The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 6. If there were 4508 no votes, what was the total
number of votes

Take

[tex]u=\ln x\implies\mathrm du=\dfrac{\mathrm dx}x[/tex]

[tex]\mathrm dv=4x^2\,\mathrm dx\implies v=\dfrac43x^3[/tex]

Then

[tex]\displaystyle\int4x^2\ln x\,\mathrm dx=\frac43x^3\ln x-\frac43\int x^2\,\mathrm dx=\frac43x^3\ln x-\frac49x^3+C[/tex]

[tex]=\boxed{\dfrac49x^3(3\ln x-1)+C}[/tex]

The required integration is,

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C

The given integral is,

∫4x² lnx dx

Using integration by parts, choose u and dv.

In this case, we choose u = lnx and dv = 4x²dx.

Using the formula for integration by parts, we have:

∫ u dv = uv - ∫ v du

Substituting the values of u and dv, we get:

∫4x² lnx dx = (lnx) (∫ 4x² dx) - ∫ [(d/dx)lnx] (∫4x² dx) dx

Simplifying the first term using the power rule of integration, we get:

∫ 4x² dx = (4/3)x³ + C₁

For the second term, we need to evaluate (d/dx)lnx,

Which is simply 1/x. Substituting this value, we get:

∫ [(d/dx)lnx] (∫4x² dx) dx = ∫ [(1/x) ((4/3)x³ + C₁)] dx

Simplifying this expression, we get:

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - ∫ [(4/3)x³/x] dx

Using the power rule of integration again, we get:

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C

Where C is the constant of integration.

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Answer:

[tex]x = { - 1, 0,1 ,2 ...}[/tex]

Step-by-step explanation:

[tex]2e - 3 < 3e - 1 = 2e - 3e < - 1 + 3 = - 1e < 2 = e > - 2[/tex]

Hope this helps ;) ❤❤❤

Answer: 3.41x10^3

Step-by-step explanation:

At the beginning of the year, we have:

R = 6.2x10 rats.

And we know that, in one year, each rat produces:

O = 5.5x10 offsprins.

Then each one of the 6.2x10 initial rats will produce 5.5x10 offsprings in one year, then after one year we have a total of:

(6.2x10)*(5.5x10) = (6.2*5.5)x(10*10) = 34.1x10^2

and we can write:

34.1 = 3.41x10

then: 34.1x10^2 = 3.41x10^3

So after one year, the average number of rats is:  3.41x10^3

Answer:

2.952755906 ft

Step-by-step explanation:

We need to convert 90 cm to inches

90 cm * 1 inch / 2.54 cm =35.43307087 inches

Now convert inches to ft

12 inches = 1ft

35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  95% interval for [tex]p_1 - p_2[/tex] is  [tex]-0.0171 ,0.0411[/tex]

Option A is correct

Step-by-step explanation:

From the question we are told that

   The sample size of male  is [tex]n_1 = 1211[/tex]

    The number of males that  said they have at least one tattoo is [tex]r = 182[/tex]

   The sample size of female is [tex]n_2 = 1041[/tex]

     The number of females that  said they have at least one tattoo is [tex]k = 144[/tex]

Generally the sample proportion of male is  

            [tex]\r p_1 = \frac{r}{ n_1}[/tex]

substituting values

            [tex]\r p_1 = \frac{ 182}{1211}[/tex]

             [tex]\r p_1 = 0.1503[/tex]

Generally the sample proportion of female is  

            [tex]\r p_2 = \frac{k}{ n_2}[/tex]

substituting values

           [tex]\r p_2 = \frac{ 144}{1041}[/tex]

           [tex]\r p_2 = 0.1383[/tex]

Given that the confidence level is  95% then the level of  significance is mathematically represented as

          [tex]\alpha =100-95[/tex]

          [tex]\alpha =5\%[/tex]

          [tex]\alpha =0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is

          [tex]Z_\frac{\alpha }{2} = 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }[/tex]

substituting values

       [tex]E = 1.96 * \sqrt{\frac{ 0.1503 (1- 0.1503)}{1211} + \frac{0.1383 (1- 0.1383)}{1041} }[/tex]

       [tex]E = 0.0291[/tex]

The 95% confidence interval is mathematically represented as

        [tex](\r p_1 - \r p_2 ) - E < p_1-p_2 < (\r p_1 - \r p_2 ) + E[/tex]

substituting values

         [tex](0.1503- 0.1383 ) - 0.0291 < p_1-p_2 < (0.1503- 0.1383 ) + 0.0291[/tex]

          [tex]-0.0171 < p_1-p_2 < 0.0411[/tex]

So the interpretation is that there is 95% confidence that the difference of the proportion is in the interval .So conclude that there is insufficient evidence of a significant difference in the proportion of male and female that have at least one tattoo

This because the difference in proportion is less than [tex]\alpha[/tex]

Answer:

P= 2

Step-by-step explanation:

10/7p+13/8+15/2p=-909/56

Combine like terms

10/7p+15/2p=-909/56-13/8

20p+105p/14=-909-13*7/56

125/14p=-909-91/56

125/14p= -1000/56

125/14p*14/125= -1000/56*14/125

simplify

P= 8/4=2

And for #8 n =1 I answered this question it

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Complete Question

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is  7.5

Answer:

The minimum sample size is  [tex]n =97[/tex]

Step-by-step explanation:

From the question  we are told that

 The margin of error is  [tex]E = 1.25[/tex]

   The  standard deviation is  [tex]s = 7.5[/tex]

Given that the confidence level is  90% then the level of significance is mathematically represented as

             [tex]\alpha = 100 - 90[/tex]  

             [tex]\alpha =10\%[/tex]  

             [tex]\alpha =0.10[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  

    The value is  [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]

   The  minimum sample size is mathematically evaluated as

         [tex]n = \frac{Z_{\frac{\alpha }{2} * s^2 }}{E^2 }[/tex]

=>        [tex]n = \frac{1.645^2 * 7.5^2 }{1.25^2 }[/tex]

=>        [tex]n =97[/tex]

-3-2g+6+4g

3+2g

hope it helps

Answer:

-2g + 18

Step-by-step explanation:

-3(2g - 6) + 4g

First we use distributive property.

-3 × 2g = -6g

-3 × -6 = 18

now we have

-6g + 18 + 4g

Now we combine the like terms

-6g + 4g = -2g

Finally we have

-2g + 18

and they are not like terms so we leave them and the equation is solved.

Answer:

1/4 of an hour

Step-by-step explanation:

2 divided by 8 = 1/4

Answer:

1/4

Step-by-step explanation:

A whole shift is 8 hours

Part over whole is the fraction

2/8

Divide top and bottom by 2

1/4

Answer:

The operation:

(a,b) is equal to the rest of the division of a by b.

Now, if we have:

(a + kb,b) = (a,b) + (k*b,b)

But if we have that k and b are integers, then:

(k*b)/b = k

So b divides k*b into a whole number, this means that (k*b,b) = 0

then:

(a + kb,b) = (a,b) + (k*b,b) = (a,b) + 0 = (a,b)

Answer:

4 consecutive goals

Step-by-step explanation:

If 3 of last 10 field goals = 30%

Which is equivalent to

(Number of goals scored / total games played) * 100%

(3 / 10) * 100% = 30%

Number of consecutive goals one has to score to raise field goal to 50% will be:

Let y = number of consecutive goals

[(3+y) / (10+y)] * 100% = 50%

[(3+y) / (10+y)] * 100/100 = 50/100

[(3+y) / (10+y)] * 1 = 0.5

(3+y) / (10+y) = 0.5

3+y = 0.5(10 + y)

3+y = 5 + 0.5y

y - 0.5y = 5 - 3

0.5y = 2

y = 2 / 0.5

y = 4

Therefore, number of consecutive goals needed to raise field goal to 50% = 4

Answer:

5/12

Step-by-step explanation:

3/4-1/3=

9/12-4/12=

5/12

Answer:

  (a) there are 10 sets of 3 friends, so in 21 games, at least one set must show 3 times

  (b) there are 20 sets of 3 friends, so  in 21 games, at least one set must show 2 times.

Step-by-step explanation:

(a) The number of combinations of 5 things taken 3 at a time is ...

  5C3 = 5!/(3!·2!) = 5·4/2 = 10

There can be 10 games in which the same 3 friends do not show up. There can be 10 more games such that the same 3 friends show up exactly twice. In the 21st game, some set of 3 friends must show up 3 times.

__

(b) The number of combinations of 6 things taken 3 at a time is ...

  6C3 = 6!/(3!·3!) = 6·5·4/(3·2) = 20

Hence, there can be 20 games in which the same 3 friends do not show up. In the 21st game, some set of 3 friends will show up a second time.

Answer:

Whatever is raised to the power of 0 is 1

SO the answer is 1

Answer:

[tex]\huge\boxed{r<8}[/tex]

Step-by-step explanation:

[tex]5 > r - 3[/tex]

Adding 3 to both sides

[tex]5 + 3 > r[/tex]

[tex]8 > r\\OR \\r < 8[/tex]

Answer: D. r<8

Step-by-step explanation:

[tex]5>r-3[/tex]

add 3 to both sides

[tex]r-3+3<5+3[/tex]

[tex]5+3=8[/tex]

simplify

[tex]r<8[/tex]

Answer:

Below

Step-by-step explanation:

Suppose that m and n are both even numbers.

So we can express them as the product of 2 and another number.

● n = 2×a

● m = 2×b

● m-n = 2b-2a

● m-n = 2(b-a)

m-n is an even number since it is divisible by 2.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Suppose that both n and m are odd numbers.

● n = 2a+1

● m = 2b+1

● m-n = 2b+1-(2a+1)

● m-n = 2b+1-2a-1

● m-n = 2b-2a

● m-n = 2(b-a)

So m-n is even since it is divisible by 2.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Suppose that m is odd and n is even ir vice versa

● n = 2a or n= 2a+1

● m = 2b+1 or m = 2b

● m-n = 2b+1-2a or m-n = 2b-2a-1

● m-n = 2(b-a) +1 or m-n = 2(b-a)-1

In both cases m-n isn't even.

■■■■■■■■■■■■■■■■■■■■■■■■■■

So m-n is even if and only if m and n are odd or m and are even

Answer:

Case 1

both m and n are even

Therefore m/2 and n/2 are integers

Then,

m-n

=2(m/2 - n/2)

Since m/2 and n/2 are integers

Then m/2 - n/2 will be an integer

Therefore,

m-n = 2(Z)

Where Z is an integer

Since 2 is a factor of m-n

Therefore m -n is even

Case 2

Both m and n are odd

m-n

= 2(½m - ½n)

When an odd number is divided by 2 it gives an integer and a remainder of 1

Therefore

½m = Y + ½

And

½n = Z + ½

Where Y and Z are integers

Then

m-n = 2(Y+½-Z-½)

= 2(Y-Z)

Y-Z will also be an integer

m-n= 2A

Therefore m-n is even

Case 3

One is odd and the other even

m-n = 2(m/2 - n/2)

Assume m is even and n is odd

From the discussions above

m-n = 2(Y - Z - ½)

m-n = 2(A - ½)

Hence m-n is not even because when is divided by two it doesn't give an integer.

Therefore for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.

Answer:

36

step by step

given length=6

so area of square is given by s2 i.e 6^2

=6×6

=36 (Ans)

Answer:

4/ (10+r) * r/ (10+r)

Step-by-step explanation:

four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag = 4+r+6 = 10+r marbles

P( blue) = blue marbles / total marbles

             = 4/ (10+r)

Then replace

P( r) = red marbles / total marbles

             = r/ (10+r)

P( blue replace ,red) =P ( blue ) * P(red)

                                    =  4/ (10+r) * r/ (10+r)

                                    = 4r / ( 10+r) ^2

Answer:

C. 4/10+r (r/10+r)

Step-by-step explanation:

EDG20

Answer:

Its 10x^2+12

Step-by-step explanation:

Answer:

-10X^2+12

Step-by-step explanation:

Answer:

The 5th term of a sequence is defined as the term with n = 5.  So for this sequence, a sub 5 = 5/6

Answer:

16/45x-11/12

Step-by-step explanation:

Multiply across

2/15x-30/40-1/6+2/9x=

Get common denominators of like terms

6/45x+10/45x-9/12-2/12=

Combine like terms

16/45x-11/12

The simplified expression is: (16/45)x - (11/12)

To simplify the given expression, we'll follow the steps:

Step 1: Distribute the fractions through the parentheses.

Step 2: Simplify the expression by combining like terms.

Let's proceed with the simplification:

Step 1: Distribute the fractions through the parentheses:

2/5 * (1/3x - 15/8) - 1/3 * (1/2 - 2/3x)

Step 2: Simplify the expression:

To distribute 2/5 through (1/3x - 15/8):

2/5 * 1/3x = 2/15x

2/5 * (-15/8) = -15/20 = -3/4

So, the first part becomes: 2/15x - 3/4

To distribute -1/3 through (1/2 - 2/3x):

-1/3 * 1/2 = -1/6

-1/3 * (-2/3x) = 2/9x

So, the second part becomes: -1/6 + 2/9x

Now, the entire expression becomes:

2/15x - 3/4 - 1/6 + 2/9x

Step 3: Combine like terms:

To combine the terms with "x":

2/15x + 2/9x = (2/15 + 2/9)x

Now, find the common denominator for (2/15) and (2/9), which is 45:

(2/15 + 2/9) = (6/45 + 10/45) = 16/45

So, the combined x term becomes:

(16/45)x

Now, combine the constant terms:

-3/4 - 1/6 = (-18/24 - 4/24) = -22/24

To simplify -22/24, we can divide both numerator and denominator by their greatest common divisor (which is 2):

-22 ÷ 2 = -11

24 ÷ 2 = 12

So, the combined constant term becomes:

(-11/12)

Putting it all together, the simplified expression is:

(16/45)x - (11/12)

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Complete question is:

Simplify the given expression: 2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)

[tex]\bold{\text{Answer:}\quad R(t)=-0.96\sin\bigg(\dfrac{\pi}{182.5}t}\bigg)+2.3}[/tex]

Step-by-step explanation:

The equation of a sin function is: y = A sin (Bx - C) + D     where

D = 2.3

It is given that t = 0 is located at 2.30.  The sin graph usually starts at 0 so the graph has shifted up 2.3 units.  --> D = 2.3

A = -0.96

The amplitude is the difference between the maximum (or minimum) and the centerline.  A = 2.30 - 1.44 = 0.96

The minimum is given as the next point. Since the graph usually has the next point as its maximum, this is a reflection so the equation will start with a negative. A = -0.96

B = π/182.5

It is given that [tex]\frac{1}{4}[/tex] Period = 91.25  --> P = 365

B = 2π/P

  = 2π/365

  = π/182.5

C = 0

No phase shift is given so C = 0

Input A, B, C, & D into the equation of a sin function:

[tex]R(t)=-0.96\sin\bigg(\dfrac{\pi}{182.5}t-0}\bigg)+2.3[/tex]

Answer:

The LCM of two numbers is the least common multiple. You want to find the least possible number that is divisible by the two numbers. So, you can list the factors of the two numbers. If there are factors that are repeated, put the repeated factors to the side. With the remaining factors, multiply the factors by each other and the repeated factors.

For example, let's try to find the least common multiple between 10 and 15.

Factors of 10: 2 * 5

Factors of 15: 3 * 5

The repeated factor is 5.

2 and 3 are left over. 2 * 3 = 6. 6 * 5 = 30. So, that is the least common multiple.

The GCF of two numbers is the greatest common factor. You want to find the greatest factor that is included in both numbers. So, again, you can list the factors of the two numbers and find the greatest factor that is repeated between the two numbers.

For example, let's try to find the greatest common factor between 30 and 45.

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 45: 1, 3, 5, 9, 15, 45

Between the two numbers, shared factors are 1, 3, 5, and 15. So, the greatest common factor is 15.

Hope this helps!

Answer:

d. 30

Step-by-step explanation:

The computation of the 35th percentile of this data set is shown below:

Before that first we have to series the number in ascending number

S. No          Numbers

1                       26

2                      29

3                      30

4                      30

5                      31

6                      32

7                      34

8                      35

9                       36

Now use the formula

Here n = 9

Percentile = 100

[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]

= 3.5th

= 3th + 0.5 (4th - 3th)

= 3th + 0.5 (30 - 30)

= 3th + 0

= 30

Answer:

[tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex]

Step-by-step explanation:

Let be [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex], this expression is simplified as follows:

1) [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex] Given

2) [tex]\sqrt[3]{4^{3}}-\sqrt[3]{2^{5}}\times \sqrt[3]{5^{3}}[/tex] Definition of power

3) [tex](4^{3})^{1/3}-(2^{2}\cdot 2^{3})^{1/3}\times (5^{3})^{1/3}[/tex] Definition of n-th root/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a^{b})^{c} = a^{b\cdot c}[/tex]

4) [tex]4 - (2^{2})^{1/3}\times 2\times 5[/tex] [tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]

5) [tex]4 - 10\times 4^{1/3}[/tex] Multiplication/Definition of power

6) [tex]4^{1/3}\cdot (4^{2/3}-10)[/tex] Distributive property/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]

7) [tex]\sqrt[3]{4}\times [(4^{2})^{1/3}-10][/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]/Definition of n-th root

8) [tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex] Definition of power/Result

Answer:

C. [tex] d = 15.81 units [/tex]

Step-by-step explanation:

Given:

2 end points on a graph => (5, 6) and (-4, -7)

Required:

Distance between them

SOLUTION:

Distance between two points in a graph can be calculated using [tex] distance (d) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

[tex] (-4, -7) = (x_1, y_1) [/tex]

[tex] (5, 6) = (x_2, y_2) [/tex]

Plug in the values into the formula and solve

[tex] d = \sqrt{(5 - (-4))^2 + (6 - (-7))^2} [/tex]

[tex] d = \sqrt{(5 + 4))^2 + (6 + 7))^2} [/tex]

[tex] d = \sqrt{(9)^2 + (13)^2} [/tex]

[tex] d = \sqrt{81 + 169} [/tex]

[tex] d = \sqrt{250} [/tex]

[tex] d = 15.81 units [/tex]

Answer:

15.81

Step-by-step explanation:

Answer:

The  upper limit is    

                   [tex]k = 52.94[/tex]

Step-by-step explanation:

From the question we  told that

     The  sample size is [tex]n = 16[/tex]

      The sample mean is  [tex]\= x = 50[/tex]

      The sample variance is  [tex]\sigma ^2 = 36[/tex]

For  a  95% confidence interval the confidence level is  95%

Given that the confidence level is 95% then the level of significance is  mathematically evaluated  as  

             [tex]\alpha = 100 - 95[/tex]

              [tex]\alpha = 5 \%[/tex]

              [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference- math dot armstrong dot edu), the value is  

              [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

             [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

 Here  [tex]\sigma[/tex] is the standard deviation which is mathematically evaluated as

                  [tex]\sigma = \sqrt{\sigma^2}[/tex]

substituting values

                  [tex]\sigma = \sqrt{36}[/tex]

=>                [tex]\sigma = 6[/tex]

So

                    [tex]E = 1.96 * \frac{6}{\sqrt{16} }[/tex]

                     [tex]E = 2.94[/tex]

The 95% confidence interval is mathematically represented as

                 [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

                [tex]50 -2.94 < \mu <50 +2.94[/tex]

                [tex]47.06 < \mu <52.94[/tex]

The  upper limit is    

                   [tex]k = 52.94[/tex]

Answer:

Step-by-step explanation:

Hello, if I take the following

2, 2, -5, 2, 2, -5, 2, 2, -5, 2, 2

The sum is 8*2-5*3=16-15=1 > 0

and

2 + 2 -5 < 0

2 - 5 + 2 < 0

-5 + 2 + 2 < 0

2 + 2 -5 < 0

2 - 5 + 2 < 0

-5 + 2 + 2 < 0

2 + 2 -5 < 0

2 - 5 + 2 < 0

-5 + 2 + 2 < 0

2 + 2 -5 < 0

2 - 5 + 2 < 0

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: It's B

Step-by-step explanation:

The table that represents the double number line is (b)

On the double number line, we have the following points

x: 0    1

y: 0    25

This means that as x increases by 1, y increases by 25.

So, we have:

x: 0  1    2    3   4

y: 0 25  50 75 100

The above is represented by the second table

Hence, the table that represents the double number line is (b)

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Answer:

60

Step-by-step explanation:

5 is 60 inch