Solve How many four-digit numbers can be formed using the numbers 2, 3, 4, 5 and 6. If the first and last digit must be even numbers and repetition is not allowed?​

Answer:

The equivalent equation is -9i-48

Step-by-step explanation:

i = √-1, i² = -1

Therefore (-√-9 + √-4) - (2√576 +√-64)

=(-√(9*(-1)) + √(4*(-1))) - (2 *24 + √(64 *(-1)))

= (-3i + 2i) - (2 * 24 + 8i)

= -i - 48 -8i

= -9i - 48

Answer:

3(8 + 2) = 3(8) + 3(2) = 3(10) = 30

The midpoint formula and distance formula can be used to find the coordinates of the midpoints of line segments RR' and SS' and the lengths of these segments. Then an equation involving these lengths can be set up and solved for m which is equal to 5.

Given a trapezoid PQRS and its image P'Q'R'S' after a reflection across Line W Y, the line of reflection.

We are also given that line segment R R prime has a midpoint at point Z and that line segment S S prime has a midpoint at point X.

We need to find the value of m. We can use the midpoint formula to find the coordinates of the midpoints Z and X.

Using the coordinates of P, Q, R, S, and the line of reflection WY, we can find the coordinates of the reflected image P', Q', R', and S'.

Now we can find the length of line segments RR' and SS' using the distance formula. Then we can set up an equation involving the length of line segments RR' and SS' and solve for m. Thus, m=5.

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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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The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.

Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.

Simplifying this, we get 2x - 80 = $670  + 80 2x = $750  x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.

The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.

The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.

Therefore, the cost of the bench is $375, and the cost of the garden table is $295.

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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

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

We can substitute this value into the function f(x) = 1/(x + 1):

1) f(g(0)) = 1/3

2) g(f(0)) = 4.

To find the value of f(g(0)), we need to first evaluate g(0) and then substitute that result into f(x).

Given the function g(x) = 2x + 2, we can find g(0) by substituting 0 for x:

g(0) = 2(0) + 2 = 0 + 2 = 2

Now that we know g(0) = 2, we can substitute this value into the function f(x) = 1/(x + 1):

f(g(0)) = f(2)

Substituting 2 for x in f(x):

f(2) = 1/(2 + 1) = 1/3

Therefore, f(g(0)) = 1/3.

Now, let's find the value of g(f(0)).

Given the function f(x) = 1/(x + 1), we need to evaluate f(0) and then substitute that result into g(x).

f(0) = 1/(0 + 1) = 1/1 = 1

Now, using the function g(x) = 2x + 2, we substitute f(0) = 1 into g(x):

g(f(0)) = g(1)

Substituting 1 for x in g(x):

g(1) = 2(1) + 2 = 2 + 2 = 4

Therefore, g(f(0)) = 4.

In summary:

f(g(0)) = 1/3

g(f(0)) = 4

Thus, fg(0) = 1/3 and g(f(0)) = 4.

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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.

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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Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

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

a = 18/tan(42)

a = 19.99

Answer:

false

Step-by-step explanation:

Its All Real Numbers

1) The expression that describes this scenario where Edmond decided to save €10,000 from his first year of work for an emergency fund, earning 6% per year and compounded annually is that the fund will grow to become equal to [tex]10,000 (1.06)^t[/tex] in t years.

2) After ten years of investing at 6%, compounded annually, the amount (future value) in the fund will be €17,908.

3) Given that the annual rate is 6%, the monthly rate will be 0.5%.

4) The exponent for the exponential function will be 120 with the 10 years in the scenario.

5) The complete expression that describes the scenario over 10 years is [tex]10,000(1.005)^{120}[/tex].

6) After ten years of investing at 6% APR compounded monthly, the amount (future value) in the fund will be €18,193.97.

7) There is more money with monthly compounding than annual compounding because the monthly interest is added and compounded more regularly, in this case, twelve times yearly than once a year.

Thus, more regular compounding increases the future value than periodic (annual, monthly, semiannual) compounding.

The future values can be determined using an online finance calculator that compounds interest per period as follows:

We can also derive the future values using the FV formula given as [tex]PV(1+r)^t[/tex].

1) Principal investment = €10,000

Compound interest rate = 6% = 0.06 (6/100)

Compound factor = 1.06 (1 + 0.06)

Compounding period = annually

Investment period = t years

Expression: €10,000 x [tex]1.06^t[/tex]

= 10,000(1.06)^t

= [tex]10,000(1.06)^t[/tex]

2) After ten years, the amount in the account will be equal to [tex]10,000(1.06)^{10}[/tex]

= 10,000 x 1.7908

= 17,908

3) Annual rate of interest = 6%

Monthly rate = 0.5% (6%/12)

4) Exponent = 120 (10 years x 12)

5) Exponential function:

[tex]10,000(1.005)^{120}[/tex]

6) Future value after 10 years:

[tex]10,000(1.005)^{120}[/tex]

= 10,000 x 1.8193967

= €18,193.97

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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:

Step-by-step explanation:

Answer:

The function value.of cos (-305.3)° is 0.5921

Explanation:

To find the value of cos (-305.3)°, we can use the periodicity property of the cosine function. Since cos (x) is a periodic function with a period of 360 degrees, we can add or subtract multiples of 360 degrees from the angle without changing the value of the cosine.

Step 1:  Convert -305.3° to an equivalent angle within period one (0 to 360 degrees).

-305.3° + 360° = 54.7°

Step 2: Calculate the cosine of the equivalent angle.

cos (54.7°)

Step 3: Use a scientific calculator or trigonometric table to find the cosine value.

cos (54.7°) ≈ 0.5921

Therefore, the value of cos(-305.3)° is approximately 0.5921

Answer:

The coreect answer o

is 14

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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There are 555 different ways for David to choose his fish according to the given combinations.

David to choose his fish, we need to consider all the possible combinations of fish he can select.

Let's break down the calculations for each combination:

Guppy fish and an angel fish:

David can choose one guppy fish from 7 options and one angel fish from 5 options.

This gives us a total of 7 × 5 = 35 different combinations.

Tetra fish and an angel fish:

David can choose one tetra fish from 13 options and one angel fish from 5 options.

This gives us a total of 13 × 5 = 65 different combinations.

Guppy fish, tetra fish, and an angel fish:

David can choose one guppy fish from 7 options, one tetra fish from 13 options, and one angel fish from 5 options.

This gives us a total of 7 × 13 × 5 = 455 different combinations.

To find the total number of different ways for David to choose his fish, we sum up the combinations from each category:

35 + 65 + 455 = 555

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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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Step-by-step explanation:

Perimeter= 12ft

Length= 4ft

Width= ?

Bedroom window = rectangle

Rectangle= l×b

= 4× ?

12÷ 4=3

Answer:

2 and 12

Step-by-step explanation:

we have 2 number cubes (dice) and try to roll specific numbers as the sum of both cubes.

4 can be achieved by rolling

1 3

2 2

3 1

so, 3 out of 36 possible combinations.

11 can be achieved by

5 6

6 5

so, 2 out of 36 possible combinations.

so, no, they do not have the save probabilty distribution, and would not have equal bars.

2 can be achieved by

1 1

so, 1 out of 36 possible combinations.

12 can be achieved by

6 6

so, 1 out of 36 possible combinations.

yes, they have the same probability distribution and would have equal bars.

6 can be achieved by

1 5

2 4

3 3

4 2

5 1

so, 5 out of 36 possible combinations.

9 can be achieved by

3 6

4 5

5 4

6 3

so, 4 out of 36 possible combinations.

so, no, they do not have the save probabilty distribution, and would not have equal bars.

5 can be achieved by

1 4

2 3

3 2

4 1

so, 4 out of 36 possible outcomes.

10 can be achieved by

4 6

5 5

6 4

so, 3 out of 36 possible outcomes.

so, no, they do not have the save probabilty distribution, and would not have equal bars.

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 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 height of the tree is approximately 87.13 feet.

To find the height of the tree, we can use trigonometric principles based on the given information.

Let's proceed with the following steps:

Draw a diagram to visualize the problem.

Visualize a right triangle where the horizontal line represents the hillside, the vertical line represents the height of the tree, and the hypotenuse represents the line from the tip of the shadow to the top of the tree. Label the given angles and lengths accordingly.

Identify the relevant trigonometric ratios.

In this case, we can use the tangent ratio (opposite/adjacent) to relate the angles and sides of the triangle.

Determine the length of the adjacent side.

The adjacent side represents the portion of the shadow cast by the tree down the hillside.

From the given information, the length of the shadow is 200ft.

Calculate the height of the tree.

To calculate the height, we can use the tangent of the angle of inclination (b) to find the ratio of the height to the adjacent side:

tan(b) = height/adjacent

tan(25) = height/200

Rearranging the equation, we have:

height = 200 [tex]\times[/tex] tan(25)

Using a calculator, we find:

height ≈ 87.13ft.

By applying trigonometric principles and using the tangent ratio, we were able to determine the height of the tree based on the given angles and length of the shadow.

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Answer:

1. Regular pay amount:

$17.40 × 37.25 = $648.15

2. Overtime pay: $0.00

3. Gross pay: $648.15

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.