Randy is walking home from school. According to the diagram above, what is his total distance from school to home? Show your work and include units. If he had a jet pack, would you use distance or displacement? Why?
Answers
Answer:
First, when he walks, we can see in the image that between the school and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.
Then he needs to walk 2km.
Now if he has a jet-pack, he can ignore the buildings and just take the shorter path, here we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.
One of the catheti is the vertical distance (two blocks of 0.5km, so this catheti has a length of 2*0.5km = 1km), and the other one is the horizontal distance, also 1km.
The actual distance of this path is given by the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse, then:
H^2 = 1km^2 + 1km^2
H = (√2)km = 1.41km.
Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, in this case the distance and the displacement would be the same.
This is because the definitions of distance and displacement are:
Distance: "how much ground an object has covered"
Displacement: "Difference between the final position and the initial position"
When he walks, the distance is 2km and the displacement is 1.41km , but when he uses the jet pack, the distance is equal to the displacement, both are 1.41km.
Answer and Step-by-step explanation:
The first thing is we can see in the image, when he walks, that between the house and his school he has to walk four times a distance of 0.5 km. The result of this is a total of 4¨*0.5 km = 2 km. The second thing is that he must walk 2 kilometers. On the other hand, if he has a jetpack, he can simply take the shorter path by ignoring all the buildings. This idea is where we can draw a triangular rectangle on the map in a way so that the hypotenuse of the triangle is the distance between the school and the home. As for the Catheti, it is a vertical distance which in this case is two blocks of 0.5 km. The result is that these catheti have a length of 2*0.5 km = 1 km. The other is the distance of the horizontal line, which is 1 km. The absolute distance of this path is given by Pythagorean's theorem, which is A^2 + B^2 = H^2. Here, A and B are the cathetus, and H is the hypotenuse, then, H^2 = 1 km^2 + 1 km^2. As well, H = (√2)km = 1.41 km. Currently, in the situation where he has a jetpack, he can literally fly to the school utilizing this hypotenuse line for the path he would need to follow. For this specific situation, the displacement, and the distance would be the exact same. The reason for this is that the definitions of displacement and distance are displacement is the difference between the final position and the initial position and distance is how much area an item has covered. Also, when he walks, the distance is 2 km and the displacement is 1.41 km. Also, when he utilizes the jet pack, the distance is equal to the displacement. Both of these are 1.41 km.
Related Questions
Actual time in seconds recorded when statistics students participated in an experiment t test their ability to determine when one minute 60 seconds has passed are shown below.Find the mean median mode of the listed numbers. 55 51 70 64 68 60 49?49
Answers
Step-by-step explanation:
mean add upp all the numbers and divide by how many they are
Simply. Who ever answers this will be marked Brainlist.
Answers
Answer:
Step-by-step explanation:
Hello,
[tex]r^3s^{-2}\cdot 8r^{-3}s^4\cdot 4rs^5\\\\=r^{3-3+1}s^{-2+4+5}\cdot 8\cdot 4\\\\\boxed{=32\cdot r\cdot s^7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A 14 sided die is rolled find the probability of rolling an odd number the set of equally likely outcomes is shown below
Answers
Answer:
Probability= 0.5
Step-by-step explanation:
A 14 sided die is rolled
Total number of occurrence= 14 numbers
Total odd numbers present
= 1,3,5,7,9,11,13
Total number of odd numvers present
= 7
Probability= number of required outcome/total possible outcome
Probability= 7/14
Probability= 0.5
The domain of the following relation has how many elements?
[(1/2, 3.14/6), (1/2, 3.14/4), (1/2, 3.14/3), (1/2,3.14/2)]
a. 0
b. 1
c. 4
Answers
Answer:
b. 1
Step-by-step explanation:
All first coordinates are 1/2.
