The population of Oak Forest is increasing at a rate of 2% per year. If the population is 53,768 today, what will it be in three years?

Answer:

[tex]a_t=ar^{t-1}[/tex]

t=6 months

Step-by-step explanation:

We are given that the number of people playing a new phone app game triples every month

When the app first launch , the number of people started playing the  game  right away=800

According to question

The number of peoples are currently playing the game=194,400

We solve by using the formula of  geometric series because we get a geometric series pattern

The number of people playing the game when app game launch=800

The number of people playing game after one month=2400

800,2400,7200,........,194,400

[tex]a_1=800,a_2=2400,a_3=7200,a_t=194,400[/tex]

We are finding common ratio

[tex]\frac{a_2}{a_1}=\frac{2400}{800}=3[/tex]

[tex]\frac{a_3}{a_2}=\frac{7200}{2400}=3[/tex]

Hence, the common ratio is 3 therefor nth term of  G.P

[tex]a_t=ar^{t-1}[/tex]

a=800,r=3,[tex]a_t=194,400[/tex]

Substitute the values then we get

[tex]194,400=800(3)^{t-1}[/tex]

[tex]\frac[194400}{800}=(3)^{t-1}[/tex]

[tex]243=3^{t-1}[/tex]

[tex]3^5=3^{t-1}[/tex]

When base are same on both side then the power are equals

Therefore, t-1=5

t=5+1=6

Hence, when there are 194,400 people currently playing the game then

the number of months ,t=6 that have passed since the app launched.

Answer:

800(3)^t = 194,400; t = 5 months

Step-by-step explanation:

Answer: 1/2, because its 0.583 and 1/2 is 0.5

Step-by-step explanation:

Answer:

Final answer is 1/2.

Step-by-step explanation:

Given numbers are 0, 1/2 and 1.

Now we need to find about which one of those three numbers is close to 7/12.

Since 7/12 has denominator 12 so let's convert each of the given number into their equivalent fractions with denominator 12.

0=0/12

1/2=6/12

1=12/12

Now we can easily compare them with 7/12 and find that 6/12 or 1/2 is closest.

Hence final answer is 1/2.

3.82 E+7  is just an engineering format, another way to write it will  be 3.82 x 10⁷ in scientific format, or just 3.82 x 10000000   <--- notice, seven zeros.

and the product of the above is just 38200000, or standard form.

Answer:

Step-by-step explanation: 4+3 =7 126/7= 18 (Ethan is 4*18) and (Aiden is 3*18) because 72+54=126 so aiden gets 54

Adíen gets 54 dollars hope this helps

Answer:

(fog)(2)=2

Step-by-step explanation:

Given

f(x)= -2x+8

and

g(x)= √(x+7)

For finding (fog)(2), we have to find (fog)(x) first

In order to find (fog)(x) we will put the value of g(x) in f(x) in place of x.

(fog)(x)= -2g(x)+8

Putting the value of g(x)  

(fog)(x)= -2√(x+7)+8

We have to find (fog)(2), so we have to put at the place of x in the composition

(fog)(x)= -2√(2+7)+8

(fog)(x)= -2√9+8

= -2(3)+8

= -6+8

=2

So,

(fog)(2)=2   ..

The answer is:

The third option,

c) [tex]h(x)=2.25x-22[/tex]

We are given the functions E(x) and K(x), since they both are function of the same variable, we need to calculate the difference between them.

From the statement we know the functions:

[tex]f(x)=9.75x+62[/tex]

and

[tex]g(x)=7.5x+84[/tex]

So, calculating the difference the functions we have:

[tex]h(x)=f(x)-g(x)[/tex]

[tex]h(x)=(9.75x+62)-(7.5x+84)[/tex]

[tex]h(x)=(9.75x+62)-(7.5x+84)[/tex]

[tex]h(x)=9.75x-7.5x+62-84[/tex]

[tex]h(x)=2.25x-22[/tex]

Hence, the answer is the third option,

c) [tex]h(x)=2.25x-22[/tex]

Have a nice day!

Answer: Option C

[tex]h(x)=2.25x-22[/tex]

Step-by-step explanation:

To find the function h(x) that models the difference between Hector's and Cari's gains, subtract the functions f(x) with g(x)

That is to say:

[tex]h (x) = f (x) -g (x)[/tex]

We know that

[tex]f (x) = 9.75x + 62\\\\g (x) = 7.5x + 84[/tex]

Then we can find the function h(x)

[tex]h(x) = 9.75x + 62 - (7.5x + 84)\\\\h(x) = 9.75x + 62 -7.5x -84[/tex]

[tex]h(x)=2.25x-22[/tex]

Answer:

There are 26 different possible outcomes. the probability of the computer choosing the first letter of your name is 1 out of 26.

Answer:

C

Step-by-step explanation:

Because if you have 75 baskets of 30 then you have to multiply 75x30 it is the same thing with 50x45. Hope this helps

Answer:C) 75x30) +(50x45)

Step-by-step explanation: 75 * 30 for the 30 apples in each basket and 50 * 45 for the 45 in each and put them into their own equation with parenthesees. Then add to find the total

Answer:

The correct answer option is [tex] \frac { 4 } { 4 9 } [/tex].

Step-by-step explanation:

We are to find the probability that both your parents were born on weekend (either Saturday or Sunday).

Total number of days in a week = [tex] 7 [/tex]

Number of days in weekend = [tex] 2 [/tex]

Probability of being born on weekend = [tex] \frac { 2 } { 7 } [/tex]

P (both parents were born on weekend) = [tex]\frac{2}{7} \times \frac{2}{7}[/tex] = 4/49

Answer:

48

Step-by-step explanation:

Here are two methods for finding the answer.

Method A.

In 1 foot, there are 4 1/4-foot pieces.

In 12 feet, there are 12 times as many as in 1 foot.

12 * 4 = 48

Method B.

Divide 12 ft by 1/4 ft.

12/(1/4) = 12 * 4/1 = 12 * 4 = 48

Answer: 48

48 cut from a 12 foot board.

Bed cradles and foot boards are devices that attach to your bed. They keep sheets and blankets from touching and rubbing your legs or feet. Foot boards will also keep your feet in proper position while you are in bed.

In 1 foot, there are 4 1/4-foot pieces.

In 12 feet, there are 12 times as many as in 1 foot.

12 ×4 = 48

Divide 12 ft by 1/4 ft.

12/(1/4) = 12 ×4/1

= 12 × 4 = 48

1/4 foot pieces can you cut from a 12 foot board = 48

To learn more about foot pieces, refer

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Answer:

[tex]\large\boxed{Q1.\ \left\{\begin{array}{ccc}y\leq-2x-1\\y\leq x+5\end{array}\right}\\\boxed{Q2.\ 6\leq y-3\leq8}\\\boxed{Q3.\ y\leq x-4}[/tex]

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded above the line

>, ≥ - shaded below the line

=================================================

The slope intercept form of a line: y = mx + b

m - slope

b - y-intercept (0, b)

If m > 0, then the function is increasing

If m < 0, then the function is decreasing

==================================================

y = -2x - 1 → m = -2 < 0 and b = -1

decreasing function, y-intercept -1 → (0, -1)

y = x + 5 → m = 1 > 0 and b = 5

increasing function, y-intercept 5 → (0, 5)

y = 2x - 1 → m = 2 > 0, and b = -1

increasing function, y-intercept -1 → (0, -1)

y = -x + 5 → m = -1 < 0 and b = 5

decreasing function, y-intercept 5 → (0, 5)

From the picture we have

(1) increasing function and y-intercept 5 → y = x + 5

shaded below the solid line → y ≤ x + 5

(2) decreasing function and y-intercept -1 → y = -2x - 1

shaded below the solid line → y ≤ -2x - 1

=======================================================

[tex]9\leq y\leq11[/tex]            subtract 3 from both sides

[tex]9-3\leq y-3\leq11-3\\\\6\leq y-3\leq8[/tex]

=======================================================

solid line (≤ or ≥)

shaded below the line (≤ or <)

y ≤ x - 4

Answer:

6y - 3y - 7 = -2 +3

Simplify both sides:

3y -7 = 1

Add 7 to both sides:

3y = 8

Divide both sides by 3:

y = 8/3 = 2 2/3

There is only one solution.

ANSWER

A. <AKC and <TKI

D. <IKR and <AKP

EXPLANATION

Vertical angles are also called X-angles.

They are angles in the opposite corners of a figure that looks like X.

From the diagram, the options that are vertical angles are:

A. <AKC and <TKI

D. <IKR and <AKP

The correct answers are A and D.

Answer:

A and D.

Step-by-step explanation:

A pair of angles are vertical if both measure the same and both are opposite by a vertex. Then, in the figure we have that

∠AKC and ∠TKI are vertical angles

∠AKP and ∠PKI are not vertical angles (∠PKI measures more than ∠AKP and these angles are not opposite by a vertex).

∠AKT and ∠PKC are not vertical angles (same reason as the second option).

∠IKR and ∠AKP are vertical angles.

Answer:

[tex]n\le 5[/tex]

Step-by-step explanation:

Let n be the number of tickets Makaya has to buy.

If the cost of one ticket is $1.5, then the cost of n tickets is $1.5n.

Makayla has $8 to buy tickets at the school fair, thus

[tex]1.5n\le 8\\ \\n\le \dfrac{8}{1.5}\\ \\n\le \dfrac{80}{15}\\ \\n\le \dfrac{16}{3}\\ \\n\le 5\dfrac{2}{3}[/tex]

The maximum number of tickets Makaya can buy is 5, so

[tex]n\le 5[/tex]

Answer:

To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. ... Divide the sum of the absolute values of the differences by the number of data values.

Sample Answer: First, find the mean of the data set by averaging. Next, find the absolute deviations for each data point. That is, find the distance each point is from the mean. Then find the mean of the absolute deviations.

Answer:

-8.5

Step-by-step explanation:

-4x+8=42

42-8=34

34/-4=8.5

Answer:

x = -8.5

Step-by-step explanation:

minus 8 on both sides and the eight should cancle on the left side

42 minus 8 is 34

then you divide negative 4 on both sides

Answer:

the equation of circle is x²  + y² + 6x - 24y + 128 = 0

Step-by-step explanation:

To find the general form of the equation of the circle with center A (-3, 12) and radius r=5,  we simply use this formula;

General Equation of a circle is   (x - a)²  +  (y-b)² = r²

(a,b) are the two point at the center of the circle which are (-3, 12)

which implies a = -3 and b = 12

r is the radius of the circle which is given as 5 from the above diagram

to get r², we simply square 5 and so r²  = 25

We can now plug in the values of our variables into the equation

(x - a)²  +  (y-b)² = r²

(x - [-3])²   +   ( y  -  12)²  =   5²

(x +3)²   +   ( y  -  12)²  =   5²

we will expand all the brackets

x² +  6x +  9  + y² -24y + 144 = 25

x² +6x + y² -24y + 153 = 25

Take 25 to the left hand side of the equation

x² +6x + y² -24y + 153  -  25 = 0

x² +6x + y² -24y + 128 = 0

Rearranging the equation to give us a standard form of the equation of the circle, we have;

x² + y² + 6x - 24y  + 128 =0

{Note:  (x + 3)²  =  (x+3)(x+3) = x² + 6x + 9 and  

(y - 12)²  = (y -12)(y-12) = y² - 24y + 144}

Therefore the general form of the equation  of a circle with center(-3, 12) and radius 5 is x² + y² + 6x - 24y  + 128 =0

Answer:

C

Step-by-step explanation:

The equation represents speed as a function of time. The point (3,120) implies that the car with a speed of 40 miles per hour, travelled a total of 120 miles in a time span of 3 hours.

In this scenario, the equation ys = 40x relates the speed of the car (40 miles per hour) to the time travelled (x in hours). The 'y' in the equation represents the distance travelled by the car. So, when interpreting the point (3,120) on the graph for this equation, '3' refers to time (hours) and '120' refers to distance travelled (miles).

Thus, the point (3,120) on the graph signifies that the car travelled 120 miles in 3 hours, so the correct answer is C. The car traveled 120 miles In 3 hours.

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Answer: [tex]f(2)=44[/tex]

Step-by-step explanation:

Given the polynomial [tex]f(x) =3x^3+5x^2+x-2[/tex], you can evaluate it for the given value of the variable "x" by substituting the value [tex]x=2[/tex] into the polynomial.

Therefore, when [tex]x=2[/tex],  you get the following result:

[tex]f(x) =3x^3+5x^2+x-2 \\\\f(2) =3(2)^3+5(2)^2+(2)-2\\\\f(2)=3(8)+5(4)+2-2\\\\f(2)=24+20\\\\f(2)=44[/tex]

Answer:

If (x+k) is a factor of f(x), then -k is a root (or solution) of f(x).

Step-by-step explanation:

Where are the answer choices?  Please share them.

If (x+k) is a factor of f(x), then -k is a root (or solution) of f(x).

If (x+k) is a factor of f(x), then f(-k) = 0

from the question, we have the following parameters that can be used in our computation:

(x + k) is a factor of f(x)

If (x+k) is a factor of f(x), then f(-k) = 0. This is known as the factor theorem.

It states that if a polynomial f(x) has a factor of (x-a), then f(a) = 0.

In this case, since (x+k) is a factor of f(x), we can substitute -k for x in the factor theorem to get f(-k) = 0.

Read more about remainder theorem at

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Answer:

[tex]\large\boxed{-\dfrac{8}{\sqrt{63}}}[/tex]

Step-by-step explanation:

[tex]\csc\theta=\dfrac{1}{\sin\theta}\\\\\cos\theta=-\dfrac{1}{8}\qquad\text{use}\ \sin^2\theta+\cos^2\theta=1\\\\\sin^2\theta+\left(-\dfrac{1}{8}\right)^2=1\\\\\sin^2\theta+\dfrac{1}{64}=1\qquad\text{subtract}\ \dfrac{1}{64}\ \text{from both sides}\\\\\sin^2\theta=\dfrac{64}{64}-\dfrac{1}{64}\\\\\sin^2\theta=\dfrac{63}{64}\to\sin\theta=\pm\sqrt{\dfrac{63}{64}}\\\\180^o<\theta<270^o\to III\ quadrant,\ \sin\theta<0.\\\\\text{Therefore}\ \sin\theta=-\sqrt{\dfrac{63}{64}}=-\dfrac{\sqrt{63}}{\sqrt{64}}=-\dfrac{\sqrt{63}}{8}.[/tex]

[tex]\csc\theta=\dfrac{1}{-\frac{\sqrt{63}}{8}}=-\dfrac{8}{\sqrt{63}}[/tex]

[tex]\bf \begin{array}{ccll} book&days\\ \cline{1-2}\\ \frac{3}{4}&2\\\\ x&4\frac{1}{3} \end{array}\implies \cfrac{~~\frac{3}{4}~~}{x}=\cfrac{~~2~~}{4\frac{1}{3}}\implies \cfrac{~~\frac{3}{4}~~}{x}=\cfrac{~~2~~}{\frac{13}{3}} \implies \cfrac{~~\frac{3}{4}~~}{\frac{x}{1}}=\cfrac{~~\frac{2}{1}~~}{\frac{13}{3}}[/tex]

[tex]\bf \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{2}{1}\cdot \cfrac{3}{13}\implies \cfrac{3}{4x}=\cfrac{6}{13}\implies 39=24x\implies \cfrac{39}{24}=x\implies \cfrac{13}{8}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 1\frac{5}{8}=x~\hfill[/tex]

Answer:

Final answer is [tex]W=\frac{CL}{100}[/tex].

Step-by-step explanation:

Given equation is [tex]C=\frac{100W}{L}[/tex].

Now we need to solve the given equation [tex]C=\frac{100W}{L}[/tex] for indicated variable W.

That means we need to isolate W. In other words move 100 and L to the right side of the equation.

[tex]C=\frac{100W}{L}[/tex]

[tex]CL=100W[/tex]

[tex]\frac{CL}{100}=W[/tex]

[tex]W=\frac{CL}{100}[/tex]

Hence final answer is [tex]W=\frac{CL}{100}[/tex].

Answer:

Subtract 360° to find a negative coterminal angle. Angles that measure 240° and –480° are coterminal with a –120° angle. For an angle θ in standard position, the reference angle is the positive acute angle formed by the terminal side of θ and the x-axis.

Step-by-step explanation:

Answer:

Bianca can make 28 pans of brownies in 7 hours

Step-by-step explanation:

As we know, 1 hour = 60 minutes

so, 1/2 hour = 30 minutes

Bianca takes 1/2 hour to make pans of brownies = 2 pans

Bianca takes 1 hour to make pans of  brownies = 2 / (1/2) pans

Bianca takes 7 hour to make pans of  brownies = 4 * 7 pans

                                                                                = 28 pans

So, Bianca can make 28 pans of brownies in 7 hours.

Combing like terms you have 0.25k - k = -0.75k

and 1.5 - 3.5 = -2.0

The answer would be -0.75k - 2.0

0.25k + 1.5 - k - 3.5

You must combine like terms. Like terms are the numbers with the same variable (letter) attached (in this case the numbers with the letter k are like terms)

(0.25k + (-k) )+ 1.5 - 3.5 <<<Remember that a variable with no number in front of it still has and invisible 1

(0.25k + (-1k) ) + 1.5 - 3.5

-0.75k + 1.5 - 3.5  

Numbers without any variable are also like terms

-0.75k + 1.5 - 3.5

-0.75k -2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

I dont know the answer

Step-by-step explanation:

But you can find the answer by figuring out what a domain and a range iss and chose which one is a domain and a range you can find what a domain and a range is on google

-The domain has all possible values of S so is the amount of sugar transported.

-The range has all possible values of C so is the cost to transport sugar

Answer:

C.  d × 15 = 100

Step-by-step explanation:

The distance d in meters that Martin covers per second is 100 m/15 sec.

We write this as: d= 100/15. It is the same as:

d × 15 = 100

Thus, the correct answer would be C.

Answer:

The answer is C for sure . Hope everyone has a good day .

Step-by-step explanation:

No because 9:6 is 1.5 and 4:3 is 1.333...

Answer:

Step-by-step explanation:

[tex]9:6=\dfrac{9}{6}=\dfrac{9:3}{6:3}=\dfrac{3}{2}\neq\dfrac{4}{3}=4:3\\\\\text{Other method:}\\\\9:6=\dfrac{9}{6}\\\\4:3=\dfrac{4}{3}\\\\\dfrac{9}{6}=\dfrac{4}{3}\qquad\text{cross multiply}\\\\(9)(3)=(6)(4)\\\\27=24\qquad\bold{FALSE}[/tex]

Answer:

x > -1/2

Step-by-step explanation:

Step 1: Use the Distributive Property

-2x - 1 < 0

Step 2: Isolate x

-2x < 1

Step 3: Simplify

x > -1/2

Note that when dividing by a negative in an inequality, reverse the inequality symbol.