In the Olympic National Park, there are currently 3310 squirrels,
and the population is increasing at an annual rate of 4%.
a. Write an exponential function to model the squirrel
population in terms of the number of years from now.
b. Explain what each value in the model represents.
Dredict the number of couvrole that will be in the region

The first statement is given, the second statement is true because they are vertically opposite angles and the third statement is true by SAS congruency of triangles.

What is congruence of triangles?

Two triangles that are congruent will have precisely the same three sides and three angles.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.

The first statement is true because this is already given in the question.

The second statement is true because ∠KLJ and ∠MLN are vertically opposite angles and we know that vertically opposite angles are always equal. Therefore, the second statement is true.

The third statement is true because of the SAS congruency of triangles.

As we are given ratio of two sides equal to ratio of corresponding sides and the angle between the sides to be equal.

Hence, the two triangles are congruent.

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The equation of the straight line will be -

y = x - 4.

The general formula of a straight line will be -

y = mx + c

Given is a graph of straight line as shown in the image.

We can write the equation as -

y = mx + c

Now, we can write the slope as -

m = (0 + 4)(4 - 0) = 4/4 = 1

{m} = 1

{y} - intercept = - 4

{c} = - 4

We can write the equation as -

y = x - 4

Therefore, the equation of the straight line will be -

y = x - 4.

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When a number is randomly selected from the set of consecutive integers, it has a 3/4 chance of being divisible by 1995.

A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A chance is a number between zero and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or chance that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed in percentages ranging from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain occurrence relative to all possible outcomes.

given

99-20+1 = 80 potential outcomes.

Now, a number that may be divided by 12 must include the digits 2*2*3.

The realisation that c(c21)(21) = c(c1)c(c+1) is the same as c3c3 is perhaps the trickiest.

The latter statement indicates that you indeed have a group of three consecutive integers that are divisible by 12. Every three consecutive integers must be divisible by three, according to a rule.

The main question is how many of the numbers you choose are divisible by 22=4 22=4.

In this scenario, c can either be 21, 23, 25, 95, 97, 99, so 99212 9921/2 + 1 = 40 OR 20, 24, 26, 92, 96, so 96204 9620/4 + 1 = 20.

Thus, 40+2080 = 60/80 and 40+20/80 = 40/80

60/80 = 3/4

When a number is randomly selected from the set of consecutive integers, it has a 3/4 chance of being divisible by 1995.

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Answer:

$1182.65

Step-by-step explanation:

(8.5/100)×$1090

(85/1000)×1090

$1853/20

=$92.65

thus, $1090+$92.65

=$1182.65

The number of  teaspoons that are there in 6 milliliters is 1.21731 US  teaspoons.

The concept that will be used here is conversion of units. Unit conversion is the process of changing measurements of the same quantity between different units by multiplying or dividing them. The act of converting something from one form to another in mathematics, such as from inches to millimeters or from liters to gallons, is known as conversion.

1 tsp  = 4.93 mL

Then Xtsp = 6ml

The cross multiply, Xtsp= (1 tsp *6ml)/4.93 mL

Then 6 milliliters= 1.21731 US  teaspoons

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Answer:15

Step-by-step explanation:

its the middle number

Answer: i think it's 15!!

hope this helps lol

The solution to the system of equations in this problem is given as follows:

(5,9).

The system of equations for this problem is defined as follows:

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

From the image given at the end of the answer, the solution to the system of equations is given as follows:

(5,9).

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The coordinates of the midpoint M of the segment FG is (-2,2).

This question is incomplete, the complete question is;

What is the midpoint M of a line having two endpoints F(-7, 12) and G(3, -8),

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point F (-7, 12)

Point G (3,-8)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( (-7 + 3 )/2, ( 12 + (-8) )/2 )

M = ( ( -4 )/2, ( 12 - 8 )/2 )

M = ( ( -4 )/2, ( 4 )/2 )

M = ( -2, 2 )

Therefore, the  midpoint M of the segment is (-2,2)

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The coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.

A coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial. It is usually a number, but sometimes may be replaced by a letter in an expression. For example, in the expression: ax2 + bx + c, x is the variable and 'a' and 'b' are the coefficients.

coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable and written next to it. The variables which do not have a number with them are assumed to be having 1 as their coefficient.

Let [tex]$x$[/tex] denote the claim sizes

[tex]& x= \begin{cases}100 & ; p=0.05 \\200 & ; p=0.2 \\300 & ; p=0.5 \\400 & ; p=0.2 \\500 & ; p=0.05\end{cases}[/tex]

[tex]& \mu_1^{\prime}=\varepsilon(x)=\sum x^0 p(x=x)=300 \\\\& \mu_2{ }^{\prime}=\sum x^2 p(x)=98000 \\\\& \mu_3^{\prime}=\sum x^3 p(x)=342 \times 10^5 \\[/tex]

[tex]& \mu_4^{\prime}=\sum x^4 p(x)=1.262 \times 10^{10} \\\\& \mu_2=\mu_2^{\prime}-\left(\mu_1^{\prime}\right)^2=8000 \\\\& \mu_3=\mu_3^{\prime}-3 \mu_2^{\prime} \\\\\mu_1^{\prime}+2\left(\mu_1^{\prime}\right)^3=0 \\\\& \mu_4=\mu_4^{\prime}-4 \mu_3^{\prime} \mu_1^{\prime}+6[/tex]

[tex]\mu_2^{\prime} \mu_1^{\prime 2}-3 \mu_1^{\prime 4} \\& \mu_4=2 \times 10^8 \\\\& \beta_1=\frac{\mu_3{ }^2}{\mu_2^3}=0 \quad \Rightarrow y_1=0 \\\\& \beta_2=\frac{\mu_4}{\mu_2{ }^2}=\frac{2 \times 10^8}{64 \times 10^6}=3.125\\ \\& y_2=\beta_2-3=0.125 \\[/tex]

Therefore, coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.

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The inequality expression that can represent the above scenario is
80x + 13600 ≤ 27000.

In mathematics, Inequality is an expression that is used for unequal comparison of two numerical expressions or algebraic expressions.

Instead of an equal sign here, we use signs like Less than (<), Greater than (>), Less than or equal (≤), Greater than or equal (≥), and Not equal (≠), etc.  

Like Linear equations here we use variables like x, y, z .. etc. to represent the unknown quantities or numbers

Here we have

A shipping container will be used to transport several 80-kilogram crates across the country by rail.  

The greatest weight that can be loaded in container is 27000 kilograms.

Other shipments weight = 13600 kilograms  

Let 'x' be the number of crates that can be transported

Weight of 'x' number of crates = 80kg × (x) = 80x  kg

As we know the greatest weight that can be loaded is 27000 kilograms. So here is the total weight of 'x' crates and the other shipment's weight must be less than 27000 kilograms but not more.  

=> 80x + 13600 ≤ 27000

Therefore,

The inequality expression that can represent the above scenario is
80x + 13600 ≤ 27000.

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As per the following table, the equation of a line of fit for the data round all values to the nearest 10th is  y = -6.199 x 85+ 548.7

In math the term called equation is known as  a mathematical statement that is made up of two expressions connected by an equal sign.

Here we have the following table with the value of ticket price and the number of tickets sold.

Here the First steps is calculated by using the linear regression feature that defines the line of best fit is

=> y = -6.199x + 548.7

When we take the value of x = 85, then we get,

=> y = -6.199 x 85+ 548.7

When we simplify this one then we get

=> y = 21.785 ≈ 22

Hence here this seems a reasonable model to predict the number of tickets sold because we can see that as the ticket price increase, and the number of tickets sold decreases.

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The likelihood of 8 occurrences in a period of 10 minutes is around 0.091 or 9.1%.

According to the Question

A Poisson distribution issue exists here. The Poisson distribution is a discrete probability distribution that quantifies the likelihood of a certain number of events occurring at a certain average rate, regardless of the interval between occurrences, in a given amount of time or space.

The following formula determines the likelihood that x will occur in a Poisson distribution with parameter λ :

P(x; λ) is equal to x / (λx * e(-λ))!

where

λ = the average number of occurrences within the specified time period.

λ in this situation is 4.2. (the mean number of occurrences in 10 minutes).

In order to determine the likelihood of 8 occurring in 10 minutes:

P(8; 4.2) = (4.2^8 * e^(-4.2)) / 8!

⇒ P(8; 4.2) = 0.091 or 9.1%.

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Answer:y=25 x 2 -8

Step-by-step explanation:

25 x 2-8

The ratio of girls to boys in the 6th grade class of 40 pupils is 18:22.

This can be calculated by first finding the total number of boys in the class. 40-18=22. We then use the formula for ratio, which is the ratio of two or more numbers. In this case, it is the ratio of girls to boys. 18:22. This ratio can also be expressed as 18/22 or 0.818181818181818181818181818181818181818181818182 (to three decimal places). A ratio is a comparison of two numbers and can be used to compare different parts of a whole. It can also be used to compare different groups or classes of people. In this case, it is used to compare the number of girls to boys in a 6th grade class.

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She should allow $4107.2 for her current assignment.

Given is that an interior designer recently spent £1359.55 buying 25 kettles and 20 toasters for a smaller group of new houses. For her current assignment she needs 80 kettles and 56 toasters.

The price of kettle and toaster is same. So, we can write -

25x + 20x = 1359.55

45x = 1359.55

x = 30.2

Therefore, the total cost of 80 kettles and 56 toasters will be -

(80 x 30.2 + 56 x 30. 2)

$4107.2

Therefore, she should allow $4107.2 for her current assignment.

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Equations -7 x+7 y = 11  and -4 x + y = 11 have answers of [tex]x=-\frac{11-7 y}{7}$$[/tex] and [tex]x=-\frac{11-y}{4}$$[/tex], respectively.

solve for [tex]$x,-7 x+7 y=11 \quad: \quad x=-\frac{11-7 y}{7}$[/tex]

-7 x+7 y = 11

-7 x = 11 - 7 y Shift 7 y to the right side and subtract 7 from both sides.

[tex]\frac{-7 x}{-7}=\frac{11}{-7}-\frac{7 y}{-7}$$[/tex]

Simplify

[tex]x=-\frac{11-7 y}{7}$$[/tex]

solve for [tex]x,-4 x+y=11: x=-\frac{11-y}{4}$[/tex]

Adjust Y to the right by -4 x=11-y.

Divide -4 from both sides.

[tex]\frac{-4 x}{-4}=\frac{11}{-4}-\frac{y}{-4}$$[/tex]

Simplify

[tex]x=-\frac{11-y}{4}$$[/tex]

Finding an equation's solutions—which are the values (numbers, functions, sets, etc.) that satisfy the equation's condition—is known as solving an equation in mathematics. An equation often consists of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

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The quadratic equation we  use to find the dimensions of the rectangle is w^2 + 6w - 16 = 0

What is Quadratic equation?

The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax^2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients.

What is Rectangle?

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.

Let W be the width of rectangle.

then, length of the rectangle is W + 6 .

and the Area, A = 16 inches^2

And the area of recatngle is A = L x W

Hence, A = (W+6)W

So, 16 = W^2 + 6W

Hence the quadratic equation whichuse to find the dimensions of the rectangle is ;

W^2 + 6W - 16 = 0

By the quadratic formula we have

[tex]w = \frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]w = \frac{-6 \pm \sqrt{6^{2}-4*1*(-16) } }{2*1}[/tex]

[tex]w = \frac{-6 \pm \sqrt{36 + 64} }{2}[/tex]

[tex]w = \frac{-6 \pm 10 }{2}[/tex]'

Hence, we take width as a positive because width never be negative .

so,the value of width is ;

w = 2

and length o rectangle is ;

l = w + 6 = 2 + 6 = 8

l = 8

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The required amount each type of solution to make mixture are  120 ml of 25% acid and 80 ml of 50% acid.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

A liquid mixture known as an acidic solution is created when water and hydrogen ions react. The Brnsted-Lowry theory states that whereas bases "receive" hydrogen protons, acids "give" hydrogen protons. Different solutions have different levels of acidity.

Let there be (200 - x) ml of 50% acid and x ml of 25% acid.

200*0.35 = 0.25x+0.5(200-x)

0.25x +100 -0.5x = 70 

30 = 0.25x 

x=120

200 - x = 200 - 120 = 80, resulting in 120 ml of 25% acid and 80 ml of 50% acid.

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For the mixture, 120 ml of 25% acid and 80 ml of 50% acid are needed for each type of solution.

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Answer: A confidence interval is a range of values that is likely to contain the true population value with a certain level of confidence. To determine a 95% confidence interval for the percentage of people who prefer Candidate A, we can use the following formula:

(Sample proportion) +/- (Margin of error)

The margin of error can be calculated using the formula:

Margin of error = (Critical value) * (Standard deviation)

The critical value is a factor used to compute the margin of error. The critical value for a 95% confidence interval is approximately 1.96. The standard deviation is calculated as:

Standard deviation = √((Sample proportion) * (1 - Sample proportion) / (Sample size))

Plugging in the given values:

Sample proportion = 80% = 0.8

Sample size = 45

Margin of error = (1.96) * √((0.8) * (1 - 0.8) / (45))

Step-by-step explanation:

we would here like to find out the values of given trigonometric ratios . A right angled triangle is given to us with perpendicular= 3 and hypotenuse= 8

Firstly by Pythagoras theorem, we have ,

[tex]\longrightarrow h^2 = p^2 + b^2\\ [/tex]

[tex]\longrightarrow 8^2 = 3^2 + b^2 \\[/tex]

[tex]\longrightarrow 64 = 9 + b^2\\ [/tex]

[tex]\longrightarrow b^2 = 64 -9 = 55\\ [/tex]

[tex]\longrightarrow b =\sqrt{55}\approx 7.41 [/tex]

now as we know that,

[tex]\longrightarrow \cos\theta = \dfrac{base}{hypotenuse}=\dfrac{7.41}{8}\\ [/tex]

[tex]\longrightarrow \underline{\underline{ \cos\theta = 0.92 \approx 1}} [/tex]

And ,

[tex]\longrightarrow \cot\theta =\dfrac{base}{perpendicular}=\dfrac{7.41}{3}\\[/tex]

[tex]\longrightarrow \underline{\underline{\cot\theta = 2.47 \approx 2 }} [/tex]

Finally,

[tex]\longrightarrow \sec\theta =\dfrac{hypotenuse}{base}=\dfrac{8}{7.41}\\[/tex]

[tex]\longrightarrow \underline{\underline{\sec\theta = 1.07 \approx 1 }} [/tex]

and we are done!

Answer: a= -9

Step-by-step explanation:

a+ (−4) = −13

a - 4 = -13 (the 4 becomes -4 as when it comes to + or - it is always -)

    a = -13 +4  (when you switch the side -4 becomes +4)

    a= -9

The slope of the line in the example is 25 and the y-intercept is 10. These values can be used to write the equation of the line in slope-intercept form, y = 25x + 10.

The slope, m, represents the rate of change of the height of the giant kelp plant. In this case, the slope is 25, meaning that for every day that passes, the height of the giant kelp plant increases by 25 centimeters.

The y-intercept, b, represents the height of the giant kelp plant at time = 0. In this case, the y-intercept is 10, meaning that the giant kelp plant is 10 centimeters tall at time = 0.

So in this situation the slope represents how much the height of the kelp plant changes with respect to time and the y-intercept represents the initial height of the kelp plant at time = 0.

To maximise the area it should be build as a square having side=250 feet each and having area=62500 feet.

what are squares?

A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.

The most important properties of a square are listed below:

Area of square=(side)²

Perimeter of square=4*side

Now,

Given

total fencing available=1000feet

perimeter=1000

4*s=1000

s=250 feet

Therefore,

Area=250^2

=62500 feet^2

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The slope of the line segment that represents the period of time during which the speed decreases is: C: The slope is -10.

The parameters given are:

Starting speed of the car = 55 km/hr

Let us suppose when t=0 , the speed of car was 55 km/hr.

Then car broke down.

The following Data are given regarding car's speed versus the amount of time elapsed from the moment that it began to brake.

Elapsed Time (sec) Speed (mph) → 1 :45 ,2 :35, 3 :25, 4 :15, 5 :15 ,6 :15

Slope of line passing through two points (a, b) and (p, q) is given by the formula:

Slope = (q - b)/(p - a)

Thus, Slope of line passing through two points (1,45) and (2,35) is:

Slope = (35 - 45)/(2 - 1)

Slope = -10

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Number of quarters and dime with Pam with the total value of $1.45 is equal to 4 and 4.5 respectively.

Let 'x' represents the number of quarters coins.

And 'y' represents the number of dimes coins.

Value of quarter and dime in dollars is :

1 quarter = $0.25

1 dime = $ 0.10

Total value of all the coins = $1.45

⇒ $0.25x + $0.10y = $1.45

⇒2.5x + y = 14.5

⇒y = 14.5 - 2.5x  __(1)

Number of coins < 9 coins

x + y < 9  

⇒ x < 9 - y  __(2)

Substitute the value of 'y' from (1) we get,

x < 9 - 14.5 + 2.5x

⇒2.5x - x > 14.5 - 9

⇒1.5x > 5.5

⇒ x > 5.5./1.5

⇒ x > 3.7

⇒ x = 4 ( next possible integer)

⇒ y = 14.5 -2.5(4)

⇒y  = 4.5

⇒ y = 4.5

Therefore, the number of quarters and dime with Pam is equal to 4 and 4.5 respectively.

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Option C is correct - X + 52 = 170.

Angle

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

Straight line

A line is a geometry object characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.

According to the question,

∠POR = 170°

∠ROQ = 52°

∠POQ = x,

it is clear by the question,

on the basis of figure attached with this solution,

two angles together make the third angle,

so,

first angle is 52 degree

second angle is x degree,

∠ROQ + ∠POQ  =∠POR  

x + 52 = 170

so the answer is x + 52 = 170.

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The  correct answer is B. $60,350.00. To calculate the value of Whitney's steel house, you need to multiply the annual premium per $100 of coverage ($0.43) by the annual property insurance premium ($603.50) and then divide that by 100. This works out to $60,350.00.

To determine the annual premium per $100 of coverage, you need to look at the table provided in the question. Since Whitney's steel house is located in the country, the annual premium per $100 of coverage is $0.43. Multiplying this by the annual property insurance premium of $603.50 gives you the total value of the house, which is $60,350.00. To summarize, the value of Whitney's steel house can be calculated by multiplying the annual premium per $100 of coverage by the annual property insurance premium and then dividing that by 100. In this case, the value of the house is $60,350.00.

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Question 5 of 10 Whitney's steel house is located in the country. If her building property insurance is $603. 50 per year, how much is her house worth? Annual Premium per $100 of coverage Brick Steel Mixed Wood Area Building Contents rating City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76 Suburb 0. 45 0. 52 0. 56 0. 63 0. 74 0. 83 0. 85 Rural 0. 6 0. 69 0. 71 0. 89 0. 91 1 1. 02 0. 72 0. 8 O A. $17,350.00  B. $60,350.00  C. $171,050.00  D. $603.50