The point P(6,4) is rotated 270° clockwise around the origin. What are the coordinates of the resulting point, P'?

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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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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he Solution:

iven:

We are required to find the amount the investment will be worth after 9 years.

he Compound interest formula:

In this case:

Substitute:

Therefore, the correct answer is $4318

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:

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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The expression (-6 - 5i) + (-1 + 7i)  in this form  a + bi  is -7 + 2i

The expression to be evaluated is as follows:

Therefore,

(-6 - 5i) + (-1 + 7i)

The expression can be express in the form a + bi as follows:

(-6 - 5i) + (-1 + 7i)

- 6 - 5i - 1 + 7i

Let's combine the like terms

- 6 - 5i - 1 + 7i

-6 - 1 - 5i + 7i

Let's do the arithmetic

-6 - 1 - 5i + 7i

Therefore,

-7 + 2i

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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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Answer:

Here's your answer :)

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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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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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Answer:

Step-by-step explanation:

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

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

Answer:

The transversal is not part of this triangle.

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

Answer:

Explanation:

A) Given the below expression;

The above can be written as;

Recall the below law of exponent;

Applying the above law of exponent to the expression, we'll have;

B) Given the below expression;

Recall the below law of exponent;

Applying the above law of exponent to the expression, we'll have;

C) Given the below expression;

Recall the below laws of exponents;

Applying the above law of exponent to the expression, we'll have;

D) Given the below expression;

Recall the below law of exponents;

Applying the above law of exponent to the expression, we'll have;

We can see from the above that the below expressions are equivalent because they both yield the same result as x;

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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That is the answer

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

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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

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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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.

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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Step-by-step explanation:

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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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By using substitution method, if Kerel has 9  quarters and nickels in his pocket and they have a combined  value of 125 cents, then he has 4 quarters and 5 nickels

Total number of coins = 9

Consider the number of quarters as x and number of nickels as y

Then the equation will be

x+y =9

x= 9-y

The combined value of the coins =  125 cents

We know

1 quarter = 25 cents

1 nickel = 5 cents

Then the equation will be

25x+5y = 125

Here we have to use the substitution method

Substitute the value of x in the equation

25(9-y)+5y = 125

225-25y+5y = 125

-20y = -100

y = 5

Substitute the value of y in the first equation

x = 9-y

x = 9-5

x= 4

Hence, by using substitution method, if Kerel has 9  quarters and nickels in his pocket and they have a combined  value of 125 cents, then he has 4 quarters and 5 nickels

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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