) Professor Jin wants to travel from place A to place B without a map. There are four ways lead away from place A. If road I is selected, the probability of arriving place B is 1/8; if road II is selected, the probability of arriving place B is 1/6; if road III is selected, the probability of arriving place B is 1/4; and if road IV is selected,the probability of arriving place B is 9/10. (a) What is the probability that professor will arrive at place B
Complete Question
Professor Jin wants to travel from place A to place B without a map. There are four ways lead away from place A. If road I is selected, the probability of arriving place B is 1/8; if road II is selected, the probability of arriving place B is 1/6; if road III is selected, the probability of arriving place B is 1/4; and if road IV is selected,the probability of arriving place B is 9/10.
(a) What is the probability that professor will arrive at place B?
(b) If Professor Jin arrives at place B, what is the probability that she chooses road IV?
Answer:
a
[tex]P(B) = 0.36[/tex]
b
[tex]P(4 /B) = 0.62[/tex]
Step-by-step explanation:
From the question we are told that
The number of ways from A to B is n = 4
The probability if road 1 is selected is [tex]P(1) = \frac{1}{8}[/tex]
The probability if road 2 is selected is [tex]P(2) = \frac{1}{6}[/tex]
The probability if road 3 is selected is [tex]P(3) = \frac{1}{4}[/tex]
he probability if road 4 is selected is [tex]P(4) = \frac{9}{10}[/tex]
The probability that professor will arrive at place B is mathematically represented as
[tex]P(B) = \frac{1}{n} * P(1) + \frac{1}{n} * P(2) + \frac{1}{n} * P(3)+ \frac{1}{n} * P(4)[/tex]
[tex]P(B) = \frac{1}{4} * \frac{1}{8} + \frac{1}{4} * \frac{1}{6} + \frac{1}{4} * \frac{1}{4} + \frac{1}{4} * \frac{9}{10}[/tex]
[tex]P(B) = 0.36[/tex]
If Professor Jin arrives at place B, what is the probability that she chooses road IV is mathematically represented as
[tex]P(4 /B) = \frac{ \frac{1}{n} * P(4)}{P(B)}[/tex]
=> [tex]P(4 /B) = \frac{ \frac{1}{4} * \frac{9}{10} }{0.36}[/tex]
=> [tex]P(4 /B) = 0.62[/tex]
Use the information to answer the question.
A store sells paint sets. Each paint set costs the same amount. During a sale, the store reduces the price of each paint set by $1.50. Logan spends
$13.47 on 3 paint sets at the sale price.
What was the price of 1 paint set before the sale? Enter the answer in the box.
Translate this phrase into an algebraic expression.
58 decreased by twice Chrissy's score
Use the variable c to represent Chrissy's score.
Answer:
2C - 58
Step-by-step explanation:
Chrissy = C
=> 2C - 58
I wrote 2C - 58 because 58 is decreased from 2 times C
=> 2 times C = 2C
=> 58 decreased = -58
=> 2C - 58
The sum of two numbers is twenty-five. One number is five less than the other.
Answer: x=15, y=10
*Note: x and y are only variables used to solve this problem, but know that the two numbers are 15 and 10.
Step-by-step explanation:
For this problem, we can use system of equations. Let's use x for one number and y for the other.
First Equation:
x+y=25
We get this equation because it states that the sum of the two numbers is 25.
Second Equation:
y=x-5
We get this equation because it says one number (y) is 5 less than the other (x).
Since we have two equations, we can use substitution method to solve.
[tex]x+(x-5)=25[/tex] [distribute 1 to (x-5)]
[tex]x+x-5=25[/tex] [combine like terms]
[tex]2x-5=25[/tex] [add both sides by 5]
[tex]2x=30[/tex] [divide both sides by 2]
[tex]x=15[/tex]
Now that we have x, we can plug it into any of the equations to find y.
[tex]x+y=25[/tex] [plug in x=15]
[tex]15+y=25[/tex] [subtract both sides by 15]
[tex]y=10[/tex]
Finally, we have our answer, x=15 and y=10.
Answer:25,-5
Step-by-step explanation:
b) The following table provides information about production at the XYZ-TV Company. Number of Workers TVs Produced 0 0 1 35 2 68 3 99 4 128 5 155 How many workers will the XYZ-TV Company hire if the going wage for TV production workers is $16,000? Show your calculation in detail.
Answer:
5
Step-by-step explanation:
Given the following :
Number of workers - - TVs produced
0 - - - - - - - - - - - - - - - - - 0
1 - - - - - - - - - - - - - - - - - - 35
2 - - - - - - - - - - - - - - - - - 68
3 - - - - - - - - - - - - - - - - - - 99
4 - - - - - - - - - - - - - - - - - - 128
5 - - - - - - - - - - - - - - - - - - 155
We need to calculate the marginal product :
Workers - - - marginal product - - - value of m/p
0 - - - - - - - - - - - ____ - - - - - - - - - - - - - - __
1 - - - - - - - - - - - 35 (35 - 0) - - - - - - 35000
2 - - - - - - - - - - - - 33 (68 - 35) - - - - 33000
3 - - - - - - - - - - - - 31 (99 - 68) - - - - - 31000
4 - - - - - - - - - - - - 29 (128 - 99) - - - - - 29000
5 - - - - - - - - - - - - 27 (155 - 128) - - - 27000
The marginal product shows the change in output due to one additional unit of a certain input of production, in this case, number of workers. If the going wage of workers is $16,000, the company can afford to hire up to 5 workers and still make profit.
The data below are the temperatures on randomly chosen days during the summer and the number of employee absences at a local company on those days. Construct a 95% prediction interval for y, the number of days absent,
given x = 95 degrees and y= 0.449x - 30.27
Temperature, x 72 85 91 90 88 98 75 100 80
Number of absences, y 3 7 10 10 8 15 4 15 5
Answer:
The critical region is t ≥ t(0.025, 7) = 2.365
Since the calculated value of t= 18.50249 falls in the critical region we reject the null hypothesis and conclude that there is sufficient reason to support the claim of a linear relationship between the two variables.
Step-by-step explanation:
We set up our hypotheses as
H0: β= 0 the two variable X and Y are not related
Ha: β ≠ 0. the two variables X and Y are related.
The significance level is set at α =0.05
The test statistic if, H0 is true, is t= b/s_b
Where Sb =S_yx/√(∑(X-X`)^2 )
Syx = √((∑(Y-Y`)^2 )/(n-2))
In the given question we have the estimated regression line as y= 0.449x - 30.27
X Y X2 Y2 XY
72 3 5184 9 216
85 7 7225 49 595
91 10 8281 100 910
90 10 8100 100 900
88 8 7744 64 704
98 15 9604 225 1470
75 4 5625 16 300
100 15 10000 225 1500
80 5 6400 25 400
∑779 77 68163 813 6995
Now finding the variances
∑(Y-Y`)^2 = ∑〖Y^2- a〗 ∑Y- b∑XY
= 813 – (- 30.27)77 - 0.449(6995)
= 813+2330.79 – 3140.755
= 3.035
∑(X-X`)^2 = ∑X^2 – (∑〖X)〗^2 /n
= 68163 – (779)2/9
= 736.22
Syx = √((∑(Y-Y`)^2 )/(n-2)) = √(3.035/7) = 0.65846 and
Sb =S_yx/√(∑(X-X`)^2 ) = (0.65846 )/27.13337 = 0.024267
t= b/s_b = 0.449/ 0.024267 = 18.50249
The critical region is t ≥ t(0.025, 7) = 2.365
Since the calculated value of t= 18.50249 falls in the critical region we reject the null hypothesis and conclude that there is sufficient reason to support the claim of a linear relationship between the two variables.
Solve the inequality. Enter any fractions as reduced improper fractions. 4x ≤ -2/5(6x + 6) The solution is _____
Answer:
x≤ -3/8
Step-by-step explanation:
[tex]4x\le \:-\frac{2}{5}\left(6x+6\right)\\[/tex]
Expand ;
[tex]\mathrm{Expand\:}-\frac{2}{5}\left(6x+6\right):\quad -\frac{12}{5}x-\frac{12}{5}[/tex]
[tex]4x\le \:-\frac{12}{5}x-\frac{12}{5}\\\\\mathrm{Add\:}\frac{12}{5}x\mathrm{\:to\:both\:sides}\\\\4x+\frac{12}{5}x\le \:-\frac{12}{5}x-\frac{12}{5}+\frac{12}{5}x[/tex]
Simplify
[tex]\frac{32}{5}x\le \:-\frac{12}{5}\\\\Multiply \:both\:sides\:by\:5\\5\times\frac{32}{5}x\le \:5\left(-\frac{12}{5}\right)\\\\Simplify\\32x\le \:-12\\\\Divide \:both\:sides\:by\:32\\\frac{32x}{32}\le \frac{-12}{32}\\\\Simplify\\x\le \:-\frac{3}{8}[/tex]
help please and no troll answers for i will report it i also need the explanation to how u get to the answer please, thank you !!
Answer:
the marked choice is correct
Step-by-step explanation:
It usually works well to follow directions: use technology. The attachment shows the use of the technology I like for short regression problems. For longer problems, a spreadsheet program is a good choice.
_____
In this problem, it is easy to eliminate the nonsensical answers, so no real use of technology is necessary.
First of all, the y-value for x=0 needs to be near 48, eliminating the last two choices.
Second, the minimum of the function corresponds to a positive x-value, so the coefficient of the x-term must have opposite sign from the coefficient of the x^2 term. This eliminates the second choice, leaving the marked choice as the only viable one.
Solve the equation: 61 – p = 14
Answer:
p= 47
Step-by-step explanation:
61 - p = 14
p = 61 - 14
p = 47.
What is the following lines is not parelle of y=4x+7
Answer: 4y - x = 8
y = 4x + 7
This equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope of this line is 4. Parallel lines have the same slope, thus a line not parallel to this line will not have a slope of 4. Let's check which of these lines does not have a slope of 4.
y - 4x = 9
y = 9 + 4x (add 4x to both sides)
y = 4x + 9 (switch the constant and x-term)
This line has a slope of 4.
4x - y = 8
-y = 8 - 4x (subtract 4x from both sides)
y = -8 + 4x (divide both sides by -1)
y = 4x - 8 (switch the constant and x-term)
This line has a slope of 4.
4y - x = 8
4y = 8 + x (add x to both sides)
y = 8/4 + x/4 (divide both sides by 4)
y = x/4 + 2 (simplify and switch constant and x-term)
This line has a slope of 1/4. It is thus not parallel to the line y = 4x + 7.
Answer: 4y - x = 8
Hoped I helped
You are selling cakes at a bake sale for $6.75 each. You spend $86 to buy ingredients and supplies.
There is no charge to have a table at the sale. Write an expression that shows your profit from
selling n cakes. Then find the profit if you sell 25 cakes.
Answer:
Profit from selling n cakes = $6.75n - $86
Profit from selling 25 cakes = $82.75
Step-by-step explanation:
You are selling cakes at a bake sale for $6.75 each.
You spend $86 to buy ingredients and supplies.
Profit from selling n cakes is;
Profit = Selling price - cost price
Profit = $6.75n - $86
Profit for selling 25 cakes is;
Profit = $6.75(25) - $86 = $82.75
Is A and V a collinear?
Yes
No
Answer:
yes
Step-by-step explanation:
yes because they are in the same line
3. If mZEFH = (5x + 1), mZHFG = 62°, and
mZEFG = (18x + 11), find each measure.
Answer/Step-by-step explanation:
Given:
m<EFH = (5x + 1)°
m<HFG = 62°
m<EFG = (18x + 11)°
Required:
1. Value of x
2. m<EFH
3. m<EFG
SOLUTION:
1. Value of x
m<EFH + m<HFG = m<EFG (angle addition postulate)
(5x + 1) + 62 = (18x + 11)
Solve for x using this equation
5x + 1 + 62 = 18x + 11
5x + 63 = 18x + 11
Subtract 18x from both sides
5x + 63 - 18x = 18x + 11 - 18x
-13x + 63 = 11
Subtract 63 from both sides
-13x + 63 - 63 = 11 - 63
-13x = -52
Divide both sides by -13
-13x/-13 = -52/-13
x = 4
2. m<EFH = 5x + 1
Plug in the value of x
m<EFH = 5(4) + 1 = 20 + 1 = 21°
3. m<EFG = 18x + 11
m<EFG = 18(4) + 11 = 72 + 11 = 83°
What is the median of these data: 67,98,78,75,83,44,98
Answer:
Median is 78
Step-by-step explanation:
The median is the number where 50% of the other numbers are lower and 50% of the other numbers are higher, the middle, so in this case 78 is the middle number.
The median of the data sets 67, 98, 78, 75, 83, 44, and 98 will be 78.
What is a median?The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.
The data is given below.
67, 98, 78, 75, 83, 44, 98
Arrange the data set in ascending order, then the data set is given as,
44, 67, 75, 78, 83, 98, 98
The number of terms in the data set will be 7.
Then the median of the data set will be 78.
More about the median link is given below.
https://brainly.com/question/300591
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How many 4-letter permutations can be made from the letters in the word “MATH”?
Answer:
There are 24 different ways using the letters from "math" can be rearranged.
Hopefully this helps! :)
Using the information regarding the proportion of work time linguists study a new language, choose the correct conclusion for this hypothesis test. H0:p=0.10 ; Ha:p>0.10 The p-value for this hypothesis test is 0.09. The level of significance is α=0.025 Select the correct answer below: A) There is sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.
B) There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.
C) There is sufficient evidence to conclude the proportion of work time linguists study a new language is more than 90%.
D) There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 90%.
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The null hypothesis is [tex]H_o : p = 0.10[/tex]
The alternative hypothesis is [tex]H_a : p > 0.10[/tex]
The p-value is [tex]p-value = 0.09[/tex]
The level of significance is [tex]\alpha = 0.025[/tex]
From the given values [tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis
So there is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.
The type of light waves that living things give off naturally is called O gamma radiation. infrared light. O visible light. O radio waves.
Answer:
Infrared light
Step-by-step explanation:
Infrared cameras capture heat signals from living or warm objects. Body heat is given off as infrared energy; our natural eyes can't see it.
Answer:
Infra-red Light
Step-by-step explanation:
3/5 is what percent less than 5/3?
v = s^2 + 1/2sh ; solve for h
please provide answer & clear explanation
Answer:
h = 2 (v − s²) / s
Step-by-step explanation:
v = s² + ½sh
Subtract s² from both sides.
v − s² = ½sh
Multiply both sides by 2.
2 (v − s²) = sh
Divide both sides by s.
2 (v − s²) / s = h
BD bisects ∠ABC. Find m∠ABD and m∠CBD.
Answer:
angle ABD=1/2 angle ABC ,Angle CBD =1/2 angleCBD
Step-by-step explanation:
The measure of angles ∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.
We have,
BD bisects the angle ABC makes two equal halves angle.
So, < ABD= < CBD.
and ∠ABD= (8x + 35)°
∠CBD= (11x + 23)°
Substituting the values of the angles
(8x + 35)° = (11x + 23)°
35-23 = 11x- 8x
3x= 12
x= 4.
Putting x=4 in (i) we have,
∠ABD= 8(4) + 35
∠ABD= 67°
As ∠ABD = ∠CBD,
∠CBD= 67°
Now, ∠ABC= ∠ABD + ∠CBD
∠ABC= 67° + 67°
∠ABC= 134°.
Hence, the measure of m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.
Learn more about Angular bisector here:
https://brainly.com/question/12896755
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Is this the correct answer for a statistical question?
Answer:
yes it think
Step-by-step explanation:
You are correct. A statistical question is one where you apply things like random sampling and averages to answer questions such as choice B. With that many people, there's variability in the height so there isn't one set height. So instead we have an average height.
The other questions are simple straightforward answers that don't require statistics. There isn't any variability in the dataset for these types of questions.
Kelsey is going to graph the ordered pairs that are represented by this table on a coordinate plane. x –6 –4 3 5 y –4 –6 –6 0 How many points should appear in Kelsey’s graph? 3 4 6 7
Answer:
The answer is B, don't listen to the dude that said is A... A is wrong
Step-by-step explanation:
De nada :)
There are 4 coordinates which means we can make 4 points on the graph.
4 points is the correct answer.
Given,
Kelsey is going to graph the ordered pairs that are represented by this table on a coordinate plane.
______________
|x| – 6 | –4 | 3 | 5|
|y| –4 | –6 | –6 | 0|
We need to find how many points should appear in Kelsey’s graph.
What are coordinates in a coordinate plane?Coordinates are the points in a given plane.
The plane can be a two-dimensional plane or a three-dimensional plane.
In a two-dimensional plane the coordinates are represented as:
(x, y).
In a three-dimensional plane the coordinates are represented as:
(x, y, z).
Find the coordinates from the given table.
We have,
There are four x values and four y values.
So,
(x, y) = { (-6, -4), (-4, -6), (3, -6), (5, 0) }
We see that we can make 4 coordinates in the coordinate plane.
Thus there are 4 coordinates which means we can make 4 points on the graph.
