Answer:
The width of the model will be 2.5 inches
Step-by-step explanation:
The tower was scaled down by a factor to a smaller size in the model. We are to, first of all, determine this factor and then use it to scale down the width of the model.
Step One: Determine the scale factor from the tower height.
The scale factor is obtained from the formula:
Scale factor = model size / observed size
This will be
Height of model tower/ height of the real tower.
The height of the model tower is 5 inches which is the same as 0.416667 ft
Scale factor = 0.416667 ft/ 40ft = 0.0104
Step two: Multiply the width of the real-life tower by the scale factor to get the model width.
Width of model =20ft X 0.0104 = 0.208ft
Step three: Convert your answer back to inches.
We will now have to convert 0.208 ft back to inches by multiplying by 12
This will be 0.208 X 12 =2.5 inches.
The width of the model will be 2.5 inches
The owner of a shoe store wanted to determine whether the average customer bought more than $100 worth of shoes. She randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below.
Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether the mean is greater than $100 and then draw a conclusion in the context of the problem. Use α=0.05.
125 99 219 65 109 89 79 119 95 135
Select the correct answer below:
A) Reject the null hypothesis. There is sufficient evidence to conclude that the mean is greater than $100.
B) Reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
C) Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is greater than $100.
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Answer:
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Step-by-step explanation:
We are given that the owner of a shoe store randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below;
X: 125, 99, 219, 65, 109, 89, 79, 119, 95, 135.
Let [tex]\mu[/tex] = average customer bought worth of shoes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $100 {means that the mean is smaller than or equal to $100}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $100 {means that the mean is greater than $100}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = $113.4
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = $42.78
n = sample of receipts = 10
So, the test statistics = [tex]\frac{113.4-100}{\frac{42.78}{\sqrt{10} } }[/tex] ~ [tex]t_9[/tex]
= 0.991
The value of t-test statistics is 0.991.
Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.
Since the value of our test statistics is less than the critical value of t as 0.991 < 1.833, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean is smaller than or equal to $100.
A man bought certain number of litches
at 20 per Rs 100 and an equal no. of 30 per
Rs 100. He mixed them and sold them at
25
per Rs 100. Find his
gain or loss
percent?
Answer: The loss is 4%
Step-by-step explanation:
Lets call litches that are 20 pcs per Rs 100 - litches A
that are 30 pcs per Rs 100- litches B
So a man can buy 2 pcs A per Rs 10
and 3 pcs B per Rs 10
OR
6x pcs A per Rs 30x
and 6x pcs B per Rs 20x
Now he gonna sell the 12x litches for y Rs
Lets find y from the proportion
12x cost y
25 cost 100
y/12=100/25
y=48 Rs
So the man bought 6x A + 6x B for 20x+30x=50 Rs
And then he sold them for 48 Rs
Obviously the man gonna loose the money.
Lets find the losses in %
(50-48)/50*100=200/50=4%
The loss is 4%
A poll reported that 66 percent of adults were satisfied woth the job the major airlines were doing. Suppose 25 adults are selected at random and the number who are satisfied is recorded.
1. Explain why this is a binomial experiment.
A. This is a binomial experiment because there are three mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
B. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a random number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
C. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success changes in each trial.
D. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
2) Find and interpret the probability that exactly 15 of them are satisfied with the airlines.
Answer:
A)Option D
B)P(X = 15) = 0.1325
Step-by-step explanation:
A) From the question, the information given follows binomial distribution because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials. The outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
So option D is correct.
B) From the question, we are told that the poll reported that 66 percent of adults were satisfied with the job. Thus, probability is; p = 0.66
Let X be the number of adults satisfied with the job. Since 25 are selected,
Thus;
P(X = 15) = C(25, 15) * (0.66)^(15) * (1 - 0.66)^(25 - 15)
P(X = 15) = 3268760 × 0.00196407937 × 0.00002064378
P(X = 15) = 0.1325
A construction crew is lengthening a road. The road started with a length of 56 miles, and the crew is adding 3 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 33 days.
Answer:
Below
Step-by-step explanation:
The initial length of the road was 56. 56 is the y-intercept assuming that the graph of this function is a line.
so the equation is:
y= mx+56
m is the slope of the function wich is by how much the function grows.
By analogy, m is the distance added to the road each day.
● y= 3x+56
X is the number of days.
■■■■■■■■■■■■■■■■■■■■■■■■■■
To find the length of the road after 33 days, replace x by 33.
y= 3*33+56 = 155
So after 33 days the road is 155 miles.
Name x1, x2, y1 and y2. Then, find the distance between the points.
Answer:
(5,6), (-2,8)
Step-by-step explanation:
I have a good math expertise. Don't question my skills as they are correct. woof woof waffling behavior. Thnak you hr welcne
Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB
Answer:
AB = 2 sqrt(35) (or 11.83 to two decimal places)
Step-by-step explanation:
Refer to diagram.
ABO'P is a rectangle (all angles 90)
=>
PO' = AB
AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)
using Pythagoras theorem.
Use all the information below to find the missing x-value for the point that is on this line. m = - 1 / 3 b = 7 ( x, 4 )
Answer:
[tex]\boxed{x = 9}[/tex]
Step-by-step explanation:
m = -1/3
b = 7
And y = 4 (Given)
Putting all of the givens in [tex]y = mx+b[/tex] to solve for x
=> 4 = (-1/3) x + 7
Subtracting 7 to both sides
=> 4-7 = (-1/3) x
=> -3 = (-1/3) x
Multiplying both sides by -3
=> -3 * -3 = x
=> 9 = x
OR
=> x = 9
Answer:
x = 9
Step-by-step explanation:
m = -1/3
b = 7
Using slope-intercept form:
y = mx + b
m is slope, b is y-intercept.
y = -1/3x + 7
Solve for x:
Plug y as 4
4 = 1/3x + 7
Subtract 7 on both sides.
-3 = -1/3x
Multiply both sides by -3.
9 = x
Suppose , varies jointly with g and v, and j = 2 when g = 4 and v= 3.
Find j when g = 8 and v= 11.
Answer:
j = 44/3
Step-by-step explanation:
j varies jointly as g and v. This can be represented mathematically as:
[tex]j \alpha gv\\j = kgv[/tex].............(1)
Where k is a constant of proportionality
j = 2 when g = 4 and v = 3
Substitute these values into equation (1)
2 = k * 4 * 3
2 = 12 k
k = 1/6
when g = 8 and v = 11:
j = (1/6) * 8 * 11
j = 44/3
Use the functions m(x) = 4x + 5 and n(x) = 8x − 5 to complete the function operations listed below. Part A: Find (m + n)(x). Show your work. (3 points) Part B: Find (m ⋅ n)(x). Show your work. (3 points) Part C: Find m[n(x)]. Show your work. (4 points)
Answer:
Step-by-step explanation:
Part A
(m + n)x = 4x + 5 + 8x - 5
(m + n)x = 12x The fives cancel
Part B
(m - n)x = 4x + 5 - 8x + 5
(m - n)x = -4x + 10
Part C
The trick here is to put n(x) into m(x) wherever m(x) has an x.
m[n(x)] = 5(n(x)) + 5
m[n(x)] = 5(8x - 5) + 5
m[n(x)] = 40x - 20 + 5
m[n(x)] = 40x - 15
expand (x+2y)^2 plzzzzzzzz
find the exact value of sin 0
Answer:
12/13
Step-by-step explanation:
First we must calculate the hypotenus using the pythagoran theorem
5²+12² = (MO)² MO = [tex]\sqrt{5^{2}+12^{2} }[/tex] MO = 13Now let's calculate sin0
sin O = 12/13So the exact value is 12/13
Answer:
C.) 12/13
Step-by-step explanation:
In a right angle triangle MN = 12, ON = 5 and; angle N = 90°
Now,
For hypotenuse we will use Pythagorean Theorem
(MO)² = (MN)² + (ON)²
(MO)² = (12)² + (5)²
(MO)² = 144 + 25
(MO)² = 169
MO = √169
MO = 13
now,
Sin O = opp÷hyp = 12÷13
A nut-raisin mix costs $5.26 a pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is A.$16 B.$22 C.$61 D.$80
Answer:
D.$80
Step-by-step explanation:
$5.26 x 15.5= $81.53
The closest amount to $81.53 is D.$80
Suppose Miss Roxanne Davenport is 25 years old right now and puts away $1,800 per quarter in an account that returns 6% interest. a.) How much will be in the account when she turns 65? b.)What is her total contribution to the account?
Answer:
a. Total amount after 65 years = $1179415.39
b. The total contribution to the account = $288000
Step-by-step explanation:
Given annuity amount = $1800
Total number of years for contribution = 65 – 25 = 40 years
Interest rate = 6%
a. Total amount after 65 years = Annuity[((1+r)^n -1) / r]
Total amount after 65 years = 1800×((1+.06/4)^(4 × 40) - 1)/(.06/4)
Total amount after 65 years = $1179415.39
b. The total contribution to the account =1800 × 4 Quarter × 40 Years
The total contribution to the account = $288000
plzzzzz helpp j + 9 - 3 < 8
Answer:
j < 2
Step-by-step explanation:
Simplify both sides of the inequality and isolating the variable would get you the answer
Please help with this question ASAP!
You are studying for the SAT and start the first week spending 2 hours studying. You plan to increase the amount you study by 10% each week. How many hours do you study in the 8th week?
Answer:
8w : 3.8974342 ≈ 3.9 or 4 (hope it help)
Step-by-step explanation:
1w : 2
2w : 2 + 10% = 2.2
3w : 2.2 + 10% = 2.42
4w : 2.42 + 10% = 2.662
5w : 2.662 + 10% = 2.9282
6w : 2.9282 + 10% = 3.22102
7w : 3.22102 + 10% = 3.543122
8w : 3.543122 + 10% = 3.8974342
3.8974342 ≈ 3.9 or 4
Determine whether 52c2y4 is a monomial, binomial, trinomial, or other polynomial.
Answer: Monomial.
Step-by-step explanation:
Ok, when we have a polynomial with only one term, this is a monomial.
If the polynomial has two terms, this is a binomial.
If the polynomial has 3 terms, this is a trinomial.
And so on.
In this particular case we have:
52*c^2*y^4
Where c and y may be variables.
We can see that here we have only one term, so this would be a monomial.
(notice that the number of variables does not affect the type of polynomial in this case, only the number of terms)
Answer:
binomial.
Step-by-step explanation:
The polynomial −50c3z3−41y220z4 has 2 terms, so it is a binomial.
Evaluate the series
Answer:
the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
C) 59
Step-by-step explanation:
Recall that;
[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]
Therefore, we can evaluate the series;
[tex]\sum_{k=1}^{6}(25-k^2)[/tex]
by summing the values of the series within that interval.
the values of the series are evaluated by substituting the corresponding values of k into the equation.
[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]
So, the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
convert the equation y= -4x + 2/3 into general form equation and find t the values of A,B and C.
Answer:
Standard form: [tex]12x+3y-2=0[/tex]
A = 12, B = 3 and C = -2
Step-by-step explanation:
Given:
The equation:
[tex]y= -4x + \dfrac{2}3[/tex]
To find:
The standard form of given equation and find A, B and C.
Solution:
First of all, let us write the standard form of an equation.
Standard form of an equation is represented as:
[tex]Ax+By+C=0[/tex]
A is the coefficient of x and can be positive or negative.
B is the coefficient of y and can be positive or negative.
C can also be positive or negative.
Now, let us consider the given equation:
[tex]y= -4x + \dfrac{2}3[/tex]
Multiplying the whole equation with 3 first:
[tex]3 \times y= 3 \times -4x + 3 \times \dfrac{2}3\\\Rightarrow 3y=-12x+2[/tex]
Now, let us take all the terms on one side:
[tex]\Rightarrow 3y+12x-2=0\\\Rightarrow 12x+3y-2=0[/tex]
Now, let us compare with [tex]Ax+By+C=0[/tex].
So, A = 12, B = 3 and C = -2
Please answer this correctly without making mistakes
Simplify the correct answer
Answer:
7/44
Step-by-step explanation:
First find the total number of presidents.
2 + 7 + 13 + 12 + 7 + 3 = 44
There were 7 presidents that were 45-49 when elected. Divide this number by the total number of presidents to find the fraction.
7/44 ≈ 0.159
Write these numbers in standard form 0.000 05
Answer:
5x 10 ^-5
Step-by-step explanation:
UHM that would be
NaN × [tex]10^{0}[/tex]
I hope this helps!
so my reasoning... Any number that can be written in the decimal form between 1.0 to 10.0 multiplied by the power of 10.
An airplane descends during the last hour of it's flight to prepare for landing. It's altitude changes at an average of -0.15 km per minute for those 60 minutes. (What is the product) How does the elevation of the airplane change in that hour? The elevation of the airplane _________ by ______ km. increases 60 decreases 9 0.15
WILL GIVE BRAINLIEST, THANKS AND FIVE STARS
Answer:
The elevation of the airplane decreases by 9 km.
Step-by-step explanation:
We use the distance-rate-time formula: d = rt.
Here, the rate is r = 0.15 km/min and the time is t = 60 min. Simply plug these into the formula:
d = rt
d = 0.15 * 60 = 9 km
So, the change in elevation in the last 60 minutes is 9 km. However, note that the rate is negative (-0.15 km/min), which means that the elevation actually is decreasing.
Thus, the answer is: the elevation of the airplane decreases by 9 km.
~ an aesthetics lover
Answer:
The elevation of the airplane _decrease_ by __9____ km
Step-by-step explanation:
Take the rate and multiply by the time to get the distance traveled
-.15 km per minute * 60 minutes
- 9 km
The plane will go down 9 km in that 60 minutes
A lease provides that the tenant pays $760 minimum rent per month plus 4% of the gross sales in excess of $150,000 per year. If the tenant paid a total rent of $20,520 last year, what was the gross sales volume?
Answer:
$435,000
Step-by-step explanation:
$760 per month * 12 months = $9,120
The minimum rent requires an annual rental cost of $9,120.
The annual rent was $20,520.
The excess was $20,520 - $9,120 = $11,400.
The amount of $11,400 of the rent was due to the gross sales in excess of $150,000.
$11,400 is 4% of the amount in excess of $150,000.
Let the amount in excess of $150,000 = x.
$11,400 = 4% of x
0.04x = 11,400
x = 285,000
$285,000 is the amount in excess of $150,000.
Total gross sales volume = $285,000 + $150,000 = $435,000
please need help with this math question
Answer:
third option
Step-by-step explanation:
We just have to calculate 2x² - 4x - (x² + 6x). 2x² - x² = x² and -4x - 6x = -10x so the answer is x² - 10x.
Answer:
x^2-10x
Step-by-step explanation:
f(x)-g(x)
(2x^2-4x)-(x^2+6x)
carry through the negative
2x^2-4x-x^2-6x
x^2-10x
You are mandated to pick 45 units per hour. You work 8.5 hours a day (minus a 1/2 hour lunch), Monday to Friday. How many units should you be picking each week?
Answer:
1912.5 unitsStep-by-step explanation:
Firstly let us calculate the amount of hours you will have to work in a week.
Since you will have to work Mondays through Fridays, hence you will be working 5 days in a week.
Hence in a week you will work 8.5*5= 42.5 hours in a week
Since in 1 hours you are mandated to pick 45 units
Hence in 42.5 hours you will pick 42.5*45= 1912.5 units
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of
carpet needed for the living room is how many times greater than the amount of carpet needed for the
bedroom?
1 1/2
2
3
3 1/2
Answer:
3
Step-by-step explanation:
let's call X the length of the bedroom, Y the wide of the bedroom, A the length of the living room and B the wide of the living room
A living room is two times as long as the bedroom, so:
A = 2X
A living room is one and one-half times as wide as a bedroom, so:
B = 1.5Y
The amount of carpet needed for the living room is A*B and the amount of carpet needed by the bedroom is X*Y
So, AB in terms of XY is:
A*B = (2X)*(1.5Y) = 3(X*Y)
It means that the amount of c arpet needed for the living room is 3 times greater than the amount of carpet needed for the bedroom.
Rewrite the equation in =+AxByC form. Use integers for A, B, and C. =−y6−6+x4
Answer:
6x + y = -18
Step-by-step explanation:
The given equation is,
y - 6 = -6(x + 4)
We have to rewrite this equation in the form of Ax + By = C
Where A, B and C are the integers.
By solving the given equation,
y - 6 = -6x - 24 [Distributive property]
y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]
y = -6x - 18
y + 6x = -6x + 6x - 18
6x + y = -18
Here A = 6, B = 1 and C = -18.
Therefore, 6x + y = -18 will be the equation.
9. A college financial advisor wants to estimate the mean cost of textbooks per quarter for students at the college. For the estimate to be useful, it should have a margin of error of 20 dollars or less. The standard deviation of prices is estimated to be around 100 dollars. How large of a sample size needs to be used to be 95% confident, with the given margin of error?
Answer: 97
Step-by-step explanation:
Formula to compute the required sample size :
[tex]n= (\dfrac{\sigma\times z_{\alpha/2}}{E})^2[/tex]
, where [tex]\sigma[/tex] = standard deviation
E= Margin of error
[tex]z_{\alpha/2}[/tex] = Two tailed z-value.
Here, E= 20
[tex]\sigma[/tex] = 100
For 95% confidence level: [tex]z_{\alpha/2}[/tex] =1.96
Required sample size:
[tex]n=(\dfrac{100\times1.96}{20})^2\\\\=(5\times1.96)^2\\\\=96.04\approx97[/tex]
Hence, the required sample size : 97
Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3. (2 points) Select one: a. x = -4 and x = -9 b. x = 4 and x = -9 c. x = -4 and x = 9 d. x = 4 and x = 9
Answer:
c. x = -4 or x = 9Step-by-step explanation:
[tex]\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}[/tex]
Domain:
[tex]x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3[/tex]
solution:
[tex]\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}[/tex]
use (a - b)(a + b) = a² - b²
[tex]\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}[/tex]
multiply both sides by (x - 3) ≠ 0
[tex]\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}[/tex]
cancel (x - 3)
[tex]\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3[/tex]
subtract [tex]\frac{4(x-3)}{x}[/tex] from both sides
[tex]\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}[/tex]
cross multiply
[tex](4)(x)=(x+3)(-x+12)[/tex]
use FOIL
[tex]4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36[/tex]
subtract 4x from both sides
[tex]0=-x^2+12x-3x+36-4x[/tex]
combine like terms
[tex]0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36[/tex]
change the signs
[tex]x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0[/tex]
The product is 0 if one of the factors is 0. Therefore:
[tex]x-9=0\ \vee\ x+4=0[/tex]
[tex]x-9=0[/tex] add 9 to both sides
[tex]x=9\in D[/tex]
[tex]x+4=0[/tex] subtract 4 from both sides
[tex]x=-4\in D[/tex]
Mia agreed to borrow a 3 year loan with 4 percent interest to buy a motorcycle if Mia will pay a total of $444 in interest how much money did she borrow how much interest would Mia pay if the simple interest rate was 5 percent
Answer:
a) $3700
b) $555
Step-by-step explanation:
The length of the loan is 3 years.
The interest after 3 years is $444.
The rate of the Simple Interest is 4%.
Simple Interest is given as:
I = (P * R * T) / 100
where P = principal (amount borrowed)
R = rate
T = length of years
Therefore:
[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]
P = $3700
She borrowed $3700
b) If the simple interest was 5%, then:
I = (3700 * 5 * 3) / 100 = $555
The interest would be $555.
A drawer contains 3 white shirts, 2 blue shirts, and 5 gray shirts. A shirt is randomly
selected from the drawer and set aside. Then another shirt is randomly selected from the
drawer.
What is the probability that the first shirt is white and the second shirt is gray?
Answer:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Given that
3 white, 2 blue and 5 gray shirts are there.
To find:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?
Solution:
Here, total number of shirts = 3+2+5 = 10
First of all, let us learn about the formula of an event E:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
[tex]P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}[/tex]
[tex]P(First\ White) = \dfrac{3}{10}[/tex]
Now, this shirt is set aside.
So, total number of shirts left are 9 now.
[tex]P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }[/tex]
So, the answer is:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]