81 x 62
Not sure how to do this lol

Answer:

Step-by-step explanation:

11 x .25 = $2.75

7 x .10 = .70

 Total $3.45

ΔABD is congruent to ΔCBD. Therefore, the statement that best describes the relationship between triangles ABD and CBD is the following option;

Congruent triangles are identical triangles that have the same shape and size.

The midpoint of the side AC = The point B

Therefore; AB is congruent to BC

AB ≅ BC

The point side BD is a common side to triangle ΔABD and triangle ΔCBD

Therefore, according to the reflexive property, BD is congruent to itself

BD ≅ BD

The length of the sides AD and CD obtained from a similar question on the website, are the same, therefore;

AD ≅ CD

Therefore, the three sides of the triangle ΔABD are congruent to the the corresponding three sides of the triangle ΔCBD, which indicates by the definition of congruency, the lengths of each of the three sides of the triangle ΔABD are the same as the lengths of the three sides of the triangle ΔCBD.

The ΔABD is congruent to ΔCBD by the Side-Side-Side, SSS congruence postulate.

The correct option is therefore;

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1 meter = 1.094 yard create a conversion factor to convert meters to yards.

Any instrument that detects and may store an electric or magnetic amount, such voltage or current, is referred to as a meter. Examples of meters include an ammeter and a voltmeter. One may refer to using this kind of device as "metering" or one could state that the volume being measured is now being "metered".

The yard (symbol: yd) is just an English unit of length that is equal to 3 feet or 36 inches according to the British imperial and American customary systems of measurement. According to an international agreement, it has been exactly regulated to 0.9144 metres since 1959. precise 0.9144 meters. One mile is 1,760 yards in length. One mile is 1,760 yards in length.

Given

[tex]1 yard=0.914 meter[/tex]

Create a convert meter to yard expression

[tex]1 yard=0.914 meter[/tex]

Divide both side by 0.914

[tex]\frac{1yard}{0.914} =\frac{0.914 meter}{0.914}[/tex]

[tex]\frac{1 yard}{0.914}= 1meter[/tex]

[tex]1.09409190372=1meter[/tex]

[tex]1meter=1.09409190372 yard[/tex]

[tex]1meter = 1.094 yard[/tex] Approx.

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This bar-interval graph suggests that there may be a difference in response rate between the three colors of paper. For a 90% confidence interval, the critical value is 1.64. Number of observations  n = 15 and number of groups k = 3, so the degrees of freedom is n-k = 15-3 = 12.

A bar-interval graph of the estimated factor level means can be created as follows:

Calculate the mean response rate for each color of paper:

Blue: (28 + 26 + 31 + 27 + 35)/5 = 30%

Green: (34 + 29 + 25 + 31 + 29)/5 = 29.4%

Orange: (31 + 25 + 27 + 29 + 28)/5 = 28%

Calculate the standard deviation for each color:

Blue: [tex]\sqrt{(((28-30)^2 + (26-30)^2 + (31-30)^2 + (27-30)^2 + (35-30)^2)/4)} = \sqrt{(6.8)} = 2.6[/tex]

Green: [tex]\sqrt{(((34-29.4)^2 + (29-29.4)^2 + (25-29.4)^2 + (31-29.4)^2 + (29-29.4)^2)/4)} = \sqrt{(11.96)} = 3.4[/tex]

Orange: [tex]\sqrt{(((31-28)^2 + (25-28)^2 + (27-28)^2 + (29-28)^2 + (28-28)^2)/4)} = \sqrt{(6)} = 2.4[/tex]

Calculate the standard error for each color:

Blue: 2.6/[tex]\sqrt{(5)}[/tex] = 1.5

Green: 3.4/[tex]\sqrt{(5)}[/tex] = 1.9

Orange: 2.4/[tex]\sqrt{(5)}[/tex] = 1.3

Calculate the 95% confidence interval for each color:

Blue: [30 - 1.96 * 1.5, 30 + 1.96 * 1.5] = [26.9, 33.1]

Green: [29.4 - 1.96 * 1.9, 29.4 + 1.96 * 1.9] = [25.2, 33.6]

Orange: [28 - 1.96 * 1.3, 28 + 1.96 * 1.3] = [25.4, 30.6]

This bar-interval graph suggests that there may be a difference in response rate between the three colors of paper. The 95% confidence interval for the mean response rate of blue paper does not overlap with the confidence intervals of the green or orange paper, which suggests that there is a significant difference in response rate between the colors.

To estimate the mean response rate for blue questionnaires with a 90% confidence interval, we can use the same calculations as above, but use a different critical value for the standard normal distribution. For a 90% confidence interval, the critical value is 1.64. The 90% confidence interval for the mean response rate of blue questionnaires is [30 - 1.64 * 1.5, 30 + 1.64 * 1.5] = [27.3, 32.7].

To test whether or not D = M3 - M2 = 0, we can use a t-test with n-k degrees of freedom, where n is the number of observations and k is the number of groups. In this case, n = 15 and k = 3, so the degrees of freedom is n-k = 15-3 = 12. The null hypothesis is H0: D = 0 and the alternative hypothesis is Ha: D ≠ 0. The decision rule is to reject.

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____ The given question is incomplete, the complete question is given below:

a. Prepare a bar-interval graph of the estimated factor level means Y. where the interval correspond to the confidence limits with a = .05. What does this plot suggest about the effect of color on the response rate? Is your conclusion in accord with the test result?

b. Estimate the mean response rate for blue questionnaires: use a 90 percent confidence interval.

c. Test whether or not D = M3-u2 = 0: use a = .10. State the alternatives, decision rule, and conclusion. In light of the result for the ANOVA test e, is your conclusion surprising? Explain.

In an experiment to investigate the effect of color of paper (blue, green, orange) on response rates for questionnaires distributed by the "windshield method" in supermarket parking lots, 15 representative supermarket parking lots were chosen in a metropolitan area and each color was assigned at random to five of the lots. The response rates (in percent) follow. Assume that ANOVA model is appropriate. i 1 2 3 4 5 1 Blue 28 26 31 27 35 2 Green 34 29 25 31 29 3 Orange 31 25 27 29 28

True. Systems that can absorb any type of data, structured or not, from any type of source are often referred to as schema-less.

In a schema-less system, there is no predefined structure or schema that the data must conform to, allowing for greater flexibility in handling a variety of data formats and sources.

This can be particularly useful in big data environments, where data may come from a wide range of sources and be in a variety of formats. Schema-less systems typically rely on techniques such as dynamic schema discovery and schema-on-read to interpret and process the data.

A schema-less system is a type of database management system that allows for flexible and dynamic data structures, without requiring a pre-defined schema or structure.  

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Answer:  1/27, or 0.037

Step-by-step explanation:

The fractional probability that Mary answered all three correctly is 1/27, or 0.037. This is because for each of the three questions, Mary had a 1 in 3 chance of getting the correct answer (1/3). Since she had three questions, the probability of her getting all three correct is the product of the three probabilities (1/3 x 1/3 x 1/3 = 1/27).

Answer:

Mary's probability of guessing all three questions correctly is 1/27 or approximately 0.037. This is because each multiple choice question has 3 possible answer choices, and her chances of randomly picking the correct choice are 1/3. Since she has three questions, the probability of randomly getting all three answers correct is 1/3 x 1/3 x 1/3, which equals 1/27.

The following are the vector equations as a matrix equation.

(a)[tex]& \Rightarrow\left[\begin{array}{ccc}3 & 7 & -2 \\-2 & 3 & 1\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{c}1 \\-1\end{array}\right][/tex]

[tex]$A=\left[\begin{array}{ccc}3 & 7 & -2 \\ -2 & 3 & 1\end{array}\right][/tex] , [tex]x=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$[/tex] [tex]$b=\left[\begin{array}{c}1 \\ -1\end{array}\right]$[/tex]

(b) [tex]$\Rightarrow\left[\begin{array}{cc}3 & 5 \\ -2 & 0 \\ 8 & 9\end{array}\right]\left[\begin{array}{c}x_1 \\ x_2\end{array}\right]=\left[\begin{array}{c}2 \\ -3 \\ 8\end{array}\right]$[/tex]

[tex]$A=\left[\begin{array}{cc}3 & 5 \\ -2 & 0 \\ 8 & 9\end{array}\right][/tex], [tex]x = \left[\begin{array}{l}x_1 \\ x_2\end{array}\right]$[/tex] [tex]$b=\left[\begin{array}{c}2 \\ -3 \\ 8\end{array}\right]$[/tex]

(c) [tex]$\Rightarrow\left[\begin{array}{cc}3 & 5 \\ -2 & 0 \\ 8 & 9\end{array}\right]\left[\begin{array}{c}x_1 \\ x_2\end{array}\right]=\left[\begin{array}{c}2 \\ -3 \\ 8\end{array}\right]$[/tex]

[tex]$A=\left[\begin{array}{cc}3 & 5 \\ -2 & 0 \\ 8 & 9\end{array}\right][/tex], [tex]x = \left[\begin{array}{l}x_1 \\ x_2\end{array}\right]$[/tex] [tex]$b=\left[\begin{array}{c}2 \\ -3 \\ 8\end{array}\right]$[/tex]

(d) [tex]& \Rightarrow\left[\begin{array}{ccc}1 & 1-2 & 1 \\0 & 2 & -8 \\-4 & 5 & 9\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{c}0 \\8 \\-9\end{array}\right][/tex]

[tex]A=\left[\begin{array}{ccc}1 & 1-2 & 1 \\0 & 2 & -8 \\-4 & 5 & 9\end{array}\right], x=\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right] x[/tex] [tex]b=\left[\begin{array}{c}0 \\8 \\-9\end{array}\right] \\[/tex]

As per the given data here we have to determine each of the following vector equations as a matrix equation.

That means we have write them in the form of matrix equation that is in the form of Ax = b

a)

[tex]3 x_1+7 x_2-2 x_3=1 \\[/tex]

[tex]-2 x_1+3 x_2+1 x_3=-1[/tex]

Write the equations in the matrix form

[tex]& \Rightarrow\left[\begin{array}{ccc}3 & 7 & -2 \\-2 & 3 & 1\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{c}1 \\-1\end{array}\right][/tex]

This is in the form of  Ax = b .

Here, [tex]$A=\left[\begin{array}{ccc}3 & 7 & -2 \\ -2 & 3 & 1\end{array}\right][/tex] , [tex]x=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$[/tex] and [tex]$b=\left[\begin{array}{c}1 \\ -1\end{array}\right]$[/tex]

b)

[tex]& 3 x_1+5 x_2=2 \\[/tex]

[tex]& -2 x_1+0 x_2=-3 \\[/tex]

[tex]& 8 x_1+9 x_2=8[/tex]

Write the equations in the matrix form

[tex]$\Rightarrow\left[\begin{array}{cc}3 & 5 \\ -2 & 0 \\ 8 & 9\end{array}\right]\left[\begin{array}{c}x_1 \\ x_2\end{array}\right]=\left[\begin{array}{c}2 \\ -3 \\ 8\end{array}\right]$[/tex]

This is in the form of Ax = b.

Here, [tex]$A=\left[\begin{array}{cc}3 & 5 \\ -2 & 0 \\ 8 & 9\end{array}\right][/tex], [tex]x = \left[\begin{array}{l}x_1 \\ x_2\end{array}\right]$[/tex] and [tex]$b=\left[\begin{array}{c}2 \\ -3 \\ 8\end{array}\right]$[/tex]

(c)

[tex]& x_1-3 x_2+5 x_3=1 \\[/tex]

[tex]& -x_2+3 x_4=7 \\[/tex]

[tex]& \Rightarrow 0 x_1-x_2+0 x_3+3 x_4=7 \\[/tex]

Write the equations in the matrix form

[tex]& \Rightarrow\left[\begin{array}{llll}1 & -3 & 5 & 0 \\0 & -1 & 0 & 3\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3 \\x_4\end{array}\right]=\left[\begin{array}{l}1 \\7\end{array}\right][/tex]

