Answers
Answer:
C
Step-by-step explanation:
The triangles are similar and the scale factor can be find out by computing 18/6=15/5=9/3=3
Related Questions
Someone please help me
Answers
Answer:
[tex]x < 4368 \frac{8}{19} [/tex]
Step-by-step explanation:
[tex]28x < 83000 + 9x[/tex]
[tex]28x - 9x < 83000[/tex]
[tex]19x < 83000[/tex]
[tex]x < 4368 \frac{8}{19} [/tex]
Find an expression for the general term of each of the series below. Use n as your index, and pick your general term so that the sum giving the series starts with n=0.
A. x^3cosx^2=x^3-(x^7)/2!+(x^11)/4!-(x^15)/6!+...
general term =
B. x^3sinx^2=x^5-(x^9)/3!+(x^13)/5!-(x^17)/7!+...
general term =
Answers
Answer:
[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
Step-by-step explanation:
A
Let's start with the first function:
[tex]x^{3}cos(x^{2})=x^{3}-\frac{x^{7}}{2!}+\frac{x^{11}}{4!}-\frac{x^{15}}{6!}+...[/tex]
In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a
[tex](-1)^{n}[/tex].
This will guarantee us that the terms will always change their signs so that will be the first part of our expression.
next, the power of the x. Notice the given sequence: 3, 7, 11, 15...
we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 3. So the power is given by 4n+3.
so let's put the two things together:
[tex](-1)^{n}x^{4n+3}[/tex]
Finally the denominator, there is also a sequence there: 0!, 2!, 4!, 6!
This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2, so in this case the sequence can be written as: (2n)!
So let's put it all together so we get:
[tex]\frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
So now we can build the whole series:
[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
B
Now, let's continue with the next function:
[tex]x^{3}sin(x^{2})=x^{5}-\frac{x^{9}}{3!}+\frac{x^{13}}{5!}-\frac{x^{17}}{7!}+...[/tex]
In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a
[tex](-1)^{n}[/tex].
This will guarantee us that the terms will always change their signs so that will be the first part of our expression.
next, the power of the x. Notice the given sequence: 5, 9, 13, 17...
we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 5. So the power is given by 4n+5.
so let's put the two things together:
[tex](-1)^{n}x^{4n+5}[/tex]
Finally the denominator, there is also a sequence there: 1!, 3!, 5!, 7!
This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2 starting from a 1, so in this case the sequence can be written as: (2n+1)!
So let's put it all together so we get:
[tex]\frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
So now we can build the whole series:
[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
Math algebra two plz show your work
Answers
Answer:
The answer is [tex]b=3, a=-2[/tex], and [tex]c=3[/tex].
Step-by-step explanation:
To solve this system of equations, start by solving for (a) in the third equation.
To solve for (a) in the third equation, add [tex]3b[/tex] to both sides of the equation, which will look like [tex]2a=-13+3b\\-a+b-c=2\\2a+3b-4c=-7[/tex]. Next, divide each term in [tex]2a=-13+3b[/tex] by 2 and simplify, which will look like [tex]\frac{2a}{2}=\frac{-13}{2} +\frac{3b}{2} \\-a+b-c=2\\2a+3b-4c=-7[/tex] = [tex]a=\frac{-13}{2} +\frac{3b}{2} \\-a+b-c=2\\2a+3b-4c=-7[/tex].
Then, replace all variables of (a) with [tex]-\frac{13}{2} +\frac{3b}{2}[/tex] in each equation and simplify, which will look like [tex]-13+6b-4c=-7\\-\frac{2c-13+b}{2}=2\\a=-\frac{13}{2}+\frac{3b}{2}[/tex].
The next step is to reorder [tex]-\frac{13}{2}[/tex] and [tex]\frac{3b}{2}[/tex], which will look like [tex]\frac{3b}{2}-\frac{13}{2}\\-13+6b-4c=-7\\-\frac{2c-13+b}{2} =2[/tex].
Then, solve for (b) in the second equation. To solve for (b) in the second equation start by moving all terms not containing (b) to the right side of the equation, which will look like [tex]6b=6+4c\\a=\frac{3b}{2}-\frac{13}{2} \\-\frac{2c-13+b}{2} =2[/tex]. Next, divide each term in ([tex]6b=6+4c[/tex]) and simplify, which will look like [tex]b=1+\frac{2c}{3} \\a=\frac{3b}{2} -\frac{13}{2\\}\\-\frac{2c-13+b}{2} =2[/tex].
Then, replace all variables of (b) with [tex]1+\frac{2c}{3}[/tex] in each equation and simplify, which will look like [tex]-\frac{2(2c-9)}{3}=2\\a=c-5\\b=1+\frac{2c}{3}[/tex].
The next step is to solve for (c) in the first equation. To solve for (c) in the first equation start by multiplying both sides of the equation by [tex]-\frac{3}{2}[/tex] and simplify, which will look like [tex]2c-9=-3\\a=c-5\\b=1+\frac{2c}{3}[/tex]. Then, move all terms not containing (c) to the right side of the equation, which will look like [tex]2c=6\\a=c-5\\b=1+\frac{2c}{3}[/tex]. Next, divide each term in [tex]2c=6[/tex] by 2 and simplify, which will look like [tex]c=3\\a=c-5\\b=1+\frac{2c}{3}[/tex].
Then, replace all variables of (c) with 3 in each equation and simplify, which will look like [tex]b=3\\a=-2\\c=3[/tex]. Finally, the list of all the solutions are [tex]b=3,a=-2[/tex], and [tex]c=3[/tex].
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and continuously.
Answers
Answer:
annual - $9,231.74
quarterly - $9,363.06
monthly - $9,394.09
continuously -$9,409.87
Step-by-step explanation:
In a shipment of toys from a manufacturer, the probability that a toy is defective is
1
50
. If Marie selects 2 toys from a shipment, what is the probability that both toys are defective?
Answers
Answer:
The probability is 1/2500. (1/50)*(1/50)
Step-by-step explanation:
20 marbles, 4 red, 6 blue,2 green, 8 yellow, one marble taken out , replaced, one taken out. Probability that he will pull red marble first, then green marble
Answers
Step-by-step explanation:
red=4/19
green2/1
i didnt get the qn prperly..was a marbke taken out second time？ and not replaced？
x °
68°
26 °
Find the measure of x (Hint: The sum of the measures
of the angles in a triangle is 180°
Answers:
6 °
86 °
90 °
180 °
Answers
Answer:
86°
Step-by-step explanation:
180° is the sum of all angles in a triangle
The two angles given are 68° and 26°
The equation is : 180° - 68° - 26° = x°
180° - 68° - 26° = 86°
x° = 86°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
I WILL MARK BRAINLIEST PLEASE HELP! This graph represents f(x), and g(x) = -7x + 8.
Which statement about these functions is true?
A.
Function f(x) is increasing, and g(x) is decreasing.
B.
Function f(x) is decreasing, and g(x) is increasing.
C.
Functions f(x) and g(x) are both decreasing.
D.
Functions f(x) and g(x) are both increasing.
Answers
Answer:
A
Step-by-step explanation:
ITS OPTION (A)
PLZ MARK ME BRAINLIEST..
What is the answer??
Answers
Answer:
Step-by-step explanation:
Let AC = x
AB - AC = 4 cm
AB = 4 +x ----------------(I)
Pythagorean theorem
AB² + AC² =BC²
(4 + x)² + x² = 9²
Use the identity (a + b)² = a² + 2ab + b² where a = 4 & b = x
4² +2*4*x +x² + x²= 81
16 + 8x + 2x² = 81
2x² + 8x + 16 - 81 = 0
2x² + 8x - 65= 0
a = 2 ; b = 8 ; c = -65
D = b² - 4ac
= 8² - 4*2*(-65)
= 64 + 520
D = 584
√D = √584 = 24.16
[tex]x=\frac{-b+\sqrt{D}}{2a} \ or \ x =\frac{-b-\sqrt{D}}{2a}\\\\x= \frac{-8+24.16}{2*2} \ or \ x = \frac{-8-24.6}{2*2}[/tex] {Ignore this as it is negative.}
x = 16.16/4
x = 4.04
AC = 4.04 Cm
AB = 4 + 4.04 = 8.04 cm
Area of triangle ABC = [tex]\frac{1}{2}* base * height[/tex]
[tex]=\frac{1}{2}*4.04 *8.04\\\\= 2.02 * 8.04[/tex]
= 16.24 sq.cm
You invest $15,000 into two different accounts. One of the accounts has 4% interest and the other has 3.2% interest. After one year, you have accumulated a total of $545.60 in interest. How much was initially invested in the account with 4% interest?
Answers
Answer:
(4%) ... $8200
Step-by-step explanation:
x + y = 15000
.04x + .032y = 545.60
y = 15000 - x
.04x + .032(15000 - x) = 545.60
.008x = 65.6
x=8200
The cost a company pays a lender for a loan is called interest.
The account received an initial investment of 8200 with 4% interest.
What is meant by interest?The cost of borrowing money is called interest, and it is typically expressed as a percentage, such as an annual percentage rate (APR). Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.
The cost a company pays a lender (creditor) for a loan is called interest. Although many different arrangements are possible, interest payments are typically based on the remaining balance of a loan and paid on a monthly basis. At a predetermined interest rate, interest is typically calculated as a percentage of the loan balance.
From the given information, we get
x + y = 15000 ........(1)
0.04x + 0.032y = 545.60 ..........(2)
From (1),
y = 15000 - x
substitute the value of y in the above equation, we get
⇒ 0.04x + 0.032(15000 - x) = 545.60
simplifying the above equation, we get
⇒ 0.008x = 65.6
x = 8200
Therefore, 8200 was initially invested in the account with 4% interest.
To learn more about Interest refer to:
https://brainly.com/question/2294792
#SPJ2
Graph the linear equation find three points that solve the equation then plot on the graph. x-y=0
Answers
Answer:
Step-by-step explanation:
> the equation given is x-y =0
> three points that will solve the equation could be
if x= -2 , y = -2 then x-y = 0 is -2 -(-2) =0 so it works point (-2,-2)
if x=1, y = 1 then x-y = 0 is 1-1 =0 is true so we have point (1, 1)
if x=2 ,y= 2 then x-y = 0 is 2-2 =0 is true so we have point (2, 2)
answer please don't skip plz answer
What is the value of x^2
-2xy+y^2
if x-y = 4 ?
please answer
Answers
Answer:
16
Step-by-step explanation:
[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]
[tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]
The value of x^2-2xy+y^2
will be 16 .
Explanation is in the attachment .
hope it is helpful to you ☺️
Is x-3 a factor of x- 9x² - 14x + 24?
Answers
9514 1404 393
Answer:
no
Step-by-step explanation:
We assume you are concerned with the cubic
x³ -9x² -14x +24
Its factors are all irrational, as shown in the attached graph. x-3 is not a factor.
__
x-3 is a factor if the expression evaluates to zero when x=3. Here, it does not.
((x -9)x -14)x +24 for x=3 is ...
((3 -9)(3) -14)(3) +24 = (-18 -14)(3) +24 = -96 +24 = -72
The remainder from division by x-3 is not zero, so x-3 is not a factor.
Eight more than one-half of a number is twenty-two. Find the number.
Answers
Answer:
Below.
Step-by-step explanation:
22-8 = 14x2 = 28.
Explanation:
The problem written in numeric form is 8 + .5X = 22
To solve that problem we minus 8 from booth sides
8 + .5X = 22
-8 -8
————————-
.5X = 14
Then we multiply by 2 to isolate X
.5X = 14
x 2 x 2
—————-
1X = 28 or X = 28
We can now see that x = 28
Hope this helps! Please consider making me the Brainliest, I work very hard and put a lot of time and effort into every answer, it’s not necessary but very much appreciated! Have a great day and stay safe and healthy! :)
Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads? P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 6 Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 9 Subscript 9 Baseline C Subscript 6 Baseline (0.5) Superscript 6
Answers
Answer:
[tex]P(3) = ^9C_3 * 0.5^3 *0.5^6[/tex]
Step-by-step explanation:
Given
[tex]n = 9[/tex] --- number of flips
Required
[tex]P(x = 3)[/tex]
The probability of getting a head is:
[tex]p = \frac{1}{2}[/tex]
[tex]p = 0.5[/tex]
The distribution follows binomial probability, and it is calculated using:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
So, we have:
[tex]P(3) = ^9C_3 * 0.5^3 * (1 - 0.5)^{9-3}[/tex]
[tex]P(3) = ^9C_3 * 0.5^3 *0.5^6[/tex]
Answer:
Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads?
Answer: A
Step-by-step explanation:
If 4x³+kx²+px +2 is divisible by x²+ α prove that kp=8.
Answers
Answer:
Attached images
It was just easier for me this way.
Let me know in comments if you have questions.
Step-by-step explanation:
Write an equation of the line that passes through the point (4, –5) with slope 2.
A. y−4=−2(x+5)
B. y+5=−2(x−4)
C. y+5=2(x−4)
D. y−4=2(x+5)
Answers
In y = mx + b form:
y = 2x - 13
What are the values of x for which the denominator is equal to zero for y=(x+3)/(x^2+4x)
Answers
9514 1404 393
Answer:
-4, 0
Step-by-step explanation:
The denominator is x^2+4x. This is zero when ...
x^2 +4x = 0
x(x +4) = 0
The zero product rule tells you the product is zero when the factors are zero.
x = 0
x +4 = 0 ⇒ x = -4
The denominator is zero for x=0 and x=-4.
The scale on a map indicates that 1 inch corresponds to an actual distance of 75 miles. Two cities are 5.5 inches apart on the map. What is the actual distance between the two cities?
Answers
Answer:
412.5
Step-by-step explanation:
Answer:
[tex]412.5[/tex] miles
Step-by-step explanation:
Since 1 inch=75 miles you just multiply [tex]75*5.5[/tex] to get how many miles 5.5 inches is.
Tammy makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Answers
Answer:
P=8(h)
Step-by-step explanation:
P is her total pay. You find that by multiplying what she makes an hour (8) by the total number of hours she has worked (h).
Answer:
p=8h
Step-by-step explanation:
Pay equals $8 per the number of hours
Use the graph to find the y-intercept and axis of symmetry
Answers
Answer:
axis of symmetry=-2
y intercept=(0,-1)
help with algebra pls help
Answers
9514 1404 393
Answer:
a. 1.48 seconds
Step-by-step explanation:
You want to find the larger value of t such that h(t) = 10.
-16t^2 +25t +8 = 10
16t^2 -25t +2 = 0 . . . . subtract the left side to get standard form
Using the quadratic formula, we find the values of t to be ...
t = (-(-25) ± √((-25)^2 -4(16)(2)))/(2(16)) = (25±√497)/32
t ≈ 0.08 or 1.48
The ball goes in the hoop about 1.48 seconds after it is thrown.
__
Additional comment
The quadratic formula tells us the solution to ...
ax² +bx +c = 0
is given by ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, we have a=16, b=-25, c=2. Of course, our variable is t, not x, but the relation is the same.
2 The product of two numbers is 5425. If one of them is 25. What is the other 2 number
Answers
Answer:
217
Step-by-step explanation:
5425/25 = 217
Which choice correctly shows the line y =
2x+3?
А
B
HN
N
1-3 -2 -1 1 2 3 4
-1
NH
-4 -3 -2 -1
1 2 3 4
D
c
2
1
1-3-2-1
1
2 3 4
-4 -3 -2
1 2 3
-1
-2
Answers
Help me pls, BRAINEST AWARD
Answers
Answer:
x = 3.7
Step-by-step explanation:
By applying sine ratio for the given angle B,
sin(39°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(39°) = [tex]\frac{AD}{AB}[/tex]
0.6293 = [tex]\frac{AD}{7}[/tex]
AD = 4.41
By applying tangent ratio for the given angle C,
tan(50°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
1.19 = [tex]\frac{AD}{x}[/tex]
1.19 = [tex]\frac{4.41}{x}[/tex]
x = 3.7
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?
Answers
Answer:
a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.
b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.
c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.
d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal 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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.
This means that [tex]\mu = 273, \sigma = 100[/tex]
A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 30, s = \frac{100}{\sqrt{30}}[/tex]
The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}[/tex]
[tex]Z = 0.88[/tex]
[tex]Z = 0.88[/tex] has a p-value of 0.8106
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}[/tex]
[tex]Z = -0.88[/tex]
[tex]Z = -0.88[/tex] has a p-value of 0.1894
0.8106 - 0.1894 = 0.6212
0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.
B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 50, s = \frac{100}{\sqrt{50}}[/tex]
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}[/tex]
[tex]Z = 1.13[/tex]
[tex]Z = 1.13[/tex] has a p-value of 0.8708
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}[/tex]
[tex]Z = -1.13[/tex]
[tex]Z = -1.13[/tex] has a p-value of 0.1292
0.8708 - 0.1292 = 0.7416
0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.
C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 100, s = \frac{100}{\sqrt{100}}[/tex]
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a p-value of 0.9452
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a p-value of 0.0648
0.9452 - 0.0648 =
0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.
D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?
None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.
C is actually 0.8904
for anybody else stuck on this wondering why cengage is telling you c is wrong
A hotel manager calculates that 12% of the hotel rooms are booked. If the manager is right, what is the probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%?
Answers
Answer:
0.0735 = 7.35% probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal 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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A hotel manager calculates that 12% of the hotel rooms are booked.
This means that [tex]p = 0.12[/tex]
Sample of 556 rooms
This means that [tex]n = 556[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.12[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.12*0.88}{556}} = 0.0138[/tex]
What is the probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%?
This is the p-value of Z when X = 0.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.1 - 0.12}{0.0138}[/tex]
[tex]Z = -1.45[/tex]
[tex]Z = -1.45[/tex] has a p-value of 0.0735
0.0735 = 7.35% probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%.
the amount of mil available per child in a day care centrr is given by the function m(x) =25/x, where x is the number of children and m is the quantity of available milk in liters. if 50 children are present on a day how much milk is available per child
Answers
Answer:
0.5 liters of milk are available per child.
Step-by-step explanation:
Amount of milk available per children:
The amount of milk, in liters, available for x children is given by:
[tex]m(x) = \frac{25}{x}[/tex]
50 children are present on a day
This means that [tex]x = 50[/tex]
How much milk is available per child?
This is m(50). So
[tex]m(50) = \frac{25}{50} = 0.5[/tex]
0.5 liters of milk are available per child.
6(5x/3 -4/3 - 2)= 6 (3 - 6x/6 +4/6)
Answers
Answer:
21/8x
Step-by-step explanation:
10x -20 = -6x+22
+6x-20 = 22
16x-20 = 22
16x +20= +20
16x/16x = 42/16x
x = 21/8x
F(x) =-2x-4 find x if f(x)=14
Answers
Answer:
14=-2x-4
18=-2x
x=-9
Hope This Helps!!!
