1600 square meters is the greatest area that may be enclosed.
Rectangle.
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
If fencing is required for 200 meters, then the enclosed area's perimeter is 200 meters.
Perimeter of rectangle = 2(L + B)
2(L+B) = 200
Divide both sides by 2
L+B = 100
L = 100 - B
Here,
Area(A) = L X B
Substitute L = 100 - B into the equation above
A = (100 - B) x B
A = 100B - B²
At maximum area dA/dB = 0
dA/dB = 100 - 2B
100 - 2B = 0
2B = 100
B = 100/2
B = 50m
So L = 100 - 50
L = 50m
Maximum area to be enclosed = 50 x 50
Maximum area to be enclosed = 2500 square meters
In conclusion, the 2500 square meters of space that the fence will enclose
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72 +1-5 x 3; value: 135
Answer:
58
Step-by-step explanation:
72 + 1 - 5 x 3
= 72 + 1 - 15
= 73 - 15
= 58
a cookie store sells 6 varieties of cookies. it has a large supply of each kind. (a) how many ways are there to select 15 cookies? (b) how many ways are there to select 15 cookies if at least three must be chocolate chip? (c) how many ways are there to select 15 cookies if at most 2 can be sugar cookies? (d) how many ways are there to select 15 cookies if at most 2 can be sugar cookies and at least 3 must be chocolate chip?
The tottal number of ways to selct 15 cookies is 15504 and the ways are there to select 15 cookies if at least three is 6188.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
we have to select 15 Cookies from 6 varieties so we can think an n₁+n2+n3+n4 + N5 +N6=15 with each o≤ni ≤15
C([tex]\frac{20}{12}[/tex]) = 15504
NOW we have One category is fixed let K Chocolate chips are Selected in I way The A we have to (15-K) Cookies from the varieties
C([tex]\frac{19-k}{15-5}[/tex])
So for k=0, C1=3876
k=1, C2 =3060
k=2, C3=2380
So C =C1+C2+C3=9316.
So the number of ways 15504-9316= 6188.
Hence, The tottal number of ways to selct 15 cookies is 15504 and ways are there to select 15 cookies if at least three is 6188.
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Question is below! Mark brainliest!
Answer: (-84, 272)
x = -84
y = 272
Hope this helps!
Answer:
Below
Step-by-step explanation:
-6x - 2y = - 40 <====multiply this entire equation by -1 to get:
6x + 2y = 40 <===== then add it to the second equation
-7x -2y = -44 to get:
-x = -4
so x = 4 use this value in one of the equations to compute y
-6(4) - 2y = -40
-2y = -16
y = 8 (4,8)
a hippogriff rancher wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). he has 590 feet of fencing available to complete the job. what is the largest possible total area of the four pens?
The largest area is found to be 8702.5 [tex]ft^{2}[/tex].
We know that area of rectangle
A = xy ........ (1)
Perimeter of rectangle (given) = 590 ft
Using x and y as two variables ;
5x + 2y = 590
solve yb in term of x
y = -5/2 x + 295......(2)
Now we will get area only in one variable from (1) and (2)
A = x ((-5/2)x + 295)
A = -5/2 [tex]x^{2}[/tex] + 295x
differentiate it with respect gto x
A' = -5x + 295........ (3)
find the critical point to get your minima and maxima value.
Put A' = 0, x = 295/5 = 59
x = 59
then , from (2)
y= (-5/2 × 59) + 295 = 147.5
y = 147.5
again differentiate (3)
A'' = -5 < 0. i.e critical point x = 59 is point of maxima.
So, maximum area = 59 × 147.5
Largest area = 8702.5 [tex]ft^{2}[/tex]
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Question
What is another way to write the expression t⋅(14−5)?
helpp meee
14t-5t is another way to write the expression t⋅(14−5)
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is t(14-5)
An expression is combination of variables, numbers and operators.
t times of fourteen minus five
Here t is the variable
We need to find other way to write this expression
t(14-5)
Apply distributive property
14t-5t
9t
Hence, 14t-5t is another way to write the expression t⋅(14−5)
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a 10 foot ladder is leaning against a wall when the base begins to slide away from the wall. when the base is 8 feet from the wall, the base is moving at the rate of 4 feet per second. how fast is the top of the ladder sliding down the wall, in feet per second?
