The fly population on an island is declining at a rate of 1. 7% per year. The population was 4600 in the year 2016. Which answer is the best prediction of the population in the year 2023?

The positive difference between the two solutions of the quadratic equation \(2x^{2}\) + 5x + 12 = 19 -7x is \(\frac{\sqrt{200} }{4}\).

We are required to determine the positive difference between the two solutions of the given quadratic equation: \(2x^{2}\) + 5x + 12 = 19 -7x

1. Move all terms to the left side of the equation to form a standard quadratic equation:

\(2x^{2}\) + 5x + 12 + 7x - 19 = 0

2. Simplify the equation: \(2x^{2}\) + 12x - 7=0.

3. Use the quadratic formula to find the solutions for x:

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

where a=2, b=12, and c=-7.

4. Substitute the values:

\(x = \frac{-12 \pm \sqrt{12^{2} -4(2)(-7)}}{2(2)}\)

5. Simplify the expression:

\(x = \frac{-12 \pm \sqrt{144 + 56}}{4}\)

6. Calculate the value under the square root:

\(x = \frac{-12 \pm \sqrt{200}}{4}\)

7. Now, we have two solutions:

\(x_{1} = \frac{-12 + \sqrt{200}}{4}x_{2} = \frac{-12 - \sqrt{200}}{4}\)

8. Find the difference between the solutions:

\(x_{1} - x_{2}\) = \(\frac{\sqrt{200} }{4}\)

The positive difference between the two solutions is\(\frac{\sqrt{200} }{4}\).

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Answer:

4x-20

Step-by-step explanation:

If the radius of circle is represented by the expression "z + 3.6" , then the value of z is 568.9 ft.

The length of the radius of the circle is measured in feet ;

the expression that represents the radius of circle is = z + 3.6 ;

also given that the diameter of the circle is = 1145 ft ;

So ,the radius will be = 1145/2 ft ;

On equating both the radius ,

we get ;

z + 3.6 = 1145/2 ;

z + 3.6 = 572.5 ;

z = 572.5 - 3.6 ;

z = 568.9 .

Therefore , the value of z is = 568.9 ft .

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Answer: The correct answer is 2.3

Step-by-step explanation: Answer confirmed correct on test so no worries

a. If 1% of the shells are actually defective and we assume Independence, the probability of 0 defective shells in the sample is 82%,

b. if 1% of the shells are actually defective and we assume independence, the probability of 1 defective shell in the sample is 16% and

c. If 1% of the shells are actually defective and we assume Independence, the probability of more than 1 defective shell in the sample is 1.58%.

Given batch = 350 shells

sample = 20 shells

Given 1%10 f shells are defective = 0.01

That is 99% are non detective = 0.99

Using binomial theorem,

1. P(zero defective shells) = 20c0 (0.01)^0(0.99)^20

= 0.82

= 82%

2. P(One defective shells) = 20c1(0.01)(0.99)^19

= 0.16

= 16%

3. P(two defective shells) = 20c2(0.01)^2(0.99)^18

= 0.0158

= 1.58%

Hence the a. If 1% of the shells are actually defective and we assume Independence, the probability of 0 defective shells in the sample is 82%, b. if 1% of the shells are actually defective and we assume independence, the probability of 1 defective shell in the sample is 16% and c. If 1% of the shells are actually defective and we assume Independence, the probability of more than 1 defective shell in the sample is 1.58%.

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Answer:

$1.29

Step-by-step explanation:

Divide 15.48 by 12

19. The radius of convergence is infinity, and the interval of convergence is (-∞, ∞).

20.  The radius of convergence is infinity, and the interval of convergence is (-∞, ∞).

21. The radius of convergence is 1/24, and the interval of convergence is (-∞, -1/24) ∪ (1/24, ∞).

To determine the radius of convergence and interval of convergence for the given power series, we can use the ratio test.

19.) For the series Σ 2n=1 (-1)^(2n - 1) / 32n:

Using the ratio test, we calculate the limit:

lim (n→∞) |((-1)^(2(n+1) - 1) / 32(n+1)) / ((-1)^(2n - 1) / 32n)|

Simplifying the expression:

lim (n→∞) |-1 / (32(n+1))|

Taking the absolute value and simplifying further:

lim (n→∞) 1 / (32(n+1))

The limit evaluates to 0 as n approaches infinity.

Since the limit is less than 1, the series converges for all values of x. Therefore, the radius of convergence is infinity, and the interval of convergence is (-∞, ∞).

20.) For the series Σ (-(x + 4))^n / (1·3·5·...·(2n - 1)):

Using the ratio test, we calculate the limit:

lim (n→∞) |((-(x + 4))^(n+1) / (1·3·5·...·(2(n+1) - 1))) / ((-(x + 4))^n / (1·3·5·...·(2n - 1)))|

Simplifying the expression:

lim (n→∞) |(-(x + 4))^(n+1) / (2n(2n + 1))|

Taking the absolute value and simplifying further:

lim (n→∞) |-(x + 4) / (2n + 1)|

The limit depends on the value of x. For the series to converge, the absolute value of -(x + 4) / (2n + 1) must be less than 1. This occurs when |x + 4| < 2n + 1.

To determine the interval of convergence, we set the inequality |x + 4| < 2n + 1 to be true:

-2n - 1 < x + 4 < 2n + 1

Simplifying:

-2n - 5 < x < 2n - 3

Since n can take any positive integer value, the interval of convergence depends on x. Therefore, the radius of convergence is infinity, and the interval of convergence is (-∞, ∞).

21.) For the series Σ (3·6·9·...·(3n)) / (72(n+1)·xn):

Using the ratio test, we calculate the limit:

lim (n→∞) |((3·6·9·...·(3(n+1))) / (72(n+2)·x^(n+1))) / ((3·6·9·...·(3n)) / (72(n+1)·xn))|

Simplifying the expression:

lim (n→∞) |(3(n+1)) / (72(n+2)x)|

Taking the absolute value and simplifying further:

lim (n→∞) (3(n+1)) / (72(n+2)|x|)

The limit evaluates to 3 / (72|x|) as n approaches infinity.

For the series to converge, the limit must be less than 1, which implies |x| > 1/24.

Therefore, the radius of convergence is 1/24, and the interval of convergence is (-∞, -1/24) ∪ (1/24, ∞).

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Answer:

7! or 5040

Step-by-step explanation:

The first song can be one of 7. The second song can be one of 6, because there is already one song as number one. This continues for each spot, so there are 7 × 6 × 5 × 4 × 3 × 2 × 1 combinations. This can be expressed as 7 factorial, or 7!. 7! = 5040

Answer:

25 feet in one second

Step-by-step explanation:

125 divided by 5 is 25

Answer:

25 feet per second

Step-by-step explanation:

Answer:

10:26

Step-by-step explanation:

Answer:

An hour and six minutes.

Step-by-step explanation:

10:40-11:40 is an hour plus six minutes.

Hope this helps!

The smallest sample size required to provide a 95% confidence interval for a mean, if it is important that the interval be no longer than 1 cm, is 34.

A confidence interval is a range of values, derived from a data sample, that is used to estimate an unknown population parameter.The confidence interval specifies a range of values between which it is expected that the true value of the parameter will lie with a specific probability.Inference using the central limit theorem (CLT):The central limit theorem states that the distribution of a sample mean approximates a normal distribution as the sample size gets larger, assuming that all samples are identical in size, and regardless of the population distribution shape.The central limit theorem enables statisticians to determine the mean of a population parameter from a small sample of independent, identically distributed random variables.Testing a hypothesis:A hypothesis test is a statistical technique that is used to determine whether a hypothesis is true or not.A hypothesis test works by evaluating a sample statistic against a null hypothesis, which is a statement about the population that is being tested.A hypothesis test is a formal procedure for making a decision based on evidence.The decision rule is a criterion for making a decision based on the evidence, which may be in the form of data or other information obtained through observation or experimentation.The decision rule specifies a range of values of the test statistic that are considered to be compatible with the null hypothesis.If the sample statistic falls outside the range specified by the decision rule, the null hypothesis is rejected.

So, the smallest sample size required to provide a 95% confidence interval for a mean, if it is important that the interval be no longer than 1cm, is 34.

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Answer:

every 3 hours

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Bernie Sanders campaign manager John Kerry has been listening too much and has not been able enough for a da in a coma for a while and the other is a

Answer:

you would need 6 scoops of sugar

Answer:

You would need 15 scoops of sugar per 3.5 oz

Step-by-step explanation:

Answer:

y ≤ 11

Step-by-step explanation:

7y ≤ 33 + 4y

3y ≤ 33

y ≤ 11

So, the answer is y ≤ 11

ANSWER- The required integral is `18re^(r/2) + C`.

The given integral is:  `∫9re^(r/2) dr`.

Now, we shall evaluate the integral as shown below:

Integration of `9re^(r/2) dr` can be done using the "Integration by Parts" formula.

The formula is given as:

`∫u dv = uv - ∫v du`.

where `u` is the first function, `v` is the second function, `du` is the derivative of the first function and `dv` is the derivative of the second function.

Let us assume:

`u = r` and `dv = e^(r/2) dr`.

Hence, `du = dr` and `v = 2 e^(r/2)`.

Now, let us substitute the assumed values in the formula:

∫9re^(r/2) dr`

= 9 ∫r e^(r/2) dr``

= 9 (r * 2 e^(r/2) - ∫2 e^(r/2) dr)`

= `9r * 2 e^(r/2) - 18 e^(r/2) + C`where `C` is the constant of integration.

Therefore, `∫9re^(r/2) dr = 18re^(r/2) - 18e^(r/2) + C` or

∫9re^(r/2) dr = 18re^(r/2) + C`.

Thus, the required integral is `18re^(r/2) + C`.

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Given integral is, ∫9re^(r/2) drWe can solve this integral using the integration by parts method. In the integration by parts method, we select one function as u and another function as dv.

The integral formula for integration by parts is ∫u dv = uv - ∫v duSo, we select functions for integration by parts. Let's select u = r and dv = 9e^(r/2) drthen, du = dr and v = 18e^(r/2)Now, we apply the formula of integration by parts and evaluate the integral.∫9re^(r/2) dr= r*18e^(r/2) - ∫18e^(r/2) dr= r*18e^(r/2) - 36e^(r/2) + CWhere C is the constant of integration.So, the value of the given integral is r*18e^(r/2) - 36e^(r/2) + C.

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Answer:

y+4=4(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=4(x-3)

y+4=4(x-3)

The percent decrease in the value of the car is 65.6%.

Given that,

The purchase value of the car is $32,000.

The worth of the car is now $5,000 that should be lower than the half of purchased value i.e.

= 50% of $32,000 - $5,000

= $16,000 - $5,000

= $11,000

Now the percentage of decrease in the value of the car is

\(= \frac {(\$32,000 - \$11,000)}{\$32,000} \\\\= \frac{\$21,000}{\$32,000}\)

= 65.6%

Therefore we can conclude that the percentage of decrease in the value of the car is 65.6%.

Therefore, all the other options are incorrect.

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Answer:

x=−7

Solving for X:

Step 1: Simplify both sides of your equation.

5x−22=7x−8

Step 2: Subtract 7x from both sides.

5x−22−7x=7x−8−7x

−2x−22=−8

Step 3: Add 22 to both sides.

−2x−22+22=−8+22

−2x=14

Step 4: Divide both sides by -2.

-2x/-2 = 14/-2

^ x = -7

THEREFORE:

x is −7

Answer:

\((a)\ (x+6)^2 + (y-5)^2 = 25\)

\((b)\ Area = 16.75cm^2\)

Step-by-step explanation:

Solving (a):

Given

\((a,b) = (-6,5)\)

\(r = 5\)

Required

The equation of the circle

This is calculated as:

\((x-a)^2 + (y-b)^2 = r^2\)

So, we have:

\((x--6)^2 + (y-5)^2 = 5^2\)

\((x+6)^2 + (y-5)^2 = 25\)

Solving (b):

Given

\(r = 8cm\)

\(\theta = 30^o\) --- Missing from the question

Required

The area of the sector

This is calculated using:

\(Area = \frac{\theta}{360} * \pi r^2\)

So, we have:

\(Area = \frac{30}{360} * 3.14 * 8^2\)

\(Area = \frac{1}{12} * 200.96\)

\(Area = 16.75cm^2\)

The vector would point upwards and to the left, at an angle of 70 degrees from the -x axis. Sketching the vectors approximately to scale would confirm the directions and magnitudes of the components.

A) To find the x component, we use cosine of the angle: x = 50.0 N * cos(60 degrees) = 25 N. To find the y component, we use sine of the angle: y = 50.0 N * sin(60 degrees) = 43.3 N. The vector would point upwards and to the right, at an angle of 60 degrees from the +x axis.

B) To find the x component, we use cosine of the angle: x = 75 m/s * cos(5pi/6 rad) = -37.5 m/s. To find the y component, we use sine of the angle: y = 75 m/s * sin(5pi/6 rad) = 64.95 m/s. The vector would point downwards and to the left, at an angle of 150 degrees from the +x axis.

C) To find the x component, we use cosine of the angle: x = 254 lb * cos(325 degrees) = -206.5 lb. To find the y component, we use sine of the angle: y = 254 lb * sin(325 degrees) = -129.6 lb. The vector would point downwards and to the left, at an angle of 35 degrees from the -x axis.

D) To find the x component, we use cosine of the angle: x = 69 km * cos(1.1pi rad) = -22.87 km. To find the y component, we use sine of the angle: y = 69 km * sin(1.1pi rad) = 66.62 km. The vector would point upwards and to the left, at an angle of 70 degrees from the -x axis.

Sketching the vectors approximately to scale would confirm the directions and magnitudes of the components.

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Summary:

The measure of the angle from the surveyor's eyes to the top of the building is approximately 78.69 degrees.

Explanation:

To calculate the measure of the angle from the surveyor's eyes to the top of the building, we can use trigonometry. First, we can visualize a right triangle with the surveyor's eye level, the top of the building, and the point where the surveyor is standing as the three vertices. The height of the building is the opposite side, the distance between the surveyor and the building is the adjacent side, and the surveyor's eye level is the third side of the triangle.

Using the tangent function, we can calculate the angle theta (θ) between the opposite and adjacent sides of the triangle, which represents the angle from the surveyor's eyes to the top of the building:

tan(θ) = opposite/adjacent

tan(θ) = 140/190

θ = tan^-1(140/190)

θ ≈ 78.69 degrees

Therefore, the measure of the angle from the surveyor's eyes to the top of the building is approximately 78.69 degrees.

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To find the volume of the given solid using polar coordinates, we integrate the function over the appropriate range of values for the radial coordinate and the angle.

The given solid consists of a cone and a ring in the xy-plane. The cone is defined by the equation z = √(x² + y²), which represents a right circular cone with its vertex at the origin and opening upwards. The ring is defined by the inequality 1 ≤ x² + y² ≤ 64, which represents a circular region centered at the origin with an inner radius of 1 unit and an outer radius of 8 units.

To evaluate the volume using polar coordinates, we can express the equations in terms of the radial coordinate (r) and the angle (θ). In polar coordinates, the cone equation becomes z = r, and the ring equation becomes 1 ≤ r² ≤ 64. To set up the integral, we need to determine the range of values for r and θ. For the radial coordinate, r ranges from 1 to 8, as that corresponds to the region defined by the ring. For the angle θ, we can integrate from 0 to 2π, covering a full revolution around the origin.

The volume integral is then given by V = ∫∫∫ r dz dr dθ over the region defined by 1 ≤ r² ≤ 64 and 0 ≤ θ ≤ 2π. By evaluating this triple integral, we can find the volume of the solid.

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Hi, I'm happy to help!

First off, we need to arrange an equation for what is being asked. 15 is 20% of her earnings and we don't know her total earnings.

15=20%×__

We can write this percentage as

15=0.2×__

We then change the equation to do the inverse operation, which is division, this makes it easier to solve.

15÷0.2=__

Now, we solve

15÷0.2=75

She earned $75

I hope this was helpful, keep learning! :D

It is the first option

Step-by-step explanation:

please mark me as brainilest

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

The "Rule of 72" is a quick estimation method to determine the time it takes for an investment or savings to double in value. By dividing 72 by the interest rate, you can obtain an approximation of the doubling time. For an interest rate of 3%, it would take approximately 24 years for the savings to double. For an interest rate of 8%, it would take around 9 years for the savings to double.

To calculate the doubling time using the Rule of 72, divide 72 by the interest rate. This provides an approximation of the number of years it takes for an investment or savings to double in value.

For an interest rate of 3%, we divide 72 by 3: 72 / 3 = 24. Therefore, it would take approximately 24 years for the savings to double.

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

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Answer:

u need to breath and calm down

Step-by-step explanation:

breath in and out for 5 sec u will feel better

A 90% confidence interval will use the same z-score as 95% of the data. 0.95 is exactly between the z-scores of 1.64 and 1.65, so estimate the z-score as 1.645. The z-score associated with a 90% confidence interval is 1.645.

To determine the value of a, we use the formula: a = z*(standard deviation/sqrt(n)). The value of a determines the size of the margin of error in our confidence interval.

The value of a is an important component in determining the 90% confidence interval. It is used to calculate the range of values that are likely to contain the true population mean with a certain level of confidence. In other words, it tells us how confident we are that the true population mean falls within a certain range of values. To determine the value of a, we use the formula: a = z*(standard deviation/sqrt(n)), where "z" is a critical value from a standard normal distribution table, "standard deviation" is the standard deviation of the sample, and "n" is the sample size. The critical value "z" is chosen based on the desired level of confidence. In this case, since we are aiming for a 90% confidence level, we would use a critical value of approximately 1.645.

A smaller value of a means a narrower interval, which in turn indicates a higher level of confidence in the interval containing the true population mean. Conversely, a larger value of a leads to a wider interval and a lower level of confidence.

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Answer:

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

Step-by-step explanation: