Answer:422977164210 or it could be [tex]4.2297716421(10) ^{11}[/tex]
Step-by-step explanation:
Activity 12-4: A large monohybrid crossa corn ear with purple and yellow kernels The total number of purple and yellow kernels on 8 different corn ears were counted: Purple kernels 3593 Yellow kernels 1102 What is the ratio of purple kernels to yellow kernels
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The number of purple kernel is [tex]n_k = 3593[/tex]
The number of yellow kernel is [tex]n_y = 1102[/tex]
Generally the ration of the purple to the yellow kernels is mathematically evaluated as
[tex]r = \frac{n_k}{n_y}[/tex]
substituting values
[tex]r = \frac{3593}{1102}[/tex]
[tex]r = 3.3[/tex]
[tex]r \approx 3[/tex]
Therefore the ratio is
[tex]1 \ Yellow : 3 \ Purple[/tex]
Heng tried to define a reflection across line r.
• Any point N on line r maps to itself.
• Any point M not on the line of reflection maps to a point M' such that the midpoint L of MM' is
on liner.
Which counterexample shows that Heng's definition does not fully define a reflection?
Choose 1 answer:
Answer:
Any point N on line r maps to itself.
Step-by-step explanation:
Reflection is one of the examples of solid transformation in which a given point, segment, or figure is flipped over a reference point or line to produce its image. The distance of the object to the reference point or line is the same as the distance of its image to the point or line. And both have the same size, but different orientation.
The option that does not fully define a reflection is; any point N on line r maps to itself, because no image of point N is produced after the operation.
Answer:
C. This matches Heng's definition, but is not a reflection, because MM'MM
′
M, M, prime is not perpendicular to line rrr.
Step-by-step explanation:
Change the polar coordinates (r, θ) to rectangular coordinates (x, y):(-2,sqrt2pi
Step-by-step explanation:
x=rcosθandy=rsinθ,. 7.7. r2=x2+y2andtanθ=yx. 7.8. These formulas can be used to convert from rectangular to polar or from polar to rectangular coordinates.
This person made a mistake. what is the mistake and what is the correct answer?!!
Answer: 44
Step-by-step explanation:
PLEAS HELP...FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?
*a clearer picture containing the graph is shown in the attachment
Answer:
20% of the class earned a D
Step-by-step Explanation:
Step 1: Determine the total number of students represented on the graph:
9 students => D
5 students => C
14 students => B
17 students => A
Total number of students = 45
Step 2: Express each category of students who scored a particular grade as a fraction and as percentage.
9 students => D => [tex] \frac{9}{45} = \frac{1}{5} [/tex] => as percentage, we have [tex] \frac{1}{5} * 100 = 20 percent [/tex]
5 students => C => [tex] \frac{5}{45} = \frac{1}{9} [/tex] => as percentage, we have [tex] \frac{1}{9} * 100 = 11.1 percent [/tex]
14 students => B => [tex] \frac{14}{45} [/tex] => as percentage, we have [tex] \frac{14}{45} * 100 = 31.1 percent [/tex]
17 students => A => [tex] \frac{17}{45} [/tex] => as percentage, we have [tex] \frac{17}{45} * 100 = 37.8 percent [/tex]
Step 3: Check each statement to see if they are true or not based on the calculations above.
Statement 1: "⅕ of the students earned a C."
This is NOT TRUE From our calculation, ⅑ of the students earned a C.
Statement 2: "3% more students earned an A than a B." This is also NOT TRUE.
37.8% earned A, while 31.1% earned a B. Thus, about 6.7% more students earned an A than a B.
Statement 3: "20% of the class earned a D". This is TRUE.
Check calculation in step 2.
Statement 4: "¼ of the class earned a B". This is NOT TRUE.
¼ is 25% of the class. Those who earned a B account for 31.1% not 25% (¼ of the class).
The correct statement is: "20% of the class earned a D"
-3(-5x-2u+1) use the distributive property to remove the parentheses
Answer:
15x+6u−3
Step-by-step explanation:
This means -3 times -5x, -3 times -2u, and -3 times 1.
Do this and you have, 15x+6u-3.
limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)
Step-by-step explanation:
I(S) = aS / (S + c)
As S approaches infinity, S becomes much larger than c. So S + c is approximately equal to just S.
lim(S→∞) I(S)
= lim(S→∞) aS / (S + c)
= lim(S→∞) aS / S
= lim(S→∞) a
= a
As S approaches infinity, I(S) approaches a.
Your job in a company is to fill quart-size bottles of oil from a full -gallon oil tank. Then you are to pack quarts of oil in a case to ship to a store. How many full cases of oil can you get from a full -gallon tank of oil?
Answer:
See below.
Step-by-step explanation:
1 gal = 4 qt
With a full gallon oil tank, you can fill 4 1-qt bottles.
The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.
Also, is the full tank really only 1 gallon, or is there a number missing there too?
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 72 58 62 38 44 66 42 49 76 52 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
Mean: 55.9
Median: 55
Mode: None
Step-by-step explanation:
First, find the mean by dividing the sum by the number of elements:
(72 + 58 + 62 + 38 + 44 + 66 + 42 + 49 + 76 + 52) / 10
= 55.9
Next, find the median by putting the numbers in order and finding the middle one:
38, 42, 44, 49, 52, 58, 62, 66, 72, 76
There is no middle number, so we will take the average of 52 and 58, which is 55.
Lastly, to find the mode, we have to find the number that occurs the most.
All of the numbers occur one time, so there is no mode.
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F. (Let y be measured in degrees Fahrenheit, and t be measured in seconds.) (a) Determine the cooling constant k. k = s−1 (b) What is the differential equation satisfied by the temperature y(t)? (Use y for y(t).) y'(t) = (c) What is the formula for y(t)? y(t) = (d) Determine the temperature of the bar at the moment it is submerged. (Round your answer to one decimal place.)
Answer:
a. k = -0.01014 s⁻¹
b. [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
c. [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
d. y(t) = 130.485°F
Step-by-step explanation:
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.
(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)
We are to determine :
a. Determine the cooling constant k. k = s−1
By applying the new law of cooling
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]
[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]
Taking the integral.
[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]
㏑ (T -60) = kt + C
T - 60 = [tex]e^{kt+C}[/tex]
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
After 20 seconds, the temperature of the bar submersion is 120°F
T(20) = 120
From equation (1) ,replace t = 20s and T = 120
[tex]120 = 60 + C_1 e^{20 \ k}[/tex]
[tex]120 - 60 = C_1 e^{20 \ k}[/tex]
[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]
After 1 min i.e 60 sec , the temperature = 100
T(60) = 100
From equation (1) ; replace t = 60 s and T = 100
[tex]100 = 60 + c_1 e^{60 \ t}[/tex]
[tex]100 - 60 =c_1 e^{60 \ t}[/tex]
[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]
Dividing equation (2) by (3) , we have:
[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]
[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]
[tex]-40 \ k = In (\dfrac{3}{2})[/tex]
- 40 k = 0.4054651
[tex]k = - \dfrac{0.4054651}{ 40}[/tex]
k = -0.01014 s⁻¹
b. What is the differential equation satisfied by the temperature y(t)?
Recall that :
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]
Since y is the temperature of the body , then :
[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
(c) What is the formula for y(t)?
From equation (1) ;
where;
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
Let y be measured in degrees Fahrenheit
[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]
From equation (2)
[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]
[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]
[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]
[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]
[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
(d) Determine the temperature of the bar at the moment it is submerged.
At the moment it is submerged t = 0
[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]
y(t) = 60 + 70.485
y(t) = 130.485°F
Please help me guys :)
Question:
In exercises 1 through 4, find the one-sided limits lim x->2(left) f(x) and limx-> 2(right) from the given graph of f and determine whether lim x->2 f(x) exists.
Step-by-step explanation:
For a left-hand limit, we start at the left side and move right, and see where the function goes as we get close to the x value.
For a right-hand limit, we start at the right side and move left, and see where the function goes as we get close to the x value.
If the two limits are equal, then the limit exists. Otherwise, it doesn't.
1. As we approach x = 2 from the left, f(x) approaches -2.
lim(x→2⁻) f(x) = -2
As we approach x = 2 from the right, f(x) approaches 1.
lim(x→2⁺) f(x) = 1
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
2. As we approach x = 2 from the left, f(x) approaches 4.
lim(x→2⁻) f(x) = 4
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
3. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are equal, so the limit exists.
lim(x→2) f(x) = 2
4. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches infinity.
lim(x→2⁺) f(x) = ∞
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
Based on a poll, 40% of adults believe in reincarnation. Assume that 4 adults are randomly selected, and find the indicated probability. Complete parts (a) through (d) below.Required:a. The probability that exactly 3 of the 4 adults believe in reincarnation is? b. The probability that all of the selected adults believe in reincarnation is? c. The probability that at least 3 of the selected adults believe in reincarnation is? d. If 4 adults are randomlyselected, is 3 a significantly high number who believe inreincarnation?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]P(3) = 0.154[/tex]
b
[tex]P(4) = 0.026[/tex]
c
[tex]P( X \ge 3 ) = 0.18[/tex]
d
option C is correct
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.4
The sample size is n= 4
This adults believe follow a binomial distribution is because there are only two outcome one is an adult believes in reincarnation and the second an adult does not believe in reincarnation
The probability of failure is mathematically evaluated as
[tex]q = 1 - p[/tex]
substituting values
[tex]q = 1 - 0.4[/tex]
[tex]q = 0.6[/tex]
Considering a
The probability that exactly 3 of the selected adults believe in reincarnation is mathematically represented as
[tex]P(3) = \left n} \atop {}} \right. C_ 3 * p^3 * q^{n-3}[/tex]
substituting values
[tex]P(3) = \left 4} \atop {}} \right. C_ 3 * (0.40)^3 * (0.60)^{4-3}[/tex]
Here [tex]\left 4} \atop {}} \right.C_3[/tex] means 4 combination 3 . i have calculated this using a calculator and the value is
[tex]\left 4} \atop {}} \right.C_3 = 4[/tex]
So
[tex]P(3) = 4* (0.4)^3 * (0.6)[/tex]
[tex]P(3) = 0.154[/tex]
Considering b
The probability that all of the selected adults believe in reincarnation is mathematically represented as
[tex]P(n) = \left n} \atop {}} \right. C_ n * p^n * q^{n-n}[/tex]
substituting values
[tex]P(4) = \left 4} \atop {}} \right. C_ 4 * (0.40)^4 * (0.60)^{4-4}[/tex]
Here [tex]\left 4} \atop {}} \right.C_3[/tex] means 4 combination . i have calculated this using a calculator and the value is [tex]\left 4} \atop {}} \right.C_4 = 1[/tex]
so
[tex]P(4) = 1* (0.4)^4 * 1[/tex]
=> [tex]P(4) = 0.026[/tex]
Considering c
the probability that at least 3 of the selected adults believe in reincarnation is mathematically represented as
[tex]P( X \ge 3 ) = P(3 ) + P(n )[/tex]
substituting values
[tex]P( X \ge 3 ) = 0.154 + 0.026[/tex]
[tex]P( X \ge 3 ) = 0.18[/tex]
From the calculation the probability that all the 4 randomly selected persons believe in reincarnation is [tex]p(4) = 0.026 < 0.05[/tex]
But the the probability of 3 out of the 4 randomly selected person believing in reincarnation is [tex]P(3) = 0.154 \ which \ is \ > 0.05[/tex]
Hence 3 is not a significantly high number of adults who believe in reincarnation because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.
A couple has a total household income of $84,000. The husband earns $18,000 less than twice what the wife earns. How much does the wife earn? Select the correct answer below:
Answer:
$34000
Step-by-step explanation:
We can set up a systems of equations, assuming [tex]h[/tex] is the husbands income and [tex]w[/tex] is the wife's income.
h + w = 84000
h = 2w - 18000
We can substitute h into the equation as 2w - 18000:
(2w - 18000) + w = 84000
Combine like terms:
3w - 18000 = 84000
Add 18000 to both sides
3w = 102000
And divide both sides by 3
w = 34000
Now that we know how much the wife earns, we can also find out how much the husband earns by substituting into the equation.
h + 34000 = 84000
h = 50000
Hope this helped!
An economist is interested in studying the income 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 income of $15,000. What is the width of the 90% confidence interval
Answer:
The width is [tex]w = 282.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The population standard deviation is [tex]\sigma = \$ 1000[/tex]
The sample size is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 90% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{0.10 }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{0.10}{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{1000 }{\sqrt{50 }}[/tex]
=> [tex]E = 141.42[/tex]
The width of the 90% confidence level is mathematically represented as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 141.42[/tex]
[tex]w = 282.8[/tex]
5 STARS IF CORRECT! In general, Can you translate a phrase or sentence into symbols? Explain the answer.
Answer:
Step-by-step explanation:
I answered this already a few minutes ago.
Answer:
yes you can
Step-by-step explanation:
you can write algebraic expressions and use variables for the unknown
f(x)=3x2+10x-25 g(x)=9x2-25 Find (f/g)(x).
Answer:
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Step-by-step explanation:
f(x) = 3x² + 10x - 25
g(x) = 9x² - 25
To find (f/g)(x) divide f(x) by g(x)
That's
[tex](f/g)(x) = \frac{3 {x}^{2} + 10x - 25 }{9 {x}^{2} - 25 } [/tex]
Factorize both the numerator and the denominator
For the numerator
3x² + 10x - 25
3x² + 15x - 5x - 25
3x ( x + 5) - 5( x + 5)
(3x - 5 ) ( x + 5)
For the denominator
9x² - 25
(3x)² - 5²
Using the formula
a² - b² = ( a + b)(a - b)
(3x)² - 5² = (3x + 5)(3x - 5)
So we have
[tex](f/g)(x) = \frac{(3x - 5)(x + 5)}{(3x + 5)(3x - 5)} [/tex]
Simplify
We have the final answer as
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Hope this helps you
Researchers recorded that a certain bacteria population declined from 450,000 to 900 in 30 hours at this rate of decay how many bacteria will there be in 13 hours
Answer:
30,455
Step-by-step explanation:
Exponential decay
y = a(1 - b)^x
y = final amount
a = initial amount
b = rate of decay
x = time
We are looking for the rate of decay, b.
900 = 450000(1 - b)^30
1 = 500(1 - b)^30
(1 - b)^30 = 0.002
1 - b = 0.002^(1/30)
1 - b = 0.81289
b = 0.1871
The equation for our case is
y = 450000(1 - 0.1871)^x
We are looking for the amount in 13 hours, so x = 13.
y = 450000(1 - 0.1871)^13
y = 30,455
please answer this question please
Step-by-step explanation:
C = Amount (A) - Principal (P)
Where
C is the compound interest
To find the amount we use the formula
[tex]A = P ({1 + \frac{r}{100} })^{n} [/tex]
where
P is the principal
r is the rate
n is the period / time
From the question
P = Rs 12, 000
r = 5%
n = 3 years
Substitute the values into the above formula
That's
[tex]A = 12000 ({1 + \frac{5}{100} })^{3} \\ A = 12000(1 + 0.05)^{3} \\ A = 12000 ({1.05})^{3} [/tex]
We have the answer as
Amount = Rs 13891.50Compound interest = 13891.50 - 12000
Compound interest = Rs 1891.50Hope this helps you
A librarian needs to package up all of the children's books and move them to a different location in the library. There are 625 books, and she can fit 25 books in one box. How many boxes does she need in order to move all of the books? 5 B. 25 C. 125 D. 600 E. 650
Answer: B. 25
Step-by-step explanation:
Given: Total books = 625
Number of books can fit in one box = 25
Now, the number of boxes she need to move all of the books = (Total books) ÷ (Number of books can fit in one box )
= 625÷25
= 25
hence, she requires 25 boxes in order to move all of the books.
So, correct option is B. 25.
Write the phrase "the product of 19 and a number" as a mathematical expression.
A 19 + x
B) 19/x
C) 19 x
(D) 19 -x
Answer:
19x
Step-by-step explanation:
product means multiply
19*x
19x
Answer:
The answer is C.
Step-by-step explanation:
if a number and a variable are next to each other, it is assumed they will be multiplied.
sam ran 63,756 feet in 70 minutes what is sam rate in miles per hour there are 5,280 feet in one mile
Answer:
simply convert first feets into miles
Given is 5280 feets=1 miles
63756 /5280=12.075 miles
70 minutes = 1.16666= 1.17 hrs
rate is 12.075 miles/1.17 hrs
Step-by-step explanation:
Each power smoothie that Theo makes has 3 scoops of mango, 1 scoop of strawberries, and 1 scoop of spinach. If Theo makes 7 power smoothies, how many scoops will he use in all?
Answer: 35 scoops total!
Step-by-step explanation: FIrst, you would add the number of scoops in total which is 3+1+1=5 scoops.
Now you would do 7*5=35
Therefore, Theo uses 35 scoops in all. I hope this helps you!
Find the sum to infinity of the series 2+5/4+11/16+23/64+..........up to the infinity.
infinity
We have
[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]
(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)
Recall for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]
4(x/2-2) > 2y-11 which of the following inequalities is equivalent to the inequality above?
1) 4x+2y-3 > 0
2) 4x-2y+3 > 0
3) 2x+2y-3 > 0
4) 2x-26+3 > 0
4) 2x-2y+3 > 0
although it is spelt "26" on the choices
What is the area of polygon EFGH?
A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.
Explain in context the conclusion of the test if H0 is rejected.
Answer:
For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value
Step-by-step explanation:
Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.
Mathematically, the null hypothesis is as expressed as below;
H0: μ = 1,200
The alternative hypothesis H1 would be;
H1: μ > 1,200
Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics
For us to reject the null hypothesis, one of two things, or two things must have occurred.
The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.
If this happens, then we can make a rejection of the null hypothesis
Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize. What is the probability that both of the members of at least one couple win prizes? Express your answer as common fraction.
Answer:
27/35
Step-by-step explanation:
We use combination to solve for this
C(n, r), =nCr = n!/r!(n - r)!
From the question, we are told that:
Four couples are at a party. Four of the eight people are randomly selected to win a prize.
Four couples = 8 people.
= 8C4 = 8!/4! (8 - 4)!
= 70
No person can win more than one prize. ( No person can win more than one prize of the 4 people selected)
This can happen in 4 ways
[4C1 × 3C2 ] × 4=
[4!/1! ×( 4 - 1)!] × [3!/2! ×(3-2)!] × 4 ways
= 4 × 3 × 4 ways
= 48
The probability that both of the members of at least one couple win prizes
48 + 4C2/ 8C4
4C2 = 4!/2!(4 - 2) !
= 6
8C4 = 8C4 = 8!/4! (8 - 4)!
= 70
48 + 6/ 70
= 54/70
= 27/35
Therefore, the probability that both of the members of at least one couple win prizes is 27/35.
The probability that both of the members of at least one couple win prizes is 27/35 and this can be determined by using the given data.
Given :
Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize.The following steps can be used in order to determine the probability that both of the members of at least one couple win prizes:
Step 1 - The concept of probability is used in order to determine the probability that both of the members of at least one couple win prizes.
Step 2 - According to the given data, the total number of people is 8.
Step 3 - So, the probability that both of the members of at least one couple win prizes is:
[tex]\rm P =\dfrac{ \;^4C_1\times \;^3C_2\times 4 + \;^4C_2}{\;^8C_4}[/tex]
Step 4 - Simplify the above expression.
[tex]\rm P =\dfrac{48+ 6}{70}[/tex]
[tex]\rm P = \dfrac{27}{35}[/tex]
So, the probability that both of the members of at least one couple win prizes is 27/35.
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https://brainly.com/question/795909
Yuko added a 15 percent tip when she paid her cab driver. If the fare was $25.50, what was the total amount she paid? A. $28 B. $30 C. $31
Answer:
B. $30
Step-by-step explanation:
First, find the amount of the tip.
Multiply the tip rate and taxi fare.
tip rate * taxi fare
The tip rate is 15% and the taxi fare is $25.50
15% * 25.50
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100=0.15
15.0 ---> 1.5 ---> 0.15
0.15 * 25.50
3.825
The tip amount is $3.825
Next, find the total amount she paid.
Add the taxi fare and the tip amount.
taxi fare + tip amount
The taxi fare is $25.50 and the tip amount is $3.825
$25.50 + $3.825
$29.325
Round to the nearest dollar. Typically, this would round down to $29, but that is not an answer choice. So, if we round up, the next best answer is $30.
Therefore, the best answer choice is B. $30
Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of smoke from a power plant. Assume that σ is in the neighborhood of .5 pH and that you want your estimate to lie within .1 of µ with probability near .95. Approximately how many rainfalls must be included in your sample (one pH reading per rainfall)? Would it be valid to select all of your water specimens from a single rainfall? Explain.
Answer:
The number of rainfalls is [tex]n =96[/tex]
The answer to the second question is no it will not be valid this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid.
Step-by-step explanation:
from the question we are told that
The standard deviation is [tex]\sigma = 0.5[/tex]
The margin of error is [tex]E = 0.1[/tex]
Given that the confidence level is 95% then we can evaluate the level of significance as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha =0.05[/tex]
Next we will obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} * \sigma }}{ E} ]^2[/tex]
substituting values
[tex]n = [\frac{1.96 * 0.5 }{ 0.1} ]^2[/tex]
[tex]n =96[/tex]
The answer to the second question is no the validity is null this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid
Two balls are drawn in succession out of a box containing 5 red and 4 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw. (A) Find the probability that at least 1 ball was red, given that the first ball was replaced before the second draw. StartFraction 24 Over 49 EndFraction (Simplify your answer. Type an integer or a fraction.) (B) Find the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw.
Answer:
The answer is below
Step-by-step explanation:
The box contains 5 red and 4 white balls.
A) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was (Upper A )Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81
P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81
The probability that at least 1 ball was red = 25/81 + 20/81 + 20/81 = 65/81
B) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was not Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)
P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72
The probability that at least 1 ball was red = 20/72 + 20/72 + 20/72 = 60/72