Answer:
(a) The event that represents success here is the percentage of adults who do not work at all while on summer vacation.
(b) X is a binomial random variable.
(c) The value of p for this binomial experiment is 0.30 or 30%.
(d) P(X = 3) = 0.2541.
(e) The probability that 2 or fewer of the 8 adults do not work during summer vacation is 0.5518.
Step-by-step explanation:
We are given that in a school it is found that 30% of adults do not work at all while on summer vacation. In a random sample of 8 adults, let X represent the number who do not work during summer vacation.
Let X = the number of adults who do not work during summer vacation
(a) The event that represents success here is the percentage of adults who do not work at all while on summer vacation.
(b) The conditions required for any variable to be considered as a random variable is given by;
The experiment consists of identical trials.Each trial must have only two possibilities: success or failure.The trials must be independent of each other.So, in our question; all these conditions are satisfied which means X is a binomial random variable.
(c) The value of p for this binomial experiment is 0.30 or 30%.
(d) The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 8 adults
r = number of success = exactly three
p = probability of success which in our question is % of adults who
do not work at all while on summer vacation, i.e; p = 0.25
SO, X ~ Binom(n = 8, p = 0.30)
Now, the probability that exactly 3 adults do not work at all while on summer vacation is given by = P(X = 3)
P(X = 3) = [tex]\binom{8}{3}\times 0.30^{3} \times (1-0.30)^{8-3}[/tex]
= [tex]56 \times 0.30^{3} \times 0.70^{5}[/tex]
= 0.2541
(e) The probability that 2 or fewer of the 8 adults do not work during summer vacation is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{8}{0}\times 0.30^{0} \times (1-0.30)^{8-0}+\binom{8}{1}\times 0.30^{1} \times (1-0.30)^{8-1}+\binom{8}{2}\times 0.30^{2} \times (1-0.30)^{8-2}[/tex]
= [tex]1 \times 0.30^{0} \times 0.70^{8}+8 \times 0.30^{1} \times 0.70^{7}+28\times 0.30^{2} \times 0.70^{6}[/tex]
= 0.5518
The world’s population is currently estimated at 7,125,000,000. What is this to the nearest billion? billion
Answer:
7,000,000,000
Step-by-step explanation:
since the closest number is less than 5 (1<5) you round down making the nearest billion 7
Answer:
7,000,000,000 OR 7 Billion
Step-by-step explanation:
Since the 1 is millions place and its less than 5, you need to round down meaning that 7,125,000,00 rounded to the nearest billion is 7 billion.
Can anyone please explain? Need some help :)
A regular hexagon is inscribed in a circle with a diameter of 12 units. Find the area of the hexagon. Round your answer to the nearest tenth. (there's no picture included)
Answer:
93.5 square units
Step-by-step explanation:
Diameter of the Circle = 12 Units
Therefore:
Radius of the Circle = 12/2 =6 Units
Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.
Area of the Hexagon = 6 X Area of one equilateral triangle
Area of an equilateral triangle of side length s = [tex]\dfrac{\sqrt{3} }{4}s^2[/tex]
Side Length, s=6 Units
[tex]\text{Therefore, the area of one equilateral triangle =}\dfrac{\sqrt{3} }{4}\times 6^2\\\\=9\sqrt{3} $ square units[/tex]
Area of the Hexagon
[tex]= 6 X 9\sqrt{3} \\=93.5$ square units (to the nearest tenth)[/tex]
State if the triangles in each pair are similar. If so, State how you know they are similar and complete the similarity statement.
Answer:
Answer is option 2
Step-by-step explanation:
We know that Angle M = Angle G (given in diagram)
We also know that Angle L in triangle LMN is equal to Angle L in triangle LGH
As two angles are equal in both triangles they are similar.
But why is it Triangle LGH instead of Triangle HGL?
As we know M=G therefore they should be in the same place in the name Of the triangle. In triangle LMN M is in the middle therefore Angle G should also be in the middle
Solve for x and then find the measure of
Answer:
150°Step-by-step explanation:
<A and <B are alternate interior angles.
So, <A = <B
plugging the values
[tex]8x - 10 = 3x + 90[/tex]
Move variable to L.H.S and change it's sign.
Similarly, Move constant to R.H.S and change it's sign
[tex]8x - 3x = 90 + 10[/tex]
Collect like terms
[tex]5x = 90 + 10[/tex]
Calculate the sum
[tex]5x = 100[/tex]
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{100}{5} [/tex]
Calculate
[tex]x = 20[/tex]
Now, Let's find the measure of <B
[tex] < b = 3x + 90[/tex]
Plugging the value of X
[tex] = 3 \times 20 + 90[/tex]
Calculate the product
[tex] = 60 + 90[/tex]
Calculate the sum
[tex] =150[/tex]
Hope this helps...
Best regards!!
The function defined by w(x)=-1.17x+1260 gives the wind speed w(x)(in mph) based on the barometric pressure x (in millibars,mb). a) Approximate the wind speed for a hurricane with the barometric pressure of 900mb. b) Write a function representing the inverse of w and interpret its meaning in context. c) Approximate the barometric pressure for a hurricane with speed 90 mph.
Answer:
a) 207 mph
b) x = (1260-w)/1.17
c) 1000 mb
Step-by-step explanation:
a) Put the pressure in the equation and solve.
w(900) = -1.17(900) +1260 = 207
The wind speed for a hurricane with a pressure of 900 mb is 207 mph.
__
b) Solving for x, we have ...
w = -1.17x +1260
w -1260 = -1.17x
x = (1260 -w)/1.17 . . . . inverse function
__
c) Evaluating the inverse function for w=90 gives ...
x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars
The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.
The function f(x) = 2x^3 + 3x^2 is:
(a) even
(b) odd
(c) neither
(d) even and odd
Answer:
neither
Step-by-step explanation:
First we must determine if both x and -x are in the domain of the function
since it is a polynomial function our first condition is satisfied
Then we should calculate the image of -x :
2x(-x)^3 + 3*(-x)² = -2x^3+3x²
it is not equal to f(x) nor -f(x)
Researchers studied the mean egg length (in millimeters) for a particular bird population. After a random sample of eggs, they obtained a 95% confidence interval of (45,60) in millimeters. In the context of the problem, which of the following interpretations is correct, if any?
A. We are 95% sure that an egg will be between 45 mm and 60 mm in length.
B. For this particular bird population, 95% of all birds have eggs between 45 mm and 60 mm.
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
D. We are 95% confident that the mean length of eggs in the sample is between 45 mm and 60 mm.
E. None of the above is a correct interpretation.
Answer:
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
For 95% confidence interval, it means that we are 95% confident that the mean of the population is between the given upper and lower bounds of the confidence interval.
For the case above, the interpretation of the 95% confidence interval is that we are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
Pls help me help me pls guys
Answer:
C
Step-by-step explanation:
[tex]-5x-49\geq 113[/tex]
[tex]-5x\geq 162[/tex]
[tex]x\leq -32.4[/tex]
(Multiplying or dividing by a negative flips the sign).
How many bits does it take to identify uniquely every person in the United States (the current population is about 300 million)?
Answer:
what's a bit
Step-by-step explanation:
2(x + 25) HELPPPPP MEEEEE
Answer:
2x+50
Step-by-step explanation:
Distributive property: 2(x)+2(25)
Simplify: 2x+50
Answer: 2x + 50
Step-by-step explanation: In this problem, the 2 distributes through the parenthses, multiplying by each of the terms inside.
So we have 2(x) + 2(25) which simplifies to 2x + 50.
An experiment consists of choosing objects without regards to order. Determine the size of the sample space when you choose the following:(a) 8 objects from 19(b) 3 objects from 25(c) 2 objects from 23
Answer:
a
[tex]n= 75, 582[/tex]
b
[tex]n= 2300[/tex]
c
[tex]n = 253[/tex]
Step-by-step explanation:
Generally the size of the sample sample space is mathematically represented as
[tex]n = \left N } \atop {}} \right. C_r[/tex]
Where N is the total number of objects available and r is the number of objects to be selected
So for a, where N = 19 and r = 8
[tex]n = \left 19 } \atop {}} \right. C_8 = \frac{19 !}{(19 - 8 )! 8!}[/tex]
[tex]= \frac{19 *18 *17 *16 *15 *14 *13 *12 *11! }{11 ! \ 8!}[/tex]
[tex]n= 75, 582[/tex]
For b Where N = 25 and r = 3
[tex]n = \left 25 } \atop {}} \right. C_3 = \frac{25 !}{(19 - 3 )! 3!}[/tex]
[tex]= \frac{25 *24 *23 *22 ! }{22 ! \ 3!}[/tex]
[tex]n= 2300[/tex]
For c Where N = 23 and r = 2
[tex]n = \left 23 } \atop {}} \right. C_2 = \frac{23 !}{(23 - 2 )! 2!}[/tex]
[tex]= \frac{23 *22 *21! }{21 ! \ 3!}[/tex]
[tex]n = 253[/tex]
In ABC,if sin A=4/5 and tan A=4/3, then what I s cos A?
What is the surface area of this regular pyramid? A. 230 in2 B. 304 in2 C. 480 in2 D. 544 in2
Answer:
B: 304in^2
Step-by-step explanation:
One triangle face: (8)(15) ÷ 2 = 60
Four triangle faces: 60 x 4 = 240
Bottom Face: (8)(8) = 64
Total Surface Area: Four triangle faces + Bottom Face
Total Surface Area: 240 + 64
Total Surface Area: 304in^2
Find the value of X
Answer:
14
Step-by-step explanation:
Chords the same distance from the center of the circle have the same length. You are shown that half the chord length is 7, so the whole chord length is
x = 14.
Translate into an equation: The cost of V ounces at $2 per ounce equals $56.
Answer:
V = number of ounces
56 = 2V
Step-by-step explanation:
Answer:28
Step-by-step explanation:V times 2= 56
Type 11/5 in the simplest form
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
11 ÷ 5 = 2 R 1 → [tex]2\frac{1}{5}[/tex]
Hope this helps! :)
What is the value of x in the figure above
the value of x is 115°.
hope its helpful to uh..
solve the exponential function 3 to the x-5 = 9
Answer:
x = 7
Step-by-step explanation:
[tex] 3^{x - 5} = 9 [/tex]
[tex] 3^{x - 5} = 3^2 [/tex]
[tex] x - 5 = 2 [/tex]
[tex] x = 7 [/tex]
Andrew plans to retire in 36 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
(b) What is the probability that the mean return will be less than 5%?
Answer:
a) 24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%
b) 13.57% probability that the mean return will be less than 5%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 8.7, \sigma = 20.2, n = 36, s = \frac{20.2}{\sqrt{36}} = 3.3667[/tex]
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
This is 1 subtracted by the pvalue of Z when X = 11.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11 - 8.7}{3.3667}[/tex]
[tex]Z = 0.68[/tex]
[tex]Z = 0.68[/tex] has a pvalue of 0.7518
1 - 0.7518 = 0.2482
24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%
(b) What is the probability that the mean return will be less than 5%?
This is the pvalue of Z when X = 5.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 8.7}{3.3667}[/tex]
[tex]Z = -1.1[/tex]
[tex]Z = -1.1[/tex] has a pvalue of 0.1357
13.57% probability that the mean return will be less than 5%
An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf:
Answer:
a) E(X) = 16.09 ft³
E(X²) = 262.22 ft⁶
Var(X) = 3.27 ft⁶
b) E(22X) = 354 dollars
c) Var(22X) = 1,581 dollars
d) E(X - 0.01X²) = 13.470 ft³
Step-by-step explanation:
The complete Correct Question is presented in the attached image to this solution.
a) Compute E(X), E(X2), and V(X).
The expected value of a probability distribution is given as
E(X) = Σxᵢpᵢ
xᵢ = Each variable in the distribution
pᵢ = Probability of each distribution
Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)
= 2.70 + 9.381 + 4.011
= 16.092 = 16.09 ft³
E(X²) = Σxᵢ²pᵢ
Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)
= 36.45 + 149.1579 + 76.6101
= 262.218 = 262.22 ft⁶
Var(X) = Σxᵢ²pᵢ - μ²
where μ = E(X) = 16.092
Σxᵢ²pᵢ = E(X²) = 262.218
Var(X) = 262.218 - 16.092²
= 3.265536 = 3.27 ft⁶
b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.
c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars
d) E(X - 0.01X²) = E(X) - 0.01E(X²)
= 16.092 - (0.01×262.218)
= 16.0926- 2.62218
= 13.46982 = 13.470 ft³
Hope this helps!!!
In her backyard, Mary is planting rows of tomatoes. To plant a row of tomatoes, mary needs 20/13 square feet. There are 40 square feet in Mary's backyard, so how many rows of tomatoes can mary plant??
Answer:
26 rows
Step-by-step explanation:
[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]
Question
An airplane is traveling at a constant speed of 585 miles per hour. How many feet does it travel in 6 seconds? Remember
that 1 mile is 5280 feet.
Convert the 6 seconds to hours:
5 seconds x x 1/60 ( minutes per seconds) x 1/60 (Hours per minute) = 6/3600 = 1/600 hours.
Distance = speed x time
Distance = 585 x 1/600 = 585/600 = 0.975 miles
Convert miles to feet:
0.975 x 5280 = 5,148 feet
The plane traveled 5,148 feet in 6 seconds.
A postal service will accept a package if its length plus its girth is not more than 96 inches. Find the dimensions and volume of the largest package with a square end that can be mailed.
Answer:
Dimension - 16in by 16in by 32inVolume - 8,192in³Step-by-step explanation:
Let the length and width of the rectangular package be x and y respectively. Since end of the package is a square, the perimeter of the package will be expressed as P = 4x+y and the volume will be expressed as V = x²y
If a postal service will accept a package if its length plus its girth is not more than 96 inches, then the perimeter is equivalent to 96 inches.
96 = 4x+y
y = 96-4x
Substituting the value of x into the formula for calculating the volume, we will have;
V(x) = x²(96-4x)
V(x) = 96x²-4x³
To get the dimensions and volume of the largest package, we will find V'(x) and equate it to zero.
V'(x) = 192x-12x²
192x-12x² = 0
Factoring out x;
x(192-12x) = 0
x = 0 and 192-12x = 0
12x = 192
x = 192/12
x = 16
This shows that we have a maximum value at x = 16 and minimum at x = 0
To get y, we will substitute x = 16 into the expression y = 96-4x
y = 96-4(16)
y = 96-64
y = 32
- The dimensions of the largest package is therefore 16in by 16in by 32in
- Volume of largest package = x²y = 16²*18 = 8,192in³
You wish to take out a $200,000 mortgage. The yearly interest rate on the loan is 4% compounded monthly, and the loan is for 30 years. Calculate the total interest paid on the mortgage. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.
Answer:
$143,739
Step-by-step explanation:
We must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk(rk).
We have P0=$200,000,r=0.04,k=12,N=30, so substituting in the numbers into the formula gives
$200,000=d(1−(1+0.0412)−30⋅12)(0.0412),
that is,
$200,000=209.4612d⟹d=$954.83.
So our monthly repayments are d=$954.83. To calculate the total interest paid, we find out the entire amount that's paid and subtract the principal. The total amount paid is
Total Paid=$954.83×12×30=$343,738.80
and therefore the total amount of interest paid is
Total Interest=$343,738.80−$200,000=$143,738.80,
which is $143,739 to the nearest dollar.
The interest paid is 2912683 dollars.
What is compound interest ?Compound interest is calculated for the principle taken as well as previous interest paid.
According to the given question Principle amount (P) taken from the bank is 2000000 dollars.
The yearly interest rate (r) compounded monthly is 4%.
Time in years (n) is 30.
We know, in the case of compound interest compounded yearly is
A = P(1 + r/100)ⁿ.
So, Amount compounded monthly will be
A = P[ 1 + (r/12)/100]¹²ⁿ.
A = 2000000[ 1 + (4/12)/100]¹²ˣ³⁰.
A = 2000000[ 1 + 0.003]³⁶⁰.
A = 2000000[ 1.003]³⁰⁰.
A = 2000000(2.456).
A = 4912583.
∴ The total interest paid on the mortgage is (4912683 - 2000000) = 2912683.
earn more about compound interest here :
https://brainly.com/question/14295570
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What is the amount of oil for a sports car? 5 gallons, 5 quarts or 5 cups
Answer:
Option A.
Step-by-step explanation:
We need to find the amount of oil for a sports car.
We know that,
1 quart = 4 cups
1 gallon = 4 quarts = 16 cups
Since, quart and cup are small units and they are not sufficient for a sports car because sports car needs more oil, therefore the amount of oil for a sports car is 5 gallons.
Therefore, the correct option is A.
Which of the following theorems verifies that HIJ MLN?
Answer:
HL (try HL, I believe that's the right answer)
Answer:
HL
Step-by-step explanation:
BRO TRUST ME
I don't know what to do.
Answer:
True.
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We can simply plug in the 3 variables to see if it forms a Pythagorean Triple:
6² + 13² = 14.32²
36 + 169 = 205.062
205 = 205 (rounded), so True.
Translate the following argument in a standard form categorial syllogims then use venn diagram or rules for syllogim to determine whether each is valid or invalid.
All of the movies except the romantic comedies were exciting. Hence, the action films were exciting,because none of them is a romantic comedies.
Answer:
couldnt tell you
Step-by-step explanation:
jkj
Human body temperatures are normally distributed with a mean of 98.2oF and a standard deviation of 0.62oF. Find the temperature that separates the bottom 12% from the top 88%.
Answer:
The temperature that separates the bottom 12% from the top 88% is 97.5°F.
Step-by-step explanation:
We are given that human body temperatures are normally distributed with a mean of 98.2°F and a standard deviation of 0.62°F.
Let X = human body temperatures
So, X ~ Normal([tex]\mu= 98.2,\sigma^{2} = 0.62^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean human body temperature = 98.2°F
[tex]\sigma[/tex] = stnadard deviation = 0.62°F
Now, we have to find the temperature that separates the bottom 12% from the top 88%, that means;
P(X < x) = 0.12 {where x is the required temperature}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12
P(Z < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12
Now, the critical value of x that represents the bottom 12% of the area in the z table is given as -1.1835, that is;
[tex]\frac{x-98.2}{0.62} = -1.1835[/tex]
[tex]{x-98.2}= -1.1835\times 0.62[/tex]
[tex]x = 98.2 -0.734[/tex] = 97.5°F
Hence, the temperature that separates the bottom 12% from the top 88% is 97.5°F.