Try It #2
A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was36,800. Assume this trend continues.
b. Identify the year in which the population will reach 54,000.

Answer:

EF = 22 , AB = 1

Step-by-step explanation:

the midsegment of a trapezoid is equal to half the sum of the parallel bases

EF = [tex]\frac{1}{2}[/tex] (AB + DC ) ← substitute values

x + 6 = [tex]\frac{1}{2}[/tex] (2x - 9 + x + 5) ← multiply both sides by 2 to clear the fraction

2x + 12 = 3x - 4 ( subtract 3x from both sides )

- x + 12 = - 4 ( subtract 12 from both sides )

- x = - 16 ( multiply both sides by - 1 )

x = 16

Then

EF = x + 6 = 16 + 6 = 22

Similarly

EF = [tex]\frac{1}{2}[/tex] (AB + DC ) , that is

x + 3 = [tex]\frac{1}{2}[/tex] (4x - 3 + 2x + 5 ) ← multiply both sides by 2 to clear the fraction

2x + 6 = 6x + 2 ( subtract 6x from both sides )

- 4x + 6 = 2 ( subtract 6 from both sides )

- 4x = - 4 ( divide both sides by - 4 )

x = 1

Then

AB = 4x - 3 = 4(1) - 3 = 4 - 3 = 1

Answer:

150

Step-by-step explanation:

The area of the trapezoid is (½)(14+10)(2) = 24.

The area of the rectangle is (14)(9) = 126.

Adding these together, we get 126 + 24 = 150.

The length of AB would be 38 units

The attached image represents the missing piece in the question

Considering the triangle BCD;

Calculate the length BC using the following Pythagoras theorem

BC^2 = CD^2 + BD^2

This gives

BC^2 = 10^2 + 8^2

Evaluate

BC^2 = 164

Considering the triangle CBA;

Calculate the length AB using the following Pythagoras theorem

AB^2 = AC^2 - BC^2

This gives

AB^2 = 40^2 - 164

Evaluate

AB^2 = 1436

Take the square root

AB = 38 (approximated)

Hence, the length of AB would be 38 units

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a) The growth function has the form:

where:

Considering the values we get the function:

b) Number of years between 2012 and 2018 is:

Find the population, using the above equation:

c) Find the value of x when P(x) = 10 million

d) Find the doubling time:

Answer:

[tex]\textsf{a)} \quad f(x)=6.93(1.0218)^x[/tex]

b)  7.89 million (2 d.p.)

c)  2019

d)  32.14 years (2 d.p.) after 2012

Step-by-step explanation:

Exponential Function

   [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part (a)

If the exponential growth rate was 2.18% per year, then each year there would be 102.18% of the previous year's population.

⇒ b = 1.0218

Given:

Substitute the given values into the formula to create an exponential growth function:

  [tex]f(x)=6.93(1.0218)^x[/tex]

Part (b)

To estimate the population of the city in 2018, determine the value of x:[tex]x = 2018 - 2012 = 6[/tex]

Substitute the found value of x into the found exponential function:

[tex]\implies f(6)=6.93(1.0218)^6=7.89 \: \sf million\:(2\:d.p.)[/tex]

Part (c)

To determine when the population of the city will be 10 million, set the function to 10 and solve for x:

[tex]\implies 6.93(1.0218)^x=10[/tex]

[tex]\implies (1.0218)^x=\dfrac{10}{6.93}[/tex]

[tex]\implies \ln (1.0218)^x= \ln \left(\dfrac{10}{6.93}\right)[/tex]

[tex]\implies x\ln (1.0218)= \ln \left(\dfrac{10}{6.93}\right)[/tex]

[tex]\implies x= \dfrac{\ln \left(\frac{10}{6.93}\right)}{\ln (1.0218)}[/tex]

[tex]\implies x=17.00496413...[/tex]

To find the year, add the found value of x to 2012:

[tex]\implies \sf 2012 + 17.00496413... = 2019[/tex]

Part (d)

To find the doubling time, set the function to double the initial population and solve for x:

[tex]\implies 6.93(1.0218)^x=6.93 \cdot 2[/tex]

[tex]\implies (1.0218)^x=2[/tex]

[tex]\implies \ln (1.0218)^x= \ln (2)[/tex]

[tex]\implies x \ln (1.0218)= \ln (2)[/tex]

[tex]\implies x = \dfrac{\ln (2)}{\ln (1.0218)}[/tex]

[tex]\implies x=32.14107014...[/tex]

Therefore, the doubling time is 32.14 years (2 d.p.) after 2012.

Answer:

65fghxtt

Step-by-step explanation:

Answer:

0.71

Step-by-step explanation:

- Please see the attached picture for full solution!:)

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Answer:

Yes, it is a function

Step-by-step explanation:

A function has only one output for each input. So a function can have the same output for different input, but one input can only have one output. In this case none of the inputs output more than one output, so it is a function.

Answer:

Yes

Step-by-step explanation:

Answer:

first type: 144 pints

second type: 36 pints

Step-by-step explanation:

So let's try to interpret the given information. So the first thing to know is how to calculate x%, to calculate this, you simply multiply the number by x/100, which is what x is in decimal form.

So let's just start off by assigning variables to each brand, with the variable representing the amount of pints. Let's say "x" is the amount of pints of the first brand, and "y" is the amount of pints of the second brand.

The next thing to do is make equations using the given information. So we want a fruit drink that is 55% pure fruit juice, and it's 180 pints. So to find what 55% is, we multiply by 55/100 or 0.55. This means that 55% is 0.55(180) = 99. So using the given information this means that 99 pints is pure fruit juice in the mixture. This comes from mixing the first two brands, so that means if we take the pure fruit juice from the first brand and add it to the second brand we get 99, and remember we are given the information that 45% of the first brand is pure fruit juice and the second is 95%, this means that 0.45x is pure fruit juice in the first brand and 0.95y is pure fruit juice in the second brand. This sets up the following equation: [tex]99 = 0.45x + 0.95y[/tex]

The second equation to set up is using the total amount of pints. x represents how much is from the first brand, and y represents how much is from the second brand. Since the mixture consists of these two brands, and the mixture is 180 pints we can form the equation: [tex]180 = x+y[/tex]

The last step is to solve the systems of equations using the two equations we formed. This can be done via substitution. We simply need to solve for either x or y, in the total amount of pints equation and then substitute it into the pure fruit juice equation. In this example I'll solve for x

Original Equation:

[tex]180 = x+y[/tex]

Subtract y from both sides

[tex]180-y=x[/tex]

So now that we solved for y in terms of x we can substitute this into the pure fruit juice equation, so that we're only dealing with one variable.

Original Equation:

[tex]99 = 0.45x + 0.95y[/tex]

Substitute 180-y as x

[tex]99 = 0.45(180-y) + 0.95y[/tex]

Distribute the 0.45

[tex]99=81-0.45y+0.95y[/tex]

Add like terms

[tex]99=81+0.5y[/tex]

subtract 81 from both sides

[tex]18=0.5y[/tex]

Divide both sides by 0.5 (same thing as multiply by 2)

[tex]36=y[/tex]

This means we have to use 36 pints of the second brand. We can substitute this into either equation to solve for x, but it's easier to substitute into the total pints equation since there are no coefficients (technically a 1 in front, but it's kind of be ignored for now), so it's pretty straightforward to solve for x

Original Equation:

[tex]180=x+y[/tex]

Substitute 36 as y

[tex]180=x+36[/tex]

Subtract 36 from both sides

[tex]144=x[/tex]

This means 144 pints from the first brand and 36 from the second

The ride takes  1.5 hours for a speed of 10 miles per hour.

The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.

A body's speed can be defined as how quickly it is going. The equation for a given body's speed can be written as,

Speed=Distance/Time

According to the question,

Speed=10 miles per hour

Distance=15 miles

Time=[tex]\frac{15}{10}[/tex]=1.5 hours

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The fourth proportionals are bc/a and st/r

Segments a, b and c

Let the fourth segment be x.

So, we have the following equivalent ratio

a : b = c : x

Express as fraction

a/b = c/x

Make x the subject

x = bc/a

Segments r, s and t

Let the fourth segment be x.

So, we have the following equivalent ratio

r : s = t : x

Express as fraction

r/s = t/x

Make x the subject

x = st/r

Hence, the fourth proportionals are bc/a and st/r

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The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)

In this question we have a trigonometric equation and we are supposed to find an expression not equivalent to the former. Herein we have that the cosine of a double angle is equivalent to the following expressions:

cos 2θ = cos² θ - sin² θ     (1)

cos 2θ = 2 · cos² θ - 1     (2)

cos 2θ = 1 - 2 · sin² θ     (3)

The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)

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Answer:

708π in³ = 2224.25 in.³

Step-by-step explanation:

The composite solid is made up of a cone, a cylinder, and a half sphere.

Recall the volume formulas:

cone: πr²h/3

cylinder: πr²h

sphere: 4πr³/3

half sphere: (1/2) × 4πr³/3

We need to find teh heoght of the cone. The slant height is 10 in. The radius is 6 in. We can use the Pythaogorean theorem to find the height of the cone.

h = √(10² - 6²) = 8

total volume = π(6 in.)²(8 in.)/3 + π(6 in.)²(13 in.) + (1/2) × 4π(6 in.)³/3

total volume = π(96 in.³ + 468 in.³ + 144 in.³)

total volume = 708π in³ = 2224.25 in.³

Answer:

There are two equations and two variables, so this is a system of linear equations.

c + h = 360

4c = h

Step-by-step explanation:

Answer:

The linear equations would be c = 4h and 1.5c + 2h = 360.

Step-by-step explanation:

First we have to create a table for our data.

c = total number of cold beverages sold.

h = total number of hot beverages sold.

The total cost of both beverages sold -

1.5c + 2h = 360

The amount of cold beverages -

c = 4h

Now we just need to substitute the second equation to the first one.

1.5 * (4h) + 2h = 360

= 6h + 2h = 360

= 8h = 360

= h = 45

Now we need to find the value of c.

c = 4* 45 = 180

Therefore 180 cold beverages were sold and 45 hot beverages were sold.

But the linear equations would be c = 4h and 1.5c + 2h = 360.

Hope this helped! :D

Answer:

f(x) = -2x - 3

g(x) = -2x³ - 5

f(5) = -2(5) - 3

f(5) = -10 - 3

f(5) = -13

g(-2) = -2(-2)³ - 5

g(-2) =-2(-8) - 5

g(-2) = 16 - 5

g(-2) = 11

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads:}[/tex]

[tex]\large\textbf{Which is equivalent to }\rm{\bf \dfrac{3}{125}}\large\textbf{ ?}[/tex]

[tex]\huge\textbf{Solving for your fraction:}[/tex]

[tex]\mathbf{\dfrac{3}{125}}[/tex]

[tex]\mathbf{= \dfrac{3\times2}{125\times2}}[/tex]

[tex]\mathbf{\approx \dfrac{3 + 3}{125 + 12{5}}}[/tex]

[tex]\mathbf{= \dfrac{6}{250}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\dfrac{6}{250}}}\huge\checkmark[/tex]

[tex]\large\text{By the way, they are a lot more fractions that are equivalent to}\\\large\text{the given equation (}\rm{\dfrac{3}{125}}\large\text{) but we only labeled one that is the very}\\\large\text{first fraction that is equal to it. }[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

um tbh me dont know

Step-by-step explanation:

Answer:

its easy

Step-by-step explanation:

you should change all into degrees

The solution to the given inequality is; x ≥ -9/4 or x ≥ 1

We want to solve the inequality;

(4x² + 5x - 9)/(x² - x - 6) ≥ 0

Let us factorize both numerator and denominator to get;

4x² + 5x - 9 = (4x + 9)(x - 1)

Similarly, x² - x - 6 when factorized gives;

x² - x - 6 = (x + 2)(x - 3)

Thus, we now have;

[(4x + 9)(x - 1)]/[(x + 2)(x - 3)] ≥ 0

Multiply both sides by [(x + 2)(x - 3)] to get;

(4x + 9)(x - 1) ≥ 0

Thus;

(4x + 9) ≥ 0 or (x - 1) ≥ 0

Thus;

x ≥ -9/4 or x ≥ 1

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Using the normal distribution, it is found that 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.

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

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

The mean and the standard deviation for the amounts are given as follows:

[tex]\mu = 3456, \sigma = 478[/tex]

The proportion is the p-value of Z when X = 4250, hence:

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

[tex]Z = \frac{4250 - 3456}{478}[/tex]

Z = 1.66

Z = 1.66 has a p-value of 0.9515.

Hence 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.

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In the given triangle, the length of BC is 10.25 cm

From the question, we are to determine the length BC

The triangle is a right triangle, then we can write that

/AB/² = /AC/² + /BC/² (Pythagorean theorem)

From the given information,

/AB/ = 13 cm

/AC/ = 8 cm

Putting the parameters into the equation, we get

13² = 8² + /BC/²

169 = 64 + /BC/²

/BC/² = 169 - 64

/BC/² = 105

/BC/ = √105

/BC/ = 10.25 cm

Hence, the length of BC is 10.25 cm

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The average selling price per box is $5.33

The core value of a set of data is expressed as the average of a list of variables. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. The average of a specific set of numerical data is also known as the mean in statistics.

Average = Sum of Values/Number of Values

The total selling price of all boxes=(8*100)+(800*6)+(600*4)

                                                   =$8000

Total number of boxes=100+800+600

                                      =1500

Average selling price per box=8000/1500=$5.33

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By seeing where the curves intercept, we conclude that the solutions are:

(0.22, -1.22) and (-2.12, 1.12)

Here we just need to graph the equations:

y = log(-5.6*x + 1.3)

y = -1 - x

And see in which points the curves intercept.

The graph can be seen below:

There we can see that the intersections (and solutions) are the points:

(0.22, -1.22) and (-2.12, 1.12)

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Answer:

1-0.07/100*7=0.9951

Answer:

x + y ≤ 12

Step-by-step explanation:

Inequality:

   Not more than 12 means less than or equal to 12

x + y ≤ 12

The volume of the sphere shown below with a radius of 9 is 3052.08 cubic units

The formula for calculating the volume of a sphere is expressed as;

V = 4/3πr³

where

r is the radius of the sphere

Substitute

V = 4/3π(9)³

V = 4/3(3.14)*729

V = 3052.08 cubic units

Hence the volume of the sphere shown below with a radius of 9 is 3052.08 cubic units

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The speed of the plane after it encounters the wind is C.285mph

Since the plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph it's velocity is v = (320cos270°)i + (320sin270°)j

= (320 × 0)i + (320 × -1)j

= 0i - 320j

= - 320j mph

Also, the plane encounters a 35 mph wind blowing directly north. The velocity of the wind is v' = 35j mph

So, the velocity of the plane after it encounters the wind is the resultant velocity, V = v + v'

= -320j mph + 35j mph

= -285j mph

So, the speed of the plane after it encounters the wind is the magnitude of V = |-285j| mph

= 285 mph

So, the speed of the plane after it encounters the wind is C.285mph

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