The Corollary to the polygon is explained below and the formula to find the measure of each interior angle is " (n - 2)×180°/n " .
The Corollary to the polygon Angle Sum Theorem states that : the sum of the interior angles of a regular n gon is written as :
that means , ⇒ Sum of interior angles = (n - 2) × 180° ...equation(1)
In a regular "n-gon" , all the interior angles are said to be congruent.
Let "x" be measure of each interior angle of a regular n-gon.
So , we can write ;
⇒ Sum of interior angles = (n)×(x) ;
Equating the above expressions with equation(1),
⇒ (n)×(x) = (n - 2) × 180° ;
On Solving for x,
⇒ x = (n - 2)×180°/n ;
Therefore, the measure of each interior angle of a regular "n-gon" is x = (n - 2)×180°/n .
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Gold Corp. has an ROE of 12% and a payout ratio of 20%.
What is its sustainable growth rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
The sustainable growth rate is calculated by subtracting the payout ratio from the ROE.
The sustainable growth rate is calculated by subtracting the payout ratio from the ROE. To calculate the sustainable growth rate for Gold Corp., we must first calculate the retention ratio. The retention ratio is calculated by subtracting the payout ratio from 100%. In this case, the retention ratio would be 100% - 20% = 80%. The sustainable growth rate is then calculated by multiplying the retention ratio by the ROE. In this case, the equation would be 80% * 12% = 9.6%. The sustainable growth rate for Gold Corp. is 9.6%, which can be rounded to 9.6%.
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what is the unknown number in sequence 2 in the chart? What rule can you write that relates sequence 2 to sequence 1
The tenth term of the second sequence is 80 and sequence 2 is formed by multiplying by 2 to sequence 1. Then the correct option is C.
What is an arithmetic sequence?Let a₁ be the first term and d be a common difference. Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
From the table, the first term of the first sequence is 4 and the first term of the second sequence is 8. If the first sequence is multiplied by 2 then we obtain the second sequence.
The common difference of the second sequence is given as,
d = 16 - 8
d = 8
Then the tenth term of the second sequence is given as,
a₁₀ = 8 + (10 - 1) x 8
a₁₀ = 8 + 72
a₁₀ = 80
The tenth term of the second sequence is 80 and sequence 2 is formed by multiplying by 2 to sequence 1. Then the correct option is C.
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The complete question is attached below.
(d) If we take 1000 samples of size n = 75 from the population of all copayments for a
month's supply of topical painkiller ointment for regular users and plot the sample means on
a dotplot, describe the shape you would expect to see in the plot and where it would be
centered.
The shape of the plot will be?
and the center will be at?
hola i can help... all you have to do is grab a calculator and add 100 to each number, them sbract them by 302
Given the sample data x: 23 17 15 30 25
(a) Find the range.
(b) Verify that sum of x= 110 and sum of x^2= 2568
(c) Use the results of part (b) and appropriate computation formulas to compute the sample variances s^2 and sample standard deviation s.
(d) Use the defining formulas to compute the sample variance s^2 and sample standard deviation s.
(e) Suppose the given data comprise the entire population of all x values. Compute the population variance ơ^2 and population standard deviation ơ.
The range of the given data is 15, the sum is 110, variance is 37.
The sample variance is a value that measures the variability of values in the data set and how much the observed values deviate from the value of the mean or central value of the data set.
X=[23,17,15,30,25]
(a)
The value of the range is the difference between the maximum value and minimum value:
range=30-15=15
(b)
Sum(x)= 23+17+15+30+25=110
the sum of x2 = [tex]23^2+17^2+15^2+30^2+25^2=2568[/tex]
(c)
from part (b)
[tex]s^2=\sum x_i-nX^2]/[n-1]\\\\=[2568-5(22)^2][5-1]\\\\=37[/tex]
(d)
Using the definition of the variance, first we calculate the mean,
u=110/5=22
u=22
[tex]v^2=\frac{1}{n-1}\sum (x_i-u)^2\\\\=148/4\\=29.6\\s=6.083.[/tex]
e)
The value of population variance is v =5.44
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Which best describes the composition of transformations that maps JKLM to PQRS?
