Answer:
0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].
150 guests booked:
This means that [tex]n = 150[/tex]
85% of booked guests show up for their room.
This means that [tex]p = 0.85[/tex]
Is the normal approximation suitable:
[tex]np = 150(0.85) = 127.5[/tex]
[tex]n(1-p) = 150(0.15) = 22.5[/tex]
Both greater than 10, so yes.
Mean and standard deviation:
[tex]\mu = E(X) = np = 150*0.85 = 127.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.85*0.15} = 4.3732[/tex]
Find the probability that if the motel books 150 guests, not enough seats will be available.
More than 140 show up, which, using continuity correction, is [tex]P(X > 140 + 0.5) = P(X > 140.5)[/tex], which is 1 subtracted by the p-value of Z when X = 140.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140.5 - 127.5}{4.3732}[/tex]
[tex]Z = 2.97[/tex]
[tex]Z = 2.97[/tex] has a p-value of 0.9985.
1 - 0.9985 = 0.0015.
0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.
find the derivative of y=(x³-5)⁴(x⁴+3)⁵
Answer:
[tex]12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}[/tex]
Step-by-step explanation:
e lifetimes of lightbulbs of a particular type are normally distributed with a mean of290 hours and astandard deviation of6 hours. What percentage of the bulbs have lifetimes that lie within 1 standarddeviation to either side of the mean
Answer:
Step-by-step explanation:
[tex]p(\overline{X}-\sigma \leq X \leq \overline{X}+\sigma)\\\\=p(\dfrac{\overline{X}-\sigma -\overline{X} }{\sigma} \leq Z \leq \dfrac{\overline{X}+\sigma -\overline{X} }{\sigma} )\\\\=p ( -1 \leq Z \leq 1)\\\\=2*(\ p (Z \leq 1)-0.5)\\\\=2*(0.8413-0.5)\\\\=0.6826\\\\\approx{68\%}[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Chapter 11 part 2:
What are three different properties of logarithmic functions when encountering the operations of addition, subtraction, and multiplication? Provide an example of each.
The three main log rules you'll encounter are
log(A*B) = log(A) + log(B)log(A/B) = log(A) - log(B)log(A^B) = B*log(A)The first rule allows us to go from a log of some product, to a sum of two logs. In short, we go from product to sum. The second rule allows us to go from a quotient to a difference. Lastly, the third rule allows to go from an exponential to a product.
Here are examples of each rule being used (in the exact order they were given earlier).
log(2*3) = log(2) + log(3)log(5/8) = log(5) - log(8)log(7^4) = 4*log(7)----------------
Here's a slightly more complicated example where the log rules are used.
log(x^2y/z)
log(x^2y) - log(z)
log(x^2) + log(y) - log(z)
2*log(x) + log(y) - log(z)
Hopefully you can see which rules are being used for any given step. If not, then let me know and I'll go into more detail.
someone help me pls i need to pass summer school
Answer:
A
Step-by-step explanation:
The be the inverse function the domain {4,5,6,7} becomes the range and the range {14,12,10,8} becomes the domain
14 → 4
12 →5
10 →6
8 →7
What is the equation of the line that passes through (4,3) and (2, -1)?
y = 4x -13
y = 6x+4
y = 2x-5
y = 1/2 x -2
Answer:
y=2x-5
Step-by-step explanation:
By using two-points form:
y-y1/y2-y1=x-x1/x2-x1
p(x1,y1)=(4,3)
p(x2,y2)=(2,-1)
Subtitute points in formula:
y-3/-1-3=x-4/2-4
y-3/-4=x-4/-2
y-3/-2=x-4/-1
1(y-3)=2(x-4)
y-3=2x-8
y=2x-8+3
y=2x-5
Note:if you need to ask any question please let me know.
One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.
9514 1404 393
Answer:
90°, 60°, 30°
Step-by-step explanation:
The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.
The first angle is 3 ratio units, or 90°.
The second angle is 2 ratio units, or 60°.
The third angle is half that, or 30°.
The three angles are 90°, 60°, 30°.
Algebra II Part 1
Choose the expression or equation that correctly represents this information
Rose works eight hours a day for five days a week. How many hours will she work in sa
weeks?
hours = 40 = 6
hours = 40.6
hours = 6 = 40
Answer:
240 i.e 40*6
Step-by-step explanation:
if rose works 8hrs per day then she works 40 hrs per week (5 days) therefore 40 hrs per 6 weeks =40*6=240
Answer:
40
Step-by-step explanation:
a man spends RS 608 a month. If he earns Rs 640, what percentage of his invome does he save??.
Please explanation
Answer:
5%
Step-by-step explanation:
given,
Earns= Rs 640
spends= Rs 608
saves= (Rs 640 - Rs 608)
=Rs 32
therefore, 32/640x100
answer = 5%
Answer From Gauth Math
Answer:
5%
Step-by-step explanation:
save=640-608=32
(32/640)*100%
5%
3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}
A.657
B.2433
C. -843
Answer:
657
Step-by-step explanation:
pemdas
The value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.
Hence option A is correct.
Given is an expression, 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}, we need to simplify it,
Let's break down the expression step by step:
First, let's simplify the expression inside the innermost parentheses:
8 - 2 x 3 = 8 - 6 = 2
Next, let's simplify the expression inside the brackets:
3 x 23 - 2 = 69 - 2 = 67
Now, let's substitute the simplified expression inside the brackets back into the original expression:
(300 - 70 ÷ 5) - 67
Next, let's simplify the expression inside the remaining parentheses:
70 ÷ 5 = 14
Now, let's substitute the simplified expression inside the parentheses back into the expression:
(300 - 14) - 67
Next, let's simplify the expression inside the remaining parentheses:
300 - 14 = 286
Now, let's substitute the simplified expression inside the parentheses back into the expression:
286 - 67
Finally, let's perform the subtraction:
286 - 67 = 219
Now, let's multiply the result by 3:
3 x 219 = 657
Therefore, the value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.
Learn more about expression click;
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596 is divisible by 2?
a.yes
b.no
Answer:
It's yes
Step-by-step explanation:
Answer:
yep
Step-by-step explanation:
number is even, so it can be evenly divided by 2. :)
After running 3/4 of a mile tess has only run 1/3 how long is the race in miles but I want to know how you did it
Complete the equation describing how x
and y are related.
Х у
y = [? ]x +
07
1 9
2 11
3 13
4 15
5 17
Enter the answer that
belongs in [?]
Answer:
Hello,
Answer 2
Step-by-step explanation:
7=2*0+7
9=2*1+7
11=2*2+7
13=2*3+7
15=2*4+7
17=2*5+7
y=2*x+7
An other way:
[tex]points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\[/tex]
The complete equation is [tex]y = 2x+7[/tex].
What is equation?An equation is a condition on a variable such that two expressions in the variable should have equal value.
What is substitution?Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
[tex]y = ax + b[/tex]
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
[tex]\implies 7 = a(0) + b\\\implies b = 7[/tex]
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
[tex]\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2[/tex]
substitute the value of a and b in the equation y = ax + b.
[tex]\implies y = 2x+ 7[/tex]
Therefore, the complete equation is [tex]y = 2x+7[/tex].
Find out more information about equation and substitution here:
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Your car can go 2/7 of the way on 3/8 of a tank of gas how far can you go on the remaining gas?
A proportion that can be used is a/b=c/d
Answer:
10/21 of the distance
Step-by-step explanation:
2/7 distance
------------------
3/8 tank
The rest of the tank is 8/8 - 3/8 = 5/8
2/7 distance x
------------------ = ----------------------
3/8 tank 5/8 tank
Using cross products
2/7 * 5/8 = 3/8x
10/56 = 3/8x
Multiply each side by 8/3
10/56 * 8/3 = 3/8x * 8/3
10/3 * 8/56=x
10/3 * 1/7 =x
10/21 =x
10/21 of the distance
I’m new to this app and I need help with those two questions please help!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilities
a. The student will correctly answer the first question after the 4th attempt.
b. The student will correctly answer three questions after 10 total attempts.
c. What is the average number and SD of attempts up to when the student answers all the questions correctly?
Solution :
a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.
P (correct in the 4th attempt)
= [tex]$(1-0.75)^3 \times 0.75$[/tex]
= 0.01171875
b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]
= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.
[tex]$E(X)=\frac{k}{p}$[/tex]
[tex]$=\frac{6}{0.75}$[/tex]
= 8
So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]
[tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]
= 1.6330
The diameters of ball bearings are distributed normally. The mean diameter is 7373 millimeters and the variance is 44. Find the probability that the diameter of a selected bearing is less than 7676 millimeters. Round your answer to four decimal places.
Answer:
0.9332
Step-by-step explanation:
We are given that
Mean diameter, [tex]\mu=73[/tex]
Variance, [tex]\sigma^2=4[/tex]
We have to find the probability that the diameter of a selected bearing is less than 76.
Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]
[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]
[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]
Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]P(x<76)=P(Z<1.5)[/tex]
[tex]P(x<76)=0.9332[/tex]
Hence, the probability that the diameter of a selected bearing is less than 76=0.9332
If side A is 10 inches long, and side B is 24 inches, find the length of the unknown side.
Step-by-step explanation:
Right Triangles and the Pythagorean Theorem. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.
identify an equation in point slope form for the line perpendicular to the y=-1/2x+11 that passes through (4,-8). a. y+8=1/2(x-4) b. y-4=2(x+8) c. y-8=1/2(x+4) d. y+8=2(x-4)
Answer:
d. y+8=2(x-4)
Step-by-step explanation:
There are 2 important parts to this question. First, understanding which slopes are perpendicular. The negative reciprocal of a number will be perpendicular to it. So, since the original slope is -1/2 the new slope should be 2.
Then, remember what the point-slope formula is. The point-slope formula is: [tex]y-y_{2}=m(x-x_{2})[/tex]. So if you plug in the point and slope the new equation looks like, [tex]y--8=2(x-4)[/tex]. Then, simplify for the final answer of [tex]y+8=2(x-4)[/tex].
I need help with ged
Answer:
General Educational Development (GED) tests
What do subject do you need help?
Step-by-step explanation:
The GED® exam is made up of 4 subjects, broken into separate exams: Mathematical Reasoning, Reasoning Through Language Arts, Social Studies, and Science.
Help me please and thank you
Answer:
Option C is correct
Step-by-step explanation:
[tex]log( {10}^{3} )[/tex]
Use logarithm rules to move 3 out of the exponent.[tex]3 \: log \: (10)[/tex]
Logarithm base 10 of 10 is 1.[tex]3×1[/tex]
Multiply 3 by 1.[tex]3[/tex]
Hope it is helpful....
I need help answering this ASAP
Answer:
A the input x=3 goes to two different output values
Step-by-step explanation:
This is not a function
x = 3 goes to two different y values
x = 3 goes to t = 10 and y = 5
Explain why the equation x=x+1 is a contradiction
Answer:
It results in no solution.
Step-by-step explanation:
If you subtract x on both sides, this will leave you with 0 ≠ 3. The result is no solution. This is why it is contradictory.
pls help! I need the answer fast!
Answer:
B is the answer
Step-by-step explanation:
hope it helps
i need help with this question asapppppp
9514 1404 393
Answer:
$11,680.58
Step-by-step explanation:
Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.
__
The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.
The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...
0.205×21,465 = 4400.325 ≈ 4400.33
The the total tax due on $70,000 is ...
$7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000
_____
Additional comments
The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.
__
Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.
≤ 48535 -- income × 0.15
≤ 97069 -- income × 0.205 -2669.425
≤ 150,473 -- income × 0.26 -8008.22
≤ 214,368 -- income × 0.29 -12,522.41
> 214,368 -- income × 0.33 -21,097.13
In this case, the second row of this simpler table would give the tax on $70,000 as ...
tax = 70,000 × 0.205 -2669.425
tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above
Plz help me i need this question solution
Answer:
your mom
Step-by-step explanation:
the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)
9514 1404 393
Answer:
all real numbers
Step-by-step explanation:
The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.
The domain of g(x) = f(-x) is all real numbers.
what Is the si unit of temperature
Answer:
the Si unit of temprature in Kelvin (K)
Step-by-step explanation:
Answer:
The answer is Kelvin (k).
Step-by-step explanation:
The kelvin (K) is defined by taking the fixed numerical value of the Boltzmann constant k to be [tex]1.380649*10^{-23}[/tex] when expressed in the unit of joule per kelvin. The temperature 0 K is commonly referred to as "absolute zero." On the widely used Celsius temperature scale, water freezes at 0 °C and boils at about 100 °C. One Celsius degree is an interval of 1 K, and zero degrees Celsius is 273.15 K. An interval of one Celsius degree corresponds to an interval of 1.8 Fahrenheit degrees on the Fahrenheit temperature scale.
The kelvin is also the fundamental unit of the Kelvin scale, an absolute temperature scale named for the British physicist William Thomson (known as Lord Kelvin). An absolute temperature scale has as its zero point absolute zero (−273.15° on the Celsius temperature scale and −459.67° on the Fahrenheit temperature scale), the theoretical temperature at which the molecules of a substance have the lowest energy; hence, all values on such a scale are nonnegative.
Find the coordinates of the vertices of the figure after the given transformation: T<0,7>
A. X′(1,−1),L′(0,2),W′(2,1)
B. X′(−4,2),L′(−5,5),W′(−3,4)
C. X′(3,2),L′(2,5),W′(4,4)
D. X′(0,−3),L′(−1,0),W′(1,−1)
Answer: B
Step-by-step explanation:
Why did historians choose to study this topic?
Help Please
2(-1+-4)-d^2
Solving Equations by Dividing 2) 9x= -135 Solve for x. 0 -144 O 126 O 15 0 -15
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{9x = -135}}[/tex]
[tex]\huge\boxed{\text{DIVIDE 9 to BOTH SIDES}}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{9x}{9}= \dfrac{-135}{9}}}[/tex]
[tex]\huge\boxed{\mathsf{\bullet \ CANCEL: \dfrac{9}{9}\ because\ it \ gives\ you\ 1}}[/tex]
[tex]\huge\boxed{\bullet\ \mathsf{KEEP: \dfrac{-135}{9}\ because\ it\ helps\ solve \ for}}\\\huge\boxed{\mathsf{the\ x-value}}[/tex]
[tex]\huge\boxed{\mathsf{x = \dfrac{-135}{9}}}\\\\\huge\boxed{\mathsf{\dfrac{-135}{9}= x}}}[/tex]
[tex]\huge\boxed{Simplify \ it\uparrow}[/tex]
[tex]\huge\boxed{\mathsf{x = \bf -15}}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your answer is: Option D. -15 }}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
