An initial population of 1,500 increases at an annual rate of 15%. Write an exponential function to model the population increase. Use the function to find the population after 15 years.

Answer:

commutative property of addition

Step-by-step explanation:

commutative property of addition means that both sides on the equal sign have the same numbers but just has is in a deferent order. It might be confusing for this one because there is a 0, but 0 is nothing so it still applies.

Hope this helps, have a great day!

Answer:

Step-by-step explanation:

f(12)=-2/3(12)+5

f(12)=-8+5

f(12)=-3

[tex]f(x)=-\frac{2}{3}x+5[/tex]

f(12) this means that x is 12, so you can plug in 12 for "x" in the function:

[tex]f(x)=-\frac{2}{3}x+5[/tex]

[tex]f(12)=-\frac{2}{3}(12)+5[/tex]

[tex]f(12)=-\frac{24}{3} +5[/tex]

f(12) = -8 + 5

f(12) = -3

Your answer is -3

Answer:

[tex] 38^\circ [/tex]

Step-by-step explanation:

We assume that the ground is horizontal and the tower is vertical. The guy wire, the ground, and the tower form a right triangle. The guy wire is the hypotenuse. I'll call the angle formed by the guy wire and the ground angle A. For angle A, the tower is the opposite leg. Since we know the opposite leg and the hypotenuse, we use the sine ratio.

[tex] \sin A = \dfrac{opp}{hyp} [/tex]

[tex] \sin A = \dfrac{13~m}{21~m} [/tex]

To find the measure of angle A, we use the inverse sine function.

[tex] A = \sin^{-1} \dfrac{13}{21} [/tex]

[tex] A = \sin^{-1} 0.6190476 [/tex]

[tex] A = 38^\circ [/tex]

Answer:

152% of 72 = 109.44

Step-by-step explanation:

2x = 15 - 3x -- add 3x to both sides

5x = 15 -- divide both sides by 5

x = 3 -- simplest form

For this case, we must find the value of "x" of the following equation:

[tex]2x = 15-3x[/tex]

We add 3x to both sides of the equation:

[tex]2x + 3x = 15-3x + 3x\\5x = 15[/tex]

We divide between 5 on both sides of the equation:

[tex]\frac {5x} {5} = \frac {15} {5}\\x = 3[/tex]

Thus, the value of x is 3.

Answer:

[tex]x = 3[/tex]

Answer:

48 spices

Step-by-step explanation:

The number of spices each has is a multiple of 5, 3, and 4.

The number of spices each has is 5x, 3x, and 4x.

Pru has 5x spices.

Piper has 3x spices.

Pru has 24 more spices than Piper, so

5x = 3x + 24

2x = 24

x = 12

Phoebe has 4x spices, so Phoebe has

4(12) = 48

So remember that ratios are part to part, not part to whole like fractions are. In this case:

5 + 3 + 4 = 12

There are 12 parts total. This means that Pru has 5/12 of the spices, Piper has 3/12 (or 1/4) of the spices and Phoebe has 4/12 (or 1/3) of the spices. Now, we also know that Pru has 24 more spices than piper. With this info, we can set up our equation as (x = total amount of spices):

[tex]\frac{5}{12}x=\frac{3}{12}x+24[/tex]

From here we can solve for the total amount of spices. Firstly, subtract both sides by 3/12x:

[tex]\frac{2}{12}x=24[/tex]

Next, multiply both sides by 12/2 (or 6):

[tex]x=144[/tex]

There are a total of 144 spices. Now, to get Phoebe's amount of spices multiply 1/3 by 144:

[tex]\frac{144}{1}*\frac{1}{3}=\frac{144}{3}=48[/tex]

In short, Phoebe has 48 spices.

[tex]3x+4y=2\qquad\text{subtract 3x from both sides}\\\\4y=-3x+2\qquad\text{divide both sides by 4}\\\\y=-\dfrac{3}{4}x+\dfrac{2}{4}\to y=-\dfrac{3}{4}x+\dfrac{1}{2}\\\\for\ x=0\to y=-\dfrac{3}{4}(0)+\dfrac{1}{2}=0+\dfrac{1}{2}=\dfrac{1}{2}\to\left(0,\ \dfrac{1}{2}\right)\\\\for\ x=2\to y=-\dfrac{3}{4}(2)+\dfrac{1}{2}=-\dfrac{3}{2}+\dfrac{1}{2}=-\dfrac{2}{2}=-1\to(2,\ -1)\\--------------------------------\\[/tex]

[tex]4x+y=-4\qquad\text{subtract 4x from both sides}\\\\y=-4x-4\\\\for\ x=0\to y=-4(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=-1\to y=-4(-1)-4=4-4=0\to(-1,\ 0)\\\\Answer:\ \boxed{A.\ (-1.4,\ 1.5)}[/tex]

The approximate solution for the system of equations 3x + 4y = 2 and 4x + y = –4 will be (–1.4, 1.5). Then the correct option is A.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

3x + 4y = 2      …1

4x + y = -4       …2

From equation 2, we have

y = –4 – 4x

Put in equation 1, we have

3x + 4(–4 – 4x) = 2

3x – 16x – 16 = 2

–13x = 18

x = –18/13

x = –1.38

x ≈ –1.4

Then the value of y will be

y = –4 – 4(–1.38)

y = 1.52

y ≈ 1.5

Then the correct option is A.

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To find the number of fictional books in the library, multiply the total number of books by 0.60 which is 138.

To find the number of fictional books in the library, we need to calculate 60% of the total number of books. Thus the concept of percentage calculation will be followed.

Calculating 60% of 230 -

= 60/100 x 230

= 13800/100

= 138

Therefore, there are 138 fictional books in the library.

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Multiply the denominators. Way 2: Move decimal points, divide, and place a decimal point in the quotient. Step 1 Write a decimal point and a zero in the dividend. Step 2 Multiply the divisor by a power of 10 to get a whole number.

Answer:

-20

Step-by-step explanation:

If we get -5 points for each question you answer incorrectly, and we answer 4 questions incorrectly, than we can simply multiply -5 by 4 to get -20.

Answer:

(-20) is an integer represents the change in score.

Step-by-step explanation:

Penalty for answering a question incorrectly = -5

Number of questions answered incorrectly = 4

If we had answered 4 question incorrectly then the penalty of marks will be:

[tex]-5\times 4=-20[/tex]

(-20) is an integer represents the change in score.

Answer:

D

Step-by-step explanation:

As the angle Known to us is (2y-3)°

Now

∠B = (2y-3)°              (when two parralel lines are cut by another line then angles opposite are equal)

∠D=180-(2y-3)°           (Because angle to the line is same as B and as on one line total angle is 180° one part equals to B so other equals to 180-∠B)

Similarly

∠Q=∠D = 180-(2y-3)°

Because interior angles of a line cutting by a same line will be equal

Answer:

P (not black ) = 5/7

Step-by-step explanation:

We need to know the total number of marbles

2 red + 3 green + 2 black = 7 marbles

P (not black ) = Not black/ total

                      = ((2 red+ 3 green)/ total

                     = 5/7

The distance between the points (2,-3) and (0,8) can be calculated using the distance formula which derives from the Pythagorean theorem. After plugging in the coordinates into the formula, we get the distance approximately equal to 11.2.

To calculate the distance between the points (2,-3) and (0,8), we can make use of the distance formula derived from the Pythagorean theorem. The distance formula is: d = √[(x2-x1)² + (y2-y1)²].

Here, (x1, y1) = (2, -3) and (x2, y2) = (0, 8).

Now, plug the coordinates into the formula:

d = √[(0 - 2)² + (8 - -3)²]

d = √[(-2)² + (11)²]

d = √[4 + 121]

d = √125

So, the distance to the nearest tenth between (2,-3) and (0,8) is approximately 11.2.

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Answer:

The right option is C) 21.75

Step-by-step explanation:

we have given,

Number of shares = 75

Cost of each share = $24.13

Total cost of shares = 75×24.13 = $1809.75

since the company paid annual dividends of $0.29 per share.

Total annual dividends company paid = 75×0.29 = $21.75

Hence the right option is C) 21.75

Answer:

Sarah spent 45.76

Jack spent 38.16

Jack spent more on tax

Step-by-step explanation:

Sarahs game costs:

tax = 44 *.04 = 1.76

Total cost = game + tax

                  = 44 + 1.76

                  =45.76

Jacks game costs:

tax = 36 *.06 = 2.16

Total cost = game + tax

                  = 36 + 2.16

                  =38.16

Jack spent more on tax

Answer:

B. (-3, -6)

Step-by-step explanation:

(1)   6x  - 4y = 6

(2) -6x + 3y = 0      Add (1) and (2)

              -y = 6       Multiply each side by -1

               y = -6      Substitute in (2)

 -6x +3(-6) = 0       Remove parentheses

    -6x – 18 = 0      Add 18 to each side

           -6x = 18      Divide each side by -6

             x = -3

The solution is (-3, -6).

Answer:

250 yellow thumbtacks

Step-by-step explanation:

7:10 ratio (17 thumbtacks)

425 / 17 = 25

7 x 25 = 175 green

10 x 25 = 250 yellow

Answer:

x = 54 cookies

Step-by-step explanation:

We can use ratios to solve this problem

1 1/3 cups chocolate chips    3 cups chocolate chips

------------------------------------  = --------------------------------------

24 cookies                                   x cookies

Using cross products

1 1/3 * x = 3 * 24

Let change 1 1/3 to an improper fraction

1 1/3 = (3*1+1)/3 = 4/3

4/3 x = 72

Multiply each side by 3/4 to isolate x

3/4 * 4/3x = 72*3/4

x = 54 cookies

Answer:

10 pounds of trial mix that costs $2.45 and 20 pounds of trial mix that costs $2.30

Step-by-step explanation:

[tex]\\\text{Let x pounds of the trial mix that costs \$2.45 per pound, and y pounds of the trial mix}\\\text{that costs \$2.30 per pound are added to get a 30 pounds of trial mix }\\\text{that costs \$2.35 per pound. since the total mixture is 30 pounds, so we get}\\\\x+y=30\ \ \ \ \ \ \  \ \ \ \ \  \  ...... (i)\\\\\text{and the total cost equation is given by}\\\\\$2.45 x + \$2.30 y=\$2.35 (30)\\\\2.45 x + 2.30 y=70.5 \ \ \ \ \ \ \ \ \ \ \ \ \ ...... (ii)\\[/tex]

[tex]\text{now to solve the equation (i) and (ii), we'll substitute }y=30-x \text{ from (i) into (ii)}\\\text{so we get}\\\\2.45x+2.30(30-x)=70.5\\\\2.45x+69-2.30x=70.5\\\\\Rightarrow 2.45x-2.30x=70.5-69\\\\\Rightarrow 0.15x=1.5\\\\\Rightarrow x=\frac{1.5}{0.15}\\\\\Rightarrow x=10\\\\\text{plug this value of x in (i), we get}\\\\y=30-x=30-10=20\\\\\text{so we must add 10 Pounds of trial mix that costs \$ 2.45 and 20 pounds of}\\\text{the trial mix that costs \$2.30}[/tex]

Final answer:

To create a 30-pound trail mix costing $2.35 per pound, mix 20 pounds of $2.45 trail mix with 10 pounds of $2.30 trail mix.

Explanation:

Trail mix costing: $2.45 per pound and $2.30 per pound must be mixed to get a 30-pound mix costing $2.35 per pound.

To calculate:

Let x = pounds of $2.45 mix and y = pounds of $2.30 mix.

Set up the system of equations: x + y = 30 and (2.45x + 2.30y)/30 = 2.35.

Solve the system to find x = 20 pounds of $2.45 mix and y = 10 pounds of $2.30 mix.

Final answer:

For two independent events A and B, the conditional probability P(A|B) is equal to the probability of A. Since P(A) is given as 0.40 and the events are independent, P(A|B) is also 0.40.

Explanation:

The question pertains to the concept of conditional probability for independent events in probability theory. When we have two independent events A and B, the conditional probability P(A|B), which is the probability of event A given that event B has occurred, is simply the probability of A, because the occurrence of B does not affect the probability of A when events are independent. This is expressed as P(A|B) = P(A).

Given P(A) = 0.40 and P(B) = 0.20, and knowing that A and B are independent, we can state that:

P(A\B) = P(A)

The probability that event A occurs given that event B has also occurred is 0.40, which is the original probability of A.

Answer:

52 miles

Step-by-step explanation:

We can use a ratio to solve this problem.  Let put miles over time.  We know that 1 hour = 60 minutes.  We need to have the units the same.

130 miles          x miles

--------------     = ---------------

150 minutes      60 minutes

Using cross products

130 * 60 = 150 x

Divide each side by 150

130/150 * 60 = 150x/150

52 =x

Answer:

L=$24.95 , G=$12.75

Step-by-step explanation:

This problem is a classic system of equations problem.  There are several methods of solving these problems, because of the circumstances and values given I think it's best to use the elimination method.  The elimination method attempts to cancel out a variable by subtracting one equation from another.  

The first statement Marie received an order of 5 trays of lasagna and 3 trays of garlic bread for a total of $163.  I'm going to use "L" for lasagna and "G" for garlic bread.  Therefore, the equation for the scenario above is:

[tex]5L+3G=163[/tex]

In the second statement Marie received an order of 4 trays of lasagna and 4 trays of garlic bread and so:

[tex]4L+4G=150.80[/tex]

Now we cannot use the elimination method directly because equation 1 and equation 2 do not have any coefficients in common.  However, we can eliminate "G" by first multiplying the top equation by 4 and the bottom equation by 3.  We are doing this because those are the coefficients of the other equation, and thus will return a common value as such:

Equation 1:

[tex]4(5L+3G=163)\\20L+12G=652[/tex]

Equation 2:

[tex]3(4L+4G=150.80)\\12L+12G=452.40[/tex]

Now we can subtract equation 2 from equation 1 and eliminate the "G" variable as such:

[tex]20L+12G=652\\-(12L+12G=452.40)\\\\8L+0G=199.60\\\\8L=199.60\\\\[/tex]

By solving for L we obtain:

[tex]8L=199.60\\\\\frac{8L}{8}=\frac{199.60}{8}\\\\L=24.95[/tex]

Therefore, one tray of lasagna is $24.95.  Now that we know the value of "L" we can use any of our original equations to figure out what "G" is.  I'll use the first equation and so:

[tex]5L+3G=163\\\\5(24.95)+3G=163\\\\124.75+3G=163\\\\124.75-124.75+3G=163-124.75\\\\3G=38.25\\\\\frac{3G}{3}=\frac{38.25}{3}\\\\G=12.75[/tex]

And so the price of a tray of garlic bread is $12.75.  So the answer is the price of lasagna = $24.95  and garlic bread = $12.75

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Answer:

lasagna = $24.95 and garlic bread = $12.75

:)

Answer: second one (B) - 2.045, 2.43, 259

Step-by-step explanation: 2.045 is the lowest value due to the 0 in the hundredths place. 2.43 has a lower value than 259, it being a decimal.

Answer:

Yes

Step-by-step explanation:

Segments AB and CD are parallel and 3 units apart.

Point D is 2 units left of point A, and point C is 2 units right of point B. The trapezoid is symmetrical about the line x = 3.5, so is isosceles.

Answer:

Isosceles trapezoid

Step-by-step explanation:

1)By definition, an isosceles trapezoid has two congruent sides and four vertices. According to the given coordinate points, what we have is an isosceles trapezoid. Graphically, we can say that:

[tex]\overline{AD} \cong \overline BC[/tex]

2) Proving with Analytical Geometry that

[tex]\overline{AD} \cong \overline BC[/tex]

[tex]D_{BC}=\sqrt{(1-4)^{2}+(7-5)^{2}}\Rightarrow D_{BC}=\sqrt{9+4}\Rightarrow D_{BC}=\sqrt{13}\cong3.61\\D_{AD}=\sqrt{(1-4)^{2}+(0-2)^{2}}\Rightarrow D_{AD}=\sqrt{9+4}\Rightarrow D_{AD}=\sqrt{13}\cong3.61[/tex]

Answer:

10 and 4

Step-by-step explanation:

So let's set up equations. So x+y=14. And 6x+8y=92. So 2y=8 or y=4. So x=10.

Adding a number to the variable moves the graph horizontally to the left.

The answer is B.

there are many combinations for it, but we can settle for say

[tex]\bf \begin{cases} f(x)=x+2\\[1em] g(x)=\cfrac{9}{x^2}\\[-0.5em] \hrulefill\\ (f\circ g)(x)\implies f(~~g(x)~~) \end{cases}\qquad \qquad f(~~g(x)~~)=[g(x)]+2 \\\\\\ f(~~g(x)~~)=\left[ \cfrac{9}{x^2} \right]+2\implies f(~~g(x)~~)=\cfrac{9}{x^2}+2[/tex]

Problem 1

One possible answer is y = -x+5

This equation has a slope of -1 as does the first equation y = -x+3. Parallel lines have equal slopes but different y intercepts.

You can change the "+5" to any number you want.

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

Problem 2

One possible answer is y = (3/4)x - 2. Like before, parallel lines have the same slope, just a different y intercept. The "-2" can be any number (negative or positive) you want as long as the slope remains 3/4.

The reference angle for [tex]31\pi[/tex] 6 by conversion of radians to degrees is [tex]210^o[/tex].

One radian is defined as the angle formed by the center of a circle intersecting an arc of length equal to the radius of the circle.

There are [tex]\pi[/tex] radians in [tex]180^o[/tex], So,[tex]\dfrac{31\pi}{6}[/tex] must be multiplied by [tex]\dfrac{180}{\pi}[/tex]to obtain the angle in degrees.

[tex]\dfrac{31\p}{6} \times \dfrac{180}{\pi}[/tex]

= [tex]\dfrac{31 \times 180}{6}[/tex]

=[tex]31 \times 30[/tex]

= [tex]930^o[/tex]

Since the reference angle is always positive and is formed with the x-axis, we need to find the acute angle formed between the terminal side of the angle and the positive x-axis.

The reference angle can be calculated by subtracting the closest multiple  [tex]180^o[/tex] from the angle in degrees.

[tex]930^o - 2\times 180^o[/tex]

= [tex]930^o - 360^o[/tex]

=[tex]570^o[/tex]

However, the reference angle should always be between [tex]0^o[/tex] and [tex]180^o[/tex] So, we take the smaller angle, which is

[tex]570^o- 360^o[/tex]

= [tex]210^o[/tex]

Therefore, the reference angle in degrees  [tex]31\pi6[/tex] is [tex]210^o[/tex]

Learn more about reference angles here:

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The reference angle of the given angle is [tex]30\textdegree.[/tex]

Converting the given angle from radians to degrees:

We know that [tex]\pi[/tex] radians is equal to 180°. Therefore,

[tex]\frac{31\pi}{6}\ radians \times \frac{180\textdegree}{\pi} = \frac{31}{6}\times 180 = 930\textdegree[/tex]

Finding the equivalent angle between 0° and 360°:

Since 930° is greater than 360°, an equivalent angle needs to be found by subtracting multiples of 360° until an angle between 0° and 360° is obtained.

930°−2×360°=930°−720°=210°

Determining the reference angle:

The reference angle is the acute angle that the given angle makes with the x-axis. Since 210° is in the third quadrant, calculating the reference angle as:

210°−180°=30°

Therefore, the reference angle for [tex]\frac{31\pi}{6}[/tex]​ is 30°.