Here is a list of numbers:
87 12 7
the median
the range
the mode
Find:
a)
b)
c)
a)
b)
C
AA
11 10 7 12
vle.mat

The t-distribution is a family of probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small or the population standard deviation is unknown.

The shape, center, and spread of t-models change as the number of degrees of freedom increases as follows:

Shape: As the number of degrees of freedom increases, the shape of the t-distribution becomes more similar to that of the standard normal distribution. Specifically, the t-distribution approaches the normal distribution in shape as the number of degrees of freedom increases.

Center: The center of the t-distribution is always located at zero. As the number of degrees of freedom increases, the mean of the t-distribution approaches zero, and the distribution becomes more symmetric around the mean.

Spread: The spread of the t-distribution decreases as the number of degrees of freedom increases. Specifically, the variance of the t-distribution decreases as the number of degrees of freedom increases. This means that the t-distribution becomes more concentrated around its mean as the number of degrees of freedom increases.

In summary, as the number of degrees of freedom increases, the t-distribution becomes more like the standard normal distribution in shape, its center remains at zero, and its spread becomes narrower. This has important implications for hypothesis testing and confidence intervals, as the t-distribution is commonly used in these statistical applications.

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Given, A random variable X takes a value k.Consider a sequence of independent coin flips with a coin that shows heads with probability p.Hence, for X to take the value k, there must be k heads and n - k tails.

The probability of k heads and n - k tails is:

\(P(X = k) = {n \choose k}p^{k}(1 - p)^{n-k}\)

Thus,  the probability of X taking the value k in a sequence of independent coin flips with a coin that shows heads with probability p is given by the formula

\(P(X = k) = {n \choose k}p^{k}(1 - p)^{n-k}\)

When the sequence of independent coin flips takes place and the coin shows heads with probability p, then X can take a value k only if there are k heads and n - k tails in the sequence. The probability of obtaining k heads and n - k tails is given by the binomial distribution formula. The formula takes the form:

\(P(X = k) = {n \choose k}p^{k}(1 - p)^{n-k}\)

where n is the number of flips, k is the number of heads, p is the probability of getting a head and 1-p is the probability of getting a tail.

Therefore, from the above explanation and derivation, we can conclude that the probability of X taking the value k in a sequence of independent coin flips with a coin that shows heads with probability p is given by the formula

\(P(X = k) = {n \choose k}p^{k}(1 - p)^{n-k}\)

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Answer:

  (s, f) = (4.5, 2.25)

Step-by-step explanation:

You want the solution to the simultaneous equations ...

Writing these in general form, we have ...

  3s +2f -18 = 0

  2s +3f -15.75 = 0

Using the "cross-multiplication method" for solution, we find ...

  ∆1 = (3)(3) -(2)(2) = 5

  ∆2 = (2)(-15.75) -(3)(-18) = 22.5

  ∆3 = (-18)(2) -(-15.75)(3) = 11.25

  s = ∆2/∆1 = 22.5/5 = 4.5

  f = ∆3/∆1 = 11.25/5 = 2.25

The solution is (s, f) = (4.5, 2.25).

__

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The flux through through the boundary of the rectangle is -sin(6x)/6.

According to the statement

we have given that the limits and the equation, and we have to find the flux of the given equation.

For this purpose, we know that the

Flux is a the surface integral of the perpendicular component of a vector field over a surface.

And the given equation is :

x^4 + 5,ycos(6x)

The given limits are:

0≤ x ≤ 2, 0 ≤ y ≤ 4

So, Integrate with the given imits,

\(\int\limits^2_0 \int\limits^4_0 {x^4 + 5,ycos(6x)} \, dx\)

When integrate these terms with dx and dy one by one then the equation become:

For the x:

\(\int\limits^2_0 {x^4 + 5,ycos(6x)} \, dx \\\bracket\limits^2_0 [{\frac{x^5}{5},{-ysin(6x)}}/{6]\)

And then integrate w.r.t the y.

Then the flux through the boundary become:

-sin(6x)/6.

So, The flux through through the boundary of the rectangle is -sin(6x)/6.

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If they give up 20 yards on the opening play, they're out. The ball is on the 30-yard line.

The starting line is the 50-yard line.

The new yard line following the first play Equals (The yard line following the first play) - (The number of yards lost)

As the football team lost 20 yards after the first play.

After the second play, the new yard line is 50 - 20 = 30 yards.

After the second play, the new yard line is 30.

The ball was on the 30-yard line at the end of the second play.

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Answer:

540 minutes or 9 hours :)

Step-by-step explanation:

What I did is I multiplied 6 hours by 60 minutes. Or for the hours skip that step.

6x60=360       or     6/300=0.02

360/300=1.2    or     0.02x450=9

1.2 x450= 540  or         9 hours

540 minutes

540 minutes or 9 hours :D

Goodluck <3

Hope this helps!

According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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A and B are mutually exclusive, with P(A) is 0.7 and P(B) is 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

To find the probability of B given A, we can use the formula:

P(B|A) = P(A and B) / P(A)

Given:

P(A) = 0.5

P(B) = 0.1

P(A and B) = 0.3

P(B|A) = 0.3 / 0.5

= 0.6

Therefore, the probability that B will occur if A occurs is 0.6.

Given:

P(A) = 0.3

P(B) = 0.4

Since A happening guarantees that B must also happen, the events A and B are not independent. In this case, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.3 + 0.4 - 0.3

= 0.4

Therefore, the probability of A or B occurring is 0.4.

Given:

P(A) = 0.7

P(B) = 0.2

Since A and B are mutually exclusive events, they cannot occur together. In this case, we have:

P(A and B) = 0

Therefore, P(B|A) = P(BIA)

= 0.

P(BIA) = P(B)

= 0.2.

So, P(BIA) < P(B) is true.

When events A and B are mutually exclusive, with P(A) = 0.7 and P(B)

= 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

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The probability P(E) is 13/15.

According to the statement

we have given that the S = {1, 3, 5, 7, 9}, E = {1, 5, 7}

And we have to find the probability P(E).

So, For this purpose

Recall the formula for the probability of an event E in case when all outcomes are equally likely:

P(E)= n(E) /n(S)

in which S is the sample space.

But we have the S = {1, 3, 5, 7, 9},

so, n(S) = Sum of all outcomes / number of outcomes

n(S) = 1+3+5+7+9 /5

n(S) = 25 /5

n(S) = 5 and

For n(E) = Sum of all outcomes / number of outcomes

n(E) = 1+5+7 /3

n(E) = 13 /3

n(E) = 13 /3

Substitute these values in the above written formula then

P(E)= n(E) /n(S)

P(E)=  (13/3)/ 5

P(E)= 13 /15

So, The probability P(E) is 13/15.

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Using the z-distribution, it is found that the 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, we have a 99% confidence level, hence\(\alpha = 0.99\), z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The other parameters are given by:

\(n = 90, \pi = \frac{12}{90} = 0.1333\)

Then, the bounds of the interval are found as follows:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 - 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.041\)

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 + 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.2256\)

The 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.

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The dimensions of the rectangle which form the dining room is 7 by 5 meters.

The perimeter of the rectangle is 24 meters.

The total length of a shape's boundaries is its perimeter. The total lengths of all other edges and sides are added to find a shape's perimeter.

Let the length be a and the width be b.

Hence 2(a + b) = 24

or, a+b = 12

Now the area of the rectangle is given as 35 square meters.

Therefore ab = 35

now we will use these two equations to find the dimension of the rectangle

a+b = 12

or, a = 12 - b

again:

ab = 35

or, (12 - b)b = 35

or, 12 b - b² = 35

or,  - b² +12b -35 = 0

or,   b² - 12b + 35 = 0

or,  (b-7) (b-5) = 0

either b = 7 or b = 5 .

Therefore the value of a from the equations is 5 or 7.

Therefore the dimensions of the dining room are 7 by 5 meters.

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Answer:

Step-by-step explanation:

You had the first part of the first question correct. The answer is 100:64

The sides of the squares

Area of e = 69% more than area of area of f

e^2: f^2 = ( 1 + 69/100 ) / 1

e^2 : f^2 = (1.69)/1            Take the square root of both sides

e:f  = 1.3:1

Answer:

-9+x=-20

Step-by-step explanation:

I am not so positive on this one, but if you are not doing inequalities, then this should be correct.

"More than" would insinuate that you are adding. In this class, you would have a number to replace that x, but since no number was given, you place the x in its place. x=-11, because when you "add" -9 with something to get -20, it would have to be -11. Negative numbers can be confusing because when you subtract a negative number by another negative, you end up with a negative. Like in this case. Normally, you would just put -11, so it would look like -9 - 11 = -20. But since this says "more than", unless you are doing inequalities, you add.

If you are doing inequalities, then your answer should be this:

-9 > x = -20

I hope this helps!

-No one

The Probability of reverse alphabetical order is 1.04x10^-26, Probability of z being the first letter is 0.0385, Probability of z preceding a is 0.5, Probability of a preceding z is 0.0385, Probability of a, m, z in order is 0.00274, Probability of m, n, o in original positions is 0.00274.

The probability that the permutation consists of the letters in reverse alphabetic order is 1/(26!), which is approximately 1.04 x 10^-26. This is because there is only one permutation out of the 26! possible permutations that satisfies this condition.

The probability that z is the first letter of the permutation is 1/26, which is approximately 0.0385. This is because there is only one way to select z to be the first letter out of the 26 possible choices.

The probability that z precedes a in the permutation is 1/2, which is 0.5. This is because in any permutation of the 26 letters, z and a are equally likely to appear before or after each other.

The probability that a immediately precedes z in the permutation is (24!)/(26!), which is approximately 0.0385. This is because once the positions of a and z are fixed in the permutation, there are 24! ways to arrange the remaining 24 letters, out of the 26! possible permutations.

The probability that a immediately precedes m, which immediately precedes z in the permutation is (23!)/(26!), which is approximately 0.00274. This is because once the positions of a, m, and z are fixed in the permutation, there are 23! ways to arrange the remaining 23 letters, out of the 26! possible permutations.

The probability that m, n, and o are in their original places in the permutation is (23!)/(26!), which is approximately 0.00274. This is because once the positions of m, n, and o are fixed in the permutation, there are 23! ways to arrange the remaining 23 letters, out of the 26! possible permutations.

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The statements that are true for each system of equations are System A and System B have unique solutions, while System C has infinitely many solutions.

System A: The system has a unique solution since it consists of two linear equations with two variables that intersect at a single point. This point can be found by solving for x and y using any of the available methods, such as substitution or elimination.

System B: The system has a unique solution since it consists of two linear equations with two variables that intersect at a single point. This point can also be found by solving for x and y using any of the available methods.

System C: The system has infinitely many solutions since the two linear equations are equivalent. This means that any point that satisfies one equation also satisfies the other. Therefore, the solution set is a line on the xy-plane.

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Answer:

her hourly pay is 15

Step-by-step explanation:

375 (earned) ÷ 25 (hrs worked) = 15

i hope this helps have a good day!

Answer:fixed ratio

Step-by-step explanation: :)

This is an illustration of a fixed ratio reinforcement schedule: after a predetermined number of responses, Frances is given a reward (in this case, $1). (every pound of worms).

An example of a reinforcement plan utilized in the behavioral psychology concept of operant conditioning is a fixed ratio reinforcement schedule. A reward or reinforcement is delivered according to this schedule after a predetermined number of actions or responses. As an illustration, a rat might receive a food pellet after every 10 lever presses.

Fixed ratio schedules work well for encouraging high response rates since the subject is driven to keep up the activity in order to earn the reward. Yet, if the reinforcement is stopped, the behavior can become less frequent or cease entirely.

Fixed ratio schedules can also cause behaviors to become rigid or stereotyped because the subject may start concentrating only on the number of responses required to earn the reward and stop considering other options or actions.

Overall, fixed ratio reinforcement regimens can be helpful in teaching both humans and animals to carry out particular tasks, but they should be utilized with caution and consideration for any unexpected consequences.

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The amount of buttermilk needed for the cake recipe, which is 170.0 mL, is approximately 0.72 cups.


To convert milliliters to cups, we need to use the given conversion factors. First, we convert milliliters to liters by dividing number by 1000 (since there are 1000 milliliters in a liter). Therefore, 170.0 mL is equal to 0.17 liters.

Next, we convert liters to quarts. Since 1 liter is approximately equal to 1.0567 quarts, we multiply 0.17 liters by 1.0567 to get 0.179939 quarts.

Finally, we convert quarts to cups. Since there are 4 cups in a quart, we multiply 0.179939 quarts by 4 to get approximately 0.72 cups.

Therefore, 170.0 mL of buttermilk is approximately equal to 0.72 cups.

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SOLUTION

I believe the following explanation should help to answer

A consistent system is a system that has at least one solution.

If a consistent system has exactly one solution, it is independent.

If a consistent system has an infinite number of solutions, it is dependent.

But, If a system has no solution, it is said to be inconsistent

Hence the answer is Inconsistent, option D

Based on the equation given, the graph that matches the equation is Graph D.

To find the graph that matches the equation, solve for the values of y based on values of x and the equation.

Assuming x is -1, y is:

= 1/5 (-1) + 2

= 1.8

x = 0

= 1/5(0) + 2

= 2

x = 1

= 1/5(1) + 2

= 2.2

The graph that has the points:

(-1, 1.8) (0, 2) and (1, 2.2) is the last graph so this is the correct graph.

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Answer:

what are the choices?

Step-by-step explanation:

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Step-by-step explanation:

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators.

Answer:

45cm

Step-by-step explanation:

Answer:

45

explain answer here:

well i just took the test..... love ya !!

hope u get a good grade !!

Answer:

she will be back at 7:30pm

Step-by-step explanation:

From the question we are given

Time that Shasta leaves for her best friend place = 5:00pm

If she is to come back after 2 and a half hour, hence we will have to add 2hr 3ominutes to the time she left to know the time she will be back as shown:

She will be back at 5:00 + 2hr 30min = 7:30pm

Hence she will be back at 7:30pm

Step-by-step explanation:

y = 200  - 3 *x  has slope = -3   this is downward sloping from L to R

Answer:downward sloping

Step-by-step explanation:

negative slope

Speed = distance / time

Tuesday: speed = 2.4km / 18 minutes = 0.13 km per minute

Friday: speed = 1.8 km / 12 minutes = 0.15 km per minute

0.15 is larger than 0.13 so she ran faster on Friday.