(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]
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
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
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
Simplify the expression by arranging the steps in sequence, based on the order of operations 1/6 (30x 24)-1/7(63x-7x) please help fast!!!!
Answer:
if you Simplify the expression it is 112x
(or 120-8x if 30x 24 is multiplication)
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
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
Given the quadratic equation: 1/2x^2+3x−10=0
Answer:
x=2.3851648071345037,−8.385164807134505
Step-by-step explanation:
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
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
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
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.
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:
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.
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
Stephanie needs to cover her yard with 410taft2of soil. She has enough for 125ft2in one bag and 65 ft2in another bag. How much more square feet of soil will she need covered?
Answer:
Stephanie needs 220ft² of more soil to cover the rest of her yard.
Step-by-step explanation:
First add the bags she already has:125ft²+65ft²+x=410ft² --> 190ft²+x=410ft²
Second use the subtraction property of equality: 190ft²-190ft²+x=410ft²-190ft² ---> x=220ft²
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
I need help on both these questions
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:
0.5= x djdododododododdodod
Answer:
25
Step-by-step explanation:
cuz
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
can somebody do this please
Answer:
12y - x - 28 = 0
Step-by-step explanation:
............
x - 2y =0
3x + y = 0
solve using the substitution method
to solve the linear system
Answer:
x=0, y=0
Step-by-step explanation:
① Label the 2 given equations.
x -2y= 0 -----(1)
3x +y= 0 -----(2)
② Make x the subject of formula in equation (1).
From (1): x= 2y -----(3)
③ Substitute equation (3) into (2):
3(2y) +y= 0
Expand:
6y +y= 0
Simplify:
7y= 0
y= 0
④ Find x.
Subst. y=0 into (3):
x= 2(0)
x= 0
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
Least to greatest 0.4, 5/8, 74%, 3/5
Answer:
0.4,3/5,5/8,74%
Step-by-step explanation:
Change them all into decimals.
Get 0.4,0.625,0.74,0.6
Then reorder and see what their original values were
Count by 5’s starting with 99
104, 109, 114, 119, 124, 129, 134, 139, 144, 149
hehe
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Why are these triangles similar?
Answer:
sas
Step-by-step explanation:
which of the following is a characteristic of the circumcenter of a triangle? multi-choice. A. it is the center of the only circle that can be inscribed in the triangle. , B. it is the center of the circle that can be inscribed in given a given triangle. C. it is the center of the only circle that can be circumscribed about the triangle. D. it is equidistant from all three sides of the triangle.
Answer:
C
Step-by-step explanation:
The circumcenter is called ”the circumcenter” because it is the center of the circle that ”circumscribes” the triangle.
I hope this helps!
Further explanation:
For a circle to circumscribe something, it circles it so that each of the vertices are on the circle, so each of the vertices are equidistant from the circumcenter. The circumcenter of a triangle is formed by the perpendicular bisectors of its sides.
Side note:
The rest of the choices describe an incenter.
plz help! will give brainliest! really easy!
Answer:
C
Step-by-step explanation:
I explained it in the comments of the other one