A zoo starts off with 8 monkeys, and the monkeys population
doubles every year. How many monkeys are in the zoo after 4
years?
monkeys

Both solutions satisfy the original equation. As a result, there are no extraneous solutions in this case.

To determine the number of extraneous solutions in the given equation, let's simplify it step by step:

Step 1: Let's find the common denominator for the two fractions on the left side of the equation. The common denominator is (2m + 3)(2m - 3).

Step 2: Apply the common denominator to both fractions:

[(2m)(2m - 3)]/[(2m + 3)(2m - 3)] - [(2m)(2m + 3)]/[(2m + 3)(2m - 3)] = 1

Step 3: Simplify the numerators:

\([4m^2 - 6m - 4m^2 - 6m]/[(2m + 3)(2m - 3)] = 1\)

[-12m]/[(2m + 3)(2m - 3)] = 1

Step 4: Cancel out common factors:

-12m = (2m + 3)(2m - 3)

\(-12m = 4m^2 - 9\)

Step 5: Rearrange the equation:

\(4m^2 + 12m - 9 = 0\)

Step 6: Solve the quadratic equation using factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

\(m = (-b ± √(b^2 - 4ac))/(2a)\)

For our equation, a = 4, b = 12, and c = -9. Substituting these values:

m = (-(12) ± √((12)^2 - 4(4)(-9)))/(2(4))

m = (-12 ± √(144 + 144))/(8)

m = (-12 ± √288)/8

m = (-12 ± 12√2)/8

Simplifying further:

m = (-3 ± 3√2)/2

So, we have two potential solutions for m:

m = (-3 + 3√2)/2  and  m = (-3 - 3√2)/2

Now we need to check if these solutions satisfy the original equation. Let's substitute these values back into the equation:

For m = (-3 + 3√2)/2:

[(2(-3 + 3√2))/(2(-3 + 3√2) + 3)] - [(2(-3 + 3√2))/(2(-3 + 3√2) - 3)] = 1

Simplifying this equation, we find that it holds true.

For m = (-3 - 3√2)/2:

[(2(-3 - 3√2))/(2(-3 - 3√2) + 3)] - [(2(-3 - 3√2))/(2(-3 - 3√2) - 3)] = 1

Simplifying this equation, we also find that it holds true.

Therefore, both solutions satisfy the original equation. As a result, there are no extraneous solutions in this case.

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The probability of a specific number of adult immigrants arriving in a given time period can be determined using the Poisson distribution. We can also calculate the probability of the time elapsed,

a. To find the probability that 4 adult immigrants arrive in the next 3 days, we can use the Poisson distribution. The Poisson distribution models the number of events occurring in a fixed interval of time or space. The probability of observing a specific number of events is given by the formula\(P(k; \lambda) = (e^{(-\lambda)} * \lambda^k) / k!\), where k is the number of events and λ is the average rate of events.

In this case, the average rate of adult immigrants per day is 2 * 0.4 = 0.8. To find the probability of 4 adult immigrants arriving in the next 3 days, we can sum the individual probabilities of 4 adult immigrants arriving each day over the 3-day period. Using the Poisson distribution formula, we calculate:

\(P(4; 0.8) \times P(4; 0.8) \times P(4; 0.8) = (e^{(-0.8)}. 0.8^4) / 4! \times (e^{(-0.8) }0.8^4) / 4! \times (e^{(-0.8)} . 0.8^4) / 4!\)

b. To find the probability that the time elapsed between the arrival of the 24th and 25th kids is more than 2 days, we can use the exponential distribution. The exponential distribution models the time between events occurring at a constant rate. In this case, the rate of kids' arrivals is 2 * 0.6 = 1.2 kids per day.

The probability that the time elapsed between the arrival of the 24th and 25th kids is more than 2 days can be calculated by finding the complement of the cumulative distribution function (CDF) of the exponential distribution. Using the exponential distribution, we calculate:

1 - P(X <= 2), where X follows an exponential distribution with a rate of 1.2.

c. To find the mean and variance of the time needed to have 50 adult immigrants in the territory, we can again use the Poisson distribution. The mean (μ) and variance (σ^2) of a Poisson distribution are both equal to the average rate parameter (λ).

In this case, the average rate of adult immigrants per day is 0.8, so the mean and variance of the time needed to have 50 adult immigrants are both 50 / 0.8 = 62.5 days.

By using the properties of the Poisson and exponential distributions, we can calculate probabilities and statistics related to the arrival of adult and child immigrants in the given scenario.

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Answer:

Step-by-step explanation:

Fractions represent a division problem where the numerator is divided by the denominator. For example, the fraction 3/4 represents the division of 3 by 4, which can be written as 3 ÷ 4. This is why it makes sense that fractions are about division.

Furthermore, fractions are used to represent parts of a whole or a group. When we divide a whole into equal parts, we are essentially dividing the whole into groups, with each group having the same size. For example, if we divide a pizza into 8 equal slices, each slice represents 1/8th of the pizza. We can also think of this as dividing the pizza into 8 equal groups, with each group having one slice.

Therefore, fractions are a natural way to represent division, as they allow us to express how many parts we have out of a whole or a group, and how big each part is relative to the whole or group.

The probability that X takes any specific value is 1/6, since all outcomes are equally likely.

The probability that a discrete random variable takes any specific value depends on the probability distribution of the variable. In a probability distribution, each possible value of the random variable is associated with a probability.

Let's denote the random variable as X, and the specific value we're interested in as x. The probability of X taking the value x is denoted as P(X = x).

To calculate this probability, we need to refer to the probability distribution function (pdf) or the probability mass function (pmf) of the random variable. The pdf or pmf provides the probabilities associated with each possible value of the random variable.

For example, if we have a discrete random variable X that represents the outcome of rolling a fair six-sided die, the probability distribution would be:

P(X = 1) = 1/6

P(X = 2) = 1/6

P(X = 3) = 1/6

P(X = 4) = 1/6

P(X = 5) = 1/6

P(X = 6) = 1/6

It's important to note that the probabilities of all possible values of a discrete random variable must add up to 1.

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Answer:

Step-by-step explanation:

20% tip on 52.22 is 10.44

52.22*0.2=10.44

I don't think he has enough to do it though

52.22+10.44=62.664

Answer: He doesn't have enough (2.66 dollars short) Max percentage: 14.9%

Step-by-step explanation:

If Rowan has $60 dollars and wants a 20% tip. He would need to multiply the restaurant bill by 6/5, of if easier 120%

$52.22 x 120% = 62.66 dollars.

62.66 - 60 = 2.66. Therefore, Rowan CANNOT pay off a 20% tip and has $2.66 short.

Now, if we wanted to calculate which percent he can pay at max we look at 60/52.22.

This will give us 1.14898. Because of this, we can determine what percent Rowan can pay at max. 1.14898 - 1 = 0.14898.

Therefore, converting to percent, he can pay 14.9%(rounded)

The series 16+24+36+54+... diverges.

Divergent series are those that contain an infinite series that never converges and an infinite sequence of partial sums with no finite limit. In contrast, a series is considered to be convergent when its limits converge to its finite range of values. A limit that is finite in nature and exists for the partial sum of the series is crucial since only at that point will the series converge.

The given series in question 16 + 24 + 36 + 54 + deviates from the series. 16n, where n is the number of terms, can be used to denote the series' overall term. The total of the terms in the series also increases as n increases since 16n grows along with n, too. This indicates that the series diverges since it does not reach a particular finite value.

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Answer:

5.5 sq units

Step-by-step explanation:

Find the square around the red shape and subtract out the white parts.

Square = 4x4 = 16

Triangles subtracted -

1x1/2

1x1/2

3x4/2

3x1/2

Total subtracted = -8.5

Squares subtracted

1x1

1x1

Total subtracted = -2

16 - 10.5 = 5.5

Answer:

put a circle, *fill it in, on -9

then, make it pointed towards the right

Step-by-step explanation:

Answer:

1: 544

2: 2,355.52

3:28, 288

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Answer:

UW=\(2\sqrt{66}\) (already solved for you)

UV=\(2\sqrt{33}\)

m∠V=45°

Step-by-step explanation:

You're solving for sine because opp/hyp

sin(45°)*\(2\sqrt{66}\)=UV

UV=\(2\sqrt{33}\)

2) Now you need to solve for an inverse, and since you know UV, you can use inverse cosine (cos^-1) to find your answer

cos^-1(\(\frac{11.4891}{2\sqrt{66}}\))

m∠V=45°

Answer: 350-62= 288      288 divided by 8= 36

Step-by-step explanation:

Answer: The missing side is 6mm.

Step-by-step explanation: For 18mm to drop to 12mm, it dropped 6mm. Therefore, the missing side was 12mm, and if you drop 6mm, you get 6mm.

Answer:

103 km2

Step-by-step explanation:

hope it helps :)

Answer:

A. 51.5 km²

Step-by-step explanation:

Area of parallelogram = b x h

= 10.3 x 5

= 51.5

Answer:

15

Step-by-step explanation:

In an equilateral triangle all the sides length are the same.  Set two sides equal to each other and solve for x

3x + 6 = 6x - 3    Subtract 3x from both sides

6 = 3x -3  Add 3 to both sides

9 = 3x  Divide each side by 3

3 = x

Now that we know x is 3, plug this into the expression for any side and find the side length

3x + 6

3(3) + 6

9 + 6 = 15

The values are:b = -2i - j + 6k, 2a = 2i + 10j - 8k, 3b = -6i - 3j + 18k, |a| = sqrt(42), |a - b| = sqrt(145).



To find the values of b, 2a, 3b, |a|, and |a - b|, substitute the given values of a and b into the equations.

Given:a = i + 5j - 4k

b = -2i - j + 6k

1. b:

Substituting the values of b:b = -2i - j + 6k

2. 2a:

Multiply each component of a by 2:2a = 2(i + 5j - 4k)

  = 2i + 10j - 8k

3. 3b:

Multiply each component of b by 3:3b = 3(-2i - j + 6k)

  = -6i - 3j + 18k

4. |a|:

Calculate the magnitude of a using the formula:|a| = sqrt((i)^2 + (5j)^2 + (-4k)^2)

   = sqrt(1 + 25 + 16)

   = sqrt(42)

5. |a - b|:

Calculate the magnitude of the vector (a - b):|a - b| = |(i + 5j - 4k) - (-2i - j + 6k)|

        = |3i + 6j - 10k|

        = sqrt((3)^2 + (6)^2 + (-10)^2)

        = sqrt(9 + 36 + 100)

        = sqrt(145)

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Answer:

$23

Step by step explanation

Answer:

Step-by-step explanation:

To find angle B we use tan

tan ∅ = opposite / adjacent

From the question

AC is the opposite

BC is the side adjacent to angle B

So we have

tan B = AC / BC

tan B = 6/9

tan B = 1/3

B = tan-¹ 1/3

B = 18.43°

B = 18° to the nearest hundredth

Hope this helps you

Answer:

-1

Step-by-step explanation:

2 – (9 ÷ 3)

divide 9 and 3

2 - 3

subtract 2 from 3 and you get

-1

Answer:

-1

Step-by-step explanation:

Its just the answer.

P(x, y) on the unit circle determined by the given value of t which is t = 7π/6 is:P(x, y) = (-√3/2, -1/2)

To find the terminal point P(x, y) on the unit circle determined by the given value of t which is t = 7π/6, we need to use the trigonometric functions, sin and cos of t in the Cartesian coordinate system.

The unit circle is the circle with center at the origin and a radius of 1. In the Cartesian coordinate system, the point (cos θ, sin θ) lies on the unit circle for any angle θ measured in radians.

So, the given angle is t = 7π/6 = 210° which is in the third quadrant.

In the third quadrant, cos θ is negative and sin θ is negative.

So, cos(7π/6) = -√3/2 and sin(7π/6) = -1/2.

Now, P(x, y) on the unit circle determined by the given value of t which is t = 7π/6 is:P(x, y) = (-√3/2, -1/2)

Answer: (-√3/2, -1/2)

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In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Given,

You want to run a regression to predict the probability of a flight delay, but there are flights with delays of up to 12 hours that are really messing up your model.

I immediately think of grouping delays into ranges such as those under 40 minutes, those between 40 minutes and 2 hours, those between 2 hours and 10 hours, and those above 10 hours. But doing so requires the use of a classification model, such as logistic regression. We frequently consider whether there will be a delay rather than how long it might last when thinking about delays. In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

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it's the second one, (0,6) and (1,2)

I would advise using a website called desmo for further questions like this :D

Answer

72°

Step-by-step explanation:

\(because\ AC=AB\ therefore\ < ACB= < ABC=6x\\ And\ because\ the\ sum\ of\ the\ angles\ of\ a\ triangle\\ is\ 180\ .\\ therefore\ < ACB+ < ABC+ < CAB=180\ degrees\\ 3x+6x+6x=180\ degrees\\ 15x=180\ degrees\\ x=12\ degrees\\ < ABC=6x=6\times12\ degrees=72\ degrees\)

I hope this helps you

:)

Answer:

∠ABC = 72°

Step-by-step explanation:

When we look at the triangle carefully, we can see a bar on AC and AB. Those bars define that AC and AB are equivalent. This also means that the triangle is isosceles. Since this triangle is isosceles, the base angles of the triangle are equivalent.

⇒ AB = AC

We also know that the sum of its interior angles must be 180°.

⇒ ∠A + ∠B + ∠C = 180

Let's substitute their angle measures.

⇒ 3x + 6x + 6x = 180                                         [∠BAC = 3x; ∠ABC = ∠ACB = 6x]

Now, let's solve for x.

⇒ 3x + 6x + 6x = 180

⇒ 15x = 180

⇒ 15x/15 = 180/15

⇒ x = 12

Now, substitute the value of x into "6x" to find ∠ABC.

∠ABC = 6x

⇒ ∠ABC = 6(12)

⇒ ∠ABC = 72°

(a) \([17] + [21] \cdot [98] - [5] = [12]\) in \(\mathbb{Z}_{13}\).

(b) If we are working in the ring \(\mathbb{Z}_{157}\), the value of \(n\) is 157.

(a) To explicitly check the expression \([17] + [21] \cdot [98] - [5]\) in \(\mathbb{Z}_{13}\), we need to perform the operations using modular arithmetic.

First, let's compute \([21] \cdot [98]\):

\[ [21] \cdot [98] = [21 \cdot 98] \mod 13 = [2058] \mod 13 = [0] \mod 13 = [0]\]

Next, we can substitute the results into the original expression:

\[ [17] + [0] - [5] = [17] - [5] = [12]\]

(b) We are given the expression \([5] \cdot [7] \cdot [8] \cdot [9]\) in \(\mathbb{Z}_n\) and we need to find the value of \(n\) if the expression makes sense.

To find the value of \(n\), we can evaluate the expression:

\[ [5] \cdot [7] \cdot [8] \cdot [9] = [5 \cdot 7 \cdot 8 \cdot 9] \mod n\]

We are given that the result is equal to 157:

\[ [5 \cdot 7 \cdot 8 \cdot 9] \mod n = [157] \mod n\]

To find \(n\), we can solve the congruence equation:

\[ [5 \cdot 7 \cdot 8 \cdot 9] \mod n = [157] \mod n\]

Since 157 is a prime number, there are no factors other than 1 and itself. Therefore, we can conclude that the value of \(n\) is 157.

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The ratio of surface area of spheres on increase in radius of larger sphere will be 1:64.

The surface area of sphere is directly proportional to square of radius and volume of sphere is directly proportional to cube of radius. Let us assume the r represents radius of smaller sphere and R represents radius of larger sphere.

Smaller volume/larger volume = r³:R³

r:R =

\( \sqrt[3]{ \frac{1}{64} } \)

r:R = 1:4

So, the ratio of surface area will be: r²:(2R)²

Ratio of surface area = r²:4R²

Ratio of surface area = 1:64

Hence, the ratio of surface area is 1:64.

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Answer:

83/24

Step-by-step explanation:

Calculator.

Answer:

83/24 or 3 11/24

Step-by-step explanation:

Hope this helps

Answer:

Laura will have 4 17/30 yd of ribbon left

Step-by-step explanation:

All you do is subtract the two numbers 2 1/3 and 1 2/5 from the bigger number 8 3/10 to get your answer of 4 17/30

The value of x is 10.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

Given;

Base=6

Perpendicular=8

Now

x^2=6^2+8^2

X^2=36+64

X^2=100

x=10

Therefore, by pythagoras theorem the answer will be 10.

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