This is in the form of Ax = b

Here, [tex]} A=\left[\begin{array}{llll}1 & -3 & 5 & 0 \\0 & -1 & 0 & 3\end{array}\right], x=\left[\begin{array}{l}x_1 \\x_2 \\x_3 \\x_4\end{array}\right][/tex] and [tex]b=\left[\begin{array}{l}1 \\7\end{array}\right] \\&\end{aligned}$$[/tex]

d)

[tex]& x_1-2 x_2+x_3=0 \\[/tex]

[tex]& 2 x_2-8 x_3=8 \\[/tex]

[tex]& -4 x_1+5 x_2+9 x_3=-9 \\[/tex]

Write the equations in the matrix form

[tex]& \Rightarrow\left[\begin{array}{ccc}1 & 1-2 & 1 \\0 & 2 & -8 \\-4 & 5 & 9\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{c}0 \\8 \\-9\end{array}\right][/tex]

This is in the form of Ax = b

Here, [tex]A=\left[\begin{array}{ccc}1 & 1-2 & 1 \\0 & 2 & -8 \\-4 & 5 & 9\end{array}\right], x=\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right] x[/tex] and [tex]b=\left[\begin{array}{c}0 \\8 \\-9\end{array}\right] \\[/tex]

Therefore all the vector equations are written as a matrix equations

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As an exponential equation, the log equation log (x²- 5x + 14) = 2x + 4 is 9514 1404 393

Given,

x² - 5x + 14 = 10^(2x +4)

The relationship is ...

log(a) = b   ⇔   a = 10^b

Using this with a = x² - 5x + 14 and b = 2x + 4, we have ...

x² - 5x + 14 = 10^(2x +4)

The complete question is:

Write the log equation as an exponential equation. You do not need to solve for x. log (x^2– 5x + 14) = 2x + 4

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answer: 7 is where they intercept I think, I also hope this helps

The probability of testing positive a second time given that they test positive once depends on the accuracy and specificity of the testing method used, as well as the prevalence of the condition being tested for in the population.

Assuming that the testing method is accurate and specific, and that the prevalence of the condition being tested for is low, then the probability of testing positive a second time given that they test positive once is still high, but less than the probability of testing positive on the first test.

This is because the second test is not completely independent of the first test, as the result of the first test provides some information about the likelihood of the individual having the condition being tested for. However, if we assume that the two tests are statistically independent given drug user status, then the probability of testing positive a second time given that they test positive once is the same as the probability of testing positive on the first test, which depends on the prevalence of the condition and the accuracy and specificity of the testing method.

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For the first equation, -x + 3y + 2z = -8, the conditions for no solution are if a=0, b=-8, and c is not equal to 8. If a=0, b=-8, and c=8, then there will be one solution. If a does not equal 0, then there will be infinitely many solutions.

For the second equation, x + ay = 0, the conditions for no solution are if a=0, b=0, and c does not equal 0. If a=0, b=0, and c=0, then there will be one solution. If a does not equal 0, then there will be infinitely many solutions.

In both equations, the conditions for no solution involve setting the coefficients of the variables in the system to 0. If the coefficients of any of the variables in the system are set to 0, then the system will not have a solution. If two of the coefficients are set to 0, then the system will have one solution. Otherwise, there will be infinitely many solutions. This is because if all the coefficients of the variables in the system are not 0, then the system can be reduced to a simpler form, with infinitely many solutions.

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The argument provided by Johannes Kepler is deductive.

This is because it uses a logical inferential link between the premises and the conclusion. Kepler presents two premises. The first premise states that the daily movement which is common to both the planets and the fixed stars is seen to travel from the east to the west. The second premise states that the far-slower single movements of the single planets travel in the opposite direction from west to east. Kepler then draws the conclusion that these movements cannot depend on the common movement of the world but should be assigned to the planets themselves.

Kepler's argument does not contain any indicator words that are commonly used in inductive arguments, such as "probably," "usually," or "likely." Instead, the argument is based on the logical connection between the premises and the conclusion. Kepler is using deductive reasoning to draw a certain conclusion from the premises that he presents. Thus, the argument is best interpreted as being deductive.

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The argument is deductive.

The deductive nature of the argument is demonstrated by the inferential link between the premises and conclusion. The premises state that the apparent daily movement of both the planets and fixed stars is from east to west, and the single movements of the planets travel from west to east. The conclusion follows deductively from these premises, as Kepler asserts that the movements of the planets cannot depend on the common movement of the world and must instead be assigned to the planets themselves.

There are no indicator words in the argument that explicitly signal inductive reasoning. Instead, the argument is based on deductive reasoning, with the premises providing evidence that supports the conclusion in a logically necessary way.

The argument is deductive.

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Answer:

(7 × 3) + (7 × 3)

Step-by-step explanation:

6 × 7 = 42

7 × 3 = 21

7 × 3 = 21

21 + 21 = 42

The sum of the expression is (-4s 9a + 4) + (2s + 2a - 8) is -2x + 11a - 4

These are expressions that are made up of variables, terms, coefficients, factors and constants.

They are also made up of operations, such as addition, multiplication, division, floor division, subtraction, bracket and parentheses.

From the information given, we have the expressions;

(-4s + 9a + 4) + (2s + 2a - 8)

expand the bracket

-4s + 9a + 4 + 2s + 2a - 8

Now, collect the like terms

-4s + 2s + 9a + 2a + 4 - 8

add or subtract the like terms

-2x + 11a - 4

Hence, the expression is -2x + 11a - 4

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Answer:

it's C

the square root of 10 is 3.162277

When two variable quantities have a constant ratio, their relationship is called a direct variation. It is said that one variable varies directly as the other. The formula for direct variation is

y

=

k

x

, where

k

is the constant of variation.

y

=

k

x

Solve the equation for

k

, the constant of variation.

k

=

y

x

Replace

x and ywith the values.k=−42Divide −4by 2.k=−2Use the formula y=kxto substitute −2for k and −6for x.y=(−2)⋅(−6)Multiply −2by −6.y=12

The goal of an experimental research study is to demonstrate the existence of a cause-and-effect relationship between two variables. This means that the researcher wants to show that changes in one variable (the independent variable) cause changes in another variable (the dependent variable).

To accomplish this goal, an experiment must control extraneous variables, manipulate an independent variable, and control an independent variable. This can be achieved through randomization, blinding, and other experimental design techniques.

Manipulating an independent variable means that the researcher wants to intentionally change the level or value of the independent variable in different groups or conditions. Controlling an independent variable means that the researcher wants to make sure that the manipulation of the independent variable is consistent across different groups or conditions.

The goal is  achieved through controlling extraneous variables, manipulating an independent variable, and controlling an independent variable.

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____The given question is incomplete, the complete question is given below:

The goal of an experimental research study is which of the following? O To make an observation to determine the correlation between two variables O To make an observation without manipulating any variables O To demonstrate the existence of a cause-and-effect relationship between two variables O To make an observation to determine the relationship among several variables To accomplish the goal, an experiment must do which of the following? Check all that apply. Control an independent variable Control extraneous variables X Manipulate an independent variable Manipulate several variables

The correct grammar for "language L" which is defined over alphabet "A" = {#, 0, 1}, consisting of all strings of form (01)ⁿ #, is  (a) S → 0S1 | #   .

In language L, every string starts with a "0"  and is followed by the digit "1" , and the string ends with the symbol "#' . The number of times that the sequence "01" appears in the string is determined by the value of n, which can be zero or any positive integer.

The grammar in Option(a) generates the language L by starting with the initial symbol "S" and using two production rules.

(i) The first rule generates a string which begins with "0", which is followed by non terminal symbol "S" , and then ends with "1".

(ii) The second rule generates the empty string "#" which marks the end of the string.

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The given question is incomplete , the complete question is

Which is a correct grammar for the following language over the alphabet

A = {#, 0, 1} , L = {(01)ⁿ # | n >=0}

(a) S → 0S1 | #

(b) S → 1S0 | #

(c) S → 01S | #

(d) S → S01 | #

Answer:3/4

Step-by-step explanation:Cho used 5/2

She used 13/4 to bake a loaf.

How much more is 13/4-5/2

=13-10/4

=3/4

Hope it helps!

The equations can be used to solve for y, the length of the room follows:

B. y² – 5y = 750, C. 750 – y(y – 5) = 0 and E. (y + 25)(y – 30) = 0

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

As per the question, we have

length L = y

width W = y - 5

Since the area of a rectangular room is 750 square feet.

So  L × W = 750

y(y - 5) = 750

y² – 5y = 750 ....(i)

This can be also written as:

750 – y(y – 5) = 0 ....(ii)

Factorizing the equation (i), we get

(y + 25)(y – 30) = 0

Thus, the correct answer would be options (B), (C), and (E).

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The mass of the drug in the organ at time t depends on the concentration of the drug in the blood entering the organ and the rate at which the blood is entering and leaving the organ. This can be calculated by multiplying the volume of the organ by the concentration of the drug in the blood.

At time t, since the rate at which the blood is entering and leaving the organ is 3 cm^3/sec, the amount of drug in the organ is equal to the amount of drug entering the organ plus the amount of drug that was initially in the organ. As there was no trace of the drug initially, the mass of the drug in the organ at time t is 3 cm^3/sec multiplied by the concentration of the drug in the blood (1/3 gm/cm3) multiplied by the volume of the organ (150 cm^3).

Therefore, the mass of the drug in the organ at time t is 150 gm.

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The measure of angle M is approximately 53.1 degrees when we are given Sin (M) = 0.8.

To find the measure of angle M, we can use the inverse sine function (sin⁻¹) on both sides of the equation:

sin⁻¹( sin (M) ) = sin⁻¹( 0.8 )

M = sin⁻¹( 0.8 )

Using a scientific calculator, we can find the value of sin⁻¹( 0.8 ), which comes out to be as follows -

M ≈ 53.13 degrees

Rounding to the nearest tenth of a degree, we get,

M ≈ 53.1 degrees

Therefore, the measure of angle M is approximately 53.1 degrees.

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The complete question is -

Find the measure of the angle given the sine, cosine, or tangent. Round to the nearest tenth of a degree. Sin (M) = 0.8 The measure of angle M.

Answer:

high BBC dry GB by in just he just had not had on

Step-by-step explanation:

no exception

The staircase function S(x) takes on the value of the largest integer less than x. To find the integral of S(x) over an interval [M, N], we can consider the area under the staircase function over each subinterval [n, n + 1] for integers n such that M <= n <= N.

The area under S(x) over the subinterval [n, n + 1] can be represented as a rectangle with height n and width 1. Therefore, the integral of S(x) over the subinterval [n, n + 1] is given by n.

Using sigma notation, we can represent the integral of S(x) over the interval [M, N] as follows:

∫_M^N S(x)dx = ∑_{n=M}^{N-1} ∫_n^{n+1} n dx = ∑_{n=M}^{N-1} n * (n+1 - n) = ∑_{n=M}^{N-1} n = (M + (M + 1) + ... + N-1) = (N^2 - M^2)/2.

So, the integral of the staircase function S(x) over the interval [M, N] is equal to (N^2 - M^2)/2.

Answer:

49 athletes attended the pizza party

Step-by-step explanation:

Number of soccer team players = 15

Number of tennis  players =  4 more than one-third that number
This translates to

Number of tennis  players = 15/3 + 4 = 5 + 4 = 9

Number of basketball players = 2 less than three times the number of students that are on the tennis team
which translates to
3 x 9 - 2 = 25

So total number of players on all teams = 15 + 9 + 25 =49

a) Probability will be [tex]nb(x; 2, 0.4) = (x + 1 choose 2) * (0.4)^2 * (0.6)^(x)[/tex]

b)Probability is b(2; 4, 0.4) = [tex](4 choose 2) * (0.4)^2 * (0.6)^2[/tex] = 0.2304 (rounded to four decimal places)

c)b(2; 2, 0.4) =[tex](2 choose 2) * (0.4)^2 * (0.6)^0[/tex] = 0.16

d)E(X) = r*(1-p)/p = 2*0.6/0.4 = 3 boxes

(a) The probability that x boxes do not have the desired prize can be modeled by a negative binomial distribution with parameters r=2 (since we want to obtain 2 prizes), p=0.4 (since the probability of obtaining the prize in any given box is 0.4), and x being the number of boxes purchased before obtaining the second prize. Therefore, the probability is given by:

[tex]nb(x; 2, 0.4) = (x + 1 choose 2) * (0.4)^2 * (0.6)^(x)[/tex]

(b) The probability of purchasing four boxes and obtaining two prizes can be modeled by a binomial distribution with parameters n=4 (since four boxes are purchased), k=2 (since we want to obtain two prizes), and p=0.4 (since the probability of obtaining the prize in any given box is 0.4). Therefore, the probability is given by:

b(2; 4, 0.4) = [tex](4 choose 2) * (0.4)^2 * (0.6)^2[/tex] = 0.2304 (rounded to four decimal places)

(c) The probability of purchasing at most four boxes and obtaining two prizes can be found by summing the probabilities of purchasing 2, 3, or 4 boxes and obtaining two prizes. Using the binomial distribution with parameters n=2 and p=0.4 for the case of purchasing 2 boxes and obtaining two prizes, we have:

b(2; 2, 0.4) =[tex](2 choose 2) * (0.4)^2 * (0.6)^0[/tex] = 0.16

Using the negative binomial distribution with parameters r=2 and p=0.4 for the case of purchasing 3 boxes and obtaining two prizes, we have:

nb(1; 2, 0.4) = (1 + 2 choose 2) * (0.4)^2 * (0.6)^1 = 0.288

Using the negative binomial distribution with parameters r=2 and p=0.4 for the case of purchasing 4 boxes and obtaining two prizes, we have:

nb(2; 2, 0.4) = (2 + 2 choose 2) * (0.4)^2 * (0.6)^2 = 0.3456

Therefore, the probability of obtaining two prizes in at most four boxes is:

0.16 + 0.288 + 0.3456 = 0.7936 (rounded to four decimal places)

(d) The expected number of boxes without the desired prize can be found by multiplying the number of boxes needed to obtain the prize (on average) by the probability of not obtaining the prize, which is given by:

E(X) = (1 - p)/p = 0.6/0.4 = 1.5 boxes

The expected number of boxes needed to obtain two prizes can be found using the negative binomial distribution with parameters r=2 and p=0.4, which gives:

E(X) = r*(1-p)/p = 2*0.6/0.4 = 3 boxes

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Answer: 25%

Step-by-step explanation: You add 3 cups of water and 1 cup of lemon concentrate to get a total of 4 cups. One cup of lemon concentrate out of four total cups is 1/4. 1/4=25%.

Answer:

the standard deviation of this probability distribution is approximately 1.39.

Step-by-step explanation:

To find the standard deviation of a probability distribution, we use the formula:

σ = sqrt[Σ(x - μ)^2P(x)]

where σ is the standard deviation, x is the value of the random variable, P(x) is the probability of that value, μ is the mean of the distribution.

First, we need to find the mean of the distribution:

μ = ΣxP(x)

= 0(0.05) + 1(0.25) + 2(0.15) + 3(0.55)

= 1.9

Next, we can calculate the standard deviation:

σ = sqrt[Σ(x - μ)^2P(x)]

= sqrt[(0 - 1.9)^2(0.05) + (1 - 1.9)^2(0.25) + (2 - 1.9)^2(0.15) + (3 - 1.9)^2(0.55)]

= sqrt[0.9025 + 0.1225 + 0.0225 + 0.8925]

= sqrt(1.94)

≈ 1.39

Therefore, the standard deviation of this probability distribution is approximately 1.39.