The gross pay of a worker in a factory is €30800.60 per annum. If €504 is deducted from his salary month,how much does he take home in a year

Answer:

82 degrees

Step-by-step explanation:

It should all equal 180 so 52+46=98 and 180-98 is 82

Answer: x=-5, y=4 (-5,4)

Step-by-step explanation:

The solution is::

2,500 Joules (J) or Newton Meter (N M) work is done on an object that is moved to acquire a displacement of 5 meters when 500 Newtons of force was exerted.

Here, we have,

Work = Force x Distance

The force in this equation is 500 Newtons.

The distance (displacement) is 5 meters.

Plug it into the equation above.

Work = 5m x 500n

Work = 2,500 Joules or Newton-Meters.

Therefore 2,500 Joules or Newton Meters of work is done on an object.

Hence, The solution is::

2,500 Joules (J) or Newton Meter (N M) work is done on an object that is moved to acquire a displacement of 5 meters when 500 Newtons of force was exerted.

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complete question:

How much work is done on an object that is moved to acquire a displacement of 5 meters when 500 Newtons of force was exerted?​

Answer:

You can buy 4 $25 tickets with $100

Step-by-step explanation:

25 X 4 = 100

For this equation, the bottom part of the equation cannot be zero, so the domain at the moment is:

    \(x > 4\)

However, also on top, the numerator includes a square root which can equal zero but cannot be negative, thus the domain is

 (6, ∞)

Hope that helps!

The after-tax cost of debt is approximately 6.32%.

To calculate the after-tax cost of debt, we need to consider the bond's trading price, face value, coupon rate, tax rate, and remaining maturity. In this case, the bond is trading at $975 with a face value of $1,000 and an annual coupon rate of 8%. The tax rate is 21%, and the bond has 7 years left until maturity.

First, we calculate the annual interest payment by multiplying the face value ($1,000) by the coupon rate (8%), which gives us $80. Since the coupon payment is taxable, we need to find the after-tax coupon payment. To do this, we multiply the coupon payment by (1 - tax rate). In this case, (1 - 0.21) = 0.79, so the after-tax coupon payment is $80 * 0.79 = $63.20.

Next, we calculate the after-tax cost of debt by dividing the after-tax coupon payment by the bond's trading price. In this case, $63.20 / $975 = 0.0648, or 6.48%. However, we need to consider that the bond has 7 years left until maturity. So, to find the annualized after-tax cost of debt, we divide the calculated after-tax cost of debt by the remaining maturity in years. 6.48% / 7 = 0.9257%, or approximately 0.93%.

Finally, to express the annualized after-tax cost of debt as a percentage, we multiply the result by 100. Therefore, the after-tax cost of debt is approximately 0.93% * 100 = 6.32%.

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30% of students mean 30 students wear contact lenses from a random selection of 100 students studying in a university.

Percentage is a fraction or a ratio of a random sample in which the value of whole is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.

Percentage is defined as a certain fraction or number out of a hundred. It is a fraction with the denominator 100, and the sign for it is "%."

Finding the proportion of a whole in terms of 100 is the goal of percentage calculations. There are two methods to calculate a percentage:

Use the unitary approach or try adjusting the fraction's denominator to 100.

How to solve?

30 % = 30/100 of a sample = 0.3 of a sample

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Answer:

Step-by-step explanation:

Find the area of the pepperoni pizza:

Two slices of pepperoni pizza has area of:

Since 78.5 in² < 80 in², Jaron is correct

Answer:

Area = l x w

Area = (x + 1)(x + 7)

Area = x² + 7x + x + 7

Area = x² + 8x + 7

Step-by-step explanation:

A discrete variable is a variable whose value is obtained by counting while a continuous variable is a variable whose value is obtained by measuring.

From the question,

The number of cars a car dealer sells in a day is a discrete variable.

The time it takes to have a medical physical exam is a continuous variable.

The recurrence relation of the running time for a recursive algorithm, prove by induction that T(n)=O(nlog

3 /2 + log₃((k + 1)/3))

       = (k + 1)(3/2 + log₃(k + 1) - log₃(3))

To prove by induction that T(n) = O(nlog₃(n)), we will first establish a base case and then assume the hypothesis for n and prove it for n + 1.

Base Case:

For n = 3, T(3) = 2T(3/3) + 3 = 2T(1) + 3 = 2(10) + 3 = 23.

Assumption:

Let's assume that for some k ≥ 3, T(n) ≤ cnlog₃(n) holds for all n ≤ k.

Inductive Step:

Now, we need to prove that T(n) ≤ cnlog₃(n) holds for n = k + 1.

T(k + 1) = 2T((k + 1)/3) + (k + 1)

Using the assumption, we have:

T(k + 1) ≤ 2c((k + 1)/3)log₃((k + 1)/3) + (k + 1)

We can simplify the logarithm using the change of base formula:

log₃((k + 1)/3) = logₓ((k + 1)/3) / logₓ(3)

Let's choose x = (k + 1)/3, so logₓ(3) = 1. Thus, we have:

log₃((k + 1)/3) = logₓ((k + 1)/3)

Substituting this back into the inequality, we get:

T(k + 1) ≤ 2c((k + 1)/3)logₓ((k + 1)/3) + (k + 1)

Expanding further:

T(k + 1) ≤ 2c(k + 1)logₓ((k + 1)/3) / 3 + (k + 1)

       = (2c / 3)(k + 1)logₓ((k + 1)/3) + (k + 1)

Since logₓ((k + 1)/3) is positive and (2c / 3)(k + 1) is also positive, we can simplify the inequality further:

T(k + 1) ≤ (2c / 3)(k + 1)logₓ((k + 1)/3) + (k + 1)

       ≤ (2c / 3)(k + 1)logₓ((k + 1)/3) + (k + 1)logₓ((k + 1)/3)

       = (k + 1)(2c / 3 + logₓ((k + 1)/3))

Now, let's choose c such that 2c / 3 ≥ 1. This ensures that (2c / 3 + logₓ((k + 1)/3)) ≥ 1.

Choosing c = 3/2 satisfies the condition. Therefore, we have:

T(k + 1) ≤ (k + 1)(2c / 3 + logₓ((k + 1)/3))

       ≤ (k + 1)(3/2 + logₓ((k + 1)/3))

       = (k + 1)(3/2 + logₓ((k + 1)/3))

       = (k + 1)(3/2 + log₃((k + 1)/3))  [since x = (k + 1)/3]

By simplifying further, we obtain:

T(k + 1) ≤ (k + 1)(3

/2 + log₃((k + 1)/3))

       = (k + 1)(3/2 + log₃(k + 1) - log₃(3))

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Answer:

The probability that a customer selected at random has an Apple device or own a smartphone or both is 0.94

Step-by-step explanation:

The percentage of costumers that have a device made by Apple = 60%

The percentage of customers that own a smartphone = 85%

The percentage of customers that use Venmo = 80%

The percentage out of the smartphone users that use Venmo = 80%

The probability both independent events A and B occurring = P(A) × P(B)

The exclusive probability of A or B occurring P(A XOR B) = P(A) + P(B) - 2 × P(A ∩ B)

Therefore, the probability of A or B or both occurring is given as follows;

P(A or B or Both) = P(A) + P(B) - 2 × P(A ∩ B) + P(A) × P(B)

Where A represent the percentage of costumers that have a device made by Apple and let B represent the percentage of users that have a smartphone, we have;

P(A or B or Both) = 0.6 + 0.85 - 2×0.6×0.85 + 0.6 × 0.85 = 0.94

Therefore, the probability that a customer selected at random has an Apple device or own a smartphone (or both), P(A or B or Both) = 0.94

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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The cost of 5 pairs of shoes is 108.78 dollars.

The cost of 3 pairs of shoes is $65.27. At this price, the cost of 5 pairs of shoes can be calculated as follows:

Let's find the cost of each pair of shoes before we can get the cost of 5 pairs of shoes.

Therefore,

3 pairs of shoe = 65.27 dollars

1 pair of shoes = ?

cross multiply

cost of each pair = 65.27 / 3

cost of each pair = 21.76 dollars

Therefore, the cost of 5 pairs of shoes can be found as follows:

cost of 5 pairs of shoes = 21.76 × 5

cost of 5 pairs of shoes = 108.783333333

Therefore,

cost of 5 pairs of shoes = 108.78 dollars

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Probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value is 0.8664, is farther than 2.5 SDs from its mean value is 0.0124 and between 1 and 2 SDs from its mean value is 0.2728.

Probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value P (μ - 1.5σ < X < μ + 1.5σ)= P(Z < 1.5) - P(Z < -1.5)Here, Z is the standard normal variable P(Z < 1.5) = 0.9332 (from standard normal table)P(Z < -1.5) = 0.0668 (from standard normal table) So, P (μ - 1.5σ < X < μ + 1.5σ) = 0.9332 - 0.0668= 0.8664

Thus, probability that the thread length of a randomly selected bolt is within 1.5 SDs of its mean value is 0.8664. Probability that the thread length of a randomly selected bolt is farther than 2.5 SDs from its mean value P (X < μ - 2.5σ) + P (X > μ + 2.5σ) = P (Z < -2.5) + P (Z > 2.5)P (Z < -2.5) = 0.0062 (from standard normal table)P (Z > 2.5) = 0.0062 (from standard normal table)

So, P (X < μ - 2.5σ) + P (X > μ + 2.5σ) = 0.0062 + 0.0062 = 0.0124  Probability that the thread length of a randomly selected bolt is between 1 and 2 SDs from its mean value P (μ - 2σ < X < μ - 1σ) = P (Z < -1) - P (Z < -2) + P (Z < 1) - P (Z < 2)P (Z < -1) = 0.1587 (from standard normal table)

P (Z < -2) = 0.0228 (from standard normal table)P (Z < 1) = 0.8413 (from standard normal table)P (Z < 2) = 0.9772 (from standard normal table) So, P (μ - 2σ < X < μ - 1σ) = 0.1587 - 0.0228 + 0.9772 - 0.8413= 0.2728

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Answer:

-11.5

Step-by-step explanation:

Answer:

half of 45.7 is 22.85

22.85^2 = 522.1225

522.1225 x pi

Meaning

522.1225π, A

Answer:

\(522.12\pi\) inches²

Step-by-step explanation:

The formula for finding the area of a circle is:

\(A=\pi r^2\)

If you put 45.7/2 (because you have the diameter and NOT the radius) instead of r you get:

\(A=22.85^2\pi\)

Now you calculate:

\(A=522.12\pi \\\) inches²

if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

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The number of hours of rain is 34.

The depth of the creek before the rain was 3 feet. There was a flood last month. The depth of the creek rose to 20 feet after the flood. The weather man said that it rained for 0.5 feet every hour.

The rise in the depth of the creek is the difference between the final and initial depths.

D = 20 - 3 = 17 feet

The number of hours for which it rained is the result of the division of the rise in the depth by the rate of rain.

N = 17/0.5

N = 34 hours

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Answer:

Its (1.0, 1.4)

Step-by-step explanation:

Cuz i said soo :3

Answer:

b

Step-by-step explanation:

just took the test : )

To prove that n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3, we can start by factoring the expression:
n^2 - 7n + 12 = (n - 4)(n - 3) . Since n ≥ 3, both factors in the expression are positive. Therefore, the product of the two factors is also positive.
(n - 4)(n - 3) > 0

We can also use a number line to visualize the solution set for the inequality:
n < 3: (n - 4) < 0, (n - 3) < 0, so the product is positive
n = 3: (n - 4) < 0, (n - 3) = 0, so the product is 0
n > 3: (n - 4) > 0, (n - 3) > 0, so the product is positive
Therefore, n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3.
Alternatively, we can complete the square to rewrite the expression in a different form:
n^2 - 7n + 12 = (n - 3.5)^2 - 0.25
Since the square of any real number is nonnegative, we have:
(n - 3.5)^2 ≥ 0
Therefore, adding a negative constant (-0.25) to a nonnegative expression ((n - 3.5)^2) still yields a nonnegative result. This confirms that n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3.

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Answer:

8.5

Step-by-step explanation:

c = 8.5

hope this helps

Answer:8.5

Step-by-step explanation:

Add 7 and 1.5

1. The conditional probability of X being 1 given that Y = 2 is 1/2. 2. The probability of X being less than or equal to 2 given that Y = 2 is 1/2.

To find the conditional probability of X given Y = 2, we need to consider the possible outcomes when Y = 2 and determine the probability of X being a specific value.

Let's calculate the conditional probability:

1. Find the conditional probability of X given Y = 2:

When Y = 2, we have two possible outcomes: (1, 2) and (3, 2). Out of these two outcomes, only one has X ≤ 2, which is (1, 2).

Therefore, the conditional probability of X being less than or equal to 2 given that Y = 2 is:

P(X ≤ 2 | Y = 2) = P(X = 1 | Y = 2) = 1/2

2. Use this to compute P(X ≤ 2 | Y = 2):

We have already determined that P(X ≤ 2 | Y = 2) = P(X = 1 | Y = 2) = 1/2.

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Answer: The answer is x/4 = 12.

Step-by-step explanation: This is because in the problem it says "How many stickers did she bring to school" so you will have to divide x by 4 in order to get 12.

For the sample given if the confidence level for both surveys is 95% (z*-value 1.96), then the statement that is true is -

Option A: The margin of error for the Camp Verde survey is larger than the margin of error for the Gilbert survey.

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

Since we know the sample size, the sample proportion, and the desired confidence level, we can calculate the margin of error for each survey.

For the Gilbert survey -

Margin of error = z*(√(p*(1-p)/n))

where -

z* is the z-value corresponding to the desired confidence level (1.96 for 95% confidence)

p is the sample proportion (0.15)

n is the sample size (300)

Plugging in the values, we get -

Margin of error = 1.96 × √(0.15 * 0.85 / 300) ≈ 0.034

So we can say with 95% confidence that the true proportion of Gilbert residents who want Arizona to start using daylight savings is between 0.15 - 0.034 = 0.116 and 0.15 + 0.034 = 0.184.

For the Camp Verde survey -

Margin of error = z*(√(p*(1-p)/n))

where -

z* is the z-value corresponding to the desired confidence level (1.96 for 95% confidence)

p is the sample proportion (0.15)

n is the sample size (100)

Plugging in the values, we get -

Margin of error = 1.96 × √(0.15 * 0.85 / 100) ≈ 0.07

So we can say with 95% confidence that the true proportion of Camp Verde residents who want Arizona to start using daylight savings is between 0.15 - 0.07 = 0.08 and 0.15 + 0.07 = 0.22.

Therefore, the correct statement is -

Option A: The margin of error for the Camp Verde survey is larger than the margin of error for the Gilbert survey.

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The measurement basis used when a reliable estimate of fair value is not available is the historical cost basis.

Historical cost basis refers to the original cost of acquiring an asset or incurring a liability. Under this basis, assets are recorded at the amount paid or the consideration given at the time of acquisition, and liabilities are recorded at the amount of consideration received in exchange for incurring the obligation.

This measurement basis is used when a reliable estimate of fair value is not available because fair value requires market prices or observable inputs, which may not be readily available in certain situations. In such cases, historical cost provides a more objective and verifiable measure of an asset's value.

For example, if a company purchases a building for $500,000, the historical cost of the building will be recorded as $500,000 on the balance sheet. Even if the fair value of the building increases or decreases over time, the historical cost will remain unchanged unless there are subsequent events that require a different measurement basis, such as impairment.

In summary, when a reliable estimate of fair value is not available, the historical cost basis is used as a measurement basis to record assets and liabilities at their original acquisition or incurrence cost.

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