Parallelogram I is a scaled copy of parallelogram H.


What scale factor takes parallelogram H to parallelogram I?

The differential equation used to solve an equation of the amount (mass) of salt within the tank at any given time t is [tex]\frac{ds}{0.04s-0.1} = dt[/tex].

Let the amount of salt any time t is given by s kg then the rate of change of s with respect to t is given by,

[tex]\frac{ds}{dt}[/tex] = (rate of salt out) - (rate of salt in)

Rate of salt in = 0.01 kg/litre × 10 litre/min = 0.1 kg/min

Rate of salt out = s/500 kg/litre × 20 litre/min = (20s/500) kg/min

A differential equation can be made on the concept that the rate of change of salt is the difference between the rate of in and the rate of out.

That gives us when combined,

[tex]\frac{ds}{dt} = 0.04s -0.1[/tex]

Now solving this differential equation,

[tex]\frac{ds}{0.04s-0.1} = dt[/tex]

Integrating both sides,

[tex]\int\ {\frac{ds}{0.04s-0.1} } \, = \int dt[/tex]

[tex]\frac{ln(0.04s -0.1)}{0.04} = t+C_{1}[/tex]

[tex]ln(0.04s - 0.1) = 0.04t +0.04C = 0.04t +C_{2}[/tex]

[tex]0.04s - 0.1 =e^{0.04t + C_{2} } =Ae^{0.04t}[/tex]

Now at t = 0, s = 10 kg

0.04(10) - 0.1 = A

A = 0.3

So the differential equation can be written as,

[tex]0.04s - 0.1 = 0.3e^{0.04t}[/tex]

Now time at which no salt is left which means s = 0 at some time t

[tex]0.1 - 0.04(0) = -0.3e^{-20t}[/tex]

The equation is not further solvable as we can see.

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It takes 1.5 years for Evelyn to reach $5,750.

In this question, it is clear that principal amount that Evelyn deposited is $5,000. The annual interest rate as per the question is 0.1%. The final amount that Evelyn gets is $5,750.

Lets assume that it will take t years for Evelyn to get a final amount of $5,750.

So,

Principal amount, P = $5,000

annual rate, r = 0.1%

Final amount, A = $5,750

From the formula for simple interest, we have,

A = P( 1 + rt)

Hence, t = (1/r)  x  { (A/P) -1 }

              = 1/0.1 x { (5750/5000) - 1}

               = 10 x { 1.15 - 1 }

               = 10 x  0.15

               =1.5

Therefore it will take 1.5 years for Evelyn to get a total amount of $5,750 provided she deposited an amount of $5,000 at an annual simple interest rate of 0.1%

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Explanation

Step 1

et

w represents the cost of gift-wrapping.

then

Jessie spent a total of $14

total= 14

the cost for postage=$2.25

the cost of the gift( itself)=9.50

in words, the total is

the total cost is the cost of the gift plus the cost of the postage plus the cost of gift-wrapping

Now,replace

For the given statement, the length and width of the pool are 141 feet and 47 feet respectively.

The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle. In the aforementioned illustration, a rectangle with dimensions of 4 inches long by 3 inches wide has a surface area of 12 square inches. 4 plus 3 equals 12, so. A rectangle's area is calculated by multiplying its length by its width. Therefore, the product "l w" is the formula for the area, "A," of a rectangle whose length and breadth are "l" and "w," respectively.

Rectangular area is equal to (length breadth) square units.

Given,

length of the pool = 3 (width of the pool)

Let width of the pool = x

Length of the pool = 3x

Area of the pool = Length × Width

6627 = x × 3x

⇒ 3x² = 6627

⇒ x² = 2209

⇒ x = 47

⇒ 3x = 47 × 3

⇒  141

This implies that the length and width of the pool are 141 feet and 47 feet respectively.

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The number of ways to choose the total number of participants required by the event coordinator is 54,600.

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By finding coterminal angles, we conclude that another way of writing the angle 530° is 170°.

For any angle A, we define the family of coterminal angles B as:

B = A + n*360°.

Where n is an integer different than zero.

In this case we have A = 530°

Then the coterminal angles are:

B = 530° + n*360°

If we define n = -1, then:

B = 530° - 360° = 170°

So 170° is another way of writing 530°.

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The rate of change of water being pumped out of the pool over time is (C) -2.

So, the linear relationship is:

Look at the values of y: 8, 6, 4, 2

So, the rate of change will be -2.

Therefore, the rate of change of water being pumped out of the pool over time is (C) -2.

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The complete question is given below:
The table shows the linear relationship between the amount of water being pumped out of a pool over time. Based on the table, what was the rate of change in the amount of water being pumped out of the pool over time?

(A) 2

(B) 10
(C) -2
(D) -10

Step-by-step explanation:

jsjsnsnsnnsnskskskskskskwwkwkkww

In a single year, factories create a total of 21550 gallons.

In both imperial and US customary units, the gallon is a unit of volume.A gallon is a unit of measurement for liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.

We have been given that

Lemonade = 11,650 gallons

Ice tea = 4,950 fewer than lemonade

Root beer = 3,500 fewer than Ice tea.

After calculating

Ice tea = 11,650 - 4,950

Ice tea = 6700 gallons

Root beer = 6700 - 3,500

Root beer = 3200 gallons

Total  factory produced in one year

= 11,650 + 6700 + 3200

Hence , 21550 gallons are total factory produced in one year.

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Based on the number of steps it took Shawn to get home from outside the basketball court, the number of steps needed for 8 one-way trips is 3,432 steps

Each trip that Shawn takes from outside the basketball court to his house, and from his house to outside the basketball court, will take 429 steps.

If Shawn then takes 8 one - way trips, the number of steps till he gets either home or the basketball courts is:

= Number of steps per trip x Number of trips

= 429 x 8

= 3,432 steps

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Different combinations of colors and dashboard options are available to the buyer who can pick between 2 of 5 seat colors and 3 of 4 options for dashboard accessories is 40.

As given in the question,

Possible combination for any buyer of a new sports car

Pick between 2 of 5 seat colors

⁵C₂ = 5! / (2!)(5-2)!

      = 5!/ (2!)(3!)

      = 10

Pick between 3 of 4 options for dashboard accessories

⁴C₃ = (4!)/ (3!)(4-3)!

     = (4!)/ (3!)(1!)

     = 4

Total different combinations of colors and dashboard options = 10 × 4

                                                                                                       = 40

Therefore, different combinations of colors and dashboard options are available to the buyer is 40.

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[tex] \frac{2}{7} \times \frac{5}{6} ( \frac{10}{3} \times \frac{2}{5} ) \times \frac{1}{5} \\ = \frac{2}{7} \times \frac{5}{6} ( \frac{20}{15} ) \times \frac{1}{5} \\ = \frac{2}{7} \times \frac{100}{90} \times \frac{1}{5} \\ = ( \frac{2}{7} \times \frac{10}{9}) \times \frac{1}{5} \\ = \frac{20}{63} \times \frac{1}{5} \\ = \frac{20}{315} \\ = \frac{4}{63} [/tex]

ATTACHED IS THE SOLUTION

The circumference of a circle with diameter 2.76 m is 8.66 m.

What is Circumference?

Circumference of a circle is perimeter of circle.

Given that;

Diameter of a circle = 2.76 m

Since, Circumference of  a circle = 2πr

Where, r is radius of circle.

Now, Diameter of a circle = 2.76 m

Then, Radius of a circle = 2.76/2 = 1.38 m

Hence, Circumference of  a circle = 2πr

Substitute all the values;

Circumference of  a circle = 2 x 3.14 x 1.38

                                        = 8.66 m

Thus, The circumference of a circle with diameter 2.76 m is 8.66 m.

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The most appropriate choice for exponent will be given by-

-31 is the required answer. The second option is correct

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2\times 2\times 2\times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a \times.....\times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^m \times a^n = a^{m + n}\\\frac{a^m}{a^n} = a^{m - n}\\a^ 0 =1\\(a^m)^n = a^{mn}\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\a^{-m} = \frac{1}{a^m}[/tex]

Here,

[tex]5s \times 2^3 + (h-1)^2\\h = 4, s = -1\\5(-1) \times 8 + (4 - 1)^2\\-40 + 9\\-31[/tex]

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Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Simplification of the given expression to single complex number are as follow :

9. -11 +4i

13. 30 - 10i

17.20

21. (3 + 5i)/2

25.  -1

As given,

To simplify the following expressions to a single complex number,

9) (- 5 + 3 i) - (6 - i)

   = - 5 + 3 i - 6 + i

   = - 5 - 6 +3i + i

   = - 11 + 4 i

13) (6 - 2 i) 5

    = (6 x 5) - (2  x 5) i

    = 30 - 10 i

17) (4 - 2 i) (4 + 2 i)

    = [tex]4^{2} - (2i)^{2}[/tex]

    = 16 - 4 [tex]i^{2}[/tex]

    = 16 - 4 (-1)

    = 16 + 4

    = 20

21) [tex]\frac{-5+3i}{2i} = \frac{i(-5+3i)}{2i^{2}} = \frac{-5i + 3i^{2} }{2(-1)}[/tex]

    = [tex]\frac{-5i+3(-1)}{-2} = \frac{3+5i}{2}[/tex]

25) [tex]i^{6} = (i^{2})^{3} = (-1)^{3} = -1[/tex]

Note: To simplify a fraction where denominator has complex component (i) as coefficient, multiply both numerator and denominator by i to eliminate i from denominator (by converting it to real number)

Therefore, simplification of  the given expression to single complex number are as follow :

9. -11 +4i

13. 30 - 10i

17.20

21. (3 + 5i)/2

25.  -1

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The correct statements regarding sum and subtraction with negative numbers are given as follows:

When two negative numbers are added, the result is negative, as we keep the signal and then add the absolute amounts of each value, for example:

-5 + (-5) = -(5 + 5) = -10.

Hence the fourth statement is correct, while the first and the third are not.

When we subtract two negative numbers, we first transform the second number to positive, meaning that the result can be either positive or negative, as the result will take the signal of the higher value and their absolute amounts are subtracted.

Hence:

Hence the fifth and the sixth statements are correct.

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The scale drawing height is 4 cm and the actual drawing length is 42 in

The complete question is added as an attachment

From the attachment, we have the ratio to be given as

Scale ratio, 1 cm : 6 in

Rewrite as

Scale measurement : Actual measurement = 1 cm : 6 in

In this question, we have

Actual measurement = 24 inches

This means that

Scale measurement : 24 in = 1 cm : 6 in

Multiply 1 cm : 6 in by 4

Scale measurement : 24 in = 4 cm : 24 in

By comparison, we have

Scale measurement = 4 cm

Hence, the scale drawing height is 4 cm

Recall that

Scale ratio, 1 cm : 6 in

Rewrite as

Scale measurement : Actual measurement = 1 cm : 6 in

In this question, we have

Scale measurement = 7 cm

This means that

7 cm : Actual measurement = 1 cm : 6 in

Multiply 1 cm : 6 in by 7

7 cm : Actual measurement = 7 cm : 42 in

By comparison, we have

Actual measurement = 42 in

Hence, the actual drawing length is 42 in

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Answer:

8 and 9

Step-by-step explanation:

consider perfect squares either side of 78

64 < 78 < 81 , then

[tex]\sqrt{64}[/tex] < [tex]\sqrt{78}[/tex] < [tex]\sqrt{81}[/tex] , that is

8 < [tex]\sqrt{78}[/tex] < 9

(a)

In order to find the function, let's use the ordered pair (-3, 8) in the given exponential function f(x).

So we have:

So the function is f(x) = (1/2)^x

(b)

The asymptote of this graph is y = 0, that is, the horizontal axis.

(c)

The domain is the values that x can assume, so the domain of this function is all real numbers, that is, (-infinity, infinity)

The range is the values that f(x) can assume, so the range of this function is y>0, that is, all positive numbers: (0, infinity)

Answer:

Here's your answer :)

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The point on the number line which represents the first tomato Carmen will eat is: B. K.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

In Mathematics, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

By critically observing the number line (see attachment) which models the weight of the tomatoes Carmen would eat, we can logically deduce that each of the interval represent 1/8 pound.

First tomato = 2/8

First tomato = 1/8 + 1/8 ≡ 2/8 = point K.

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Complete Question:

Carmen has 4 tomatoes she will eat this week. The first tomato Carmen will eat weighs 2/8 of a pound. Which point on the number line represents the first tomato Carmen will eat?

A. J

B. K

C. L

D. M

Answer:

Shifty to right 1

Not shift to

2

Step-by-step explanation:

The transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.

What do you mean by transformation of a graph ?

The modification of an existing graph or graphed equation to create a different version of the following graph is known as transformation.

The functions given are :

f(x) = x²

and

g(x) = (x - 1)² + 3

Now , we know that , the horizontal shift depends on the value of h. The horizontal shift is described as:

g(x) = f (x + h)

Then , the graph is shifted to left by h units.

and

g(x) = f (x - h)

Then , the graph is shifted to right by h units.

If we compare f(x) with g(x) , their is a difference of -1 , it meant shift is right by 1 units.

Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:

g(x) = f(x) + k

Then , the graph is shifted up by k units.

and

g(x) = f(x) - k

Then , the graph is shifted down by k units.

Here , if we compare f(x) with g(x) there is addition of 3 in g(x) , this meant the graph is shifted upward by 3 units.

The graph of the function is attached  below. Here , both of the functions are graphed.

Therefore , the transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.

EXPLANATION

Let's see the facts:

Sunrise temperature = 25°

Rate= 5°/hour

So, the temperature after x hours is given by the expression:

Temperature after x hours= Sunrise temperature + Number of hours*Rate

Substituting terms:

T= 25 + 5x

Now, with this relationship we can build the graph:

Answer:

C. the dilate with scale of 2

Step-by-step explanation:

when you dilate, a scale bigger than 1 means you enlarge the figure A

no other choices make figure a bigger to 'fit into' or be the same as figure B

so thus, the answer is C.

Answer:

C.

Step-by-step explanation:

as we can clearly see, when going from figure A to figure B every length and coordinate is doubled. that means a constant scale factor of 2 for all of that. but the angles and the general structure of the object remained the same (so, both are similar).

B

1) To solve this question, we can write out two equations within this expression:

So we can do it with 10L of that 30% solution.

2)Let's find the other volume, plugging into that x=10, since the whole volume of this new solution is 30L we can subtract from that 30L that 10L we have just found:

3) So we found 20l of the 15% solution.

Thus the answer is B

Let

[tex]\displaystyle f(x) = \sum_{n=2}^\infty \frac{x^n}{n^2(n^2-1) \binom{2n}n}[/tex]

Differentiate and multiply by [tex]x[/tex].

[tex]\displaystyle xf'(x) = \sum_{n=2}^\infty \frac{x^n}{n(n^2-1) \binom{2n}n}[/tex]

Now differentiate twice.

[tex]\displaystyle x f''(x) + f'(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{(n^2-1)\binom{2n}n}[/tex]

[tex]\displaystyle xf'''(x) + 2f''(x) = \sum_{n=2}^\infty \frac{x^{n-2}}{(n+1)\binom{2n}n}[/tex]

Multiply by [tex]x^3[/tex].

[tex]\displaystyle x^4 f'''(x) + 2x^3 f''(x) = \sum_{n=2}^\infty \frac{x^{n+1}}{(n+1)\binom{2n}n}[/tex]

Differentiate one last time and multiply by [tex]\frac1x[/tex].

[tex]\displaystyle x^3 f^{(4)}(x) + 6x^2 f'''(x) + 6x f''(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{\binom{2n}n}[/tex]

Now integrate with the fundamental theorem of calculus, noting that [tex]f(0)=f'(0)=0[/tex] follows from our series definition. We do this twice and make use of the recurrence

[tex]I_n = \displaystyle \int_0^x y^n f^{(n+1)}(y) \, dy = x^n f^{(n)}(x) - n I_{n-1}[/tex]

Integrating once yields

[tex]\displaystyle x^3 f'''(x) + 3x^2 f''(x) = \sum_{n=2}^\infty \frac{x^n}{n \binom{2n}n}[/tex]

Multiply by [tex]\frac1x[/tex].

[tex]\displaystyle x^2 f'''(x) + 3x f''(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{n \binom{2n}n}[/tex]

Integrating once more yields the ordinary differential equation

[tex]\displaystyle x^2 f''(x) + x f'(x) - f(x) = \sum_{n=2}^\infty \frac{x^n}{n^2 \binom{2n}n}[/tex]

and we recognize the right side as the series

[tex]\displaystyle \sum_{n=2}^\infty \frac{x^n}{n^2 \binom{2n}n} = 2\arcsin^2\left(\frac{\sqrt x}2\right) - \frac x2[/tex]

Solving the differential equation is quite doable with the variation of parameters method; we ultimately find

[tex]\displaystyle f(x) = \frac12 + \frac{7x}8 - \left(\frac1x+\frac12\right) \sqrt x \sqrt{4-x} \, \arcsin\left(\frac{\sqrt x}2\right) + 2 \left(\frac1x-1\right) \arcsin^2\left(\frac{\sqrt x}2\right)[/tex]

Recover the sum we want by letting [tex]x=-1[/tex]. Recall that

[tex]\arcsin(iz) = i \,\mathrm{arsinh}(z) = i\ln(z + \sqrt{1+z^2})[/tex]

Then we have the following equivalent results involving our old friend [tex]\phi[/tex].

[tex]\displaystyle f(-1) = -\frac38 - \frac{\sqrt5}2\, \mathrm{arsinh}\left(\frac12\right) + 4 \,\mathrm{arsinh}^2\left(\frac12\right) \\\\ f(-1) = -\frac38 - \frac{\sqrt5}2 \ln\left(\frac{1+\sqrt5}2\right) + 4 \ln^2\left(\frac{1+\sqrt5}2\right) \\\\ f(-1) = \boxed{-\frac38 - \left(\frac12 - \phi\right) \ln(\phi) + 4 \ln^2(\phi)}[/tex]

Using the normal distribution, it is found that:

a) The probability of a defect is of 0.4532, and out of 1000 parts, 453 will be classified as defective.

b) The probability of a defect is of 0.0324, and out of 1000 parts, 32 will be classified as defective.

c) The reduction in the variability also reduces the number of defective parts.

The z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

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

For item a, the mean and the standard deviation are given as follows:

[tex]\mu = 15, \sigma = 0.2[/tex]

The proportion of defectives is two times the p-value of Z when X = 14.85, as 14.85 and 15.15 are the same distance from the mean and the normal distribution is symmetric, hence:

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

Z = (14.85 - 15)/0.2

Z = -0.75

Z = -0.75 has a p-value of 0.2266.

2 x 0.2266 = 0.4532 = 45.32%

Out of 1000, the number of defectives is:

0.453 x 1000 = 453.

For item b, we have that [tex]\sigma = 0.07[/tex], hence:

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

Z = (14.85 - 15)/0.07

Z = -2.14

Z = -2.14 has a p-value of 0.0162.

2 x 0.0162 = 0.0324.

Out of 1000, the number of defectives is:

0.032 x 1000 = 32.

For item c, we can see that the reduction of variability will make the parts having measures closer to the desired, hence reducing the number of defectives.

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