Answer: b. 1
Calcule o valor de x nas equações literais: a) 5x – a = x+ 5a b) 4x + 3a = 3x+ 5 c) 2 ( 3x -a ) – 4 ( x- a ) = 3 ( x + a ) d) 2x/5 - (x-2a)/3 = a/2 Resolva as equações fracionárias: a) 3/x + 5/(x+2) = 0 , U = R - {0,-2} b) 7/(x-2) = 5/x , U = R - {0,2} c) 2/(x-3) - 4x/(x²-9) = 7/(x+3) , U = R - {-3,3}
Answers
Answer:
1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]
Step-by-step explanation:
1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]
[tex]5\cdot x - x = 5\cdot a + a[/tex]
[tex]4\cdot x = 6\cdot a[/tex]
[tex]x = \frac{3}{2}\cdot a[/tex]
b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]
[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]
[tex]x = 5-3\cdot a[/tex]
c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]
[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]
[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]
[tex]-x = a[/tex]
[tex]x = -a[/tex]
d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]
[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]
[tex]2\cdot x = 5\cdot a[/tex]
[tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]
[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]
[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]
[tex]3\cdot x +6 +5\cdot x = 0[/tex]
[tex]8\cdot x = - 6[/tex]
[tex]x = -\frac{3}{4}[/tex]
b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]
[tex]7\cdot x = 5\cdot (x-2)[/tex]
[tex]7\cdot x = 5\cdot x -10[/tex]
[tex]2\cdot x = -10[/tex]
[tex]x = -5[/tex]
c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]
[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]
[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]
[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]
[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]
[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]
[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]
[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]
[tex]-9\cdot x = -27[/tex]
[tex]x = 3[/tex]
henry incorrectly said the rate 1/5 pound/ 1/20 quart can be written as the unit rate 1/100 pound per quart. What is the correct unit rate? What error did Henry likely make?
Answers
Answer:
4 pounds per quart
Step-by-step explanation:
Henry divided by 20 instead of multiplying by 20.
1/5 pound is the numerator and 1/20 quart is the denominator. To make the denominator equal to 1 quart, you need to multiply by 20.
So 1/5 x 20 = 4 pounds.
Literally, a unit rate means a rate for one.
The unit rate is 4 pounds per quartHenry used the wrong arithmetic operatorThe rate is given as:
[tex]\mathbf{Rate = \frac{1}{5}\ pound\ per\ \frac{1}{20}\ quart}[/tex]
Per means divide.
So, the expression becomes
[tex]\mathbf{Rate = \frac{1}{5}\ pound\ \div \frac{1}{20}\ quart}[/tex]
Express as products
[tex]\mathbf{Rate = \frac{1}{5}\ pound\ \times \frac{20}{1\ quart}}[/tex]
Simplify
[tex]\mathbf{Rate = \frac{1}{1}\ pound\ \times \frac{4}{1\ quart}}[/tex]
Rewrite as:
[tex]\mathbf{Rate = \frac{4\ pound}{1\ quart}}[/tex]
So, the unit rate is 4 pounds per quart
Henry's error is that: He multiplied 1/5 by 1/20, instead of dividing 1/5 by 1/20
Read more about unit rates at:
https://brainly.com/question/18065083
Find the distance between (-8, 4) and (-8, -2).
10 units
2 units
6 units
8 units
Answers
Answer:
10
Step-by-step explanation:
i need help will rate you branliest
Answers
Hope
Answer:
D. the bottom one is the answer, because hyperbola is two curves that curve infinitely
There were 18,652 geese on a lake. What is this number rounded to the ten
thousands place?
Answers
Answer:
20,000
Step-by-step explanation:
To round a number to the nearest ten thousands place, we have to look at the thousand place and see whether it crosses the "hill" of 5 as it's digit.
The thousand digit is 8, so it will round UP, making 18,652 become 20,000.
Hope this helped!
Answer:
[tex]\boxed{20,000}[/tex]
Step-by-step explanation:
Hey there!
Well the ten thousands number is 1 and the 1rst thousands place number is 8 so since 8 is more than 5 we have to round 1 UP to 2,
so the answer is 20,000.
Hope this helps :)
A professional soccer player kicked a ball across the field. The ball’s height, in meters, is modeled by the function graphed below. What's the average rate of change between the point when the ball reached its maximum height and the point where it hit the ground?
Answers
Answer:
Hey there!
You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.
Let me know if this helps :)
Answer:
–3 meters per second
Step-by-step explanation:
Evaluate 1 + (-2/3) - (-m) where m = 9.2.
Answers
Answer:
9.533
Step-by-step explanation:
1+(-2/3)-(-9.2)
1-2/3--9.2
1-2/3+9.2=9.533
Explanation:
1 + (-2/3) - (-m)
m = 9.2
1 - 2/3 + m
= 1 - 2/3 + 9.2
= 3/3 - 2/3 + 9.2
= 1/3 + 9.2
= 1/3 + 27.6/3
= 28.6/3
Find the volume of the cylinder. Round your answer to the nearest tenth.
Answers
Answer:
716.75 m^3
Step-by-step explanation:
Volume of a cylinder:
=> PI x R^2 x H
H = Height
R = Radius
=> PI x 3.9^2 x 15
=> PI x 15.21 x 15
=> PI x 228.15
=> 228.15 PI
or
=> 228.15 x 3.14159
=> 716.75 m^3
Find the minimum and maximum values of 3 sin^2x – 2 cos^2x + 9
Answers
(Algebra) PLZ HELP ASAP!
Answers
Answer: Its everthing except irrational
Step-by-step explanation:
An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average expense of $15,000. What is the width of the 99% confidence interval for the mean of expense? a. 364.28 b. 728.55 c. 329.00 d. 657.99
Answers
Answer:
The width is [tex]w = \$ 729.7[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma = \% 1,000[/tex]
The sample size is [tex]n = 50[/tex]
The sample mean is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 99% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 99[/tex]
=> [tex]\alpha = 1\%[/tex]
=> [tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 364.9[/tex]
The width of the 99% confidence interval is mathematically evaluated as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 364.9[/tex]
[tex]w = \$ 729.7[/tex]
The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with \sigmaσσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the critical value? Round your answer to the nearest hundredths.
Answers
Answer:
Yes it can be concluded that state employees earn on average less than federal employees
The critical value is [tex]Z_{\alpha } = - 2.33[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 59593[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$ 58800[/tex]
The standard deviation is [tex]\sigma = \$ 1500[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 59593[/tex]
The alternative hypothesis is [tex]H_a : \mu < \$ 59593[/tex]
The critical value of [tex]\alpha[/tex] from the normal distribution table is [tex]Z_{\alpha } = - 2.33[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]
=> [tex]t = -2.896[/tex]
The p-value is obtained from the z-table
[tex]p-value = P(t < -2.896) = 0.0018898[/tex]
Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees
A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is
Answers
Answer:
Step-by-step explanation:
let present age of father=y
present age of son=x
then y=3x
after 15 years age of father=y+15
and age of son=x+15
∴y+15=2(x+15)
y+15=2x+30
y-2x=30-15
y-2x=15
∴3x-2x=15
x=15
y=3x=15×3=45
father's present age=45 years
A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 307 persons, the following data was compiled. Can we conclude that brand perception is dependent on age?
Age Favorable Unfavorable Neutral Total
18-30 67 24 20 111
30-45 50 14 16 80
Over 45 69 41 26 116
Total 186 59 62 307
Find the value of the test statistic.
Answers
Answer:
The value for the Chi -square test statistics = 1.149
Step-by-step explanation:
The observed value Table can be shown better as:
Observed Value
Age Favorable Unfavorable Neutral Total
18-30 67 24 20 111
30-45 50 14 16 80
Over 45 69 21 26 116
Total 186 59 62 307
NOTE: when computing the question, in the third row and the second column, there is a mistake , the value is supposed to be 21 and not 41 because :
69 +21+ 26 will eventually give = 116
69 + 41 + 26 = 136
With that error being fix , let's get started.
Expected Value
The expected value can be determined by using the formula:
[tex]Expected \ Value = \dfrac{ row \ total \times column \ total }{grand \ total }[/tex]
For 67; (111 * 186)/307 = 67.251
For 24 : (111 * 59)/307 = 21.332
For 20 : (111 * 62)/307 = 22.417
For 50 :(80*186)/307 = 48.469
For 14 : (80* 59)/307 = 15.375
For 16 : ( 0 * 62)/307 = 16.156
For 69 : (116 * 186)/307 = 70.280
For 21 : (116* 59)/307 = 22.293
For 26 : (116*62)/307 = 23.427
Expected Value :
Age Favorable Unfavorable Neutral Total
18-30 67.251 21.332 22.417 111
30-45 48.469 15.375 16.156 80
Over 45 70.280 22.293 23.427 116
Total 186 59 62 307
The Chi - square test statistics = [tex]\dfrac{(observed \ value - Expected \ value)^2}{Expected \ value}[/tex]
For 67.251 : ( 67 - 67.251)²/67.251 = 0.0009
For 21.332 : ( 24 - 21.332)²/21.332 = 0.3337
For 22.417 : ( 20 - 22.417)²/ 22.417 = 0.2606
For 48.469 : ( 50 - 48.469)²/ 48.469 = 0.0484
For 15.375 : ( 14 - 15.375)²/ 15.375 = 0.1230
For 16.156 : ( 16 - 16.156)²/ 16.156 = 0.0015
For 70.280 : ( 69 - 70.280)²/ 70.280 = 0.0233
For 22.293 : ( 21 - 22.293)²/ 22.293 = 0.0750
For 23.427 : ( 26 - 23.427)²/ 23.427 = 0.2826
The chi square table is as follows:
Age Favorable Unfavorable Neutral Total
18-30 0.0009 0.3337 0.2606 0.5952
30-45 0.0484 0.1230 0.0015 0.1729
Over 45 0.0233 0.0750 0.2826 0.3809
Total 0.0726 0.5317 0.5447 1.149
The value for the Chi -square test statistics = 1.149
What is the range of g?
