Find the cost of fencing a square plot area 11025 sq m. at the rate of rupees 85 per sq m.

Answer:

4x^2-22x+30

=2(2x^2 - 11x + 15)

=2(2x^2 -6x -5x +15)

= 2 { 2x(x-3) - 5(x-3) }

= 2 (x-3) (2x - 5)

Step-by-step explanation:

Hey, there!!!

The answer is option B

here, we have;

=4x^2-22x+30

=4x^2-(10+12)x+30

= 4x^2-10x-12x+30

now, taking common,

=2x(2x-5) -6(2x-5)

= 2(x-3)(2x-5).

Hope it helps

Answer:

The sequence is 14, 19, 24, 29, 34, 39.

Step-by-step explanation:

Let's call the common difference (the difference between two consecutive terms) as d. We see that the second term is 19 and the 5th term is 34 and since 5 - 2 = 3, we add d 3 times to 19 to get 34 so therefore:

19 + 3d = 34

3d = 15

d = 5 so the first term is 19 - 5 = 14, the third would be 19 + 5 = 24, the fourth would be 24 + 5 = 29 and the sixth would be 34 + 5 = 39.

Answer:

(a) After t years, the height is

18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Step-by-step explanation:

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

Answer:

Explained below.

Step-by-step explanation:

Let X = systolic blood pressure measurements.

It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].

(a)

Compute the percentage of measurements that are between 71 and 89 as follows:

[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]

                        [tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]

The percentage is, 0.9973 × 100 = 99.73%.

Thus, the percentage of measurements that are between 71 and 89 is 99.73%.

(b)

Compute the probability that a person's blood systolic pressure measures more than 89 as follows:

[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]

                [tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]

Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.

(c)

Compute the probability that a person's blood systolic pressure being at most 75 as follows:

Apply continuity correction:

[tex]P(X\leq 75)=P(X<75-0.5)[/tex]

                [tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]

Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.

(d)

Let x be the blood pressure required.

Then,

P (X < x) = 0.15

⇒ P (Z < z) = 0.15

⇒ z = -1.04

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]

Thus, the 15% of patients are expected to have a blood pressure below 76.9.

(e)

A z-score more than 2 or less than -2 are considered as unusual.

Compute the z score for [tex]\bar x[/tex] as follows:

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

  [tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]

The z-score for the mean blood pressure measurement of 3 patients is more than 2.

Thus, it would be unusual.

Answer:

Expression = 2n³ - 20n

Step-by-step explanation:

Find:

Expression

Computation:

Assume given number is 'n'

Cube of number = n³

Twice of cube = 2n³

Subtract number = 20n

Expression = 2n³ - 20n

Answer:

Step-by-step explanation:

Hello, please consider the following.

a)

[tex](2x-2)^2 - (x+4)^2 \\\\=(2x-2-(x+4))(2x-2+x+4)\\\\=(2x-2-x-4)(3x+2)\\\\=\boxed{(x-6)(3x+2)}[/tex]

b)

[tex](3x+4) (3x-4)\\\\=(3x)^2-4^2\\\\=\boxed{9x^2-16}[/tex]

Thank you.

Answer: S₁₉ = 855

Step-by-step explanation:

T₄ = a + ( n - 1 )d  = 5 , from the statement above , but n = 4

       a + 3d  = 5 -------------------------1

S₆ = ⁿ/₂[(2a + ( n - 1 )d]  =  10, where n = 6

    = ⁶/₂( 2a + 5d )         = 10

    = 3( 2a + 5d ) = 10

    = 6a + 15d      = 10 -----------------2

Now solve the two equation together simultaneously to get the values of a and d

   a + 3d     = 5

   6a + 15d = 10

from 1,

a = 5 - 3d -------------------------------3

Now put (3) in equation 2 and open the brackets

6( 5 - 3d )  + 15d = 10

30 - 18d + 15d      = 10

30 - 3d                 = 10

            3d            = 30 - 10

             3d           = 20

                         d = ²⁰/₃.

Now substitute for d to get a in equation 3

           a = 5 - 3( ²⁰/₃)

           a = 5 - 3 ₓ ²⁰/₃

              = 5 - 20

          a  = -15.

Now to find the sum of the first 19 terms,

we use the formula

S₁₉ = ⁿ/₂( 2a + ( n - 1 )d )

     = ¹⁹/₂( 2 x -15 + 18 x ²⁰/₃ )

     = ¹⁹/₂( -30 + 6 x 20 )

     = ¹⁹/₂( -30 + 120 )

     = ¹⁹/₂( 90 )

     = ¹⁹/₂ x 90

     = 19 x 45

     = 855

Therefore,

S₁₉ = 855

Answer:

$12,78

Step-by-step explanation:

$142 × 0,15 = $21,3

$21,3 × 0,6 = $12,78

Part a)

There are 52 letters (26 lowercase and 26 uppercase), 10 digits, and 6 symbols. There are 52+10+6 = 68 different characters to choose from.

Adding up those subtotals gives

68^8+68^9+68^10+68^11+68^12 = 9.9207 * 10^21

different passwords possible.

======================================================

Part b)

Let's find the number of passwords where we don't have a special symbol

There are 52+10 = 62 different characters to pick from

Adding those subtotals gives

62^8+62^9+62^10+62^11+62^12 = 3.2792 * 10^21

different passwords where we do not have a special character. Subtract this from the answer in part a) above

( 9.9207 * 10^21)  - (3.2792 * 10^21) = 6.6415 * 10^21

which represents the number of passwords where we have one or more character that is a special symbol. I'm using the idea that we either have a password with no symbols, or we have a password with at least one symbol. Adding up those two cases leads to the total number of passwords possible.

======================================================

Part c)

The answer from part a) was roughly 9.9207 * 10^21

It will take about 9.9207 * 10^21  nanoseconds to try every possible password from part a).

Divide 9.9207 * 10^21  over 1*10^9 to convert to seconds

(9.9207 * 10^21 )/(1*10^9) = 9,920,700,000,000

This number is 9.9 trillion roughly.

It will take about 9.9 trillion seconds to try every password, if you try a password per second.

------

To convert to hours, divide by 3600 and you should get

(9,920,700,000,000)/3600 = 2,755,750,000

So it will take about 2,755,750,000 hours to try all the passwords.

------

Divide by 24 to convert to days

(2,755,750,000)/24= 114,822,916.666667

which rounds to 114,822,917

So it will take roughly 114,822,917 days to try all the passwords.

------

Then divide that over 365 to convert to years

314,583.334246576

which rounds to 314,583

It will take roughly 314,583 years to try all the passwords

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

All values are approximate, and are roughly equivalent to one another.

A) 9,920,671,339,261,325,541,376 different passwords are available for this computer system.

B) 875,353,353,464,234,606,592 of these passwords contain at least one occurrence of at least one of the six special characters.

C) It would take 314,582.42 years for a hacker to try every possible password.

To determine how many different passwords are available for this computer system; how many of these passwords contain at least one occurrence of at least one of the six special characters; and how long it takes a hacker to try every possible password, assuming that it takes one nanosecond for a hacker to check each possible password, the following calculations must be performed:

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Answer:

Step-by-step explanation:

The comparison will be the same if you subtract the right side and compare to zero:

  a/b ?? c/d . . . . . . . using ?? for the unknown comparison symbol

  a/b - c/d ?? 0 . . . . subtract the fraction on the right

  (ad -bc)/bd ?? 0 . . . combine the two fractions

  ad - bc ?? 0 . . . . . . multiply by bd to make the job easier

__

5/6 and 2/5

  5(5) -6(2) = 25 -12 > 0   ⇒   5/6 > 2/5

4/10 and 7/8

  4(8) -10(7) = 48 - 70 < 0   ⇒   4/10 < 7/8

3/12 and 1/4

  3(4) -12(1) = 0   ⇒   3/12 = 1/4

_____

Of course, you can use your calculator (or your memory) to change each of these to a decimal equivalent. The comparison should be easy at that point.

  0.833 > 0.400

  0.400 < 0.875

  0.250 = 0.250

Answer:

3  -1  -2

5   1  6

Step-by-step explanation:

An augmented system has the coefficients for the variables and then the solution going across

Rewriting the equations to get them in the form

ax + by = c

-3x+y =2

3x-y =-2

5x+y = 6

The matrix is

3  -1  -2

5   1  6

Answer: a) 0.003

b) 0.125

c) 0.047

Step-by-step explanation:

We have a set of 8 numbers {1,2,...,8}

Let's analyze each case:

a) 5 and 8 are picked. The probability here is:

In the first selection, we have two possible picks (we can pick 5 or 8), so we have two possible outcomes out of 8 total outcomes,  the probability for the first selection is:

P = 2/8 = 1/4.

Now, if one of those numbers was picked in the first selection, only one outcome is possible in this second selection, (if before we picked a 5, here we only can pick an 8, or if in the first selection we picked an 8, here we only can pick a 5.)

the probability is:

P = 1/8

The joint probability is equal to the product of the individual probabilities, so here we have:

P = (1/4)*(1/8) = 1/32 = 0.003

b) The numbers match (we draw two sixes, for example) :

In the first selection, we can have any outcome (the only requirement is that in the second selection we pick the same outcome), so the probability is:

P = 8/8 = 1

in the second selection, we can have only one outcome, so here the probability is:

P = 1/8

The joint probability is p = 1/8  = 0.125

c) The sum is smaller than 4:

The combinations are:

1 - 1  , 1 - 2  and 2 - 1

We have 3 combinations, and the total number of possible combinations is:

8 options for the first number and 8 options for the second selection:

8*8  = 64

The probability is equal to the number of outcomes that satisfy the sentence (3) divided by the total number of outcomes (64):

P = 3/64 = 0.047

Answer:

25 CAN be written as a fraction.

=> 250/10 = 25

Square root of 14 is 3.74165738677

It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION,  but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION

=> 374/100

-1.25 CAN be written as a fraction.

=> -5/4 = -1.25

Square root of 16 CAN also be written as a fraction.

=> sqr root of 16 = 4.

4 can be written as a fraction.

=> 4 = 8/2

Pi = 3.14.........

It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION

=> 314/100

.6 CAN be written as a fraction.

=> 6/10 = .6

Answer: (16,3)  and (4,0)

Step-by-step explanation:

Using the equation x-4y=4  is asking what is the value of x if the value of y is 3. So plot it into the equation and solve for x.

x-4(3)=4  multiply the left side

x - 12 = 4   add  12 to both sides

x= 16

You will now have the coordinates (16,3)  

In the second pair it gives the x coordinate which is 4 but we need to solve for y.  

4 - 4y=4  subtract 4 from both sides

-4        -4

 -4y = 0  Divide both sides by 4

    y = 0

The ordered pair will be (4,0)

Answer:

1. add 1/2x to both sides

a. you want to combine the like terms. in this case, it is the x variable.

you are left with 7/6x = 5

2. multiply by 6/7

a. the reciprocal of 7/6 will cancel out the values

Answer:

D. The zeros are the hot dog prices that give $0.00 profit (no profit).

Step-by-step explanation:

Given the function  y=-2(x-3)² + 4

The zeros of the function are the points at which the graph of the function crosses the x axis if plotted. y is the daily profit (in hundreds of dollars) and x is the price of the hot dog. To find the zeros, we substitute x = 0 and solve.

Therefore:  y=2(x-3)² + 4

0 = 2(x-3)² + 4

-2(x² - 6x + 9) + 4 = 0

-2x² + 12x - 18 + 4 = 0

2x² - 12x + 18 - 4 = 0

2x² - 12x + 14 = 0

2(x² - 6x + 7) = 0

x² - 6x + 7 = 0

Solving the quadratic equation gives:

x = 3 + √2 and x = 3 - √2

This means that the graph crosses x at 3 + √2 and 3 - √2.

The zeros of the function are 3 + √2 and 3 - √2. The zeros of the function is the point where y = 0, that is the point that the hot dog prices that give $0.00 profit (no profit).

Answer:

Step-by-step explanation:

( See the attached picture )

Now,

Mean = [tex] \mathsf{\frac{Σfx}{n} }[/tex]

[tex] \mathsf{ = \frac{250}{19} }[/tex]

[tex] \mathsf{ = 13.15}[/tex]

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

In the case of repeated data , follow the steps given below to calculate the mean :

Hope I helped!

Best regards!

Answer:

29 years of experience.

Step-by-step explanation:

So let's take the expression step by step.  Remember that you need to follow the order of precedence here for the operations.  Parentheses, exponentials, multiplication, and addition.

-5 + { 4 * 6 + 3 + 1 + [ 3 - ( 4 - 8 ) + ( 3 - 2 ) ] }

-5 + { 4 * 6 + 3 + 1 + [ 3 - ( -4 ) + ( 1 ) ] }

-5 + { 4 * 6 + 3 + 1 + [ 3 + 4 + 1 ] }

-5 + { 4 * 6 + 3 + 1 + [ 8 ] }

-5 + { 24 + 3 + 1 + 8 }

-5 + { 36 }

29

So the teacher has 29 years of experience.

Cheers.

Answer:

DE

Step-by-step explanation:

I hope this helps!

Answer: You will need 8 cup scales

Step-by-step explanation:

kg=1000 grams

2000/250=8

Answer:

Step-by-step explanation:

Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.

A) The polynomial in standard form is therefore   - 3x⁸ + 2x⁵ + 4x³. We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.

B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8

C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵,  4x³ and - 3x⁸.

D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as  -3x⁸ + 2x⁵ + 4x³, the leading term will be  - 3x⁸

E) Given the leading term to be  - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3

Answer:

When all possible differences between pairs of population means are evaluated not with an F test, but with a series of regular t tests, the probability of at least one:

A. type I error is larger than the specified level of significance.

B. type II error is larger than the specified level of significance.

C. type I error is smaller than the specified level of significance.

D. type II error is smaller than the specified level of significance.

Answer :  Type I error is larger than the specified level of significance.( A )

Step-by-step explanation:

An F test is a test that is used to test whether the variances between pairs of populations are equal while a T test is a test used to check if a pair of population are equal not considering the fact that the variances of the population are different .

When a T test is used to evaluate all possible differences between pairs of population instead of F test there is a probability of atleast one type 1 error larger than the specified level of significance.

Answer:

Y

Step-by-step explanation:

You see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.

Y represents the greater number.

We see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.

A set of values that display an actual role. On graphs it is also a pair of numbers: the first variety indicates the gap along, and the second variety indicates the distance up or down. As an example, the factor (12,5) is 12 units long, and five units up.

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#SPJ2

See the attached picture

[tex]\bold{\text{Answer:}\quad \dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1}[/tex]

Step-by-step explanation:

A "horizontal" ellipse means that the x-radius is bigger than the y-radius.  Thus, x is the major axis and y is the minor axis.

The equation of an ellipse is: [tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]      where

It is given that the center is at (-4, 5) --> h = -4, k = 5

It is given that the major axis has a length of 18 --> x-radius = 9

It is given that the minor axis has a length of 10 --> y-radius = 5

Input those values into the equation of an ellipse to get:

[tex]\dfrac{(x-(-4))^2}{9^2}+\dfrac{(y-5)^2}{5^2}=1[/tex]

Simplify to get:

[tex]\dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1[/tex]

Answer:

Step-by-step explanation:

Interesting problem.

At 6<x<8,

f(x) = x-7

at 5<x<8

g(x) = (15-x)/2

=>

y(x)

= f(x)*g(x)

= (x-7)(15-x)/2

= (x^2+22x-105)/2

differentiate y(x) with respect to x,

y'(x) = -x+11

at x = 7,

y'(7) = -(7) + 11 = 4

Answer:

The  estimate is

             [tex]52.02 < \mu < 55.78[/tex]

Step-by-step explanation:

From the question we are told that

    The sample mean is [tex]\ = x = 53.9[/tex]

     The sample size is  n =  24

      The standard deviation is  [tex]\sigma = 5.6[/tex]

Given that the confidence level is  90% 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} } =Z_{\frac{0.10 }{2} } = 1.645[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because    [tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (  [tex]1 - \alpha[/tex] ) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

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

substituting values

         [tex]E = 1.645 * \frac{5.6 }{ \sqrt{24} }[/tex]

          [tex]E = 1.880[/tex]

The  estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as

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

substituting values

         [tex]53.9 - 1.880 < \mu < 53.9 + 1.880[/tex]

         [tex]52.02 < \mu < 55.78[/tex]

Answer:

c = 0.25m + 50

Step-by-step explanation:

Let c = cost; let m = number of minutes.

c = 0.25m + 50

Answer:

k = -2

Step-by-step explanation:

83=4k-7(1+7k)

Distribute

83=4k-7-49k

Combine like terms

83 = -45k -7

Add 7 to each side

83+7 = -45k-7+7

90 = -45k

Divide each side by -45

90/-45 = -45k/-45

-2 = k

Answer:

Step-by-step explanation:

Step 1: Use 7 to open the bracket :

-7(1+7k)=-7-49k

Step 2: Collect like terms

Step 3 : Divide both sides of the equation by -45

[tex]83=4k-7(1+7k) \\ \\83 = 4k-7-49k\\\\ 83+7=4k-49k\\\\90 = -45k\\\\\frac{90}{-45} = \frac{-45k}{-45} \\\\k = -2[/tex]

Answer:

154.2

Step-by-step explanation:

143 plus

156 plus

172 plus

133 plus

167 = 771

divide by 5 equals 154.2