The formula to use is
A = P(1+r)^t
where,
A = final amount after t years
P = initial amount = 4100
r = rate of increase or decay = -3.75% = -3.75/100 = -0.0375
t = number of years = 11
The value of r is negative to indicate exponential decay. Also notice that I divided by 100 to convert from -3.75% to -0.0375
Using those values, we plug them into the formula to get,
A = P(1+r)^t
A = 4100(1+(-0.0375))^11
A = 4100(1-0.0375)^11
A = 4100(0.9625)^11
A = 4100*0.65676215615721
A = 2692.72484024457
A = 2693
Rounding to the nearest whole number, the answer is approximately 2693 km^2.
What is the solution to 4 x + 6 less-than-or-equal-to 18?
Answer:
a
Step-by-step explanation:
edge 2020-2021 <3333
(have an amazing day lovely)
The average retirement age for a certain country was reported to be 56.4 years according to an international group dedicated to promoting trade and economic growth. With the pension system operating with a deficit, a bill was introduced by the government during the summer to raise the minimum retirement age from 60 to 62. Suppose a survey of 40 retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire. Assume the standard deviation of the retirement age is 55 years. Using α=0.10
Required:
Calculate the probability of a Type II error occurring if the actual population age is 57.5 years old.
Answer:
|Z| = |-0.126| = 0.126 < 1.645
Null hypothesis is accepted
The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.
μ = 57.5
Step-by-step explanation:
Explanation:-
The average retirement age for a certain country was reported to be 56.4 years
The mean of the sample x⁻ = 56.4
The standard deviation of the Population 'σ'= 55 years
The mean of the population μ = 57.5
Null hypothesis: H₀:The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.
μ = 57.5
Alternative Hypothesis : H₁: μ ≠57.5
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
critical value:
[tex]Z_{\frac{\alpha }{2} } = Z_{0.05} =1.645[/tex]
[tex]Z = \frac{56.4-57.5 }{\frac{55}{\sqrt{40} } } = -0.126[/tex]
|Z| = |-0.126| = 0.126 < 1.645
The null hypothesis is accepted
Conclusion:-
The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.
μ = 57.5
Perhaps the most popular fighter since the turn of the decade, Ronda Rousey is famous for defeating her opponents quickly. The five number summary for the times of her first 12 UFC (Ultimate Fighting Championship) fights, in seconds, is .(a) Only three of her fights have lasted more than a minute, at 289, 267, and 66 seconds, respectively. Use the IQR method to see which, if any, of these values are high outliers. (b) Are there any low outliers in these data, according to the IQR method? (c) Draw the boxplot for Ronda Rousey's fight times. (d) Based on the boxplot or five number summary, would we expect Ronda's mean fight time to be greater than or less than her median?
Answer:
Step-by-step explanation:
Hello!
The variable of interest is "the time a fight lasts" measured in seconds
The five number summary for her first 12 UFC fights are:
Minimum: Min= 14
First Quartile: Q₁= 25
Second Quartile/Median: Me= 44
Third Quartile: Q₃= 64
Maximum: Max= 289
a)
Three of her fights lasted more than one minute: 289, 267, 66. Out of these three fights, you have to determine if they are outliers using the IQR method.
The IQR is the distance between the third quartile and the first quartile
IQR= Q₃ - Q₁= 64 - 25= 39
Remember, an outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.
Considering the 1st quartile (Q₁), the 3rd quartile (Q₃) and the interquartile range IQR, any value X is considered an outlier if:
X < Q₁ - 1.5 IQR
X > Q₃ + 1.5 IQR
Or extreme outliers if:
X < Q₁ - 3 IQR
X > Q₃ + 3 IQR
The limits that define if a value is an outlier or not are:
X < 25 - 1.5*39 = -33.5
X > 64 + 1.5*39= 122.5
And for extreme outliers:
X < 25 - 3*39 = -92
X > 64 + 3*39= 181
So fights that lasted less than -33.5 or more than 122.5 seconds are to be considered outliers, and those who lasted less than -92 or more than 181 seconds are extreme outliers.
Out of the three fights, the ones that lasted 289 and 267 seconds can be considered extreme values.
b) The minimum observed value for this data set is 14 seconds, values are considered to be outliers if they are less to -33.5, so there is no low outliers on the sample.
As you can see, both values that allow you to determine if the observation is an outlier or not are negative, since the variable is "the time a fight lasts" it is impossible for it to have negative values. The lowest value of time a fight can last is "zero seconds". Although mathematically correct, these values make no sense.
c)
See attachment.
d)
The average or mean is a measurement of central tendency that shows you the value around which most of the distribution will be. It is very affected by the presence of outliers, especially extreme ones. Outliers make the mean "move" towards them, this means, that if there are small outliers, then the mean will move to the lower side of the distribution. But if the outliers are big, then the mean will move to the higher side of the distribution.
For example, let's say 5 of the fight times were:
10, 37, 49, 51, 68
For these values the mean would be:
X[bar]₀= ∑X/n= (10+37+49+51+68)/5= 215/5= 43
Now let's change one of these values for an extreme one:
Small value:
0, 37, 49, 51, 68
X[bar]₁= ∑X/n= (0+37+49+51+68)/5= 205/5= 41
⇒ As you can see, one change for a smaller value reduces the mean value X[bar]₁ < X[bar]₀
Big value:
10, 37, 49, 51, 268
X[bar]₂= ∑X/n= (10+37+49+51+268)/5= 415/5= 83
⇒ In this case, changing one of the 5 values to a bigger one moved the mean to the right: X[bar]₀ < X[bar]₂
So for the given distribution, since there are at least two high outliers, you'd expect the mean to be greater than the median.
I hope this helps!
Indigo Depot is having a clearance sale of their summer items. A swimsuit that originally cost $120 before any discount is on sale for 15% off. If the swimsuit is then put on clearance for an additional 40% off the sale price, what is the final price? Round your answer to the nearest cent, if necessary.
Answer:
20
Step-by-step explanation:
Answer:
$61.20
Step-by-step explanation:
15% sale:
$120 - 15%= $120*0.85= $10240% sale:
$102 - 40%= $102*0.6= $61.20Please answer this correctly
Answer:
SA = 1,176 ft².
Step-by-step explanation:
To find the surface area of the triangular prism, we can solve for the rectangular base, both triangular faces, and lateral sides separately.
For the rectangular base: (Use formula l×w)
20 × 18 = 360 ft²
For the triangular faces: (Use formula 1/2(b·h)
1/2(18 × 12) = 108 ft²
Since there are two faces, we need to double the amount.
108 × 2 = 216 ft².
Finally, solve for the lateral sides:
20 × 15 = 300 ft².
There are two sides, so:
300 × 2 = 600 ft².
Add up all of these areas:
600 + 216 + 360 = 1,176 ft²
How much will you save If you buy an Item listed at $575.50 at a 30 percent discount?
OA. $172.65
OB.
$176.25
O C. $185.63
Reset
Next
Answer:
Answer is A $172.25
Step-by-step explanation:
Step 1: Our output value is 575.50.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$575.50=100\%$.
Step 4: Similarly, $x=30\%$.
Step 5: This results in a pair of simple equations
$575.50=100\%(1)$.
$x=30\%(2)$.
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
$\frac{575.50}{x}=\frac{100\%}{30\%}$
Step 7: Again, the reciprocal of both sides gives
$\frac{x}{575.50}=\frac{30}{100}$
$\Rightarrow x=172.65$
Therefore, $30\%$ of $575.50$ is $172.65$
Answer:
The total that will be saved at a 30% discount is $172.65
Explanation:
Since, the marked up price of the item will be $575.50,
and the discount percentage is 30%,
Therefore, $ 172.65 will be saved.
Find the nth term of this number sequence 7,10,13,16
Answer:
aₙ = 7 +3(n -1)
Step-by-step explanation:
The numbers in the given sequence have a common difference, so this is an arithmetic sequence. The formula for the n-th term applies.
aₙ = a₁ +d(n -1)
ApplicationThe first term is 7. The common difference is 10-7 = 3. Using the above formula for the n-th term, we find it to be ...
aₙ = 7 +3(n -1)
__
Additional comment
This can be simplified to ...
aₙ = 3n +4
This equation is an example of:
A. Dividing two binomials
B. FOIL
C. Vertical multiplication
D. Complex conjugates
Answer:
B. FOIL
Step-by-step explanation:
FOIL stands for Firsts, Outsides, Insides, and Lasts
This is a mnemonic to help you to remember how to multiply two binomials
From the image, we can see that the on the right side of the equals,
[tex](x)(-5x^2)[/tex] is the product of the firsts of the binomials
[tex](x)(x)[/tex] is the product of the outsides of the binomials
[tex](-2)(-5x^2)[/tex] is the product of the insides of the binomials
[tex](-2)(x)[/tex] is the product of the lasts of the binomials.
Answer:
B. FOIL
Step-by-step explanation:
"FOIL" is an acronym for First, Outer, Inner, Last. It refers to the relative positions of the terms in the multiplication of binomials.
The given equation shows the result of such a multiplication. It is an example of the application of FOIL.
Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally
symmetric if the grid can be rotated 90, 180, or 270 degrees to achieve the same pattern.
Two colorings are called rotationally distinct if neither can be rotated to match the
other. How many rotationally distinct ways are there for Sam to color the grid such
that the colorings are not rotationally symmetric?
Answer:
65,280
Step-by-step explanation:
Consider the 4×4 grid ...
[tex]\left[\begin{array}{cc}a&b\\d&c\end{array}\right][/tex]
where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.
The same will be true of 270° rotational symmetry, for the same reason.
__
For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)
__
The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...
65,536 -256 = 65,280 . . . . colorings not rotationally symmetric
There are 11 apples in a basket. 9 of these apples are green. The rest of them are red. What is the ratio of red apples to all apples in the basket? What is the ratio of red apples to green apples?
Answer:
Red apples to all apples =2/11
Red apples to green apples =2/9
Step-by-step explanation:
There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples
The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11
The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9
Answer:
Red apples to all apples =2/11
Red apples to green apples =2/9
Step-by-step explanation:
There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples
The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11
The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9
Step-by-step explanation:
The amount of Jen’s monthly phone bill is normally
distributed with a mean of $55 and a standard deviation of $12. What percentage of her phone bills are between $19 and $91?
Answer:
[tex]P(19<X<91)=P(\frac{19-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{91-\mu}{\sigma})=P(\frac{19-55}{12}<Z<\frac{91-55}{12})=P(-3<z<2)[/tex]
And we can find this probability with this difference and using the normal standard distribution
[tex]P(-3<z<3)=P(z<3)-P(z<-3)=0.9987 -0.00135 =0.9974[/tex]
Step-by-step explanation:
Let X the random variable that represent the amount of Jen monthly phone of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(55,12)[/tex]
Where [tex]\mu=55[/tex] and [tex]\sigma=12[/tex]
We are interested on this probability
[tex]P(19<X<91)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Replacing the info we got:
[tex]P(19<X<91)=P(\frac{19-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{91-\mu}{\sigma})=P(\frac{19-55}{12}<Z<\frac{91-55}{12})=P(-3<z<2)[/tex]
And we can find this probability with this difference and using the normal standard distribution
[tex]P(-3<z<3)=P(z<3)-P(z<-3)=0.9987 -0.00135 =0.9974[/tex]
laura quiere cúbrir con papel de china una puerta como la que se muestran el dibujo cuánto centímetros cuadrados es la que tendra que cubrir con papel de china
Answer:
Necesita cubrir 4800 cm^2.
Step-by-step explanation:
La pregunta está incompleta:
Laura quiere cubrir con papel de china una puerta como la que se muestra en el dibujo. Las medidas son 80 cm de largo y 60 cm de ancho.
Tenemos que calcular la superficie de la puerta, cuyas medidas son 80 cm de largo y 60 cm de ancho.
Para calcular el área simplemente multiplicamos las medidas de ambos lados:
[tex]A=80\,cm\cdot 60\,cm=4800\,cm^2[/tex]
Select the correct answer from each drop-down menu. A quadrilateral has vertices A(11, -7), B(9, -4), C(11, -1), and D(13, -4). Quadrilateral ABCD is a . If the vertex C(11, -1) were shifted to the point C′(11, 1), quadrilateral ABC′D would be a .
Answer:
Quadrilateral ABCD is a Quadrilateral with four equal sides so either a rhombus or square
But
Quadrilateral ABC'D is a quadrilateral with two adjacent sides equal so it's a kite shape
Step-by-step explanation:
(11, -7), B(9, -4), C(11, -1), and D(13, -4).
Let's take out the values of x and y coordinate with the way they are arranged
X = 11,9,11,13
Y = -7,-4,-1,-4
So we observe that distance of the coordinates on either x is 2 units and y is 3 units.
But when the the value was changed to
C′(11, 1), (11, -7), B(9, -4), C′(11, 1), and D(13, -4).
There was difference of 2 unit and 4 unit making the new shape a kite.
The diagram attached explain better
Answer:
1. rhombus with non-perpendicular adjacent sides
2. kite
Step-by-step explanation:
i just got it right on edmentum.
Please mark as brainliest.
Mars, Inc. candy company claims the overall proportions for the colors of M&M’s are: .24 blue, .13 brown, .20 green, .16 orange, .13 red, and .14 yellow. You buy a large bag of M&M’s and observe the following counts: 105 blue, 72 brown, 89 green, 84 orange, 70 red, 80 yellow. At the 0.05 level of significance, is there evidence that the overall proportions for the colors are as stated above?
Answer:
There is insufficient statistical evidence to prove that the companies stated color distribution is not correct therefore, the overall proportions of the colors are correctly stated as above
Step-by-step explanation:
We have that
H₀: 0.24 blue, 0.13 brown, 0.20 green, 0.16 orange, 0.13 red and 0.14 yellow
The Data given are as follows;
Hₐ: The stated distribution of M&M is incorrect
Blue Brown Green Orange Red Yellow Total
Observed: 105 72 89 84 70 80 500
Expected: 120 65 100 80 65 70
We have;
[tex]\chi ^{2}=\dfrac{\left (105-120 \right )^{2}}{120}+ \dfrac{\left (72-65\right )^{2}}{65} + \dfrac{\left (89-100\right )^{2}}{100} + \dfrac{\left (84-80\right )^{2}}{80} + \dfrac{\left (70-65\right )^{2}}{65} + \dfrac{\left (80-70\right )^{2}}{70} = 5.85[/tex]
At 6 - 1 = 5 degrees of freedom we find the p-value from the chi squared table as follows
P(0.05) at 5% degrees of freedom =11.070 hence our P-value is larger than 0.05 and we fail to reject the null hypothesis, hence there is insufficient statistical evidence to prove that the companies stated color distribution is not correct.
How much money does the average professional hockey fan spend on food at a single hockey game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $ 18.00 and $ 2.75, respectively. Use this information to create a 90% confidence interval for the mean. Express the answer in the form x overbar plus or minus t Subscript alpha divided by 2 Baseline (s divided by StartRoot n EndRoot ).
Answer:
Now we have everything in order to replace into formula (1):
[tex]18-2.262\frac{2.75}{\sqrt{10}}=16.03[/tex]
[tex]18+2.262\frac{2.75}{\sqrt{10}}=19.97[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=18[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=2.75 represent the sample standard deviation
n=10 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical vaue would be [tex]t_{\alpha/2}=2.262[/tex]
Now we have everything in order to replace into formula (1):
[tex]18-2.262\frac{2.75}{\sqrt{10}}=16.03[/tex]
[tex]18+2.262\frac{2.75}{\sqrt{10}}=19.97[/tex]
Determine the center and radius of the circle described by the question.
(X+2)
The question is incomplete, I will however explain, with an illustration, how to determine the center and radius of a circle.
Step-by-step explanation:
The standard equation of a circle is given as:
(x - a)² + (y - b)² = r² ........................(1)
Where (a, b) is the center of the circle, and r is the radius.
An expression can be given for us to find the center and the radius of the circle.
Suppose we were given the expression:
x² + y² - 10x + 4y - 7 = 0.....................(2)
To find the center and the radius, it is left for us to rewrite (2) in the form of (1).
Rearranging (2), we have
(x² - 10x) + (y² + 4y) = 7
Completing the squares of each bracket
(x² - 10x + 25 - 25) + (y² + 4y + 4 - 4) = 7
(x² - 10x + 25) + (y² + 4y + 4) - 25 - 4 = 7
(x² - 10x + 25) + (y² + 4y + 4) - 29 = 7
(x - 5)² + (y + 2)² = 7 + 29
(x - 5)² + (y + 2)² = 36
Or
(x - 5)² + (y + 2)² = 6² .....................(3)
Comparing (3) with one, we see that
a = 5, b = -2, and r = 6
Therefore it is a circle centered at (5, -2) with a 6 unit radius.
You are renting a car that charges a $30 fee plus 40 cents a mile. The rate of change
is $30.
True
False
Answer:
true
is the answer
Determine the least number of patties that will share equally among groups og 6, 9, 12
Answer:
72.
Step-by-step explanation:
Given a group of 6, 9 and 12.
We are to determine the least number of patties that will be shared equally among the groups.
This we do by determine the Least common multiple of the three numbers.
[tex]6=2 X 3\\9 = 3 X 3\\12 =2 X 2 X 2\\L.C.M.=2^3X3^2=72[/tex]
Therefore, the least number of patties that can be shares equally among groups of 6, 9 and 12 is 72.
Please answer this correctly
Answer:
10.71
Step-by-step explanation:
The arc length is
2*3*3.14/4 = 4.71
Add to the two side lengths to get the perimeter
4.71+3+3 = 10.71
[tex]answer = 10.71 \: millimeters \\ solution \\ radius = 3 \: millimeters \\ perimeter \: of \:quarter \: circle \\ = \frac{2\pi \: r}{4} + 2r \\ = \frac{2 \times 3.14 \times 3}{4} + 2 \times 3\\ = \frac{18.84}{4} + 6 \\ = \frac{18.84 + 6 \times 4}{4} \\ = \frac{18.84 + 24}{4} \\ = \frac{42.84}{4} \\ = 10.71 \: millimeters \\ hope \: it \: helps[/tex]
A researcher reports a 98% confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be [0.34, 0.38). Therefore, there is an approximate probability of 0.98 that the proportion of Drosophola with this mutation is between 0.34 and 0.38.1. True 2. False
Answer:
[tex] 0.34 \leq p \leq 0.38[/tex]
For this case we can conclude that with 98% of confidence the true proportion of Drosophila in a population would be between 0.34 and 0.38.
But that doesn't means that we have 98% of PROBABILITY that the true proportion would be between 0.34 and 0.38, because we are constructing a confidence interval with sample data and we can't analyze this using probability.
Then the best answer is:
2. False
Step-by-step explanation:
For this case we have a confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be given by:
[tex] 0.34 \leq p \leq 0.38[/tex]
For this case we can conclude that with 98% of confidence the true proportion of Drosophila in a population would be between 0.34 and 0.38.
But that doesn't means that we have 98% of PROBABILITY that the true proportion would be between 0.34 and 0.38, because we are constructing a confidence interval with sample data and we can't analyze this using probability.
Then the best answer is:
2. False
Does anybody know how to do this it's about angles
Answer:
isn't X=21 because it's a right angle and you just do 90-69=21?
Answer:
alpha = 21°
Step-by-step explanation:
You see that this rectangle has four right angles, meaning each of 90 °
That is why it is called a rectangle in the first place. ( The 'rec' in rectangle stands for 'right' or 'streight' and it indicates all angles in the rectangle being 90 °).
Anyway, corner alpha added with the given angle of 69 ° must there fore add up to the value of a streight corner, right?
apha + 69 = 90
alpha = 90 - 69
alpha = 21°
Write the equation of the line that passes through the points (6,2) (4,1)
Answer: y=1/2x-1
Step-by-step explanation:
To find the equation of the line that passes through the points, we need to find out slope, m.
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
We plug our points into this formula to find slope.
[tex]m=\frac{1-2}{4-6} =\frac{-1}{-2} =\frac{1}{2}[/tex]
Our slope is 1/2. To find our y-intercept, b, we would plug any point into the equation for slope-intercept form.
y=mx+b
y=1/2x+b
1=1/2(4)+b
1=2+b
b=-1
Now that we know b, our equation is y=1/2x-1.
graph the function f(x)=(x+2)(x-4). Which describes all of the values for which the graph is negative and decreasing?
Answer:
[tex]x\in(-2,1)[/tex]
Step-by-step explanation:
We are given that a function
[tex]f(x)=(x+2)(x-4)[/tex]
[tex]f(x)=x^2-2x-8[/tex]
Differentiate w.r.t x
[tex]f'(x)=2x-2[/tex]
[tex]f'(x)=0[/tex]
[tex]2x-2=0[/tex]
[tex]2x=2\implies x=\frac{2}{2}=1[/tex]
Therefore, intervals
[tex](-\infty,1),(1,\infty)[/tex]
Interval :[tex](-\infty,1)[/tex]
x=0
[tex]f'(0)=-2<0[/tex]
Decreasing function.
Interval:[tex](1,\infty)[/tex]
Substitute x=2
[tex]f'(2)=2(2)-2=2>0[/tex]
Function increasing.
From given graph we can see that function is negative for the values of x
-2<x<4
Hence, the graph is negative and decreasing for the values of x
[tex]x\in(-2,1)[/tex]
Answer:the answer is c/ all real values of x where 1<x<4
Step-by-step explanation:
edge 2020
A fluid has density 860 kg/m3 and flows with velocity v = z i + y2 j + x2 k, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the cylinder x2 + y2 = 25, 0 ≤ z ≤ 1.
You can use the divergence theorem:
[tex]\vec v=z\,\vec\imath+y^2\,\vec\jmath+x^2\,\vec k[/tex]
has divergence
[tex]\mathrm{div}\vec v=\dfrac{\partial z}{\partial x}+\dfrac{\partial y^2}{\partial y}+\dfrac{\partial x^2}{\partial z}=2y[/tex]
Then the rate of flow out of the cylinder (call it R) is
[tex]\displaystyle\iint_{\partial R}\vec v\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec v\,\mathrm dV[/tex]
(by divergence theorem)
[tex]=\displaystyle2\int_0^{2\pi}\int_0^5\int_0^1r^2\sin\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
(after converting to cylindrical coordinates)
whose value is 0.
what’s the correct answer for this question?
State if each scenario involves a permutation or a combination. Then find the number of possibilities.
The batting order for seven players on a 8 person team.
a)Permutations: 120.960
b)Combinations: 20,160
c)Permutations: 40320
d)Combinations: 8
Answer:
c) Permutations: 40320
Step-by-step explanation:
We have that permutations are groupings in which the order of the objects matters. Combinations are groupings where content matters but order does not.
In this case, then the batting order, therefore the order does matter, therefore, it would be a permutation, where n = 8 and r = 7
nPr = n! / (n-r)!
Replacing:
8P7 = 8! / (8-7)! = 40320
Which means that the answer is c) Permutations: 40320
What is the measure of <6?
Answer: Choice B. 54degrees
Step-by-step explanation:
Angles 1 4 5 8 are equal and angles 2 3 6 7 are also equal. These two sets of angles of supplementary(you‘d get 180 by adding them).
so
13x+9=180-(5x+9)
by simplifying the equation youll get
18x+18=180
x=9
so angle 7(and therefore angle 6) equals
5*9+9=54
Suppose an All Greens store in Sonoma, California, wants to estimate a range of advertising costs appropriate to its store. If it spends too little on advertising, it will not reach enough customers. However, it does not want to overspend on advertising for this type and size of store. At this store, x1 = 163, x2 = 2.4, x3 = 188, x5 = 6.6, and x6 = 10. Use these data to predict x4 (advertising costs) and find an 80% confidence interval for your prediction. (Use 2 decimal places.)
Answer:
The advertising cost, X₄ = 5.626 million
The 80% confidence limits for X₄ is (5.041 , 6.100)
The 80% prediction limits for X₄ is (4.048 , 7.094)
Step-by-step explanation:
Using MINITAB
The regression equation is X₄ = 4.14 + 0.0431 X₁ - 0.800 X₂ + 0.00059 X₃ - 0.661 X₅ + 0.057 X₆
Predictor Coef SE Coef T P
Constant 4.142 1.626 2.55 0.019
X₁ 0.043089 0.009466 4.55 0.000
X₂ -0.7998 0.2515 -3.18 0.005
X₃ 0.000590 0.004221 0.14 0.890
X₅ -0.6606 0.1542 -4.28 0.000
X₆ 0.0574 0.1254 0.46 0.652
S = 1.07911 R-Sq = 93.4% R-Sq(adj) = 91.8%
Analysis of Variance
Source DF SS MS F P
Regression 5 345.966 69.193 59.42 0.000
Residual Error 21 24.454 1.164
Total 26 370.420
Source DF Seq SS
X₁ 1 309.464
X₂ 1 8.699
X₃ 1 5.994
X₅ 1 21.566
X₆ 1 0.244
Unusual Observation
Obs X₁ X₄ Fit SE Fit Residual St Resid
17 398 5.500 7.714 0.641 -2.214 -2.55 R
27 400 7.000 7.366 1.025 -0.336 -1.00 X
Where R is observation with a large standardized residual.
Where X is observation whose X values give it large influence.
Predicted values for new Observations
New
Obs Fit SE Fit 80% Cl 80% Pl
1 5.571 0.400 (5.041 , 6.100) (4.048 , 7.094)
Values of Predictors for New Observations
New
Obs X₁ X₂ X₃ X₅ X₆
1 163 2.40 188 6.60 10.0
∴ The advertising cost, X₄ = 5.626 million, The 80% confidence limits for X₄ is (5.041 , 6.100), and The 80% prediction limits for X₄ is (4.048 , 7.094)
A research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years. When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years
a) What is the population of interest in this situation?
b) How many samples were described?
c) Is the average age of 37 years a parameter or a statistic?
d) Tell whether this information represents a quantitative or qualitative variable? - age of the visitor - whether the visitor has a season pass
e) What possible explanation is there for the large difference in age between the two samples?
Answer:
(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.
(b) Two samples are described in the above situation, that is;
A survey of 100 randomly selected park visitors on a weekday in May.A survey of 100 randomly selected park visitors on a Saturday in May.(c) The average age of 37 years is a statistic.
(d) The above information represents a quantitative variable.
(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.
Step-by-step explanation:
We are given that a research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years.
When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years.
(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.
(b) Two samples are described in the above situation, that is;
A survey of 100 randomly selected park visitors on a weekday in May.A survey of 100 randomly selected park visitors on a Saturday in May.(c) The average age of 37 years is a statistic as it is the sample average age of visitors to the park on a weekday, i.e. [tex]\bar X_1[/tex] = 37 years.
(d) The above information represents a quantitative variable because in this we are concerned about the average age of visitors in the park which is a numeric value and we are not interested in any qualitative aspect.
(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.
But during weekends like Saturday, the schools or coaching institutions are generally closed due to which they are able to come to parks to play and because of this there are large number of children below 20 years of age who visit parks on weekends.
EXREAMLY URGENT!! WILL FOREVER THANK YOU!!!! PLS JUST TAKE A LOOK!!!!! 1. What is the ratio of the sides of triangle XYZ?
Answer:
Dear Laura Ramirez
Answer to your query is provided below
The ratio of triangle XYZ is 1:√3 :2.
Step-by-step explanation:
A 30-60-90 right triangle (literally pronounced "thirty sixty ninety") is a special type of right triangle where the three angles measure 30 degrees, 60 degrees, and 90 degrees. The triangle is significant because the sides exist in an easy-to-remember ratio: 1:√3 :2.