Learn more about matching the coordinates with the points on the coordinate plane here:
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I need the slope-intercept form equation for the line shown in the graph
Answer: y=-8/5x+2
Step-by-step explanation:
The equation for slope-intercept form is y=mx+b. We know that m is the slope and b is the y-intercept. We can determine that b=2 because the y-intercept passes through the y-axis. This line passes through the y-axis at y=2. Now, all we have to do is find the slope. We can do that by using any two points on the graph. Let's use (-5,10) and (5,-6). The formula for slope is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
[tex]m=\frac{-6-10}{5-(-5)} =\frac{-16}{10} =-\frac{8}{5}[/tex]
With our slope, we can piece together the slope-intercept form equation.
y=-8/5x+2
Central High wants to estimate the number of seniors who plan to go to a 4-year college. Answer the following.
Answer:
plz ask question correctly
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU:)
Answer:
10 c
Step-by-step explanation:
4 c = 2 qt
8c + 2c = 10c
Solve the following for y: 4x + 2y = −2 (5 points)
Answer:
y= -1-2x
Step-by-step explanation:
[tex]4x + 2y = −2[/tex]
Move 4x to the right and change it's sign
[tex]2y = - 2 - 4x[/tex]
Divide through by 2
[tex] \frac{2y}{2} = \frac{ - 2}{2} - \frac{4x}{2} [/tex]
Simplify
[tex]y = - 1 - 2x[/tex]
A car traveled at a constant speed for 4 hours and covered 144.6 miles. It used 12 gallons of gas to travel this distance. How far did the car go in 1 hour? How far did the car travel on 1 gallon of gas? The car traveled miles in 1 hour. The car traveled miles on 1 gallon of gas.
Answer:
36.15 miles, 12.05 miles on one gallon
Step-by-step explanation:
4hours=144.6 miles
1 hour= x
Therefore it traveled 36.15 miles per hour.
12 gallon = 144.6 miles.
1 gallon = x
12.05 miles on one gallon
Limit (sin4x-4sinx)/x^3 when x close to zero
[tex]\Large \boxed{\sf \bf \ \ \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}=-10 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
Using Maclaurin series expansion, we can find an equivalent of sin(x) in the neighbourhood of 0.
[tex]sin(x) \sim \left(x-\dfrac{x^3}{3!}\right)\\\\\text{So, in the neighbourhood of 0}\\\\\begin{aligned}(sin(4x)-4sin(x)) &\sim \left( 4x-\dfrac{(4x)^3}{3!}-4x+\dfrac{4x^3}{3!}\right)\\\\&\sim \left(\dfrac{x^3*4*(1-4^2)}{3*2}\right)\\\\&\sim \left(\dfrac{x^3*2*(-15)}{3}\right)\\\\&\sim \left(x^3*2*(-5)\right)\\\\&\sim \left(x^3*(-10)\right)\\\end{aligned}[/tex]
Then,
[tex]\displaystyle \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}\\\\= \lim_{x\rightarrow0} \ {\dfrac{-10*x^3}{x^3}}\\\\=-10[/tex]
Thank you
Answer:
-10
Step-by-step explanation:
L' Hopital's rule can be used to solve it.
We search for lim (f(x)/g(x))
this is the same as lim (f' (x)/g' (x))
this is the same as lim f'' (x)/g'' (x)
so here we have f(x) =sin(4x)-4sin(x)
g(x)=x^3
g'' (x)= 6x
f'' (x)=-16sin(4x)+4sin(x)
so lim f'' (x) / g ''(x) = -16/6 lim sin(4x)/x + 4/6 lim (sin(x)/x)
= -16*4/6+4/6
=(-64+4)/6=-60/6=-10
A whale that is 460 feet below sea level rises up and breaches out of water to a height of 27 feet above sea level. What is the vertical distance the whale travels.
Answer:
487ftStep-by-step explanation:
Let the initial point of of the sea level be 0. If the whale was initially 460 feet below sea level, then its distance from the surface of sea level to the 460ft below the sea level will be 460 - 0 = 460ft.
Also, if the whale rises up and breaches out of water to a height of 27 feet above sea level, then its distance from the surface of sea level to the 27ft above the sea level will be 0 - 27 = 27ft.
The vertical distance that the whale travels = distance from the sea level to 460ft below the sea level + distance from the sea level to 27ft above the sea level
The vertical distance that the whale travels = 460ft + 27ft
The vertical distance that the whale travels = 487ft
(20a - 1) ÷ b when a= 2 and b= 13
Answer:
3
Step-by-step explanation:
(20a - 1) ÷ b
a = 2
b = 13
(20(2) - 1) ÷ 13
(40-1)÷13
39÷ 13
= 3
answer: 32a^{13}b
your welcome