Adult men have heights that a normally distributed with a mean of 69.5 inches and a standard deviation of 2.4 inches. Adult women have heights that a normally distributed with a mean of 63.8 inches and a standard deviation of 2.6 inches. Between a man with a height of 74 inches and a women with a height of 70 inches, who is more unusually tall within his or her respective sex ?
Answer:
Step-by-step explanation:
From the information given:
For Adult Men
Mean [tex]\mu[/tex] = 69.5
Standard deviation [tex]\sigma[/tex] = 2.4
observed value X = 74
For Adult Women
Mean [tex]\mu[/tex] = 63.8
Standard deviation [tex]\sigma[/tex] = 2.6
observed value X = 70
Therefore ; the values for their z scores can be obtained in order to determine who is more unusually tall within his or her respective sex
For Adult Men :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]z = \dfrac{74- 69.5}{2.4}[/tex]
[tex]z = \dfrac{4.5}{2.4}[/tex]
z = 1.875
For Adult Women :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]z = \dfrac{70- 63.8}{2.6}[/tex]
[tex]z = \dfrac{6.2}{2.6}[/tex]
z = 2.3846
Thus; we can conclude that , the women is more unusually tall within his or her respective sex
A) The perimeter of a rectangle is the sum of the lengths of its four sides. Write an expression for the perimeter of the rectangle and then evaluate when x=1/2 foot? B) The area of a rectangle is the product of its length and width. Write an expression for the area of the rectangle and then evaluate when x=1/2 feet?
Answer:
Below
Step-by-step explanation:
The length of this triangle is 3x+1 and the width is x.
The perimeter P is:
P= 2(3x+1)+2*x
P= 6x+2+2x
P= 8x+2
Let's evaluate it when x=1/2
●1/2 =0.5
P= 8*0.5+2 =4+2= 6 ft
●●●●●●●●●●●●●●●●●●●●●●●●
The area A is:
A = (3x+1)*x
A= 3x^2 +x
Let's evaluate it when x=0.5 feet
A= 3*0.5^2 +0.5
A= 3*0.25+0.5
A= 0.75 +0.5
A= 1.25 ft^2
Find the surface area of the solid shown or described. If necessary, round to the nearest tenth
7cm
10cm
14 cm
Answer:
616cm²or³
Step-by-step explanation:
SA = 2(lw)+2(lh)+2(hw)
SA=2(10×14) + 2(10×7) + 2(7×14)
SA= 2(140) + 2(70) + 2(98)
SA=280+140+196
SA=616cm²or³
A line passes through the points (6, 10) and (4, -2). What is the equation of the line
Answer:
y = 6x - 26
Step-by-step explanation:
1. find slope: (y₂ - y₁) / (x₂ - x₁)
(-2 - 10) / (4 - 6) = -12 / -2 = 6
basic equation: y = 6x + b
2. plug in (x,y) value using one set of coordinates.
10 = 6(6) + b
10 = 36 + b
b = 10 - 36
b = -26
3. plug b in to find full equation.
y = 6x -26
Answer:
y = -1/6 x + 11
Step-by-step explanation:
In order to write an equation of a line you need slope (m) and y-intercept (b) or where the graph grosses the y- axis. since you are given two points (6, 10) and (4, -2). Slope when given two points is (y - y) / (x - x)
so (-2 - 10) / (6 - 4) = 6 / - 1 =- 6
use the equation y = mx + b and substitute either point (6, 10) or (4, -2) as a replacement for x and y respectively. (I chose (6, 10) because they are positive numbers. Substituting x = 6 and y = 10 and m = -6 into y = mx + b
10 = -6(6) + b
10 = -36 + b
b = 46 (add -36 to both sides)
so our equation: y = -6x + 46 :-)
A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer. It costs $4 to store one can of paint for one year and $500 to set up the plan for production of the primer. Let x be the number of cans of paint produced during each production run, and let y be the number of production runs. Then the setup cost is 500y and the storage cost is 2.c, so the total storage and setup cost is C = 500y +2.c. Furthermore, .cy = 16,000 to account for the annual demand. How many times a year should the company produce this primer in order to minimize the total storage and setup costs?
A. The company should have 6 production runs each year.
B. The company should have 8 production runs each year.
C. The company should have 10 production runs each year.
D. The company should have 11 production runs each year.
Answer:
B. The company should have 8 production runs each year.
Step-by-step explanation:
From the given information:
A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer
It costs $4 to store one can of paint for one year
$500 to set up the plan for production of the primer
Let x be the number of cans of paint produced during each production run
Let y be the number of production runs.
If the total storage and setup cost is C = 500y + 2c
and cy = 16000
Then c = 16000/y
From;
C = 500y + 2c
Replacing c with 16000/y, we have;
C = 500y + 2(16000/y)
C = 500y + 32000/y
in order to minimize the total storage and setup costs [tex]C_{min} = C[/tex]
Therefore [tex]\dfrac{dc}{dy}=0[/tex]
⇒ 500 - 32000/y² =0
y² = 32000/500
y² = 320/5
y² = 64
y = (√64)
y = 8
Therefore; The company should have 8 production runs each year in order to minimize the total storage and setup costs
Solve the proportion below.
X =
A. 24
B. 49
c. 27
D. 6
Answer:
A. 24
Step-by-step explanation:
4/9 = x/54
x= 54*4/9 ===== multiplying both sides by 54
x= 24
Answer is 24, choice A is correct one
Pecans sell for 7.95 per round. How much will 3.2 pounds cost? NEED STEP BY STEP EXPLANATION.
Answer:
$25.44
Step-by-step explanation:
if they sell for 7.95 and you get 3.2 you do 7.95 times 3.2
find the slope for (-4,-2)(-3,-6)
Answer:
The slope is -4.
Step-by-step explanation:
The values -2 and -6 are 4 values apart.
The values -4 and -3 are 1 value apart.
Since the second coordinate is lower than the first one, the slope of this is negative.
4 / 1 = 1
Negating 1 gets us -1.
Hope this helped!
Answer:
[tex] \frac{y}{x} = \frac{ - 4}{1} = - 4[/tex]
Step-by-step explanation:
[tex]x = ( - 3) - ( - 4) = 1[/tex]
[tex]y = ( - 6) - ( - 2) = - 4[/tex]
Each of the following linear equations defines y as a function of x for all integers x from 1 to 100. For which of the following equations is the standard deviation of the y-values corresponding to all the x-values the greatest?
a) y = x/3
b) y = x/2+40
c) y = x
d) y = 2x + 50
e) y = 3x − 20
Answer:
Option E
Step-by-step explanation:
y = x /3
let x = 1, 2, 3
y = 0.333, 0.667, 1
y = x/2 + 40
let x = 1, 2, 3
y = 40.5, 41, 41.5
y = x
let x = 1, 2, 3
y = 1, 2, 3
y = 2x + 50
let x = 1, 2, 3
y = 52, 54, 56
y = 3x - 20
let x = 1, 2, 3
y = -17, -14, -11
The standard deviation is the spread of data, the data that is most spread is option E.
please help me with this problem
Answer:
A
Step-by-step explanation:
In standard form, an ellipse's major axis is indicated by the [tex]a^{2}, b^{2}[/tex] terms like this:
[tex]\frac{{(y-k)}^{2}}{a^{2}}+\frac{(x-h)^{2}}{b^{2}}, a>b[/tex]
[tex]\frac{{(x-h)}^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}, a>b[/tex]
In the top equation, the vertical axis is primary and in the second the horizontal axis is primary. That's a bit more info than the question asked, but I thought it may be helpful to understand the answer.
Now, a co-vertex is the intersection point between an ellipse and its minor axis. On the graph of the ellipse, the [tex]b[/tex] is the distance from the center to where the ellipse intersects its minor axis, so our answer is A.
If a graphical representation would be helpful, I would take a look at the Math Warehouse article on the Equation of an Ellipse in Standard Form.
The graphed line shown below is y = negative 4 x minus 12. On a coordinate plane, a line goes through (negative 3, 0) and (negative 2, negative 4). Which equation, when graphed with the given equation, will form a system that has no solution? y = 4 x + 12 y = negative 4 x y = negative 12 y = negative 4 (x + 3)
Answer:
y = -4x or the second option on edge.
This is because after you form it into the given equation, it equals y = -4x.
In order to clarify, edge also states that's the answer.
Answer:
2nd option
Step-by-step explanation:
If an office is 12 feet by 16 feet with 8 foot ceilings and I have 4 feet by 8 feet paneling sheets for the walls, not the ceiling for 4 walls. How many panels do I need?
Answer:
14 panels
Step-by-step explanation:
Area of four walls is given by 2*(length + width)*height
_______________________________________
Given dimension
Length = 16 feet
width = 12 feet
height = 8 feet
Thus, area of four walls of office = 2(16+12)8= 448
_____________________________________________
dimension of paneling sheets
length = 8 feet
width = 4 feet
area of paneling sheets = 8*4 = 32 sq. feet
Let the number of paneling sheets required by n
thus, total area of n paneling sheets = n*area of paneling sheets = 32n
This, area of paneling sheets (32n) should be same as 448 area of four walls
as given " I have 4 feet by 8 feet paneling sheets for the walls"
thus,
32n = 448
n = 448/32 = 14
Thus, 14 panels are needed.
Example 2: The GPAs of 20 students are listed.
Make a stem-and-leaf plot for this data.
1.8 2.9 0.9 4.0 3.3
2.4 2.3 1.6 1.6 4.0
1.7 0.5 3.6 3.4 1.9
4.0 2.1 1.9 1.1 0.5
How do I make a stem and leaf plot for these numbers?
Answer/Step-by-step Explanation:
To create a stem-and-leaf plot for the GPAs of the 20 students that were listed in the above question, take the following steps:
Step 1: for easy plotting, write down the GPAs in an ordered manner, that is, from the smallest value to the largest.
0.5, 0.5, 0.9, 1.1, 1.6, 1.6, 1.7, 1.8, 1.9, 1.9, 2.1, 2.3, 2.4, 2.9, 3.3, 3.4, 3.6, 4.0, 4.0, 4.0
Step 2: divide each set of data into a stem and a leaf. For example, for a GPA, 0.5, 0 would be the stem, while 5 would be the leaf.
For a GPA listed, 2.9, 2 is the stem, 9 is the leaf. Same applies to all the other GPAs.
Step 3: All stems should be written in ascending order, vertically, from the smallest to the largest. From the listed GPAs, you would observe that the highest stem value would be 4, while the lowest would be 0.
Therefore, write down your stems vertically, in ascending order as shown below:
0 |
1 |
2 |
3 |
4 |
Step 4: All leaves should be written also in ascending order to their corresponding stem, from the smallest to the largest, as shown below:
Stem | Leaf
0 | 5 5 9
1 | 1 6 6 7 8 9 9
2 | 1 3 4 9
3 | 3 4 6
4 | 0 0 0
Thus,
0 | 5 5 9 represents => 0.5, 0.5, 0.9
*See attachment below for the stem-and-leaf plot.
when a stone falls freely, the time taken to hit the ground varies as the square root of the distance fallen. If it takes four seconds th fall 78.4m, find how long would it takefor a stone to fall 500m
Answer:
The stone would take approximately 10.107 seconds to fall 500 meters.
Step-by-step explanation:
According to the statement of the problem, the following relationship of direct proportionality is built:
[tex]t \propto y^{1/2}[/tex]
[tex]t = k\cdot t^{1/2}[/tex]
Where:
[tex]t[/tex] - Time spent by the stone, measured in seconds.
[tex]y[/tex] - Height change experimented by the stone, measured in meters.
[tex]k[/tex] - Proportionality constant, measured in [tex]\frac{s}{m^{1/2}}[/tex].
