The population of rabbits on an island is growing exponentially. In the year 1990, the population of rabbits was 740, and by 1997 the population had grown to 870. Predict the population of rabbits in the year 2002, to the nearest whole number.

Answer:

100.32

Step-by-step explanation:

1.) 100% + 14% = 114

2.) 114 divided by 100 = 1.14 (the multiplier)

3.) 88 x 1.14 = 100.32

Answer:

90g strawberry jelly, 6 sponge fingers, 315ml custard and 45g tinned fruit

Step-by-step explanation:

just divide everything by 4 to see the value for one and then multiply that value by three!

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129. We can assume a linear growth model on the based of given information.

The given data states that in the year 1985, there were 13 US billionaires. Whereas in 1990, there were 99 US billionaires. We have to find out the formula that predicts the number of US billionaires in any given year (t).

The yearly increase remains constant, so we can consider the formula for the linear function.f(t) = mt + b

where

t is the year and f(t) is the number of US billionaires in that year (t).

m is the slope of the line and b is the y-intercept.

The slope of the line is given by the formula:m = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given values to find the slope of the line.m = (99 - 13) / (1990 - 1985)m = 86 / 5m = 17.2 .The y-intercept of the line can be found by substituting the values of t and f(t) from any of the given points into the equation of the line.

Let's use the point (1985, 13).f(t) = mt + b => f(1985) =17.2(1985) + b => f(1985) = 34,142 + b =>b = 13 - 34,142 & b = -34,129.

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129

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As, we have :

Therefore,

f(3) = 2(3) - 1 = 6 - 1 = 5

Now, g(x) = 9x

Therefore,

g(1) = 9(1) = 9

Now, we have to find value of f(3) + g(1) :

By substituting values, we have :

f(3) + g(1) = 5 + 9 = 14

Hence, value of f(3) + g(1) is 14.

Answer:

\(→f(x) = 2x - 1 \\→ g(x) = 9x \\→ f(3) = 2(3) - 1 \\ f(3) = 6 - 1 \\ f(3) = 5 \\→ g(1) = 9(1) \\ g(1) = 9 \\→ f(3) + g(1) = 5 + 9 \\ \boxed{f(3) + g(1) = 14}\)

Answer:

\( 1400 = x(x+10)= x^2 +10x\)

We can rewrite this expression like this:

\( x^2 +10 x -1400 =0\)

And we can use the quadratic formula given by:

\( x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}\)

Where \( a =1 , b=10 , c= -1400\)

And replacing we got:

\( x = \frac{-10 \pm \sqrt{10^2 -4(10)(-1400)}}{2*1}\)

And solving we got:

\( x_1 =32.75 , x_2 = -42.75\)

And since the value can't be negative the answer would be x = 32.75 and the value of y = 32.75+10 =42.75

Step-by-step explanation:

For this case we know that we have a rectangular playground and the area can be founded with this formula:

\( A = xy\)

Where x represent the width and y the length. From the problem we know that A =1400 m^2 and the heigth is 10m longer than the wide so we can write this condition as:

\( y = 10 +x \)

And replacing this formula into the area we got:

\( 1400 = x(x+10)= x^2 +10x\)

We can rewrite this expression like this:

\( x^2 +10 x -1400 =0\)

And we can use the quadratic formula given by:

\( x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}\)

Where \( a =1 , b=10 , c= -1400\)

And replacing we got:

\( x = \frac{-10 \pm \sqrt{10^2 -4(10)(-1400)}}{2*1}\)

And solving we got:

\( x_1 =32.75 , x_2 = -42.75\)

And since the value can't be negative the answer would be x = 32.75 and the value of y = 32.75+10 =42.75

Answer:

Step-by-step explanation:

Given Data:

Area = 1400m²

L = 4+w

W= w

Area = L * W

1400 = ( 4+W) W ²

1400 = 4w + w ²

w ² + 4w - 1400 = 0

- b ± √ b ² - 4ac / 2a

Where;

a = 1

b = 4

c = -1400

- 4 ± √4² - 4(1)(-1400) / 2(1)

= - 4 ± 74.94 /2

= - 4 + 74.94 / 2 or - 4 - 74.94 / 2

= 35.47 or - 39.47

Answer:

d = 10

Step-by-step explanation:

Ok, so we know that the horizontal distance between the points is 6 and the vertical distance is 8.  Using the Pythagorean theorem we know that 8^2+6^2=d^2 (d is the distance between points). When solving we get

8^2+6^2=d^2

64+36=d^2

100=d^2

d=10

Answer:

359.2 cubic inches

Step-by-step explanation:

An equation with the steepest graph has the largest absolute value of slope.

The equation with the steepest graph is the equation with the largest absolute value of slope.

A slope is a measure of how steep a line is.

If a line has a positive slope, it is rising to the right.

If a line has a negative slope, it is falling to the right.

If the slope of a line is zero, the line is horizontal.

To multiply the square root of 2 + i and its conjugate, you can use the complex multiplication formula.

(a + bi)(a - bi) = \(a^2 - abi + abi - b^2i^2\)

where the number is √2 + i. Let's do a multiplication with this:

(√2 + i)(√2 - i)

Using the above formula we get:

\((\sqrt{2})^2 - (\sqrt{2})(i ) + (\sqrt{2} )(i) - (i)^2\)

Further simplification:

2 - (√2)(i) + (√2)(i) - (- 1)

Combining similar terms:

2 + 1

results in 3. So (√2 + i)(√2 - i) is 3.

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To test if someone is trying to poison your water using spectrophotometry, you would perform a series of tests to analyze the composition of the water and detect any potentially harmful substances.

Spectrophotometry is a technique that measures the absorption or transmission of light by a substance, allowing for the identification and quantification of specific chemicals.

In order to conduct a spectrophotometric analysis of your water, you would need access to a spectrophotometer, which is a device that emits light at various wavelengths and measures the amount of light absorbed or transmitted by a sample. Firstly, you would obtain a sample of the water you suspect may be contaminated. Then, you would prepare a series of reference solutions containing known concentrations of potentially toxic substances that you suspect might have been used in the poisoning attempt.

Next, you would measure the absorption spectrum of each reference solution using the spectrophotometer and record the absorbance values at specific wavelengths. By comparing the absorbance values of the reference solutions with the absorbance of the suspect water sample, you can identify any significant differences. If the absorbance of the suspect water sample matches or closely resembles the absorbance of the reference solution containing the toxic substance, it could indicate the presence of the poison in your water.

It is important to note that spectrophotometry alone cannot definitively confirm the presence of a specific poison or toxin. If you have reason to believe your water has been tampered with, it is essential to involve authorities and follow proper protocols for water testing and analysis.

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the arc length of the graph of y = cosh(x), from (0,1) to (1, cosh(1)), is approximately 1.175 units.

To find the arc length, we need to integrate the square root of the sum of the squares of the derivatives of x and y over the given interval.

First, we find the derivative of y = cosh(x):

y' = sinh(x)

Next, we calculate the derivative of x:

x' = 1

Using these derivatives, we can calculate the integrand for the arc length formula:

√(1 + (sinh(x))^2)

To find the arc length, we integrate this expression with respect to x over the interval [0, 1]:

∫[0,1] √(1 + (sinh(x))^2) dx

Using numerical integration techniques, the arc length is approximately 1.175 units.

Therefore, the arc length of the graph of y = cosh(x), from (0,1) to (1, cosh(1)), is approximately 1.175 units.

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To solve this problem, we can use the binomial probability distribution. Let's define a "success" as scoring a goal and a "failure" as missing a goal.

Then, each attempt by Sky can be considered a Bernoulli trial with probability of success p = 1/2.

Let X be the number of goals that Sky scores in five attempts. Then, X follows a binomial distribution with parameters n = 5 and p = 1/2.

To find the probability that Sky scores at least two goals, we need to calculate the probability of the following events:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

We can use the binomial probability formula to calculate these probabilities:

P(X = k) = (n choose k) * \(p^k\) *\((1-p)^(n-k)\)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we get:

P(X = 2) = (5 choose 2) * \((1/2)^2\) * \((1/2)^3\) = 10/32

P(X = 3) = (5 choose 3) * \((1/2)^3\) * \((1/2)^2\) = 10/32

P(X = 4) = (5 choose 4) * \((1/2)^4\) *\((1/2)^1\) = 5/32

P(X = 5) = (5 choose 5) * \((1/2)^5\) * \((1/2)^0\) = 1/32

Therefore, the probability that Sky scores at least two goals is:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = (10 + 10 + 5 + 1)/32 = 26/32 = 13/16

So the probability that Sky scored at least two goals is 13/16.

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The total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. So the probability that Sky scored at least two goals is 13/16.

To find the probability that Sky scored at least two goals, we can use complementary probability, which means finding the probability that she scored fewer than two goals (either 0 or 1 goal) and subtracting that from 1.1.

Probability of scoring 0 goals: Since there are 5 attempts and she is equally likely to make a goal or miss (1/2 chance for each), the probability of missing all 5 is (1/2)^5 = 1/32.2.

Probability of scoring 1 goal: Sky could score in any of the 5 attempts, so we need to consider all possible ways of scoring one goal.

There are 5 ways (score in the 1st, 2nd, 3rd, 4th, or 5th attempt). The probability for each of these scenarios is (1/2)^5 = 1/32.

Therefore, the total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

To express this as a common fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:26/32 = (26/2) / (32/2) = 13/16So the probability that Sky scored at least two goals is 13/16.

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Answer:

a

Step-by-step explanation:

sin G=(opposite side)/hypotenuse=x/z

A. The units of these decision variables are in quantities (pieces).

B. Maximize Profit = 20x1 + 85x2 + 35x3

The objective function calculates the total revenue by multiplying the unit selling price of each product with its corresponding quantity (decision variable). The goal is to maximize this total profit.

a) Decision Variables:

Let's define the decision variables as follows:

x1: The number of fabric necklaces produced.

x2: The number of bags produced.

x3: The number of scarves produced.

The units of these decision variables are in quantities (pieces).

b) Objective Function:

The objective function represents the goal or objective to be optimized. In this case, the objective is to maximize the total profit generated from the sale of necklaces, bags, and scarves. The objective function can be written as follows:

Maximize Profit = 20x1 + 85x2 + 35x3

The objective function calculates the total revenue by multiplying the unit selling price of each product with its corresponding quantity (decision variable). The goal is to maximize this total profit.

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The answers are:

To calculate the interest and maturity value, we need to use the formula:

Interest = Principal x Rate x Time

Maturity Value = Principal + Interest

Where:

For the given information, we have:

Drum Set:

Principal = $900.00

Rate = 4% = 0.04

Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)

Interest = $900.00 x 0.04 x 0.0274 = $0.98

Maturity Value = $900.00 + $0.98 = $900.98

Used Car:

Principal = $1,960.00

Rate = 6% = 0.06

Time = 9/365 = 0.0247 years (assuming an exact interest calculation based on days)

Interest = $1,960.00 x 0.06 x 0.0247 = $2.88

Maturity Value = $1,960.00 + $2.88 = $1,962.88

Used Dirt Bike:

Principal = $4,800.00

Rate = 4% = 0.04

Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)

Interest = $4,800.00 x 0.04 x 0.0274 = $5.23

Maturity Value = $4,800.00 + $5.23 = $4,805.23

School Tuition for Twins:

Principal = $9,675.00

Rate = 6% = 0.06

Time = not specified

We don't have the time period for this investment, so we can't calculate the interest or maturity value without that information.

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Answer:

It is NOT a function because when putting a vertical line at a point of a graph it crosses 2 points.

Step-by-step explanation:

There will be approximately 2.098 inches of space on either side of the sphere if it is placed on the center of a pedestal 9 inches across.

What is volume of a sphere ?

V = 4/3 π r³,where V is the volume and r is the radius, is the formula for a sphere's volume. A sphere's radius is equal to half of its diameter.

To solve this problem, we first need to find the radius of the sphere:

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

So we have:

28.73 = (4/3)πr³

Multiplying both sides by 3/4π, we get:

r³ = (28.73 × 3/4π)

r³ ≈ 7.177

Taking the cube root of both sides, we get:

r ≈ 1.952 inches

Now we can find the amount of space on either side of the sphere by subtracting the diameter of the sphere (which is twice the radius) from the width of the pedestal, and then dividing by two:

Space on either side = (9 - 2 × 1.952) / 2

Space on either side ≈ 2.098 inches

Therefore, there will be approximately 2.098 inches of space on either side of the sphere if it is placed on the center of a pedestal 9 inches across.

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By using the concept of cryptography, it can be concluded that

A solution that is now widely used to allow two parties to secretly exchange keys is Deffie - Hellman protocol

What is cryptography?

Cryptography refers to secure information and communication techniques derived from mathematical concepts and a set of rule-based calculations called algorithms, to transform messages in ways that are hard to decipher.

This is a concept of Cryptography

Diffie–Hellman key exchange establishes a shared secret between two parties which will be used for secret communication for exchanging data over a public network.

A solution that is now widely used to allow two parties to secretly exchange keys is Diffie - Hellman protocol

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The normalization of a vector of u and v are (15/17)i+(-6/17)j+(8/17)k and (pi/sqrt(pi^2+50))i+(7/sqrt(pi^2+50))j-(1/sqrt(pi^2+50))k, (5/sqrt(26))j-(1/sqrt(26))i and (-1/sqrt(2))j+(1/sqrt(2))i, (7/sqrt(66))i-(1/sqrt(66))j+(4/sqrt(66))k and (1/sqrt(3))i+(1/sqrt(3))j-(1/sqrt(3))k respectively.

To normalize a vector, first find its magnitude, which is the square root of the sum of the squares of its components. Then, divide each component by the magnitude. After normalization, the vector will have a magnitude of 1 and can be used in various calculations such as dot product and cross product.

For vector u,

||u||=sqrt(15^2+(-6)^2+8^2)=17

u_normalized=u/||u||=(15/17)i+(-6/17)j+(8/17)k

For vector v,

||v||=sqrt(pi^2+7^2+(-1)^2)=sqrt(pi^2+50)

v_normalized=v/||v||=(pi/sqrt(pi^2+50))i+(7/sqrt(pi^2+50))j-(1/sqrt(pi^2+50))k

For vector u,

||u||=sqrt(5^2+(-1)^2)=sqrt(26)

u_normalized=u/||u||=(5/sqrt(26))j-(1/sqrt(26))i

For vector v,

||v||=sqrt((-1)^2+1^2)=sqrt(2)

v_normalized=v/||v||=(-1/sqrt(2))j+(1/sqrt(2))i

For vector u,

||u||=sqrt(7^2+(-1)^2+4^2)=sqrt(66)

u_normalized=u/||u||=(7/sqrt(66))i-(1/sqrt(66))j+(4/sqrt(66))k

For vector v,

||v||=sqrt(1^2+1^2+(-1)^2)=sqrt(3)

v_normalized=v/||v||=(1/sqrt(3))i+(1/sqrt(3))j-(1/sqrt(3))k

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The correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores. This suggests that as study times increase, there is a tendency for test scores to also increase. However, the relationship is not extremely strong.

The correlation coefficient, denoted by 'r', ranges from -1 to 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other tends to increase as well. In this case, the correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores.

It's important to note that the correlation coefficient of 0.49 falls between 0 and 1, closer to 1. This suggests that there is a tendency for test scores to increase as study times increase, but the relationship is not extremely strong. Other factors may also influence test scores, and the correlation coefficient does not imply causation.

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Answer:

VW = 1

Step-by-step explanation:

Tan 45 = 4/VW

VW = 4/Tan 45 = 1

Answer:

(a) \(x=\frac{19}{4}=4.75\)

(b) \(x=-\frac{1+\sqrt{193}}{6}\approx-2.4821, x=-\frac{1-\sqrt{193}}{6}\approx2.1487\)

Step-by-step explanation:

The detailed explanation is shown in the attached documents below.

Answer:

Step-by-step explanation:

It's given that, The height of three basketball players is 210 cm, 220 cm and 191 cm.

h₁ = 210 cm

h₂ = 220 cm

h₃ = 191 cm

Total number of observations = 3.

Average = Sum of all observations/Total number of observations.

↠ Average = h₁ + h₂ + h₃/3

↠ Average = 210 +220 + 191 /3

↠ Average = 430 + 191/3

↠ Average = 621/3

↠ Average = 207

Therefore, The required average height is 207 cm.

Answer:

1/18 :)

Step-by-step explanation:

Answer:

1/18

Step-by-step explanation:

I can explain it later in the comment if you like

Answer:

A is the answer

Step-by-step explanation:

Here is one way     pick two easy points  (-4,0) and  (0,-3)

  and sub into each of the equations until you find the one that 'fits'

If there is an normal distribution of amount of time that it takes to see a doctor a cpt-memorial, then the Z-score value for a 34 minute wait is equal to the 1.1.

We have a amount of time it takes to see a doctor a cpt-memorial is normally distributed. Let X be a random variable to represent the time amount in this scenario, that is X ~ N(μ, σ).

Mean, \(, \mu\) = 23 minutes

Standard deviations, \( \sigma\)

= 10 minutes

We have to calculate Z-score for 34 a minute wait. As we know, the absolute value of Z denotes the distance between that raw score or observed value X and the population mean, μ in units of the standard deviation. Mathematically, formula for Z-score is \(Z = \frac{ X - \mu } {\sigma} \)

where, Z --> Z-score

X--> observed value

σ --> standard deviations

μ --> population mean

Here, X = 34 minutes so plug all known values, \(Z = \frac{34 - 23}{10}\)

=> Z = 11/10 = 1.1

Hence, the required Z-score value is 1.1.

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In mutually exclusive data, you cannot find any overlap or intersection between the categories or events being analyzed.

This means that the occurrence of one event or category precludes the occurrence of the other. On the other hand, in dependent data, the occurrence of one event or category may have an effect on the occurrence of the other, and thus, they are not completely independent or separate. Therefore, in both cases, you cannot find any shared or common outcomes or occurrences between the categories or events being analyzed.

You cannot find a direct correlation or causal relationship between mutually exclusive or dependent data. In mutually exclusive events, the occurrence of one event prevents the occurrence of the other, meaning they cannot happen at the same time. In dependent events, the probability of one event happening is influenced by the outcome of a previous event. Due to these characteristics, it is not possible to establish a direct correlation or causal relationship between such events.

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Answer:

exponent of x is 33

exponent of y is 0

Step-by-step explanation:

you need to combine all powers (exponents) of x, and all exponents of y separately.

remember : x to the power of a divided by x to the power of b is x to the power of (a-b).

when multiplying, the "-" turns into a "+".

so, we have actually for x the exponent calculation :

8 - 14 -(-39) = 8 - 14 + 39 = 33

so, x³³ remains.

and for the y exponents

-26 -(-5) -(-21) = -26 + 5 + 21 = 0

so, all the y expressions eliminate each other and y⁰ remains.

Answer: x = -9

Step-by-step explanation:

When you look at the line, you can see it's plotted on the x-axis. From there you know the solution will be equal to x. Since the line passes right through the number -9 on the x-axis line, the answer would be x = -9. The line is straight which means it has no y intercept which is why x is only equal to -9.

The Fraction for the given word problem is x/y = 9/11

A fraction, which derives from the Latin word fractus, meaning "broken," is a portion of a whole or, more broadly, any number of equal parts. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in everyday speech.

Let the fraction be x/y

The numerator of a fraction is 2 minus its denomination.

⇒ x = y - 2 .....(i)

When 3 is subtracted from numerator and from denomination the new fraction obtained is 3/4

⇒ x - 3/y - 3 = 3/4

Can also be written as

⇒ 4(x + 3) = 3(y - 3)

⇒ 4x - 12 = 3y - 9

⇒ 4x - 3y = -9 + 12

⇒ 4x - 3y = 3 .....(ii)

Substitute the value of (i) in (ii)

⇒ 4x - 3y = 3

⇒ 4(y - 2) - 3y = 3

⇒ 4y - 8 - 3y = 3

⇒ y - 8 = 3

⇒ y = 3 + 8

⇒ y = 11

Putting the value of y in (i).

⇒ x = y - 2

⇒ x = 11 - 2

⇒ x = 9

Hence, Fraction = x/y = 9/11

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