40/3 feet /second fast the top of the ladder sliding down the wall.
What is ladder?
A ladder is a piece of gear used for climbing up or down objects that consists of repeated bars or steps (rungs) between two upright lengths of metal, wood, or rope.
Typically, these ladders work best for outdoor tasks like roof access or exterior painting. A straight ladder's reach is typically two feet higher than its height.
Given:
A 10 foot ladder is leaning against a wall when the base begins to slide away from the wall. when the base is 8 feet from the wall, the base is moving at the rate of 4 feet per second.
We have dx/dt = 4 feet per second
We want to find dy/dt.
From given information,
x^2 + y^2 = 10^2 ..(1)
When x = 8
⇒ y = √(10^2 - 8^2)
y = √(100 - 64)
y = √36
y = 6 feet
Now differentiate equation (1) with respect to t
[tex]2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\ x\frac{dx}{dt} + y\frac{dy}{dt} = 0\\ \frac{dy}{dt} = -\frac{x}{y} \frac{dx}{dt}[/tex]
Plug x = 8, y = 6 and dx/dt = 10
⇒
[tex]\frac{dy}{dt} = -\frac{8}{6}(10)\\ \frac{dy}{dt} = -\frac{40}{3}[/tex]
Hence, 40/3 feet /second fast the top of the ladder sliding down the wall.
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
show your work.
(1/2 + 1/3)÷1/12 - 2^3
Answer: 2
Step-by-step explanation:
solve in parentesis than divide by 0.5 or 1/2 then 2^3= 4 so
that minus 4 equals 2
Please help me with this!
answer:
I believe it's D
Alto and Sheryl both worked hard over the summer. Together they earned a total of $500. Sheryl earned $100 more than Alto.
(a) Write a system of equations for the situation. Use s for the amount Sheryl earned and a for the amount Alto earned.
(b) Graph the equations of the system on the graph provided on the next page. a. Note: Insert->Shape will allow you to add lines, draw dots, and otherwise insert shapes in both Microsoft Word and LibreOffice. The graph should be big enough for you to easily plot points using this method. b. If you do not want to graph using the drawing tools built into Microsoft Word or LibreOffice you may also print out, graph by hand, and scan the page. Please note it’s perfectly okay to upload multiple files.
(c) Use Elimination or Substitution to solve the system.
(d) Use your graph to estimate how much each person earned, check your work with part C, and explain your results in complete sentences.
Alto earned $200 while Sheryl earned $300 over the summer.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Consider x represent the amount of money earned by Alto and y represent the amount of money earned by Sheryl
Together they earned a total of $500.
Hence the system of equations for the situation
x + y = 500 (1)
Sheryl earned $100 more than Alto:
y = x + 100
-x + y = 100(2)
Using Substitution to solve the system.
Solving equations 1 and 2 simultaneously gives:
x = 200 , y = 300
Therefore Alto earned $200 while Sheryl earned $300 over the summer.
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8. An organization published an article stating that in any one-year period, approximately 8.3 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country.
Part (a)
Is this a test of one mean or proportion?
State the null and alternative hypotheses.
Is this a right-tailed, left-tailed, or two-tailed test?
What symbol represents the random variable for this test?
In words, define the random variable for this test.
Calculate the following.
(i) Enter your answer as a whole number.
x =
(ii) Enter your answer as a whole number.
n =
(iii) Enter your answer to two decimal places.
p' =
Part (g)
Calculate σx. (Round your answer to three decimal places.)
Show the formula set-up.
State the distribution to use for the hypothesis test.
Find the p-value. (Round your answer to four decimal places.)