Answer:
D
Step-by-step explanation:
The notation is not what I am used to, but I think that I understand. To go from the large figure to the smaller figure. You need to dilate your figure by 1/3 . The length of the big figure is 6 and 1/3 of that is a length of 2. The width of the big figure is 3. !/3 of that is 1 and that is what I see on the smaller figure.
Assuming the center of the dilation is point J. If you move the shrunken figure 2 to the left and 5 down, it would fit right on top of the smaller figure.
The correct translation rule is given as -
(D_1/3 . T_<-2,-5> ) JKLM.
What is translation?Translation is defined as the movement of graphical image over the two
dimensional plane. In genera, we can write the translation as -
(x, y) → (x ± k, y ± a)
here, we have,
Given is the composition of transformations that maps JKLM to PQRS.
Firstly →
The image is first translated according to the rule -
(x, y) → (x - 2, y - 5).
Secondly -
The image is then dilated by the scale factor -
{K} = 1/3.
Therefore, the correct translation rule is given as -
(D_1/3 . T_<-2,-5> ) JKLM.
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Use the t-table to find the t-score that cuts off 2.5% in the upper tail for a t-distribution with 24 degrees of freedom
a: 1.711
b: 2.064
c: 2.492
d: 2.069
We can see from a t-table with right-tail probabilities that the probability value that is closest to 2.5% is 0.0250, which is represented by a t-score.
The row in the table that corresponds to the number of degrees of freedom (df) must be found before the column that corresponds to the desired level of significance or alpha value in order to use the t-table to determine a t-score that cuts off a specific percentage in the upper tail for a t-distribution with a given number of df.
Since there are 24 degrees of freedom in this situation, we need to identify the t-score that removes 2.5% of the upper tail. We will be looking at the column for the right-tail probabilities because this test has one tail (upper tail), making it a one-tailed test.
Therefore, We can see from a t-table with right-tail probabilities that the probability value that is closest to 2.5% is 0.0250, which is represented by a t-score.
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Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.[1 h 43 6 8]
The value of h such that the matrix is the augmented matrix of a consistent linear system is 2
For the given matrix to be the augmented matrix of a consistent linear system, we need to check whether the matrix is in row echelon form or not. If the matrix is in row echelon form and the last row is not all zeros, then the linear system is consistent.
We can use elementary row operations to transform the matrix into row echelon form.
[tex]\left[\begin{array}{ccc}1&h&4\\3&6&8\end{array}\right][/tex]
R2 <- R2 - 3R1
[tex]\left[\begin{array}{ccc}1&h&4\\0&6-3h&-4\end{array}\right][/tex]
The matrix is in row echelon form. Now, we need to check whether the last row is all zeros or not.
If 6-3h = 0, then the last row will be all zeros, which implies that the linear system is inconsistent.
If 6-3h ≠ 0, then the last row will not be all zeros, which implies that the linear system is consistent.
Therefore, we need to solve the equation 6-3h = 0 to determine the value of h that makes the linear system consistent.
6-3h = 0
3h = 6
h = 2
So, the value of h that makes the matrix the augmented matrix of a consistent linear system is h = 2.
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1Caleb started saving money in a cookie jar. He started with $25 He adds $10 to the cookie jar each week. Write an equation where wis the number of weeks Caleb
saves his money andt is the total amount in dollars in the cookie jar. Determine which variable is the independent variable and which is the dependent variable. Then, graph the total amount in the cookie jar for w being less than 6 weeks.
The linear equation is y = $25 + $10*w, and its graph is on the image at the end.
How to write the equation?Here we know that he started with $25 He adds $10 to the cookie jar each week. Then we can model this with a linear equation:
y = $25 + $10*w
Where w is the number of weeks.
Now we want to graph this, to do so, we just need to find two points on the line.
if w = 0
y = $25 + $10*0 = $25
if w = 6
y = $25 + $10*6 = $85
So we need to graph the points (0, 25) and (6, 85) and connect them witha line.
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What is the square root of 7 to the nearest hundredths
The square root of 7 is approximately 2.65 when rounded to the nearest hundredth.
W2 OFFERS, On June 1, Jack placed an ad in a local newspaper, to be run on the following Sunday, June 5,
offering a reward of $100 to anyone who found his wallet. When his wallet had not been returned by
June 12, he purchased another wallet and took steps to obtain duplicates of his drivers' license,
credit cards, and other items the he had lost. He also, placed another ad in the same newspaper revoking
his offer. The second ad was the same size as the original. On June 15, Sam, who had seen Jack's first
ad in the paper, found Jack's wallet, returned it to Jack, and asked for the $100. Is Jack obligated to pay
Sam the $100? Why or why not?
Jack may not be obligated to pay Sam the $100 reward because he revoked the offer before Sam found the wallet.
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
The amount of reward= $100
Now,
An offer can be revoked at any time before acceptance, and the revocation must be communicated to the offeree. In this case, Jack placed a second ad in the same newspaper revoking his offer before Sam found the wallet. Therefore, Sam did not accept the offer before it was revoked.
Additionally, Sam may not have provided consideration for the reward. Consideration is something of value given in exchange for a promise. In this case, Sam found the wallet before the reward was offered, so he did not provide consideration for the reward when he returned the wallet.
since the offer was revoked before acceptance and Sam did not provide consideration for the reward,
Therefore, by unitary method Jack may not be obligated to pay Sam the $100.
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an amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. two alternative loading/unloading methods have been proposed. to account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. use the following data to test for any significant effect due to the load
The signficant changes that are happening as per the information provided in the question will be as follows:
1. The p-value for Factor A is 0.4194 option e. greater than 0.10.
2. The conclusion with respect to Factor A will be option b. Factor A is not significant.
3. The conclusion with respect to Factor B will be option b. Factor B is not significant.
4. The p-value for the interaction of factors A and B is 0.1621 option e. greater than .10
5. There is no effect of decreasing the waiting time and changing the loading and unloading methods between the rides.
Here, we are going to perform two-way ANOVA Observation
A B C
41, 43, 49 52, 44, 46 50, 46, 48
49, 50, 48 50, 46, 48 48, 44, 46
Sums of row and column
A B C Row total (xa)
133 142 144 419
147 144 138 429
Col total (xb)
280 286 282 848
For A,
∑x²=412+432+492+...+482+442+462=40088
∑x²b/ra =1/3⋅2(280²+286²+282²)
=1/6(78400+81796+79524)
=1/6(239720)
For B,
=39953.3333
∑x²a/rb=1/3⋅3(419²+429²)
=1/9(175561+184041)
=1/9(359602)
For C,
=39955.7778
∑∑x²ab/r= 1/3(133²+142²+144²+147²+144²+138²)
=1/3(17689+20164+20736+21609+20736+19044)
=1/3(119978)
=39992.6667
For D,
(∑x)²/rab
=(848)²/3⋅2⋅3
=719104/18
=39950.2222
Sum of squares total
SST=∑x²-(∑x)²/n
Now we subtract A and D
=(A)-(D)
=40088-39950.2222
=137.7778
Sum of squares between rows will be,
SSA=∑x²a/rb-(∑x)²/n
Now, we subtract C and D
=(C)-(D)
=39955.7778-39950.2222
=5.5556
Sum of squares between columns
SSB=∑x²b/ra- (∑x)²/n
Now, we subtract B and D
=(B)-(D)
=39953.3333-39950.2222
=3.1111
Sum of squares between columns
SSAB=∑∑x²ab/r-(∑x)²/n-SSA-SSB
Now we subtract B, D and Sum of squares between columns
=(B)-(D)-SSA-SSB
=39992.6667-39950.2222-5.5556-3.1111
=33.7778
The residual value of sum of squares Error,
SSE=SST-SSA-SSB-SSAB
=137.7778-5.5556-3.1111-33.7778
=95.3333
ANOVA table
Source. Sums Degrees Mean Squares Square
of squares of freedom variation freedom
SS DF MS F
A SSA=5.5556 a-1=1 MSR=5.5556 0.6993 0.4194 (p-value)
B SSB=3.1111 b-1=2 MSC=1.5556 0.1958
0.8247 (p-value)
AB SSAB=33.7778 2 MSAB=16.8889 2.1259 0..1621 (p-value)
Error (residual) SSE=95.33 12 MSE= 7.9444
Total of SST=137.7778 will be 17
In conclusion,
1. F for between columns, the critical value F(1,2) at 0.05 level of significance will be 4.7472. As computed that FR=0.6993<4.7472
H0 has been accepted, thus, there is no significant difference between rows.
P value is 0.4194 > 0.05. Hence, we fail to reject H0
2. F for between columns, the critical value F(2,2) at 0.05 level of significance will be 3.8853. As computed, FC=0.1958<3.8853. Thus, H0 is accepted and there is no significant difference between columns. P value is 0.8247 > 0.05. Hence, we fail to reject H0
3. The interaction between the Factors AB, there is no sufficient evidence to support the claim of interaction between the factors. Thus, P value is 0.1621 > 0.05. Hence, we fail to reject H0.
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Note that the full question is:
An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/ unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = .05. Use both p-Value and Critical-Value approaches.Type of Ride
Roller Coaster Screaming Demon Log Flume
Method 1 41 52 50
43 44 46
49 46 48
Method 2
49 50 48
51 46 44
47 48 46
1. The p-value for Factor A is:__________.
a. less than .01
b. between .01 and .025
c. between .025 and .05
d. between .05 and .10
e. greater than .10Item 18
2. What is your conclusion with respect to Factor A?
a. Factor A is significant
b. Factor A is not significant
3. The p-value for Factor B is:_______.
a. less than .01
b. between .01 and .025
c. between .025 and .05
d. between .05 and .10
e. greater than .10
3. What is your conclusion with respect to Factor B?
a. Factor B is significant
b. Factor B is not significant
4. The p-value for the interaction of factors A and B is:_______.
a. less than .01
b. between .01 and .025
c. between .025 and .05
d. between .05 and .10
5. What is your recommendation to the amusement park?
Brandon has a certain amount of money. If he spends $24, then he has of the original amount left.
How much money did Brandon have originally?
Brandon have a total of $32 originally
How much money did Brandon have originally?From the question, we have the following parameters that can be used in our computation:
When he spends $24, he has 3/4 of the original amount left
Using the above as a guide, we have the following:
24 = Original * 3/4
Make "Original" the subject of the formula
So, we have the following representation
Original = 24/(3/4)
Evaluate the expression
Original = 32
Hence, the amount is $32
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Imani increased her 401k contributions which decreased her net pay from $637 to 588 determine the percent that imanis net pay was decreased
It would be 20 because of the numbers
what part of 18 is 4
9. 0/10 points Previous Answers EppDiscMaths 2.2.035. My Notes Ask Consider the following statement. Sam will be allowed on Signe's racing boat only if he is an expert sailor. Rewrite the statement in if-then form in two ways, one of which is the contrapositive of the other. Use the formal definition of "only if." (Select all that apply.) If Sam is not an expert sailor, then he will be allowed on Signe's racing boat. If Sam is allowed on Signe's racing boat, then he is not an expert sailor. If Sam is allowed on Signe's racing boat, then he is an expert sailor. If Sam is not allowed on Signe's racing boat, then he is an expert sailor. If Sam is an expert sailor, then he will not be allowed on Signe's racing boat. If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat. Need Help? Read It Talk to Tutor
If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat. and If Sam is allowed on Signe's racing boat, then he is an expert sailor.
are both correct if-then forms of the given statement, with the first being the contrapositive of the second. The other options are not correct if-then forms.
