(a)
Evaluate each of the following:
(i)
10! X 20!
17! X 9!
Answer:
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
Step-by-step explanation:
1)
Given the expression
[tex]10!\times \:20![/tex]
[tex]\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n[/tex]
[tex]10!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10[/tex]
[tex]20!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20[/tex]
Now, multiplying the result
[tex]10!\times \:20!= 1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20[/tex]
so
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
Thus, we conclude that:
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
2)
Given the expression
[tex]17!\:\times \:9![/tex]
[tex]\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n[/tex]
[tex]17!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17[/tex]
[tex]9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9[/tex]
Now, multiplying the result
[tex]17!\:\times \:9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9[/tex]
so
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
Thus, we conclude that:
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
Explain how to graph 8 is greater than it equal to y
Answer:
t w e n t y c h a r e c t e r s l o n g
whats 7, −6, 4, −10, 3 least to greatest
Answer:
-10, -6, 3, 4, 7
Step-by-step explanation:
Hope it helps ^^
0.5= x djdododododododdodod
Answer:
25
Step-by-step explanation:
cuz
NEED ANSWER ASAP! CORRECT ANSWER GETS BRAINLIEST!
An oil company fills 1 over 12 of a tank in 1 over 3 hour. At this rate, which expression can be used to determine how long it will take for the tank to fill completely?
1 over 12 ⋅ 3 hours
1 over 3 ⋅ 12 hours
1 over 3 ⋅ 1 over 12 hour
3 ⋅ 12 hours
Answer:
4 hours
Step-by-step explanation:
1/12 time what equals 1? 12 so do it to the other equation and simplify 12/3 to get 4.
Solve for x = X-16/x+6= 3/5
Answer:
-16/29
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
i did the test
A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
Answer:
3 ft.
Step-by-step explanation:
15:20 and x:4 you can cross multiply or if you reduce 15:20, the answer is 3:4
If 1 yard = 3 feet and 1 mile = 5,280 feet, how many yards are there in 4 miles?
Answer:
7040 Yards
Step-by-step explanation:
First, you have to divide 5280 by 3, to get 1760 yards
Then you have to multiply 1760 by 4
Finally, you should get the answer of 7040 yards :D
Answer:
The other person who answered it already explained it but the answer is 7,040
Step-by-step explanation:
The largest prime number that is a factor of 35 is multiplied by the smallest prime number
Answer:
the largest factor of 35 is 35 and the smallest prime number is 2 so 35 times two is 70
Step-by-step explanation:
Write an inequality. Marianda is packing eggs in cartons. Each carton holds 12 eggs. She has already filled 3 cartons. How many more eggs does she need to fill at least 17 cartons?
14 x 12= 168. (she already filled 3 cartons. so, 17-3 =14.) she needs 168 eggs to fill the other 14 cartons.
Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened in the bank
Answer:
Step-by-step explanation:
False,true,true
Juanita earns $36 for 3 hours of work. At that rate, how long would she have to work to earn $720?
Answer:
She has to work for 60hours in order to earn $720.
Step-by-step explanation:
Amount of money earned in 1hour=36÷3
=12$
Total time required=720÷12
=60hours
pitcher can hold 1,200 milliliters of tea. How many liters of tea are in the pitcher?
Answer:
1.2 Liters
Step-by-step explanation:
There are 1000 mL in 1 L. divide 1200 by 1000 and you get 1.2
Consider this function.
(r) = -3r + 3
Which graph represents the inverse of function ?
9514 1404 393
Answer:
C. graph Y
Step-by-step explanation:
Starting with f(r) = -3r +3, the inverse function can be found from ...
r = f(y)
r = -3y +3
r -3 = -3y
(r -3)/-3 = y
y = -1/3r +1
The inverse function will have a slightly negative slope and a y-intercept of 1. This matches graph Y.
n order to test the null hypothesis of equal means (alternative hypothesis says they are unequal), two simple random samples are obtained.In sample 1, the mean and standard deviation are 10 and 6 respectively.In sample 2, the mean and standard deviation are 16 and 4 respectively.Each sample is of size 6.The data are normally distributed.The true standard deviations of the two populations may be assumed to be equal.What can you say about the P-value for the test of equal means? --> It must be
Complete Question
In order to test the null hypothesis of equal means (alternative hypothesis says they are unequal), two simple random samples are obtained.In sample 1, the mean and standard deviation are 10 and 6 respectively.In sample 2, the mean and standard deviation are 16 and 4 respectively.Each sample is of size 6.The data are normally distributed.The true standard deviations of the two populations may be assumed to be equal.What can you say about the P-value for the test of equal means? -->
It must be that the resulting P-value must be
A) Greater than 0.2
B) Between 0.19 and 0.10
C) Between 0.09 and .05
D) Between .049 and .02
E) Less than 0.02
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The mean of sample 1 is [tex]\= x_1 = 10[/tex]
The standard deviation is [tex]s_1 = 6[/tex]
The mean of sample two is [tex]\= x_2 = 16[/tex]
The standard deviation is [tex]s_2= 4[/tex]
The sample size for both samples is [tex]n_1 = n_2 = n = 6[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 \ne \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x_1 - \= x_2 }{ \sqrt{ \frac{s^2_1}{n_1} +\frac{s^2_1}{n_2} } }[/tex]
=> [tex]z = \frac{ 10 - 16 }{ \sqrt{ \frac{6^2}{6} +\frac{4^2}{6} } }[/tex]
=> [tex]z = -1.3646[/tex]
From the z table the area under the normal curve to the left corresponding to -1.3646 is
[tex]P(Z < -1.3646) = 0.086189[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 P(Z < -1.3646)[/tex]
=> [tex]p-value = 0.086189 * 2[/tex]
=> [tex]p-value = 0.1724[/tex]
So the p-value is Between 0.19 and 0.10
The area of rectangle is 35 square feet.the length of rectangle is 5feet what is the width of the rectangle
Answer:
the answer should be 7
Step-by-step explanation:
Pls answer this is very easy
Answer:
A and B
Step-by-step explanation:
The original equation simplifies down to -4m - 2
Answer A and B also simplify down to -4m -2, and therefor are equivalent
A: -2(4m + 1) + 4m
-8m - 2 + 4m
-4m - 2
B: 2(2m - 1) - 8m
4m - 2 - 8m
-4m - 2
18. Find the missing length indicated.
Find HJ
x+27
X+ 17
Answer:
The answer ia -30. Hope i help
Answer:
The answer is 30 hope it helps
Why are these triangles similar?
Answer:
sas
Step-by-step explanation:
For a Biology assignment, Lisa collected data on plant growth of a sunflower every week for 9 weeks. When Lisa first planted the sunflower, it was 10 centimeters tall. The time (in weeks) is plotted against the height (in centimeters) as shown below. Using the best-fit line, approximately how tall was the sunflower plant during the fifth week? 33 centimeters 34 centimeters 35 centimeters 30 centimeters
Answer:
I think it was 34 cm because it should be not too long
Step-by-step explanation:
this is from my logic perspective
please help
An auditorium sold 500 tickets for a play and raised $3400. Let x represent the number of adult tickets sold at $8 each and let y represent the number of student tickets sold at $5 each. Write and solve a system of equations to determine the number of adult tickets and the number of student tickets that were sold.
Answer:
answer is attached in the figure below hope it helps please mark it as brainlist
If Zuri continues to travel at 0.2 miles per minute. how far will she travel in one hour?
Answer:
1.2 miles yr welcome
Help me with this plz!?!? I will mark brainliest!!!
Need help geometric sequences see pic for details
Given:
The recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]
[tex]a_1=-3[/tex]
To find:
The explicit formula of the given geometric sequence.
Solution:
We know that, first term of geometric sequence is [tex]a_1=-3[/tex].
Recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\times r[/tex] ...(i)
where, r is common ratio.
We have,
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]r=\dfrac{1}{8}[/tex]
The explicit formula of a geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]
Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get
[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]
Therefore, the correct option is D.
HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
Applesauce recipe for 8 uses 3 quarters of water. How much water for 12 people
Answer:
4.5 quartsStep-by-step explanation:
We use a proportion to solve this.
8/3 = 12/x
Cross-multiply to get:
8x = 36
x = 4.5
The answer to the question is 4.5
Maggie is participating in her school reading challenge. She reads 80 books in 6 months. If 40 of the books are fiction, then what percent of the books that she read are fiction?
Answer:
50%
Step-by-step explanation:
*In this question, the 6 does not matter*
If 40/80 books are fiction, and if you simplify that fraction, you get 1/2.
Percentages are just fancy fractions and decimals. 50% means 1/2.
Thus, the answer is 50%
Delete this already.
I need help on both these questions
MY HRW ‼️ Solve the equation. You may find using algebra tiles helpful in solving this problem.
X +6=-X-6
Answer:
x=-6
Step-by-step explanation:
x+6=-x-6
(-6)+6=(6)-6
0=0
Answer:
Solve the equation. You may find using algebra tiles helpful in solving this problem. X +6=-X-6 X= -6
Given
f
(
x
)
=
−
x
−
3
f(x)=−x−3, solve for
x
x when
f
(
x
)
=
−
2
f(x)=−2.
Answer:
-5
Step-by-step explanation:
Substitute every part of the equation where x appears with the value of x, which is -2
f(-2)=-2-3
f(-2)=-5
So, f(x)=-5