Answer:
[tex]78,\!624,\!000[/tex].
Step-by-step explanation:
Note the requirements:
Repetition of letter or digit is not allowed.The order of the letters and digits matters.Because of that, permutation would be the most suitable way to count the number of possibilities.
There are [tex]\displaystyle P(26,\, 3) = \frac{26!}{(26 - 3)!} = 26 \times 25 \times 24 = 15,\!600[/tex] ways to arrange three out of [tex]26[/tex] distinct letters (without replacement.)
Similarly, there are [tex]\displaystyle P(10,\, 4) = \frac{10!}{(10 - 4)!} = 10 \times 9 \times 8 \times 7= 5,\!040[/tex] ways to arrange four out of [tex]10[/tex] distinct numbers (also without replacement.)
Therefore, there are [tex]15,\!600[/tex] possibilities for the three-letter section of this password, and [tex]5,\!040[/tex] possibilities for the four-digit section. What if these two parts are combined?
Consider: if the first three letters of the password were fixed, then there would be [tex]5,\!040[/tex] possibilities. However, if any of the first three letters was changed, the result would be another [tex]5,\!040\![/tex] possibilities, all of which are different from the previous [tex]5,\!040\!\![/tex] possibilities. These two three-letter sections along will give [tex]2 \times 5,\!400[/tex] possibilities. Since there are [tex]15,\!600[/tex] three-letter sections like that, there would be [tex]15,\!600 \times 5,\!400 = 78,\!624,\!000[/tex] possible passwords in total. That gives the number of possible passwords that satisfy these requirements.
What did this person do wrong? Honestly really stuck and do not remember geometry!
Answer:
See below.
Step-by-step explanation:
Using the right triangle altitude theorem, the correct proportions are:
[tex] \dfrac{AB}{AC} = \dfrac{AC}{AD} [/tex]
[tex] \dfrac{AB}{x} = \dfrac{x}{AD} [/tex]
[tex] \dfrac{25}{x} = \dfrac{x}{16} [/tex]
[tex] x^2 = 25 \times 16 [/tex]
[tex] x = 20 [/tex]
AC = 20 cm
[tex] \dfrac{AB}{CB} = \dfrac{CB}{DB} [/tex]
[tex] \dfrac{AB}{y} = \dfrac{y}{DB} [/tex]
[tex] \dfrac{25}{y} = \dfrac{y}{9} [/tex]
[tex]y^2 = 25 \times 9[/tex]
[tex]y = 15[/tex]
CB = 15 cm
find the derivative of e power ax divide by log bx
Answer:
Step-by-step explanation:
what is the graph of −36≤2x+4(x−3)
please solve quick
Answer:
x = 5
AC = 6
DC = 8
Step-by-step explanation:
∆ABC ~ ∆CDE
Therefore, [tex] \frac{AB}{ED} = \frac{AC}{DC} [/tex]
AB = 3
ED = 4
AC = x + 1
DC = x + 3
Plug in the values and solve for x:
[tex] \frac{3}{4} = \frac{x + 1}{x + 3} [/tex]
Cross multiply
[tex] 3(x + 3) = 4(x + 1) [/tex]
[tex] 3x + 9 = 4x + 4 [/tex]
[tex] 3x - 4x = -9 + 4 [/tex]
[tex] -x = -5 [/tex]
[tex] x = 5 [/tex]
Plug in the value of x and find AC and DC
AC = x + 1 = 5 + 1 = 6
DC = x + 3 = 5 + 3 = 8
Molly’s house is located at point X. Molly wants Sophia and Cole to meet at her house because she thinks it is the same distance from Sophia’s house and Cole’s house. Which could prove that Molly’s house is the samedistance from Sophia’s and Cole’s houses?
Answer:
Cole's House
Step-by-step explanation:
Cole house is closer because molly and Sophia can go there together because there both girls
A.Yes, since the slopes are the same and the y-intercepts are the same.
B.No, since the y-intercepts are different.
C.Yes, since the slopes are the same and the y-intercepts are different.
D.No, since the slopes are different.
Answer:
C
Step-by-step explanation:
one line is
y = 3x/7 + 11
its slope is 3/7
the y-intercept is, of course, when x=0. there y=11
the other is
-3x + 7y = 13
7y = 3x + 13
y = 3x/7 + 13/7
its slope is 3/7 (the same as the other line)
the y-intercept (x=0) is y = 13/7 (different to the other line)
Answer:
C. Yes, since the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
[tex]y=\frac{3}{7} x+11[/tex] and [tex]-3x+7y=13[/tex]
→ Rearrange the second equation to make y the subject
7y = 3x + 13
→ Divide everything by 7
[tex]y=\frac{3}{7} x+\frac{13}{7}[/tex]
F(x)=x^2 what is g(x)
Answer:
stop spamming
Step-by-step explanation:
A box is 1 m high, 2.5 m long, and 1.5 m wide, what is its volume?
Answer:
3.75
Step-by-step explanation:
[tex]v = lbh \\ 2.5 \times 1.5 \times 1 \\ = 3.75[/tex]
The volume of the rectangular prism will be 3.75 cubic meters.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
A box is 1 m high, 2.5 m long, and 1.5 m wide.
Then the volume of the rectangular prism will be
V = L x W x H
V = 1 x 2.5 x 1.5
V = 3.75 cubic meters
Thus, the volume of the rectangular prism will be 3.75 cubic meters.
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Which property is not used to simplify the following expression 2* (x+5)+7x=(2x+10)+7x
Hence, the commutative property of addition is not used.
What is an expression?
A mathematical expression is in form of variables and constants separated by their arithmetic operation.
As we know that, there are three types of properties they are associative property which is [tex](a+b) + c = a + (b+c)[/tex],
Distributive property which is [tex]a(b+c) = ab + ac[/tex],
Commutative property which is [tex]a + b = b + a[/tex].
Here given that,
[tex]2 (x+5)+7x=(2x+10)+7x[/tex]
[tex](2x+10)+7x=(2x+10)+7x[/tex] ( distributive property of multiplication)
[tex](2x+7x)+10=(2x+7x)+10[/tex] ( it is associative property of addition)
[tex](8x)+10=(8x)+10[/tex] ( it is a commutative property)
Hence, the commutative property of addition is not used.
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[tex]4x - 2x = [/tex]
Answer:
2x
Step-by-step explanation:
These are like terms so we can combine them
4x-2x
2x
Answer:
2x
Explanation:
Since both terms in this equation are common, we can simply subtract them.
4x - 2x = ?
4x - 2x = 2x
Therefore, the correct answer should be 2x.
In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.
THIS IS THE COMPLETE QUESTION BELOW;
In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.
What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?
A. 0.10
B.0.50
C. 0.66
D. 0.06
Answer:
OPTION D is correct
d)0.06
the probability that a randomly selected team from Littletown goes to the city and state playoffs is [tex]0.06[/tex]
Step-by-step explanation:
The probability that a baseball team goes to city playoffs is 0.30.
P(baseball team goes to city playoffs)=0.30
The probability that the team goes to state playoffs given that the team goes to the city playoffs is 0.20.
P(team goes to state playoffs given that the team goes to the city playoffs)=0.20
From our knowledge of set, we know that
P(A | B)= P(A ∩ C)/P(C)
where A= city playoffs
B= state playoffs
P(State play off | city play off)=0.20
P(State play off ∩ city play off)/P(city play off,)=0.20
P(State play off ∩ city play off)/0.30 =0.20
P(State play off ∩ city play off)= 0.30 × 0.20
= 0.06
Hence,the probability that a randomly selected team from Littletown goes to the city and state playoffs is 0.06
Greg is 10 years older than his brother gabe. He is also 3 times as old as gabe. How old is Greg?
Answer: 30 i think 10x3=30
Step-by-step explanation:
A polling company reported that 53% of 1018 surveyed adults said that secondhand smoke issecondhand smoke is "very harmful.""very harmful." Complete parts (a) through (d) below.
a. What is the exact value that is 53% of 1018?
b. Could the result from part (a) be the actual number of adults who said that secondhand smoke issecondhand smoke is "very harmful" question mark "very harmful"? Why or why not?
c. What could be the actual number of adults who said that secondhand smoke issecondhand smoke is "very harmful" question mark "very harmful"?
d. Among the 10181018 respondents, 260260 said that secondhand smoke issecondhand smoke is "not at all harmful.""not at all harmful." What percentage of respondents said that secondhand smoke issecondhand smoke is "not at all harmful" question mark "not at all harmful"?
Answer:
a. 539.54
b. No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.
c. 540
d. 25.54%
Step-by-step explanation:
Given that:
A polling company reported that 53% of 1018 surveyed adults said that secondhand smoke is "very harmful."
Complete parts (a) through (d) below.
a. What is the exact value that is 53% of 1018?
The 53% of 1018 is :
=[tex]\dfrac{53}{100} \times 1018[/tex]
= 0.53 × 1018
= 539.54
b. Could the result from part (a) be the actual number of adults who said that secondhand smoke is ''very harmful"? Why or why not?
No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.
c. What could be the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful"?
Since, a count of people must result into a whole number, the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful" can be determined from the approximation of the exact value into whole number which is 539.54 [tex]\approx[/tex] 540.
d. Among the 1018 respondents, 260 said that secondhand smoke is is "not at all harmful.'' What percentage of respondents said that secondhand smoke is "not at all harmful"?
Since 260 respondents out of 1018 respondents said that the second hand smoke is not harmful, then the percentage of the 260 respondents is :
= [tex]\dfrac{260}{1018} \times 100 \%[/tex]
= 25.54%
Find the greatest number than divides 45, 60 and 75 without leaving remainder
Answer:
15
Step-by-step explanation:
15×3=45
15×4=60
15×5=75
Answer:
15
Step-by-step explanation:
45 = 1 × 3^2 × 5
60 = 2^2 × 3 × 5
75 = 3 × 5^2
greatest number than divides 45, 60 and 75 without leaving remainder = GCF of 45,60,75 = 3 × 5 = 15
What is the solution of the linear equation? LaTeX: 5k\:+\:3.8\:=\:3k\:+\:95 k + 3.8 = 3 k + 9 Group of answer choices 26 6.4 .065 2.6
Answer:
[tex]k = 2.6[/tex]
Step-by-step explanation:
Given
[tex]5k + 3.8 = 3k + 9[/tex]
Required
Solve
[tex]5k + 3.8 = 3k + 9[/tex]
Collect like terms
[tex]5k -3k+ 3.8 = 3k -3k + 9[/tex]
[tex]2k+ 3.8 = 9[/tex]
Subtract 3.8 from both sides
[tex]2k+ 3.8 - 3.8= 9 - 3.8[/tex]
[tex]2k= 9 - 3.8[/tex]
[tex]2k = 5.2[/tex]
Divide through by 2
[tex]k = 5.2/2[/tex]
[tex]k = 2.6[/tex]
0.3,1/5,1/2,0.706,7/8,57.1%
Place following in ascending order
Answer:
the answer is 0.31/ 5.1/8.57.1% /207067
Step-by-step explanation:
ascending order from the smallest to the largest
The first step in a mathematical induction proof is to divide by n. (True or False).
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
will rate you brainliest
Answer:
[tex] \frac{11x}{3y} [/tex]
Step-by-step explanation:
[tex] \frac{7x}{3y} + \frac{12x}{9y} [/tex]
Make both a single fraction by adding together.
[tex] \frac{3(7x) + 1(12x)}{9y} [/tex]
[tex] \frac{21x + 12x}{9y} [/tex]
[tex] \frac{33x}{9y} [/tex]
Simplify
[tex] \frac{3(11)x}{3(3y)} [/tex]
[tex] \frac{11x}{3y} [/tex]
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement [Mark 4]
ii. How far west is Musah’s final point from the centre?
Answer:
Inokkohgy8uokokj76899
Factorize the following:
cosB + 5cosB - 6
[tex]\\ \rm\Rrightarrow cosB+5cosB-6[/tex]
Add cos[tex]\\ \rm\Rrightarrow (1+5)cosB-6[/tex]
[tex]\\ \rm\Rrightarrow 6cosB-6[/tex]
Take 6 common[tex]\\ \rm\Rrightarrow 6(cosB-1)[/tex]
Answer:
6(cosB - 1)
BRAINLIEST, PLEASE!
Step-by-step explanation:
cosB + 5cosB - 6
6cosB - 6
6(cosB - 1)
Which of the following equations has the same solution as 5 x + 8 = x − 9?
A) 4 x = −1
B) 4 x = 17
C) 6 x = −17
D) 6 x = 17
E) 4 x = −17
Please give me a explanation! Willing to give a Brainliest.
[tex]4x=-17[/tex] has the same solution as [tex]5x+8=x-9[/tex]
Option (E) is correct
What is Equation?"An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =."
We have,
[tex]5x+8=x-9[/tex]
By solving the given equation
⇒[tex]5x-x=-9-8[/tex]
⇒[tex]4x=-17[/tex]
Clearly, Option (E) is correct
⇒[tex]x=\frac{-17}{4}[/tex]
Explanation for other options:
(A) [tex]4x=-1[/tex]
⇒[tex]x=\frac{-1}{4}[/tex]
(B) [tex]4x=17[/tex]
⇒[tex]x=\frac{17}{4}[/tex]
(C) [tex]6x=-17[/tex]
⇒[tex]x=\frac{-17}{6}[/tex]
(D) [tex]6x=17[/tex]
⇒[tex]x=\frac{17}{6}[/tex]
∴ [tex]4x=-17[/tex] has the same solution as [tex]5x+8=x-9[/tex]
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I need help with this balance mobile please:)
Answer:
blue 1
orange 5
green 3
I hope it is helpful and mark me as brainlest and follow me plz
An experimental probability is ______ likely to approach the theoretical probability if the number of trials simulated is larger. A. as B. more C. less D. not
Answer:
B. More
Step-by-step explanation:
This is according to the law of large numbers
An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.
What is an experimental probability and theoretical probability?Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.
An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed
Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.
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In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
a. Convenience sampling
b. Cluster sampling
c. Stratified sampling
d. Systematic sampling
Answer:
C Stratified sampling
Step-by-step explanation:
Stratified sampling : Stratified sampling is a type of sampling technique in which the total population is divided into smaller groups or strata to complete the sampling process. The strata is formed based on some common characteristics in the data of the population.
One of the advantage of stratified random sampling is that it covers important population characteristics in the sample.
Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result to 4 decimal places. B) Find the continuous decay rate and round final result to 4 decimal places. C) How long will it take for a 10 gram sample to decay to 1 gram? Round to nearest year and interpret your result with a complete sentence. D) Complete this statement: as x goes to infinity, y goes to ___.
Answer:
0.02280.0231100 years0Step-by-step explanation:
The exponential equation for the fraction remaining after x years can be written as ...
y = (1/2)^(x/30)
A) For x=1, the fraction remaining is ...
y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228
Of the original amount, 0.0228 decays each year.
__
B) The continuous decay rate is the natural log of the growth factor, so is ...
ln(0.97716) = -0.0231
The continuous decay rate is 0.0231 of the present amount (per year).
__
C) For y=.10 (1/10 of the original amount) we find x to be ...
.1 = .5^(x/30)
ln(.1) = (x/30)ln(.5) . . . . . take the natural log
30ln(0.1)/ln(0.5) = x ≈ 100 . . . years
It will take 100 years for a 10-gram sample to decay to 1 gram.
__
D) As x goes to infinity, y goes to zero.
_____
The relationship between growth rate and growth factor is ...
growth factor = 1 + growth rate
When the growth rate is negative, it is called a decay rate.
Can someone help with this please
Answer:
x2 1-
Step-by-step explanation:
Answer:
x ≥ 0
Step-by-step explanation:
Domain of a function is the x values of a function
The graph extends from 0 to positive infinity.
Since the point at x=0 is closed, the graph includes 0
7. 20x + 10 = 110
a. X= 1
b. X= 5
c. x= 12
Answer:
b x=5
Step-by-step explanation:
20x+10=110
20x+10-10=110-10
20x/20=100/20
x=5
Answer:
x=5
Step-by-step explanation:
20x + 10 = 110
Subtract 10 from each side
20x +10-10 = 110-10
20x = 100
divide by 20
20x/20 =100/20
x= 5
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
Y=-3x+1
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
The equation is already solved for y
It's in y = mx+b form where
m = -3 = slope
b = 1 = y intercept
The graph is shown below. It's a straight line through the two points (0,1) and (1,-2).
Note that (0,1) is the y intercept. We use the slope = -3 = -3/1 to move 3 units down and 1 unit to the right to arrive at (1,-2).
Find the 14th term in the sequence 1, 1/3, 1/9, … Find the sum of the first 10 terms of the sequence above.
Answer:
This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term
Let Pn represent the nth term in the sequence
Then Pn = (1/3)^n-1
From this P14 = (1/3)^13 = 1/1594323
5. The sum of the first n terms of a GP beginning a with ratio r is given by
Sn = a* (r^n+1 - 1)/(r - 1)
With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500
Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = 5 + ln(t), y = t2 + 2, (5, 3)
Answer:
Step-by-step explanation:
Given that:
[tex]x = 5 + In (t)[/tex]
[tex]y = t^2+2[/tex]
At point (5,3)
To find an equation of the tangent to the curve at the given point,
By without eliminating the parameter
[tex]\dfrac{dx}{dt}= \dfrac{1}{t}[/tex]
[tex]\dfrac{dy}{dt}= 2t[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{ \dfrac{dy}{dt} }{\dfrac{dx}{dt} }[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{ 2t }{\dfrac{1}{t} }[/tex]
[tex]\dfrac{dy}{dx}= 2t^2[/tex]
[tex]\dfrac{dy}{dx}_{ (5,3)}= 2t^2_{ (5,3)}[/tex]
t² + 5 = 4
t² = 4 - 5
t² = - 1
Then;
[tex]\dfrac{dy}{dx}_{ (5,3)}= -2[/tex]
The equation of the tangent is:
[tex]y -y_1 = m(x-x_1)[/tex]
[tex](y-3 )= -2(x - 5)[/tex]
y - 3 = -2x +10
y = -2x + 7
y = 2x - 7
By eliminating the parameter
x = 5 + In(t)
In(t) = 5 - x
[tex]t =e^{x-5}[/tex]
[tex]y = (e^{x-5})^2+5[/tex][tex]y = (e^{2x-10})+5[/tex]
[tex]\dfrac{dy}{dx} = 2e^{2x-10}[/tex]
[tex]\dfrac{dy}{dx}_{(5,3)} = 2e^{10-10}[/tex]
[tex]\dfrac{dy}{dx}_{(5,3)} = 2[/tex]
The equation of the tangent is:
[tex]y -y_1 = m(x-x_1)[/tex]
[tex](y-3 )= -2(x - 5)[/tex]
y - 3 = -2x +10
y = -2x + 7
y = 2x - 7