A pyramid has a square base that is 160 m on each side. What is the perimeter of the base in kilometers? Question 19 options:

Answer:

  Reflection across the x-axis

Step-by-step explanation:

The only apparent transformation is negation of the y-coordinate, corresponding to reflection across the x-axis.

Answer:

 Reflection across the x-axis

Step-by-step explanation:

The only apparent transformation is negation of the y-coordinate, corresponding to reflection across the x-axis.

Answer:

(- 6, 6 )

Step-by-step explanation:

Assuming the centre of dilatation is the origin, then

The coordinates of the image points are 3 times the original points

B = (- 2, 2 ), then

B' = ( 3 × - 2, 3 × 2 ) = (- 6, 6 )

Answer:

[tex]\tt B. \ \ \ \cfrac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}[/tex]

Step-by-step explanation:

[tex]\displaystyle\tt \tan75^o=\tan(45^o+30^o)=\frac{\tan45^o+\tan30^o}{1-\tan45^o\cdot\tan30^o} =\frac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}[/tex]

For this case we have to define that:

[tex]tg (x + y) = \frac {tg (x) + tg (y)} {1-tg (x) * tg (y)}[/tex]

So, according to the problem we have:

[tex]tg (45 + 30) = \frac {tg (45) + tg (30)} {1-tg (45) * tg (30)}[/tex]

By definition we have to:

[tex]tg (45) = 1\\tg (30) = \frac {\sqrt {3}} {3}[/tex]

Substituting we have:

[tex]tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1-1 * \frac {\sqrt {3}} {3}}\\tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1- \frac {\sqrt {3}} {3}}[/tex]

Answer:

option B

Answer:

Step-by-step explanation:

This equation is a positive parabola, opening upwards.  Parabolas of this type have a vertex that is a minimum value.  In order to find the year where the population was the lowest, we have to complete the square to find the vertex.  The rule for completing the square is to first set the parabola equal to 0, then next move the constant over to the other side of the equals sign.  The leading coefficient on the x-squared term HAS to be a positive 1.  Ours is a .5, so will factor it out.  Doing those few steps looks like this:

[tex].5(t^2-19.3t)=-100[/tex]

Next we take half the linear term, square it, and add it to both sides.  Don't forget the .5 sitting out front there as a multiplier.  Our linear term is 19.3.  Taking half of that gives us 9.65, and 9.65 squared is 93.1225

[tex].5(t^2-19.3t+93.1225)=-100+46.56125[/tex]

In this process, we have created a perfect square binomial on the left.  Stating that binomial and doing the addition on the right looks like this:

[tex].5(t-9.65)^2=-106.8775[/tex]

Now finally we will divide both sides by .5 then move over the constant again to get the final vertex form of this quadratic:

[tex](t-9.65)^2+106.8775=y[/tex]

From this we can see that the vertex is (9.65, 106.8775) which translates to the year 2009 and 107,000 approximately.

In our situation, that means that the population was at its lowest, 107,000 in the year 2009.

For part b. we will replace the y in the original quadratic with a 200,000 and then factor to find the t values.  Setting the quadratic equal to 0 allows us to factor to find t:

[tex]0=.5t^2-9.65t-199900[/tex]

If you plug this into the quadratic formula you will get t values of

642.02 and -622.72

The two things in math that will never EVER be negative are distances/measurements and time, so we can safely disregard the negative value of t.  Since the year 2000 is our t = 0 value, then we will add 642 years to the year 2000 to get that

In the year 2642, the population in this town will reach 200,000 (as long as it grows according to the model).

Answer:

$1.45

Step-by-step explanation:

The cost of a dozen doughnuts in 1970 is $1.44.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

To calculate the cost of a dozen doughnuts in 1970 we have to know the percentage increase in the price index from 1960 to 1970 and this will be:

Rate = [(48.2 – 29.6) / 29.6] × 100%

Rate = (18.6 / 29.6) × 100%

Rate = 62.83 %

Let's represent the price of a dozen doughnuts in 1970 by X and solve. This will be:

62.83  = (X - 0.89) × 100 / 0.89

(62.83  × 0.89 ) = 100X - 89

55.9 = 100X - 89

100X = 144.9

X = 144.9 / 100

X = $1.44

X = $1.44

Therefore, the cost of a dozen doughnuts in 1970 is $1.44.

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Answer:

The mean of these statistic is 2.18.

Step-by-step explanation:

According to the chart, from 1986-1996, unintentional drug overdose deaths per 100,000 population began to rise.

The given data set is

2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3

Formula for mean:

[tex]Mean=\frac{\sum x}{n}[/tex]

Using this formula, the mean of the data is

[tex]Mean=\frac{2+1+2+2+1+2+2+3+3+3+3}{11}[/tex]

[tex]Mean=\frac{24}{11}[/tex]

[tex]Mean=2.181818[/tex]

[tex]Mean\approx 2.18[/tex]

Therefore the mean of these statistic is 2.18.

The mean of these statistics is [tex]\large{\boxed{\bold{2.18}}[/tex]

Statistics is a study of a collection, preparation, analysis,presentation/conclusions from some data

Data is a collection of information presented in the form of numbers

Data collection can be done through a sample that represents all data (can be called a population) that is used as research

Data information can be stated in tables, diagrams or graphs

The average value or mean is a measure to provide an overview of a set of data

Mean is the average of a number of data

To determine the mean: the sum of all data divided by the amount of data

General formula

[tex]\large{\boxed{\bold{mean=\frac{\sum_{xi}}{n} }}}[/tex]

xi = data

n = amount of data

The numbers for each year for unintentional drug overdose deaths per 100,000 population are: 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3

Total amount of data:

[tex]\displaystyle 2+1+2+2+1+2+2+3+3+3+3=\large{\boxed{24}[/tex]

Amount of data: [tex]\large{\boxed{11}}[/tex]

So the mean value:

[tex]\displaystyle mean=\frac{\sum_{xi}}{n}=\frac{24}{11}=\large{\boxed{\bold{2.18}}}[/tex]

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Answer:

0.75

Step-by-step explanation:

Total number of people = 400

Number of people who say yes to gun laws being more stringent = 300

Number of people who say no to gun laws being more stringent = 100

The proportion of people who will say yes = Number of people who say yes to gun laws being more stringent / Total number of people

[tex]\text{The proportion of people who will say yes}=\frac{300}{400}\\\Rightarrow \text{The proportion of people who will say yes}=\frac{3}{4}=0.75[/tex]

∴ Proportion in the population who will respond "yes" is 0.75

Answer:

160

Step-by-step explanation:

Add the ratios together to get the sum of them is 19.  Since the perimeter is 380, divide 380 by 19 to get 20.  

The shortest side is 3(20) = 60,

the next side is 5(20) = 100, and

the longest side is 8(20) = 160

Answer:

[tex]\large\boxed{x>-2+\sqrt{14}\ \vee\ x<-2-\sqrt{14}}\\\boxed{x\in(-\infty,\ -2-\sqrt{14})\ \cup\ (-2+\sqrt{14},\ \infty)}[/tex]

Step-by-step explanation:

[tex]x^2+4x>10\\\\x^2+2(x)(2)>10\qquad\text{add}\ 2^2=4\ \text{to both sides}\\\\x^2+2(x)(2)+2^2>10+4\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2>14\Rightarrow x+2>\sqrt{14}\ \vee\ x+2<-\sqrt{14}\qquad\text{subtract 2 from both sides}\\\\x>-2+\sqrt{14}\ \vee\ x<-2-\sqrt{14}[/tex]

The value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1

According to the law of base change

[tex]\rm \log _b a = \dfrac{ log _d b}{log_d a}[/tex]

The given expression is

[tex]\rm { log _3 5}\times{log_{25} 9}[/tex]

This can be written as

[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 9 }{log_{10} 3*log _{10}25}[/tex]

[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 3^2 }{log_{10} 3*log _{10}5^2}[/tex]

[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *2log _{10} 3 }{log_{10} 3* 2 log _{10}5}[/tex]

On solving this the value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1

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Answer:

Step-by-step explanation:

Answer:

  0.148623∠321.93°

Step-by-step explanation:

You can work these without too much brain work by converting the coordinates to rectangular coordinates, adding those, then converting back to a vector length and angle as may be required.

  0.111∠90° + 0.234∠300° = 0.111(cos(90°), sin(90°)) +0.234(cos(300°), sin(300°))

  = (0, 0.111) + (0.117, -0.2026499) = (0.117, -0.0916499)

The magnitude of this is found using the Pythagorean theorem:

  |E+F| = √(0.117² +(-0.0916499)²)  ≈ 0.148623

The angle can be found using the arctangent function, paying attention to the quadrant. This sum vector has a positive x-coordinate and a negative y-coordinate, so is in the 4th quadrant.

  ∠(E+F) = arctan(y/x) = arctan(-0.0916499/0.117) ≈ -38.07° = 321.93°

The vector sum is E+F = 0.148623∠321.93°.

__

You can also draw the triangle that has these vectors nose-to-tail and find the magnitude of the sum using the Law of Cosines. The two sides of the triangle are the lengths of the given vectors and the angle between those can be seen to be 30°. Then the length of the 3rd side of the triangle is ...

  |E+F|² = |E|² +|F|² -2·|E|·|F|·cos(30°) = .012321 +.054756 -.044988 = 0.0220887

  |E+F| = √0.0220887 ≈ 0.148623

The direction of the vector sum can be figured from the direction of vector E and the internal angle of the triangle between vector E and the sum vector. That angle can be found from the law of sines to be ...

  (angle of interest) = arcsin(sin(30°)·|F|/|E+F|) = 128.07°

Then the angle of the vector sum is 450° -128.07° = 321.93°.

A diagram is very helpful for keeping all of the angles straight.

  |E+F| = 0.148623∠321.93°

Answer:

[tex]\large\boxed{n\leq9\ or\ n>13\to n\in\left(-\infty;\ 9\right]\ \cup\ (13,\ \infty)\to\{x\ |\ x\leq9\ or\ x>13\}}[/tex]

Step-by-step explanation:

[tex]n-12\leq-3\ or\ 2n>26\\\\n-12\leq-3\qquad\text{add 12 to both sides}\\n\leq9\\\\2n>26\qquad\text{divide both sides by 2}\\n>13\\\\n\leq9\ or\ n>13\to n\in\left(-\infty;\ 9\right]\ \cup\ (13,\ \infty)\to\{x\ |\ x\leq9\ or\ x>13\}[/tex]

Answer:

y = 107x + 20

Step-by-step explanation:

The points that represent the number of credits and the cost of those credits in coordinate form are (9, 983) and (13, 1411).

We can use the slope formula to first find the slope of the line containing those 2 points:

[tex]m=\frac{1411-983}{13-9}=\frac{428}{4}=107[/tex]

The slope is 107.  Now we can pick one of the 2 points and use it in the point-slope form of a line to get the equation we are looking for:

[tex]y-983=107(x-9)[/tex] simplifies to

[tex]y-983=107x-963[/tex] so in slope-intercept form:

y = 107x + 20

Answer:

The first choice is the one you want.

Step-by-step explanation:

If we plot the point (5, -12) we will be in QIV.  Connecting the point to the origin and then drawing in an altitude to the positive x axis creates a right triangle with side adjacent to the angle being 5 units long, and the altitude being |-12|.  To find the sin of theta, we need the side opposite (got it) over the hypotenuse (don't have it).  We solve for the length of the hypotenuse using Pythagorean's Theorem:

[tex]c^2=12^2+5^2[/tex] and

[tex]c^2=169[/tex] so

c = 13.  

Now we can find the sin of the angle in the side opposite the angle over the hypotenuse:

[tex]sin\theta=-\frac{12}{13}[/tex]

The first choice in your answers is the one you want.

To find the sine of an angle, we use the point given on its terminal side to represent a right triangle. The sine is calculated as the ratio of the opposite side to the hypotenuse. Using the point (5, -12), our calculation gives sin(θ) as -12/13.

The question asks about the value of sin 0 where the point on the terminal side is (5, -12). However, in trigonometry, we more commonly write it as sin(θ) such that θ is the angle being referenced. Specifically, we are being asked to find the value of sin(θ) when a point on the terminal side of the angle is (5, -12).

To figure out what sin(θ) is, we use the mathematical definition of sine which states that sin(θ) = opposite/hypotenuse. In this context, we can treat the point (5,-12) as a representation of a right triangle. The x-coordinate is adjacent to the angle and the y-coordinate is opposite the angle. Accordingly, we can say that sin(θ) = -12/13.

This is because the hypotenuse can be calculated using Pythagoras' theorem, where hypotenuse = √[(x-coordinate)^2 + (y-coordinate)^2] which equals  √[(5)^2 + (-12)^2] = √169 = 13. Hence, sin(θ) = (-12)/13.

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Answer:

  (x +8)² +(y +6)² = 100

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r can be written:

  (x -h)² +(y -k)² = r²

For your given values of h=-8, k=-6, r=10, the equation is ...

  (x +8)² +(y +6)² = 100

Answer: 15 yards per mistake.

Step-by-step explanation:

Given : A football team had 4 big mistakes in a game.

i.e. the number of big mistakes done by the football team = 4

The total lost of yards because of the big mistakes done by football team = 60 yards

Now, the portion of  team's yardage change per mistake is given by :-

[tex]\dfrac{\text{Total lost of yards}}{\text{Number of big mistakes}}\\\\=\dfrac{60}{4}=15\text{ yards}[/tex]

Hence, the team's yardage changes by 15 yards per mistake.

Answer:

-15 yardage per mistake

Step-by-step explanation:

Answer:

only C

Step-by-step explanation:

Answer:

546 nuts

Step-by-step explanation:

727272 / 666 = 1092 nuts in each location

crow stole half nuts in 1 location

1092 / 2 = 546 nuts stolen

Answer:

6 nuts.

Step-by-step explanation:

The number of nuts in each location  is 72 / 6 = 12 nuts.

So the crow stole 1/2 * 12 = 6 nuts.

Answer:

Step-by-step explanation:

It can be easier to see the answer if you subtract the right side of the equation from both sides, then simplify.

1. 2(x + 2) + 2 = 2(x + 3) + 1

  2(x + 2) + 2 - (2(x + 3) + 1) = 0

  2x +4 +2 -2x -6 -1 = 0

  -1 = 0 . . . . no solution

__

2. 2x + 3(x + 5) = 5(x – 3)

  2x + 3(x + 5) - 5(x – 3) = 0

  2x +3x +15 -5x +15 = 0

  30 = 0 . . . . no solution

__

3. 4(x + 3) = x + 12

  4(x + 3) - (x + 12) = 0

  4x +12 -x -12 = 0

  3x = 0 . . . . one solution, x=0

__

4. 4 – (2x + 5) = (–4x – 2)

  4 – (2x + 5) - (–4x – 2) = 0

  4 -2x -5 +4x +2 = 0

  2x +1 = 0 . . . . one solution, x=-1/2

__

5. 5(x + 4) – x = 4(x + 5) – 1

  5(x + 4) – x - (4(x + 5) – 1) = 0

  5x +20 -x -4x -20 +1 = 0

  1 = 0 . . . . no solution

Answer:

The answer is a,b and e.

Step-by-step explanation:

a. 2(x + 2) + 2 = 2(x + 3) + 1

b. 2x + 3(x + 5) = 5(x – 3)

e. 5(x + 4) – x = 4(x + 5) – 1

i just did this question on my test hope that helps ;) !

Answer:

x = 18.

Step-by-step explanation:

As they are congruent, BC = DC  so

x + 12 = 2x - 6

12 + 6 = 2x - x

x = 18.

Answer:

x=18

Step-by-step explanation:

Because of the SSS criterion, The congruent sides are equal to each other. Meaning, Side AB is congruent to side AD. With this, you can set side BC and side DC equal to each other to solve for x.

x+12=2x-6

You subtract x to both sides;

12=x-6

You then add 6 to both sides to get x alone.

18=x or x=18.

Answer:

Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available

Step-by-step explanation:

Creating a stuffed animal when there are 6 animals, 3 fur colors, and 12 clothing themes available

This condition requires multiplication or factorials to determine outcomes

Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available

This situation requires the addition counting principle to determine the number of possible outcomes as there is only one car to be picked so all the numbers 10+5+3 = 18 will be added to get the possible outcomes ..

Answer:

C [tex]P(v)=2(v+7)[/tex]

Step-by-step explanation:

Lets say that [tex]P(v)=y[/tex] for simplicity.

In order to find the inverse of a function, we must switch the location of the variable, v, and y. Then we have to solve for y.

As we are already given the inverse, doing the same process again will give us the original function.

First we can set up the equation

[tex]y=\frac{1}{2} v-7[/tex]

Next we can switch the location of the variables

[tex]v=\frac{1}{2} y-7[/tex]

Now we can solve for y

[tex]v=\frac{1}{2} y-7\\\\v+7=\frac{1}{2} y\\\\y=2(v+7)\\\\P(v)=2(v+7)[/tex]

This gives us the function

[tex]P(v)=2(v+7)[/tex]

Answer:

C P(v) = 2(v+7)

Step-by-step explanation:

To find P(v), we need to take the inverse of P^-1 (v)

y = 1/2 v-7

Exchange y and v

v = 1/2 y-7

Solve for y

Add 7 to each side

v+7 = 1/2 y -7+7

v+7 = 1/2y

Multiply each side by 2

2(v+7) = 1/2 y*2

2(v+7) = y

P(v) = 2(v+7)

Answer: [tex]278\°14'24''[/tex]

Step-by-step explanation:

 You know that:

[tex]1\ hour=60\ minutes\\\\1\ minute=60\ seconds[/tex]

Then, in order to convert the given decimal degree to Degrees Minutes Seconds (DMS), you need to follow these steps:

1) The whole number  278 gives you the degrees.

2)  Multiply 0.24 by 60:

[tex]0.24*60=14.4[/tex]

The whole number 14 gives you the minutes.

3)  Multiply 0.4 by 60:

[tex]0.4*60=24[/tex]

This gives you the seconds.

Therefore, 278.24 written in DMS form is:

[tex]278\°14'24''[/tex]

Answer:

The answer is 278°14'24''

Step-by-step explanation:

Given :  278.24

To find : written in DMS form.

Solution : We have given that 278.24

Multiply 24 by 60 to convert it into minute

We can write it as  278 + .24(60).

278°14.4'

Rewrite 278°14+.4'

4' = 4 ( 60) to convert minute in to second.

278°14+.4(60)

278°14'24''

The answer is 278°14'24'' ....

Answer:

The probability of hitting the bullseye at least once in 6 attempts is 0.469.

Step-by-step explanation:

It is given that a mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt.

The probability of hitting bullseye in each attempt, p = 0.10

The probability of not hitting bullseye in each attempt, q = 1-p = 1-0.10 = 0.90

Let x be the event of  hitting the bullseye.

We need to find the probability of hitting the bullseye at least once in 6 attempts.

[tex]P(x\geq 1)=1-P(x=0)[/tex]       .... (1)

According to binomial expression

[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]

where, n is total attempts, r is number of outcomes, p is probability of success and q is probability of failure.

The probability that the dart thrower not hits the bullseye in 6 attempts is

[tex]P(x=0)=^6C_0(0.10)^0(0.90)^{6-0}[/tex]

[tex]P(x=0)=0.531441[/tex]

Substitute the value of P(x=0) in (1).

[tex]P(x\geq 1)=1-0.531441[/tex]

[tex]P(x\geq 1)=0.468559[/tex]

[tex]P(x\geq 1)\approx 0.469[/tex]

Therefore the probability of hitting the bullseye at least once in 6 attempts is 0.469.

Answer:

  (x, y, z) = (3, 1, 2)

Step-by-step explanation:

Solving using a calculator, I would enter the coefficients of 1/x, 1/y, 1/z as they are given. The augmented matrix in that case looks like ...

[tex]\left[\begin{array}{ccc|c}\frac{1}{2}&\frac{1}{4}&-\frac{1}{3}&\frac{1}{4}\\1&-\frac{1}{3}&0&0\\1&-\frac{1}{5}&4&\frac{32}{15}\end{array}\right][/tex]

My calculator shows the solution to this set of equations to be ...

So, (x, y, z) = (3, 1, 2).

___

Doing this by hand, I might eliminate numerical fractions. Then the augmented matrix for equations in 1/x, 1/y, and 1/z would be ...

[tex]\left[\begin{array}{ccc|c}6&3&-4&3\\3&-1&0&0\\15&-3&60&32\end{array}\right][/tex]

Adding 3 times the second row to the first, and adding the first row to the third gives ...

[tex]\left[\begin{array}{ccc|c}15&0&-4&3\\3&-1&0&0\\21&0&56&35\end{array}\right][/tex]

Then adding 14 times the first row to the third, and dividing that result by 77 yields equations that are easily solved in a couple of additional steps.

[tex]\left[\begin{array}{ccc|c}6&3&-4&3\\3&-1&0&0\\3&0&0&1\end{array}\right][/tex]

The third row tells you 3/x = 1, or x=3.

Then the second row tells you 3/3 -1/y = 0, or y=1.

Finally, the first row tells you 15/3 -4/z = 3, or z=2.

Answer:

[tex]w=\frac{A}{l}[/tex]

Step-by-step explanation:

The formula to find the area of a rectangle is: [tex]A=w \times l[/tex], where [tex]w[/tex] is width and [tex]l[/tex] is length.

So, if we knoe the area [tex]A[/tex] and the length [tex]l[/tex], we can find the width with the formula

[tex]w=\frac{A}{l}[/tex]

You can get this answer by using the defintion of area, which is the first equation, and isolating [tex]w[/tex].

Remember, when we want to move a factor to the other side of the equalty, we must pass it with the opposite operation. So, in this case, width was multiplying, and it passed to the other side dividing.

Therefore, the answer here is [tex]w=\frac{A}{l}[/tex]

Answer:

B. 259

Step-by-step explanation:

This is an exercise in PEMDAS, the order of mathematical operations:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction

Parentheses:          [(18 − 6)⋅3 + 1]⋅7

       Subtraction: = [(12)·3 +1]·7

    Multiplication: = [36 + 1]·7

            Addition: = [37]·7

Parentheses:       = 37·7

    Multiplication: = 259

Answer:

259

Step-by-step explanation:

Answer:

  2√13

Step-by-step explanation:

The distance formula is useful for this. One end of the vector is (0, 0), so the measure of its length is ...

  d = √((x2 -x1)² +(y2 -y1)²) = √((6 -0)² +(-4-0)²)

  = √(36 +16) = √52 = √(4·13)

  d = 2√13 = |(6, -4)|

Answer:

I'm not quite sure but I think it's either 21.6 miles or 22 (Mostly 21.6 though, is what i think at least).

Answer:

20%

Step-by-step explanation:

Population of white-tailed deer in 1991 = 25 deer per square mile

Population of white-tailed deer in 1992 = 30 deer per square mile

We have to find the percentage increase in the deer population. The formula for percentage change is:

[tex]\frac{\text{New Value - Original Value}}{\text{Original Value}} \times 100 \%[/tex]

Original value is the population in 1991 and the New value is the population in 1992.

Using the values, we get:

[tex]\frac{30-25}{25} \times 100 \%\\\\ = 20%[/tex]

Thus, the deer population increased by 20% from 1991 to 1992

Final answer:

The deer population in the state park in Indiana increased by 20% from 1991 to 1992.

Explanation:

The question asks by what percentage the deer population increased between 1991 and 1992 in a state park in Indiana. To calculate the percentage increase, we use the formula: Percentage Increase = ((New population - Original population) / Original population) × 100%. Applying this formula to the given numbers, we have:

Original population in 1991 = 25 deer per square mile

New population in 1992 = 30 deer per square mile

Percentage Increase = ((30 - 25) / 25) × 100% = (5 / 25) × 100% = 20%

Therefore, the deer population increased by 20% from 1991 to 1992.