45 POINTS ANSWER FOR BRAINLIST AND HEARTS

The no. of ways or Probability can a student select 2 from each set of books = 13860

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

By multiplying the number of possibilities there are to choose books from each kind, separately, one can determine the maximum number of ways a student can choose two books from each subject.

Rule for Multiplication:

If an event A can be performed in m different ways and another event B in n different ways, then the two events together can be performed in (mn) different ways.

A combination problem is created by the various ways that math, science, and literature books might be chosen.

As a result, the total number of choices can be calculated as follows: (Number of math books chosen) x (Number of scientific books chosen) x (Number of literature books selection)

= C ( 7,2) * (12,2) * (5,2)

= C (7*6/2!) * (12*11/2!) * (5*4/2!)

= 21 * 66* 10

= 13860

The no. of ways or Probability can a student select 2 from each set of books = 13860

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The given statement "the coefficients of dummy variables in multiple regression models must always be positive." is True.

Regression model:

In statistics, regression model means a statistical technique that relates a dependent variable to one or more independent variables.

Given,

Here we have the statement the coefficients of dummy variables in multiple regression models must always be positive.

Now, we have to find whether the given statement is true or not.

In order to find the statement creditability, we must know the definition of the terms coefficient and dummy variables.

Dummy variable refers the variable that takes values of 0 and 1, where the values indicate the presence or absence of something

Where as the coefficient means a number or symbol by which another number or symbol is multiplied.

Based on this definition we have found that the given statement is true.

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The partial derivative dy/dx at x = e is given as follows:

[tex]\frac{dy}{dx}(e) = -\frac{2}{e}[/tex]

The function in this problem is defined as follows:

y = tan(u).

The function y is a function of the variable u, which is a function of the variable v, which is a function of variable x, then the function of variable x can be written as follows:

[tex]y = \tan{\left(\ln{x} - \frac{1}{\ln{x}}\right)}[/tex]

Then, applying the chain rule, the derivative is the derivative of the outer tangent function multiplied by the derivative of the inner ln function.

The inner function is of:

[tex]\ln{x} - \frac{1}{\ln{x}}[/tex]

Which has a derivative of:

[tex]\frac{1}{x} + \frac{1}{x\ln^2{x}}[/tex]

The outer tangent function has a derivative of:

-sec²(x).

Then the complete derivative is of:

[tex]\frac{dy}{dx} = -\sec^2{\left(\ln{x} - \frac{1}{\ln{x}}\right)} \times \left(\frac{1}{x} + \frac{1}{x\ln^2{x}}\right)[/tex]

At x = e, the numeric value of the derivative is given as follows:

[tex]\frac{dy}{dx}(e) = -\sec^2{0} \times \frac{2}{e}[/tex]

[tex]\frac{dy}{dx}(e) = -\frac{2}{e}[/tex]

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The isotopes in the set I are [tex]^{14} _{7} B[/tex] and [tex]^{15} _{7} C[/tex] and set II are [tex]^{20} _{10} E, ^{21} _{10}F[/tex] and [tex]^{22} _{10} G[/tex].

Isotopes are variations of chemical elements that have a varied number of neutrons but the same number of protons and electrons. In other words, isotopes are different forms of the same element that have different amounts of nucleons (the sum of protons and neutrons) because of variations in the total number of neutrons in each of their individual nuclei.

Isotopes are elements with the same atomic number but different mass.

In this case, the elements in set I- B and C has the same atomic number 7 but had different mass numbers and the elements in set II- E, F and G had the same atomic number 10 and different mass numbers, therefore they are known as isotopes.

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The value of a=12

Simply use cross multiplication :

The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equals to symbol. Cross multiplication is a method for comparing fractions.

Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.

[tex]\frac{a}{15}=\frac{4}{5}[/tex]

or, 5a=4*15

or, a= 4*15/5

or, a= 12

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The chi-square goodness-of-fit test is a statistical test that is used to determine whether a sample comes from a population with a specific distribution. There are a few conditions that must be met in order to use this test:

1. The data must be collected from a random sample. This ensures that the sample is representative of the population, which is necessary for the test to be valid.

2. The data must be categorical. This means that the observations must fall into distinct categories, rather than being continuous or ordinal.

3. The expected frequencies for each category should be at least 5. This ensures that the chi-square test statistic is approximately normally distributed, which is necessary for the test to be valid.

4. The data must be independent. This means that the outcome of one observation should not influence the outcome of another observation.

If these conditions are not met, the chi-square goodness-of-fit test may not be appropriate. In such cases, it may be necessary to use a different statistical test.

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The simplified expression of the statement is -41.66

From the question, we have the following parameters that can be used in our computation:

negative 17 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 4 squared minus 4 and 7 tenths

Rewrite properly

So, we have

(-17 - 3.7 + 9.15)/5 * 4² - 4.7

Evaluate the sum and the difference in the expression

So, we have

-11.55/5 * 4² - 4.7

Evaluate the exponent and the quotient

-2.31 * 16 - 4.7

So, we have

-36.96 - 4.7

Evaluate

-41.66

Hence, the solution is -41.66

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Using the concept of unit price, we see that;

Unit price of Brand A  = $0.3654

Unit price of Brand B = $0.3785

The better buy is Brand A

A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint, which can then be used to compare the same type of goods sold in differing weights and amounts.

Now, we are told that brand A has a pack of 24 pencils for $8.77. Thus;

Unit price of Brand A = 8.77/24 = $0.3654

We are told that brand B has a pack of 26 pencils for $9.84. Thus;

Unit price of Brand B= 9.84/26 = $0.3785

Thus;

Unit price of Brand A  = $0.3654

Unit price of Brand B = $0.3785

Thus, brand A has the cheaper unit price and is thus the better buy.

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Answer:

0.0474

Step-by-step explanation:

mean = \mu = 0.8

Using the Poisson probability formula,

P(X = x) = (e-\mu * \mux ) / x!

P(X > 2) = 1 - P(x \le 2)

= 1 - P(x = 0) - P(x = 1) - P(x = 2)

= 1 - (e^-0.8 * 0.80 ) / 0! - (e^-0.8 * 0.8^1 ) / 1! - (e^-0.8 * 0.8^2 ) / 2!

=  0.0474

So, the answer is 0.0474

The value after simplifying the number 10^3(10)^4 is 10⁷.

The simplification of given number can be done through the rule of exponent -

[tex] {a}^{m} [/tex] × [tex] {a}^{n} [/tex] = [tex] {a}^{m+n} [/tex], where m and n are the powers of a.

Now, keeping the values in formula -

Value = [tex] {10}^{3} [/tex] × [tex] {10}^{4} [/tex]

Based on the rule, the simplified for these powers will be

Value = [tex] {10}^{3+4} [/tex]

Performing addition of powers on Right Hand Side of the equation

Value = [tex] {10}^{7} [/tex]

Alternatively, the numbers can be expanded and multiplied. Further write the result in scientific notation as above. However, it will a long method which is not practical for very large numbers.

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Answer:

x = 8/3

y = 10/3

Step-by-step explanation:

We add (1) and (2) to get 3x = 8. This means that x = 8/3. We substitute it back into (1) to get 8/3 + y = 6 which shows that y = 10/3

Answer:

Step-by-step explanation:

following the rule of the Pythagorean triple the answer is yes

Actually a 30 , 40 , 50 triangle is just a scaled up 3 , 4 , 5 triangle, which is a well known right angled triangle

The complex numbers are

a.  11 - 3i

b. 2 + i

c. 5 - 6i

A complex number is a number in the complex plane. It is written in the form r = a + bi where a and b are real numbers and i = √(-1). Also, a is the real part and ib is the complex part of the complex number

a. Given that the complex number is denoted by r = a + ib where

Since we have for the given complex number

So, r = real part + imaginary part = 11 + (-3i)

= 11 - 3i

So, the complex number is 11 - 3i

b. Given that the complex number is denoted by r = a + ib where

Since we have for the given complex number

So, r = real part + imaginary part = 2 + i

= 2 + i

So, the complex number is 2 + i

c. Given that the complex number is denoted by r = a + ib where

Since we have for the given complex number

So, r = real part + imaginary part = 5 + [-6√(-1)]

= 5 - 6√(-1)

= 5 - 6i (since i = √(-1))

So, the complex number is 5 - 6i

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Answer:

blip

Step-by-step explanation:

blipgg

Simple probability is the calculation of an outcome or the chance of an event ever happening.

18.65% probability that the person is from Washington

Two events, A and B.

[tex]P(B/A)=\frac{P(B)*P(A/B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Arrived by train.

Event B: From Washington.

15% are from Washington

This means that [tex]P(B)=0.15[/tex]

12% of the attendees from Washington came to the conference by train.

This means that [tex]P(A/B)=0.12[/tex]

Probability of arriving by train:

6% of 60%(from California), 17% of 25%(from Oregon) or 12% of 15%(from Washington). So

[tex]P(A)=0.06*0.6+0.17*0.25+0.12*0.15=0.0965[/tex]

If an attendee is selected at random and found to have arrived by train,

[tex]P(B/A)=\frac{0.15+0.12}{0.0965} =0.1865[/tex]

=0.1865

18.65% probability that the person is from Washington

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10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.

percentage, a relative value indicating hundredth parts of any quantity.

The formula for quarterly compound interest formula:

[tex]A=P(1+\frac{r}{4} )^{4t}[/tex]

P is the principle amount

t is time

r is rate of interest

A is final amount

[tex]1750=1000(1+\frac{0.0575}{4} )^{4t}[/tex]

[tex]1750=1000(1+0.0144)^{4t}[/tex]

[tex]1750=1000(1.0144)^{4t}[/tex]

Divide both sides by 1000

[tex]1.75=1.0144^{4t}[/tex]

Take log on both sides

log1.75=4tlog1.0144

0.243=4t(0.006)

0.243=0.024t

Divide both sides by 0.024

t=10.12

t=10 years

Hence, 10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.

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Answer:

18 tiles

Step-by-step explanation:

There are 20 tiles in total.  Red is 6 of the 20, or 6/20.  That is 3/10 or 30%

Each draw has a 30% chance of being red.  30% or 20 tiles is 1.8 tiles.  Over 30 draws, that would mean a total of 600 tiles are drawn,  The overall chance of red is still 30%, so after 30 draws, the number of red tiles would be predicted to be 30% of 600:

 (0.30)*(600) = 18 tiles will be red.

The expected profit that the contractor will earn from the sale is equal to $177600.

Whenever a contactor does sale of a certain commodities, he expects that whatever he does he earns a profit from the sales. Profit is earned when the selling price of the commodity is more than the price at which the commodity was brought by the contractor.

The expected profit from the sale is calculated as the sum of the profits multiplied by their respective probabilities. In this case, the expected profit is given by:

Expected profit = (240000.0 * 0.76) + (-20000.0 * 0.24) = 182400.0 + (-4800.0) = $177,600

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The number of party popper she bought is 32 and the number of balloons she bought is 18.

The first step is to form a system of equations using the information provided in the question.

0.20x + 0.50y = $20 equation 1

x + y = 52 equation 2

The solution using the elimination method :

Multiply equation 2 by 0.20

0.20x + 0.20y = 10.40 equation 3

Subtract equation 3 from equation 2 :

0.30y = 9.60

Divide both sides of the equation by 0.30

y = 9.60 / 0.30

y = 32

The solution using the substitution method:

Make x the subject of the formula in equation 2

x = 52 - y equation 3

Substitute for x in equation 1 :

0.20(52 - y) + 0.50y = $20

10.40 - 0.20y + 0.50y = $20

Combine similar terms together

0.50y - 0.20y = $20 - $10.40

0.30y = $9.60

y = 9.60 / 0.30

y = 32

x = 50 - 32

x = 18

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The probability of rolling a number greater than 5 or doubles will be 0.78.

       P(A)  =  n(A)/n(S)

        where -

       n(A) = Number of outcomes favorable to event A.

        n(S) = Total number of outcomes.

We have two dices are rolled.

The sample space for sum greater than 5 will be 26. For doubles, we will add 2 pairs (1, 1) and (2, 2) to 26 to get a total sample space of 28. Remaining doubles are already in 26. So, the probability of rolling a number greater than 5 or doubles will be -

P(A) = 28/36 = 0.78

Therefore, the probability of rolling a number greater than 5 or doubles will be 0.78.

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[Question in english -

From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]

−32i is the answer if you use DeMoivre's theorem to find (1−i)^10.

A formula for determining the powers of complex numbers is provided by De Moivre's theorem. It might be easier to comprehend de Moivre's theorem if we first look at what happens when we multiply a complex number by itself. This illustrates how the argument is multiplied by two and the absolute value is squared when squaring a complex number.

One of the most important and useful theorems in the study of complex numbers is DeMoivre's Theorem, which combines trigonometry with complex numbers. It's also helpful to find relationships between trigonometric functions at different angles. The name of the theorem pays homage to the well-known mathematician De Moivre, who made several contributions to mathematics, notably in the areas of probability theory and algebra. Attached below is the answer.

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Therefore, the limitations census of entire population can be described in  major points like  it can be Since surveys rely on self-reporting, some misrepresentation or mistake is unavoidable and further more

A key component of the U.S. Federal Statistical System, the United States Census Bureau, or Bureau of the Census, is in charge of gathering information on the population and economy of the United States.

Here,

Therefore ,the limitations of generalizing census findings back to the entire population are:-

The homeless population is underrepresented in the findings even though every home is required to complete a census report. This is because they are frequently impossible to reach, interview, and count.

People who do not speak either English or Spanish as their first language and whose primary language is one of those two are more likely to be overlooked in the census.

Since surveys rely on self-reporting, some misrepresentation or mistake is unavoidable.

The population fluctuates constantly, so it is unlikely that the population on the day the census results are released would closely resemble the population as described in the census.

Those who entered the country illegally but intend to stay do not submit a report.

Therefore , there are 5 major limitation described above .

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In percent, the fraction [tex]\frac{1}{9}\\\\[/tex] can be calculated as 11.11%.

A percentage is a common way to represent statistical data, and it is usually used to indicate one-hundredth, with the symbol "%." To calculate the percentage, it is given by:

Percentage (%) = value ÷ total value multiplied by 100%

In conclusion, the percentage of a fraction [tex]\frac{1}{9}\\\\[/tex] is 11.11%.

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Answer:

-4/7

Step-by-step explanation:

The slope of the given line is [tex]\frac{3-(-4)}{4-0}=\frac{7}{4}[/tex].

Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is [tex]-4/7[/tex].

The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.

We have,

Let's first find the slope of the given line passing through (4, -3) and

(0, -4):

slope = (change in y) / (change in x)

= (-4 - (-3)) / (0 - 4)

= (-4 + 3) / (-4)

= -1 / (-4)

= 1/4

The slope of the given line is 1/4.

Now, to find the slope of a line perpendicular to this line, we take the negative reciprocal of the slope:

[tex]slope_{perpendicular} = -1 / slope[/tex]

= -1 / (1/4)

= -4

Therefore,

The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.

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Answer:

  x = 3

Step-by-step explanation:

You want to know how to solve 2x +3 = 9.

A solution is an equation of the form ...

  x = constant

You can get a clue to the solution process by considering what happens to the variable. Here, ...

The solution process reverses these operations, starting with the last one first. The properties of arithmetic and equality are used.

We can undo the addition of 3 by adding -3 to both sides of the equation.

  2x +3 -3 = 9 -3

  2x +0 = 6 . . . . . . . . . . . adding 3 and its additive inverse gives zero

  2x = 6 . . . . . . . . . . . . . 0 is the additive identity element, so 2x+0 = 2x

We can undo the multiplication by multiplying by the multiplicative inverse of 2. That is, we can multiply by 1/2.

  (1/2)2x = (1/2)6

  1x = 3 . . . . . . . multiplying 2 and its multiplicative inverse gives 1

  x = 3 . . . . . . 1 is the multiplicative identity element, so 1x = x

Please note that multiplying by 1/2 is the same thing as dividing by 2. That is, multiplication and division are inverse operations.

The solution is x = 3.

It is wise to check that the solution you found makes the equation be true.

  2x +3 = 9

  2(3) +3 = 9 . . . . . substitute for x

  6 + 3 = 9 . . . . . . . true

__

Additional comment

This solution process works for just about any "solve for ..." situation, if an algebraic solution is possible. In high school math, you are introduced to just about every kind of equation we know how to solve. The list is fairly short.

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On solving the provided question, we got to know that, Blenders sold as a percentage of food processors sold is 30/20, or 3/2.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Compared to mixers, the dealer sold twice as many food processors.

Let M be the quantity of mixers sold.

Therefore, 2M is the quantity of food processors sold.

A total of 60 of the three appliances were sold by the dealer.

M + 2M = 3M

Thus, 3M is a representation of the whole sales of mixers and food processors.

60 appliances were purchased in total, thus 60 - 3M equals the quantity of blenders purchased.

Everything was sold by the merchant for a total of $4,200.

We get: (30)(M) + (120)(2M) + (50)(60 - 3M) = 4,200

30M + 240M + 3000 - 150M = 4200

130M + 3000 = 4200

120M = 1200

M = 10

The retailer so sold 10 mixers.

This indicates that the vendor sold 20 food processors and 30 food processors.

Blenders sold as a percentage of food processors sold is 30/20, or 3/2.

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If two men refuse to serve together we can choose in a) 1275 ways. If b) 2 women refuse to serve together we can choose in 110 ways and if c) 1 man and 1 woman refuse to serve together then we can choose in 750 ways.

a)

Here we can get 3 cases.

The first man is elected

The second man is elected

Neither f the 2 is included

In the first 2 cases, we need to choose 4 men from 7 while in the third case we need to choose 4 men from 6.

Therefore we get

⁷C₄ X ⁶C₄  +  ⁷C₄X ⁶C₄  +  ⁶C₄X ⁶C₄

35 X 15  +  35 X 15  +  15 X 15

= 1275 ways

b)

Just like before we will have 3 cases here.

Here we will have to choose 4 women from 5 for the first 2 cases and 4  from 4 for the third case. Hence we get

⁵C₄ X ⁸C₄  +  ⁵C₄ X ⁸C₄  +  ⁴C₄ X ⁸C₄

= 50  +  50  +  10

= 110 ways

c)

Here we will have 3 cases again

The man is included

The woman is included

neither is included

Therefore we will get

⁸C₄ x ⁵C₄  +  ⁷C₄ X ⁶C₄  +  ⁷C₄ X ⁵C₄

= 10 X 5  +  35 X 15  +  35 X 5

= 750 ways

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