Answer:
This is a binomial experiment .
Step-by-step explanation:
As the percent is not indicated the success is the amount of percent (if given) say it is 10 % . So p will be equal to = 0.1 and q will be = 1-0.1= 0.9
and n would be five or any number as a binomial experiment is repeated for a fixed number of times.
And x would take any value of n i.e.
X= 0,1,2,3,4,5
If it is 20 % . So p will be equal to = 0.2 and q will be = 1-0.2= 0.8
The probability is the number of the percent indicated. But as it is not indicated we assume it to be 10 % or 20 % .Or suppose any number for it to be a binomial experiment.
The number of trials n would be fixed .
The success remains constant for all trials.
All trials are independent.
Given the following hypotheses: H0: μ = 490 H1: μ ≠ 490 A random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9. Using the 0.01 significance level:
a.) State the decision rule.
b.) Compute the value of the test statistic.
c.) What is your decision regarding the null hypothesis?
Answer:
We conclude that the population mean is equal to 490.
Step-by-step explanation:
We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490 {means that the population mean is equal to 490}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490 {means that the population mean is different from 490}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_1_4[/tex]
where, [tex]\bar X[/tex] = sample mean = 495
s = sample standard deviation = 9
n = sample of observations = 15
So, the test statistics = [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= 2.152
The value of t-test statistics is 2.152.
Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that the population mean is equal to 490.
x = 4: 3x3 - 2x2 +10
Answer:
170
Step-by-step explanation:
3(4)³ - 2(4)² + 10
192 - 32 + 10 = 170
The length of each side of a cubical wooden block is 16 inches. What is the volume of
the block
Hey there! I'm happy to help!
To find the volume of a cube, you simply take whatever the side length is and multiply it by itself 3 times, which is also known as cubing the number!
16×16×16=4096
You can also write it as 16³=4096
This is because the length is 16, the width is 16, and the height is 16, so you multiply them all together!
I hope that this helps! Have a wonderful day!
Determine if the process appears to be within statistical control. If not, state the reason why not.
a. It does not appear to be within statistical control because there is an upward shift.
b. It appears to be within statistical control.
c. It does not appear to be within statistical control because there is an upward trend.
d. It does not appear to be within statistical control because there is increasing variation.
Answer:
c. It does not appear to be within statistical control because there is an upward trend.
Step-by-step explanation:
Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.
Which of the following is true about congruent figures?
They're the same shape and the same size.
They're the same size, but not the same shape.
They're not the same shape or size.
They're the same shape, but not the same size.
Answer:
A
Step-by-step explanation:
congruent means they have the same shape and size. hope this helps :)
The balances in two separate bank accounts that grow each month at different rales are represented by the functions f(x) and gix) In what month do the funds in the f(x) bank account exceed those in the glx)
bank account?
Month (x) f(x) = 2* g(x) = 4x + 12
1
2
16
2.
4
20
O Month 3
O Month 4
O Month 5
O Month 6
Answer:
The balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?
Answer:
6 months
A function is a relationship between inputs where each input is related to exactly one output.
x = 5,
f(5) = [tex]2^5\\[/tex] = 32
g(5) = 4 x 5 + 12 = 20 + 12 = 32
x = 6,
f(6) = [tex]2^6[/tex] = 64
g(6) = 4 x 6 + 12 = 24 + 12 = 36
At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = [tex]2^{x}[/tex]
g(x) = 4x + 12
x = number of months
Now,
x = 3,
f(3) = 2³ = 8
g(3) = 4 x 3 + 12 = 12 + 12 = 24
x = 4,
f(4) = [tex]2^4[/tex] = 16
g(4) = 4 x 4 + 12 = 16 + 12 = 28
x = 5,
f(5) = [tex]2^5\\[/tex] = 32
g(5) = 4 x 5 + 12 = 20 + 12 = 32
x = 6,
f(6) = [tex]2^6[/tex] = 64
g(6) = 4 x 6 + 12 = 24 + 12 = 36
We see that,
At x = 6,
f(5) = 64
g(5) = 36
Thus,
At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.
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A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year. 1 year 5 years 2 years 16 years
Answer:
6 years
Step-by-step explanation:
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
Answer:
5 years
Step-by-step explanation:444
Use the frequency distribution, which shows the number of American voters (in millions) according to age, to
find the probability that a voter chosen at random is in the 18 to 20 years old age range
Ages
18 to 20
21 to 24
25 to 34
35 to 44
45 to 64
65 and over
Frequency
4.2
7.8
20.8
23.7
50.1
28 2
Date
07/2
3:29
The probability that a voter chosen at random is in the 18 to 20 years old age range is 0.0311
(Round to three decimal places as needed.)
07/2
8:52
Question Viewer
07/1
8:03
07/1
5:46
>
07/1
12:2
07/1
5:39
07/1
2:42
Question is complete. Tap on the red indicators to see incorrect answers.
07/1
12:00
Answer:
The probability that a voter chosen at random is in the 18 to 20 years old age range is = 4.2/ 134.8= 0.0311572
Step-by-step explanation:
We can find the probability by simply dividing the frequency of the ages range of 18-20 by the total frequency.
Ages Frequency
18 to 20 4.2
21 to 24 7.8
25 to 34 20.8
35 to 44 23.7
45 to 64 50.1
65 and over 28.2
∑ 134.8
The probability of an event is given by the occurrence of an event by the total occurrences .
So
Here the occurrence of ages 18-20 is given by 4.2
and the total frequency is 134.8
The probability that a voter chosen at random is in the 18 to 20 years old age range is = 4.2/ 134.8= 0.0311572
a lottery offers one $1000 prize one $500 and two $50 prizes. one thousand tickets are sold at $2.50. what is the expectived profit
Answer:
$900
Step-by-step explanation:
To begin with let us estimate the total cash value of the prices
$1000 x 1= 1000
$500 x 1= 500
$50 x 2= 100
Total = $1600
Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets
2.5*1000= $2,500
Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600
Then the expected profit is = $2,500-$1600= $900
solve the following inequalities 7 x minus 5 / 8 x + 3 >4
Answer:
[tex]x> \frac{8}{51} [/tex]
Step-by-step explanation:
[tex]7x - \frac{5}{8} x + 3>4[/tex]
Bring constants to one side, simplify:
[tex] \frac{51}{8} x>4 - 3 \\ \frac{51}{8} x>1 \\ x>1 \div \frac{51}{8} \\ x>1 \times \frac{8}{51} \\ x> \frac{8}{51} [/tex]
*Note that the inequality sign only changes when you divide the whole inequality by a negative number.
Answer:
[tex]x>\frac{8}{51}[/tex]
Step-by-step explanation:
[tex]7x-\frac{5}{8}x+3>4\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\7x-\frac{5}{8}x+3-3>4-3\\\mathrm{Simplify}\\7x-\frac{5}{8}x>1\\\mathrm{Multiply\:both\:sides\:by\:}8\\7x\times \:8-\frac{5}{8}x\times \:8>1\times \:8\\\mathrm{Simplify}\\56x-5x>8\\51x>8\\\mathrm{Divide\:both\:sides\:by\:}51\\\frac{51x}{51}>\frac{8}{51}\\\\x>\frac{8}{51}[/tex]
I hope it helps :)
Yelena needs to swim a total of 8 miles this
week. So far, she swam 5 miles. Use the
equation 5 + m=8 to find how many more
miles Yelena needs to swim.
Answer:
3 miles
Step-by-step explanation:
5 + m=8
Subtract 5 from each side
5-5 + m=8-5
m = 3
She needs to swim 3 more miles
Answer:
Yelena needs to swim 3 more miles
Step-by-step explanation:
You need to solve for the variable "m", which represents the miles. Based on the information, Yelena swam 5 miles and she needs to swim 8. Solve:
[tex]5+m=8[/tex]
To find the value of m, you need to isolate it on one side of the equation. To do this, you need to get the 8 and 5 on the same side of the equal operation. For this, you need to use reverse operations. This undoes the value from one side and does the same on the other, keeping the equation balanced. Since we have a "positive 5", we take the opposite, which would be a "negative 5". So subtract 5 from both sides of the equation:
[tex]5-5+m=8-5[/tex]
Simplify. The 5's cancel each other out, leaving 0. 8-5 is 3:
[tex]m=3[/tex]
The total miles left that Yelena needs to swim is 3 miles.
:Done
Which is a factor of: 2x2+10x+8 ?
Answer:
2 ( x+4) ( x+1)
Step-by-step explanation:
2x^2+10x+8
Factor out 2
2 ( x^2 +5x+4)
What two numbers multiply to 4 and add to 5
4*1 = 4
4+1 = 5
2 ( x+4) ( x+1)
[tex] \large{ \underline{ \underline{ \bf{ \pink{To \: factorise}}}}}[/tex]
2x² + 10x + 8Factorisation:By middle term factorisation,
⇛ 2x² + 2x + 8x + 8
⇛ 2x(x + 1) + 8(x + 1)
⇛ (2x + 8)(x + 1)
⇛ 2(x + 4)(x + 1)
☃️ Now you can break it down and check which are the factors of the polynomial according to options.
━━━━━━━━━━━━━━━━━━━━
Find the sum of the even numbers between 199 to 1999
[tex]S_n=\dfrac{n(a_1+a_n)}{2}\\a_1=200\\a_n=1998\\n=?\\\\a_n=a_1+(n-1)d\\d=2\\1998=200+(n-1)\cdot2\\2n-2=1798\\2n=1800\\n=900\\\\S_{900}=\dfrac{900\cdot(200+1998)}{2}=450\cdot 2198=989100[/tex]
The Sum is 989100.
what is sum of Even numbers?The sum of even numbers formula is determined by using the formula to find the arithmetic progression. The sum of even numbers goes on until infinity. The sum of even numbers formula can also be evaluated using the sum of natural numbers formula. We need to obtain the formula for 2 + 4+ 6+ 8+ 10 +...... 2n.
The sum of even numbers = 2(1 + 2+ 3+ .....n). This implies 2(sum of n natural numbers) = 2[n(n+1)]/2 = n(n+1)
Given:
a1 = 200
an= 1998
So, using formula
S= n(a1 + an)/2
now,
d=2
an= a1+(n-1)d
1998= 200 + (n-1) 2
1998-200= (n-1)2
1798/2=n-1
n= 900
S900= 900( 200 + 1998)/2
=450*2198
= 989100
Hence, the sum is 989100.
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Time spent using e-mail per session is normally distributed with a mean = to 8 minutes and standard deviation = 2minutes. If a random samples of 36 sessions were selected, the computed sample standard deviation would be
a. 0.25
b. 0.3333
c. 0.42
d. 0.48
Answer:
The correct option is (b) 0.3333.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].
The standard error is given as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]
Compute the standard deviation of the sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]
Thus, the standard deviation of the sample mean is 0.3333.
What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)? 3 6
Answer:
6
Step-by-step explanation:
The constant of variation is the slope
k = (y2-y1)/(x2-x1)
= (30-18)/(5-3)
=12/2
= 6
The value of constant of variation, k, is,
⇒ k = 6
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Here, the constant of variation, k, of the line y = kx through (3,18) and (5,30)
Since, The constant of variation is the slope,
Hence, We get;
k = (y₂ - y₁)/(x₂ - x₁)
= (30 - 18)/(5 - 3)
= 12/2
= 6
Thus, the value of constant of variation, k, is,
⇒ k = 6
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una compañía sabe que si produce "x" unidades mensuales su utilidad "u" se podría calcular con la expresión:
u(x)=-0.04x^2+44x-4000
donde "u" se expresa en dólares. Determine la razón del cambio promedio de la utilidad cuando el nivel de producción cambia de 600 a 620 unidades mensuales. Recuerde que la pendiente de la recta secante a la gráfica de la función representa a la razón de cambio promedio.
porfavor alguien que me explique el procedimiento :(
Answer:
Δf(u) /Δx = 92,8 ( razón de cambio promedio)
Step-by-step explanation:
La expresión de la utilidad de la empresa u(x) en función de la cantidad de unidades producidas "x" es:
u(x) = 0,04*x² + 44*x -4000
Entonces la razón de cambio promedio en un intervalo (a ; b) en este caso ( 620 ; 600 ) viene dada por la expresión:
Δf(x)/ Δx = [ f(b) - f(a) ]/( b - a )
en donde f(b) y f(a) se obtienen por sustitución de los valores a y b es decir 600 y 620 respectivamente en la función f(x) = u(x) entonces
Δf(u) /Δx = [ u(b) - u(a) ]/( b -a ) (1)
u(b) = 0,04*(620)² + 44*(620) - 4000
u(b) = 15376 + 27280 -4000
u(b) = 2656 unidades
u(a) = 0,04* (600)² + 44* 600 - 4000
u(a) = 14400 + 26400 - 4000
u(a) = 800
Sustituyendo esos valores en la ecuación 1
Δf(u) /Δx = 2656 - 800 / 620 - 600
Δf(u) /Δx = 92,8
Which is the exponential form of log9 5 = y
Answer:
Step-by-step explanation:
[tex]\log _9\left(5\right)=y\\y=\log _9\left(5\right)[/tex]
if G is the midpoint of FH, FG = 14x + 25 and GH = 73 - 2x, find FH.
Answer:
FH = 134
Step-by-step explanation:
From the question given:
G is the midpoint of FH
FG = 14x + 25
GH = 73 - 2x
FH =?
Next, we shall determine the value of x. The value of x can be obtained as follow:
Since G is the midpoint of FH, this implies that FG and GH are equal i.e
FG = GH
With the above formula, we can obtain the value of x as follow:
FG = 14x + 25
GH = 73 - 2x
x =?
FG = GH
14x + 25 = 73 - 2x
Collect like terms
14x + 2x = 73 - 25
16x = 48
Divide both side by 16
x = 48/16
x = 3
Next, we shall determine the value of FG and GH. These can be obtained as shown below:
FG = 14x + 25
x = 3
FG = 14x + 25
FG = 14(3) + 25
FG = 42 + 25
FG = 67
GH = 73 - 2x
x = 3
GH = 73 - 2x
GH = 73 - 2(3)
GH = 73 - 6
GH = 67
Finally, we shall determine FH as follow:
FH = FG + GH
FG = 67
GH = 67
FH = FG + GH
FH = 67 + 67
FH = 134
Therefore, FH is 134
What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square root of 82. units square root of 85. units square root of 89. units
Answer:
[tex]\sqrt{85}[/tex].
Step-by-step explanation:
[tex]x[/tex]-coordinates:
First point: [tex]-1[/tex].Second point: [tex]6[/tex].Difference: [tex]|-1 - 6| = |-7| = 7[/tex].[tex]y[/tex]-coordinates:
First point: [tex]4[/tex].Second point: [tex]-2[/tex].Difference: [tex]|4 - (-2)| = |6| = 6[/tex].Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:
the difference between the two [tex]x[/tex]-coordinates, [tex]7[/tex], and the difference between the two [tex]y[/tex]-coordinates, [tex]6[/tex].Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)
[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}[/tex].
Answer:
C
Step-by-step explanation:
WILL GIVE BRAINLEST PLEASE!!!!!!!! Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table: Color of Tile Purple Pink Orange Number of times the tile is drawn 6 18 26 What is the experimental probability that Jenny will pull out a purple tile? fraction 6 over 50 fraction 44 over 50 fraction 6 over 44 fraction 18 over 44
Answer:
6/50
Step-by-step explanation:
There are 50 tiles
6 purple
18 pink
26 orange
P( purple) = purple/ total
= 6/50
What is the sum of the geometric sequence?
Answer:
B. 259
Step-by-step explanation:
6^(i - 1) for i = 1 to 4
sum = 6^(1 - 1) + 6^(2 - 1) + 6^(3 - 1) + 6^(4 - 1) =
= 6^0 + 6^1 + 6^2 + 6^3
= 1 + 6 + 36 + 216
= 259
Answer: B. 259
One of two small restaurants is chosen at random with equally likely probability, and then an employee is chosen at random from the chosen restaurant. Restaurant #1 has 10 full-timers and 6 part-timers. Restaurant #2 has 7 full-timers and 9 part-timers. What is the probability that Restaurant #1 was chosen at random, given that a full-time employee was chosen? Your answers should be rounded to 4 digits after the decimal.
Answer:
P(1 |F) = 10/17
Step-by-step explanation:
Let events
1 = restaurant 1
2 = restaurant 2
F = full-time worker chosen
P = part-time worken chosen
P(1 and F) = 1/2 * 10/16 = 5/16
P(2 and F) = 1/2 * 7/16 = 7/32
P( (1 or 2) and F ) = P(F) = 5/16+7/32 = 17/32
P(1 | F) Probability of choosing restaurant 1 given a full-time was chosen
= P(1 and F) / P(F)
= 5/16 / (17/32)
= 5/16 * 32/17
= 10 / 17
Translate and solve: 54 greater than x is greater than 216
Answer:
x >162
Step-by-step explanation:
x+54 > 216
Subtract 54 from each side
x+54-54 > 216 - 54
x >162
Answer:
[tex]\huge \boxed{{x>162}}[/tex]
Step-by-step explanation:
[tex]x+54 > 216[/tex]
[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]
[tex]x+54 -54> 216-54[/tex]
[tex]x>162[/tex]
Does anyone know the answers to the graded activities on plato?
Answer:
Explanation
There are some activities in Courseware content that report scores and some that just report mastery and/or completion status.
Resolution
Dynamic vs. Non-dynamic mastery tests
Mastery tests give mastery status if the score is 80% or higher, but not all tests report a score. There are two types of mastery tests in Courseware content:
Non-dynamic tests: Those that do report a score, such as those in the Writing Process and Practice titles, in the Grammar and Mechanics modules, give the same number of questions each time; these are non-dynamic tests. For example, Splitting Fused Run-ons: Mastery Test presents ten questions. Even if the Learner answers the first three questions incorrectly and is, at that point, no longer able to answer eight correctly to achieve mastery, the remaining seven questions are presented.
Dynamic tests: Mastery tests from some content titles, such as Essential Reading Skills, however, are dynamic, which means they adapt to the Learner's responses. These tests do not always give the maximum number of questions; instead, they will end sooner if 80% is either achieved or no longer achievable. These tests show mastery if 80% or better was achieved, but do not show a score. For example, in Essential Reading Skills, Pronouns: Mastery Test, the maximum number of questions presented is five; mastery requires four questions are answered correctly. The test will end early if the student answers the first four correctly or two incorrectly out of the first four. Mastery is still based on achieving 80% or better, but the score is not fully determined, so no score is reported, by design.
Step-by-step explanation:
normal population has a mean of 63 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places): Greater than 65.
Answer:
0.2207
Step-by-step explanation:
Here, we want to find the probability that the sample mean is greater than 25.
What we use here is the z-scores statistic
Mathematically;
z-score = (x-mean)/SD/√n
From the question;
x = 65, mean = 63, SD = 13 and n = 25
Plugging these values in the z-score equation, we have
Z-score = (65-63)/13/√25 = 2/13/5 = 0.77
So the probability we want to calculate is ;
P(z > 0.77)
This can be obtained from the standard normal distribution table
Thus;
P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p
(Small sample confidence intervals for a population mean) suppose you are taking a sampling of 15 measurements. you find that x=75 and s =5. assuming normality, the 99% confidence interval for the population mean is:__________
Answer:
The 99% confidence interval is [tex]71.67 < \mu < 78.33[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 15[/tex]
The sample mean is [tex]\= x = 75[/tex]
The standard deviation is [tex]s = 5[/tex]
Given that confidence is 99% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical values of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]
Generally the margin for error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{ s}{ \sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{ 5}{ \sqrt{15} }[/tex]
=> [tex]E = 3.3307[/tex]
The 99% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]75 - 3.3307 < \mu <75 + 3.3307[/tex]
=> [tex]71.67 < \mu < 78.33[/tex]
A new fast-food firm predicts that the number of franchises for its products will grow at the rate dn dt = 6 t + 1 where t is the number of years, 0 ≤ t ≤ 15.
Answer:
The answer is "253"
Step-by-step explanation:
In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:
Given:
[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]
[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]
integrate the above value:
[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]
When the value of n=1 then t=0
[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]
so the value of n is:
[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]
when we put the value t= 15 then,
[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 229 customers on the number of hours cars are parked and the amount they are charged.
Number of Hours Frequency Amount Charged 1 16 $ 3 2 34 6 3 51 12 4 39 16 5 34 21 6 16 24 7 9 27 8 30 29 229
a. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.) Hours Probability 1 2 3 4 5 6 7 8
a-2. Is this a discrete or a continuous probability distribution?
b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)
b-2. How long is a typical customer parked? (Do not round intermediate calculations. Round your final answers to 3 decimal places.)
c. Find the mean and the standard deviation of the amount charged. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)
Answer:
a
See in the explanation
a-2.
Discrete
b-1.
Mean = 4.201
Standard Deviation = 2.069
b-2.
4.201
c.
Mean = 16.153
Standard Deviation = 8.079
Step-by-step explanation:
Given Data:
Number of Hours Frequency Amount Charged
1 16 $3
2 34 6
3 51 12
4 39 16
5 34 21
6 16 24
7 9 27
8 30 29
∑f = 229
a. Convert the information on the number of hours parked to a probability distribution:
The probability is calculated by dividing each frequency by 229. For example probability of Hour 1 is calculated as:
16 / 229 = 0.06987
This way all the hours probabilities are computed. The probability distribution is given below
Hours Probability
1 0.06987
2 0.14847
3 0.2227
4 0.1703
5 0.1485
6 0.0699
7 0.0393
8 0.1310
∑ 1
a-2. Is this a discrete or a continuous probability distribution?
This is a discrete probability distribution as the probability of each hour of between 0 and 1 and the sum of all the probabilities of hours is 1.
b-1. Find the mean and the standard deviation of the number of hours parked.
First multiply each value of Number of hours by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:
Number of Hours Parked
fx
16
68
153
156
170
96
63
240
Now add the above computed products.
∑fx = 16+68+153+156+170+96+63+240 = 962
Compute Mean:
Now the formula to calculate mean:
Mean = Sum of the value / Number of value
= ∑fx / ∑f
= 962 / 229
Mean = 4.201
Compute Standard Deviation:
Let x be the Number of hours.
Let f be the frequency
First calculate (x-x_bar) where x is each number of hours and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 4.201
For example for the Hour = 1 , and mean = 4.201
Then (x-[tex]\frac{}{x}[/tex]) = 1 - 4.201 = -3.201
So calculating this for every number of hour we get:
(x-[tex]\frac{}{x}[/tex])
-3.201
-2.201
-1.201
-0.201
0.799
1.799
2.799
3.799
Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])
For example the first entry of below calculation is computed by:
(x-[tex]\frac{}{x}[/tex])² = (-3.201 )² = 10.246401
(x-[tex]\frac{}{x}[/tex])²
10.246401
4.844401
1.442401
0.040401
0.638401
3.236401
7.834401
14.432401
Next multiply each entry of (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:
(x-[tex]\frac{}{x}[/tex])² * f = 10.246401 * 16 = 163.942416
(x-[tex]\frac{}{x}[/tex])² * f
163.942416
164.709634
73.562451
1.575639
21.705634
51.782416
70.509609
432.97203
Now the formula to calculate standard deviation is:
S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n
Here
n = ∑f = 229
∑(x-[tex]\frac{}{x}[/tex])² * f is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f
∑(x-[tex]\frac{}{x}[/tex])² * f = 980.759829
S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n
= √980.759829 / 229
= √4.2827940131004
= 2.0694912449924
S = 2.069
b-2) How long is a typical customer parked?
That is the value of mean calculated in part b-1. Hence
Typical Customer Parked for 4.201 hours
c) Find the mean and the standard deviation of the amount charged.
First multiply each value of Amount Charged by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:
fx
48
204
612
624
714
384
243
870
Now add the above computed products.
∑fx = 48+204+612+624+714+384+243+870 = 3699
Compute Mean:
Now the formula to calculate mean:
Mean = Sum of the value / Number of value
= ∑fx / ∑f
= 3699 / 229
Mean = 16.153
Compute Standard Deviation:
Let x be the Amount Charged.
Let f be the frequency.
First calculate (x-x_bar) where x is each value of Amount charged and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 16.153
For example for the Amount Charged = 3 , and mean = 16.153
Then (x-[tex]\frac{}{x}[/tex]) = 3 - 16.153 = -13.153
So calculating this for every number of hour we get:
(x-[tex]\frac{}{x}[/tex])
-13.153
-10.153
-4.153
-0.153
4.847
7.847
10.847
12.847
Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])
For example the first entry of below calculation is computed by:
(x-[tex]\frac{}{x}[/tex])² = (-13.153 )² = 173.001409
(x-[tex]\frac{}{x}[/tex])²
173.001409
103.083409
17.247409
0.023409
23.493409
61.575409
117.657409
165.045409
Next multiply each entry of (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:
(x-[tex]\frac{}{x}[/tex])² * f = 173.001409 * 16 =
(x-[tex]\frac{}{x}[/tex])² * f
2768.022544
3504.835906
879.617859
0.912951
798.775906
985.206544
1058.916681
4951.36227
∑(x-[tex]\frac{}{x}[/tex])² = 14947.65066
Now the formula to calculate standard deviation is:
S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n
Here
n = ∑f = 229
∑(x-[tex]\frac{}{x}[/tex])² * f is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f
∑(x-[tex]\frac{}{x}[/tex])² * f = 14947.65066
S = √∑(x-[tex]\frac{}{x}[/tex])² * f/ ∑f
= √65.273583668122
= 8.0792068712295
S = 8.079
An angle is 100° angle. how many degrees will you add it to make it a linear pair ?
Answer:
80
Step-by-step explanation:
linear pair = 180
Now,
100 + 80 = 180
What is the midline equation of the function h(x) = -4 cos(5x - 9) - 7?
Answer: Midline equation: y = -7
Step-by-step explanation: This function is a sinusoidal function of the form:
y = a.cos(b(x+c))+d
Midline is a horizontal line where the function oscillates above and below.
In the sinusoidal function d represents its vertical shift. Midline is not influenced by any other value except vertical shift. For that reason,
Midline, for the function: [tex]h(x) = -4cos(5x-9) - 7[/tex] is y=d, i.e., [tex]y=-7[/tex]
Answer:
y=-7
Step-by-step explanation: