Which expressions are equivalent to the given expression? (- sqrt -9 + sqrt -4) - (2 sqrt 576 + sqrt -64)

Answer:

Step-by-step explanation:

To show that a² + b² = p² + q², we can start by squaring the given equations and adding them together:

(a sin θ - b cos θ)² + (a cos θ - b sin θ)² = p² + q²

Expanding the squared terms:

(a² sin² θ - 2ab sin θ cos θ + b² cos² θ) + (a² cos² θ - 2ab sin θ cos θ + b² sin² θ) = p² + q²

Combining like terms:

a² sin² θ + a² cos² θ + b² sin² θ + b² cos² θ - 2ab sin θ cos θ - 2ab sin θ cos θ = p² + q²

Using the trigonometric identity sin² θ + cos² θ = 1:

a² + b² - 2ab sin θ cos θ - 2ab sin θ cos θ = p² + q²

Rearranging and factoring out a common factor of 2ab:

(a² + b² - 2ab sin θ cos θ - 2ab sin θ cos θ) = p² + q²

2ab (1 - sin θ cos θ - sin θ cos θ) = p² + q²

2ab (1 - 2 sin θ cos θ) = p² + q²

Using the trigonometric identity 2 sin θ cos θ = sin 2θ:

2ab (1 - sin 2θ) = p² + q²

2ab - 2ab sin 2θ = p² + q²

2ab(1 - sin 2θ) = p² + q²

Since 1 - sin 2θ = cos 2θ:

2ab cos 2θ = p² + q²

Dividing both sides by 2ab:

cos 2θ = (p² + q²) / (2ab)

Using the double angle formula for cosine: cos 2θ = 2cos² θ - 1:

2cos² θ - 1 = (p² + q²) / (2ab)

Rearranging and simplifying:

2cos² θ = (p² + q²) / (2ab) + 1

2cos² θ = (p² + q² + 2ab) / (2ab)

Dividing both sides by 2:

cos² θ = (p² + q² + 2ab) / (4ab)

Using the Pythagorean identity sin² θ + cos² θ = 1, we have:

sin² θ = 1 - cos² θ

sin² θ = 1 - (p² + q² + 2ab) / (4ab)

Rearranging and simplifying:

4ab sin² θ = 4ab - p² - q² - 2ab

4ab sin² θ = 2ab - p² - q²

Multiplying both sides by a² + b²:

4ab (a² + b²) sin² θ = (2ab - p² - q²) (a² + b²)

Expanding both sides:

4a³b sin² θ + 4ab³ sin² θ = 2a³b - p²a² - q²a² - 2ab

The expression that represent the relationship is 7 / 2 x - 15 / 2 = 4.

An equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Therefore, let's find the equation that represents the relationship as follows:

Three consecutive numbers, four times the third decreased by on-half, the second is 4.

Therefore,

Let

x = first number

second number = x + 1

third number  = x + 2

Therefore,

4(x + 2)  - 1 / 2(x + 1) = 4

4x + 8 - 1 / 2x - 1 / 2 = 4

4x - 1 / 2x + 8 - 1 / 2 = 4

7 / 2 x - 15 / 2 = 4

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The average rate of change in the population between 2002 and 2004 is one thousand per year, and between 2002 and 2006 is 1.75 thousand per year.

To calculate the average rate of population change, we need to find the difference in population between the given years and divide it by the difference in years.

Between 2002 and 2004:

Population change = 80 - 82 = -2 (decrease of 2, as the population decreased)

Year difference = 2004 - 2002 = 2

Average rate of change = Population change / Year difference

Average rate of change = -2 / 2 = -1 (thousands per year)

Between 2002 and 2006:

Population change = 75 - 82 = -7 (decrease of 7, as the population decreased)

Year difference = 2006 - 2002 = 4

Average rate of change = Population change / Year difference

Average rate of change = -7 / 4 = -1.75 (thousands per year)

Therefore, the average rate of change of population between 2002 and 2004 is 1 thousand per year, and between 2002 and 2006 is 1.75 thousand per year.

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Answer:

The coreect answer o

is 14

Answer:

Step-by-step explanation:

When conducting hypothesis testing, the p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.In this case, if the p-value is 0.15 and the significance level (alpha) is set at 0.01, we can interpret the results as follows:Since the p-value (0.15) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the observed results are statistically significant at the 0.01 level. However, it's important to note that the decision of whether to reject or fail to reject the null hypothesis is based on the chosen significance level, and it's possible that the result may be considered statistically significant at a higher significance level.In summary, the conclusion would be that there is not enough evidence to reject the null hypothesis at the 0.01 significance level.

1. A table showing your salary for the first five years on the job is shown below.

2. Your cousin's salary would be $56243.2 in the year you started working.

3. A formula for your salary is [tex]P(t) = 37000(1.06)^t[/tex]

A formula for your cousin's salary is [tex]P(t) = 50000(1.04)^t[/tex]

4. A graph of your salary and your cousin's salary is shown below.

It would take about 16 years before your salary exceed your cousin's salary.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]P(t) = I(1 + r)^t[/tex]

Where:

Part 1.

We can create a table of values to model your salary for the first five years on the job as follows;

Years               1                2               3                4                 5

Salary ($)    39,220    41,573.2    44,067.6    46,711.7     49,514.4

Part 2.

For your cousin's salary three years after, we have:

y = 50,000(1.04)³

y = $56243.2.

Part 3.

We can write a formula for your salary as follows;

[tex]P(t) = 37000(1 + 0.06)^t\\\\P(t) = 37000(1.06)^t[/tex]

For your cousin's salary, we have:

[tex]P(t) = 50000(1 + 0.04)^t\\\\P(t) = 50000(1.04)^t[/tex]

Part 4.

In order to plot a graph of your salary and your cousin's salary, we would use an online graphing tool with a scale of 1 units for 1 year on the x-axis and a scale of 50 units for 1000 dollars on the y-axis.

Since the lines representing both salaries intersect at 15.808, we can logically deduce that it would take approximately 16 years for your salary to exceed your cousin's salary.

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The period of the function in this problem is given as follows:

5 units.

A periodic function is a function that has the behavior repeating over intervals in the domain of the function.

Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.

The distance between peaks of the function in this problem is of 5 units, which represents the period of the function.

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Answer:

Step-by-step explanation:

You want an exponential function of the form y = a(b^x) that models algae growth that initially covers 3 square meters of a pond and doubles in area each day.

The function y = a(b^x) has an initial value of 'a', which the problem statement tells us is 3 (square meters). The value 'b' is the growth factor, which the problem statement tells us is 2 each day.

The desired exponential equation is ...

  y = 3(2^x)

When x=4, the function evaluates to ...

  y = 3(2^4) = 3(16) = 48 . . . . square meters

After 4 days, 48 square meters of the pond is expected to be covered by algae.

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Answer:

Step-by-step explanation: a = o/t

a = 18/tan(42)

a = 19.99

Answer:

22

Step-by-step explanation:

You can do it by 220 divided by 10, which gives an answer of 22.

The simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).

First, let's focus on simplifying the numerator and denominator separately:

Numerator:

The numerator is 1 divided by (4n - 1/2). We can simplify this by finding a common denominator. The denominator of 1/2 is 2, so we rewrite the expression as:

1/(4n - 12) = 1/(4n - 2/4) = 1/(4n - 2/4) = 1/((16n - 2)/4) = 4/(16n - 2)

Denominator:

The denominator is (n/5 - 1/20n). To simplify this, we find a common denominator. The denominator of 1/20n is 20n, so we rewrite the expression as:

n/5 - 1/20n = (20n^2)/(5 * 20n) - 1/(20n) = (20n^2 - 1)/(100n)

Now, let's simplify the entire expression by dividing the numerator by the denominator:

(1/(4n - 1/2)) ÷ (n/5 - 1/20n) = (4/(16n - 2)) ÷ ((20n^2 - 1)/(100n))

To divide by a fraction, we multiply by its reciprocal:

(4/(16n - 2)) ÷ ((20n^2 - 1)/(100n)) = (4/(16n - 2)) * (100n/(20n^2 - 1))

Next, we can simplify the numerator and denominator separately:

Numerator:

4 * 100n = 400n

Denominator:

(16n - 2) * (20n^2 - 1) = 320n^3 - 52n - 40n^2 + 2

Finally, we substitute the simplified numerator and denominator back into the expression:

(4/(16n - 2)) * (100n/(20n^2 - 1)) = (400n)/(320n^3 - 52n - 40n^2 + 2)

Thus, the simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).

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i) It has been proven that CD/GH​ =  AC/FG by Corresponding Sides of Similar Triangles

ii)  △DCB ∼△HGE by the AA criterion of similarity

iii) △DCA ∼△HGF by the AA criterion of similarity

In △ABC and △FEG, we are told that they are similar and as such we can denote as:

△ABC ∼ △FEG

Thus, we can say that:

∠ACB = ∠EGF (Corresponding angles of similar triangles)

We are told that, CD and GH are bisectors of ∠ACB and ∠EGH respectively and as such we can say that:

∠ACB = 2∠ACD = 2∠BCD

∠EGF = 2∠FGH = 2∠HGE

Thus, by substitution, we can say that:

∠ACD = ∠FGH and ∠DCB = ∠HGE ...................(1)

Similarly:

∠A = ∠F and ∠B = ∠E ...............(2)

With respect to equations 1 and 2 we can establish that:

△ACD ∼ △FGH by the AA criterion of similarity

Similarly, △DCA ∼△HGF

Thus:

CD/GH​ =  AC/FG (Corresponding Sides of Similar Triangles)

Similarly, In △DCB and △HGE, we can also establish that

△DCB ∼△HGE by the AA criterion of similarity

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a. The maximum population of the squirrels is 1800.

b. The number of squirrels that were introduced to the island are 200 squirrels.

In Mathematics and Geometry, a logistic growth function can be represented by using the following mathematical equation:

[tex]f(x) = \frac{L}{1\;+\;e^{-k(x-x_0)}}[/tex]

Where:

Based on the information provided above, the population of squirrels can be modeled by the following logistic growth function;

[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}[/tex]

Part a.

By comparison, the maximum value or supremum population of the squirrels is 1800 squirrels.

Part b.

When t = 0, the initial number of squirrels that were introduced to this island can be calculated as follows;

[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}\\\\P(0) = \frac{1800}{1\;+\;8e^{-0.3(0)}}[/tex]

P(0) = 1800/9

P(0) = 200 squirrels.

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9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth.

To find how many days on Earth are equivalent to 9 1/2 years on Venus, we need to use the ratio of 224.7 days on Earth to 1 year on Venus. First, we convert 9 1/2 years to a decimal form, which is 9.5 years. Then, we multiply 9.5 years by the conversion ratio: 9.5 years * 224.7 days/year = 2137.65 days on Earth. Therefore, 9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth in decimal form.

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The sample standard deviation for the given data set is approximately 2.77.

Let's calculate the sample standard deviation for the given data set:

Calculate the mean

Sum of all data points = 8 + 5 + 2 + 4 + 4 + 9 + 9 + 7 + 3 + 5 + 2 + 4 + 4 + 7 + 10 + 5 + 1 + 8 + 9 + 8 + 3 + 3 + 8 + 7 = 137

Mean = Sum of all data points / Number of data points = 137 / 24 = 5.71 (rounded to two decimal places)

Subtract the mean from each data point and square the result

(8 - 5.71)^2 = 2.4361

(5 - 5.71)^2 = 0.5041

(2 - 5.71)^2 = 15.1361

(4 - 5.71)^2 = 2.9241

(4 - 5.71)^2 = 2.9241

(9 - 5.71)^2 = 10.3961

(9 - 5.71)^2 = 10.3961

(7 - 5.71)^2 = 1.6641

(3 - 5.71)^2 = 8.2561

(5 - 5.71)^2 = 0.5041

(2 - 5.71)^2 = 15.1361

(4 - 5.71)^2 = 2.9241

(4 - 5.71)^2 = 2.9241

(7 - 5.71)^2 = 1.6641

(10 - 5.71)^2 = 23.7761

(5 - 5.71)^2 = 0.5041

(1 - 5.71)^2 = 21.8441

(8 - 5.71)^2 = 2.4361

(9 - 5.71)^2 = 10.3961

(8 - 5.71)^2 = 2.4361

(3 - 5.71)^2 = 8.2561

(3 - 5.71)^2 = 8.2561

(8 - 5.71)^2 = 2.4361

(7 - 5.71)^2 = 1.6641

Find the sum of all the squared differences

Sum of squared differences = 2.4361 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 10.3961 + 10.3961 + 1.6641 + 8.2561 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 1.6641 + 23.7761 + 0.5041 + 21.8441 + 2.4361 + 10.3961 + 2.4361 + 8.2561 + 8.2561 + 2.4361 + 1.6641 = 174.07 (rounded to two decimal places)

Divide the sum by the number of data points minus 1

Variance = Sum of squared differences / (Number of data points - 1) = 174.07 / (24 - 1) = 7.67 (rounded to two decimal places)

Take the square root of the variance

Sample Standard Deviation = √(Variance) = √(7.67) = 2.77 (rounded to two decimal places)

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La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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Answer:

Once

Step-by-step explanation:

Simple, once. If you do 600-457, you get an answer of 143, which you cannot subtract another 457 because it will turn negative.

Step-by-step explanation:

Perimeter= 12ft

Length= 4ft

Width= ?

Bedroom window = rectangle

Rectangle= l×b

= 4× ?

12÷ 4=3

Answer:

897

Explanation:
Start with replacing all the [tex]t[/tex] with 2.

[tex](t^{2} + 6t+7)(3t^{2} +3)[/tex]
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]

Deal with the exponent before multiplying and adding.

[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 12+7)(((3)(2))^{2} +3)[/tex]
[tex](23)(((3)(2))^{2} +3)[/tex]

Now I believe here is where you made your mistake, you should first multiply 3 and 2 instead of evaluating the exponent straight away, because [tex]3t[/tex] was squared together.

[tex](23)(((3)(2))^{2} +3)[/tex]
[tex](23)(6^{2} +3)[/tex]
[tex](23)(36 +3)[/tex]

Then after adding, just multiply to get your answer, 897.

[tex](23)(36 +3)[/tex]
[tex](23)(39) = 897[/tex]

Answer:

4,5x>225--> x>225:4,5

Step-by-step explanation:

The answer is:

Work/explanation:

To solve this inequality, begin by adding 100 on each side:

[tex]\sf{4.5x-100 > 125}[/tex]

[tex]\sf{4.5x > 125+100}[/tex]

[tex]\sf{4.5x > 225}[/tex]

Now, divide each side by 4.5.

[tex]\sf{x > 50}[/tex]

Answer:

1. Regular pay amount:

$17.40 × 37.25 = $648.15

2. Overtime pay: $0.00

3. Gross pay: $648.15

The 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).

To calculate the 90% confidence interval for the mean tail length of all newts in the population, we can use the formula:

Confidence Interval = Sample Mean ± Margin of Error

Given:

- Sample size (n) = 25

- Sample Mean (xbar) = 5 cm

- Standard Deviation of the population (σ) = 0.2 cm

- Confidence level = 90% (which corresponds to a z-score of 1.645 for a two-tailed test at a 90% confidence level)

First, we need to calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √Sample Size)

In this case, the critical value for a 90% confidence level is 1.645. Let's substitute the values:

Margin of Error = 1.645 * (0.2 / √25)

Margin of Error = 1.645 * 0.04

Margin of Error ≈ 0.0658

Now, we can calculate the confidence interval:

Confidence Interval = Sample Mean ± Margin of Error

Confidence Interval = 5 ± 0.0658

Confidence Interval ≈ (4.9342, 5.0658)

Therefore, the 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).

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The solution to the composite functions from the graph are:

(f * g)(2) = 16

(f - g)(0) = -5

Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, then the function “ f of g of x”, is the composition of the two functions.

a) Using the concept of composite functions, we can say that:

(f * g)(x) = f(x) * g(x)

Thus:

(f * g)(2) = f(2) * g(2)

f(2) = 4

g(2) = 4

Thus:

(f * g)(2) = 4 * 4

(f * g)(2) = 16

b) Using the concept of composite functions, we can say that:

(f - g)(x) = f(x) - g(x)

Thus:

(f - g)(0) = f(0) - g(0)

f(0) = 1

g(0) = 6

Thus:

(f - g)(0) = 1 - 6

(f - g)(0) = -5

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Answer:

false

Step-by-step explanation:

Its All Real Numbers

Using proportions, it is found that the table is completed as follows:

                        Original Ratio Number in the zoo

Baby camels     5                     20

Adult camels     6                     24

Total camels     11                    44

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

At the zoo, for every 6 adult camels, there are 5 baby camels, hence, out of 11 camels, 5 are baby and 6 are adult.

Thus, out of 44 camels, we have that:

The table is:

                        Original Ratio Number in the zoo

Baby camels     5                     20

Adult camels    6                     24

Total camels     11                     44

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Your question was incomplete, the complete question is-

At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoo.

Complete the table.

Original ratio Number in the zoo

Baby camels 5 ?

Adult camels 6 ?

Total camels ? 44

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

[tex] \sqrt{ {( - 4 - 2)}^{2} + {(1 - 0)}^{2} } = \sqrt{ {( - 6)}^{2} + {1}^{2} } = \sqrt{36 + 1} = \sqrt{37} [/tex]

The number 37 goes beneath the radical symbol.