Answer:
(a) The average baggage-related revenue per passenger is $15.70.
(b) The standard deviation of baggage-related revenue is $19.95.
(c) The expected revenue for 120 passengers is $1,884.
Step-by-step explanation:
Let the random variable X represent the baggage-related revenue per passenger.
It is provided that the baggage fees is $25 for the first bag and $35 for the second.
The probability model is:
X : 0 25 60
P (X) : 0.54 0.34 0.12
(a)
Compute the average baggage-related revenue per passenger as follows:
[tex]E(X)=\sum {X\times P (X)}[/tex]
[tex]=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70[/tex]
Thus, the average baggage-related revenue per passenger is $15.70.
(b)
Compute the standard deviation of baggage-related revenue as follows:
[tex]E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\[/tex]
[tex]SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}[/tex]
[tex]=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95[/tex]
Thus, the standard deviation of baggage-related revenue is $19.95.
(c)
Compute the expected revenue for 120 passengers as follows:
[tex]E(R)=n\times E(X)[/tex]
[tex]=120\times 15.7\\\\=1884[/tex]
Thus, the expected revenue for 120 passengers is $1,884.
What is the insignificant digit in 0.09040?
Answer:
0
Step-by-step explanation:
The 0, or the last digit is the insignificant digit because it serves no purpose.
Answer:
The last zero in the number is insignificant.
Step-by-step explanation:
The 0 at the extreme right indicates that the number is accurate to the fifth decimal place, that is, one in ten thousandths.
Let mu denote the true average number of minutes of a television commercial. Suppose the hypothesis H0: mu = 2.1 versus Ha: mu > 2.1 are tested. Assuming the commercial time is normally distributed, give the appropriate rejection region when there is a random sample of size 20 from the population and we would like to test at the level of significance 0.01. Let T be the appropriate test statistic.
A, T > 2.539
B. > 2.845
C. T> .528D. T >2.861
Answer:
A. T > 2.539
Step-by-step explanation:
We have a hypothesis test of the mean, with unknown population standard deviation.
The hypothesis are:
[tex]H_0: \mu = 2.1 \\\\H_a: \mu > 2.1[/tex]
From the hypothesis we can see that the test is right-tailed, so the critical value of t should be a positive value.
The degrees of freedom can be calculated as:
[tex]df=n-1=20-1=19[/tex]
The significance level is 0.01, so the critical value tc should be the one that satisfies:
[tex]P(t>t_c)=0.01[/tex]
Looking up in a t-table, for 19 degrees of freedom, this critical value is tc=2.539.
samantha is making punch for a class picnic. there are 25 students in her class. Samantha uses 1 gallon 2 quarts of orange juice, 3 quarts of lemonade, and 1 gallon 3 quarts of sparkling water. How much punch did samantha make? will there be enough for each student to make two 1 cup servings of punch?
Answer:
4 gallonsyesStep-by-step explanation:
A quart is 1/4 gallon, so the total of liquid ingredients for the punch is ...
(1 2/4 gal) +(3/4 gal) +(1 3/4 gal) = 2 8/4 gal = 4 gal
Samantha made 4 gallons of punch.
__
1 cup is 1/16 gallon, so 2 cups each for 25 students requires ...
(1/16 gal)(2)(25) = 50/16 gal = 3 1/8 gal
Samantha made more punch than that, so there will be enough for 2 1-cup servings for each student.
Can someone help me with this is the hardest one by far
Answer:
10 units
Explanation:
Create a right triangle, determine the a and b side lengths of the triangle by looking at the graph. (See image)
Then use the Pythagorean theorem to find c.
a² + b² = c²
(8)² + (6)² = c²
64 + 36 = c²
100 = c²
Square root both sides to get c.
[tex]\sqrt{100}[/tex] = c
10 = c
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Frequency Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100 Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the critical value is:
Answer:
The degrees of freedom are given by;
[tex] df =n-1= 5-1=4[/tex]
The significance level is 0.1 so then the critical value would be given by:
[tex] F_{cric}= 7.779[/tex]
If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays
Step-by-step explanation:
For this case we have the following observed values:
Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100
For this case the expected values for each day are assumed:
[tex] E_i = \frac{100}{5}= 20[/tex]
The statsitic would be given by:
[tex] \chi^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i}[/tex]
Where O represent the observed values and E the expected values
The degrees of freedom are given by;
[tex] df =n-1= 5-1=4[/tex]
The significance level is 0.1 so then the critical value would be given by:
[tex] F_{cric}= 7.779[/tex]
If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays
(AAAA HELP PLS XD WILL MARK BRAINLIEST) Nhia is setting up a marble tournament for the kids in her
apartment complex. So far, 47 kids have signed up to play. Each
player needs 10 marbles. Nhia found a discount store that sells
bags of 24 marbles. Round each amount to the nearest ten to find
a reasonable estimate for the number of bags of marbles Nhia will
have to buy to be sure to have enough marbles.
A) 18
B) 25
C) 32
D) 39
Given that we have 47 kids and each kid needs 10 marbles, find out how many bags of 24 marbles will we need.
First, we will multiply 47 by 10 to get the amount of marbles needed.
47 x 10 = 470
So, that means we need 470 marbles in total.
Then, we divide 470 by 24 to see how many bags of 24 marbles 470 marbles is.
470 / 24 = 19.5833
Since, we can't have 19.5833 bags, we have to check what it would be if we only used 19.
19 x 24 = 456
470 - 456 = 14
Since, 18 is the closest number of bags but it has less than 470 it would not be correct.
Therefore, the best answer would be B. 25 since it is better to have extra marbles but not a very wide margin.
Dan earns £388 over the course of a five-day week. How much is that per day?
Answer:
£77.6 per day
Step-by-step explanation:
388/5 = 77.6
Answer:
£77.60
Step-by-step explanation:
388/5=77.6
but remember that this is money so add the 0.
Eric’s average income for the first 4 months of the year is $1,450.25, what must be his
average income for the remaining 8 months so that his average income for the year is
$1,780.75?
Answer:
$1946
Step-by-step explanation:
Eric’s average income for the first 4 months of the year is $1,450.25
Therefore, his total earning in the first four months
= 4 X $1,450.25
=$5,801
Let the average income for the remaining 8 months= x
Then:
[tex]\text{Eric's Yearly Average Income}=\dfrac{5801+8x}{12} \\1,780.75=\dfrac{5801+8x}{12} \\$Cross multiply\\12*1,780.75=5801+8x\\21369=5801+8x\\8x=21369-5801\\8x=15568\\Divide both sides by 8\\x=\$1946[/tex]
Therefore, to get an average income for the year of $1,780.75, Eric must earn an average income of $1946 for the remaining 8 months.
Solve for x.
Solve for x.
Answer:
20
Step-by-step explanation:
x is the radius of the circle. The tangent line is perpendicular to the radius line at that point. Using Pythagorean theorem:
x² + 15² = (x + 5)²
x² + 225 = x² + 10x + 25
225 = 10x + 25
200 = 10x
x = 20
Answer is:
x = 20. hope this helps
What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
A tangent to a circle forms a right angle with the radius
As it is a right angled triangle, we can use Pythagoras' theorem
a^2 + b^2 = c^2
Rearrange this for a side length:
a^2 = c^2 - b^2
Sub the values in:
a^2 = 6.5^2 - 6^2
a^2 = 6.25
Square root this for the answer
a = 2.5
Thus, your answer is option D
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
2.5 ft
Step-by-step explanation:
As radius is perpendicular to tangent ,
LT [tex]\perp[/tex]KT
By pythagoras theorem:
LT² = LK² - KT²
LT² = (6.5)² - 6²
LT² = 42.25 - 36
LT² = 6.25
LT = 2.5 ft
LT = radius = 2.5 ft
PLEASE HELP I DON'T UNDERSTAND THE QUESTION. THANK YOU :)
ABC and DEC are similar, since the line segments AB and DE are parallel.
This means corresponding sides of these triangles occur in a fixed ratio with one another.
In particular, this tells us
DE/AB = DC/AC
or
7/11 = 15/(15 + x)
Solve for x:
11/7 = (15 + x)/15
11/7 = 1 + x/15
4/7 = x/15
x = 60/7
Some smells are perceived as being more feminine or more masculine. Researchers asked a random sample of 300 American adults to score quantitatively the perceived gender-orientation of lavender. Smaller scores indicate a more feminine scent and larger scores a more masculine scent. In this design, a gender-neutral scent would have a perceived gender-orientation score of 12. The participants gave the scent of lavender an average score of 10.28
a. Is this evidence that the scent of lavender is not gender-neutral, on average? State H0cap h sub zero and Hacap h sub a in the corresponding test, indicating what the parameter in your hypotheses is.
b.The researchers report that "p<.01p less than full stop 01 (2-tail)" for this test. Explain the meaning of "p<.01p less than full stop 01" and "2-tail."
c.Assuming that the conditions for inference were met, conclude in the context of this study.
Answer:
a) We are told smaller scores indicate a more feminine scent and larger scores a more masculine scent, also a score of 12 represents a gender-neutral scent.
Here the average from the sample for lavender is 10.28
To test for the evidence that lavender is not gender neutral on average, the null hypothesis H0 would take that lavender is gender-neutral, while the alternative hypothesis would take that the score of lavender is not gender neutral. We now have the null and alternative hypotheses as:
H0 : u = 12
H1 : u ≠ 12
Here, u represents the mean gender-orientation score for lavender. The alternative is two sided because we want to test if lavender is not gender neutral. Which means lavender might be more masculine of more feminine.
b) Given: p < 0.01 (2 tailed)
This means the p-value is less than level of significance 0.01.
Since the pvalue is less than the level of significance, we reject null hypothesis H0. This means there is sufficient evidence to conclude that the smell is not gender-neutral.
There is no reason to prefer a particular gender, that's why this is a two tailed hypothesis.
c) c.Assuming that the conditions for inference were met, which means the p-value is less than 0.01 so the null hypothesis H0 is rejected.
The conlusion would be that there is enough evidence to conclude that lavender is not gender-neutral
Joe says, "I have found an interesting fact! Twenty-five percent of thirty dollars is
the same as thirty percent of twenty-five dollars." Is Joe correct? Please explain
your thinking to show that Joe is right or wrong.
Answer:
Joe Is RightStep-by-step explanation:
Twenty-five percent of thirty dollars is $7.50
(30 x 25)/100 = $7.50
Thirty percent of twenty-five dollars is $7.50
(25 x 30)/100 = $7.50
Therefore he is right
I hope this helps
Sophie Ruth is eating a 50-gram chocolate bar which contains 30 percent cocoa.
How many grams of cocoa are in the chocolate bar?
grams
hope it helps :] !!!!!!
Answer:
15 grams hope this helps
Hal has 24 video games 6 if his games are sports related and the rest are role playing games which ratio represent the number of his role playing games
Answer:
It would be 18;24 or simplified it would be 3;4
Step-by-step explanation:
24-6=18 so there are 18 role playing games. So the ratio could be 18;24 but if it needs to be simplified you can divide both numbers by 6. 18/6=3 and 24/6=4
what are the solutions to the following system -2x^2+y= -5 y= -3x^2+5
[tex](x1,y1)= (- \frac{\sqrt{15} }{2} , \frac{5}{4} )\\(x2,y2)= (\frac{\sqrt{15} }{2} ,\frac{5}{4} )[/tex]
Answer:
Answer C.
Step-by-step explanation:
hope this helps <3
pls help i give brainliest
you buy a bag of crisps in an airport.After take off you take the crisps out of your ruck sack why has the bag expanded
Answer:
Step-by-step explanation:
there is a pressure difference between inside and outside the container and if the — bag, bottle, whatever — is flexible enough it will either expand as the ambient air pressure decreases when climbing or collapse when the aircraft is descending and the pressure is increasing.......
this is ur answer ....
Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69. Group of answer choices Men aged 20-29: 4.8% Men aged 60-69: 10.6% There is substantially more variation in blood pressures of the men aged 60-69. Men aged 20-29: 4.4% Men aged 60-69: 8.3% There is substantially more variation in blood pressures of the men aged 60-69. Men aged 20-29: 4.6% Men aged 60-69: 10.2 % There is substantially more variation in blood pressures of the men aged 60-69. Men aged 20-29: 7.6% Men aged 60-69: 4.7% There is more variation in blood pressures of the men aged 20-29.
Here is the correct computation of the question given.
Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69.
Men aged 20-29: 117 122 129 118 131 123
Men aged 60-69: 130 153 141 125 164 139
Group of answer choices
a)
Men aged 20-29: 4.8%
Men aged 60-69: 10.6%
There is substantially more variation in blood pressures of the men aged 60-69.
b)
Men aged 20-29: 4.4%
Men aged 60-69: 8.3%
There is substantially more variation in blood pressures of the men aged 60-69.
c)
Men aged 20-29: 4.6%
Men aged 60-69: 10.2 %
There is substantially more variation in blood pressures of the men aged 60-69.
d)
Men aged 20-29: 7.6%
Men aged 60-69: 4.7%
There is more variation in blood pressures of the men aged 20-29.
Answer:
(c)
Men aged 20-29: 4.6%
Men aged 60-69: 10.2 %
There is substantially more variation in blood pressures of the men aged 60-69.
Step-by-step explanation:
From the given question:
The coefficient of variation can be determined by the relation:
[tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]
We will need to determine the coefficient of variation both men age 20 - 29 and men age 60 -69
To start with;
The coefficient of men age 20 -29
Let's first find the mean and standard deviation before we can do that ;
SO .
Mean = [tex]\dfrac{\sum \limits^{n}_{i-1}x_i}{n}[/tex]
Mean = [tex]\frac{117+122+129+118+131+123}{6}[/tex]
Mean = [tex]\dfrac{740}{6}[/tex]
Mean = 123.33
Standard deviation [tex]= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }[/tex]
Standard deviation =[tex]\sqrt{\dfrac{(117-123.33)^2+(122-123.33)^2+...+(123-123.33)^2}{(6-1)} }[/tex]
Standard deviation = [tex]\sqrt{\dfrac{161.3334}{5}}[/tex]
Standard deviation = [tex]\sqrt{32.2667}[/tex]
Standard deviation = 5.68
The [tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]
[tex]coefficient \ of \ variation = \dfrac{5.68}{123.33}*100[/tex]
Coefficient of variation = 4.6% for men age 20 -29
For men age 60-69 now;
Mean = [tex]\dfrac{\sum \limits^{n}_{i-1}x_i}{n}[/tex]
Mean = [tex]\frac{ 130 + 153 + 141 + 125 + 164 + 139}{6}[/tex]
Mean = [tex]\dfrac{852}{6}[/tex]
Mean = 142
Standard deviation [tex]= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }[/tex]
Standard deviation =[tex]\sqrt{\dfrac{(130-142)^2+(153-142)^2+...+(139-142)^2}{(6-1)} }[/tex]
Standard deviation = [tex]\sqrt{\dfrac{1048}{5}}[/tex]
Standard deviation = [tex]\sqrt{209.6}[/tex]
Standard deviation = 14.48
The [tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]
[tex]coefficient \ of \ variation = \dfrac{14.48}{142}*100[/tex]
Coefficient of variation = 10.2% for men age 60 - 69
Thus; Option C is correct.
Men aged 20-29: 4.6%
Men aged 60-69: 10.2 %
There is substantially more variation in blood pressures of the men aged 60-69.
Old McDonald has a farm with 36 cows and goats the number of cars he has 10 more than the number of coats how many of each animal does old McDonald have right to equations you think you solve the problem you see to represent the number of cars in on
Answer:
13 goats and 23 cows
Step-by-step explanation:
Use x to solve :) it's a hint
Answer:
g=goats
c=cows
a=cars
g + c = 36
10 + g = a
Step-by-step explanation:
the number of cows and goats together are equal to 36, so for the first equation you can write g + c = 36.
For the second equation, the number of cars he has is equal to the number of goats he has plus 10, so you can express that as 10 + g = a. (I used a since I already used c for the cows)
I think this is what you need if you need 2 equations to represent how many cars he has.
I'm not entirely sure what its asking you can comment if you need more or something else.
An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown. Which best describes the range of possible values for the third side of the triangle? A x 18.9 B 12.5 26 D 6 < x < 26
Solution:
12.5 < x < 18.9
Reason:
To solve this problem, we can apply Pythagorean's theorem.
To find the upper bound:
We can set the two given legs as the 2 legs of a right triangle. This allows us to keep the angle under 90 degrees. So if we set the legs to be 10 and 16, then the third side must be:
10^2 + 16^2 = x^2
x^2 = 356
x is roughly equal to 18.9
For the lower bound, this time, we set x as one of the legs, and 10 as the other let. Since we know that the longest side is 16, we can set up an equation again:
x^2 + 10^2 = 16^2
x^2 = 16^2 - 10^2
x^2 = 156
x is roughly equal to 12.5
So we have found the bounds to be 12.5 < x < 18.9
Answer:
its B
Step-by-step explanation:
A paper company produces 4,675 notebooks in 5 days. How many notebooks can it produce in 13 days?
OA. 12,155
OB. 2,431
OC. 4,473
OD. 12,100
Answer:
OA. 12,155
Step-by-step explanation:
A paper company produces 4,675 notebooks in 5 days. How many notebooks can it produce in 13 days?
--------
in 5 days= 4675
in 13 days= 4675/5*13= 12155
Answer
A OR D
Step-by-step explanation:
Use the horizontal number line to find the distance between -5 and 0.
1
-5 -4 -3 -2 -1 0
1
2 3 4
5
The distance between -5 and O is
<
The absolute value of -5 is
Answer:
I think +5 or 5
Answer:
there both 5
Step-by-step explanation: did the question on edg
The ratio between the exterior and interior angle of a regular polygon is 1:5, find
a. the measure of each exterior angle.
b. the measure of each interior angle.
c. the number of sides of the polygon.
Answer:
Exterior and interior angles are supplementary, meaning they sum to 180 degrees. If the exterior and interior angles are x and 5x respectively, we can write x + 5x = 180, and solving for x we get x = 30°. This means that the answer to a) is 30° and the answer to b) is 30 * 5 = 150°.
For c), to find the number of sides we can do:
180 - 150 = 30
180 / 30 = 6 so the answer to c) is 6.
12. Jeremy got quote from iVan to move him into his new home. One quote was for a weekday move which is
for 8 hours of loading/unloading and 6 hours of packing/unpacking for $890. The other quote was for a
weekend move which is for 5 hours of loading/unloading and 3 hours of packing/unpacking for $515. If
iVan has set hourly rates for loading/unloading and packing/unpacking, what are these hourly rates?
Answer:
Loading/unloading hourly rate: $70
Packing/unpacking hourly rate: $55
Step-by-step explanation:
We can write this as a system of linear equations.
We define L as the loading/unloading hourly rate, and P as the packing/unpacking hourly rate.
"One quote was for a weekday move which is for 8 hours of loading/unloading and 6 hours of packing/unpacking for $890":
[tex]8L+6P=890[/tex]
"The other quote was for a weekend move which is for 5 hours of loading/unloading and 3 hours of packing/unpacking for $515":
[tex]5L+3P=515[/tex]
If we express L in function of P in the first equation, and then replace this value in the second equation, we have:
[tex]8L+6P=890\\\\8L=890-6P\\\\L=\dfrac{890-6P}{8}[/tex]
[tex]5L+3P=515\\\\5\cdot \dfrac{890-6P}{8}+3P=515\\\\556.25-3.75P+3P=515\\\\-0.75P=515-556.25=-41.25\\\\P=41.25/0.75=55[/tex]
Then, L is:
[tex]L=\dfrac{890-6P}{8}=\dfrac{890-6(55)}{8}=\dfrac{890-330}{8}=\dfrac{560}{8}=70[/tex]
There are 560 third- and fourth-grade students in King Elementary School. If there are 80 more third-graders than fourth-graders, how many third-graders are there in the school? work has to be shown
Answer:
There are 200 4th grades and 360 third graders
Step-by-step explanation:
560/2=280-80=200 280+80=360
The table shows input and output values of the function y = x2 + 12x – 2. What is an approximate solution of the equation x2 + 12x – 2 = 0?
Answer:
The solutions for the equations are x = 0.1644 and x = -12.1644
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]x^{2} + 12x - 2 = 0[/tex]
So
[tex]a = 1, b = 12, c = -2[/tex]
[tex]\bigtriangleup = 12^{2} - 4*1*(-2) = 152[/tex]
[tex]x_{1} = \frac{-12 + \sqrt{152}}{2} = 0.1644[/tex]
[tex]x_{2} = \frac{-12 - \sqrt{152}}{2} = -12.1644[/tex]
The solutions for the equations are x = 0.1644 and x = -12.1644
A rectangle has a base length of 12 inches and an unknown height, h. The area of the rectangle is less than 60 square inches. Which inequality can be used to model the problem?
12h < 60
12h > 60
12 + h < 60
12 + h > 60
Answer:
12h < 60
Step-by-step explanation:
A rectangle, with height h and base length l, has the following area.
[tex]A = l*h[/tex]
In this question:
[tex]l = 12, A < 60[/tex]
So
[tex]A < 60[/tex]
[tex]l*h < 60[/tex]
[tex]12h < 60[/tex]
So the correct answer is:
12h < 60
Answer:
12h < 60
hope this helps, its right because i took the test and it shows
Simplify (20!+21!+22!)/44
Answer:
11*20!
Step-by-step explanation:
(20!+21!+22!)/44=
20!(1+21+21*22)/44=
20!(22+22*21)/44=
20!*22*22/44= 11*20!
The simplified expression of (20!+21!+22!)/44 is 20! * 11
How to simplify the expression?The expression is given as:
(20!+21!+22!)/44
The factorial of a number n is:
n! = n * (n - 1)!
So, we start by expanding 22!
(20!+21!+22!)/44 = (20!+21!+22 * 21 * 20!)/44
Next, we expand 21!
(20!+21!+22!)/44 = (20!+21 * 20!+22 * 21 * 20!)/44
Factor out 20!
(20!+21!+22!)/44 = 20! * (1 + 21 + 22 * 21)/44
Evaluate the expression in the bracket
(20!+21!+22!)/44 = 20! * 484/44
Divide
(20!+21!+22!)/44 = 20! * 11
Hence, the simplified expression of (20!+21!+22!)/44 is 20! * 11
Read more about simplified expression at:
https://brainly.com/question/723406
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2. A 175g sample of radioactive kryptonite-344 has a half-life of 122 days.
a) Write the exponential equation that gives the amount of kryptonite that remains after t days.
Write equation in the form M(t)= ab* where x=
elapsed time
half-life time
Answer:
[tex]M(t) = 175(0.9943)^{t}[/tex]
Step-by-step explanation:
The amount of kryptonite-344 after t days is given by the following equation:
[tex]M(t) = ab^{t}[/tex]
In which a is the initial amount.
175g sample:
This means that [tex]a = 175[/tex]
So
[tex]M(t) = 175b^{t}[/tex]
Half-life of 122 days.
This means that [tex]M(122) = 0.5*175 = 87.5[/tex]
So
[tex]M(t) = 175b^{t}[/tex]
[tex]87.5 = 175b^{122}[/tex]
[tex]b^{122} = 0.5[/tex]
[tex]\sqrt[122]{b^{122}} = \sqrt[122]{0.5}[/tex]
[tex]b = 0.9943[/tex]
So
[tex]M(t) = 175(0.9943)^{t}[/tex]
Find the value of x in the triangle shown below.
8
3
Answer:
[tex] \sqrt{55}[/tex]
Step-by-step explanation:
Given is a right angled triangle.
Therefore, by Pythagoras theorem:
[tex] {x}^{2} = {8}^{2} - {3}^{2} \\ = 64 - 9 \\ = 55 \\ x = \sqrt{55} [/tex]