Answer:
Step-by-step explanation:
From the given information:
The number of different license plate the country can produce is in the form:
=L₁L₂L₃L₄ or L₁L₂L₃L₄L₅ or D₁L₁L₂L₃L₄ or D₁L₁L₂L₃L₄L₅
∴
The Total number of the license plate that can be produced is;
= 26⁴ + 26⁵ + (10 × 26⁴) + (10 × 26⁵)
= 456976 + 11881376 + 4569760 + 118813760
= 135721872
Number of license plate with no repeated letter = P(26,4) + P(26,5) + 10 P(26,4) + 10 P(26,5)
= 11 P(26,4P + 11 P(26,5)
[tex]=11 \times \dfrac{26!}{(26-4)!} + 11 \times \dfrac{26!}{(26-5)!}[/tex]
= 90776400
c) The number of the licensed plate with 1 repeated letter = Total number of the licensed plate - number of the licensed plate with no repeated letter.
= 135721872 - 90776400
= 44945472
d) The probability that a licensed plate has repeated letter is:
[tex]= \dfrac{no(rep \ letter) }{n (total)} \times 100\%[/tex]
[tex]= \dfrac{44945472}{135721872}\times 100\%[/tex]
= 33.12%
A) The country can produce 118,813,760 different licence plates.
B) 78,936,000 license plates have no repeated letter.
C) 39,877,760 license plates have at least one repeated letter.
D) The probability that a license plate has a repeated letter is 33.56%.
Given that in a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the Roman alphabet, to determine (A) how many different license plates can the country produce; (B) how many license plates have no repeated letter; (C) how many license plates have at least one repeated letter; and (D) what is the probability that a license plate has a repeated letter, the following calculations must be performed:
A)
10 x 26 x 26 x 26 x 26 x 26 = X 10 x 11,881,376 = X 118,813,760 = X
B)
10 x 26 x 25 x 24 x 23 x 22 = X 10 x 7,893,600 = X 78,936,000 = X
C)
118,813,760 - 78,936,000 = X 39,877,760 = X
D)
118,813,760 = 100 39,877,760 = X 39,877,760 x 100 / 118,813,760 = X 33.56 = XLearn more about quantities in https://brainly.com/question/12161780
For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders. Find the radius and height of a container if it has a capacity of 44 in.3 and is constructed using the least amount of metal. (Round your answers to two decimal places.)
Answer:
[tex]1.91\ \text{in}[/tex]
[tex]3.84\ \text{in}[/tex]
Step-by-step explanation:
V = Volume of cylinder = [tex]44\ \text{in}^3[/tex]
h = Height of cylinder
r = Radius of cylinder
Volume of cylinder is given by
[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{44}{\pi r^2}[/tex]
Total surface area of a cylinder is given by
[tex]S=2\pi r^2+2\pi rh\\\Rightarrow S=2\pi r^2+2\pi r\times\dfrac{44}{\pi r^2}\\\Rightarrow S=2\pi r^2+\dfrac{88}{r}[/tex]
Differentiating with respect to radius
[tex]\dfrac{dS}{dr}=4\pi r-\dfrac{88}{r^2}[/tex]
Equating with zero
[tex]4\pi r-\dfrac{88}{r^2}=0\\\Rightarrow 4\pi r=\dfrac{88}{r^2}\\\Rightarrow r^3=\dfrac{88}{4\pi}\\\Rightarrow r=(\dfrac{22}{\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.91\ \text{in}[/tex]
Double derivative of S
[tex]\dfrac{d^2S}{dr^2}=4\pi+176>0[/tex]
So [tex]r[/tex] is minimum at [tex]\dfrac{dS}{dr}=0[/tex]
[tex]h=\dfrac{44}{\pi r^2}=\dfrac{44}{\pi 1.91^2}\\\Rightarrow h=3.84\ \text{in}[/tex]
So the radius and height of the cylinder is [tex]1.91\ \text{in}[/tex] and [tex]3.84\ \text{in}[/tex] respectively such that the least amount of metal is used.
Solve the problem. Sven can type 57 words per minute. How many words would he type in hour (40 minutes)? 2280 words 86 words 38 words 1520 words
Answer:
Sven would type 2280 words every 40 minutes.
Step-by-step explanation:
Multiply 57 by 40 and that should get you 2280.
Now, if it was truly an hour, you would multiply 57 by 60. The answer should be 3420.
Write the conclusion:
If Charlie goes to the store, then Harry loves school
A. Charlie doesn't go to the store
B. Harry does not love school
C. Charlie goes to the store
D. Harry loves school
a. then Harry loves school
b. Harry loves school
c. Charlie goes to the store,
d. Then Charlie goes to the store,
Question 5
Write the converse:
If the team does not play on Tuesday then the project is not due Friday.
a. If the project is not due Friday then the team does not play on Tuesday
b. If the team plays on Tuesday then the project is due FridayThis answer is incorrect.
c. If the project is due Friday then the team plays on Tuesday
d. The team plays on Tuesday if and only if the project is due Friday.
Question 7
Write the converse:
If Don goes to the store then George doesn't go to the store.
A. If George doesn't go to the store then Don goes to the store
B. Don doesn't go to the store if and only if George goes to the store.
C. If George goes to the store then Don doesn't go to the store
D. If Don doesn't go to the store then George goes to the store
a. If George doesn't go to the store then Don goes to the store
b. Don doesn't go to the store if and only if George goes to the store.
c. If George goes to the store then Don doesn't go to the store
d. If Don doesn't go to the store then George goes to the store
Question 9
Write a counterexample:
If the product of two numbers is 80, then one number must be 10.
a. x = 10 and y = 8
b. x = 1 and y = 8
c. x = 10 and y = 80
d. x = 1 and y = 80
Answer:
A
Step-by-step explanation:
beacause Harry loves school so he go to school
What is the first step needed to solve 2 over 5 multiplied by x minus 6 equals negative 16?
Subtract 16 from both sides
Add 6 to both sides
Divide both sides by 5
Multiply both sides by 2
Answer:
The correct answer is D.
Step-by-step explanation:
can u pls help me with this question
What is the perimeter of the figure?
A. 20.0 cm
B. 23.0 cm2
C. 25.0 cm2
D. 11.0 cm
Answer:
Answer is D, all you do is add the numbers
The perimeter of the figure is 20 cm.
The perimeter of the figure is the sum of the whole sides. When the whole sides of the figure is added the perimeter is known. Therefore,
perimeter = 5 cm + 3 cm + 1 cm + 2cm + 4cm + 5 cm
perimeter = 8 cm + 3cm + 9cm
perimeter = 20 cm
The perimeter of the figure = 20 cm
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Haven’t been able to figure this out, can someone help?
Answer:
D reorder the terms using communitive properties
because there is nothing else to do with this problem
Step-by-step explanation:
8 3√25 k
I checked the other problems and K was 12
Hope this helps ?
This is statistics. Please answer fast
Answer:
This is a normal distribution and we can use the standard score to compute for probabilities. We compute the standard score of the given.
Step-by-step explanation:
z = (x - mu)/sd
z = (2625 - 2600)/50 = 25/50 = 0.5.
Consulting the z-table, P(z <= 0.5) = 0.6915.
P(z > 0.5) = 1 - P(z <= 0.5) = 1 - 0.6915 = 0.3085.
I hope this helped! <3
Probability please answer♀️ Helppp please
find the expectation e(x) and variance var(x) for the task
suppose you choose a real number x from the interval [2, 10] with a density function of the form f(x) = c/x , where c is a constant
Step-by-step explanation:
Let X be a random variable with PDF given by
fX(x)={ cx2 |x|≤1 0 otherwise
Find the constant c.
Find EX and Var(X).
Find P(X≥
1
2
).
The radius of a circle is 3 feet. What is the circle's area?
Answer:
6
Step-by-step explanation:
Answer:1.5 feet
Step-by-step explanation: your welcome
3(x+6)=3x + _
Please asap
Answer:
3x + 18
General Formulas and Concepts:
Pre-Alg
Distributive PropertyStep-by-step explanation:
Step 1: Define expression
3(x + 6)
Step 2: Expand
Distribute 3 to both terms: 3x + 18Answer
3x+18 or 3x+9 but I'm not sure which one
for f(x) =4x-1 and g(x) = x2 - 5, find (f-g)(x)
Answer:
(f - g)(x) = -x² + 4x + 4
General Formulas and Concepts:
Pre-Algebra
PropertiesAlgebra I
Combining like termsFunction notationStep-by-step explanation:
Step 1: Define
f(x) = 4x - 1
g(x) = x² - 5
(f - g)(x) = f(x) - g(x)
Step 2: Find
Substitute: (f - g)(x) = 4x - 1 - (x² - 5)Distribute: (f - g)(x) = 4x - 1 - x² + 5Combine like terms: (f - g)(x) = -x² + 4x + 4The life expectancy (M) in the United States is 85 with a standard deviation of 6 years. A random sample of 36 individuals is selected. What is the probability that the sample mean will be between 82.5 and 86 years?
Answer:
The probability that the sample mean will be between 82.5 and 86 years is 0.8351.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu\\[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=85\\\sigma=6\\n=36[/tex]
As the sample size is large enough the Central Limit Theorem can be used to approximate the sampling distribution of sample mean life expectancy (M) in the United States.
Compute the probability that the sample mean will be between 82.5 and 86 years as follows:
[tex]P(82.5<\bar X<86)=P(\frac{82.5-85}{6/\sqrt{36}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{86-85}{6/\sqrt{36}})\\\\=P(-2.5<Z<1)\\\\=P(Z<1)-P(Z<-2.5)\\\\=0.84134-0.00621\\\\=0.83513\\\\\approx 0.8351[/tex]
Thus, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.
The probability that the sample mean will be between 82.5 and 86 years is 0.8351.
Standard deviation σ = 6
Sample size n =36
What is the central limit theorem?The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution.
Since the sample size is significant i.e. large, so the given scenario can be treated as normally distributed as per the central limit theorem.
So, the standard deviation of sample means = σ/√n
The probability that the sample mean will be between 82.5 and 86 years:
[tex]P(82.5 < X < 86) = P(\frac{82.5-85}{\frac{6}{\sqrt{36} } } < Z < \frac{86-85}{\frac{6}{\sqrt{36} } } )[/tex]
[tex]P(-2.5 < Z < 1)=P(Z < 1)-P(Z < 2.5)[/tex]
[tex]P(-2.5 < Z < 1) =0.8413-0.0062=0.8351[/tex]
Therefore, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.
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A book company publishes 749 copies of
a novel and distributes them to 7 bookstores.
If each bookstore were to receive the same
number of copies, how many copies would
be sent to each store?
Answer:
107 copies to each books store
You have $20 to spend on lip balm and hand sanitizer. The equation $1.5x+2.5y=20$ represents this situation, where x is tubes of lip balm and y is bottles of hand sanitizer. How many bottles of hand sanitizer can you buy when you do not buy any tubes of lip balm?
Answer:
13
Step-by-step explanation:
20÷1.5 since there is not X
The difference between a number y and 9 is -34. What is the number?
Answer:
y-9=34
y=34+9
y= 43
Step-by-step explanation:
please Mark as brainliest
Answer:
y= -25 because if you add -25 to 9 it gives you -34
Which product matches the shading on the grids?
Answer:
I believe it is D. not sure tho
What is the most logical explanation for why kilo is a more important prefix to remember than ""tera"" (the metric prefix for 1 trillion)?
We want to compare two prefixes, kilo and tera, and see why one seems to be more important than the other.
The prefix "kilo" is used for thousands, while the prefix "tera" is used for trillions.
Now if you go to your day-to-day life, you will see that the thousands appear a lot more than the trillions.
For example, is more common to walk one or two kilometers than one terameter.
Or also is more common to buy a kilogram of potatoes than one teragram of potatoes.
This is mainly why kilo is more important (actually is more used, I wouldn't say that is more important) than tera.
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Pllls Help ill give brainliesstttt
Number one is 16
number two is 30
Number 3 is 100
Number four is 50
What equation represents the line shown
A.y=2x+2
B.y=-2x+2
C.y=1/2x+2
D.y=1/2x+-2
Answer:
The answer must be either C or D but I think it is D
Step-by-step explanation:
sorry if I am wrong
help help help pls pls ASAP
Answer:
#6 slope is -1/2 and y intercept is 4
#8 slope is 1/3 and y intercept is -2
Step-by-step explanation:
A company refinishes wood floors for $1.50 per square foot. Makayla hires the company to refinish 1,000 square feet
in her home. How much does she pay for the refinishing work?
$500
$1,000
$1,500
$5,000
Answer:
The correct answer is $1,500
Step-by-step explanation:
hope this helps
4.5.36
A smoke jumper jumps from a plane that is 1500 ft above the ground. The function h= - 16t^2+ 1500 gives the jumper's height h in feet during the free fall att seconds
a. How long is the jumper free fall if the parachute opens at 1000 ft?
b. How long is the jumper in free fall if the parachute opens at 940 ft?
c. What is a reasonable domain and range for the function h?
We have a jumper that jumps from 1500ft above the ground, such that its height as a function of time is given by:
h(t) = -16*t^2 + 1500
The solutions are:
A) 5.59 seconds
B) 5.91 seconds
C) D = (0s, 9.68s)
R = [0ft, 1500ft]
Notice that when t = 0, h = 1500, then at the initial time (t = 0) the height is 1500 (in ft), which means that the zero of the height is the ground.
a) How long is the jumper free fall if the parachute opens at 1000 ft?
Here we need to solve:
h = 1000 = -16*t^2 + 1500
Now we just need to solve this for t:
16*t^2 = 1500 - 1000 = 500
t^2 = 500/16 = 31.25
t = √31.25 = 5.59
So it takes 5.59 seconds to open the parachute.
B) similar to before, this time we need to solve:
h = 940 = -16*t^2 + 1500
16*t^2 =1500 - 940 = 560
t^2 = 560/16 = 35
t = √35 = 5.91
So it takes 5.91 seconds to open the parachute.
C) The domain is the set of inputs that we can use in the function.
The minimum of the domain is t = 0, when the jumper jumps.
To find the maximum of the domain we need to find the maximum time at which he could open the parachute, that is when h = 0ft, just in the ground.
Then we solve:
h = 0 = -16*t^2 + 1500
16*t^2 = 1500
t = √(1500/16) = 9.68
Then a reasonable domain is (0s, 9.68s)
And the range is the set of possible outputs, which will be all the possible heights of the jumper. We know that all of these are between 0ft and 1500ft, thus the range is [0ft, 1500ft]
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Can you please help me solve for the area
Answer:
area is equal to 198 cm^2
Step-by-step explanation:
the height h of the left triangle can be obtained by
Pytagoras theorem:
[tex]5^2+h^2=13^2\\25+h^2=169\\h^2=169-25\\h^2=144\\h=\sqrt{144} \\h=12[/tex]
the, the area of the left triangle is
[tex]A_1=\frac{5*12}{2} \\A_1=5*6\\A_1=30[/tex]
the area of the right triangle is
[tex]A_2=\frac{2*12}{2} \\A_2=12[/tex]
and the area of the rectangle in the middle is
[tex]A_3=(13)(12)\\A_3=156[/tex]
Por tanto, el area total sera
[tex]A=A_1+A_2+A_3\\A=30+12+156\\A=198[/tex]
Jessie is playing a game and bets $5 on the come out roll. If a 7 or 11 is rolled, she wins $5. This happens with a probability of 29. If a 2,3,or12 is rolled, she loses her $5. This has a probability of 19. If any other number is rolled, she does not win or lose, and the game continues. Find the expected value for Jessie on the come out roll.
Answer:
.
Step-by-step explanation:
We want to find the expected value for Jessie on the come out roll.
The expected value is EV = $0.50
We know that for an event with outcomes {x₁, x₂, ..., xₙ}, each with probability {p₁, p₂, ..., pₙ}, the expected value is given by:
EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ
Where the probabilities are written in decimal form.
We have the outcomes:
x₁ = winning $5.
p₁ = 0.29
x₂ = losing $5
p₂ = 0.19
x₃ = not win nor lose
p₃ = 1 - 0.19 - 0.29 = 0.52
Then the expected value is:
EV = $5*0.29 - $5*0.19 + $0*0.52 = $0.50
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p=3y/q solve for y make sure to add steps pls
Answer:
Solving for y gives:
[tex]y = \frac{pq}{3}[/tex]
Step-by-step explanation:
Linear equations are the equations that are degree one equations. When it is asked to solve an equation for a specific variable that means that the specified variable has to be isolated on one side of the equation i.e. in the given question solving for y means isolating y on one side of the equation.
Given equation is:
[tex]p = \frac{3y}{q}[/tex]
Multiplication property of equality(Multiplying both sides by q)
[tex]p*q = \frac{3y}{q} * q\\pq = 3y[/tex]
Division property of equality(Dividing both sides by 3)
[tex]\frac{pq}{3} = \frac{3y}{3}\\\frac{pq}{3} = y[/tex]
Hence,
Solving for y gives:
[tex]y = \frac{pq}{3}[/tex]
Leanne runs on the treadmill and rides the exercise bike at the gym to stay in shape. She burns 15 calories per minute on the treadmill and 9 calories per minute on the bike. She wants to ride the bike 2.5 times as long as she runs on the treadmill and burn a total of 580 calories. The system of equations below can be used to find the number of minutes, t, she should run on the treadmill and the number of minutes, b, she should ride the bike.
According to this system of equations, can Leanne meet both her goals?
A.
Yes, she can run on the treadmill for 15 minutes 28 seconds.
B.
No, she cannot ride the exercise bike a negative number of minutes.
C.
Yes, she can ride the exercise bike for 15 minutes 28 seconds.
D.
No, she cannot run on the treadmill for a fractional number of minutes.
Answer: C
Step-by-step explanation:
step 1: I
step 2: just
step 3: took
step 4: it
final answer: i took the test and got a 100 so its definitely C.
<3
Which number has a value between -8.423 and -8.395?
A. -8.1
B. -8.75
C. - 8 1/2
D. 8 2/5
Answer:
Step-by-step explanation:
Jmeu eimejrimr
The number between -8.423 and -8.395 will be - 8 2/5.
What is Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
Two numbers are,
⇒ - 8.423 and - 8.395
Now,
Since, Two numbers are,
⇒ - 8.423 and - 8.395
Clearly, - 8.1 is greater than - 8.423 and - 8.395.
Hence, It is not between the numbers - 8.423 and - 8.395.
Clearly, - 8.75 is less than - 8.423 and - 8.395.
Hence, It is not between the numbers - 8.423 and - 8.395.
Clearly, - 8 1/2 is less than - 8.423 and - 8.395.
Hence, It is not between the numbers - 8.423 and - 8.395.
Clearly, - 8 2/5 = - 8.4 is in between - 8.423 and - 8.395.
Hence, It is between the numbers - 8.423 and - 8.395.
Thus, The number between -8.423 and -8.395 will be - 8 2/5.
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In this picture B and F are
midpoints.
x=[ ? ]
Answer: x = 10
see in the picture, ΔACE has:
+) BF//AE
+) B and F are midpoints.
=> BF is the median line of the triangle ACE
=> BF = 1/2. AE
=> AE = 2BF
⇔ 5x - 4 = 2.23 = 46
⇔ 5x = 46 + 4 = 50
⇔ x = 50/5 = 10
Step-by-step explanation:
Leila bought 3 bananas, which weighed a total of 3/4 of a pound . if each banana weighed the same amount , what is the weight of each banana ?
Answer:
1/4
Step-by-step explanation:
3/4 (total weight)
3 bananas
(3/4)/3=1/4
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