The value of homes sold in Hampton VA are normally distributed with a mean of $200,000 and a standard deviation of $10,000. If 1216 houses were sold in 2012 what percentage of houses sold fall between $190,000 and 230,000?

Since density is equal to mass per unit volume, mass is equal to density times volume. So we split up the lamina into tiny regions with "volume" (area) equal to dA, multiplied by the density, and integrated over the entirety of the lamina.

This is best done in polar coordinates:

[tex]\begin{cases}x=u\cos v\\y=u\sin v\end{cases}\implies\mathrm dA=\mathrm dx\,\mathrm dy=u\,\mathrm du\,\mathrm dv[/tex]

so that [tex]x^2+y^2=u^2\cos^2v+u^2\sin^2v=u^2[/tex].

The lamina is then the set of points

[tex]L=\left\{(u,v)\mid1\le u\le2\land0\le v\le\dfrac\pi2\right\}[/tex]

Now compute the integral: the mass of the lamina is

[tex]\displaystyle\iint_L(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^2u^3\,\mathrm du\,\mathrm dv=\frac\pi2\int_1^2u^3\,\mathrm du=\frac{15\pi}8[/tex]

Answer:

x= 13.7 (nearest tenth)

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

Step-by-step explanation:

A) Let x represent minutes used, and C represent monthly charge. We are given two (x, C) pairs: (370, 133.00) and (530, 181.00)

We can use these in the 2-point form of the equation for a line.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  C = (181 -133)/(530 -370)(x -370) +133

  C = 48/160(x -370) +133

  C = 0.30x -111 +133

  C = 0.30x +22

__

B) For x = 477 minutes, the charge will be ...

  C = 0.30(477) +22 = $165.10 . . . . for 477 minutes

The monthly cost C =   $22 + $0.30x

Jane's bill for August is $165.10

The total amount Jane pays is the sum of the monthly fee and the charge per minute.

Total amount = monthly fee + charge per minute

Two equations can be derived from the question

a + 370b = 133 equation 1

a + 530b = 181 equation 2

Where:

a = monthly fee

b = charge per minute

This equation would be solved using simultaneous equation

Subtract equation 1 from equation 2

160b = 48

Divide both sides of the equation by 160

b = 48 / 160

b = 0.30

Substitute for b in equation 1

a + 370(0.30) = 133

a + 111 = 133

a = 133 - 111

a = 22

Based on the above calculations,  the monthly fee is $22 and the charge per minute is $0.30

Equation for monthly cost = $22 + $0.30x

If Jane used 477 minutes, total charge :

$22 + $0.30(477) =

22 + 143.10

= $165.10

A similar question was solved here: https://brainly.com/question/17911105?referrer=searchResults

Answer:

Step-by-step explanation:

If they earned $440 in 40 hours

This means they earned 440÷40=11 in one hour

Sam makes x-2 amount of money per hour so the difference between Sam's and Joe's salary is $2

Find two numbers that add up to Ten and can subtract to make a difference of 2 (I am starting with ten as it is easier) 6+4=10 6-4=2

So to make 6 and. 4 add to make a 11 we need to add a 0.5 to each of them so 6.5+4.5=11 and 6.5-4.5= $2.

Therefore Joe makes $6.50 an hour and Sam makes £4.50

Answer:

yes

Step-by-step explanation:

Answer:

1 = D 75 inches

2 = A 27

Step-by-step explanation:

1 - 6.3 times 12 = 75.6

2 - 6 times 9 = 54

54/2 = 27

:)

Answer:

Maths anxiety

Step-by-step explanation:

In a typical research study, there are basically 2 types of variables involved, which are the dependent and the independent variable.

The dependent variable is affected by other factors or the independent variable involved in the study. The dependent variable would change is the independent variable is manipulated, changed or varied.

The dependent variable in Joe's dissertation is MATHS ANXIETY, which is dependent on the gender of students. Gender is the independent variable as he wants to find out if there's any difference in maths anxiety between males and females.

The dependent variable is Math Anxiety which is dependent on gender of the students.

Answer:

Not correct

Step-by-step explanation:

Sample 8 has one free throw, sample 9 has 3 free throw success,

sample 10 has 3 free throw success

sample 11 has 5 free throw success

sample 12 has 5 free throw success

sample 13 has 2 free throw success

sample 14 has 1 free throw success;

See one sample should contain 15 free throw and the probability of success should be 0.7

Let's look at sample 8

Total no of success is 1

Total no of free throws 15

Probability is 1/15 = 1/15 * 100 =6.67%

Similarly you can do so for the others.

Answer:

(-5,13)

Step-by-step explanation:

because t=3

[tex]x = 1 - 2 \times 3 = - 5 \\ y = 4 \times 3 + 1 = 13[/tex]

Answer:

Step-by-step explanation:

Answer:

1/8 but idk im not good with math

Step-by-step explanation:

Answer:

16-25

Step-by-step explanation:

Step  1  :

           2

Simplify   —

           5

Equation at the end of step  1  :

  24    2

 ——— +  —

 100    5

Step  2  :

            6

Simplify   ——

           25

Equation at the end of step  2  :

  6    2

 —— +  —

 25    5

Answer:

Yes I believe the answer will be the same.

Step-by-step explanation:

Answer:

A=9404

Step-by-step explanation:

Answer:

9404

Step-by-step explanation:

Answer:

27.94%

Step-by-step explanation:

The statement tells us that we have 5 red balls and 6 blue balls, that is, there are 11 in total (5 + 6)

So the probability of red balls = 5/11 and blue balls probability = 6/11

Let X be the number of red balls of those 5 selected balls.

 Then X follows a binomial distribution with the following parameters:

n = 5

p = 5/11

q = 6/11

P (X) = nCx * p ^ (x) * q ^ (n -x)

required probability is P (X = 3), replacing:

P (X = 3) = 5C3 * (5/11) ^ (3) * (6/11) ^ (5 -3)

P (X = 3) = 5! / (3! (5-3)!) * 0.02794

P (X = 3) = 10 * 0.02794

P (X = 3) = 0.2794

Which means that the probability is 27.94%

Answer:

To simplify

√(-x) = √((x)(-1)) = √((x)(i^2))

√(-x) = √(i^2) × √x = i√x

For example;

Simplify √-9

√-9 = √(-1×9) = √-1 × √9

√-9 = √(i^2) × √9 = i × 3

√-9 = 3i

Step-by-step explanation:

Given a negative square root √(-x);

From our knowledge of complex numbers, we know that

i^2 = -1 and vise versa

To simplify

√(-x) = √((x)(-1)) = √((x)(i^2))

√(-x) = √(i^2) × √x = i√x

For example;

Simplify √-9

√-9 = √(-1×9) = √-1 × √9

√-9 = √(i^2) × √9 = i × 3

√-9 = 3i

Step-by-step explanation:

The square root of a number A, is a number B such that, when it is multiplied by itself, the result is A.

If A × A = B

Then √B = A.

Now the multiplication of two numbers gives a positive number if both numbers are positive, or both numbers are negative.

2 × 2 = -2 × -2 = 4

3 × 3 = -3 × - 3 = 9

And so on.

So, the square root of 4 = 2 or -2

The square root of 9 = 3 or -3

But if one of the numbers is positive while the other is negative, then the result is negative.

2 × -2 = -4

3 × -3 = -9

Clearly, √(-4) ≠ 2 ≠ -2

√(-9) ≠ 3 ≠ -3

It is impossible to find the square root of negative numbers on the real line. This gives rise to the introduction of Complex Number.

Let i² = -1, then we have that

√(-1) = i.

This is the idea of Complex number, and it helps solve the problem of the negative square roots, and every negative number can be written as the multiplication of -1 and the inverse of the number.

-A = -1 × A

So, √(-A) = √(-1 × A)

= √(-1) × √A

= i × √A

= i√A

Example, to simplify √(-16)

√(-16) = √(-1 × 16)

= √(-1) × √16

= i × ±4

= ±4i

Answer: (11/8)

Step-by-step explanation:

I will answer this in English.

a person collects 7/4 of an amount, spends 1/4 and lends 1/8. What fraction of the amount collected is left?

If the amount is A, then he collects:

C = (7/4)*A

Now, he spends 1/4 and lends 1/8 of the amount A, so the fraction left is:

Left = (7/4)*A - (1/4)*A - (1/8)*A

now i will write 7/4 as 14/8 and 1/4 as 2/8.

left = (14/8)*A - (2/8)*A - (1/8)*A  = ((14 - 2 - 1)/8)*A = (11/8)*A

Answer:

All real numbers

Step-by-step explanation:

The domain is just what values of x you can plug in as an input. In this case, you can plug in any number, as the graph is just a line that has no restrictions. An example of a case where the domain isnt just any number would be g(x) = 5/x, because in that case, x couldn't be 0 because you cant divide by zero.

Answer: all real numbers

Step-by-step explanation:

Answer:

34.83% of the population scored higher than Tim on the mathematics portion of the ACT

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 22, \sigma = 5.1[/tex]

Tim scored 24. What percent of the population scored higher than Tim on the mathematics portion of the ACT?

The proportion is 1 subtracted by the pvalue of Z when X = 24. The percentage is the proportion multiplied by 100.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{24 - 22}{5.1}[/tex]

[tex]Z = 0.39[/tex]

[tex]Z = 0.39[/tex] has a pvalue of 0.6517

1 - 0.6517 = 0.3483

34.83% of the population scored higher than Tim on the mathematics portion of the ACT

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test.

For the null hypothesis,

H0 : p ≥ 0.25

For the alternative hypothesis,

H1 : p < 0.25

b) from the given information,the sample proportion or point estimate for the population proportion is

1219/3532 = 0.35

Confidence interval = sample proportion ± margin of error

Margin of error = z × √pq/n

p = 0.35

q = 1 - 0.35 = 0.65

z score for 95% confidence level is 1.96

Margin of error = 1.96 × √(0.35 × 0.65)/3532 = 0.016

Confidence interval = 0.35 ± 0.016

c) Given that the 95% confidence interval is (0.329 , 0.361), it means that the lower limit of the confidence interval is 0.329 and the upper limit is 0.361

If more than a quarter of all North Americans have hypertension. It means that the true proportion can be within this interval. 95% confidence interval is a high degree of confidence. Therefore, we can say that with a high degree of confidence that more than a quarter of all North Americans have hypertension.

d) it would get narrower

Answer:

1st one is 2. 2nd one is 5. 3rd one is less than. 4th one is, is smaller

Step-by-step explanation:

Answer:

  f(n) = -n^2 -3n +5

Step-by-step explanation:

Suppose the formula is ...

  f(n) = an^2 +bn +c

Then we have ...

  f(1) = 1 = a(1^2) +b(1) +c

  f(2) = -5 = a(2^2) +b(2) +c

  f(3) = -13 = a(3^2) +b(3) +c

__

Here's a way to solve these equations.

Subtract the first equation from the second:

  -6 = 3a +b . . . . . 4th equation

Subtract the second equation from the third:

  -8 = 5a +b . . . . . 5th equation

Subtract the fourth equation from the fifth:

  -2 = 2a

  a = -1

Then substituting into the 4th equation to find b, we have ...

  -6 = 3(-1) +b

  -3 = b

and ...

  1 = -1 +(-3) +c . . . . . substituting "a" and "b" into the first equation

  5 = c

The formula is ...

  f(n) = -n^2 -3n +5

Answer:

The minimum score required for an A grade is 85.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 76, \sigma = 7.9[/tex]

Find the minimum score required for an A grade.

The top 13% of the scores are A, so the minimum is the 100-13 = 87th percentile, which is X when Z has a pvalue of 0.87. So X when Z = 1.127.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.127 = \frac{X - 76}{7.9}[/tex]

[tex]X - 76 = 7.9*1.127[/tex]

[tex]X = 84.9[/tex]

Rounding to the nearest whole number:

The minimum score required for an A grade is 85.

Answer:

9x^3-21x^2+19x-6

Step-by-step explanation:

First you have to distribute the first equation into the second since the two are being multiplied:

(3x^2-5x+3)(3x-2)

9x^3-6x^2-15^2+10x+9x-6

(simplify)

9x^3-21x^2+19x-6

9x^3-21x^2+19x-6

First you have to distribute the first equation into the second since the two are being multiplied:

(3x^2-5x+3)(3x-2)

9x^3-6x^2-15^2+10x+9x-6

(simplify)

9x^3-21x^2+19x-6 is the answer to the question

Answer:

D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.

Step-by-step explanation:

The scale factor is equal to 1. Hence, the quadrilateral A'B'C'D' will be identical to quadrilateral ABCD, whose vertices are the same.

The algebraic expression of the dilation is:

[tex](x',y') = (x,y)[/tex]

Besides, the coordinates of the new quadrilateral are A'(3, 3), B'(5, 3), C'(7, 1), and D'(1, 1)

And quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.

Therefore, the right answer is D.

Answer: D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.

Step-by-step explanation: just did a test with this question and got it right. Hope this helped! thx for the points :D

Answer:

Temperature after 1 minute = 184 ° F

Step-by-step explanation:

starting temperature = 200 °F

rate of decrease = 8% per minute

Temperature lost = 8% of 200 = 8/100 × 200 = 0.08 × 200 = 16 °F

It therefore means that after 1 minute, the cup of coffee loses 16 °F,

∴ Temperature after 1 minute = (starting temperature) - (lost temperature)

= 200 - 16 = 184 °F

Answer:

2.5 ft

Step-by-step explanation:

As radius is perpendicular to tangent ,

LT [tex]\perp[/tex]KT

By pythagoras theorem:

LT² = LK² - KT²

LT² = (6.5)² - 6²

LT² = 42.25 - 36

LT² = 6.25

LT = 2.5 ft

LT = radius = 2.5 ft

The answer is [ 2 2 1]

look at the attached picture

Hope it helps

Good luck on your assignment

Answer:

The area of the region is 25,351 [tex]units^2[/tex].

Step-by-step explanation:

The Fundamental Theorem of Calculus: if [tex]f[/tex] is a continuous function on [tex][a,b][/tex], then

                                   [tex]\int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) | {_a^b}[/tex]

where [tex]F[/tex] is an antiderivative of [tex]f[/tex].

A function [tex]F[/tex] is an antiderivative of the function [tex]f[/tex] if

                                                    [tex]F^{'}(x)=f(x)[/tex]

The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.

To find the area of the region between the graph of the function [tex]x^5 + 8x^4 + 2x^2 + 5x + 15[/tex] and the x-axis on the interval [-6, 6] you must:

Apply the Fundamental Theorem of Calculus

[tex]\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx[/tex]

[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx[/tex]

[tex]\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2[/tex]

Answer:

2nd branch > 1st branch > 3rd branch

or

[tex]\dfrac{2}{2} > \dfrac{2}{3} > \dfrac{2}{8}[/tex]

Step-by-step explanation:

Length of First branch = [tex]\frac{2}{3}[/tex] foot

Length of second branch = [tex]\frac{2}{2}[/tex] foot

Length of third branch = [tex]\frac{2}{8}[/tex] foot

Let us convert the fractions in decimal forms:

[tex]1.\ \dfrac{2}{3} = 0.67[/tex]

[tex]2. \dfrac{2}{2} = 1[/tex]

[tex]3.\ \dfrac{2}{8} = \dfrac{1}{4}=0.25[/tex]

It can be clearly seen that 1 is the largest value among the three values.

So, 2nd branch is the largest.

Now, let us have a look at the values of first and third branches:

0.67 and 0.25.

Clearly, 0.67 is greater than 0.25.

So, the correct order is:

2nd branch > 1st branch > 3rd branch

OR

We can use other method to see it.

Here, all the 3 fractions have same numerator.

So, denominator can help us decide the which fraction has a large value.

If numerator is same, the larger denominator will have smaller fractions.

The denominators are 2, 3 and 8.

8 > 3 > 2

So, the answer is

2nd branch > 1st branch > 3rd branch

or

[tex]\dfrac{2}{2} > \dfrac{2}{3} > \dfrac{2}{8}[/tex]