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.
A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by performing yoga exercises. A treatment group and a control group are selected. The sample statistics are given below. Construct a 90% confidence interval for the difference between the two population means, Would you recommend using yoga exercises? Treatment Group Control Group n1 = 100 n2 = 100 1 = 178 2 = 193 s1 = 35 s2 = 37
Answer:
90% confidence interval for the difference between the two population means
( -23.4166 , -6.5834)
Step-by-step explanation:
Step(i):-
Given first sample size n₁ = 100
Given mean of the first sample x₁⁻ = 178
Standard deviation of the sample S₁ = 35
Given second sample size n₂= 100
Given mean of the second sample x₂⁻ = 193
Standard deviation of the sample S₂ = 37
Step(ii):-
Standard error of two population means
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]
Degrees of freedom
ν = n₁ +n₂ -2 = 100 +100 -2 = 198
t₀.₁₀ = 1.6526
Step(iii):-
90% confidence interval for the difference between the two population means
[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]
(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)
(-15-8.4166 , -15 + 8.4166)
( -23.4166 , -6.5834)
Why is a rhombus considered a type of quadrilateral?
Answer:
Well a rhombus is considered a quadrilateral because it has 4 sides and 4 angles.
Just like a square and rectangle they both are quadrilaterals with 4 angles and sides.
A rhombus is considered a type of quadrilateral because it has four sides and four angles
How to determine the reason?As a general rule, a shape that is considered a quadrilateral must have:
4 sides4 anglesSince a rhombus has four sides and four angles, then it is considered a type of quadrilateral
Read more about rhombus at:https://brainly.com/question/20627264
#SPJ6
Which phrase represents t times 33 he quotient of a number and 33 the product of a number and 33 the quotient of 33 and a number the difference of a number and 33
Answer:
the product of a number and 33
Step-by-step explanation:
The operation "times" is what is used to form the product of two operands.
"t times 33" is "the product of t and 33"
The U.S. National Whitewater Center in Charlotte uses a pump station to provide the flow of water necessary to operate the rapids. The pump station contains 7 pumps, each with a capacity to deliver 80,000 gallons per minute (gpm). The water channels and ponds in the facility contain 13 million gallons of water. If the pump station is operating 5 pumps simultaneously, assuming ideal conditions how long will it take to completely pump the volume of the system through the pump station
Answer:
t = 32,5 minutes
Step-by-step explanation:
Volume to fill = 13000000 Gal
5 pumps delivering 80000 gal/min
5 * 80000 = 400000 gal/min
If we divide the total volume by the amount of water delivered for the 5 pumps, we get the required time to fill the volume, then
t = 13000000/ 400000
t = 32,5 minutes
60 is x% of 12. Find the value of x.
Answer:
20
Step-by-step explanation:
We can set up a percentage proportion to find the value of x.
[tex]\frac{12}{x} = \frac{60}{100}[/tex]
Now we cross multiply:
[tex]100\cdot12=1200\\\\1200\div60=20[/tex]
Hope this helped!
more math questions if you would
Answer:
A.
Step-by-step explanation:
So we are given the function:
[tex]f(x)=7x+8[/tex]
To find the inverse of the function, we simply need to flip f(x) and x and then solve for f(x). Thus:
[tex]x=7f^{-1}(x)+8\\x-8=7f^{-1}(x)\\f^{-1}(x)=\frac{x-8}{7}[/tex]
So the answer is A.
Answer:
[tex]\large \boxed{\mathrm{Option \ A}}[/tex]
Step-by-step explanation:
f(x) = 7x+8
Write f(x) as y.
y = 7x + 8
Switch variables.
x = 7y + 8
Solve for y to find the inverse.
x - 8 = 7y
[tex]\frac{x-8}{7}[/tex] = y
The mean temperature for the first 4 days in January was 8°C. The mean temperature for the first 5 days in January was 7°C. What was the temperature on the 5th day? SOMEONE HELP FIRST ANSWER BRAINLIEST THIS TIME I PROMISE LOL
Answer:
The temperature of the 5th day was 3°C
Step-by-step explanation:
Mean temperature of the first 4 days = 8°C
Note that:
Mean = Sum of temperatures ÷ number of days
∴ 8 = sum of temperature ÷ 4
[tex]= 8 = \frac{sum\ of\ temperatures}{4}[/tex]
[tex]= sum\ of\ temperatures\ = 8\ \times\ 4 = 32[/tex]
Therefore the sum of the first 4 days = 32
Let the temperature of the next day (the fifth day) be m
Hence,
sum of the temperatures of first 5 days = 32 + m - - - - (1)
Next, the sum of the first 5 days can be calculated from the given average of the first 5 days as follows:
Mean temperature of the first 5 days = 7
[tex]Mean = \frac{sum\ of\ temperatures}{number \ of\ days}\\\\7 = \frac{sum\ of\ temperatures}{5} \\sum\ of\ temperatures\ = \ 7\ \times\ 5\ = 35\\sum\ of\ temperature\ of\ the\ first\ 5\ days\ =\ 35 - - - - - (2)[/tex]
Now, you will notice that equation (1) = equation (2)
∴ 32 + m = 35
m = 35 - 32 = 3
therefore, the temperature of the 5th day was 3°C
area please it's easy plzzzzzzzzzz
a ) Now as you can see, the white region is composed of a triangle and a rectangle. This triangle has a height of 5, as it is composed of the respective blank triangles. It's base is 5 meters as well, by properties of a rectangle - which is sufficient information to solve for the area of the triangle.
Area of Triangle : 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 5 = 2 [tex]*[/tex] 5 = 10 m²
The area of this rectangle will be 3 [tex]*[/tex] 4 = 12 m², considering it's given dimensions are 3 by 4. Therefore the area of this white region will be 10 + 12 = 22 m²
b ) Now this striped region will be the remaining area, or the area of the white region subtracted from the area of the outer rectangle.
Area of Outer Rectangle : 10 [tex]*[/tex] 4 = 40 m²,
Area of Striped Region : 40 - 22 = 18 m²
Hello again. if someone gives me a hand with this book thickness excercise please thanks
Answer:
Known:
• a book have front, back and 200 pages
• front= 0.7 mm
• back= 0.7 mm
• each page= 0,14 mm
ask:
calculate the minimum thickness...?
answer:
a. 200 p × 0,14 = 28 mm
b. front + back = 0.7+0.7= 1.4 mm
Thickness= 28+1,4 = 29,4 mm
I hope this helps
if u have question let me know in comments^_^
in the diagram EF and GH are straight lines. Find the values of a,b,c and d
Please answer this correctly without making mistakes
Answer:
1,377/2 and 688 1/17
Step-by-step explanation:
Find the work done by the force field F(x,y,z)=6xi+6yj+6k on a particle that moves along the helix r(t)=3 cos(t)i+3sin(t)j+2 tk,0≤t≤2π.
Answer:
the work done by the force field = 24 π
Step-by-step explanation:
From the information given:
r(t) = 3 cos (t)i + 3 sin (t) j + 2 tk
= xi + yj + zk
∴
x = 3 cos (t)
y = 3 sin (t)
z = 2t
dr = (-3 sin (t)i + 3 cos (t) j + 2 k ) dt
Also F(x,y,z) = 6xi + 6yj + 6k
∴ F(t) = 18 cos (t) i + 18 sin (t) j +6 k
Workdone = 0 to 2π ∫ F(t) dr
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (18 cos (t) i + 18 sin (t) j +6k)(-3 sin (t)i+3cos (t) j +2k)\ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (-54 \ cos (t).sin(t) + 54 \ sin (t).cos (t) + 12 ) \ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} 12 \ dt}[/tex]
[tex]\mathbf{= 12 \times 2 \pi}[/tex]
= 24 π
a data set includes 110 body temperatures of healthy adult humans having a mean of 98.1F and a standard deviation of 0.64F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans
Answer:
The 99% confidence interval is [tex]97.94 < \mu < 98.26[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 110
The sample mean is [tex]\= x = 98.1 \ F[/tex]
The standard deviation is [tex]\sigma = 0.64 \ F[/tex]
Given that the confidence level is 99% the level of significance i mathematically evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution, the values is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]
[tex]E = 0.1574[/tex]
Generally the 99% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]
[tex]97.94 < \mu < 98.26[/tex]
Answer:
Step-by-step explanation:
A mail truck traveled 82 miles in 4 1/2 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?
Answer:
= 18.2 miles per hour
Step-by-step explanation:
Speed = distance / time
=82 miles / 4.5 hours
=18.22222222 miles per hour
Rounding
= 18.2 miles per hour
Answer:
Given that
Distance = rate × time
82 = r × 4½
r = 18.2 mph
(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) (a) σ = 18, n = 9 (b) σ = 18, n = 36 (c) σ = 18, n = 144
Answer:
a) 6.00
b) 3.00
c) 1.50
Step-by-step explanation:
Sample error of the mean is expressed mathematically using the formula;
SE = σ /√n where;
σ is the standard deviation and n is the sample size.
a) Given σ = 18, n = 9
Standard error of the mean = σ /√n
Standard error of the mean = 18/√9
Standard error of the mean = 18/3
Standard error of the mean = 6.00
b) Given σ = 18, n = 36
Standard error of the mean = σ /√n
Standard error of the mean = 18/√36
Standard error of the mean = 18/6
Standard error of the mean = 3.00
c) Given σ = 18, n = 144
Standard error of the mean = σ /√n
Standard error of the mean = 18/√144
Standard error of the mean = 18/12
Standard error of the mean = 3/2
Standard error of the mean = 1.50
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 3%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that
Answer:
The probability that none of the LED light bulbs are defective is 0.7374.
Step-by-step explanation:
The complete question is:
What is the probability that none of the LED light bulbs are defective?
Solution:
Let the random variable X represent the number of defective LED light bulbs.
The probability of a LED light bulb being defective is, P (X) = p = 0.03.
A random sample of n = 10 LED light bulbs is selected.
The event of a specific LED light bulb being defective is independent of the other bulbs.
The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.03.
The probability mass function of X is:
[tex]P(X=x)={10\choose x}(0.03)^{x}(1-0.03)^{10-x};\ x=0,1,2,3...[/tex]
Compute the probability that none of the LED light bulbs are defective as follows:
[tex]P(X=0)={10\choose 0}(0.03)^{0}(1-0.03)^{10-0}[/tex]
[tex]=1\times 1\times 0.737424\\=0.737424\\\approx 0.7374[/tex]
Thus, the probability that none of the LED light bulbs are defective is 0.7374.
Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a confidence level of 98%, and use the results from a prior Harris poll that gave a confidence interval of (0.44, 0.51) for the proportion of Democrats who have a sibling.
Answer:
The minimum sample size is [tex]n =135[/tex]
Step-by-step explanation:
From the question we are told that
The confidence interval is [tex]( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)[/tex]
The margin of error is [tex]E = 0.1[/tex]
Generally the sample proportion can be mathematically evaluated as
[tex]\r p = \frac{ upper \ limit + lower \ limit }{2}[/tex]
[tex]\r p = \frac{ 0.51 + 0.44}{2}[/tex]
[tex]\r p = 0.475[/tex]
Given that the confidence level is 98% then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 98[/tex]
[tex]\alpha = 2\%[/tex]
[tex]\alpha =0.02[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
Generally the minimum sample size is evaluated as
[tex]n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )[/tex]
[tex]n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )[/tex]
[tex]n =135[/tex]
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen and bedroom)?
Answer:
The area of the house is A. 1,108
How many different sets of polar coordinates can be given for a point, within one rotation? I thought it was infinite, but the given options are 1, 2, 3, and 4.
Answer:
the answer is 4
Step-by-step explanation:
so 1 rotation is like a circle 1 unit circle requires 4 quadrant to be in this is the most simplified i can get
Answer:
Solution : 4
Step-by-step explanation:
The question asks us how many polar coordinates are possible for one rotation. For one rotation there will be 4 polar coordinates, one present in each quadrant such that,
( r, theta ), ( r, theta ), ( - r, theta ), ( - r, theta )
Respectively if theta was q say,
( r, q ), ( r, - q ), ( - r, q ), ( - r, -q )
Therefore there are 4 sets of polar coordinates for one rotation, in each of the 4 quadrants.
find the circle through (-4,sqrt(5) with center (0,0)
Answer:
Circle Equation : x² + y² = 21
Step-by-step explanation:
So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.
The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,
( √5 )² + ( 4 )² = r²,
5 + 16 = r²,
r = √21
In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -
( x - 0 )² + ( y - 0 )² = (√21 )²
Circle Equation : x² + y² = 21
PLEASE HELP!!! Determine the domain and range of the following function. Record your answers in set notation.
Answer:
Ok so to help you out, first, off you need to be sure that the sets domain and range use the proper variable. After that, you are going to want to just plug it into the equation. I am going to link a screenshot to the correct answer if you are still have trouble finding it.
Anyways hoped this helped and I got to this question in time c:
Kelly bought a cup of coffee and drank 58 of it. Write an addition equation to represent how much coffee is remaining.
Answer:
[tex]L + \frac{5}{8} = 1[/tex]
Step-by-step explanation:
Given
A cup of coffee
Kelly drank 5/8 of the coffee
Required
Determine how much is left
Start by representing the amount of coffee left with L
Because the amount of coffee Kelly drank is in fraction (5/8), the total cup of coffee will equate to 1;
Hence, the addition equation as requested in the question to represent the scenario is
[tex]L + \frac{5}{8} = 1[/tex]
GCF/LCM of 8 and 24 the reduce 8/24
Answer:
GCF(8, 24) = 8LCM(8, 24) = 248/24 = 1/3Step-by-step explanation:
Since 8 is a factor of 24, 8 is the GCF of the pair, and 24 is the LCM of the pair.
__
The ratio 8/24 is reduced by observing that 24 = 8·3:
8/24 = 8/(8·3) = (8/8)·(1/3)
8/24 = 1/3
Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)
Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99 using the cumulative standard normal distribution table
Answer:
6.642
Step-by-step explanation:
Given that mean = 2
standard deviation = 2
Let X be the random Variable
Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])
X [tex]\sim[/tex] N(2,2)
By Central limit theorem;
[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]
[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]
P(X<x) = 0.09
[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]
[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]
P(X < x) = 0.99
[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]
[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]
[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]
[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]
[tex]( \dfrac{X-2}{2})= 2.321[/tex]
X -2 = 2.321 × 2
X -2 = 4.642
X = 4.642 +2
X = 6.642
1f 12% of x is equal to 6% of y, then 18% of x will be equal to how much percent ofy?
Answer:
9%
Step-by-step explanation:
12x=6y eq 1
18x=9y eq 2
what is ap in math abreviation and explain my math teacher was drunk so he couldn't teach nothing
Step-by-step explanation:
n mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.
help asap!! will get branliest.
Answer:
5/2
Step-by-step explanation:
5^(-3). 2^2.5^6 / (2^3.5^2)
By the law of indices,
=5^(-3+6-2).2^(2-3)
=5^1.2^(-1)
=5. 2^-1
=5/2
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste?
Answer:
eddfdgdccggģdffcdrrfxddxcvgfx
Please help me so confused
Answer:
m = 15
Step-by-step explanation:
m/9 + 2/3 = 7/3
Subtract 2/3 from each side
m/9 + 2/3 -2/3= 7/3 -2/3
m/9 = 5/3
Multiply each side by 9
m/9 *9 = 5/3 *9
m = 15
PLEASE HELP!!!
Evaluate the expression when b=4 and y= -3
-b+2y
Answer: -10
Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.
1. -4+2(-3)
2. -4+(-6)
3.-4-6
4.-10
Answer:
8
Step-by-step explanation:
-b + 2y
if
b = 4
and
y = 3
then:
-b + 2y = -4 + 2*6 = -4 + 12
= 8