The original statement is "Sam will be allowed on Signe's racing boat only if he is an expert sailor." This statement can be rewritten in if-then form using the formal definition of "only if," which means "if and only if" or "implies and is implied by."
One possible if-then form is "If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat." This is the contrapositive of the original statement, which means that it is logically equivalent to the original statement. It asserts that if Sam is not an expert sailor, then he cannot be on Signe's racing boat.
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Show your work, and graph the piecewise function below.
For x ≤ -1, the function is given by f(x) = 4x + 1. This is a linear function with a slope of 4 and y-intercept of 1. The graph of this part of the function is a straight line passing through (0, 1) with a steep slope, extending towards negative x-values.
What is function?In mathematics, a function is a rule that associates each element in one set (called the domain) to a unique element in another set (called the range). Functions are one of the most important concepts in mathematics and have a wide range of applications in various fields.
A function is usually denoted by a letter, such as f(x), where x is an element in the domain and f(x) is the corresponding element in the range. The domain of a function is the set of all possible values of x for which the function is defined, and the range is the set of all possible values of f(x).
To graph the piecewise function f(x), we will graph each part of the function separately.
For -1 < x < 2, the function is given by f(x) = -2x - 3. This is also a linear function with a slope of -2 and y-intercept of -3. The graph of this part of the function is a straight line passing through (-1, 1) with a gentle slope, extending towards positive x-values until it reaches x=2.
For x ≥ 2, the function is given by f(x) = 5. This is a horizontal line at y=5, which is a constant function. The graph of this part of the function is a horizontal line at y=5 starting from x=2.
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Find the greatest common factor of the expression (8 + 12). Rewrite the expression as a multiple of a sum of two whole numbers with no common factor.
Step-by-step explanation:
To find the greatest common factor (GCF) of the expression (8 + 12), we need to first simplify the expression by finding the sum, which is 20. Therefore, the GCF of (8 + 12) is simply the GCF of 20, which is 20.
To rewrite the expression as a multiple of a sum of two whole numbers with no common factor, we can factor out the GCF of 4 from both 8 and 12, giving us:
(8 + 12) = 4(2 + 3)
The expression (8 + 12) is thus a multiple of the sum of the whole numbers 2 and 3, which have no common factor.
bo is buying a board game that usually cost b dollars
The amount to be paid by Bo is 0.82B
What is percent?A percent of a number is the 100th part of it.
Given that, the board game costs B dollars. Price is reduced by 18%. we need to calculate the final bill.
Cost of game = B dollars
Discount = 18% = 0.18
Discount amount = 0.18B
Final cost = B-0.18B
Amount to pay = 0.82B
Hence, the amount to be paid by Bo is 0.82B
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The complete question is:-
Bo is buying a board game which usually costs B dollars. The game is on sale, and the price has been reduced by 18% There are different ways of thinking about how to calculate Bo's final bill. Match the expressions to their meanings.
plese help asap pleaaaaaaaaaase!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 63
63-15=48
Step-by-step explanation:
Square BCDE with vertices B(-6, 4), C(-2, 3), D(-3, -1) and E(-7, 0) is reflected over the y-axis. What are the new coordinates?
Answers:
B ' (6, 4)
C ' (2, 3)
D ' (3, -1)
E ' (7, 0)
=================================================
Explanation:
The y-axis reflection rule is:
[tex](\text{x},\text{y})\to (-\text{x},\text{y})[/tex]
The x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.
So for example, the point B(-6,4) moves to B ' (6, 4).
You can use a graphing tool like GeoGebra to confirm the answers are correct.
Find the mean absolute deviation (MAD) of the data in the bar chart below.
Please answer
Mean absolute deviation of the data is 1.
What is mean absolute deviation?The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.
Given, In bar chart
Number of artists n = 4
Number of albums for Lil Shane x₁ = 7
Number of albums for Ben Raises x₂ = 9
Number of albums for Nicky x₃ = 6
Number of albums for Underdog x₄ = 6
Mean of the number of albums
μ = (7 + 9 + 6 + 6)/4 = 28/4 = 7
|μ - x₁| = |7 - 7| = 0
|μ - x₂| = |7 - 9| = |-2| = 2
|μ - x₃| = |7 - 6| = 1
|μ - x₄| = |7 - 6| = 1
Mean absolute deviation = ∑|x - μ|/n
= (0 + 2 + 1 + 1)/4
= 1
Hence, 1 is the mean absolute deviation (MAD) of the data in the bar chart.
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Which expression represents the distance
between point J and point K?
|-9|+|-2| |6|+|-9|
|-9|-|-2|
16|-|-2|
-10
10+ y
0
-10-
-J (6,-2)
K (6,-9)
10
The expression showing the distance between point J and point K is |-9|-|-2|
What is distance between points?Distance between two points is the length of the line segment that connects the two given points.
Given that, two points J(6, -2) and k(6, -9), we need to find the distance between them,
The distance between two pints is given by,
D = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here, the points are, (6, -2) and (6, -9)
Therefore,
|JK| = [tex]\sqrt{(0-0)^2+(-9+2)^2}[/tex]
|JK| = √7²
|JK| = 7 units
Therefore, the expression showing the distance between point J and point K is |-9|-|-2|
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Which of the following best describes the relationship between the amount of time spent snoozing and the amount of time slept?
A. no association
B. positive association
C. positive and negative association
D. negative association
Answer: It is D.
Step-by-step explanation:
Find an infinite set of positive integers such that the sum of any two distinct elements has an even number of distinct prime factors
One possible set of positive integers that satisfies the given condition is the set of powers of 2, i.e., {2, 4, 8, 16, 32, ...}.
To see why this set works, note that any two distinct powers of 2 have a different binary representation, differing in at least one bit. This means that their sum will have one more "1" bit in its binary representation than either of the two numbers being added.
Since any prime number greater than 2 is odd, it follows that the sum of any two distinct powers of 2 will have an even number of distinct prime factors, namely the powers of 2 that appear in its binary representation.
First, let's note that every positive integer can be uniquely expressed as a product of prime powers, e.g., 36 = 2^2 * 3^2. The prime factors of an integer are the primes that appear in its prime factorization, e.g., the prime factors of 36 are 2 and 3.
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The downtime per day for a computing facility has mean 4 hours and standard deviation .8 hour.
a Suppose that we want to compute probabilities about the average daily downtime for a period of 30 days.
i What assumptions must be true to use the result of Theorem 7.4 to obtain a valid approximation for probabilities about the average daily downtime?
ii Under the assumptions described in part (i), what is the approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours?
b Under the assumptions described in part (a), what is the approximate probability that the total downtime for a period of 30 days is less than 115 hours?
i. The assumptions required to use Theorem 7.4 are that the daily downtimes are independent and identically distributed with a mean of 4 hours and a standard deviation of .8 hour.
ii. The approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours is about 0.998.
b. The approximate probability that the total downtime for a period of 30 days is less than 115 hours is about 0.03.
a) i) The assumptions that must be true to use the result of Theorem 7.4 (Central Limit Theorem) are:
The daily downtime observations must be independent.
The number of daily downtime observations, n = 30, must be large enough such that the normal approximation is valid. A general guideline is n >= 30, but for this specific case, n = 30 is sufficient.
The individual daily downtime observations must have the same mean and standard deviation, with mean μ = 4 hours and standard deviation σ = 0.8 hours.
ii) Under these assumptions, we can use the Central Limit Theorem to approximate the distribution of the average daily downtime as normal with mean μ = 4 hours and standard deviation σ/√n = 0.8/√30 = 0.17 hours.
Using a standard normal table or calculator, we can find that the approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours is:
P(1 < μ_bar < 5) = P( (1-4)/0.17 < Z < (5-4)/0.17 ) = P(-23.53 < Z < 2.94) = 0.998
So, the answer is approximately 0.998 or 99.8%.
b) Under the same assumptions, the total downtime for a period of 30 days is a sum of 30 independent daily downtime observations, and we can use the central limit theorem to approximate its distribution as normal with mean 30*4 = 120 hours and standard deviation 0.8 * sqrt(30) = 2.7 hours.
Using a standard normal table or calculator, we can find that the approximate probability that the total downtime for a period of 30 days is less than 115 hours is:
P(X < 115) = P((115-120)/2.7 < Z) = P(-1.85 < Z) = 0.03
So, the answer is approximately 0.03 or 3%.
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Plans were made for a rectangular garden to be planted outside a library. The plans use a scale of 1.6cm=2cm. If the Girardeau is 14cm by 10cm on the scale, find the actual dimensions
The actual dimensions of the rectangular garden are 17.5 cm by 12.5 cm
How to determine the actual dimensionsFrom the question, we have the following parameters that can be used in our computation:
Scale: 1.6 cm = 2 cm
A scale is the ratio of the size of the drawing to the size of the actual object.
Given that the dimension is
14 cm by 10 cm
Using the above as a guide, we have the following equation
Actual = 14 * 2/1.6 cm by 10 * 2/1.6 cm
Evaluate
So, we have the following representation
Actual = 17.5 cm by 12.5 cm
Hence, the actual is 17.5 cm by 12.5 cm
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Solve for a and c 20A + 15C = 340
Answer:
Below
Step-by-step explanation:
You have ONE equation and TWO unknowns, so there is infinite solutions for a and c......you cannot solve for a specific a and c unless you have another equation relating the two or a definition of one of them.
You can Solve for a
20a + 15 c = 340
20 a = 340-15c
a = ( 340 -15c) / 20 = 17 - 3/4 c
Similarly:
20 a + 15 c = 340
15c = 340 - 20 a
c = (340-20a)/15
The ratio of students to teachers is 72 : 3. Which statement describes this relationship?
Responses
A There are 3 students for each teacher.There are 3 students for each teacher.
B There are 8 students for every 9 teachers.There are 8 students for every 9 teachers.
C There are 36 students for every 2 teachers.There are 36 students for every 2 teachers.
D There are 24 students for each teacher.
A major corporation is building a 4325 acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Clove's population (in thousands) t yr from now will be given by the following function.P(t)= 35t^2 + 125t + 200 / t^2 + 4t + 40(a) What is the current population of Glen Cove?
(b) What will be the population in the long run?
(a) Glen Cove's current population is 5,000.
In order to determine Glen Cove's current population, we must calculate P(0) because P(t) provides the population (in thousands) for t years in the future. In other words,
P(0) = (35(0)2 + 125(0) + 200) / (02 + 4(0) + 40)
= 200 / 40
= 5.
Since P(t) yields the population in thousands, Glen Cove's current population is 5,000.
(b) The population in the long run (as t approaches infinity) is 35,000.
As t approaches infinity, we must discover the limit of P(t) in order to determine the population over the long term. To do this, we can divide the function's numerator and denominator by t2, which results in the formula: P(t) = (35 + 125/t + 200/t2) / (1 + 4/t + 40/t2).
The terms 125/t and 200/t2 get smaller and smaller as t increases, so we can ignore them in the numerator. We can therefore disregard the terms 4/t and 40/t2 because they also degenerate in the denominator to lower and smaller values. Thus, we are left with:
P(t) ≈ 35/1 \s = 35
Since P(t) represents the population in thousands, the population in the long run (as t approaches infinity) is 35,000.
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Do the ratios 5/10 and 6/12 form a proportion
Answer:
Step-by-step explanation:
if we simplify both of them,
5/10=1/2
and
6/12=1/2
then it means they are equal