Answer:
(1) B
(2) A
(3) C
Step-by-step explanation:
A random variable is a variable that denotes a set of all the possible outcomes of a random experiment. It is denotes by a single capital letter such as X or Y.
There are two types of random variables.
Discrete random variable: These type of random variable takes finite number of values, such as 0, 1, 2, 3, 4, ... For example, number of girl child in a neighborhood.Continuous random variable: These type of random variables takes infinite number of possible values. For example, the height, weight.(1)
Exact weight of quarters now in circulation in the United States.
The variable weight is a continuous variable.
Thus, the exact weight of quarters now in circulation in the United States is a continuous random variable.
(2)
Shoe sizes of humans.
The shoe size of a person are discrete and finite values.
Thus, the shoe sizes of humans are discrete random variables.
(3)
Political party affiliations of adults in the United States.
This variable is not a quantitative variable.
It is a qualitative variable.
Thus, the political party affiliations of adults in the United States is no random variable.
When you enter the Texas Turnpike, they give you a ticket showing the time and place of your entry. When you exit, you turn in this ticket and they use it to figure your toll. Because they know the distance between toll stations, they can also use it to check your average speed against the turnpike limit of 65 mph. On your trip, heavy snow limits your speed to 40 mph for the first 120 mi. At what average speed can you drive for the remaining 300 mi without having your ticket prove that you broke the speed limit?
Answer:
87 mph
Step-by-step explanation:
Total distance needed is 120 mi + 300 mi and that is 420 mi.
Driving at 65 mph means that it would take
420 / 65 hours to reach his destination.
6.46 hours .
at the first phase, he drove at 40 mph for 120 mi, this means that it took him
120 / 40 hours to complete the journey.
3 hours.
the total time needed for the whole journey is 6.46 hours, and he already spent 3 hours in the first phase. To keep up with the 6.46 hours required, in the second phase, he has to drive at a speed of
6.46 - 3 hours = 3.46 hours.
300 mi / 3.46 hours => 86.71 mph approximately 87 mph
Therefore, he needs to drive at not more than 87 mph to keep up with the journey while not breaking his speed limit
Given the number of trials and the probability of success, determine the probability indicated: a. n = 15, p = 0.4, find P(4 successes) b. n = 12, p = 0.2, find P(2 failures) c. n = 20, p = 0.05, find P(at least 3 successes)
Answer:
A)0.126775 B)0.000004325376 C) 0.07548
Step-by-step explanation:
Given the following :
A.) a. n = 15, p = 0.4, find P(4 successes)
a = number of trials p=probability of success
P(4 successes) = P(x = 4)
USING:
nCx * p^x * (1-p)^(n-x)
15C4 * 0.4^4 * (1-0.4)^(15-4)
1365 * 0.0256 * 0.00362797056
= 0.126775
B)
b. n = 12, p = 0.2, find P(2 failures),
P(2 failures) = P(12 - 2) = p(10 success)
USING:
nCx * p^x * (1-p)^(n-x)
12C10 * 0.2^10 * (1-0.2)^(12-10)
66 * 0.0000001024 * 0.64
= 0.000004325376
C) n = 20, p = 0.05, find P(at least 3 successes)
P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)
To avoid complicated calculations, we can use the online binomial probability distribution calculator :
P(X≥ 3) = 0.07548
Are we adding all 4 sides ?
Answer:
Yes
Step-by-step explanation:
you would do 2(5x-10) + 2(8x+4)= 26x-12
Answer:
26x - 12
Step-by-step explanation:
The perimeter is the sum of all the exterior sides of a figure.
Here, we have a parallelogram, and its sides are 5x - 10, 8x + 4, 5x - 10, and 8x + 4. Adding these, we get:
(5x - 10) + (8x + 4) + (5x - 10) + (8x + 4) = 26x - 12
Thus, the answer is 26x - 12. Note that since the problem doesn't give a value for x, this cannot be simplified further.
~ an aesthetics lover
find out what's wrong with this graph
Answer:
The y-axis is upside down, meaning that instead of the values increasing as they go up, they decrease.
Could anyone help me with this question please? Thank you.
Answer:
C) 549 km²
Step-by-step explanation:
The area of the regular pentagon is given by ...
A = (1/2)Pa
where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.
The lateral area is the product of the perimeter and the height:
LA = Ph
Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...
total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)
= (45 km)(6 km +6.2 km) = 549 km^2
What is the solution to the linear equation?
2/5 + p = 4/5 + 3/5p
Answer:
p = 1Step-by-step explanation:
[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]
Multiply through by the LCM
The LCM for the equation is 5
That's
[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]
We have
2 + 5p = 4 + 3p
Group like terms
5p - 3p = 4 - 2
2p = 2
Divide both sides by 2
We have the final answer as
p = 1Hope this helps you
Solve for W.
W/9 = g
Answer:
W = 9 * g
Step-by-step explanation:
W/9 = g
W = 9 * g
The expression W/9 = g can be written as W = 9g after cross multiplication.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
W/9 = g
To solve for W
Make subject as W:
W = 9g
By cross multiplication.
Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
sasha has some pennies nickels and dimes in her pocket. the number of coins is 18 the expression is 0.01p+0.05n+0.10d represents the value of the coins which is 1.08 she has twice as many dimes as pennies. How many of each coin does Sasha have
Answer:
3 pennies, 9 nickels, and 6 dimes
Step-by-step explanation:
We have three conditions:
(1) p + n + d = 18
(2) 0.01p + 0.05n + 0.10d = 1.08
(3) d = 2p
Multiply (2) by 100 and rearrange (3) to get a standard array.
(4) p + n + d = 18
(5) p + 5n + 10d = 108
(6) -2p + d = 0
Subtract (4) from (5). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(6) -2p + d = 0
Multiply (4) by 2 and add to (6). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(8) 2n + 3d = 36
Double (8) and subtract from (7). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(9) 3d = 18
Divide (9) by 3. This gives
(10) d = 6
Substitute (10) into (7). This gives
4n + 9(6) = 90
4n + 54 = 90
4n = 36
(11) n = 9
Substitute (10) and (11) into (4). This gives
p + 9 + 6 = 18
p + 15 = 18
p = 3
Sasha has 3 pennies, 9 nickels, and 6 dimes.
Consider the age distribution in the United States in the year 2075 (as projected by the Census Bureau). Construct a cumulative frequency plot and describe what information the plot communicates about the distribution of ages in the future.
Answer:
The cumulative frequency plot is also attached below.
Step-by-step explanation:
The data provided is as follows:
Age Group Frequency
0 - 9 34.9
10 - 19 35.7
20 - 29 36.8
30 - 39 38.1
40 - 49 37.8
50 - 59 37.8
60 - 69 34.5
70 - 79 27.2
80 - 89 18.8
90 - 99 7.7
100 - 109 1.7
Consider the Excel output attached.
The cumulative frequency are computed in the Excel sheet.
The cumulative frequency plot is also attached below.
From the cumulative frequency plot it can be seen that in the future most people will belong to a higher age group rather then the lower ones.
8.What side of the road will you see speed, yield, and guide signs on ?
Answer:
we see it in our left side of the road
Hi i need help on this im not that smart sorry, what is the x-intercept of the graph that is shown below
Answer:
(3, 0)
Step-by-step explanation:
x-intercept is where the line touches the x-axis
It is the point on the line where y=0
Answer:
3,0
Step-by-step explanation:
the point where the line cuts the x axis is the x-intecept
Hi people, Please if someone can give me a hand, l already have done the first part of the exercise, but l cant make Angle CAB= X^0 c) calculate the lower bound for the value of tan X^0 there is the answer 1.02 (2dp) but l have no clue how to get it thanks i used Toa (Tan = Opp/ adj) but l couldnt find it thanks
Answer:
(c) 1.02
Step-by-step explanation:
(c) The tangent is the ratio of Opposite to Adjacent. Its lowest value will be found where Opposite is lowest, and Adjacent is highest:
min tan(A) = (min BC)/(max AB) = 75/73.5 ≈ 1.020408...(42-digit repeat)
The general manager, marketing director, and 3 other employees of CompanyAare hosting a visitby the vice president and 2 other employees of CompanyB. The eight people line up in a randomorder to take a photo. Every way of lining up the people is equally likely.Required:a. What is the probability that the bride is next to the groom?b. What is the probability that the maid of honor is in the leftmost position?c. Determine whether the two events are independent. Prove your answer by showing that one of the conditions for independence is either true or false.
Answer:
Following are the answer to this question:
Step-by-step explanation:
Let, In the Bth place there are 8 values.
In point a:
There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: [tex]\to 7 \times 2= 14\\\\ \{(1,2),(2,1),(2,3),(3,2),(3,4),(4,3),(4,5),(5,4),(5,6),(6,5),(6,7),(7,8),(8,7),(7,6)\}\\[/tex][tex]\therefore[/tex] required probability:
[tex]= \frac{14}{8!}\\\\= \frac{14}{8\times7 \times6 \times 5 \times 4 \times 3\times 2 \times 1 }\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\=\frac{1}{2880}\\\\=0.00034[/tex]
In point b:
Calculating the leftmost position:
[tex]\to \frac{7!}{8!}\\\\\to \frac{7!}{8 \times 7!}\\\\\to \frac{1}{8}\\\\\to 0.125[/tex]
In point c:
This option is false because
[tex]\to P(A \cap B) \neq P(A) \times P(B)\\\\\to \frac{12}{8!} \neq \frac{14}{8!}\times \frac{1}{8}\\\\\to \frac{12}{8!} \neq \frac{7}{8!}\times \frac{1}{4}\\\\[/tex]
What is the solution set for StartAbsoluteValue z + 4 EndAbsoluteValue greater-than 15? 11 less-than z less-than 19 Negative 19 less than z less-than 11 z less-than negative 19 or z greater-than 11 z less-than 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11Step-by-step explanation:
Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.
For the positive value of the function;
[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]
For the negative value of the function we have;
[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]
Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'
[tex]-(-z)< -19\\\\z<-19[/tex]
Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11
Step-by-step explanation:
Blake bought two iced coffees from Dutch Bros. He originally had $13.50 and now has $9. Write and solve an equation to find out how much each iced
coffee cost.
Answer:
each ice coffee is $2.25
Step-by-step explanation:
13.50 - 9 = 4.50
4.50 / 2 = 2.25
Find interval of increase and decrease of f(x) = 8 sin(x) + cot(x), −π ≤ x ≤ π
Answer:
Given f(x)=8sin(x)+cot(x) for -pi<x<pi :
Note that:
f'(x)=8cos(x)-csc^2(x)
f''(x)=-8sin(x)+2csc^2(x)cot(x)
(1) To find the intervals where f(x) is increasing or decreasing we use the first derivative test; if the first derivative is positive on an interval the functio is increasing, negative implies the functio is decreasing.
Using technology we find the approximate zeros of f'(x) on -pi<x<pi :
x~~-1.443401
x~~-.3752857
x~~.3752857
x~~1.443401
Plugging in test values on the intervals yields:
f'(x)<0 on (-pi,-1.443401)
f'(x)>0 on (-1.443401,-.3752857)
f'(x)<0 on
Plz correct me if wrong
State the correct polar coordinate for the graph shown.
It is not the option selected.
One way to write this polar coordinate is to say (2.5, pi/2) meaning we move 2.5 units away from the origin toward the pi/2 direction
pi/2 radians = 90 degrees
An alternative is to write (-2.5, 3pi/2) which is where we aim at the 3pi/2 direction (270 degrees) and walk backward while still facing directly south, and we'll arrive at the same location.
Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.
Answer:
The area of the pyramid is 360 unit²
Step-by-step explanation:
Given
Base Edge, a = 10
Height, h = 12
Required
Determine the surface area
The surface area of a regular pyramid is calculated as thus;
[tex]A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}[/tex]
Substitute values for a and h
[tex]A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}[/tex]
Evaluate all squares
[tex]A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}[/tex]
[tex]A = 100 + 2 * 10 * \sqrt{25 + 144}[/tex]
[tex]A = 100 + 2 * 10 * \sqrt{169}[/tex]
Take positive square root of 169
[tex]A = 100 + 2 * 10 * 13[/tex]
[tex]A = 100 + 260[/tex]
[tex]A = 360[/tex]
Hence, the area of the pyramid is 360 unit²
Answer:
B.) 360 units2
Step-by-step explanation:
I got it correct on founders education
Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5 v plus 7 f equals 28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies?
Answer:
(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.
what must be added to 2/3 of 5.25 to make it 7.00
Answer:
3.5
Step-by-step explanation:
Well you have to find first 2/3 of 5.25. This means multiplication, which is 3.5. so to find how much to add to this to get 7, we have to subtract 3.5 from 7. 7-3.5=3.5. so we must add 3.5 to get 7. Hope this helps :D
make a box-and-whisker plot for the data. numbers of colors in a country's flag :3,2,2,4,4,3,6,3,5,3,4,1
Answer: see attachment
Step-by-step explanation:
Put the numbers in order from smallest to biggest:
1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 6
↓ ∨ ↓
Q1 Median Q3
Q1 median = (2+3)/2 = 2.5 <---- left side of box plot
Median = (3+3)/2 = 3 <---- Vertical Line of box plot
Q3 median = (4+4)/2 = 4 <---- right side of box plot
Find the measure of ∠BEF
Please HELP ASAP
Answer:
100°
Step-by-step explanation:
We know that angles EFD and AEF are the same as they are alternate interior angles.
We also can note that BEF and AEF are supplementary, meaning their angle lengths will add up to 180°.
So we can create an equation:
(2x + 60) + (3x + 20) = 180
Combine like terms:
5x + 80 = 180
Subtract 80 from both sides
5x = 100
Divide both sides by 5
x = 20.
Now we can use this to find the measure of BEF.
[tex]2\cdot20 + 60[/tex]
[tex]40 + 60 = 100[/tex]
Hope this helped!
Answer:
BEF = 100
Step-by-step explanation:
The angles are same side interior angles and same side interior angles add to 180 degrees
2x+60 + 3x+20 = 180
Combine like terms
5x+80 = 180
Subtract 80
5x = 100
Divide by 5
5x/5 = 100/5
x = 20
We want BEF
BEF = 2x+60
= 2x+60
= 2*20 +60
= 40+60
= 100
Find the length of GV¯¯¯¯¯¯¯¯ A. 43.92 B. 33.1 C. 41.45 D. 68.87
Answer:
The answer is option AStep-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find GV
To find GV we use cosine
cos∅ = adjacent / hypotenuse
From the question
GV is the adjacent
GC is the hypotenuse
So we have
[tex] \cos(37) = \frac{GV}{GC} [/tex]GC = 55°
GV[tex] \cos(37) = \frac{GV}{55} [/tex]GV = 55 cos 37
GV = 43.92495
We have the final answer as
GV = 43.92Hope this helps you
23. f(x) is vertically shrank by a factor of 1/3. How will you represent f(x) after transformation?
A. f(3x)
B. 3f(x)
C. 13f(x)
D. f(13x)
Answer:
Step-by-step explanation:
vertical stretching / shrinking has the following transformation.
f(x) -> a * f(x)
when a > 1, it is stretching
when 0< a < 1, it is shrinking.
when -1 < a < 0, it is shringking + reflection about the x-axis
when a < -1, it is stretching + reflection about the x axis.
Here it is simple shrinking, so 0 < a < 1.
I expect the answer choice to show (1/3) f(x).
However, if the question plays with the words
"shrink by a factor of 1/3" to actually mean a "stretching by a factor of three", then B is the answer (stretch by a factor of three).
What is the equation of the line of best fit for the following data? Round the
slope and y-intercept of the line to three decimal places.
Answer:
the line of best fit can be approximated to:
y = -1.560 x + 22.105
Step-by-step explanation:
You are most likely expected to use a graphing tool are statistical program to calculate this. So enter the list of x-values separate from the list of y values and run the tool in linear regression mode.
Look at the attached image with the actual results including the line of best fit.
The equation can be written (rounding slope and y-intercept to 3 decimals) as:
y = -1.560 x + 22.105
If sin∠M = cos∠N and m∠N = 30°, what is the measure of ∠M?
Step-by-step explanation:
sin∠M = cos∠N
sin∠M = cos(30°)
sin∠M = √3 / 2
m∠M = 60° or 120°
If ∠M is acute, m∠M = 60°.
Answer: The measure of ∠M is 60°
Step-by-step explanation:
The complement of 30° is 60°
sin∠M =cos∠N
sin∠60°=cos∠30°
the measure of ∠M is 60°
If the sample size is increased and the standard deviation and confidence level stay the same, then the margin of error will also be increased.
a. True
b. False
False!
The answer is: False.
Whomever stated the answer is "true" is wrong.
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 15/ms2. If the same force acts upon another object whose mass is
10kg, what is this object's acceleration?
Answer:
[tex]a = 6m/s^2[/tex]
Step-by-step explanation:
Given
When mass = 4kg; Acceleration = 15m/s²
Required
Determine the acceleration when mass = 10kg, provided force is constant;
Represent mass with m and acceleration with a
The question says there's an inverse variation between acceleration and mass; This is represented as thus;
[tex]a\ \alpha\ \frac{1}{m}[/tex]
Convert variation to equality
[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)
Make F the subject of formula;
[tex]F = ma[/tex]
When mass = 4kg; Acceleration = 15m/s²
[tex]F = 4 * 15[/tex]
[tex]F = 60N[/tex]
When mass = 10kg; Substitute 60 for Force
[tex]F = ma[/tex]
[tex]60 = 10 * a[/tex]
[tex]60 = 10a[/tex]
Divide both sides by 10
[tex]\frac{60}{10} = \frac{10a}{10}[/tex]
[tex]a = 6m/s^2[/tex]
Hence, the acceleration is [tex]a = 6m/s^2[/tex]
The table shows the probability distribution of student ages in a high school
with 1500 students. What is the expected value for the age of a randomly
chosen student?
Age
13
14
15
16
17
18
Probability 0.01 0.23 0.26 0.28 0.20 0.02
Answer:
Exoected age is 15.49 years
Step-by-step explanation:
Expected age
= E(x)
= sum (p(i)*i)
= 13*0.01+14*0.23+15*0.26+16*0.28+17*0.20+18*0.02
= 15.49
What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.
x = i and x = i5
x=+ i and x
x= +115
O x=V-1 and x = = -5
x=+ -1 and x = = -5
Answer:
A; The first choice.
Step-by-step explanation:
We have the equation [tex]x^4+6x^2+5=0[/tex] and we want to solve using u-substitution.
When solving by u-substitution, we essentially want to turn our equation into quadratic form.
So, let [tex]u=x^2[/tex]. We can rewrite our equation as:
[tex](x^2)^2+6(x^2)+5=0[/tex]
Substitute:
[tex]u^2+6u+5=0[/tex]
Solve. We can factor:
[tex](u+5)(u+1)=0[/tex]
Zero Product Property:
[tex]u+5=0\text{ and } u+1=0[/tex]
Solve for each case:
[tex]u=-5\text{ and } u=-1[/tex]
Substitute back u:
[tex]x^2=-5\text{ and } x^2=-1[/tex]
Take the square root of both sides for each case. Since we are taking an even root, we need plus-minus. Thus:
[tex]x=\pm\sqrt{-5}\text{ and } x=\pm\sqrt{-1}[/tex]
Simplify:
[tex]x=\pm i\sqrt{5}\text{ and } x=\pm i[/tex]
Our answer is A.
