Answer:
< DKC = [tex]60^{0}[/tex]
Step-by-step explanation:
A square is a quadrilateral that has equal length of side. While an equilateral triangle is one with equal length of sides and equal values of angles.
Given square ABCD and that equilateral triangle ABK is outside the square, both figures share side AB. This shows that the length of the sides of the triangle is the same as the length of the side of the square.
i.e /AD/ = /CD/ = /BC/ = /AB/ = /AK/ = /KB/
Thus, < DKC = [tex]60^{0}[/tex] (property of angles in an equilateral triangle)
if mRS=x then write an equation that could be used to solve for x and find the value of x
Answer:
a) x = 30°
b) mRS = x = 30°
mST = 4x = 4(30°) = 120°
mTU = 4x = 4(30°) = 120°
mUR = 3x = 3(30°) = 90°
Question:
The complete question as found on Chegg website:
In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs
intercepted have the following ratio of measurements:
mRS : mST :MTU : mUR=1:4:4:3
(a) If mRS = x, then write an equation that could be used to solve for x
and find the value of x.
(b) State the measure of each of the four arcs.
mRS =
mST =
MTU
MUR =
Step-by-step explanation:
Find attached the diagram related to the question
mRS : mST : mTU : mUR = 1:4:4:3
Since mRS = x
Writing the ratios of the measure of angle in terms of mRS:
mST = 4× mRS = 4×x = 4x
mTU = 4× mRS = 4×x = 4x
mUR= 3× mRS = 3×x = 3x
The sum of measure the 4 measures of arc = 360° (sum of angle in a circle)
mRS + mST + mTU + mUR = 360°
x + 4x + 4x + 3x = 360
12x = 360
x = 360/12
x = 30°
b) The measure of angle
mRS = x = 30°
mST = 4x = 4(30°) = 120°
mTU = 4x = 4(30°) = 120°
mUR = 3x = 3(30°) = 90°
n a random sample of 10 residents of the state of Florida, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.64 pounds. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Florida. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places
Answer:
The critical value is T = 2.2622.
The 95% confidence interval for the mean waste recycled per person per day for the population of Florida is between 1.352 pounds and 4.248 pounds.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622, which is the critical value.
The margin of error is:
M = T*s = 2.2622*0.64 = 1.448
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 1.448 = 1.352 pounds
The upper end of the interval is the sample mean added to M. So it is 2.8 + 1.448 = 4.248 pounds
The 95% confidence interval for the mean waste recycled per person per day for the population of Florida is between 1.352 pounds and 4.248 pounds.
Find the population mean or sample mean as indicated.
Sample: 17, 11, 8, 12, 22
Answer:
mean:12
Step-by-step explanation:
The population mean or sample mean as indicated in the given samples is 14
What is mean?A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.
Mathematically,
Mean = Sum of the observations/number of observations
Now the given sample is,
17, 11, 8, 12, 22
So, Number of sample = 5
Thus, Mean = Sum of the sample /number of sample
Mean = (17 + 11 + 8 + 12 + 22) / 5
⇒ Mean = 70/5
⇒ Mean = 14
Thus, the population mean or sample mean as indicated in the given samples is 14
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In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)
Here is the full question.
The average finishing time among all high school boys in a particular track event in a certain state is 5 minutes 17 seconds. Times are normally distributed with standard deviation 12 seconds.
A. The qualifying time in this event for participation in the state meet is to be set so that only the fastest 5% of all runners qualify. Find the qualifying time in seconds (round it to the closest second). (Hint: Convert minutes to seconds.)
B. In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)
Answer:
a. x ≅ 337 seconds.
b. P(x > 337 ) = 0.1056
Step-by-step explanation:
A.
Given that ;
Mean [tex]\mu =[/tex] 5 minutes 17 seconds =( (60× 5)+17 ) seconds = 317 seconds ( since 60 seconds make 1 minute.
Standard deviation: [tex]\sigma[/tex] = 12 seconds.
Only the fastest 5% of all runners qualify
The objective is to determine the qualifying time in seconds
Let's look for the Z-score of 0.95;
The Z-score is 1.645 from the tables
[tex]x= ( \sigma * z ) + \mu[/tex]
[tex]x = ( 12 * 1.645 ) + 317 \\ \\x = 336.74[/tex]
x ≅ 337 seconds.
B. Given that the standard deviation = 12 seconds
Mean = 5 minutes 22 seconds = (5 × 60 + 22 )seconds = 322 seconds
he objective is to find P(x > 337 ) i.e the proportion of boys from this region who qualify to run in this event in the state meet.
we are using command normalcdf (SEE THE ATTACHED FILE BELOW FOR THE COMPUTATION)
we have P(x > 337 ) = 0.1056
Dan earns £8.10 per hour how much will he earn for 7 hours work
which of the following expressions is equal to -3x^2-12??!!! please help him
Answer:
-3 ( x+2i) (x-2i)
Step-by-step explanation:
-3x^2-12
Factor out a -3
-3(x^2 +4)
Rewrite
-3 ( x^2 - -4)
-3 ( x^2 - (-2i)^2) This is the difference of squares ( a^2 -b^2 ) = (a-b)(a+b)
-3 ( x- -2i) (x+2i)
-3( x+2i) (x-2i)
what is the name of the shape graphed by the function: r=2cos theta
Answer:
Circle
Step-by-step explanation:
r = 2 cos θ
Multiply both sides by r.
r² = 2r cos θ
Convert to rectangular.
x² + y² = 2x
x² − 2x + y² = 0
Complete the square.
x² − 2x + 1 + y² = 1
(x − 1)² + y² = 1
This is a circle with center (1, 0) and radius 1.
The given function r = 2 cos θ is a circle with a center (1, 0) and radius of 1.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
Given function is r = 2 cos θ
Now, Multiply both sides by r.
r² = 2r cos θ
Convert to rectangular form;
x² + y² = 2x
x² − 2x + y² = 0
Using Complete the square.
x² − 2x + 1 + y² = 1
(x − 1)² + y² = 1
Hence, This is a circle with a center (1, 0) and radius of 1.
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Makeeya only has $25 to spend on a custom T-shirt. It costs $10 for a plain T-shirt, and there is a charge of $$1.50 for each square inch of design added to the T-shirt. Which solution represents the number of square inches of design,x , Makeeya can put on her T-shirt?
Answer:
10 square inches
Step-by-step explanation:
cost of a plain t-shirt = $10
cost of 1 square inch of design addition = $1.50
let there be x square inches of design
then cost of x square inches of design = x*cost of 1 square inch of design
= 1.50*x = 1.5x
Total cost for t-shirt with x square inches of design = cost of a plain t-shirt + cost of x square inches of design = 10 + 1.5 x
It is given that Makeeya has only $25, then total cost which can be afforded by him will be $25 only
Thus,
10 + 1.5 x = 25
=> 1.5x = 25-10 = 15
=> x = 15/1.5 = 10
Thus, Makeeya can put 10 square inches of design on her T-shirt.
A construction company has to complete a project no later than 4 months from now or there will be significant cost overruns. The manager of the construction company believes that there are four possible values for the random variable X, the number of months from now it will take to complete this project: 2, 2.5, 3, and 3.5. It is currently believed that the probabilities of these four possibilities are .4, .3, .2, and .1, respectively. What is the expected completion time (in months) of this project from now?
Answer:
The expected completion time of this project from now is 2.5 months.
Step-by-step explanation:
To find the expected completion time for the project, we multiply each projection by it's probability.
We have that:
0.4 = 40% probability it takes 2 months to complete the project.
0.3 = 30% probability that it takes 2.5 months to complete the project.
0.2 = 20% probability it takes 3 months to complete the project.
0.1 = 10% probability it takes 3.5 months to complete the project.
What is the expected completion time (in months) of this project from now?
E = 0.4*2 + 0.3*2.5 + 0.2*3 + 0.1*3.5 = 2.5
The expected completion time of this project from now is 2.5 months.
A 17-inch candle is lit and burns at a constant rate of 1.3 inches per hour. Let t represent the number of hours since the candle was lit, and suppose f is a function such that f ( t ) represents the remaining length of the candle (in inches) t hours after it was lit. Write a function formula for f . f ( t )
Answer
Since the lyla deleted it actually for a good reason let me explain. But you dont just delete random answers, you can give a comment. I can report you for doing that.
So since it burns at 1.3 per hour. Notice that since it gets removed per hour. so it would be 1.3t so it multiplies per hour. Then we need to subtract. Thats because it lowers the length of the candle. So we get the original length - 17 and get the function
f(t) = 17-1.3t
5. (03.02 MC)
If f(x) = 2х2 - 30, find f(4). (1 point)
НА
Мен
ка
ООО
Амер
-14
2
o17
Answer:
f(4) =2
Step-by-step explanation:
f(x) = 2х^2 - 30,
Let x=4
f(4) = 2 (4)^2 -30
= 2*16 -30
=32-30
= 2
How long is a average teen suppose to be
Answer:
The way adolescents spend their time can strongly influence their health later in life. For youth to maintain a healthy future, they need plenty of sleep; good nutrition; regular exercise; and time to form relationships with family, friends, and caring adults. Additionally, the time adolescents spend in school and in after-school activities with peers and adults can advance healthy academic, emotional, social, and physical development. The amount of time they spend on screens and in social media may also influence adolescents’ overall well-being.
The American Time Use Survey, collected by the U.S. Bureau of Labor Statistics, contains detailed information about how individuals ages 15 and older use their time and provides a picture of a typical weekday and weekend day for a high school teen during the school year. Here we specifically analyze how adolescents ages 15-19 who are enrolled in high school spend their time.
Step-by-step explanation:
2. CTfastrak bus waiting times are uniformly distributed from zero to 20 minutes. Find the probability that a randomly selected passenger will wait the following times for a CTfastrak bus. b. Between 5 and 10 minutes. c. Exactly 7.5922 minutes. d. Exactly 5 minutes. e. Between 15 and 25 minutes.
Answer:
b. 0.25
c. 0.05
d. 0.05
e. 0.25
Step-by-step explanation:
if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:
[tex]P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05[/tex]
Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:
[tex]P(X<x)=\frac{x-a}{b-a}=\frac{x-0}{20-0}=\frac{x}{20}[/tex]
Then, the probability that a randomly selected passenger will wait:
b. Between 5 and 10 minutes.
[tex]P(5<x<10) = P(x<10) - P(x<5)\\P(5<x<10) = \frac{10}{20} -\frac{5}{20}=0.25[/tex]
c. Exactly 7.5922 minutes
[tex]P(7.5922)=0.05[/tex]
d. Exactly 5 minutes
[tex]P(5)=0.05[/tex]
e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:
[tex]P(15<x<25)=P(15<x<20) \\P(15<x<20)=P(x<20) - P(x<15)\\P(15<x<20) = \frac{20}{20} -\frac{15}{20}=0.25[/tex]
Solve (x - 3)2 = 49. Select the values of x.
52
DONE
Answer:
Step-by-step explanation:
[tex](x-3)^2=49[/tex]
<=>
[tex](x-3)^2-49=0\\\\<=> (x-3)^2-7^2=0\\\\<=> (x-3-7)(x-3+7)=0\\<=> (x-10)(x+4)=0\\<=> x -10=0\ or \ x+4=0\\<=> x = 10 \ or\ x = -4[/tex]
solutions are -4 and 10
do not hesitate if you need further explanation
if you like my answer, tag it as the brainliest :-)
help pls take your time..
Answer:
As [tex]{x \to \infty}, \,\,{f(x) \to -\infty[/tex] and as [tex]{x \to -\infty}, \,\,{f(x) \to \infty[/tex]
Step-by-step explanation:
Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards minus infinity).
As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)
A car is discounted 10% and sells for $15,673. What was the discount amount?
Answer:
$1741.44
Step-by-step explanation:
The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:
10% = 90% × 1/9
The discount was ...
$15,673/9 = 1,741.44
_____
Check
The original is the sum of the discounted amount and the discount:
original price = $15,673.00 +1,741.44 = $17, 414.44
10% of that value is 1,741.44, as shown above.
Using a 40% solution, make 100 mL of a 10% solution?
Answer:
I don't know
Step-by-step explanation:
but that looks like chemistry not biology
Hue wants to buy two necklaces, one for her sister and one for herself. The necklace for her sister costs $43.25, and the necklace for herself costs $26.25. The sales tax on the purchases is 3%. Find the total cost of Hue's purchases, including sales tax.
Answer:
$71.59
Step-by-step explanation:
43.25+26.25
=69.5
69.5×103/100
=71.585
Solve for X 10(x-1) = 8x-2
Answer:
X = 4 x
over 5 ( x − 1 ) − 1 5 ( x − 1 )
Answer:
x = 4
Step-by-step explanation:
10(x-1) = 8x-2
Distribute
10x-10 = 8x-2
Subtract 8 from each side
10x-10-8x = 8x-2-8x
2x-10 = -2
Add 10 to each side
2x-10+10 = -2+10
2x = 8
Divide each side by 2
2x/2 = 8/2
x = 4
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).
ASK YOUR TEACHER Two streets meet at an 84° angle. At the corner, a park is being built in the shape of a triangle. Find the area of the park if, along one road, the park measures 190 feet, and along the other road, the park measures 235 feet. (Round your answer to the nearest whole number.)
Answer:
22,203 ft^2
Step-by-step explanation:
The area of a triangle with angle ∅ and two sides a and b is;
Area A = 1/2 × absin∅ ......1
The park is in the shape of a triangle, with two sides and an angle given;
Given;
a = 190 ft
b = 235 ft
∅ = 84°
Substituting the values into equation 1;
Area of the park;
A = 1/2 × 190 × 235 × sin84°
A = 22,202.70131409 ft^2
A = 22,203 ft^2 (to the nearest whole number)
Area of the park is 22,203 ft^2
Determine the interest earned on a 3 and 1/4 year investment of $2880 at a rate of 4.5%
Answer:
The interest earned is $421.2.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
In this question:
[tex]P = 2880, I = 0.045, t = 3 + \frac{1}{4} = 3.25[/tex]
So
[tex]E = P*I*t[/tex]
[tex]E = 2880*0.045*3.25[/tex]
[tex]E = 421.2[/tex]
The interest earned is $421.2.
Answer for (12x+5)x-7x+2
Answer:
(12x2-2x+2)
Step-by-step explanation:
(12x)(x)+(5)(x)+-7x+2
12x2+5x+-7x+2
(12x2)+(5x+-7x)+(2)
12x2+-2x+2
2. En la ciudad de Quito, en la temporada fría, se registran temperaturas que van desde los 5 °C hasta los 18 °C. En la temporada cálida, el registro de la temperatura va desde los 4 °C hasta los 30 °C.
a. Representamos estas temperaturas en forma de intervalo y como conjunto.
b. ¿A qué intervalo pertenece la temperatura de la ciudad de Quito?
c. ¿Qué temperaturas son comunes en las temporadas fría y cálida?
d. ¿Qué temperaturas son posibles solo en la temporada fría?
e. ¿Qué temperaturas son posibles solo en la temporada cálida?
Answer:
(See explanation below for further detail/Véase la explicación abajo para mayores detalles)
Step-by-step explanation:
(This exercise is written in Spanish and explanations will be held in such language)
a) Las temperaturas quedan representadas a continuación:
Quito - Temporada Fría
Intervalo
[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada fría)
Conjunto
[tex]C = \{\forall t \in \mathbb {R}| 5 \leq t \leq 18\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada fría)
Quito - Temporada Cálida
Intervalo
[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada cálida)
Conjunto
[tex]H = \{\forall t \in \mathbb {R}| 4 \leq t \leq 30\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada cálida)
b) La temperatura de la ciudad de Quito pertenece esencialmente a dos intervalos:
Intervalo de Temporada Fría:
[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex]
Intervalo de Temporada Cálida:
[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex]
c) Toda temperatura mayor o igual que 4 °C y menor o igual que 30 °C.
d) Temperaturas mayores o iguales a 5 °C y menores o iguales a 18 °C.
e) Temperaturas mayores o iguales a 4 °C y menores o iguales a 30 °C.
Which value of a in the exponential function below would cause the function to shrink? f(x) = a(three-halves) Superscript x Four-fifths Five-fourths Three-halves Seven-fourths
Answer:
Four-fifths
Step-by-step explanation:
As we know that
By multiplying the function by a constant, we may expand or shrink the function in the y-direction.
Now we have
[tex]y=a(b^{x})[/tex]
if [tex]a> 1[/tex] > the function would enlarge
if [tex]0< a < 1[/tex] > the function would shrinks
Now
For case A
[tex]a = \frac{4}{5}[/tex]
[tex]0 < (\frac{4}{5} )< 1[/tex] ....... > the function would shrinks
For case B
[tex]a = \frac{5}{4}[/tex]
[tex](\frac{5}{4} )>1[/tex] .......> the function would enlarge
For case C
[tex]a = \frac{3}{2}[/tex]
[tex](\frac{3}{2} )>1[/tex] .........> the function would enlarge
For case D
[tex]a = \frac{7}{4}[/tex]
[tex](\frac{7}{4} )>1[/tex] .........> the function would enlarge
Therefore the second option is correct
Answer: 4/5
Step-by-step explanation: E2020
Please help! Correct answer only, please! Jason has the following averages in his math class: homework avg: 80 quiz avg: 84 test avg: 74 final exam: 60 if the teacher weights homework at 20%, quizzes at 30%, tests at 40%, and the final exam at 10%, what is jason's class average? A. 74 B. 77 C. 79 D. 82
Answer:
77
Step-by-step explanation:
80*0.2 + 84*0.3 + 74*0.4 + 60*0.1 = 76.8 = 77
The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: "Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, some what agree, some what disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, said that they some what agree, said they some what disagree, and said they strongly disagree with this statement.
Required:
a. Do the responses for this statement provide categorical or quantitative data?
b. Would it make more sense to use averages or percentages as a summary of the responses for this statement?
c. What percentage of respondents strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
Step-by-step explanation:
a. It would provide a quantitative data
b. Yes, it would make more sense to use percentages rather than averages as this is estimating a proportion.
c. 44% of the respondents strongly agree
d. the results do not indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving as the only respondents will be those that agree with the researchers claim and the study will be biased against those who do not agree.
CAN SOMEONE HELP ME IN THIS INTEGRAND QUESTION PLS PLS PLS PLS
''Find the surface area between the z = 1 and z = 4 planes of z = x ^ 2 + y ^ 2 paraboloid.''
Answer:
Step-by-step explanation:
Answer:
S = ⅙ π (65^³/₂ − 5^³/₂)
Step-by-step explanation:
z = x² + y², 1 < z < 4
Surface area is:
S = ∫∫√(1 + (fₓ)² + (fᵧ)²) dA
where fₓ and fᵧ are the partial derivatives of f(x,y) with respect to x and y, respectively.
fₓ = 2x, fᵧ = 2y
S = ∫∫√(1 + (2x)² + (2y)²) dA
S = ∫∫√(1 + 4x² + 4y²) dA
For ease, convert to polar coordinates.
S = ∫∫√(1 + 4r²) dA
S = ∫∫√(1 + 4r²) r dr dθ
At z = 1, r = 1. At z = 4, r = 4.
So 1 < r < 4, and 0 < θ < 2π. These are the limits of the integral.
S = ∫₀²ᵖⁱ∫₁⁴√(1 + 4r²) r dr dθ
To integrate, use u-substitution.
u = 1 + 4r²
du = 8r dr
⅛ du = r dr
When r = 1, u = 5. When r = 4, u = 65.
S = ∫₀²ᵖⁱ∫₅⁶⁵√u (⅛ du) dθ
S = ∫₀²ᵖⁱ (⅛ ∫₅⁶⁵√u du) dθ
S = ∫₀²ᵖⁱ (¹/₁₂ u^³/₂ |₅⁶⁵) dθ
S = ∫₀²ᵖⁱ (¹/₁₂ (65^³/₂ − 5^³/₂)) dθ
S = (¹/₁₂ (65^³/₂ − 5^³/₂)) θ |₀²ᵖⁱ
S = (¹/₁₂ (65^³/₂ − 5^³/₂)) (2π)
S = ⅙ π (65^³/₂ − 5^³/₂)
Statistics show that about 42% of Americans voted in the previous national election. If three Americans are randomly selected, what is the probability that none of them voted in the last election
Answer:
19.51% probability that none of them voted in the last election
Step-by-step explanation:
For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
42% of Americans voted in the previous national election.
This means that [tex]p = 0.42[/tex]
Three Americans are randomly selected
This means that [tex]n = 3[/tex]
What is the probability that none of them voted in the last election
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951[/tex]
19.51% probability that none of them voted in the last election
Ravi's age is six times that of Gaurav's. After 8 years Ravi will be twice as old as Gaurav. What are their present ages?
Answer:
10 and 2
Step-by-step explanation
Nitesh is currently 10 and Ravi is currently 2
(2 times 5 is 10)
in 2 years Nitesh will be 12 and Ravi will be 4
(4 times 3 is 12)