First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:
[tex]k = \frac{t}{y^{1/2}}[/tex]
If [tex]t = 4\,s[/tex] and [tex]y=78.4\,m[/tex], then:
[tex]k = \frac{4\,s}{(78.4\,m)^{1/2}}[/tex]
[tex]k \approx 0.452\,\frac{s}{m^{1/2}}[/tex]
Then, the expression is [tex]t = 0.452\cdot y^{1/2}[/tex]. Finally, if [tex]y = 500\,m[/tex], then the time is:
[tex]t = 0.452\cdot (500\,m)^{1/2}[/tex]
[tex]t \approx 10.107\,s[/tex]
The stone would take approximately 10.107 seconds to fall 500 meters.
Ernie deposits $5,500 into a pension fund. The fund pays a simple interest rate of 6% per year. What will the balance be after one year?
Answer:
Balance after one year will be $5830.
a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. The probability is . (Round to three decimal places as needed.) b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters. The probability is . (Round to three decimal places as needed.) c. What do the preceding results suggest?
Answer:
Hello your questions is incomplete attached below is the missing part of the question
answer : A ) 0.647 , (B) 0.353, (C) students are more likely to spend the money than to have kept it
Step-by-step explanation:
from the attached table below
Given data :
Total number of students = Number of students who spent money + number of students who kept money
Total number of students = (33+13 ) + (18 + 27 ) = 91
p(Number of students given four quarters) = (33 +18 ) / 91 = 51/91
p( number of students who spent money ) = ( 33 +13 ) / 91 = 46/91
p( number of students who saved money ) = (18 +27 ) / 91 = 45 /91
p( number of students who spent money and given four quarters ) = 33/91
p( number of students who saved money and given four quarters ) = 18/91
A) The probability of randomly selecting a student who spent the money and also given four quarters
= p ( 33/91 | 51/91 )
= 33/91 * 91/51
= 33/51 = 0.647
B ) The probability of randomly selecting a student who kept the money and given that the student was given four quarters
= p ( 18/91 | 51/91 )
= 18/91 * 91/51
= 18 /51 = 0.353
C) students are more likely to spend the money than to have kept it
I NEED HELP ASAP PLEASE 20 POINTS
Answer:
B.
Step-by-step explanation:
[tex]\sqrt[4]{2x^2} * \sqrt[4]{2x^3}[/tex]
= [tex]2^{1/4}x^{2/4} * 2^{1/4}x^{3/4}[/tex]
= B. [tex]2^{2/4}x^{5/4}[/tex].
Hope this helps!
The slope of the line below is 5/7 Write a point-slope equation of the line
using the coordinates of the labeled point.
O A. y+2 --$(x+6)
O B. y-6--(x-2)
O C. y+6 -- (x + 2)
O D, y-2 - (x - 6)
Answer:
The option are incorrect because as its slope is only 5/7 the answer will never come like that.
Step-by-step explanation:
Here,
Given,
The dlope of a line is 5/7 and (6,2) is a point.
By one point formulae,
(y-y1)= m (x-x1).
or, (y-2)=5/7(x-1)
or, y = 5/7x -5/7+2
taking lcm of -5/7 and 2. we get,
or, y= 5/7 x -5+7/7
Therefore, the equation is y = 5/7 x -2/7.
Hope it helps..
Solve the system by substitution. x−5y=13 4x−3y=1 Enter your answer as an ordered pair (x,y).
Answer:
(-2,-3)
Step-by-step explanation:
Well in the system,
x−5y=13
4x−3y=1
We need to find x or y in either equation.
Let's do x - 5y = 13 for x.
+5y to both sides
x = 5y + 13
Now we substitute 5y + 13 for y in 4x - 3y = 1.
4(5y + 13) - 3y = 1
20y + 52 - 3y = 1
17y + 52 = 1
-52 to both sides
17y = -51
Divide all by 17
y = -3
Now we can substitute -3 for y in 4x - 3y = 1.
4x - 3(-3) = 1
4x + 9 = 1
-9 to both sides
4x = -8
Divide 4 to both sides
x = -2
Thus,
the solution is (-2,-3).
Hope this helps :)
Answer:
( - 2 , - 3 )Step-by-step explanation:
x - 5y = 13
4x - 3y = 1
Solve the equation for x
[tex]x - 5y = 13[/tex]
Move '5y' to R.H.S and change it's sign
[tex]x = 13 + 5y[/tex]
Substitute the given value of X into the equation
4x - 3y = 1
[tex]4(13 + 5y) - 3y = 1[/tex]
Solve the equation for y
distribute 4 through the parentheses
[tex]52 + 20y - 3y = 1[/tex]
Collect like terms
[tex]52 + 17y = 1[/tex]
Move constant to R.H.S and change it's sign
[tex]17y = 1 - 52[/tex]
Calculate
[tex]17y = - 51[/tex]
Divide both sides of the equation by 17
[tex] \frac{17y}{17} = \frac{ - 51}{17} [/tex]
Calculate
[tex]y = - 3[/tex]
Now, substitute the given value of y into the equation
x = 13 + 5y
[tex]x = 13 + 5 \times ( - 3)[/tex]
Solve the equation for x
Multiply the numbers
[tex] = 13 - 15[/tex]
Calculate the difference
[tex] = - 2[/tex]
The possible solution of the system is the ordered pair
( x , y )
( x , y ) = ( - 2 , - 3 )
-----------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex] - 2 - 5 \times ( - 3) = 15[/tex]
[tex]4 \times ( - 2) - 3 \times ( - 3) = 1[/tex]
Simplify the equalities
[tex]13 = 13[/tex]
[tex]1 = 1[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( - 2 , - 3 )Hope this helps..
Best regards!!
Given: angle 1 congruent angle2 prove: p||q
Please hurry
Answer:
converse of alternate exterior angle theorem
Step-by-step explanation:
um im not sure if i should explain the full proof but
hhhelpp meeee!! I WILL GIVE BRAINLIEST
Answer:
We're solving for CD. If we look at ΔABD we notice that it's a 30-60-90 triangle which has a side length ratio of 1:√3:2 and in this case the 1 is 300 so side BD = 300√3. Similarly, ΔABC is also a 30-60-90 triangle but this time the √3 is 300 so side BC = 100√3. We know that CD = BD - BC using PWP so the answer is 300√3 - 100√3 = 200√3 = 346.4 feet.
I BEG OF YOU HELPPPP Twice last month, Judy Carter rented a car in Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 440 miles, and the rental cost her $286. On her second business trip she drove 190 miles in 3 days, and paid $165.50 for the rental. Find the daily fee and the mileage charge.
Answer:
the daily fee =33 dollars
and the mileage charge.=0.35
Step-by-step explanation:
let d: be daily fee and m for mileage
cost of rental =(d*number of days)+ (m*number of mileage)
her first trip: 4d+440m=286
her second trip: 3d+190m=165.5
solve by addition and elimination
4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286
3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)
12d+1320m=858
12d+760m=662
subtract two equation to eliminate d
12d+1320m-12d-760m=858-662
560m=196
m=7/20=0.35 for on mileage
d: 4d+440m=286
4d=286-440(0.35)
d=(286-154)/4 33 dollars
3+x=8 What would like match this answer
Answer:
x = 5
Step-by-step explanation:
x = 8 - 3
Thus, x = 5
Describe how to simplify the expression
3^-6
3^-4
Answer:
For 3^-6 = 1/3^6 = 726 and for 3^-4 = 1/3^4 = 81
Step-by-step explanation:
ARE THE NUMBERS SEPARATED OR THEY ARE TO BE JOIN TOGETHER,IF THERE ARE SEPARATED THE SOLUTION IS GOING TO BE...
3^-6
using law of indices x^-a = 1/x^a
So 3^-6 = 1/3^6
Now find the power of 3^6
which is the same as 3×3×3×3×3×3 = 729
therefore 1/3^6 = 729
For 3^-4
using the above method
3^-4 is same as 1/3^4
which is equal to
finding the nominator
3×3×3×3 = 81
so the answer is 81
taking a test- Which expression represents the surface area of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. S A = pi r l + pi r squared (pi) (6) (10) + (pi) (6 squared) (pi) (8) (10) + (pi) (8 squared) (pi) (12) (10) + (pi) (12 squared) (pi) (10) (12) + (pi) (10 squared)
Answer:
[tex]SA = \pi (6) * 10+\pi ( 6)^2[/tex]
Step-by-step explanation:
The surface area of a cone is given by
[tex]SA = \pi rl +\pi r^2[/tex]
r is the radius and l is the slant height.
The diameter is 12 inches, the radius is 12/2 = 6 inches.
The slant height is 10 inches.
[tex]SA = \pi (6) * 10+\pi ( 6)^2[/tex]
Answer:
SA of cone = [tex](\pi )(6)(8) + (\pi )(6)^2[/tex]
Step-by-step explanation:
Surface Area of cone = [tex]\pi rh+\pi r^2[/tex]
Where r = 6 inches (Diameter = 12 inches) , h = 8 inches (We'll not consider the slant height)
SA of cone = [tex](\pi )(6)(8) + (\pi )(6)^2[/tex]
Verify the Cauchy-Schwarz Inequality and the triangle inequality for the given vectors and inner product.
p(x)=5x , q(x)= -2x^2+1, (p,q)= aobo+ a1b1+ a2b2
Required:
a. Compute (p,q)
b. Compute ||p|| and ||q||
Answer:
To verify the Cauchy-Bunyakovsky-Schwarz Inequality, (p,q) must be less than (or equal to) ||p|| • ||q||
(1,1,1) is not equal to (-10,5)
Step-by-step explanation:
a°b° + a^1b^1 + a^2b^2 < 5x (-2x^2 + 1)
Any algebra raised to the power of zero is equal to 1.
a°b° = 1 × 1 = 1
1 + ab + a^2b^2 < -10x^3 + 5x
The vectors:
(1,1,1) < (-10,5)
This verifies the Cauchy-Schwarz Inequality
Triangle Inequality states that for any triangle, the sum of the lengths of two sides must be greater than or equal to the length of the third side.
PLEASE HELP HOW DO I TRANSLATE IT TO A PROPORTION!!
Answer:
See below.
Step-by-step explanation:
A proportion is setting two ratios equal to each other.
Look at the info you are given for price in $ and area in sq ft:
$385 for 70 sq ft
That allows you to write a ratio. The ratio of dollars to square feet is
385/70 (notice it's dollars divided by sq ft)
Now you look at the part of the problem that has an unknown, and you set up the same type of ratio (dollars to sq ft) using x for the unknown.
x dollars to 200 sq ft
The ratio is
x/200 (notice that, again, it's dollars divided by sq ft)
In both cases the ratios are dollars to sq ft.
To set up a proportion, you just set the ratios equal to each other.
385/70 = x/200
Now we solve the proportion. We can cross multiply.
385/70 = x/200
70x = 385 * 200
70x = 77,000
x = 1100
They would charge $1100 to install 200 sq ft of tile.
The unit price is obtained by dividing a cost by the corresponding area in sq ft. you can use either ratio.
unit price = ($385)/(70 sq ft) = $5.5/sq ft
($1100/200 sq ft also works since it is also equal to $5.5/sq ft)
Bill shops in a candy store where chocolate bars are $1 and lollipops are $0.50 He can spend at most $5 and he wants to buy at least 3 more lollipops than chocolate bars. Which of the following graphs represent the possible candy combinations?
Answer:
Step-by-step explanation
Write an equation for the amount of money, m, that will be collected if C- chocolate bars are sold and L- lollipops. Which is the independent variable and which is the dependent variable?
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]
Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 kmh slower than the other. If the two buses are 1356 kilometers apart after 6 hours, what is the rate of each bus?
Answer:
106 km / hour
Step-by-step explanation:
Givens
Total time: 6 hours
Total distance: 1356 km
First bus rate: r
Second bus rate: r - 14
Formula
d = r * t
Solution
r*6 + (r - 14)*6 = 1356 Remove the brackets
6*r + 6*r - 84 = 1356 Add like terms
12r - 84 = 1356 Add 84 to both sides
12r + 84 - 84 = 1356-84 Combine
12r = 1272 Divide by 12
r = 1272/12
r = 106 km/hr