Answers
Answer:
R: {y∈R | -1 ≤ y ≤ 5}
Step-by-step explanation:
the lowest point is -1 and the highest point is 5.
Identifying the Property of Equality
Quick
Check
Identify the correct property of equality to solve each equation.
3+x= 27
X/6 = 5
Answers
Answer:
a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication
Step-by-step explanation:
a) This expression can be solved by using the Compatibility of Equality with Addition, that is:
1) [tex]3+x = 27[/tex] Given
2) [tex]x+3 = 27[/tex] Commutative property
3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition
4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property
5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction
6) [tex]x=24[/tex] Modulative property/Subtraction/Result.
b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:
1) [tex]\frac{x}{6} = 5[/tex] Given
2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division
3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication
4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property
5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse
6) [tex]x = 30[/tex] Modulative property/Result
Answer:
3 + x = 27
✔ subtraction property of equality with 3
x over 6 = 5
✔ multiplication property of equality with 6
Megan’s room is expanded so the width is 150% of 3 meters. What is the new width?
Answers
Work Shown:
The keyword "of" means "multiply".
150% = 150/100 = 1.5
150% of 3 = 1.5*3 = 4.5
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
100% = 3 meters
150% = 4.5 meters
The new width is 4.5 meters.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Megan’s room is expanded so the width is 150% of 3 meters.
This means,
100% = 3 meters
Multiply 150/100 on both sides.
150% = 150/100 x 3
150% = 4.5 meters
Thus,
The new width is 4.5 meters.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ2
Annie has 3/2 pounds of cookie dough. If she needs 1/16 of a pound of cookie dough to make one cookie, how many cookies can she make
Answers
Answer:
[tex]\boxed{\sf 24\ cookies}[/tex]
Step-by-step explanation:
1 cookie = 1/16 of a pound of cookie
If we want to find how many cookies can be made by 3/2 pounds ( 1.5 pounds) then we need to divide 3/2 pounds by 1/16
=> [tex]\frac{3}{2} / \frac{1}{16}[/tex]
=> [tex]\frac{3}{2} * 16[/tex]
=> 3*8
=> 24 cookies
Answer:
24 cookies
Step-by-step explanation:
3/2= 1.5 and 1/16= 0.0625
if you divide the amount of dough you have by the amount needed for each cookie you will have 24
1.5/0.0625=24
Question:
If V7 - y = 6, then y =
A. -29
B. -5
C. 1
D. 29
[tex] \sqrt{7 - y = 6} [/tex]
Answers
Answer:
-29
Step-by-step explanation:
[tex] {\sqrt{7 - y }}^{2} = {6}^{2} [/tex]
[tex]7 - y = {6}^{2} [/tex]
y = 7-36
y = -29
Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −4 is the only other zero, leading coefficient is 4. setup problem so I can solve, thanks!!
Answers
Answer:
Step-by-step explanation:
Hello,
degree 5
4 is a zero of multiplicity 3 -> (x-4)^3 is a factor
-4 is the only other zero, so the multiplicity is 5-3=2 -> (x+4)^2 is a factor
leading coefficient is 4 so we can write
[tex]\boxed{4(x-4)^3(x+4)^2}[/tex]
If there is something that you do not understand or you are blocked somewhere let us know what / where.
Thank you.
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 6 3/4" by 4 1/2" on the drawing, how large is the bedroom? Please Help! (No other information was given.)
Answers
1 inch = four 1/4’s
1 inch = 4 feet
6 X 4 = 24 feet
3/4 inches = 3 feet.
6 3/4 inches = 27 feet
4 x 4 = 16
1/2 inch = 2 feet
4 1/2 inches = 18 feet
Room is 27 feet x 18 feet
A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4. A die is selected at random and rolled four times. You are told that two rolls were 1's and two were 4's. Find the probability the die chosen was green.
Answers
Answer:
the probability the die chosen was green is 0.9
Step-by-step explanation:
Given that:
A bag contains two six-sided dice: one red, one green.
The red die has faces numbered 1, 2, 3, 4, 5, and 6.
The green die has faces numbered 1, 2, 3, 4, 4, and 4.
From above, the probability of obtaining 4 in a single throw of a fair die is:
P (4 | red dice) = [tex]\dfrac{1}{6}[/tex]
P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]
A die is selected at random and rolled four times.
As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]
The probability of two 1's and two 4's in the first dice can be calculated as:
= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]
= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]
= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]
= [tex]6 \times ( \dfrac{1}{6})^4[/tex]
= [tex](\dfrac{1}{6})^3[/tex]
= [tex]\dfrac{1}{216}[/tex]
The probability of two 1's and two 4's in the second dice can be calculated as:
= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]
= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]
= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]
= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]
= [tex]\dfrac{9}{216}[/tex]
∴
The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )
The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]
The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]
The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]
By applying Bayes Theorem; the probability that the die was green can be calculated as:
P(second die (green) | two 1's and two 4's ) = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]
P(second die (green) | two 1's and two 4's ) = 0.9
Thus; the probability the die chosen was green is 0.9
PLEASE HELP!!! The question is.. [tex]163-y=-5[/tex] ANSWER GETS BRAINLIEST
Answers
Answer:
y = 168Step-by-step explanation:[tex]163 -y =-5\\Collect\:Like\:terms\\163+5 = y\\Simplify\\168 =y\\\\y = 168[/tex]
Hello There!
Answer: [tex]163-168=-5[/tex]Explanation:[tex]163-y=-5[/tex]
To solve your equation, you can just change the -5 to 5 and move it to where y is. After that, change the minus sign to addition.
[tex]163+5=y[/tex]
Now all you have to do is sum it up.
[tex]163+5=168[/tex]
So y = to 168
So your answer is
[tex]163-168=-5[/tex]
Hope this Helps!
I need some help pls! I'm getting stuck!
Answers
Answer: 3 pounds.
Step-by-step explanation:
We have two metals:
One that contains 20% nickel, let's call it metal A.
One that contains 80% nickel, let's call it metal B.
We have 6 pounds of metal B, in those 6 punds we have:
0.80*6lb = 4.8lb of nickel.
Now, if we add X pounds of metal A, then we will have:
X + 6lb in total weight.
4.8lb + 0.2*X of nickel.
And we want to have exactly 60% of nickel, so we must have that the quotient between the amount of nickel and the total weight is equal to 0.6
(4.8lb + 0.2*X)/(6lb + X) = 0.6
now we solve it for X:
(4.8lb + 0.2*X) = 0.6*(6lb + X) = 3.6lb + 0.6*X
4.8lb - 3.6lb = 0.6*X - 0.2*X
1.2lb = 0.4*X
1.2lb/0.4 = 3lb = X
We should use 3 pounds of the metal with 20% of nickel.
EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a function f, then
Answers
If there is such a scalar function f, then
[tex]\dfrac{\partial f}{\partial x}=4y^2[/tex]
[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}[/tex]
[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}[/tex]
Integrate both sides of the first equation with respect to x :
[tex]f(x,y,z)=4xy^2+g(y,z)[/tex]
Differentiate both sides with respect to y :
[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}[/tex]
[tex]\implies\dfrac{\partial g}{\partial y}=4e^{4z}[/tex]
Integrate both sides with respect to y :
[tex]g(y,z)=4ye^{4z}+h(z)[/tex]
Plug this into the equation above with f , then differentiate both sides with respect to z :
[tex]f(x,y,z)=4xy^2+4ye^{4z}+h(z)[/tex]
[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]
Integrate both sides with respect to z :
[tex]h(z)=C[/tex]
So we end up with
[tex]\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}[/tex]
Megan has 12 pounds of cheesecake. On Monday, she and her friends eat 4 pounds. On Tuesday, she and her friends eat another 3 pounds. On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. On Friday, she gives 3 pounds to her dog. On Saturday, her mom gives her one more pound. On Sunday, how many pounds of cheesecake does Megan have left?
Answers
Answer:
Step-by-step explanation:
First we start with 12 pounds
On Monday, she and her friends eat 4 pounds. So we have 8 now.
On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.
On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15
On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.
On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.
On Saturday, her mom gives her one more pound. 2 + 1 = 3.
On Sunday, she finally has 3 pounds.
Answer:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Step-by-step explanation:
