What value of p makes the equation true?

Step-by-step explanation:

simply take the average of the x and y coordinates

The sample space for the experiment of tossing a pair of dice consists of all possible outcomes of the two dice rolls. Using a rule method, we can represent the sample space as S = {(1,1), (1,2), (1,3), ..., (6,5), (6,6)}.

(a) The event A corresponds to the sum of the outcomes being greater than 8. The elements of event A are (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).
(b) The event B corresponds to a 2 occurring on either die. The elements of event B are (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (1,2), (3,2), (4,2), (5,2), (6,2).
(c) The event C corresponds to a number greater than 4 appearing on the green die. The elements of event C are (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
(d) The event A∩C corresponds to the outcomes where both the sum is greater than 8 and a number greater than 4 appears on the green die. The elements of event A∩C are (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).
(e) The event A∩B corresponds to the outcomes where both the sum is greater than 8 and a 2 occurs on either die. There are no elements in this event.
(f) The event B∩C corresponds to the outcomes where both a 2 occurs on either die and a number greater than 4 appears on the green die. The elements of event B∩C are (5,2), (6,2).
(g) The Venn diagram illustrating the intersections and unions of the events A, B, and C would have three overlapping circles representing each event. The area where all three circles intersect represents the event A∩B∩C, which is empty in this case. The area where circles A and C intersect represents the event A∩C, and the area where circles B and C intersect represents the event B∩C. The unions of the events can also be represented by the combinations of overlapping areas.

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2.4

(a) Sample space S: {(1, 1), (1, 2), ... (6, 5), (6, 6)}

(b) Rule method: S = {(x, y) | x, y ∈ {1, 2, 3, 4, 5, 6}}

2.8

(a) A: {(3, 6), (4, 5), ... (6, 6)}

(b) B: {(1, 2), (2, 1), (2, 2)}

(c) C: {(5, 1), (5, 2), ... (6, 6)}

(d) A∩C: {(5, 4), ... (6, 6)}

(e) A∩B: {}

(f) B∩C: {}

2.4

(a) Sample space S by listing the elements (x, y):

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

(b) Sample space S using the rule method:

S = {(x, y) | x, y ∈ {1, 2, 3, 4, 5, 6}}

2.8

(a) Elements corresponding to event A (the sum is greater than 8):

A = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

(b) Elements corresponding to event B (a 2 occurs on either die):

B = {(1, 2), (2, 1), (2, 2)}

(c) Elements corresponding to event C (a number greater than 4 on the green die):

C = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

(d) Elements corresponding to event A∩C:

A∩C = {(5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

(e) Elements corresponding to event A∩B:

A∩B = {} (No common elements between A and B)

(f) Elements corresponding to event B∩C:

B∩C = {} (No common elements between B and C)

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The corresponding point on the unit circle for the angle θ = 5pi/3  is given by: (0,5, -0.866).

What is the unit circle?

Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.

What is area of circle ?

The area of circle can be defined as the product of pi and square of radius of a given circle.

In this problem, we have that θ = 5pi/3 , hence:

cos θ = 0.5

sin θ = -0.866

Thus the point is (0,5, -0.866).

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The probability that an athlete who tests negative actually did not take steroids is approximately 0.926 or 92.6%.

Let's assume that 100 athletes were tested that day. Of these, 10 are expected to have taken steroids, and 90 are expected to have not taken steroids.

Of the 10 athletes who took steroids, the test is accurate 95% of the time, so 9 of them are expected to test positive for steroids, and 1 is expected to test negative.

Of the 90 athletes who did not take steroids, the test is accurate 97% of the time, so 87 of them are expected to test negative for steroids, and 3 are expected to test positive.

Therefore, out of the 100 athletes tested, a total of 90 + 1 + 3 = 94 are expected to test negative for steroids.

Since we know that the test is accurate, the probability that an athlete who tests negative actually did not take steroids is:

(Probability that athlete did not take steroids and tested negative) / (Probability of testing negative)

= 87 / 94

= 0.9255 (rounded to four decimal places)

Therefore, the probability that an athlete who tests negative actually did not take steroids is approximately 0.926 or 92.6%.

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The statement in part (a) is False. According to the definition of matrix multiplication, if A is an mxn matrix and B is an nxp matrix with columns b₁, ..., bp, then the product AB is an mxp matrix.

The entry in the i-th row and j-th column of AB is obtained by taking the dot product of the i-th row of A and the j-th column of B.

Therefore, the product AB cannot be represented simply as {\(a_1b_1 a_2b_2\)}, but rather as a matrix with appropriate entries based on the dot products.

The correct representation of AB will involve the dot products of the corresponding rows and columns, resulting in a 2x2 matrix.

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Answer:

34/24

Step-by-step explanation:

x-3/4+2/3=17/12

x-17/12=17/12

X=17/12+17/12

X=34/24

Answer:

c = 4y

Step-by-step explanation:

Are there more, Chihuahuas or Yorkies?

Does  the word 'times' mean add, subtract, multiply or divide?

The way I look at it,  there are more Chihuahuas and 'times' means multiply.  Do you agree?

Therefore, I need to multiply 4 times the no. of Yorkies to get the no. of Chihuahuas

So,  c = 4y

Now, I don't see an equation in the list to choose from.  So, I don't know what to do from here.  I am guessing that c = 4y is what you want.

Treatment Group:

$\mu = 22, \sigma = 2.30$

Placebo Group:

$\mu = 22, \sigma= 0.77$

In the standard curve for nitrophenol generated for use in this experiment, the nitrophenol concentration is reported on the x - axis.

What is standard curve?

A calibration curve, sometimes referred to as a standard curve, is a common technique used in analytical chemistry to compare an unknown sample to a group of standard samples with known chemical concentrations.

In order to calculate the nitrophenol concentration in mole/ml based on absorbance readings, the standard curve is drawn.

Based on the optical density, or OD410, or absorbance at 410 nm, this standard curve of absorbance is used to calculate the quantity of nitrophenol.

Therefore, the nitrophenol concentration is displayed on the x axis of the standard curve.

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Answer:

your question is incomplete but I imagine that your asking how many bags of popcorn they can buy? the answer is 3 or 15/4 depending on what your asking.

Step-by-step explanation:

(3/4)5

15/4

Answer:

3 bags your welcome! :D it's right in khan!

Step-by-step explanation:

5 half-dozens he should buy to make enough cookies.

What is an average?

Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or a figure that lies halfway between two extremes.

Here, we have

If 108 students eat 2 cookies on average, there will need to be 108× 2 = 216 cookies.

There are 15 cookies per pan, meaning there need to be {216}/{15} = 14.4 pans.

However, since half-recipes are forbidden, we need to round up and make{216}/{15} = 15 pans.

1 pan requires 2 eggs, so 15 pans require 2×15 = 30 eggs.

Since there are 6 eggs in a half dozen,

we need 30/6 = 5 half-dozens of eggs.

Hence, 5 half-dozens he should buy to make enough cookies.

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Answer:

N is greater than or equal to 0. N is an integer

Answer:

See attachement

Step-by-step explanation:

The interval 0-20 on vertical axis will be skipped on paper graph and graph will start from 20.

Answer: 0 and -5

Step-by-step explanation:

Answer:

-5 and 0 make the inequality true.

Step-by-step explanation:

-5 and 0 are less than 1, making 1 and 5 greater than one (so 1 and 5 don't apply to this situation)

Brute force approach to analyzing all subsets of a set of 24 experiments for space launch problem becomes impractical due to exponential increase in number of subsets, resulting in longer execution times.

The brute force approach to solving the space launch problem becomes increasingly impractical as the size of the experiment set grows. When doubling the size from 12 to 24 experiments, the number of subsets to analyze increases exponentially from 4,096 to 16,777,216. This poses a significant computational challenge for a computer.

To assess the execution time of the "find_optimal_subset" function on a set of 24 experiments, we can generate a new 2D list representing these experiments. Each experiment can be assigned an ID number ranging from 1 to 24, and the masses and value ratings can be randomly generated using the randint function from the random module in Python. By measuring the elapsed time using Python's process_time function, we can determine the runtime of the function.

For instance, on a desktop with a stock Ryzen 9 5900X processor, running Windows 10 Pro and Python 3.9.2 (64-bit), the execution time is approximately 97-98 seconds. However, it's important to note that the exact execution time may vary depending on the specific hardware and software configuration.

In summary, the brute force approach becomes increasingly time-consuming as the size of the experiment set grows. Doubling the size of the set from 12 to 24 experiments leads to a drastic increase in the number of subsets to analyze. Timing the execution of the "find_optimal_subset" function on the larger set reveals the practical challenges posed by the exponential growth in computation time.

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To check that data follows a continuous distribution using the goodness-of-fit procedure you can change the continuous variable into categorical.

In this question we need to describe how would the goodness-of-fit procedure be modified to check that data follows a continuous distribution.

We know that the Chi - square goodness of fit test can be applied to discrete distributions such as binomial, Poisson, etc.

For continuous distributions we can use Kolmogriv - Smirnov test, t-test ( the single-sample, paired t-test, and the two-sample, unpaired t-test)

A goodness-of-fit test is concerned with the question whether a data set may have been generated by a certain distribution.

Therefore, to check that data follows a continuous distribution we need to change the continuous variable into categorical.

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Answer:

XN = 6

Step-by-step explanation:

Use the Angle Bisector Theorem to solve this:  An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

12/4 = 18/XN

12(XN) = 18(4)

XN = 72/12 = 6

The value οf sin F is 5/6.

The branch οf Mathematics which helps in dealing with measure οf three sides οf a right-angled triangle is called Trigοnοmetry.

sin θ  = Perpendicular/Hypοtenuse

cοs θ = Base/Hypοtenuse

tan θ = Perpendicular/Base

cοsec θ = Hypοtenuse/Perpendicular

sec θ = Hypοtenuse/Base

cοt θ = Base/Perpendicular

Cοs D = 5/6 (given)

We knοw, cοs θ =Base / Hypοtenuse

Thus, base = 5  and hypοtenuse = 6

Therefοre, DE = 5 and DF = 6

Sin  θ = Perpendicular / Hypοtenuse

Sin F = DE / DF

Sin F = 5/6

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Answer:

4 if rong so so sorry

Step-by-step explanation:

The square of a number is increased by 5 times the number \(6x^{2} +5x-4=0\)

What is quadratic equation?
A quadratic equation is a second order equation written as a\(x^{2}\) + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Product of 6 and the square of a number is increased by 5 times the number, he result is 4.

Consider x as the number,

The question can be written as:

\(6(x^{2} )+5(x)=4\)

\(6(x^{2} )+5(x)-4=0\)

Hence, the answer for the given question is \(6x^{2} +5x-4=0\).

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Answer:

Great

Step-by-step explanation:

However, you're missing a factor of 9.

Answer:

1x81 =81

3x27=81

9 x 9 =81

1,3,27,81 These are factors too, but you missed of the number 9.

Answer:

\(y=60\textdegree\)

Step-by-step explanation:

The Tangent-Secant Interior Angle Measure Theorem states that the measure of an angle formed by a tangent and a secant of a circle at the point of tangency is equal to half of the measure of its intercepted arc.

Therefore, \(y=\frac{1}{2} *120\textdegree = \bf 60\textdegree\). Hope this helps!

Answer:

15 Apr 2018 — Area of path parallel to the remaining length of ... Area of parallelogram ABCD = AB × AE = 8 × 4 cm2 ... We can also calculate area of shaded portion by using area of..

Answer:

185.25 cm^2

Step-by-step explanation:

since only length is given i considered the wall as square shape. So given :

length = 13.5 cm

area of the wall = l^2

= 13.5^2

=182.25 cm^2

Answer:

Factor analysis

Step-by-step explanation:

A statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion.

The statistical technique that would allow a researcher to cluster is called Cluster Analysis. It is a statistical technique that enables researchers to cluster groups of objects that share certain similarities based on their attributes, observations, or characteristics.What is cluster analysis?Cluster analysis is a data-driven technique that helps in grouping similar objects based on the data provided. It is often used in many fields, including data mining, machine learning, and bioinformatics. Cluster analysis is used to find the natural groupings of objects, which have similar attributes or characteristics. For instance, it is used to group customers based on their behavior, cluster genetic markers in DNA, cluster galaxies in the universe, and much more. Cluster analysis helps in analyzing large datasets by grouping similar objects into smaller groups that are easier to understand.The Cluster analysis technique is a valuable tool in statistical analysis and it is used in different fields like market research, bioinformatics, genetics, etc. It is a method of statistical data analysis that helps researchers identify groups or clusters of data. It is a commonly used technique that is used to identify natural patterns within large datasets.

We can reject the null hypothesis at the 0.05 level and accept the alternative hypothesis.

A one-sided test will test using the full alpha to test whether the result is far enough in one direction. A two-sided test will split the alpha in half to test whether the result is too big or too small.

The null hypothesis is:

\(\mathit{H}_{0}: \mu= 2.5\)

The alternative hypothesis is:

\(\mathit{H}_{1}: \mu > 2.5\)

The z-score for a mean of 3 is:

\(z = (x- \mu)/ (\sigma/ \sqrt{n})) \\ = (3-2.5)/(1.8/\sqrt{n})) \\ = (.5)/(1.8/6)) \\ = (.5)/(.3)) \\ = 1.666666667\)

The z-score for the 0.05 significance level is 1.645, which is less than the mean of 3 z score of 1.67.

Hence, we can go ahead and reject the null hypothesis

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Answer:

£32.76

Step-by-step explanation:

21/500=0.042

780x0.042 = 32.76

Answer:  1/10 or 0.1

For example, going from 700 to 70 is

700*(1/10) = 700*0.1 = 70

which is us going from the hundreds place value to the tens place value.

If we move to the left instead of right, we would multiply each item by 10.

Answer:

7/12.

Step-by-step explanation:

=x/x+5.

x-5/x+5+4=⅛

x-5/x+9=⅛

x-5=⅛(x+9)

x-5=⅛x+1⅛

x-⅛x=1⅛+5

⅞x=49/8

7x=49

x=7

thus the initial fraction is x/x+5= 7/12

A rational number is a fraction