The population of a city in 2005 was 18,000. By 2010 the city's population had grown to 45,000. Economists have determined that the population growth follows an exponential model. If they are correct, what is the projected population for 2015?​

Answer:

Adult tickets cost 10$

Step-by-step explanation:

You would have to multiple the cost of child ticket by the number purchased, subtract that number from the total amount spent, and then divide it by 2 to get the cost of an adult ticket.

B.) 66

arc PN is 114 degrees bc it’s congruent to the central angle. therefore, the rest of the circle is 246 degrees bc 360-114=246. divide the difference of intercepted arcs (246 and 114) by 2 to get the angle formed by the tangents. (246-114)/2=66

If Point O is the center of the circle then value of x is 66 degrees

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that Point O is the center of the circle

We have to find the value of x

arc PN is 114 degrees because it’s congruent to the central angle.

We know that the total measure of triangle is 360 degrees

By removing arc PN  the remaining circle has 246 degrees of measure

Divide the difference of intercepted arcs (246 and 114) by 2 to get the angle formed by the tangents.

(246-114)/2

=66 degrees

Hence, if Point O is the center of the circle then value of x is 66 degrees

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ANSWER

No solution

EXPLANATION

The first equation is

[tex]y = {x}^{2} - 2x[/tex]

and the second equation is

[tex]y = - 2x - 1[/tex]

We equate the two equations to obtain;

[tex] {x}^{2} - 2x = - 2x - 1[/tex]

This implies that

[tex] {x}^{2} = - 2x + 2x - 1[/tex]

[tex] {x}^{2} = - 1[/tex]

There is no real number whose square is -1.

Therefore, the equation has no solution.

Answer: no solution

Step-by-step explanation: no cap

Im pretty sure that the answer would be 3 cm, answer letter A

Answer:

B

Step-by-step explanation:

did it on edge

Answer:

10 - 3x

Step-by-step explanation:

given

12 - [tex]\frac{6x+4}{2}[/tex]

= 12 - [tex]\frac{6x}{2}[/tex] - [tex]\frac{4}{2}[/tex]

= 12 - 3x - 2 ← collect like terms

= 10 - 3x

Answer:

-135

Step-by-step explanation:

The summation notation of 10∑n=2 -2n-3.

We can find the values by substituting n into -2n-3.

Let's begin where n = 2

-2(2) - 3 = -7

-2(3) - 3 = -9

-2(4) - 3 = -11

-2(5) - 3 = -13

-2(6) - 3 = -15

-2(7) - 3 = -17

-2(8) - 3 = -19

-2(9) - 3 = -21

-2(10) - 3 = -23

This gives us:

-7 + -9 + -11 + -13 + -15 + -17 + -19 + -21 + -23 = -135

The question is likely related to evaluating a summation sequence using sigma notation, but the specifics are unclear due to possible typos. The correct approach would be to substitute values of n into the given expression and sum the results, but the question needs clarification.

The student's question appears to involve the concept of a summation, indicated by the sigma notation (Σ), which is a common topic in high school mathematics, particularly in algebra, pre-calculus, or AP statistics. However, the question, as written, is incomplete or contains typos that make it unclear. The phrase '10 sigma n=2 -2n-3' is not sufficient to provide a full context for an evaluation. It is likely that the student is asking to evaluate a summation formula that starts at n=2, but the upper limit of the summation (10) and the actual expression to be summed (-2n-3) are not clearly linked.

If the student intended to ask for the evaluation of the summation of the expression -2n-3 from n=2 to n=10, then we would calculate the sum as follows:

However, without clarification from the student, we cannot proceed with certainty. It is important to understand the exact parameters of the summation when dealing with sigma notation and summation formulas.

Answer:

Step-by-step explanation:

3a-4=a(a-3)

3a-4=a²-3a

3a=a²-3a+4

0=a²-6a+4

a=(6±√[36-4(1)(4)])/2(1)

a=(6±√(36-16))/2

=(6±√20)/2

=3±(2√5)/2

=3±√5

a=3+√5

a=3-√5

Answer:   3 ± √5

Step-by-step explanation:

[tex]3a-4=a(a-3)\\\\3a-4=a^2-3a\qquad distributed\ "a"\ on\ the\ right\ side\\\\0=a^2-6a+4\qquad subtracted\ 3a-4\ from\ both\ sides\\\\a=1,\ b=-6,\ c=4\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4(1)(4)}}{2(1)}\\\\\\.\ =\dfrac{6\pm \sqrt{36-16}}{2}\\\\\\.\ =\dfrac{6\pm \sqrt{20}}{2}\\\\\\,\ =\dfrac{6\pm 2\sqrt5}{2}\\\\\\.\ =3\pm\sqrt5[/tex]

Answer:

-5

Step-by-step explanation:

We can just see what x has to be smaller than (or plug in the numbers, but that is more time-consuming).

-3x + 7 < 11 -> -3x < 4 -> x > -4/3

-5 is the only number that is less than or equal to -4/3.

-5 Is not a solution to the inequality

Both Spencer and Jeremiah are correct

The given equation;

6x - 2 = -4x + 2

The first step is obtaining the solution to the given equation is to collect similar terms together.

Add 4x to both sides of the equation;

6x + 4x - 2 = -4x + 4x + 2

10x - 2 = 2

Or

Subtract 6x from both sides of the equation;

6x - 6x - 2 = -4x - 6x

-2 = -10x + 2

Thus, both Spencer and Jeremiah are correct.

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Answer:

2x^2-4x-6

Step-by-step explanation:

I don't know what kind of math this is, but simply add up all of the like-terms.

There are 2 +x^2 --> 2x^2

There are 4 -x --> -4x

There are 6 - --> -6

The answer is A

There are two x squared tiles, there are four negative x tiles and there are six single negative tiles

QUESTION 5

The side length of the first tra-pezoid and the second tra-pezoid are in the ratio [tex]5:7[/tex].

To find the corresponding ratio of their area, we square each term in the ratio.

The ratio of the area of the first figure, to the ratio of the area of the second is

[tex]5^2:7^2=25:49[/tex]

QUESTION 6

The side length of the first figure and the second figure are in the ratio [tex]12:7[/tex].

To find the corresponding ratio of their area, we square each term in the ratio.

The ratio of the area of the first figure, to the ratio of the area of the second figure is

[tex]12^2:7^2=144:49[/tex]

QUESTION 7

Let [tex]h[/tex] represent the height of this triangle.

[tex]\sin 30\degree=\frac{h}{6}[/tex]

This implies that;

[tex]h=6\sin 30\degree[/tex]

[tex]h=3ft[/tex]

The area of the triangle is [tex]=\frac{1}{2}bh[/tex]

The base is 9 ft and the height is 3 ft.

We substitute these values to obtain;

[tex]A=\frac{1}{2}(9)(3)[/tex]

[tex]A=13.5ft^2[/tex] to the nearest tenth.

QUESTION 8

The area of a parallelogram is [tex]base\times\:height[/tex]

Let h represent the height of this parallelogram.

[tex]\sin60\degree=\frac{h}{6}[/tex]

[tex]h=6\sin60\degree[/tex]

[tex]h=3\sqrt{3}m[/tex]

The area of the parallelogram is [tex]=10\times3\sqrt{3}m^2[/tex]

[tex]=30\sqrt{3}m^2[/tex]

[tex]=52.0m^2[/tex] to the nearest tenth.

Final answer:

To find f(x) at x = 2.5 in the given function, substitute the value of x into the function and simplify the expression, giving us f(2.5) = 12.

Explanation:

To find the value of f(x) at x = 2.5, we substitute the value of x into the given function: f(2.5) = [tex]2(2.5)^2[/tex] + 7.

Simplifying this expression, we get f(2.5) = 2(6.25) - 7.5 + 7 = 12.5 - 7.5 + 7 = 12.5 - 0.5 = 12.

Therefore, f(2.5) = 12.

Answer:

A

Step-by-step explanation:

The area (A) is calculated using

A = [tex]\frac{1}{2}[/tex] bc sinA ← substitute values

A = 0.5 × 14 × 8 × sin30° = 28 units² → A

Answer:

13.

Step-by-step explanation:

12.9 is closer to 13.

square root 167 is 12.923, this rounded to the nearest unit is 13

Answer: 3x+8y=100

x+y=20

x=12

y=8

Step-by-step explanation: x would represent the number of multiple choice questions and y would represent the number of short response questions. the multiple choice questions were 3 points meaning that you need to find x. the short answer response questions were 8 points meaning you need to find y. altogether you need to get 100 points. for the second equation you have 20 questions that need to be both multiple choice and short response. therefore the second equation would be x+y=20. if you solved this, the answer would be that x equals 12 and y equals 8. hope this helped! :))

Your answer would be 200ft I believe. 20 times 5 times 2 :)

Answer:

The area of the plate is 21 inches

Step-by-step explanation:

* Lets revise some rules of a circle

- The circumference of a circle = 2πr , where r is the radius of it

- The area of the circle = πr²

* Lets solve the problem

∵ A circular plate has circumference 16.3 inches

∵ The circumference = 2πr

∵ π = 3.14

- Lets find the radius of the plate

∵ 16.3 = 2(3.14)r

∴ 16.3 = 6.28r

- Divide both sides by 6.28

∴ r = 16.3/6.28 = 2.5955 ≅ 2.6

∴ The radius of the plate is 2.6 inches

* Lets find the area of the plate

∵ The area = πr²

∵ π = 3.14

∵ 4 = 2.6

∴ The area = 3.14(2.6)² = 21.22 ≅ 21

* The area of the plate is 21 inches

To find the area of a circle with a circumference of 16.3 inches using 3.14 for pi, you first calculate the radius and then use the formula A = πr² to get the area, which when rounded to the nearest whole number is approximately 21 inches².

To calculate the area of a circular plate when given its circumference, we first need to find the radius of the circle. We use the formula for the circumference of a circle, C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius. The student has provided the circumference as 16.3 inches, so we solve for r:

C = 2πr

16.3 inches = 2 × 3.14 × r

16.3 inches / (2 × 3.14) = r

16.3 inches / 6.28 = r

2.597 inches = r

Now that we have the radius, we can use the area formula for a circle, A = πr². Plugging in our radius we get:

A = 3.14 × (2.597 inches)²

A = 3.14 × 6.7473 inches²

A = 21.205 inches²

Rounding to the nearest whole number:

A ≈ 21 inches²

the answer is since A = l × w

A= 30 × 40

A= 1200 square inches

The answer would be 8 inches.

Answer:

W = 8 inches

Step-by-step explanation:

Volume of a rectangular prism is V= LWH,

we are given V = 528, L = 12, and H = 5 1/2.  Plug  them in and find W..

First convert 5 1/2 to an improper fraction

5 1/2 becomes 11/2

   528 = (12)(11/2)W

      528 = (132/2)W

        528 = 66W

            8 = W  (divide both sides by 66)

Answer:

64 ft

Step-by-step explanation:

if a projectile is fired straight upward from the ground with an initial speed of 64 feet per second, then its height in feet after seconds is given by the function h(t)=-16t^2 + 64t. find the maximum height of the projectile.

***

h(t)=-16t^2 + 64t

complete the square

h(t)=-16(t^2 -4t+4)+64

h(t)=-16(t-2)^2+64

This is an equation of a parabola that opens upward with vertex at (2,64)

maximum height of the projectile=64 ft (2 sec after it is fired)

Answer:

Smaller x   -10

Larger x     -2

Step-by-step explanation:

f(x) = (x+6) ^2 - 16

To find the zero's, we set the function equal to zero

0 =  (x+6) ^2 - 16

Add 16 to each side

16 =  (x+6) ^2 - 16 + 16

16 = (x+6)^2

Take the square root of each side

±sqrt(16) = sqrt((x+6)^2))

±4 = x+6

Subtract 6 from each side

-6±4 = x+6-6

-6±4 = x

-6 -4 = x        -6+4 =x

-10 =x                 -2 =x

Smaller x   -10

Larger x     -2

Answer:

Smaller x: -10

Larger x: -2

Step-by-step explanation:

You are looking for where the function equals 0. So, you can set f(x) equal to 0:

f(x) = [tex]0=(x+6)^{2} -16[/tex]

Now add 16 to both sides:

[tex]16=(x+6)^{2}[/tex]

Now that you have a perfect square on both sides, you can take the square root of both sides. On the right, this would simply remove the exponent. On the left, you have the square root of 16, or 4. It is important to remember that this can be positive or negative (since -4 squared also equals 16).

±4 = x + 6

To find your two solutions, you have to then evaluate the equation for 4 and -4. First, with -4:

-4 = x + 6       subtract 6 from both sides

-10 = x

Now, with 4:

4 = x + 6        subtract 6 from both sides

-2 = x

And there are your two solutions. Since -10 < -2, -10 is the smaller x and -2 is the larger one.

Answer:

[tex]x=-7[/tex]

Step-by-step explanation:

We can write them both like functions like this

[tex]A=5x-4[/tex]

[tex]B=3x+8[/tex]

Where

x=input

A=Output A

B=Output B

We want the output of A 3 times the output of B this can be written like this:

[tex]A=3B[/tex]

we replace with the functions

[tex]5x-4=3(3x+8)[/tex]

we solve for x

[tex]5x-4=9x+24\\5x-9x=24+4\\-4x=28\\x=\frac{28}{-4}\\x=-7[/tex]

The output that makes the out put of A 3 times teh output of B is [tex]-7[/tex]

To find the input that makes the output of A three times the output of B, solve the equation 3(B's output) = A's output by plugging in the values for each machine. The input that satisfies this equation is X = -7.

To find the input that makes the output of A three times the output of B, we need to solve the equation 3(B's output) = A's output. Let's plug in the given values into the machines to solve for X:

Now we can set up the equation and solve for X:

3(3X + 8) = 5X - 4

9X + 24 = 5X - 4

9X - 5X = -4 - 24

4X = -28

X = -7

Therefore, the input that makes the output of A three times the output of B is X = -7.

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Answer:

about $5,203.02

Step-by-step explanation:

5000(1+(.04/4))^4

The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 4% per year compounded 1 times per year over 3 years is $5,624.32.

Given Data

A = P + I where

P (principal) = $5,000.00

I (interest) = $624.32

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 5,000.00(1 + 0.04/1)^(1)(3)

A = 5,000.00(1 + 0.04)^(3)

A = $5,624.32

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Answer:

14

Step-by-step explanation:

Using the law of cosines on ΔRST, then

s² = 9² + 8² - (2 × 9 × 8 × cos111° )

   = 81 + 64 - ( 144 × cos111° )

   = 145 - (- 51.6)

   = 145 + 51 . 6 = 196.6 ( take the square root of both sides )

s = [tex]\sqrt{196.6}[/tex] ≈ 14

The answer is: 14

Using the law of cosines and the given information, we can find the value of s.

Law of cosines is:

[tex]a^{2}=b^{2}+c^{2}-2abcos(A)[/tex]

Where,

[tex]a=s\\b=9\\c=8\\A=111(degrees)[/tex]

By substituting we have:

[tex]s=\sqrt{9^{2}+8^{2}-2*9*8*cos(111)}\\\\s=\sqrt{81+64-(144)*(-0.35)}=\sqrt{145+50.4}=\sqrt{195.4}=13.98=14[/tex]

So, the correct answer is:

[tex]s=14[/tex]

Have a nice day!

The height is 3 feet long

you multiply 5 by 4 and get 20 and 20x3=60 therefore 3 is your answer

Answer:

height = 3

Step-by-step explanation:

length X width X height = volume

5 X 4 X 3 = 60

an easy way if you have two of them and volume is putting random numbers till it equals the correct volume

Answer:

In 286 different ways 10 players can be selected.

Step-by-step explanation:

There are 6 girls and 7 boys in a class. So in total there are 6+7 = 13 number of students in the class.

A team of 10 players is to be selected from the class.

As there is no other conditions are given, we can pick any 10 students from 13 students.

The way we can select 10 players from 13 students is;

= (13 10)

= 13!/10!(13-10)!

= 13!/10! 3!

= (13 × 12 × 11 × 10!)/ 10! 3!

= ( 13 × 12 × 11)/6

= 286

Answer:

$291,016.80

A is correct.

Step-by-step explanation:

You are applying for an 80/20 mortgage to buy a house costing $145,000.

Loan Formula:

[tex]EMI=\dfrac{P\cdot r}{1-(1+r)^{-n}}[/tex]

Case 1:

Loan amount, P = 80% of 145000 = $ 116,000

Rate of interest, r = 4.75% = 0.0475

Time of loan, n = 30 years = 360 months

Substitute the values into formula.

[tex]EMI=\dfrac{116000\cdot \frac{0.0475}{12}}{1-(1+\frac{0.0475}{12})^{-360}}[/tex]

[tex]EMI=605.11[/tex]

Total payment for case 1: 605.11 x 360 = $217,839.60

Case 2:

Loan amount, P = 20% of 145000 = $ 29,000

Rate of interest, r = 4.75% = 0.07525

Time of loan, n = 30 years = 360 months

Substitute the values into formula.

[tex]EMI=\dfrac{29000\cdot \frac{0.07525}{12}}{1-(1+\frac{0.07525}{12})^{-360}}[/tex]

[tex]EMI=203.27[/tex]

Total payment for case 1: 203.27 x 360 = $73,177.20

Total amount of the mortgage = $217,839.60 + $73,177.20

                                                    = $291,016.80

Hence, The total amount of the mortgage is $291,016.80

Answer:

B. Jacobs monthly bill shall be $48.75

Step-by-step explanation:

On this specific mont, Jacob used 124.8 minutes.

Considering that every fraction of a minute is rounded off to the next minute,

Jacob used 125 minutes.

Each minute goes for $0.35

Now multiply total nomber of minutes by $0.35 rate

0.35 * 125 = 43.75

This is bill for the minutes used.

The bill for service is $5 per month.

To get the total bill, we add $5 to $43.75

Which gives us $48.75

x = 899xy + 63

29x31xy + 29x^2+5

29(31y+2)+85

=29

63-58=5

The remainder will be 5.

Answer:

Your answer would be C. 5

Step-by-step explanation: