Mark did a survey.
He asked pupils in his school:

‘Do you like the colour of the school uniform?’

Mark asked this question to 40 pupils in year 11

25% said ‘Yes’. 50% said ‘No’. The rest said ‘Don’t know’.

Complete the table to show how many pupils from year 11 gave each answer.

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

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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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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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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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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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:

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 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 locations on the function's graph that are most near the specified point f(x) = x2, (0,9) are approximately 3 units to the right and left, respectively, or (sqr8.5, 8.5).

The initial estimate would be rough to the right and left by around 3 units, or (sqr8.5, 8.5), rounded to the nearest decimal place.

Visually, it is most likely just below y=9 and just below x=3. Additionally, roughly (-3, 9) slightly lower than 3 and 9

Connect the parabola's nearest point to the point at (0,9). Where the two intersect, its slope is the negative inverse of the parabola's slope. The derivative's slope is 2x for the equation f(x) = x2. -1/2x is its inverse negative. The line from (0,9) to the parabola's nearest point has a slope that is perpendicular to the tangent to the parabola at that location.

Get the equation of the line joining (0,9) and the nearest point (x,y) on the parabola using the point-slope formula: 8.5 or y=-1/2 + 9 = (-1/2x)(x)

The closest point's y coordinate is that. The square root of 8.5, including both positive and negative square roots, is the closest point's x coordinate (-sqr8.5, 8.5)

Sqr8.5 =[tex]\sqrt{8.5}[/tex], or approximately 2.91 or -2.91

The process entails finding the equation for the line connecting (0,9) with the parabola's nearest point and then setting the two equations equal. Set the line equation to y=(-1/2x), the parabola equation. The parabola equation is y=[tex]x^{2}[/tex] and the line equation is x + 9.

Equalize them, then find x using the square of the result. The closest point is at x,y. There are two places that are equally far from (0,9), both of which are as close as they can be to 3 at (3,9). (0,9). At the parabola point, that line is not perpendicular to the tangent line (3,9). The line must be perpendicular to the tangent line, which is the slope of the parabola, in order to be closest.

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Answer:

-6y + 13.3 = 0

y = 13.3/6

Step-by-step explanation:

This equation don't need any step-by-step explanation :). Hope it helps!

The given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).

A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image).

We can picture what would happen if you turned the form across the line to graph a reflection.

So, we have a triangle with coordinates:

(8, 2), (3, 4), (2, 7)

Now, we will reflect it according to the rule:

(x, y)→(−x, y)

Then, the coordinates will be:

(-8, 2), (-3, 4), (-2, 7)
(Refer to the graph attached below)

Therefore, the given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).

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Answer:

13.3 ft

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\\\end{minipage}}[/tex]  [tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

The surface area of a square-based pyramid is made up of:

Given:

Find the area of the square base and the area of one of the triangles by substituting the given values into the formulas:

[tex]\textsf{Area of the square base} = 5^2 = 25\; \sf ft^2[/tex]

[tex]\textsf{Area of one of the side triangles} = \dfrac{1}{2} \cdot 5 \cdot l= 2.5l \; \sf ft^2[/tex]

Substitute these values along with the given total surface area into the formula and solve for l:

[tex]\begin{aligned}\textsf{Total Surface Area}&=\sf square+4\;triangles\\\implies 158&=25+4\left(2.5l)\\158&=25+10l\\133&=10l\\l&=\dfrac{133}{10}\\l&=13.3\; \sf ft\end{aligned}[/tex]

Therefore, the missing length is 13.3 feet.

The type of analysis used to identify the source of the bias is known as Differential Item Functioning Analysis.

Analysis

In statistics, analysis is to break a topic or concept down into its parts in order to inspect and understand it, and to restructure those parts in a way that makes sense to you.

Given,

Here we need to find the type of analysis used to identify sources of bias.

While we looking into the given question, we have used by ETS.

And it identifies items that are specifically biased against any ethnic, racial or gender group.

And we also know that the first analysis equates groups on the basis of overall scores.

By using these groups it evaluates differences in performance between sub groups on particular items.

And the Items that differ significantly between the groups are thrown out.

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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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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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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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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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A random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm is 0.0749.

In the given question,

18-year-old American males stated that the sample mean waist circumference was 86.3 cm.

The populations mean waist size is 85 cm.

The population standard deviation is 15 cm.

We have to find, a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm.

H(0): μ = 85

H(A): μ > 85

Sample mean(X) = 86.3

Standard deviation(σ) = 15

Standard error of mean =σ/√n

Standard error of mean (SE) = 15/√277

SE = 15/16.6433

SE = 0.9013

z = (X- μ)/SE

z=(86.3-85)/0.9013

z = 1.4424

P(z > 1.4424) = 0.0749

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The right question is;

The National Health Statistics Reports dated Oct. 22, 2008 stated that for a sample size of 277. 18-year-old American males stated that the sample mean waist circumference was 86.3 cm.

Suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. how likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (Round your answers to four decimal places.)

The data does contradict with the prior evidence

To determine whether the data presented here are significantly inconsistent with previous assumptions, a statistical test was performed to verify that the observed relationship between tendon length and cranial volume was significantly greater than the expected relationship. You have to decide if they are different.

To do this, fit a line to the data using linear regression analysis and test the hypothesis that the slope of the line is equal to 20 cm3/mm. If the p-value for this hypothesis test is less than 0.05, you can conclude that the data are inconsistent with previous assumptions at the 0.05 significance level.

It is crucial to realize that this analysis assumes that the relationship between tendon length and cranial volume is linear.

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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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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 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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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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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 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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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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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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