Answers
Answer:
B) 5
Step-by-step explanation:
Proportions:
8 ⇒ 10
20 ⇒ 5x
5x = 20*10/8
5x = 25
x = 25/5
x = 5
Related Questions
A research center poll showed that % of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? 78 The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)
Answers
Question:
A research center poll showed that 78% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)
Answer:
[tex]q = 0.22[/tex]
Step-by-step explanation:
Given
Let p represent the given proportion
p = 78%
Required
Determine the probability that someone holds a contrary belief
Start by converting the given proportion to decimal
[tex]p = 78\%[/tex]
[tex]p = \frac{78}{100}[/tex]
[tex]p = 0.78[/tex]
In probability, the sum of opposite probability is equal to 1
Represent the probability that someone holds a contrary belief with q
So;
[tex]p + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - p[/tex]
Substitute 0.78 for p
[tex]q = 1 - 0.78[/tex]
[tex]q = 0.22[/tex]
Hence, the probability that someone does not believe is 0.22
Choose the correct ray whose endpoint is B.
Answers
Answer:
The second option.
Step-by-step explanation:
The first option consists of a line that extends at both opposite sides to infinity, with no precise end.
The third option is a ray that has an endpoint of A, and extends to infinity towards B.
The fourth option is a line segment. It has two endpoints, B and A.
The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.
The answer is the 2nd option.
Let R be a system consisting of rational expressions. Which operations are closed for R?
Answers
Answer:
D
Step-by-step explanation:A set is said to be closed under an operation when the application of the operation between any two elements of the set leads to an element that belongs to the same set. If a set is closed under an operation, it is said to have the closure property of that operation. When we combine two rational expressions by adding, subtracting, multiplying, or dividing, we get a rational expression. This pattern indicates that rational expressions are closed for all four operations.
A box contain 12 balls in which 4 are white 3 are blue and 5 are red.3 balls are drawn at random from the box.find the chance that all three are selected
Answers
Answer:
3/11
Step-by-step explanation:
In the above question, we have the following information
Total number of balls = 12
White balls = 4
Blue balls = 3
Red balls = 5
We are to find the chance of probability that if we select 3 balls, all the three are selected.
Hence,
Probability ( all the three balls are selected) = P(White ball) × P(Blue ball) × P( Red ball)
Probability ( all the three balls are selected) = 4/12 × 3/11 × 5/10
= 60/1320
= 1/22
The number of ways by which we can selected all the three balls is a total of 6 ways:
WBR = White, Blue, Red
WRB = White, Red, Blue
RBW = Red, Blue, White
RWB = Red, White, Blue
BRW = Blue, Red, White
BWR = Blue, White, Red
Therefore, the chance that all three are selected :
1/22 × 6 ways = 6/22 = 3/11
Assume the triangular prism has a base area of 49cm^2 and a volume of 588cm^3. What side length does the rectangular prism need to have the same volume?
Answers
Answer:
Length = Width = 7 cm
Step-by-step explanation:
Volume of a triangular prism is represented by the formula,
Volume = (Area of the triangular base) × height
588 = 49 × h
h = [tex]\frac{588}{49}[/tex]
h = 12 cm
We have to find the side length of a rectangular prism having same volume.
Volume = Area of the rectangular base × height
588 = (l × b) × h [l = length and b = width ]
588 = (l × b) × 12
l × b = 49 = 7 × 7
Therefore, length = width = 7 cm may be the side lengths of the rectangular prism to have the same volume.
PLS HELP:Find all the missing elements:
Answers
Answer:
b = 9.5 , c = 15Step-by-step explanation:
For b
To find side b we use the sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |b| }{ \sin(B) } [/tex]a = 7
A = 23°
B = 32°
b = ?
Substitute the values into the above formula
That's
[tex] \frac{7}{ \sin(23) } = \frac{ |b| }{ \sin(32) } [/tex][tex] |b| \sin(23) = 7 \sin(32) [/tex]Divide both sides by sin 23°
[tex] |b| = \frac{7 \sin(32) }{ \sin(23) } [/tex]b = 9.493573
b = 9.5 to the nearest tenthFor cTo find side c we use sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]C = 125°
So we have
[tex] \frac{7}{ \sin(23) } = \frac{ |c| }{ \sin(125) } [/tex][tex] |c| \sin(23) = 7 \sin(125) [/tex]Divide both sides by sin 23°
[tex] |c| = \frac{7 \sin(125) }{ \sin(23) } [/tex]c = 14.67521
c = 15.0 to the nearest tenthHope this helps you
You know only the given information about
the measures of the angles of a triangle. Find the probability that the triangle is equiangular.
39. Each is a multiple of 12.
Answers
Since they are multiples if 12
The possibilities are
12, 12, 156
12,24,144
12,36,132
12,48,120
12,60,108
12,72,96
12,84,84
24,24,132
24,36,120
24,48,108
24,60,96
24,72,84
36,36,108
36,48,96
36,60,84
36,72,72
48,48,84
48,60,72
60,60,60
Hence the probability is 1/19 or 0.0526
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two. What is the probability of no defects in 10 feet of steel
Answers
Answer:
the probability of no defects in 10 feet of steel = 0.1353
Step-by-step explanation:
GIven that:
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.
Let consider β to be the average value for defecting
So;
β = 2
Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.
Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2
i.e
[tex]Y \sim P( \beta = 2)[/tex]
the probability mass function can be represented as follows:
[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]
where;
y = 0,1,2,3 ...
Hence, the probability of no defects in 10 feet of steel
y = 0
[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]
[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]
P(y =0) = 0.1353
A football team starts on the 10 yard line moving toward the 50 yard line so they can score on the other side of the field. In three plays they gain 14 yards, lose 12 yards, and gain 4 more yards. What yard line do they start their fourth play?
Answers
Answer:
16 yard line
Step-by-step explanation:
The football team is starting on the 10 yard line. In the first play, they move up to the 24 yard line. Then in the second play, they go back to the 12 yard line since they lost 12 yards. Then in the third play, they gain 4 yards so you add 4 to 12. They end up at the 16 yard line after the third play. This means that they're going to start their fourth play at the 16 yard line.
Answer:
16 yards.
Step-by-step explanation:
They start at 10 yards. They are moving towards the 50 yard line, so gaining yards will add to the 10 yards instead of subtract from the 10 yards.
In the first play, they gain 14 yards. 10 + 14 = 24 yards.
In the second play, they lose 12 yards. 24 - 12 = 12 yards.
In the third play, they gain 4 yards. 12 + 4 = 16 yards, which is where they start their fourth play.
Hope this helps!
How many cabinets must he sell to break even?
Answers
Answer: He must sell 7 cabinets.
Step-by-step explanation:
So it gives us the equations y= 400x + 1400 and the equations y=600x and to find the break even point we need to set the two equations equal each other to solve for x.
400x + 1400 = 600x
-400x -400x
1400 = 200x
x = 7
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answers
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain. Yes, since the coin is fair. No, each outcome is equally likely regardless of the previous outcome. Yes, tails will always result on the second toss. No, tails will never occur on the second toss.
Answers
Answer:
No, each outcome is equally likely regardless of the previous outcome.
Let A and B be events. The symmetric difference A?B is defined to be the set of all elements that are in A or B but not both.
In logic and engineering, this event is also called the XOR (exclusive or) of A and B.
Show that P(AUB) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.
Answers
Correction:
P(AΔB) = P(A) + P(B) - 2P(AnB)
is what could be proven using the axioms of probability, and considering the case of symmetric difference given.
Answer:
P(AΔB) = P(A) + P(B) - 2P(AnB)
Has been shown.
Step-by-step explanation:
We are required to show that
P(AUB) = P(A) + P(B) - 2P(AnB)
directly using the axioms of probability.
Note the following:
AUB = (AΔB) U (AnB)
Because (AΔB) U (AnB) is disjoint, we have:
P(AUB) = P(AΔB) + P(AnB)..................(1)
But again,
P(AUB) = P(A) + P(B) - P(AnB)...............(2)
Comparing (1) with (2), we have
P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)
P(AΔB) = P(A) + P(B) - 2P(AnB)
Where AΔB is the symmetric difference of A and B.
If possible, find AB. & State the dimension of the result.
Answers
Answer:
The answer is "[tex]AB= \left[\begin{array}{cc} -2 &51 \\-8&33\\0&27&\end{array}\right][/tex]"
Step-by-step explanation:
If the value of A and B is:
[tex]A= \left[\begin{array}{cc}-1&6\\-4&5\\0&3\end{array}\right][/tex]
[tex]B=\left[\begin{array}{cc}2&3\\0&9\end{array}\right][/tex]
Find the value of A[tex]\times[/tex]B:
[tex]AB =\left[\begin{array}{cc}-1 \times 2+6 \times 0 &-1 \times 3+6 \times 9\\ -4 \times 2+5 \times 0& -4 \times 3+5 \times 9\\ 0 \times 2+3 \times 0&-1 \times 2+3\times 9\end{array}\right] \\ \\\\AB =\left[\begin{array}{cc}-2+0 &- 3+54\\ -8+0& -12+45\\ 0+ 0&-2 +27\end{array}\right] \\ \\[/tex]
[tex]AB= \left[\begin{array}{cc} -2 &51 \\-8&33\\0&27&\end{array}\right][/tex]
a westward moving motorcycle slows down from 24.0 m/a to 12.0 m/s in 3.0 seconds. what is the magnitude and direction of the acceleration
Answers
Answer:
0
Step-by-step explanation:
In a study of academic procrastination, researchers reported that for a random sample of 41 undergraduate students preparing for a psychology exam, the mean time spent studying was 11.9 hours with a standard deviation of 4.5 hours. Compute a 95% confidence interval for μ, the mean time spent studying for the exam among all students taking this course.
Answers
Answer:
The 95% confidence interval is [tex]10.5 < \mu <13.3[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 41[/tex]
The sample mean is [tex]\= x = 11.9 \ hr[/tex]
The standard deviation is [tex]\sigma = 4.5[/tex]
For a 95% confidence interval the confidence level is 95%
Given that the confidence level is 95% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical values of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 4.5 }{ \sqrt{41} }[/tex]
[tex]E = 1.377[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x - E[/tex]
substituting values
[tex]11.9 - 1.377 < \mu <11.9 + 1.377[/tex]
[tex]10.5 < \mu <13.3[/tex]
An airline claims that the proportion of no-shows for passengers who booked on its flights is less than 0.06. In a random sample of 380 reservations, 19 were no-shows. A hypothesis test is to be performed to test the airline's claim that the proportion of no-shows on its flights is less than 0.06. Calculate the test statistic associated with this sample. An airline claims that the proportion of no-shows for passengers who booked on its flights is less than 0.06. In a random sample of 380 reservations, 19 were no-shows. A hypothesis test is to be performed to test the airline's claim that the proportion of no-shows on its flights is less than 0.06. Calculate the test statistic associated with this sample.
Answers
Answer:
≈ -0.821
Step-by-step explanation:
Given:
n= 380, samplex= 19, no-shows countp = 0.06, proportion of no-showsThen, the sample proportion is:
p' = x/n = 19/ 380 = 0.05Hypothesis test:
H₀: p = 0.06H₁: p< 0.06Test statistics:
z = (p' - p) /[tex]\sqrt{p(1-p)/n}[/tex] z = (0.05 - 0.06)/[tex]\sqrt{006(1-0.06)/380}[/tex] ≈ -0.821Sharvay spends $15 to buy 17 pieces of candy. M&M’s cost $0.75 and candy bars cost $1. How many M&M’s and candy bars did Sharvay buy?
Answers
Answer:
8 M&Ms and 9 Candy Bars
Step-by-step explanation:
$15 dollars could buy 15 candy bars, and there are 17 pieces of candy total.
Prioritizing the number of bars:
0.75 * 2 = 1.50
1.50 * 2 = 3
At least $3 were spend on M&Ms, meaning 4 M&Ms and 12 candy bars, which is only 16 candy pieces...
8 M&Ms and 9 candy bars is equivalent to 17 total candy pieces.
Given the set of data: 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25 a. Find the mode. b. Find the median. c. Find the mean, to the nearest tenth. d. Find the midrange. e. Find the standard deviation, to the nearest hundredth. f. Determine the quartiles.
Answers
Answer: a. 43
b. 27
c. 34.8
d. 45
e. 17.72
f. First quartile = 23
Second quartile = 27
Third quartile =43
Step-by-step explanation:
The given set of data: 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25
Arrange in Ascending order:
12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25 , 29, 31, 43, 43 , 43 , 53 , 53, 65 , 78
Total data points: n= 18 ( even)
a. Mode= Most repeated data value = 43
i.e. mode =43
b. Median = [tex]\dfrac{(\frac{n}{2})^{th}\text{term}+(\frac{n}{2}+1)^{th}\text{term}}{2}[/tex]
[tex]=\dfrac{(\frac{18}{2})^{th}\text{term}+(\frac{18}{2}+1)^{th}\text{term}}{2}\\\\=\dfrac{9^{th}\text{term}+10^{th}\text{term}}{2}\\\\=\dfrac{25+29}{2}\\\\=27[/tex]
i.e. median = 27
c. Mean = (sum of data points)÷n
Sum =12+18+18 + 20 +23 +24 + 24 +25 + 25 + 29+ 31+ 43+ 43 + 43 + 53 + 53+ 65 + 78=627
Mean = 627 ÷ 18 ≈34.8
i.e. Mean = 34.8
d. Mid range = [tex]\dfrac{\text{Maximum value +Minimum value}}{2}[/tex]
[tex]=\dfrac{78+12}{2}\\\\=\dfrac{90}{2}\\\\=45[/tex]
e. Standard deviation =[tex]\sqrt{\dfrac{\sum (x-mean)^2}{n}}[/tex][tex]\sum (x-\mean)^2=(12-34.8)^2+(18-34.8)^2+(18 -34.8)^2+( 20 -34.8)^2+(23 -34.8)^2+(24 -34.8)^2+( 24 -34.8)^2+(25 -34.8)^2+2( 25 -34.8)^2+( 29-34.8)^2+( 31-34.8)^2+( 43-34.8)^2+( 43 -34.8)^2+( 43 -34.8)^2+( 53 -34.8)^2+( 53-34.8)^2+( 65 -34.8)^2+( 78-34.8)^2\\\\=5654.56[/tex]
[tex]\sqrt{\dfrac{5654.56}{18}}=\sqrt{314.1422}\approx17.72[/tex]
f. First quartile = Median of first half (12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25)
= 23 (middle most value)
Second quartile = Median = 27
Third quartile = Median of second half (29, 31, 43, 43 , 43 , 53 , 53, 65 , 78)
= 43 (middle most value)
What is an equation of the line that passes through the points (2, -7) and (8, -4)?
Answers
Answer:
The answer is
[tex]y = \frac{1}{2} x - 8[/tex]Step-by-step explanation:
To find the equation of the line that passes through two points , first find the slope and then use the formula
y - y1 = m(x - x1)
where m is the slope
(x1 , y1) are any of the points
To find the slope of the line using two points we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Slope of the line using points
(2, -7) and (8, -4) is
[tex] \frac{ - 4 + 7}{8 - 2} = \frac{3}{6} = \frac{1}{2} [/tex]Now the equation of the line using point (2 , - 7) and slope 1/2 is
[tex] y + 7 = \frac{1}{2} (x - 2)[/tex][tex]y + 7 = \frac{1}{2} x - 1[/tex][tex]y = \frac{1}{2} x - 1 - 7[/tex]We have the final answer as
[tex]y = \frac{1}{2} x - 8[/tex]Hope this helps you
The first step in a mathematical induction proof is to divide by n. (True or False).
Answers
Answer:
Step-by-step explanation:
Hello, this is false.
The first step of a mathematical induction proof is to prove the statement for the initial value, which is most of the time for n = 0 or n = 1.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which part of an I-statement involves a description of your needs or feelings?
Answers
Answer:
the answer is c
Step-by-step explanation:
Rewrite the expression as an equivalent ratio of logs using the indicated base.log17(52.875) to base 10.
Answers
Answer:
[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Step-by-step explanation:
Given
[tex]log_{17}(52.875)[/tex]
Required
Convert to base 10
To do this, we make use of the following logarithm laws;
[tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]
In the given parameters;
[tex]a = 52.875[/tex]
[tex]b = 17[/tex]
Substitute these values in [tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]
[tex]log_{17}52.875 = \frac{log_{10}52.875}{log_{10}17}[/tex]
Represent as a ratio
[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Hence;
[tex]log_{17}(52.875)[/tex] is represented as [tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Expression [tex]log_{17} 52.875[/tex] can be written as in form of ratio of log [tex]\frac{log_{10} 52.875}{log_{10} 17}[/tex] .
Any logarithmic expression [tex]log_{a} b[/tex] can we written as in form of ratio of log on base 10.
[tex]log_{a} b=\frac{log_{10} b}{log_{10} a}[/tex]
Here logarithmic expression is, [tex]log_{17} 52.875[/tex] comparing with above expression.
We get, [tex]b=52.875,a=17[/tex]
Substitute values of a and b in above expression.
We get, [tex]log_{17} 52.875=\frac{log_{10} 52.875}{log_{10} 17}[/tex]
Learn more:
https://brainly.com/question/12049968
What is the solution to the linear equation?
2/5 + p = 4/5 + 3/5p
Answers
Answer:
p = 1Step-by-step explanation:
[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]
Multiply through by the LCM
The LCM for the equation is 5
That's
[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]
We have
2 + 5p = 4 + 3p
Group like terms
5p - 3p = 4 - 2
2p = 2
Divide both sides by 2
We have the final answer as
p = 1Hope this helps you
What is the image of point (8,-4) under the rotation R90° about the origin?
A) (8,4)
B) (4,8)
C) (-4,8)
D) (-4,-8)
Answers
Answer:
D). (-4,-8)
Step-by-step explanation:
An image at (8,-4) if rotated at an angle of 90° wipl have another location.
First of all, an image at (8,-4) is in the fourth quadrant, and if it's to rotate clockwise at 90° iths supposed to be in the third quadrant.
And in the third quadrant both x and y is negative.
So the new position is at (-4,-8)
Complete each equation with a number that makes it true. 5⋅______=15 4⋅______=32 6⋅______=9 12⋅______=3
Answers
Answer: blank 1: 3 Blank 2: 8 blank 3: 1.5 blank 4: 0.25
Step-by-step explanation:
5 times 8=15
4 times 8=32
6 times 1.5=9
12 times 0.25=3
The complete equation is
5⋅____3__=15
4⋅___8___=32
6⋅___1.5___=9
12⋅__0.25____=3
What is Multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.
Multiplication Formula
The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:
Multiplicand: The first number (factor).Multiplier: The second number (factor).Product: The final result after multiplying the multiplicand and multiplier.Multiplication symbol: '×' (which connects the entire expression)5 * 3=154 * 8=326 * 1.5=912 * 0.25=3Learn more about multiplication here:
https://brainly.com/question/5992872
#SPJ2
Consider a bag of jelly beans that has 30 red, 30 blue, and 30 green jelly beans. a) How many color combinations of 15 beans have at least 6 green beans
Answers
Answer:
680
Step-by-step explanation:
Number of red beans = 30
Number of Blue beans = 30
Number of green beans = 30
How many color combinations of 15 beans have at least 6 green beans?
Since at least 6 of the beans must be green,
Then (15 - 6) = 9
Then, the remaining 9 could be either red, blue or green.
Therefore, C(9 + (9 - 1), 3)
C(17, 3) = 17C3
nCr = n! ÷ (n-r)! r!
17C3 = 17! ÷ (17 - 3)! 3!
17C3 = 17! ÷ 14!3!
17C3 = (17 * 16 * 15) / (3 * 2)
17C3 = 4080 / 6
17C3 = 680 ways
Using the combination formula, it is found that there are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.
The order in which the beans are chosen is not important, hence, the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Th total number of combinations of 15 beans from a set of 30 + 30 + 30 = 90 is:
[tex]C_{90,15} = \frac{90!}{15!75!} = 45795674000000000[/tex]
With less than 6 green, we have:
0 green:
[tex]C_{30,0}C_{60,15} = \frac{60!}{15!45!} = 53194089000000[/tex]
1 green:
[tex]C_{30,1}C_{60,14} = \frac{30!}{1!29!} \times \frac{60!}{14!46!} = 520376960000000[/tex]
2 green:
[tex]C_{30,2}C_{60,13} = \frac{30!}{2!28!} \times \frac{60!}{13!47!} = 2247585600000000[/tex]
3 green:
[tex]C_{30,3}C_{60,12} = \frac{30!}{3!27!} \times \frac{60!}{12!48!} = 5681396900000000[/tex]
4 green:
[tex]C_{30,4}C_{60,11} = \frac{30!}{4!26!} \times \frac{60!}{11!49!} = 9391696900000000[/tex]
5 green:
[tex]C_{30,5}C_{60,10} = \frac{30!}{5!25!} \times \frac{60!}{10!50!} = 10744101000000000[/tex]
Hence, the total for the number of combinations with less than 5 green is:
[tex]53194089000000 + 520376960000000 + 2247585600000000 + 5681396900000000 + 9391696900000000 + 10744101000000000 = 28638351000000000[/tex]
Subtracting the total amount of combinations from the number with less than 5 green, the number of combinations with at least 6 green is:
[tex]T = 45795674000000000 - 28638351000000000 = 17157323000000000[/tex]
There are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.
A similar problem is given at https://brainly.com/question/24437717
) If the half-life of 238Pu is 87.7 yr, write a function of the form =QtQ0e−kt to model the quantity Qt of 238Pu left after t years. Round the value of k to five decimal places. Do not round intermediate calculations.
Answers
Answer:
0.079
Step-by-step explanation:
According to the given situation, the calculation of the value of k is presented as follows:
[tex]Q(t)= Q_0e^{-kt}\\\\ 0.5Q_0 = Q_0e^{-k(97.7)}\\\\ 0.5 = e^{-k(87.7)}[/tex]
now,
[tex]k = \frac{In0.5}{-87.7}[/tex]
After solving the above equation we will get the value of k.
= 0.079
Therefore for determining the value of k we simply solve the above equation i.e. by considering all the information mentioned in the question
Answer:
3.5e^-0.0079t
Step-by-step explanation:
None, Good luck mate
What is lim x → 0 e^2x - 1/ e^x - 1
Answers
Hello, please consider the following.
[tex]\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }[/tex]
Thank you
Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 5x − 4 x(x2 + 7)2
Answers
Answer:
[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{5x-4}{x(x^2+7)^2}[/tex], we are to re-write the expression in form of a partial fraction.
Before we write in form of a partial fraction, we need to note the expression at the denominator. Since the expression in parenthesis is a quadratic equation, the equivalent numerator must be a linear expression.
Also the quadratic equation is a repeated form since it is squared. This means that we are to repeat the quadratic equation twice when writing as a partial fraction.
[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]
From the above partial fraction, it can be seen that x² + 7 in parenthesis was repeated twice and their equivalent expressions at the numerator are both linear i.e Bx+E and Dx+ E where A, B, C, D and E are the unknown constant.
