Which represents the solution(s) of the equation x2 = 36?

Answer:

[tex]y = \frac{\sqrt{2}x}{3} - \frac{\sqrt{2}\pi}{3} + 1.5[/tex]

Step-by-step explanation:

The equation to the line normal to the curve has the following format:

[tex]y - y(x_{0}) = m(x - x_{0})[/tex]

In whicm m is the derivative of y at the point [tex]x_{0}[/tex]

In this problem, we have that:

[tex]x_{0} = \pi[/tex]

[tex]y(x) = 3\cos{\frac{x}{3}}[/tex]

[tex]y(\pi) = 3\cos{\frac{\pi}{3}} = \frac{3}{2}[/tex]

The derivative of [tex]\cos{ax}[/tex] is [tex]a\sin{ax}[/tex]

So

[tex]y(x) = 3\cos{\frac{x}{3}}[/tex]

[tex]y'(x) = 3*\frac{1}{3}\sin{\frac{x}{3}} = \sin{\frac{x}{3}}[/tex]

[tex]m = \sin{\frac{\pi}{3}} = \frac{\sqrt{2}}{3}[/tex]

The equation of the line normal to the curve of y=3cos1/3x is:

[tex]y - y(x_{0}) = m(x - x_{0})[/tex]

[tex]y - \frac{3}{2} = \frac{\sqrt{2}}{3}(x - \pi)[/tex]

[tex]y = \frac{\sqrt{2}}{3}(x - \pi) +  \frac{3}{2}[/tex]

[tex]y = \frac{\sqrt{2}x}{3} - \frac{\sqrt{2}\pi}{3} + 1.5[/tex]

Answer:

Step-by-step explanation:

The relative frequencies are 0.15, 0.08, 0.39, and 0.38 for the respective classes while 38% of the observations are at least 300 but less than 350.

The cumulative relative frequency distribution given can be used to construct a relative frequency distribution. To find the relative frequency for each class, subtract the cumulative frequency of the previous class from the cumulative frequency of the current class. Therefore:

The Total relative frequency is the sum of all the relative frequencies and should equal 1 (or almost equal to 1 due to rounding differences)

For the second part of your question: 'what percent of the observations are at least 300 but less than 350?', since this is the relative frequency distribution, it means that class 300 to 350 has already been expressed as a percentage (since relative frequency is a proportion and can be expressed as a percentage). So, 38% of the observations are at least 300 but less than 350.

https://brainly.com/question/32829405

#SPJ2

Answer:

0.0625

Step-by-step explanation:

The prevalence of gene a = 25 %, P (a) = 0.25

birth defect occurs when both parents have prevalence of gene a.

P (Defect) = P ( Both parents have gene a)

If both parents inherit the gene a independently, the the individual will have a birth defect when both parents have gene a.

P ( Father having gene a) = 0.25

P ( Mother having gene a) = 0.25

Hence,

P (Birth Defect) = P ( Both parents have gene a) = 0.25 * 0.25 = 0.0625

Answer:

inverse f-1 (x) = x/18

Step-by-step explanation:

To find the inverse of a function f-1 (x), we represent f(x) by y or let f(x) = y

then make x the subject of the formula,

f(x) = 18x

Let f(x) = y

hence Y = 18x, make x the subject of the formula, do that by dividing both sides by 18,

Y/18 = x or x = Y/18

Interchanging or swapping x and y, therefore f-1 (x) = x/18

therefore, F(x) = 18x, the inverse f-1 (x) = x/18

Answer: N >/= 7 bits

Minimum of 7 bits

Step-by-step explanation:

The minimum binary bits needed to represent 65 can be derived by converting 65 to binary numbers and counting the number of binary digits.

See conversation in the attachment.

65 = 1000001₂

65 = 7 bits :( 0 to 2^7 -1)

The number of binary digits is 7

N >/= 7 bits

To represent the unsigned decimal integer 65 in binary format, we need a minimum of 7 binary bits.

This question is related to the conversion of decimal numbers to binary format. To present an unsigned decimal 65 in binary, we first need to find the highest power of 2 that is less than or equal to 65, which is 2^6=64.

Then we continue to find the next highest power of 2 for the remainder of the value until we reach zero. This process would require a total of 7 bits. Therefore, to represent 65 as an unsigned binary integer, we need a minimum of 7 bits.

https://brainly.com/question/33578281

#SPJ3

Answer: m1 = 4

m2 = 5

m3 = 2

Step-by-step explanation:

given (21/11, 6/11) = m1 (-1/3) + m2 (3, -2) + m3 (5, 2)

= (-m1 + 3m2 + 5m3) / 11 = 21/11

= (3m1 + (-2)m2 + 2m3) / 11 = 6/11

so that m1 + m2 +m3 = 11

-m1 + 3m2 + 5m3 = 21

3m1 - 2m2 + 2m3 = 6

from this, we get the augmented matrix as

\left[\begin{array}{cccc}-1&1&1&11\\-1&3&5&21\\3&-2&2&6\end{array}\right]

= \left[\begin{array{cccc}-1&1&1&11\\0&4&6&32\\0&-5&-1&-27\end{array}\right]  \left \{ {{R2=R2 + R1} \atop {R3=R3 -3R1 }]} \right.

= \left[\begin{array}{cccc}-1&1&1&11\\0&1&3/2&8\\0&-5&-1&-27\end{array}\right]

= \left[\begin{array}{cccc}-1&1&1&11\\0&1&3/2&8\\0&0&13/2&13\end{array}\right]

(R3 = R3 + 5R2)

this gives m1 + m2 + m3 = 11

m2 + 3/2 m3 = 8

13/2 m3 = 8

13/2 m3 = 13

m3 = 2

m2 = 8 -3/2 (2) = 5

= m1 = 11- 5 - 2 = 4

this gives

m1 = 4

m2 = 5

m3 = 2

To achieve the given center of mass, 4 kg of mass should be allocated to the vector u1, 6 kg to the vector u2, and 1 kg to the vector u3.

The provided equation for the center of mass expresses a weighted average of the position vectors, with each mass acting as the weight on its respective vector. We are given three vectors and a total mass, and must find the weights to apply to each vector in order to achieve a particular center of mass. Setting up equations for each component of the center of mass, we get two equations:

21/11 = (-1m1 + 3m2 + 5m3) / 11 and 6/11 = (3m1 - 2m2 + 2m3) / 11.

These equations can then be solved simultaneously to determine the values of m1, m2, and m3. Solving these equations gives m1 = 4 kg, m2 = 6 kg, and m3 = 1 kg. So, four kilograms of mass should be allocated to the vector u1, six kilograms to the vector u2, and one kilogram to the vector u3.

https://brainly.com/question/34640951

#SPJ3

Answer:

95%

Step-by-step explanation:

The empirical rule states that if data follows normal distribution then the percentage of observations falls within one, two and three standard deviation around the mean are

i) 68% falls within one standard deviation

ii) 95% falls within two standard deviation

iii) 99.7% falls within three standard deviation.

Hence 95% of the observations will fall within two standard deviations around the mean if the data follows normal distribution.

According to the empirical rule, approximately 95 percent of observations in a bell-shaped normal distribution fall within two standard deviations of the mean.

According to the empirical rule, if the data form a bell-shaped normal distribution, approximately 95 percent of the observations will fall within two standard deviations around the mean. This statistical concept is an important part of descriptive statistics and is crucial when studying the Normal or Gaussian probability distribution.

In a normal distribution, the data is symmetric around the mean, and as dictated by the empirical rule, about 68% of the data lies within one standard deviation, while approximately 95% lies within two standard deviations, and over 99% within three standard deviations of the mean.

Answer:

number of subsets of a set with 13 elements are: [tex]2^{13}[/tex]

Step-by-step explanation:

In order to solve this intuitively, we can start by a set with lesser elements. This will reveal a pattern that will be used to solve for the subsets of the 13 element set.

If we start with a set B. which contains only 3 elements.

[tex]B = \{1,2,3\}[/tex]

how many subsets of B are there? well we can count them. [the set containing {1,2} and {2,1} are the same, arrangement doesn't matter]

[tex]B_{0} = \{\}\\B_{1a}=\{1\}\\B_{1b}=\{2\}\\B_{1c}=\{3\}\\B_{2a}=\{1,2\}\\B_{2b}=\{2,3\}\\B_{2c}=\{3,1\}\\B_{3a}=\{1,2,3\}\\[/tex]

there are a total of 9 subsets here.

Similarly, if you try a with a subset with only two elements you'll find that it has a total of 4 subsets.

We can see that combinatorics is at play here.

for the set B. the number of subsets can be written as:

[tex]\text{\# of subsets of B} = ^3C_0+^3C_1+^3C_2+^3C_3\\\text{\# of subsets of B} = 1+3+3+1\\\\text{\# of subsets of B} = 8[/tex]

if we try with a 2-element set:

[tex]\text{\# of subsets} = ^2C_0+^2C_1+^2C_2\\\text{\# of subsets} = 1+2+1\\\ \text{\# of subsets} = 4[/tex]

We can use the same technique to find the number of subsets of the 13 element set.

But if you recognize a pattern here that this sets of combinations are actually part of the pascal triangle, the sum of each row of the triangle is 2^{the row's number}. hence.

[tex]\text{\# of subsets of B} = 2^3\\\ \text{\# of subsets of B} = 8[/tex]

So finally, the subsets of a 13-element set A will be

[tex]\text{\# of subsets of A} = ^{13}C_0+^{13}C_1+^{13}C_2+^{13}C_3\cdots+^{13}C_{12}+^{13}C_{13}\\OR\\\text{\# of subsets of A} = 2^{13}\\\text{\# of subsets of A} = 8192[/tex]

If the set A has 13 elements, the number of different subsets is [tex]2^{13}=8192[/tex]

All the possible subsets that can be formed from any given set is called the Power set of that set. Generally, if we had a set [tex]H[/tex] such that

[tex]|H|=k[/tex]

Where [tex]|H|[/tex] denotes the cardinality, or number of elements, in [tex]H[/tex], the power set of [tex]H[/tex], denoted by [tex]P(H)[/tex], has the following formula

[tex]P(H)=2^k\text{ elements}[/tex]

So, given the set [tex]A[/tex] such that

[tex]|A|=13[/tex]

the power set of [tex]A[/tex] will have [tex]2^{13} \text{ or } 8192 \text{ elements}[/tex]

Learn more about number of different subsets here: https://brainly.com/question/13266391

Answer:

[tex]lim_{n \to \infty} A_n = \frac{R}{i}[/tex]

Step-by-step explanation:

For this case we have this expression:

[tex] A_n = R [\frac{1 -(1+i)^{-n}}{i}][/tex]

The lump sum investment of An is needed to result in n periodic payments of R when the interest rate per period is i.

And we want to find the:

[tex] lim_{n \to \infty} A_n[/tex]

So we have this:

[tex] lim_{n \to \infty} A_n = lim_{n \to \infty}R [\frac{1 -(1+i)^{-n}}{i}] [/tex]

Then we can do this:

[tex] lim_{n \to \infty} A_n = lim_{n \to \infty} R [\frac{1 -\frac{1}{(1+i)^n}}{i}][/tex]

[tex]lim_{n \to \infty} A_n = R lim_{n \to \infty} [\frac{1 -\frac{1}{(1+i)^n}}{i}][/tex]

And after find the limit we got:

[tex] lim_{n \to \infty} A_n = R [\frac{1-0}{i}][/tex]

Becuase : [tex] \frac{1}{(1+i)^{\infty}} =0[/tex]

And then finally we have this:

[tex]lim_{n \to \infty} A_n = \frac{R}{i}[/tex]

Answer:

break even point = 8000 socks produced or $36000 in costs

Step-by-step explanation:

the cost function of the firm is

total cost = fixed cost + variable cost = $20000 + $2*Q

where Q= number of socks

the revenue from sales is

sales = Price* Q = $4.50*Q

the break even point is reached when the net profit is = 0 ( that is, the total cost is equal to the revenue from sales) , then

total cost = sales

$20000 + $2*Q =$4.50*Q

Q= $20000/($4.50-$2) = 8000 socks

that represents

total cost = $20000 + $2*8000  = $36000

then

break even point = 8000 socks produced or $36000 in costs

Answer: x =6 1/3

Step-by-step explanation:

Whichever value of x from the given option that make f(x) = 0 is the zero of f(x). x = 6 1/3 satisfies this, you can check by replacing 6 1/3 by x in the equation. 6 1/3 can be written as 19/3

f(19/3) = 9(19/3)² - 54(19/3) - 19

= 9(361/9) - 54(19/3) - 19

= 361 - 342 - 19

= 0.

The remaining values don't give 0.

In this problem you will calculate ∫302+4 by using the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ].

(a) The interval [0,3] is divided into equal subintervals of length Δ. What is Δ (in terms of )? Δ =

(b) The right-hand endpoint of the th subinterval is denoted ∗. What is ∗ (in terms of and )? ∗ =

Answer:

a) Δ= [tex]\frac{3}{n}[/tex]

b) [tex]x^{*}_{k} = \frac{3k}{n}[/tex]

Step-by-step explanation:

a)  If the interval [0,3] , i.e let a = 0 , b =3 and n=n.

So [0,3] divide into n equal subintervals;

Therefore, the length Δ= [tex]\frac{b-a}{n}[/tex]

Δ= [tex]\frac{3-0}{n}[/tex]

Δ= [tex]\frac{3}{n}[/tex]

b) To calculate [tex]x^{*}_{k}[/tex];

[tex]x^{*}_{k}[/tex] = a + k . Δ          (where n= 0, Δ = [tex]\frac{3}{n}[/tex])

= 0 + k . [tex]\frac{3}{n}[/tex]

[tex]x^{*}_{k}[/tex]  =  [tex]\frac{3}{k}[/tex]

The right-hand endpoint of the kth subinterval, denoted x∗k, can be expressed as a function of both k and n (the total number of subintervals). The formula x∗k = k/n can be used in this context, where k denotes the position of the subinterval and n represents the total number of subintervals.

In the context of subintervals, x∗k represents the right-hand endpoint of the kth subinterval. When a range is divided into n subintervals, the right-hand endpoint of the kth subinterval could be represented as a function of both k and n. Thus, x∗k can be expressed as k/n.

To illustrate, suppose we have a range from 0 to 1 (inclusive) and want to split it into 4 subintervals (n=4). The right endpoint of the 1st subinterval (k=1) would be 1/4 = 0.25. For the 2nd subinterval (k=2), the endpoint would be 2/4 = 0.5. And so on.

https://brainly.com/question/34618561

#SPJ3

Answer:

angle CAB = 113.8 degree

angle ABC = 35.6 degree

angle BCA = 30.6 degree

Step-by-step explanation:

Given data:

A(1, 0, −1),

B(5, −3, 0),

C(1, 5, 2)

calculate the length of side by using the distance formula

so

AB = (5,-3,0) - (1,0,-1) = (4,-3,1)

AC= (1,5,2) - (1,0,-1) = (0,5,3)

|AB|

|AC| =[tex]\sqrt {(0 + 5^2+3^2)} = \sqrt{34}[/tex]

From following formula, calculate the angle between the two side i.e Ab and AC

AB.AC = |AB|*|AC| cos ∠CAB

(4,-3,1).(0,5,3)

4*0 -3*5 +1*3

-12 =

cos ∠CAB = - 0.404

angle CAB = 113.8 degree

BA =B- A =  (1,0,-1) - (5,-3,0) = (-4,3,-1)

BC = (1,5,2)-(5,-3,0) = (-4,8,2)

|BA| = \sqrt{(26)}

|BC| [tex]= \sqrt {(4^2 + 8^2 + 2^2)} = \sqrt{(84)}[/tex]

BA.BC = |BA|*|BC|* cosABC

(-4,3,-1).(-4,8,2) =[tex]\sqrt{(26)} * \sqrt{(84)} *cosABC[/tex]

16+24-2

cos ∠ABC = 0.813

angle ABC = 35.6 degree

we know sum of three angle in a traingle is 180 degree hence

sum of all three angle = 180

angle BCA + 35.6 + 113.8 = 180

angle BCA = 30.6 degree

Answer:

see the picture of work shown

Answer:she has 5 dimes and 15 quarters.

Step-by-step explanation:

A dime is worth 10 cents. Converting to dollars, it becomes

10/100 = $0.1

A quarter is worth 25 cents. Converting to dollars, it becomes

25/100 = $0.25

Let x represent the number of dimes that she has.

Let y represent the the number of quarters that she has

Patrice Patriot has a total of 20 coins. It means that

x + y = 20

The total worth of dimes and quarters that she has in a piggy bank is $4.25. It means that

0.1x + 0.25y = 4.25 - - - - - - - - - -1

Substituting x = 20 - y into equation 1, it becomes

0.1(20 - y) + 0.25y = 4.25

2 - 0.1y + 0.25y = 4.25

- 0.1y + 0.25y = 4.25 - 2

0.15y = 2.25

y = 2.25/0.15

y = 15

x = 20 - y = 20 - 15

x = 5

To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 154

3X + 3 = 154

3X + 3 - 3 = 154 - 3

3X = 151

3X/3 = 151/3

X = 50 1/3

Since 50 1/3 is not an integer, there is no true answer to this problem.

To solve for three consecutive even integers where the sum of the first two equals 154, we assign x, x + 2, and x + 4 to those integers. Solving the equation results in x = 76, thus the three integers are 76, 78, and 80.

In Mathematics, specifically in algebra, this problem involves solving for unknowns. Let's call our three consecutive even numbers x, x + 2, and x + 4. This is because two integers are even if they differ by 2. The equation given by the problem is x + (x + 2) = 154, as we are told that the sum of the first and second of the three numbers is 154.

To solve this equation, firstly, combine like terms, you get 2x + 2 = 154. Secondly, isolate the variable x by subtracting 2 from both sides of this equation, you get 2x = 152. Thirdly, to solve for x, divide both sides of the equation by 2. The result is x = 76. This gives you the first integer. Since we know that the integers are consecutive even numbers, the other two integers are 76 + 2 = 78 and 76 + 4 = 80. Therefore, the three consecutive even integers are 76, 78, and 80.

Learn more about Consecutive Even Integers here:

https://brainly.com/question/34290341

#SPJ6

If events A and B are mutually exclusive, the probability of A or B occurring is equal to the sum of the probabilities of A and B. Given that P(A or B) = 0.5 and P(B) = 0.3, P(A) can be calculated as 0.2.

If events A and B are mutually exclusive, the probability of A or B occurring is equal to the sum of the probabilities of A and B. So, we have P(A or B) = P(A) + P(B). Given that P(A or B) = 0.5 and P(B) = 0.3, we can substitute these values into the formula to solve for P(A).

0.5 = P(A) + 0.3.

Now, subtract 0.3 from both sides to isolate P(A):

0.5 - 0.3 = P(A).

P(A) = 0.2.

Therefore, the probability of event A occurring is 0.2.

Answer:

A.positive and fairly strong

Step-by-step explanation:

Since an increase in food quantity usually means an increase in price, quantity and price are directly proportional, which configures a positive correlation.

Since it is stated that this relationship in observed at most restaurants, it can be concluded that there is a fairly strong correlation between  the amount of food served per person and the price paid for it.

Therefore, the answer is, A.positive and fairly strong

Answer:

The answer is A which is Positive and fairly strong.

Step-by-step explanation:

To properly do justice to the selected answer above, we describe a simple scenario.

Imagine yourself, content and perhaps a bit over-full after a lovely meal at a local restaurant. Then, the extravagant bill arrives.

Does  this high cost affirm your belief that this meal was valuable and thereby  influence your reordering of it?

Or does the cost of the meal overshadow your  enjoyment of it and leave you wishing you had chosen a simple meal at a better price point?

What features must an expensive restaurant  provide you over a bargain one to justify the extra cost?

Based of the question asked in respect to the scenario above, researchers went on a an experiment collecting different data from a restaurant and used the Latent Dirichlet Allocation (LDA) model to classify each review of the data and key words like ( e.g. food, service, price, ambiance, anecdotes, miscellaneous) were paid attention to.

After analysis, it was perceived that the value is such a tricky parameter to measure, marketers,  restaurateurs and economists often overlook it, instead focusing on objective  restaurant price and quality’s effect on customer satisfaction.

Answer:

A researcher studies length of time in college, first through fourth year, and its relation to academic motivation. To get the most detail out of her measures, she assesses each student in both the fall and spring semesters of each of their four years in school. She finds that students have increasingly higher motivation from their first semester to their seventh semester (the start of their fourth year), with a trailing off in the last semester. The independent variable are:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

You have the information about light bulbs (i believe is their lifespan in hours) And need to organize the information in a frequency table.

The first table will be with a class width of 20, starting with 800. This means that you have to organize all possible observations of X(lifespan of light bulbs) in a class interval with an amplitude of 20hs and then organize the information noting their absolute frequencies.

Example

1) [800;820) only one observation classifies for this interval x= 819, so f1: 1

2)[820; 840) only one observation classifies for this interval x= 836, so f2: 1

3)[840;860) no observations are included in this interval, so f3=0

etc... (see attachment)

[ means that the interval is closed and starts with that number

) means that the interval is open, the number is not included in it.

fi: absolute frequency

hi= fi/n: relative frequency

To graph the histogram you have to create the classmark for each interval:

x'= (Upper bond + Lower bond)/2

As you can see in the table, there are several intervals with no observed frequency, this distribution is not uniform least to say symmetric.

To check the symmetry of the distribution is it best to obtain the values of the mode, median and mean.

To see if this frequency distribution has one or more modes you have to identify the max absolute frequency and see how many intervals have it.

In this case, the maximal absolute frequency is fi=6 and only one interval has it [1000;1020)

[tex]Mo= LB + Ai (\frac{D_1}{D_1+D_2} )\\[/tex]

LB= Lower bond of the modal interval

D₁= fmax - fi of the previous interval

D₂= fmax - fi of the following interval

Ai= amplitude of the modal interval

[tex]Mo= 1000 + 20*(\frac{(6-3)}{(6-3)+(6-4)} )=1012[/tex]

This distribution is unimodal (Mo= 1012)

The Median for this frequency:

Position of the median= n/2 = 40/2= 20

The median is the 20th fi, using this information, the interval that contains the median is [1000;1020)

[tex]Me= LB + Ai*[\frac{PosMe - F_{i-1}}{f_i} ][/tex]

LB= Lower bond of the interval of the median

Ai= amplitude of the interval

F(i-1)= acumulated absolute frequency until the previous interval

fi= absolute frequency of the interval

[tex]Me= 1000+ 20*[\frac{20-16}{6} ]= 1013.33[/tex]

Mean for a frequency distribution:

[tex]X[bar]= \frac{sum x'*fi}{n}[/tex]

∑x'*fi= summatory of each class mark by the frequency of it's interval.

∑x'*fi= (810*1)+(230*1)+(870*0)+(890*2)+(910*4)+(930*0)+(950*4)+(970*1)+(990*3)+(1010*6)+(1030*4)+(1050*0)+(1070*3)+(1090*2)+(1110*4)+(1130*0)+(1150*2)+(1170*1)+(1190*1)+(1210*0)+(1230*1)= 40700

[tex]X[bar]= \frac{40700}{40} = 1017.5[/tex]

Mo= 1012 < Me= 1013.33 < X[bar]= 1017.5

Looking only at the measurements of central tendency you could wrongly conclude that the distribution is symmetrical or slightly skewed to the right since the three values are included in the same interval but not the same number.

*-*-*

Now you have to do the same but changing the class with (interval amplitude) to 100, starting at 800

Example

1) [800;900) There are 4 observations that are included in this interval: 819, 836, 888, 897 , so f1=4

2)[900;1000) There are 12 observations that are included in this interval: 903, 907, 912, 918, 942, 943, 952, 959, 962, 986, 992, 994 , so f2= 12

etc...

As you can see this distribution is more uniform, increasing the amplitude of the intervals not only decreased the number of class intervals but now we observe that there are observed frequencies for all of them.

Mode:

The largest absolute frequency is f(3)=15, so the mode interval is [1000;1100)

Using the same formula as before:

[tex]Mo= 1000 + 100*(\frac{(15-12)}{(15-12)+(15-8)} )=1030[/tex]

This distribution is unimodal.

Median:

Position of the median n/2= 40/2= 20

As before is the 20th observed frequency, this frequency is included in the interval [1000;1100)

[tex]Me= 1000+ 100*[\frac{20-16}{15} ]= 1026.67[/tex]

Mean:

∑x'*fi= (850*4)+(950*12)+(1050*15)+(1150*8)+(1250*1)= 41000

[tex]X[bar]= \frac{41000}{40} = 1025[/tex]

X[bar]= 1025 < Me= 1026.67 < Mo= 1030

The three values are included in the same interval, but seeing how the mean is less than the median and the mode, I would say this distribution is symmetrical or slightly skewed to the left.

I hope it helps!

Answer:

If a 1% level of significance is used to test a null hypothesis, there is a probability of ____ less than 1%______ of rejecting the null hypothesis when it is true

Step-by-step explanation:

Given that a hypothesis testing is done.

Level of significance used is 1%

i.e. alpha = 1%

When we do hypothesis test, we find out test statistic Z or t suitable for the test and find p value

If p value is < 1% we reject null hypothesis otherwise we accept null hypothesis.

So p value can be atmost 1% only for accepting null hypothesis.

So the answer is 1%

If a 1% level of significance is used to test a null hypothesis, there is a probability of ____less than 1%______ of rejecting the null hypothesis when it is true.

Hi, you haven't provided the system of linear equations that you need to solve. Therefore, I'll just explain how to use Gauss-Jordan in a system of equations and you can apply the same method to the system of equations you have.

Answer with explanation and step by step solution:

1. For the system of equations:

[tex]4X_{1} + 8X_{2} + 12X_{3} = 36\\8X_{1} + 10X_{2} + 12X_{3} = 48\\4X_{1} + 14X_{2} + 24X_{3} = 60\\[/tex]

2. We can represent it as a matrix by placing every number of the equation as follow:  

[tex]\left[\begin{array}{ccccc}4&8&12&|&36\\4&5&6&|&24\\2&7&12&|&30\end{array}\right][/tex]

3. As you can see all the coefficients in the equation are divisible by two, so we can express the system of equations as follow:  

 [tex]\left[\begin{array}{ccccc}2&4&6&|&18\\4&5&6&|&24\\2&7&12&|&30\end{array}\right][/tex]

4. Gauss-Jordan method solves the system of equations by applying simple operations to the Matrix: Multiplication by non-zero numbers, adding a multiple of one row to another and swapping rows.

Step by step solution:  

Divide both sides of equation one by two:

[tex]\left[\begin{array}{ccccc}1&2&3&|&9\\4&5&6&|&24\\2&7&12&|&30\end{array}\right][/tex]

Subtract two times the equation two to the equation three:  

[tex]\left[\begin{array}{ccccc}1&2&3&|&9\\4&5&6&|&24\\-6&-3&0&|&-18\end{array}\right][/tex]

Divide equation number three by minus three and subtract two times the equation one to equation two:

[tex]\left[\begin{array}{ccccc}1&2&3&|&9\\2&1&0&|&6\\2&1&0&|&6\end{array}\right][/tex]

Subtract the equation two to the equation three:  

[tex]\left[\begin{array}{ccccc}1&2&3&|&9\\2&1&0&|&6\\0&0&0&|&0\end{array}\right][/tex]

Because now we have two equations for three unknown values X1, X2 and X3 the system has an infinite number of solutions.  

Equivalente system (From matrix to equation notation):  

[tex]1X_{1} + 2X_{2} + 3X_{3} = 9\\2X_{1} + 1X_{2} = 6\\[/tex]

Conclusion:  

For whatever system you have you need to convert the system into a matrix notation and using the basic operations, described here, reduce the complexity of the system until:  

You have a solution, you discover that the system has an infinite number of solutions or the system of equation is inconsistent.  

Example of inconsistency

If after making the basic operations to your system you get a result like this

[tex]\left[\begin{array}{ccccc}7&0&4&|&9\\2&1&0&|&6\\0&0&0&|&-1\end{array}\right][/tex]  

You can say that the system is inconsistent because zero is not equal to minus one.  

Example of solution  

If after making the basic operations to your system you get a result like this

[tex]\left[\begin{array}{ccccc}1&0&0&|&9\\0&1&0&|&-6\\0&0&1&|&-1\end{array}\right][/tex]

You can say that the system have a solution in which X1 = 9, X2 = -6 and X3 = -1

To solve a system of linear equations using Gaussian elimination with back-substitution or Gauss-Jordan elimination, follow the steps of writing the equations in matrix form, performing row operations, creating a diagonal of 1's, and using back-substitution to find the variable values.

To solve a system of linear equations using Gaussian elimination with back-substitution or Gauss-Jordan elimination, follow these steps:

Example: Solve the system of equations 2x + 3y = 8 and 4x - 2y = 10 using Gaussian elimination with back-substitution.

The solution to the system of equations is x = 23/8 and y = 3/4.

https://brainly.com/question/33609849

#SPJ3

Answer:

D

Step-by-step explanation:

cumulative property of multiplication

Final answer:

The distributive property is not used in the simplification of the expression 2×(x+5)+7x. The expression is simplified using the associative and commutative properties of addition.

Explanation:

The property that is not used to simplify the following expression 2×(x+5)+7x=(2x+10)+7x=(10+2x)+7x=10 +(2x+7x)=10 + 9x=9x + 10 is C. distributive property. Let's look at how each property is applied in the simplification:

Associative property of addition: This property is used when the expression goes from 2×(x+5)+7x to (2x+10)+7x and again from (10+2x)+7x to 10 +(2x+7x).

Commutative property of addition: This property is used when the terms 2x and 10 are rearranged as (10+2x) and also when the final step changes 10 + 9x to 9x + 10.

The distributive property is not used at any step in this problem. This property would involve multiplication across a sum, such as a(b + c) = ab + ac, which is not seen in the simplification process.

The commutative property of multiplication is also not used, as there is no rearrangement of multiplication terms.

Answer:

a) 38.3% probability that an 18-year-old man selected at random is between 68 and 70 inches tall.

b) 95.44% probability that the mean height x is between 68 and 70 inches.

Step-by-step explanation:

To solve this question, it is important to know the normal probability distribution and the Central Limit Theorem.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex].

In this problem, we have that:

[tex]\mu = 69, \sigma = 2[/tex]

(a) What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall?

This is the pvalue of Z when X = 70 subtracted by the pvalue of Z when X = 68. So

X = 70

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 69}{2}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a pvalue of 0.6915.

X = 68

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{68 - 69}{2}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a pvalue of 0.3085.

So there is a 0.6915 - 0.3085 = 0.383 = 38.3% probability that an 18-year-old man selected at random is between 68 and 70 inches tall.

(b) If a random sample of sixteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches?

Now we use the Central Limit Theorem, with [tex]n = 16, s = \frac{2}{\sqrt{16}} = 0.5[/tex]

The probability is also the pvalue of Z when X = 70 subtracted by the pvalue of Z when X = 68, but with s as the standard deviation. So

X = 70

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{70 - 69}{0.5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772.

X = 68

[tex]Z = \frac{X - \mu}{0.5}[/tex]

[tex]Z = \frac{68 - 69}{0.5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228.

So there is a 0.9772 - 0.0228 = 0.9544 = 95.44% probability that the mean height x is between 68 and 70 inches.

In the case of normal distribution, the probability that a random 18-year-old man's height is between 68 and 70 inches is 0.383, while the probability that the mean height of a random sample of 16 men falls in the same range is approximately 0.999.

This question pertains to the statistical concept of normal distribution.

(a) To find the probability that a randomly selected 18-year-old man is between 68 and 70 inches tall, we first need to convert these heights to Z-scores. Given the mean height is 69 inches and the standard deviation is 2 inches, the Z-score for 68 inches is [tex](68-69)/2=-0.5[/tex] and for 70 inches it is [tex](70-69)/2=0.5[/tex]. The area between these Z-scores on a standard normal distribution chart represents the probability of a man being between 68 and 70 inches tall. This probability is approximately 0.383.

(b) In this part, we are dealing with a sample mean rather than individual values. Because of the Central Limit Theorem, a distribution of sample means will have a standard deviation equal to the population standard deviation divided by the square root of the sample size. So, our new standard deviation becomes 2/√16 = 0.5. Then we compute the Z-scores for 68 inches and 70 inches with this new standard deviation, and find the probability corresponding to the area between these Z-scores, which is considerably higher than individual case, almost 0.999.

https://brainly.com/question/34741155

#SPJ12

Answer:

Step-by-step explanation:

Given that price, p, and quantity, x, are inearly related

We are given two points on this line as (p,x) = (96.90, 121) and (40.20,310)

Using two point formula we find linear equation as

[tex]\frac{y-121}{310-121} =\frac{0-96.90}{40.20-96.90} \\(x-121)(-56.70)=189(p-96,.90)\\189p+56.70x =25174.80[/tex]

a)[tex]189p+56.70x =25174.80[/tex] is the linear equation

b) A(x)

Substitute to get

189(50.70)+56.70x = 25174.80

x=275 units

c) This is linear function hence no local maxima or minima

d) No maximia or minima

Answer:

70.19% probability that on a given day the supermarket will sell below 449 gallons of milk.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 436.6, \sigma = 23.23[/tex]

What is the probability that on a given day the supermarket will sell below 449 gallons of milk?

This is the pvalue of Z when X = 449. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{449 - 436.6}{23.23}[/tex]

[tex]Z = 0.53[/tex]

[tex]Z = 0.53[/tex] has a pvalue of 0.7019.

So there is a 70.19% probability that on a given day the supermarket will sell below 449 gallons of milk.

Answer:

The question is not so clear and complete

Step-by-step explanation:

But for questions like this, since the equation has been given, what is expected is for us to make comparison, compare the RHS with the LHS or by method of comparing coefficients.

We follow the stated conditions since we are told that b and c are both integers which are greater than 1 and b is less than the product of cb. from these conditions, we can compare and get the values of b , c and d.

Another approach is to assume values, make assumptions with the stated conditions, however, our assumptions must be valid and correct if we substitute the assumed values of b, c and d in the equation, it must arrive at the same answer for the RHS. i.e LHS = RHS

Answer:

Step by step approach is as shown

Step-by-step explanation:

recalling from commutative law that A + B = B + A and since A is a scalar, and from scalar multiplication of matrix.

Complete question

The complete question is shown on the first uploaded image

Answer:

The solution and the explanation is on the second third and fourth uploaded image

Answer:

[tex]182.167-2.03\frac{114.05}{\sqrt{36}}=143.580[/tex]  

[tex]182.167+2.03\frac{114.05}{\sqrt{36}}=220.754[/tex]  

So on this case the 95% confidence interval would be given by (143.580;220.754)  

Step-by-step explanation:

Assuming the following dataset:

77, 349,417,349, 167 , 225, 265, 360,205

145,335,40,139, 177,108, 163, 202, 22

123,439, 125,135, 86,43, 217,49, 156

119,178, 151, 61, 350, 312, 91, 89,89

We can calculate the sample mean with the followinf formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}= 182.167[/tex]

And the sample deviation with:

[tex] s = \sqrt{\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}}=114.05[/tex]

The sample size on this case is n =36.

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]\bar X=182.167[/tex] represent the sample mean  

[tex]\mu[/tex] population mean (variable of interest)  

s=114.05 represent the sample standard deviation  

n=36 represent the sample size    

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 point estimate of the population mean is [tex]\hat \mu = \bar X =182.167[/tex]

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:  

[tex]df=n-1=36-1=35[/tex]  

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,35)".And we see that [tex]t_{\alpha/2}=2.03[/tex]  

Now we have everything in order to replace into formula (1):  

[tex]182.167-2.03\frac{114.05}{\sqrt{36}}=143.580[/tex]  

[tex]182.167+2.03\frac{114.05}{\sqrt{36}}=220.754[/tex]  

So on this case the 95% confidence interval would be given by (143.580;220.754)  

The question is asking for a 95% confidence interval for the mean weight of bears in a park. The confidence interval is a range of values, derived from the data collected, that is estimated to contain the true population mean. 95% of such confidence intervals are expected to contain the true value.

In statistics, we often

use sample data to make generalizations

about an unknown population. This part of statistics is known as

inferential statistics

. The sample data help us to make an estimate of a population parameter. We realize that the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, which are often called confidence intervals.

A confidence interval is a type of estimate but, instead of being just one number, it is an interval of numbers. The interval of numbers is a range of values calculated from a given set of sample data. The confidence interval is likely to include an unknown population parameter.

In this case, you've been asked to calculate a 95% confidence interval for the mean weight of bears in a park. From the provided data, you would calculate the sample mean and standard deviation, and use a statistical formula to calculate the confidence interval. For example, if the confidence level is 95 percent, then we say, 'We estimate with 95 percent confidence that the true value of the population mean is between x and y.'.

https://brainly.com/question/34700241

#SPJ3

To determine the volume of water evaporated from the pool at the El Cheapo Motel, we converted all measurements to a common unit and calculated the volume of water evaporated. The motel has to add approximately 946.13 gallons of water weekly, considering there is no rain.

To answer this question, we first need to convert the measurements to a common unit. Given that the pool is 5.0 m wide and 12.0 m long (a total area of 60.0 m2) and the weekly evaporation is 2.35 inches, we first convert the inches to meters. Since 1 inch is equal to 0.0254 meters, 2.35 inches equals 0.05969 meters.

Then, we calculate the volume of water evaporated in a week, which is calculated by multiplying the surface area of the pool by the depth of the water evaporated. Hence, it's 60.0 m2 * 0.05969 m = 3.58 m3. As 1 m3 is approximately 264.17 gallons, 3.58 m3 equals 946.1296 gallons approximately.

In conclusion, the El Cheapo Motel needs to add around 946.13 gallons of water to their pool on a weekly basis, if there is no rain.

https://brainly.com/question/32822827

#SPJ3