f(n) = 5n for n = 2

Answer:

Step-by-step explanation:

Answer:

Now we have everything in order to replace into formula (1):

[tex]18-2.262\frac{2.75}{\sqrt{10}}=16.03[/tex]    

[tex]18+2.262\frac{2.75}{\sqrt{10}}=19.97[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X=18[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=2.75 represent the sample standard deviation

n=10 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]

The Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical vaue would be [tex]t_{\alpha/2}=2.262[/tex]

Now we have everything in order to replace into formula (1):

[tex]18-2.262\frac{2.75}{\sqrt{10}}=16.03[/tex]    

[tex]18+2.262\frac{2.75}{\sqrt{10}}=19.97[/tex]    

You can use the divergence theorem:

[tex]\vec v=z\,\vec\imath+y^2\,\vec\jmath+x^2\,\vec k[/tex]

has divergence

[tex]\mathrm{div}\vec v=\dfrac{\partial z}{\partial x}+\dfrac{\partial y^2}{\partial y}+\dfrac{\partial x^2}{\partial z}=2y[/tex]

Then the rate of flow out of the cylinder (call it R) is

[tex]\displaystyle\iint_{\partial R}\vec v\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec v\,\mathrm dV[/tex]

(by divergence theorem)

[tex]=\displaystyle2\int_0^{2\pi}\int_0^5\int_0^1r^2\sin\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

(after converting to cylindrical coordinates)

whose value is 0.

Answer:

Answer is given below.

Step-by-step explanation:

let us solve the numerator first

=4x²-14x+6

=2(2x²)+2(-7x)+2(3)

= GCF of the terms of the numerator is 2.

denominator

x³-7x²+12x

x(x²)+x(-7x)+x(12)

GCF of the terms of the denominator is x.

factorise the numerator

4x²-14x+6

4x²-2x-12x + 6  (by splitting the middle term; the numbers should produce the product  4*6 and when the no.s are added they should give -14)

(4x²-2x) + (-12x+6)

2x(2x-1) -6(2x-1)

(2x-6)(2x-1)

factors are

(2x-6), (2x-1)

denominator

this can also be done by splitting the middle term

x³-7x²+12x

x³-3x²-4x²+12x

(x³-3x²) + (-4x²+12x)

x²(x-3) -4x(x-3)

(x²-4x)(x-3)

factors are

(x²-4x), (x-3)

Answer:

10.71

Step-by-step explanation:

The arc length is

2*3*3.14/4 = 4.71

Add to the two side lengths to get the perimeter

4.71+3+3 = 10.71

[tex]answer = 10.71 \: millimeters \\ solution \\ radius = 3 \: millimeters \\ perimeter \: of \:quarter \: circle \\ = \frac{2\pi \: r}{4} + 2r \\ = \frac{2 \times 3.14 \times 3}{4} + 2 \times 3\\ = \frac{18.84}{4} + 6 \\ = \frac{18.84 + 6 \times 4}{4} \\ = \frac{18.84 + 24}{4} \\ = \frac{42.84}{4} \\ = 10.71 \: millimeters \\ hope \: it \: helps[/tex]

Answer:

[tex] 0.34 \leq p \leq 0.38[/tex]

For this case we can conclude that with 98% of confidence the true proportion of Drosophila in a population would be between 0.34 and 0.38.

But that doesn't means that we have 98% of PROBABILITY that the true proportion would be between 0.34 and 0.38, because we are constructing a confidence interval with sample data and we can't analyze this using probability.

Then the best answer is:

2. False

Step-by-step explanation:

For this case we have a confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be given by:

[tex] 0.34 \leq p \leq 0.38[/tex]

For this case we can conclude that with 98% of confidence the true proportion of Drosophila in a population would be between 0.34 and 0.38.

But that doesn't means that we have 98% of PROBABILITY that the true proportion would be between 0.34 and 0.38, because we are constructing a confidence interval with sample data and we can't analyze this using probability.

Then the best answer is:

2. False

Answer and Step-by-step explanation: Standard Deviation is the measure of how diferent a number is from the mean of the data set. It is the spread of a data set. To calculate it manually:

1) Find the mean of the data set. Mean, represented by μ, is the sum of all the values divided by the total number of elements forming the set;

2) Subtract each number with the Mean and square the result;

3) Add the differences and divide it by the total number of elements of the set;

4) Take the square root of the result and that is the Standard Deviation.

The calculations can be done by a calculator like Excel:

1) In each cell of a same column, write the data you want to know the deviation.

2) On the last cell, write: =stdev.p(A1:A10) or =stdev.s(A1:A10).

3) Press Enter. The deviation will appeared on the same cell.

The function STDEV.P is used when the data represents the entire population, whereas STDEV.S is used when the data is for a sample of the population. Inside the parenthesis, put the cells where your data is. For example, if you put your data in the column A, from cell 1 to cell 10, you write like it's written above.

Answer:

a) 15

b) 65

Step-by-step explanation:

Adjunto se encuentra el diagrama asociado a esta situación. Comenzamos por ubicar aquellas afirmaciones que relacionan todos los deportes. Sabemos que 10 personas no prefieren ningún deporte. Luego, ubicamos 10 fuera de los conjuntos mostrados. Sabemos que 30 personas prefieren sólo surf y 20 personas prefieren sólo Tenis. Es decir, hay 30 personas en el conjunto S que no intersectan a los otros dos.  En este momento, hemos ubicado a 60 personas. Nos hacen falta 30 personas. La afirmación "15 personas prefieren Golf" significa que la suma de los números dentro del conjunto G es 15.  La afirmación "ninguno de los que prefieren los deportes Tenis o Surf prefieren el golf. Es decir, que la intersección de G con T y con S son vacías. Es decir que las 15 personas que prefieren golf, lo prefieren únicamente. Esto nos deja con 15 personas por ubicar. El único lugar donde podemos ubicar a dichas 15 personas es en en la intersección de T y S.

a). ¿cuántas personas prefieren dos de estos deportes? Por el diagrama, son aquellas personas que prefieren Tenis o Surf. Es decir, 15.

b) ¿Cuánto prefieren sólo uno de estos deportes? Es la suma de aquellos que prefieren sólo un deporte. Es decir, sólo G, sólo T o sólo S. Es decir 15+20+30 = 65.

Answer:

765 J

Step-by-step explanation:

We are given;

Mass of bucket = 30 kg

Mass of rope = 0.3 kg/m

height of building= 30 meter

Now,

work done lifting the bucket (sand and rope) to the building = work done in lifting the rope + work done in lifting the sand

Or W = W1 + W2

Work done in lifting the rope is given as,

W1 = Force x displacement

W1 = (30,0)∫(0.2x .dx)

Integrating, we have;

W1 = [0.2x²/2] at boundary of 30 and 0

W1 = 0.1(30²)

W1 = 90 J

work done in lifting the sand is given as;

W2 = (30,0)∫(F .dx)

F = mx + c

Where, c = 30 - 15 = 15

m = (30 - 15)/(30 - 0)

m = 15/30 = 0.5

So,

F = 0.5x + 15

Thus,

W2 = (30,0)∫(0.5x + 15 .dx)

Integrating, we have;

W2 = (0.5x²/2) + 15x at boundary of 30 and 0

So,

W2 = (0.5 × 30²)/2) + 15(30)

W2 = 225 + 450

W2 = 675 J

Therefore,

work done lifting the bucket (sand and rope) to the top of the building,

W = 90 + 675

W = 765 J

Answer:

23,098; 23,208 ; 234,358

Step-by-step explanation:

Hope this helps

Answer:

The advertising cost, X₄ = 5.626 million

The 80% confidence limits for X₄ is (5.041 , 6.100)

The 80% prediction limits for X₄ is (4.048 , 7.094)

Step-by-step explanation:

Using MINITAB

The regression equation is X₄ = 4.14 + 0.0431 X₁ - 0.800 X₂ + 0.00059 X₃ - 0.661 X₅ + 0.057 X₆

Predictor Coef SE Coef T P

Constant 4.142 1.626 2.55 0.019

X₁ 0.043089 0.009466 4.55 0.000

X₂ -0.7998 0.2515 -3.18 0.005

X₃ 0.000590 0.004221 0.14 0.890

X₅ -0.6606 0.1542 -4.28 0.000

X₆ 0.0574 0.1254 0.46 0.652

S = 1.07911 R-Sq = 93.4% R-Sq(adj) = 91.8%

Analysis of Variance

Source DF SS MS F P

Regression 5 345.966 69.193 59.42 0.000

Residual Error 21 24.454 1.164

Total 26 370.420

Source DF Seq SS

X₁ 1 309.464

X₂ 1 8.699

X₃ 1 5.994

X₅ 1 21.566

X₆ 1 0.244

Unusual Observation

Obs X₁ X₄ Fit SE Fit Residual St Resid

17 398 5.500 7.714 0.641 -2.214 -2.55 R

27 400 7.000 7.366 1.025 -0.336 -1.00 X

Where R is observation with a large standardized residual.

Where X is observation whose X values give it large influence.

Predicted values for new Observations

New

Obs Fit SE Fit 80% Cl 80% Pl

1 5.571 0.400 (5.041 , 6.100) (4.048 , 7.094)

Values of Predictors for New Observations

New

Obs X₁ X₂ X₃ X₅ X₆

1 163 2.40 188 6.60 10.0

∴ The advertising cost, X₄ = 5.626 million, The 80% confidence limits for X₄ is (5.041 , 6.100), and The 80% prediction limits for X₄ is (4.048 , 7.094)

Answer:

5x^2+5x+3/3x^2+3x

Step-by-step explanation:

Answer:

There is insufficient statistical evidence to prove that the companies stated color distribution is not correct therefore, the overall proportions of the colors are correctly stated as above

Step-by-step explanation:

We have that

H₀: 0.24 blue, 0.13 brown, 0.20 green, 0.16 orange, 0.13 red and 0.14 yellow

The Data given are as follows;

Hₐ: The stated distribution of M&M is incorrect

                        Blue   Brown   Green    Orange   Red    Yellow   Total

Observed:        105     72          89          84           70       80          500

Expected:         120     65         100         80           65       70      

We have;

[tex]\chi ^{2}=\dfrac{\left (105-120 \right )^{2}}{120}+ \dfrac{\left (72-65\right )^{2}}{65} + \dfrac{\left (89-100\right )^{2}}{100} + \dfrac{\left (84-80\right )^{2}}{80} + \dfrac{\left (70-65\right )^{2}}{65} + \dfrac{\left (80-70\right )^{2}}{70} = 5.85[/tex]

At 6 - 1 = 5 degrees of freedom we find the p-value from the chi squared table as follows

P(0.05) at 5% degrees of freedom =11.070 hence our P-value is larger than 0.05 and we fail to reject the null hypothesis, hence there is insufficient statistical evidence to prove that the companies stated color distribution is not correct.

Answer:

2 is the answer

Step-by-step explanation:

area=1/2*base*height

as height = 2*base and area =4 it comes

1/2*2*base*base=4

so base *base=4

so base = 2

Answer: Choice B. 54degrees

Step-by-step explanation:

Angles 1 4 5 8 are equal and angles 2 3 6 7 are also equal. These two sets of angles of supplementary(you‘d get 180 by adding them).

so

13x+9=180-(5x+9)

by simplifying the equation youll get

18x+18=180

x=9

so angle 7(and therefore angle 6) equals

5*9+9=54

Answer:

The students should request an examination with 5 examiners.

Step-by-step explanation:

Let X denote the event that the student has an “on” day, and let Y denote the

denote the event that he passes the examination. Then,

[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]

The events ([tex]Y|X[/tex]) follows a Binomial distribution with probability of success 0.80 and the events ([tex]Y|X^{c}[/tex]) follows a Binomial distribution with probability of success 0.40.

It is provided that the student believes that he is twice as likely to have an off day as he is to have an on day. Then,

[tex]P(X)=2\cdot P(X^{c})[/tex]

Then,

[tex]P(X)+P(X^{c})=1[/tex]

⇒

[tex]2P(X^{c})+P(X^{c})=1\\\\3P(X^{c})=1\\\\P(X^{c})=\frac{1}{3}[/tex]

Then,

[tex]P(X)=1-P(X^{c})\\=1-\frac{1}{3}\\=\frac{2}{3}[/tex]

Compute the probability that the students passes if request an examination with 3 examiners as follows:

[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]

        [tex]=[\sum\limits^{3}_{x=2}{{3\choose x}(0.80)^{x}(1-0.80)^{3-x}}]\times\frac{2}{3}+[\sum\limits^{3}_{x=2}{{3\choose x}(0.40)^{3}(1-0.40)^{3-x}}]\times\frac{1}{3}[/tex]

       [tex]=0.715[/tex]

The probability that the students passes if request an examination with 3 examiners is 0.715.

Compute the probability that the students passes if request an examination with 5 examiners as follows:

[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]

        [tex]=[\sum\limits^{5}_{x=3}{{5\choose x}(0.80)^{x}(1-0.80)^{5-x}}]\times\frac{2}{3}+[\sum\limits^{5}_{x=3}{{5\choose x}(0.40)^{x}(1-0.40)^{5-x}}]\times\frac{1}{3}[/tex]

       [tex]=0.734[/tex]

The probability that the students passes if request an examination with 5 examiners is 0.734.

As the probability of passing is more in case of 5 examiners, the students should request an examination with 5 examiners.

Answer:

Step-by-step explanation:

Given that :

The probability of winning is 0.8

i.e P(winning) = 0.8

Then P(losing) = 0.2

a) Y ~ Geometric distribution

[tex]P = P(loose) =0.2 \\ \\ \mu_{\delta} = \dfrac{1}{P}= \dfrac{1}{0.2}\\ \\ = 5.0 \\ \\ \\ \dfrac{\sigma ^2 }{\delta } = \dfrac{1-P}{P^2} \\ \\ =\dfrac{0.8}{0.04} \\ \\ = 20[/tex]

b) Y ~ Negative Binomial Distribution

[tex]P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_{\delta} = \dfrac{\delta}{P} \\ \\ =\dfrac{4}{0.2} \\ \\ = 20 \\ \\ \\ \sigma ^2_{\delta} = \dfrac{\delta (1-P)}{P^2} \\ \\ = \dfrac{4*0.8}{0.04}\\ \\ = 80[/tex]

c) Y ~ Binomial Distribution;

n = 100 ; P = 0.8

[tex]\mu_{\delta} = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_{\delta}^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16[/tex]

Answer:

1) 23/2

2) 529/25

Step-by-step explanation:

Transformation:

[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]

[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]

A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]

-----------------------------

Transformation:

[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]

A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]

Answer:

465

Step-by-step explanation:

Margin of error = critical value × standard error

ME = CV × SE

Assuming 95% confidence, CV = z = 1.96.

Standard error is:

SE = σ / √n

SE = 3.3 / √n

Given margin of error of 0.3:

0.3 = 1.96 × 3.3 / √n

n = 465

Answer:

72.

Step-by-step explanation:

Given a group of 6, 9 and 12.

We are to determine the least number of patties that will be shared equally among the groups.

This we do by determine the Least common multiple of the three numbers.

[tex]6=2 X 3\\9 = 3 X 3\\12 =2 X 2 X 2\\L.C.M.=2^3X3^2=72[/tex]

Therefore, the least number of patties that can be shares equally among groups of 6, 9 and 12 is 72.

Answer:

  65,280

Step-by-step explanation:

Consider the 4×4 grid ...

  [tex]\left[\begin{array}{cc}a&b\\d&c\end{array}\right][/tex]

where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.

The same will be true of 270° rotational symmetry, for the same reason.

__

For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)

__

The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...

  65,536 -256 = 65,280 . . . . colorings not rotationally symmetric

Answer:

|Z| = |-0.126| = 0.126 < 1.645

Null hypothesis is accepted

The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.

μ = 57.5

Step-by-step explanation:

Explanation:-

The average retirement age for a certain country was reported to be 56.4 years

The mean of the sample x⁻ = 56.4

The standard  deviation of the Population 'σ'= 55 years

The mean of the population μ = 57.5

Null hypothesis: H₀:The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.

μ = 57.5

Alternative Hypothesis : H₁: μ ≠57.5

Test statistic

         [tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

critical value:

[tex]Z_{\frac{\alpha }{2} } = Z_{0.05} =1.645[/tex]

[tex]Z = \frac{56.4-57.5 }{\frac{55}{\sqrt{40} } } = -0.126[/tex]

|Z| = |-0.126| = 0.126 < 1.645

The null hypothesis is accepted

Conclusion:-

The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.

μ = 57.5

Answer:

B. FOIL

Step-by-step explanation:

FOIL stands for Firsts, Outsides, Insides, and Lasts

This is a mnemonic to help you to remember how to multiply two binomials

From the image, we can see that the on the right side of the equals,

[tex](x)(-5x^2)[/tex] is the product of the firsts of the binomials

[tex](x)(x)[/tex] is the product of the outsides of the binomials

[tex](-2)(-5x^2)[/tex] is the product of the insides of the binomials

[tex](-2)(x)[/tex] is the product of the lasts of the binomials.

Answer:

  B.  FOIL

Step-by-step explanation:

"FOIL" is an acronym for First, Outer, Inner, Last. It refers to the relative positions of the terms in the multiplication of binomials.

The given equation shows the result of such a multiplication. It is an example of the application of FOIL.

Answer:

a. Calculate the prevalence rate of autism for these children for the two age categories.

b. Convert the prevalence rate to a rate per 1,000

Step-by-step explanation:

Generally prevalence is calculated using the following formula:

(number of people with autism / number of people measured) x 100%

age category

3-5: prevalence rate = (19/3,479) x 100% = 0.55%

6-10: prevalence rate = (17/5,417) x 100% = 0.31%

if you want to convert to a rate per 1,000, allyou need to do is multiply by 1,000 instead of 100

3-5: prevalence rate = (19/3,479) x 1,000 = 5.5

6-10: prevalence rate = (17/5,417) x 1,000 = 3.1

Answer:

A.

f is a quadratic function, which means it's graph is a parabola.

Notice that the coefficient of is negative, so the parabola opens downwards.

the x-coordinate of a parabola is always determined by the formula: 

where a is coefficient of the  term, and b is the coefficient of the x term.

Thus, x-coordinate of the vertex of the graph of f is :

the y-coordinate of the vertex is f(8)=-8*8+16*8-60=4.

The vertex is (8, 4).

This means that the maximum daily profit is when exactly 8 candles are sold.

B.

The x-intercepts are the values of x such that f(x)=0,

so to find these values we solve:

complete the square:

so x-8=2      or x-8=-2

the roots are x=10 and  x=6, are the roots.

This means that when the shop sells exactly 6 or 10 candles, it makes no profit.

Answer: d (8, 4); The vertex represents the maximum profit.

Explanation: i got it right on the test

Answer:

Necesita cubrir 4800 cm^2.

Step-by-step explanation:

La pregunta está incompleta:

Laura quiere cubrir con papel de china una puerta como la que se muestra en el dibujo. Las medidas son 80 cm de largo y 60 cm de ancho.

Tenemos que calcular la superficie de la puerta, cuyas medidas son 80 cm de largo y 60 cm de ancho.

Para calcular el área simplemente multiplicamos las medidas de ambos lados:

[tex]A=80\,cm\cdot 60\,cm=4800\,cm^2[/tex]

Answer:

10.1%

Step-by-step explanation:

The first thing we should do is calculate the total volume of the solution when mixing them would be:

0.7 + 0.3 = 1

Now, we have that the resulting concentration (x) would be equal to the sum of the multiplications between the volumes and the concentrations to be mixed, as follows:

x * 1 = 0.7 * 0.05 + 0.3 * 0.22

x = 0.035 + 0.066

x = 0.101

That is, the concentration of the resulting mixture would be 10.1% (0.101 * 100)

Answer:

true

is the answer

Answer:

(a)0.0005

(b)0.2720

Step-by-step explanation:

Total Number of Transistors = 16

To find the probability that 4 selected at random are defective (or non-defective), we find the probability of the 1st, 2nd, 3rd, and 4th defective (or non-defective) items in that order, Note that the selection is without replacement.

(a)Probability that  all are defective

Number of Defective Transistors =4

P(all are defective) [tex]=\dfrac{4}{16} \times \dfrac{3}{15} \times \dfrac{2}{14} \times \dfrac{1}{13}[/tex]

=0.0005

(b)Probability that  none are defective

Number of Non-Defective Transistors =16-4=12

P(none are defective) [tex]=\dfrac{12}{16} \times \dfrac{11}{15} \times \dfrac{10}{14} \times \dfrac{9}{13}[/tex]

=0.2720