[tex]z = \frac{0.08 - 0.083}{\sqrt{0.083 * 0.917/100} }[/tex]
= 0.108
pₐ = P( z < -0.108 ) = 0.4562
So the p-value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%)
Data given and notation
n = 100 represent the random sample taken
X=8 represent the people with depression or a depressive illness
p = 8/100 = 0.08 estimated proportion of people with depression or a depressive illness
p₀ = 0.083 is the value that we want to test
α = 0.05 represent the significance level assumed
Confidence = 83% or 0.83 assumed
z would represent the statistic (variable of interest)
pₐ represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportions of people with depression or a depressive illness is lower than the general adult population value of 8.3% or 0.083:
Null hypothesis:
p ≥ 0.083
Alternative hypothesis:
p < 0.083
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z = \frac{p- p_{0} }{\sqrt{p_{0} ( 1 - p_{0} )/ n } }[/tex] --------------------- (1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z = \frac{0.08- 0.083 }{\sqrt{0.083 ( 1 - 0.083 )/ 100 } }[/tex]
= - 0.083 / √ 0.0076
= -0.083 / 0.028
= -0.108
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed is α = 0.05 . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
pₐ = P( z < -0.108 ) = 0.4562
So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%).
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Jasmine checks rental car rates. She discovers that a midsize car costs $50.00 plus $19.99 per day to rent. Which recursive formula shows the sequence of costs to rent the car for 1 day, 2 days, 3 days, and so on? Responses an=19.99+50.00an−1 where n>1 a n = 19.99 + 50.00 a n − 1 where n > 1 an=50.00+19.99an−1 where n>1 a n = 50.00 + 19.99 a n − 1 where n > 1 a1=69.99an=an−1+19.99 where n>1 a 1 = 69.99 a n = a n − 1 + 19.99 where n > 1 a1=50.00an=an−1+19.99 where n>1 a 1 = 50.00 a n = a n − 1 + 19.99 where n > 1
Recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex] where n>1
What do you mean by recursive realtion?
A recursive sequence is one in which terms are defined by reference to one or more previously defined terms.
The recursive formula [tex]a_{n+1}=a_{n}[/tex] + d can be used to find the (n+1)th term of an arithmetic series if you know the nth term and the common difference, d.
It is given that cost of midisze car is $50.00
Rent per day = $19.99
We need to find the sequence of costs to rent the car for 1 day, 2 days, 3 days, and so on.
According to the question:
Cost become = 50.00 + 19.99n where n represents the number of days
Recursive formula become:
[tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex] where n>1
Therefore, recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex] where n>1
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The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon. A number of different independent variables were collected. The following regression output (with some values missing) was recently presented to the editors by the magazine's analysts:
Based on this output and your understanding of multiple regression analysis, what is the critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance?
o Nearly F = 3.80
o About F = 5.92
o Approximately F = 2.50
o None of the above
Based on this output of multiple regression analysis, critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance is Approximately F = 2.50.
What exactly is multiple regression analysis?A single dependent variable and a number of independent variables can be analyzed using multiple regression, a statistical approach. Using independent variables whose values are known, multiple regression analysis aims to predict the value of the single dependent value.
What is multiple regression analysis example?When doing multiple regression, each independent variable's value is taken into account in order to predict the value of the single dependent variable. Example: A researcher chooses to examine student performance at a certain school over time.
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Help please!
-8+2(3 + 8) = -4(g + 1)
Answer: -9/2
Let's solve this equation step-by-step.
−8+2(3+8)=−4(g+1)
Step 1: Simplify both sides of the equation.
−8+2(3+8)=−4(g+1)
−8+2(3+8)=(−4)(g)+(−4)(1) (Distribute)
−8+22=−4g+−4
(−8+22)=−4g−4 (Combine Like Terms)
14=−4g−4
Step 2: Flip the equation.
−4g−4=14
Step 3: Add 4 to both sides.
−4g−4+4=14+4
−4g=18
Step 4: Divide both sides by -4.
−4g/−4 = 18/−4
g = −9/2
Which graph shows the solution of the inequality ? x+5_> 2
The graph of the solution of the inequality is shown in figure.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ x + 5 ≥ 2
Now,
Since, The inequality is,
⇒ x + 5 ≥ 2
Hence, Simplify the inequality as;
⇒ x + 5 ≥ 2
Subtract 5, we get;
⇒ x + 5 - 5 ≥ 2 - 5
⇒ x ≥ - 3
Thus, The graph of the solution of the inequality is shown in figure.
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- Clare removed marbles from a container of
water. When she removed 2 marbles, the
water level was 80 ml. When she removed
4 more marbles, the water level was 40 ml.
Write an equation for the water level y after
x marbles are removed.
Answer:
y = 100 - 10x
Step-by-step explanation:
Let y₀ be the original water level before any marbles were removed
Let y = water level after x marbles are removed.
Let d be the water level drop for every marble removed
Then we have the general equation:
y = y₀ - x.d
We have to find d and y₀
So we get one equation for the water level after removal of 2 marbles
80 = y₀ - 2d [1]
After 4 more marbles were removed, the water level drops to 40ml. That means for 4 marbles removed, the water level drops from 80 to 40. So drop in water level for 4 marbles = 80-40 = 40ml
For each marble then, water level drop = 40/4 = 10ml. This is the value of d
Plug this value of d into [1] to get the original water level y₀
80 = y₀ - 2( 10)
80 = y₀ - 20
100 = y₀
or,
y₀ = 100
So original water level is 100ml and the equation for water level after x marbles are removed is
y = 100 - 10x
5. What must the complement of the supplement
of an obtuse angle be?
(A) an acute angle
(B) a right angle
(C) an obtuse angle
(D) a straight angle
(E) a reflex angle
**I’ll give 20 points!
Answer:
A Acute angle (Give me pointssss)
Step-by-step explanation:
Its right bc im smart
tickets to movie cost $5 for adults and $3 for students. A group of friends purchased 18 tickets for $82.00. How many adults ticket did they buy
Answer: 14 Adult tickets
Step-by-step explanation:
The equation for the total number of tickets would be
x+y=18
5x+3y=82
y=18-x
5x+3(18-x)=82
2x=28
x=14
x= Number of adult tickets
The value of y varies exponentially with respect to x and the 1-unit growth factor is 1.7. Which of the following is the best explanation for the meaning of this growth factor?Whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.Whenever x changes by 1, the value of y becomes 11.7 times as large as its previous value.Whenever x changes by 1.7, the value of y doubles its previous value.Whenever x changes by 1.7, the value of y becomes 1 unit larger than its previous value.Whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value
We concluded that whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.
What is the growth factor?
The rate at which a quantity multiplies itself over time is known as its growth factor. A quantity's growth rate is the factor by which it grows (or shrinks) over time.
Here, we have
The required expression for y with respect to x is:
y = (1.7)ˣ.......(1)
Where, 1.7 = 1-unit growth factor
Now we check,
Whenever x changes by 1
x →x +1 .....(2)
Now we put Equation (2) in (1) and we get
y' = (1.7)ˣ⁺¹
y' = (1.7)ˣ (1.7).....(3)
Taking the ratio of equations 3 & 1, we get
y'/y = (1.7)ˣ (1.7)/(1.7)ˣ
y' = 1.7y
Hence, we observe that whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.
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values for the random variables or uncertain variable inputs to a simulation are a. randomly generated from the specified probability distributions b. equal to the most likely value c. selected by the decision maker d. calculated by fixed mathematical formulas e. controlled by the decision maker
The correct option is:
a. randomly generated from the specified probability distributions
Given,
In the question:
Values for the random variables or uncertain variable inputs to a simulation are:-
a. randomly generated from the specified probability distributions
b. equal to the most likely value
c. selected by the decision maker
d. calculated by fixed mathematical formulas
e. controlled by the decision maker
Choose the correct one.
Now, According to the question:
Let's Know:
How do you generate a random number from a probability distribution?
In general, generating a random number from a probability distribution means transforming random numbers so that the numbers fit the distribution. Perhaps the most generic way to do so is called inverse transform sampling: Generate a uniform random number in [0, 1].
The correct option is:
a. randomly generated from the specified probability distributions
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complete the table of values y=x² - 4x - 2
Let f(x) = 4x and g (x) = (4) ^x-1 + 2. Which transformations are needed to transform the graph f (X) to the graph of g (X)? Select each correct answer.
1. horizontal translation 2 units left
2. vertical translation 1 unit down
3. vertical translation 2 units up
4. horizontal translation 1 unit right
5. horizontal translation 1 unit left
6. vertical translation 1 unit up
How much sales taxes will cody have in his pay of purchase
Answer:
Where is the equation? It's ok but still.
Step-by-step explanation:
a variable is normally distributed with mean 23 and standard deviation 6. use your graphing calculator to find each of the following areas. write your answers in decimal form. round to the nearest thousandth as needed. a) find the area to the left of 25. 0.557 b) find the area to the left of 16. c) find the area to the right of 22. d) find the area to the right of 28. e) find the area between 16 and 30.
a) The area to the left of 25 is 0.63056
b) The area to the left of 16 is 0.12167
c) The area to the right of 22 is 0.56618
d) The area to the right of 28 is 0.20233
e) The area between 16 and 30 is 0.75666
Given,
The mean of the distribution = 23
Standard deviation = 6
We have to find the following areas
(a) Entering the values
Lower : -999999999Upper : 25Area (probability): 0.63056(b) Entering the values
Lower : -999999999Upper : 16 Area (probability): 0.12167(c) Entering the values
Lower : 22 Upper : 999999999 Area (probability): 0.56618(d) Entering the value
Lower : 28 Upper : 999999999 Area (probability): 0.20233(e) Entering the values
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a random sample of 46 salespersons was asked how long on average they were able to talk to a potential customer. their answers revealed a mean of 8.90 with a variance of 6 minutes. construct a 95% confidence interval for the time it takes a salesperson to talk to a potential customer.
With 95% of confidence interval for the time it takes salesperson to talk to a potential customer is (12.42 , 5.38).
A Random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimizing the risk of selection bias.
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ ² ,s² ,Var(X) , or V(X).
A confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level represents the long-run proportion of corresponding CIs that contain the true value of the parameter. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.
Given in the question:
n = 46
x = 8.90
σ = 6
α = 0.95
As we know that:
[tex]X[/tex] ±[tex]Z_{\alpha /2} * \frac{\beta }{\sqrt{n} }[/tex]
putting the values we get,
8.90 ± Z (0.95/2) ×6/√46
Now, considering the positive sign, we get,
= 8.90 + 3.52
= 12.42
Now considering the negative sign,
8.90 ± Z (0.95/2) ×6/√46
= 8.90 - 3.52
= 5.38
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Multiply the following polynomials. Write the simplified answer in descending order. Use the ^ (shift + 6) to indicate exponents.
DO NOT add spaces between any numbers or characters. For example: (x+2)(x+3) = x^2+5x+6.
(2x - 3y)(4x - y)
Answer:
8x^2-14xy+3y^2 (I think)
Step-by-step explanation:
You probably don't need it now but like here
Find the slope of the line that passes through each pair of points.
(5, 7), (1, -3)
Answer:
5/2 or 2.5
Step-by-step explanation:
Slope is rise/run. We take the difference of the y-coordinates and divide it by the difference of the x-coordinates.
From this, we get [tex](7--3)/(5-1)[/tex], or [tex]10/4[/tex], which can be simplified to 5/2, or 2.5.
A data collection protocol calls for a questionnaire to be administered to patients having knee replacement surgery after the third physical therapy appointment. Errors can be introduced into the study by.
The way that errors can be introduced are;
Giving the questionnaire to all participants when they arrive for their appointment does not follow the protocol;
The participant could fill out the questionnaire before experiencing the therapy session.
How to identify errors in statistics study?Statistical errors are defined as errors that describe the difference that exists between a value obtained from a data collection process and the 'true' value for the population. Thus, the greater the error, the less representative the data will be of the population.
There are two main errors in this case which are type I error and type II error.
A type I error is called false-positive and it occurs if an investigator rejects a null hypothesis that is actually true in the population.
A type II error is called false-negative and it occurs if the investigator fails to reject a null hypothesis that is actually false in the population.
Now, from the question, since the data collection protocol alls for a questionnaire to be administered to patients having knee replacement surgery after the third physical therapy appointment, then we can introduce an error by;
Giving the questionnaire to all participants when they arrive.
The participant could fill out the questionnaire before experiencing the therapy session.
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Giving a questionnaire to all par-ticipants follows the timing of theprotocol.
BReading the questionnaire to par-ticipants with poor reading skillsfollows the timing of the protocol.
CGiving the questionnaire to allparticipants when they arrive fortheir appointment does not fol-low the protocol; the participantcould fill out the questionnairebefore experiencing the therapysession.
DGiving the questionnaire to theparticipants after the appoint-ment to be completed while theyhave a snack follows the timingof the protocol.
an item is regulary priced at $40. Brian bought it at 40% off the regular price. HOw much did brian pay
Answer: Brian payed $24.00
How u do it:
Discount= original price x discount%/100
Discount = 40 × 40%/100
Discount = 40 x 0.4
You save = $16.00
Final Price = Original Price - Discount
Final Price = 40 - 16
Final Price = $24.00
what is the probability of first drawing a red card, then a jack, and then a black card? do not round your intermediate computations. round your final answer to four decimal places.
The probability of first drawing a red card, then a jack, and then a black card is 0.0612
First we will describe the standard deck of 52 cards in terms of black, red and face cards found in a standard deck
Following is a table of distribution of colored and face card found in a standard deck:
Type Number of cards
1 - 10 40
Black 26
Red 26
Face 12
The numerical cards from digit ( 1 to 10 ) are found in all 4 suits ( Clubs, Diamonds, Spades, and Hearts ). Hence, 10 x 4 = 40
- The entire deck is split in two colors ( Red and Black ) equally. So, the number of Black and Red cards are = 52 / 2 = 26 cards.
- The face cards are of three types ( King, Queen and Jack ). These three face cards are found in each of the 4 suits. Hence, Total number of face cards are = 4 * 3 = 12
- We will now consider the probabilities associated with each type. We will define 3 events and write down their probability as expressed:
Event ( A ): First draw is a red card.
- The probability of this event can be determined with the help of the table given above. There are a total of 26 red card in a standard deck of 52 cards. Hence,
p ( A ) = [ Number of red cards ] / [ Total cards in a deck ]
p ( A ) = [ 26 ] / [ 52 ]
p ( A ) = 1 / 2
- After we make the first draw of a red card. Our deck distribution is changed to Number of Red cards remaining = 25 and total deck now has 51 cards remaining.
- We will define the next event as:
Event ( B ): The second draw is a face card.
- The probability of this event can be determined with the help of the table given above. There are a total of 12 face cards in a standard deck of 52 cards which is now down to 51 cards. Hence,
p ( B ) = [ Number of face cards ] / [ Total cards in a deck ]
p ( B ) = [ 12 ] / [ 51 ]
p ( B ) = 4 / 17
- After we make the first draw of a face card. Our deck distribution is changed to Number of Face cards remaining = 11 and total deck now has 50 cards remaining.
- We will define the next event as:
Event ( C ): The third draw is a black card.
- The probability of this event can be determined with the help of the table given above. There are a total of 26 black cards in the deck. The total number of cards are down to 50 cards only. Therefore,
p ( C ) = [ Number of black cards ] / [ Total cards in a deck ]
p ( C ) = [ 26 ] / [ 50 ]
p ( C ) = 13 / 25
- The entire drawing process consists of 3 events which are dependent on each draw. However, for the overall event to occur i.e drawing a red card , then a face card, and then a black card. We will multiply all three outcomes as follows:
p ( T ) = p ( A ) * p ( B ) * p ( C )
p ( T ) = [ 1 / 2 ] * [ 4 / 17 ] * [ 13 / 25 ]
p ( T ) = [ 26 / 425 ] ≈ 0.0612
Hence we get the required answer.
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Luke climbed from an elevation of 23,201 ft up to the summit of k2 which is at 28,251 ft. How many ft did Luke climb?
I need to explain the variable
write an equation
and solve it
The number of ft that Luke climbed, given the elevation he started from, and the summit, is 5, 050 ft
How to find the feet climbed?The number of feet that Luke climbed, can be found by the formula:
Number of feet climbed = Summit of K2 - Luke's starting elevation
Summit of K 2 = 28, 251 ft
Luke's starting elevations = 23, 201 ft
Elevation climbed by Luke was therefore:
= 28, 251 - 23, 201
= 5, 050 ft
In conclusion, the total elevation that Luke climbed from his starting point to the summit of K2 is 5, 050 ft.
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