Cot A Cot B + 1 ) = (3/2)*(-5/3 )+ 1 = -5/2 +1 = (-5+2)/2 = -3/2
(Cot B - Cot A) = -5/3 -3/2 = (-5*2) + (-3*3) / 2 = -10 -9/2 = -19/2
Thus,
cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A) = -3/2 / -19/2 = 3/19
Thus,
cot(A-B) = 3/19
3(x + 2) = 12 solve for x
Answer:
x = 2.
Step-by-step explanation:
3(x + 2) = 12
3x + 6 = 12
3x = 6
x = 2
Hope this helps!
Answer:
4
Step-by-step explanation:
the line through (5, 7) and (1, - 5)
Answer:
Hey there!
Slope of the line: [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope of the line: [tex]\frac{12}{4}[/tex], which is equal to 3.
Point slope form: y2-y1=m(x2-x1)
Point slope form: y-7=3(x-5)
Y intercept form: y-7=3x-15
Y intercept form: y=3x-8
Let me know if this helps :)
Problem of the Day
The tortoise and the hare were arguing: who's the fastest? The tortoise boasted he
could swim 220 miles in 10 hours. The hare bragged he could hop 90 miles in 2 hours.
But who is faster? How can you tell?
Answer:
hare
Step-by-step explanation:
Their average rates are ...
tortoise: (220 mi)/(10 h) = 22 mi/h
hare: (90 mi)/(2 h) = 45 mi/h
The hare has a faster speed than the tortoise.
Which ordered pair is a solution of this equation?
-2x + 9y = -26
(-4,-4)
(4,4)
(-4,-5)
(-5,-4)
What amount invested at 10% compounded semiannually will be worth $6380.00 after 38 months? Calculate the result to the nearest cent.
Given Information:
Annual interest rate = r = 10%
Accumulated amount = A = $6380.00
Semi-annual compounding = n = 2
Number of years = t = 38/12 = 19/6
Required Information
Principle amount= P = ?
Answer:
Principle amount= P = $4,684.05
Step-by-step explanation:
The principal amounts in terms of compound interest is given by
[tex]$ P = \frac{A}{(1 + i)^N} $[/tex]
Where
i = r/n
i = 0.10/2
i = 0.05
N = n*t
N = 2*19/6
N = 19/3
So, the principal amount is
[tex]P = \frac{6380.00}{(1 + 0.05)^{19/3}} \\\\P= \$4,684.05 \\\\[/tex]
Therefore, you need to invest $4,684.05 at 10% compounded semiannually for 38 months to get $6380.00 in savings.
The function graphed is reflected across the x-axis to create a new function. Which is true about the domain and range of each function? Both the domain and range change. Both the range and domain stay the same. The domain stays the same, but the range changes. The range stays the same, but the domain changes.
Answer:
Domain stays the same while the range changes
Step-by-step explanation:
While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.
=> x- coordinate = Domain
=> y-coordinate = Range
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
What is the domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.
When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.
The Domain represent as x-coordinate and the range as y-coordinate
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
Hence, option C is correct.
Learn more about appropriate domain here:
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Bargains Galore marked down a $82 cappuccino machine to $72. Calculate the following (if necessary, round your answer for markdown percent to the nearest hundredth percent):
Answer:
12.2%
Step-by-step explanation:
82 · [tex]\frac{100-x}{100}[/tex] = 72 When multiplied by a certain percent we get 72
82(100-x) = 7200
100(A whole as you may say) - *a percent* = the markdown
8200-82x=7200
82x = 1000
x ≈ 12.2
Tell me if you need further explanation
Answer:
12.20%
Step-by-step explanation:
$82 went down to $72.
$82 - $72 = $10
The price went down $10.
Now we find the percent that $10 is of $82.
percent = part/whole * 100%
percent = 10/82 + 100% = 12.195%
Answer: 12.20%
What is the product of (2p + 7)(3p2 + 4p – 3)?
6p3 + 29p2 – 34p + 21
6p3 + 29p2 – 22p + 21
6p3 + 29p2 + 22p – 21
6p3 + 29p2 + 34p – 21'
Answer: 6p^3+29p^2+22p-21
[tex] 3 {x}^{2} - 15x = 15[/tex]
[tex]3x^2-15x= 15\\\\x^2 -5x = 5\\\\x^2-5x-5=0\\\\\Delta = 25+20\\\\\Delta = 45\\\\\\x = \dfrac{5\pm \sqrt{\Delta}}{2}\\\\\\x = \dfrac{5\pm \sqrt{45}}{2}\\\\\\x = \dfrac{5\pm 3\sqrt{5}}{2}\\\\\\[/tex]
A car is driving at 100 kilometers per hour. How far, in meters, does it travel in 3 seconds?
Answer:
The car travels 83 1/3 meters in 3 seconds.
Step-by-step explanation:
Speed of car = 100 KM/ hour
1 km= 1000m
1 hour = 3600 seconds
Lets find speed of car in Meters/second
speed of car in m/sec = 100*1000 m/3600 second
here we have taken 1000 for km and 3600 for hour
speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second
speed of car in m/sec = 250/9 m per sec
We know that
distance = speed*time
speed = 250/9 m per sec
time =3 second
distance = 250/9 * 3 meters = 250/3 meters = 83 1/3 meters.
Thus, car travels 83 1/3 meters in 3 seconds.
Which product will result in a sum or difference of cubes?
A (x + 7)(x2 – 7x + 14)
B (x + 8)(x2 + 8x + 64)
C (x – 9)(x2 + 9x + 81)
D (x – 10)(x2 – 10x + 100)
Answer:
C. (x - 9)(x^2 + 9x + 81).
Step-by-step explanation:
The cube identities are
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Checking against the list the one that fits is the difference formula:
x^2 - 9^2 = (x - 9)(x^2 + 9x + 81).
a=1, b = 9, ab = 1 *9 = 9.
A teacher based in California calculated a particular date in the calendar and named it Square Root Day. Try and find out why the day was named so. Can you find more such days? When was last square root day and when is next square root day
Answer:
may 5 the is squareroot day and it is when the day and the month has the first two digits in the date are the square root of the last two digits. examples 2nd February,2004 3rd March 2009 and the last time we had one was April 4th 2016. The next square root day is May 5th 2025
15 liters of water flow
through a water pipe
and enter a tank
within 4.5 minutes
How much time does
it take to pump 727.5
liters of water into a
water tank using 2
similar water pipes?
Answer:
Step-by-step explanation:
Since 15 liters of water flow through a water pipe and enter a tank within 4.5 minutes, the same amount of water would flow through a similar pipe at the same time. Therefore, if two similar water pipes are used, the volume of water that would flow into the tank in 4.5 minutes is 15 × 2 = 30 liters
Therefore, the time it will take to pump 727.5 liters of water into a water tank using 2 similar water pipes is
(727.5 × 4.5)/30 = 109.125 minutes
Please answer this correctly
798/8×41 rounded to one significant figure
Answer:
2.5
Step-by-step explanation:
the other persons answer is wrong
The number after rounding to the one significant figure is 4000.
What is significant figure?
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number
According to the given question we have an expression.
[tex]\frac{798}{8} (41)[/tex]
When we evaluate this expression we get
[tex]\frac{798}{8} (41)[/tex]
[tex]=99.75(41)[/tex]
[tex]= 4089.75[/tex]
Here, the first significant figure is 4 and the second one is 0 which is less than 5.
Hence, the number after rounding to the one significant figure is 4000.
Find out more information about rounding off here:
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answer of this please
Answer: 205 and 1/7
Step-by-step explanation:
Hope this helped!
<!> Brainliest is appreciated! <!>
AHH!! IM STUCK PLEASE HELP! :(
Think about this. If we were to align the coefficients with their solutions to form this matrix, it would be the following -
[tex]\begin{bmatrix}2&-6&-2&|&1\\ 0&3&-2&|&-5\\ 0&2&2&|&-3\end{bmatrix}[/tex]
Now this is one way to assign the coefficients. As you can see, 2, - 6, - 2 are present as the coefficients for the first row. Similarly 0, 3, - 2 are present as the coefficients for the second row - ( as one term is missing from this row, it is replaced with a " 0 " ). The same applies for the third row. The end values of the system of equation is present as the last column.
The options are assigned in a manner with which the coefficients and variables are present in two columns, while the end values of the system of equation given, is present as the last column. Knowing the arrangement of both the coefficients and the end values of the system of equation, all we have to do is add these " variables " as one column -
Solution = Option B
Please answer this correctly
Answer:
25%
Step-by-step explanation:
Total cards = 4
The number 4 = 1
p(4) = 1/4
In %age:
=> 25%
Answer:
25%
Step-by-step explanation:
There is only 1 four card from the 4 cards.
1 card out of 4 cards.
1/4 = 0.25
P(4) = 25%
If (x) = 3x - 5 and g(x) = x + 3, find (f - g)(x).
O A. 8 - 2x
O B. 2x-2
O c. 2x-8
O D. 4x-2
Answer:
C
Step-by-step explanation:
(f-g)(x)=(3x-5)-(x+3) = 3x-5-x-3 = 2x-8
Answer:
2x -8
Step-by-step explanation:
f (x) = 3x - 5
g(x) = x + 3,
(f - g)(x) = 3x - 5 - ( x+3)
Distribute the minus sign
= 3x-5 -x-3
Combine like terms
= 2x -8
During a football game, a team lost 12 yards on the first play and then gained 5 yards on each of the next 3 plays. Which method finds the total yards at the end of the first four plays?
A) add –12 to 3 times 5
B) add 12 to 3 times 5
C) add –12, 5, and 3
D) add 12, 5, and 3
They got 5 yards on 3 plays. For total yards multiply the 3 plays by 5 yards. The first play was negative, so add the negative value. The answer is A.
Answer:
A
Step-by-step explanation: