What is an equivalent form of 15(p + 4) − 12(2q + 4)?

15p − 24q + 12
15p − 24q + 8
60p − 72q
−9pq

Answer:

[tex]\sf 10m\sqrt{3xm}[/tex]

Step-by-step explanation:

To simplify the expression, factorize 12. For every  two items inside the square root, take one outside.

[tex]\sf 5\sqrt{12xm^3} = 5\sqrt{2*2*3*x*m*m*m}[/tex]

              [tex]\sf = 5*2*m\sqrt{3xm}\\\\=10m\sqrt{3xm}[/tex]

The equation that suits the model is given as  I = Prt and the interest the friend will have after her college graduation in 4 years will be $240

The formula to be used to is given as :

              I = Prt      (1)

where, I = simple interest

            P = principal amount or amount initially deposited.

            r = annual interest rate

            t = time

According to the question we have been given that

        P = $1000

        r = 0.06

        t = 4 years

Putting the required values in equation (1) we get

       I = 1000*0.06*4

       I = 240

hence the equation that suits the model is given as

           I = Prt

and the interest the friend will have after her college graduation in 4 years will be $240

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Answer:

K is the midpoint of JL, so it is halfway between J and L (see diagram).  If JK is 7 units long, then so is KL. The length of the entire segment JL is 4x - 2, so

4x -2=14

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

[tex]A=\begin{bmatrix}2 & 2 \\3 & 4 \end{bmatrix}\\\\\\B=\begin{bmatrix}0 & 4 \\2 & -3 \end{bmatrix}\\\\\\C=\begin{bmatrix}4 & 6 \\5 & 6 \end{bmatrix}\\\\\\(X-4B)*A=C\\\\X-4B=C*A^{-1}\\\\X=C*A^{-1}+4B\\[/tex]

[tex]\begin{array}{|cc|cc|}A&&A^{-1}&\\---&---&---&---\\2&2&1&0\\3&4&0&1\\---&---&---&---\\1&1&\frac{1}{2}&0\\0&1&\frac{-3}{2}&1\\---&---&---&---\\1&0&2&-1\\0&1&\frac{-3}{2}&1\\---&---&---&---\\\end {array}\\\\[/tex]

[tex]X=C*A^{-1}+4B=\begin{bmatrix}4 & 6 \\5 & 6 \end{bmatrix}*\begin{bmatrix}2&-1\\\frac{-3}{2}&1\end{bmatrix}+4*\begin{bmatrix}0 & 4 \\2 & -3 \end{bmatrix}[/tex]

[tex]X=\begin{bmatrix}-1 & 2 \\1 & 1 \end{bmatrix}+\begin{bmatrix}0 & 16 \\8 & -12 \end{bmatrix}\\\\\\X=\begin{bmatrix}-1 & 18 \\9 & -11 \end{bmatrix}\\[/tex]

Answer:

Step-by-step explanation:

First term of the sequence is 10 and common difference is 3.

a

1

​

 = 10 and d = 3

Next term = a

2

​

=a

1

​

+d=10+3=13

a

3

​

=a

2

​

+d=13+3=16

Thus, first three terms of the sequence are 10, 13 and 16.

Let 100 be the nth term of the sequence.

a

n

​

=a

1

​

+(n−1)d

100=10+(n−1)3

90=(n−1)3

n−1=30

n=31, which is a whole number.

Therefore, 100 is the 31

st

 term of the sequence.

The value of x in the equation x² - 2 x + 5 = 2 is 1 ± i √2.

We are given the equation:

x² - 2 x + 5 = 2

We need to solve the equation to find the value of x.

For this, we will first subtract 2 from both the sides:

x² - 2 x + 5 - 2 = 2 - 2

x² - 2 x + 3 = 0

Now, we will solve for the value of x:

D = b² - 4 ac

D = (- 2)² - 4 (3)(1)

D = 4 - 12

D = - 8

√D = 2 i √2

Now putting it in quadratic formula, we get that:

x = (- b ± √D) / 2 a

x = (2 ± 2 i √2) / 2 (1)

x = 1 ± i √2

Therefore, the value of x in the equation x² - 2 x + 5 = 2 is 1 ± i √2.

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Your question is incomplete. Please refer the content below:

What is the solution to the equation for x:

x² - 2 x + 5 = 2

The entries that complete the blanks are 20.39, 20.78, 21.17 and 20 + 0.39n

The given parameters are

Invitation = $20

Stamps = $0.39 per stamp

So, the total amount spent is calculated as

Total = Invitation + Stamps * Number stamps

This gives

Total = 20 + 0.39 * Number stamps

For stamps 1, 2, 3 and n, we have

Total = 20 + 0.39 * 1 = 20.39

Total = 20 + 0.39 * 2 = 20.78

Total = 20 + 0.39 * 3 = 21.17

Total = 20 + 0.39 n

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Answer:

2 and 2/25 miles per hour.

Step-by-step explanation:

Harry's speed = distance / time

                        = 10 4/10 / 5

                        = 104/10 * 1/5

                         = 104/50

                          = 2 4/50

                          = 2 2/25

Answer:

3

Step-by-step explanation:

[tex]\mathrm{a = \sqrt{A} = \sqrt{9} = 3}[/tex]

The two triangles are similar triangles and the graph of the triangles are attached

The coordinates of the triangle are given as

A (0, 3), B (3, 3) and C (3, -1)

So, we enter the above coordinates in a graphing calculator

See attachment for the graph of the triangle

Multiply each coordinate by a scale factor of 3 (k=3).

Here, we have

A' 3 * (0, 3), B' 3 * (3, 3) and C' 3 * (3, -1)

This gives

A' (0, 9), B' (9, 9) and C' (9, -3)

Next, we enter the above coordinates in a graphing calculator

See attachment for the graph of the triangle

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Answer:

In this particular type of question we need to understand that perfect squares are the squares of the integers numbers and perfect square always end in 0,1,4,5,6,9.A perfect square number never ends with 2,3,7 or 8 .This is the first observation you will make to check if the number is a perfect square or not.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The diameter of the tank is 25.8 feet.

We are given the volume of water tank. Also, we are provided the formula relating volume and density.

Rewriting the formula -

V = 1/6×π×d³, where d represents the diameter. Taking the value of π as 3.14

Rewriting the formula according to diameter -

d³ = 6V/π

Keep the values in formula to find the value of diameter of water tank

d³ = 6×9000/3.14

Performing multiplication and division to find the value of diameter

d³ = 54000/3.14

Performing division to find the value of diameter of water tank

d³ = 17197.45

d = ∛17197.45

Taking square root to find the value of diameter of water tank

d = 25.8 feet

Hence, the diameter of tank is 25.8 feet.

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16504 divided by 55 equals

300+ 4/55.

First we know about -

Divisor: The number by which the dividend is divided.

Quotient: The result of division.

Remainder: The amount that is left over after division.

Rules for the Division -

1. Take the first digits of the dividend, the same number of digits that the divisor has. If the number taken from the dividend is smaller than the divisor, you need to take the next digit of the dividend.

2. Divide the first number of the dividend (or the two first numbers if the previous step took another digit) by the first digit of the divisor. Write the result of this division in the space of the quotient.

3. Multiply the digit of the quotient by the divisor, write the result beneath the dividend and subtract it. If you cannot, because the dividend is smaller, you will have to choose a smaller number in the quotient until it can subtract.

4. After subtraction, drop the next digit of the dividend and repeat from step 2 until there are no more remaining numbers in the dividend.

        0 0 3 0 0

5 5 ) 1 6 5 0 4

 − 0        

   1 6      

 −   0      

   1 6 5    

 − 1 6 5    

       0 0  

     −   0  

         0 4

       −   0

           4

16504 divided by 55 equals

300 with a remainder of 4

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The irrational number in this data-set is given by the square root of 3.

In this problem, we have that:

Hence:

The irrational number in this data-set is given by the square root of 3.

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Answer:

x=1 & y=0

Step-by-step explanation:

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 5}(x-\stackrel{x_1}{7})[/tex]

Given that there are 6 circles and 3 squares, the simplest ratio of squares to circles is 1 : 2 or 1 to 2 or 1/2.

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

It can be expressed in different ways:

1) Use the ":" to separate the values : a : b

2) Use the word "to" : a to b

3) Write it in fraction: a / b

If there are 6 circles and 3 squares. then the ratio of squares to circles can be written as:

3 : 6 or 3 to 6 or 3/6

To simplify the ratio, divide both numbers in the ratio by the same number until they cannot be divided any more.

Divide both number by 3.

3 : 6    =    1 : 2

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Step-by-step explanation:

y=3x

y=x-4

3x=x-4

2x=4

x=2

y=3*2

y=6

(2,6)

x=2

y=6

The probability that the sample contains 2 female voters is 0.31104

Binomial distribution uses two values; n and p. n represent the counts of sample that are being collected. On the other hand, p represents the chances of being successful on any trial. Using the two values, the probabilities are computed for binomial distribution.

Probability that a random voter is female is 0.40(p).

Sampled voters are 6(n).

Let X be the number of females in the sampled voters.

Then,

X∼ Bin (n, p)

∼Bin (6,0.4)

Probability that the sample contains exactly 2 female voters is,

P (X =2) = 6C2 (0.4)2 (1−0.4)6−2

=0.31104

Therefore, the probability that the sample contains exactly 2 female voters is 0.31104

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Answer:

25

Step-by-step explanation:

Arrange numbers to ascending order :

5,8,10,20,25,30,35,40,45

Cross of the smallest and biggest number until you left with one in the middle

1. The y-intercept is: 12.

2. The y-intercept represent the initial cost that excluding the cost per DVD.

3. Your friend is incorrect. A dozen DVD's is gotten for $84.

4. 50 DVD's from the website would cost: $312.

The y-intercept is the value of the y-coordinate of the point where the line intercepts the y-axis.

The y-intercept is referred to as the starting value or initial value. At this point, x = 0.

1. First, find the slope (m) of the line using two points, (1, 18) and (2, 24):

Slope (m) = change in y/change in x = (24 - 18)/(2 - 1) = 6/1

Slope (m) = 6

Substitute m = 6 and (x, y) = (1, 18) into y = mx + b to find the y-intercept, b:

18 = 6(1) + b

18 - 6 = b

b = 12 (y-intercept)

Substitute m = 6 and b = 12 into y = mx + b:

y = 6x + 12

The y-intercept that connects all the data points is: 12.

2. The y-intercept in this context represents the initial cost that excludes the charge for each DVD.

3. Substitute x = 12 into y = 6x + 12 and solve to see if y equals 90:

y = 6(12) + 12

y = 84 [not equal to $90)]

Thus, your friend is incorrect. a dozen DVD's can be gotten for $84.

4. Substitute x = 50 into y = 6x + 12:

y = 6(50) + 12

y = 312

It would cost $312 to get 50 DVD's from the website.

The graph for the points (1, 18), (2, 24) , and (3, 33) is shown below.

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to get the equation of any straight line, we simply need two points off of it, hmmm let's take a peek at the y-intercept of the line above

[tex]y = 5x \stackrel{\stackrel{b}{\downarrow }}{+2} \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies \stackrel{y-intercept}{(0~~,~~2)}[/tex]

so we're really looking for the equation of a line that passes through (2 , -3) and (0 , 2)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{2}}} \implies \cfrac{2 +3}{-2} \implies -\cfrac{ 5 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-\cfrac{ 5 }{ 2 }}(x-\stackrel{x_1}{2}) \implies y +3= -\cfrac{ 5 }{ 2 } (x -2)[/tex]

Based on the number of customers who owned parrots, dogs and parrots, and dogs, the number who owned either a dog or a parrot were 55 customers

The number of people who owned a parrot was 42. 33 people also owned a dog. Some of these people owned both a dog and a parrot and they numbered 20.

To find the number of customers who owned either a dog or a parrot, the formula is:
= Number of customers who owned a dog + Number of customers who owned a parrot - Number of customers who owned both a dog and parrot

= 33 + 42 - 20

= 75 - 20

= 55 customers

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After pumping all of container A into container B there will remain empty space in B = 78.5 ft³

The percentage for this empty space is of the entire volume is = 3.4 %

What is volume of cylinder?

Volume of cylinder is calculated as;

v = π r² h  

Since, Container A has a diameter of 18 feet and a height of 9 feet.

Then, Radius = 18/2 = 9 ft

Hence, Volume of Container A = π r² h  

                                                = 3.1416 * 9 * 9 * 9

                                                = 2,290.22 ft³

Since,  Container B has a diameter of 16 feet and a height of 11 feet.

Then, Radius = 16/2 = 8 ft

Hence, Volume of Container B = π r² h

                                               = 3.1416 * 8 * 8 * 11

                                               = 2,211.68 ft³

After pumping all of container A into container B there will remain empty space in B = 2,290.22 - 2,211.68 = 78.5 ft³

And, The percentage for this empty space is of the entire volume is,

78.5/2,290.22 = 0.03427 *100 = 3.4 %

So, After pumping all of container A into container B there will remain empty space in B = 78.5 ft³

The percentage for this empty space is of the entire volume is = 3.4 %

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Answer: No

Step-by-step explanation:

a) The explosion does violate the town regulation

b) The two physical quantities are the I(intensity of the sound) and

       [tex]I_{o}[/tex] (detectable intensity)

The values that we have been given are

        L = loudness of the sound = 10 log(I/[tex]I_{o}[/tex])

        I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]

        [tex]I_{o}[/tex] = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]

Putting the required value in the equation of the loudness we get

      a)       L = [tex]10 log(\frac{1.65*10^{2} }{10^{-12} } )\\[/tex]

             L = 10 * 14.217 dB = 142.17 dB

And according to the town regulation the loudness of the construction work should not exceed 100dB.

Thus the explosion is  in violation of the town regulation as it exceeds 100dB.

b)  the two physical value we have to calculate are I which is intensity of the sound in watts per square meter and [tex]I_{o}[/tex] which is intensity of barely audible sound. The respective values are

        I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]

        [tex]I_{o}[/tex] = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]

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