is dilated by a scale factor of 3 to form . Point O, which lies on , is the center of dilation.

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:

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:

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:

[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:

|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:

Step-by-step explanation:

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:

  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:

Step-by-step explanation:

Hello!

The variable of interest is "the time a fight lasts" measured in seconds

The five number summary for her first 12 UFC fights are:

Minimum: Min= 14

First Quartile: Q₁= 25

Second Quartile/Median: Me= 44

Third Quartile: Q₃= 64

Maximum: Max= 289

a)

Three of her fights lasted more than one minute: 289, 267, 66. Out of these three fights, you have to determine if they are outliers using the IQR method.

The IQR is the distance between the third quartile and the first quartile

IQR= Q₃ - Q₁= 64 - 25= 39

Remember, an outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.  

Considering the 1st quartile (Q₁), the 3rd quartile (Q₃) and the interquartile range IQR, any value X is considered an outlier if:

X < Q₁ - 1.5 IQR

X > Q₃ + 1.5 IQR

Or extreme outliers if:

X < Q₁ - 3 IQR

X > Q₃ + 3 IQR

The limits that define if a value is an outlier or not are:

X < 25 - 1.5*39 = -33.5

X > 64 + 1.5*39= 122.5

And for extreme outliers:

X < 25 - 3*39 = -92

X > 64 + 3*39= 181

So fights that lasted less than -33.5 or more than 122.5 seconds are to be considered outliers, and those who lasted less than -92 or more than 181 seconds are extreme outliers.

Out of the three fights, the ones that lasted 289 and 267 seconds can be considered extreme values.

b) The minimum observed value for this data set is 14 seconds, values are considered to be outliers if they are less to -33.5, so there is no low outliers on the sample.

As you can see, both values that allow you to determine if the observation is an outlier or not are negative, since the variable is "the time a fight lasts" it is impossible for it to have negative values. The lowest value of time a fight can last is "zero seconds". Although mathematically correct, these values make no sense.

c)

See attachment.

d)

The average or mean is a measurement of central tendency that shows you the value around which most of the distribution will be. It is very affected by the presence of outliers, especially extreme ones. Outliers make the mean "move" towards them, this means, that if there are small outliers, then the mean will move to the lower side of the distribution. But if the outliers are big, then the mean will move to the higher side of the distribution.

For example, let's say 5 of the fight times were:

10, 37, 49, 51, 68

For these values the mean would be:

X[bar]₀= ∑X/n= (10+37+49+51+68)/5= 215/5= 43

Now let's change one of these values for an extreme one:

Small value:

0, 37, 49, 51, 68

X[bar]₁= ∑X/n= (0+37+49+51+68)/5= 205/5= 41

⇒ As you can see, one change for a smaller value reduces the mean value X[bar]₁ < X[bar]₀

Big value:

10, 37, 49, 51, 268

X[bar]₂= ∑X/n= (10+37+49+51+268)/5= 415/5= 83

⇒ In this case, changing one of the 5 values to a bigger one moved the mean to the right: X[bar]₀ < X[bar]₂

So for the given distribution, since there are at least two high outliers, you'd expect the mean to be greater than the median.

I hope this helps!

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:

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]

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:

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 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:

Red apples to all apples =2/11

Red apples to green apples =2/9

Step-by-step explanation:

There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples

The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11

The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9

Answer:

Red apples to all apples =2/11

Red apples to green apples =2/9

Step-by-step explanation:

There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples

The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11

The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9

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]    

Answer:

SA = 1,176 ft².

Step-by-step explanation:

To find the surface area of the triangular prism, we can solve for the rectangular base, both triangular faces, and lateral sides separately.

For the rectangular base: (Use formula l×w)

20 × 18 = 360 ft²

For the triangular faces: (Use formula 1/2(b·h)

1/2(18 × 12) = 108 ft²

Since there are two faces, we need to double the amount.

108 × 2 = 216 ft².

Finally, solve for the lateral sides:

20 × 15 = 300 ft².

There are two sides, so:

300 × 2 = 600 ft².

Add up all of these areas:

600 + 216 + 360 = 1,176 ft²

Answer:

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

Step-by-step explanation:

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:

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:

true

is the answer

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:

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:

c) Permutations: 40320

Step-by-step explanation:

We have that permutations are groupings in which the order of the objects matters. Combinations are groupings where content matters but order does not.

In this case, then the batting order, therefore the order does matter, therefore, it would be a permutation, where n = 8 and r = 7

nPr = n! / (n-r)!

Replacing:

8P7 = 8! / (8-7)! = 40320

Which means that the answer is c) Permutations: 40320

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:

[tex]P(19<X<91)=P(\frac{19-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{91-\mu}{\sigma})=P(\frac{19-55}{12}<Z<\frac{91-55}{12})=P(-3<z<2)[/tex]

And we can find this probability with this difference and using the normal standard distribution

[tex]P(-3<z<3)=P(z<3)-P(z<-3)=0.9987 -0.00135 =0.9974[/tex]

Step-by-step explanation:

Let X the random variable that represent the amount of Jen monthly phone of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(55,12)[/tex]  

Where [tex]\mu=55[/tex] and [tex]\sigma=12[/tex]

We are interested on this probability

[tex]P(19<X<91)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Replacing the info we got:

[tex]P(19<X<91)=P(\frac{19-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{91-\mu}{\sigma})=P(\frac{19-55}{12}<Z<\frac{91-55}{12})=P(-3<z<2)[/tex]

And we can find this probability with this difference and using the normal standard distribution

[tex]P(-3<z<3)=P(z<3)-P(z<-3)=0.9987 -0.00135 =0.9974[/tex]

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:

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

The question is incomplete, I will however explain, with an illustration, how to determine the center and radius of a circle.

Step-by-step explanation:

The standard equation of a circle is given as:

(x - a)² + (y - b)² = r² ........................(1)

Where (a, b) is the center of the circle, and r is the radius.

An expression can be given for us to find the center and the radius of the circle.

Suppose we were given the expression:

x² + y² - 10x + 4y - 7 = 0.....................(2)

To find the center and the radius, it is left for us to rewrite (2) in the form of (1).

Rearranging (2), we have

(x² - 10x) + (y² + 4y) = 7

Completing the squares of each bracket

(x² - 10x + 25 - 25) + (y² + 4y + 4 - 4) = 7

(x² - 10x + 25) + (y² + 4y + 4) - 25 - 4 = 7

(x² - 10x + 25) + (y² + 4y + 4) - 29 = 7

(x - 5)² + (y + 2)² = 7 + 29

(x - 5)² + (y + 2)² = 36

Or

(x - 5)² + (y + 2)² = 6² .....................(3)

Comparing (3) with one, we see that

a = 5, b = -2, and r = 6

Therefore it is a circle centered at (5, -2) with a 6 unit radius.