If the demand function for a commodity is given by the equation p2 + 16q = 1200 and the supply function is given by the equation 300 − p2 + 10q = 0, find the equilibrium quantity and equilibrium price. (Round your answers to two decimal places.)

The population of Tacoma in 2017 would be 865,527.

If the population grows by 9% every year, the population would grow at a compound rate each year and the equation that can be used to determine the population in 2017 would be an exponential equation.

Compound growth is when both the existing population and the increase in population every year.

The equation that can be used to determine the population of Tacoma in 2017 is:

The formula for calculating future value:

FV = P (1 + r)^n

Where:

200,000 x (1 + 0.09)^17

200,000 x (1.09^17) = 865,526.68

In order to round  865,526.68 to the nearest whole number , look at the tenth figure, if it is greater or equal to 5, add one to the units digit and change the tenth and hundredth digit to 0. So,  865,526.68 becomes  865,527.

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Using Distributive Property, we have;

13) 5(m - 2) = ((5*m) + (5 * -2))

14) 8(y + 2) = ((8*y) + (8 * 2))

15) -3(m + 4) = ((-3*m) + (-3 * 4))

16) a(a + 3) = ((a*a) + (a * 3))

17) h(h - 2) = ((h*h) + (h * -2))

18) 2m(m + 4) = ((2m*m) + (2m * 4))

19) -2(z - 8) = ((-2*z) + (-2 * -8))

20) -4x(x - 10) = ((-4x*x) + (-4x * -10))

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC

13) 5(m - 2) expressed using distributive property is;

((5*m) + (5 * -2))

14) 8(y + 2) expressed using distributive property is;

((8*y) + (8 * 2))

15) -3(m + 4) expressed using distributive property is;

((-3*m) + (-3 * 4))

16) a(a + 3) expressed using distributive property is;

((a*a) + (a * 3))

17) h(h - 2) expressed using distributive property is;

((h*h) + (h * -2))

18) 2m(m + 4) expressed using distributive property is;

((2m*m) + (2m * 4))

19) -2(z - 8) expressed using distributive property is;

((-2*z) + (-2 * -8))

20) -4x(x - 10) expressed using distributive property is;

((-4x*x) + (-4x * -10))

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We get that the correct option is option (C) for the graph of the function as it is increasing before x = -2 and from x = 0 to x = 2.

We are given a graph of a function.

A graph of a function is a special case of a relation.

In mathematics, the graph of a function f is the set of ordered pairs, where f(x)=y.

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Here, we can see that function increases before x = - 2, then it decreases till x = 0, then it again increases from x = 0 to x = 2 and then it again decreases.

Therefore, we get that the correct option is option (C) for the graph of the function as it is increasing before x = -2 and from x = 0 to x = 2.

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The solution to the geometric sequence in the question are;

First part;

r = 3

[tex]a_{8} = 8748 [/tex]

Second part;

r = 4

[tex]a_{6} = 9216 [/tex]

Practice:

r = 8

[tex]a_{7} = 0.3125 [/tex]

Third part;

Please see the detailed reasons in following section

Fourth part;

[tex] {a}_{n} = 4 × {a}_{n-1}[/tex]

[tex] {a}_{n} = 0.2 × {a}_{n-1}[/tex]

First part;

The formula for geometric progression can be presented as follows;

[tex] a_{n} = a_{1} \times {r}^{n - 1} [/tex]

[tex]a_{4} =108 = a_{1} \times {r}^{4 - 1} [/tex]

Where;

[tex]a_{1} = 4 \: and \: a_{4} = 108[/tex]

We have;

[tex]a_{4} =108 = 4 \times {r}^{4 - 1} = 4 \cdot {r}^{3} [/tex]

Which gives;

[tex] {r}^{3} = \frac{108}{4} = 27[/tex]

[tex]r = \sqrt[3]{27} = 3[/tex]

r = 3

Therefore;

[tex]a_{8} = 4 \times {3}^{7} = 8748 [/tex]

Second part;

Where;

[tex]a_{1} = 9 \: and \: a_{3} = 144[/tex]

Therefore;

[tex] {r}^{2} = \frac{144}{9} = 16[/tex]

[tex]r = \sqrt{16} = 4[/tex]

r = 4

Which gives;

[tex]a_{6} = 9 \times {4}^{5} = 9216 [/tex]

Practice;

[tex]a_{1} = 3 \: and \: a_{4} = 1536[/tex]

Therefore;

[tex] {r}^{3} = \frac{1536}{3} = 512[/tex]

[tex]r = \sqrt[3]{512} = 8[/tex]

r = 8

[tex]a_{1} = 20 \: and \: a_{3} = 5[/tex]

Therefore;

[tex] {r}^{2} = \frac{5}{20} = 0.25[/tex]

[tex]r = \sqrt{0.25} = 0.5[/tex]

Which gives;

[tex]a_{7} = 20 \times {0.5}^{6} = 0.3125 [/tex]

Third part

Recursively means expression in terms of previous terms

The meaning of the equation is that each term of a geometric sequence is given by the product of the common ratio and the previous term

Fourth part;

The recursive formula for the sequence, {2, 8, 32, 128...} is found as follows;

r = 8/2 = 4

Therefore;

[tex] {a}_{n} = 4 × {a}_{n-1}[/tex]

Part;

The sequence is {200, 40, 8, 1.6...}

The common ratio is; 40/200 = 0.2

The recursive formula is therefore;

[tex] {a}_{n} = 0.2 × {a}_{n-1}[/tex]

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Answer:

3/20 = 15%

Step-by-step explanation:

Answer:

3/20 = 0.15 = 15%

By critically observing the graph shown above, the set of ordered pairs include the following:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.

Note: Let each box/cell in the graph represent 1 unit.

By critically observing the graph shown above, we can logically deduce that the set of ordered pairs include the following:

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Answer:

2 because the unit rate is not the same for all the others it is consistant

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

because it has two straight lines

4(4+7) is the equivalent expression uses GCF and Distributive Property to find the sum of to 16+28.

The greatest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x and y. As a result, the greatest common factor is also referred to as the Highest Common Divisor (HCD), the Highest Common Factor (HCF), or the Greatest Common Divisor (GCD).

According to the distributive property, an expression in the form A (B + C) can be solved as A (B + C) = AB + AC. This distributive law also applies to subtraction and is denoted by A (B - C) = AB - AC. This means that the other two operands share operand A.

The given expression is 16 + 28.

The greatest common factor is 4.

So taking the greatest common factor from the both the numbers.

We get, 4 (4+7)

So the resultant expression is 4 (4+7).

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Answer:

Step-by-step explanation:

There will be 5 cases and 10 additional units.

Here, we are given that 60 units are needed with 14 units per case.

The total number of units required = 60

Units required for 1 case = 14

Let the total number of cases = n

Thus, total number of units required for n cases = 14n

⇒ 60 = 14n

14n = 60

n = 60/ 14

n = 4.285

Thus, we get that the number of cases = 4.285

But, since cases cannot be in decimals, we need to round off n to 5 ( as 4 cases won't add up to 60).

Thus, the total number of cases are 5.

Additional units = 14 × 5 - 60

= 70 - 60

= 10

Thus, the number of additional units are 10.

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Answer:

(-4, 0); x = -4, y = 0

Step-by-step explanation:

The solution is the point that satisfies both equations. It is the point of intersection of the two lines.

Answer: (-4, 0)

We know that the irrational number is between:

6 < √45 < 7

And a good estimation is √45 = 6.71

Here we just need to find a lower and upper bound for the given irrational number.

To do it, we just need to find a square number larger and a square number smaller than the number inside the square root.

The larger one will be:

7*7 = 49

The smaller one will be:

6*6 = 36

Then we can write:

√36 < √45 < √49

6 < √45 < 7

So we now know that our number is between 6 and 7, that is already a good estimation, now you can also try to see if it is closer to 6 or 7, by taking the direct square root you will get:

Now just take the product between numbers of the form:

6.10*6.10 = 37.21

And so on, until we almost reach 45.

We will get:

6.71*6.71 = 45.02

So a good estimation is √45 = 6.71

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If the speed limit in Canada is 100km/hr than it's limit in mi/hr will be 62.15 mi/hr.

It is given in the question that 1.609 km = 1 mi

So , 1km= 1/1.609 mi

1km = 0.6215 mi

So if a car travels 1 km in 1 hr then it will travel 0.6215 miles in hr.

that means 1km/hr = 0.6215mi/hr

Now ,

to convert 100km/hr to mi/hr

we have  ,

100km/hr = 100*0.6215 mi/hr

=62.15 mi/hr

Therefore , If the speed limit in Canada is 100km/hr than it's limit in mi/hr will be 62.15 mi/hr.

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Answer:

19

Step-by-step explanation:

Formula

h(x) = 4x + 3

Givens

x = 4

Comment

h(x) is the same thing as y. So the equation can be written as y = 4x + 3

Now it is a simple matter of solving 4x  + 3 given that x = 4.

Solution

f(4) = 4*4 + 3          Combine

f(4) = 16 + 3            Add

Answer

f(4) = 19

Mr. Farley used 0.4 pounds of hamburger per patty.

The unitary method is a technique used to find the solution by first finding the value of a single unit and then multiplying the value to get the required answer.

Here, we are given that Mr. Farley used 4 pounds of hamburger to

make 10 hamburger patties.

Given that all of these patties are of the same size, an equal amount of hamburger will be used to make each patty.

We have,

For 10 patties, we need ⇒ 4 pounds of hamburger.

Therefore, for 1 patty we will need ⇒ 4/10 pounds

= 0.4 pounds

Thus, Mr. Farley used 0.4 pounds of hamburger per patty.

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Answer:

b= √2ca /a

Step-by-step explanation:

it was a question on my test yesterday

It is given that Dodi has two cups of liquid starch

2 cups =16 fluid ounces

1 container  can hold 6 fluid ounces

We are required to find that how many containers are required

1 container contains 6 ounces

Hence 16 ounces will be contained in 3 containers

Hence Dodi will required 3 containers.

Disclaimer:

The question is incomplete and jumbled

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Work Shown:

1 cm = 0.01 yards

66.75*(1 cm) = 66.75*(0.01 yards)

66.75 cm = 0.6675 yards

1 yard = 3 feet

0.6675*(1 yard) = 0.6675*(3 feet)

0.6675 yards = 2.0025 feet

1 foot = 12 inches

2.0025*(1 foot) = 2.0025*(12 inches)

2.0025 feet = 24.03 inches

The given equation r² - 15 = t + 19 is the equation of a parabola with vertex at (h, k) = (0, -34) and focal length |p| = 1/4.

I assume that the question is to describe or graph the equation r² - 15 = t + 19.

The given equation r² - 15 = t + 19 is the equation of a parabola with vertex at (h, k) = (0, -34) and focal length |p| = 1/4.

4p(y - k) = (x - h)² is the common equation for a parabola that faces up and down and has a vertex at (h, k) and a focal length of |p|.

Let us re-write the given equation in the standard form.

r² - 15 = t + 19

⇒ r² = t + 19 + 15

⇒ r² = t + 34

⇒ (r - 0)² = t + 34 (r can be written as r - 0)

⇒ (r - 0)² = t - (-34) (+34 is written as -(-34))

⇒ (r - 0)² = 4 × 1/4 × (t - (-34))

(4 × 1/4 is equal to 1. The given equation is unaffected by a multiplication by 1.)

⇒ 4 × 1/4 × (t - (-34)) = (r - 0)²  this equation is in the standard form. And here we have |p| = 1/4 and (h, k) = (0, -34).

Refer to the attached image for the graph of this equation.

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The time taken to  fill the tank using a pump that pumps 25L per minute

is 30.4 minutes

Given that A 1000L tank now contains 240L of water and asked the time taken to  fill the tank using a pump that pumps 25L per minute.

The amount of water that can be filled in tank=760L

Given that a pump that pumps 25L per minute ,

The time required to fill 760L {if a pump that pumps 25L per minute }=[tex]\frac{760}{25}[/tex]

The time required to fill 760L {if a pump that pumps 25L per minute }=30.4 minutes

Therefore,The time taken to  fill the tank using a pump that pumps 25L per minute is 30.4 minutes

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1. Euphoria's opportunity cost of producing a a bushel of rye is 4 pairs of jeans.

Contentes opportunity cost of producing a bushel of rye is 2 pairs of jeans.

2. Contente has comparative advantage in producing rye

Euphoria has comparative advantage in jeans production

For Euphoria:

The opportunity cost of producing a unit of rye in terms of jeans is;

Opportunity Cost = 20/5 = 4

For contente:

The opportunity cost of producing a unit of rye in terms of jeans is;

Opportunity Cost = 16/8 = 2

The opportunity cost of producing 1 unit of jean in terms of unit of rye:

For euphoria = 5/20 = 1/4

For contente = 8/16 = 1/2

1. Euphoria's opportunity cost of producing a a bushel of rye is 4 pairs of jeans.

Contentes opportunity cost of producing a bushel of rye is 2 pairs of jeans.

2. Contente has comparative advantage in producing rye

Euphoria has comparative advantage in jeans production

3. Contente produces 8 bushels of rye so with 4 million hours of labor = 8x4 = 32 million bushels in a week.

Euphoria 20 pairs of jean in a week, using 4 million hours of labor. 20x4 = 80 pairs of jean a week

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Answer:

-7

Step-by-step explanation:

f(x)=4x+5
f(-3)=4x+5
=4(-3)+5
-12+5
f(-3)= -7

The "x" in f(x) is the "x" in the equation

70? Is this a trick question?

Answer:

It will be 70

Step-by-step explanation:

Because poor number from 0 to 4

We're given:

Determine f(-5):

[tex]f(a) = 3a - a^2\\f(-5) = 3(-5) - (-5)^2\\f(-5) = -15 - 25\\f(-5) = -40[/tex]

Therefore, this statement is true.

Determine f(4):

[tex]f(a) = 3a - a^2\\f(4) = 3(4) - (4)^2\\f(4) = 12 - 16\\f(4) = -4[/tex]

Therefore, this statement is true as well.

Determine f(-1):

[tex]f(a) = 3a - a^2\\f(-1) = 3(-1) - (-1)^2\\f(-1) = -3 - 1\\f(-1) = -4[/tex]

Therefore, this statement is not true.

Determine f(0):

[tex]f(a) = 3a - a^2\\f(0) = 3(0) - (0)^2\\f(0) = 0 - 0\\f(0)=0[/tex]

Therefore, this statement is also not true.

f(-5) = -40

f(4) = -4

Answer:

I think is higher

Step-by-step explanation: