Andrew is descending 57 feet underwater while scuba diving. If he descends at a rate of 3 feet per second, how many seconds will it take Andrew to descend the full distance?

The probability of a linear regression being significant in at least one of the 60 regressions is 1 - 0.860  0.999998, so the expected number of significant regressions is 60  (1 - 0.860)  0.001236, or 0.1% of the total regressions.

the significance level is 0.2, which means that the probability of significance by chance is 0.2. Hence, the probability of insignificance by chance is 1 - 0.2 = 0.8.Therefore, the probability of significance by chance for each linear regression is 0.2. The probability of insignificance by chance for each linear regression is 0.8.The probability of a linear regression being insignificant in all 60 regressions is 0.8 raised to the power of 60. Hence, the probability of a linear regression being significant in at least one of the 60 regressions is 1 - 0.8⁶⁰ ≈ 0.999998.By using the complement of this probability, we can find the expected number of significant regressions as follows: Expected number of significant regressions = 60 × (1 - 0.8⁶⁰)≈ 0.001236, or about 0.1% of the total regressions. Thus, we can expect around 0 or 1 regression to show significance by chance out of the total 60 linear regressions.

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Answer: 5.7 (rounded)

Step-by-step explanation: The formula to find the diagonal of a square is \(\sqrt{2\) * a, where a is a side length on the square. Since we are solving for half of a diagonal, we use this formula and divide our result by two. We start by multiplying root 2 by 8 and we get 11.31371, next we divide by two and we get 5.656855 which is 5.7 when rounded.

Answer:

h = 6

Step-by-step explanation:

Solving for variables is a quick and easy concept to learn. Solving for variables is simple. All you need to do is figure out what number can replace the variable.

Vocabulary

variable - a symbol that represents a mathematical object.

The equation: -6h + 12 = -36

Lets solve this step by step!

When a variable is right next to a number, for example, -6h, this means the same as 6 · h and 6 × h. This means we will be multiplying. The equation can be represented as -6(h) + 12 = -36. Because we know that negative + negative = positive, we know h cannot be a negative number as the answer is -36. What we can do to solve this is substitute numbers as h to see what can equal -36. -6(8) + 12 = -36, so, this means that h = 8.

Answer:

h = 8

Assuming that x ≥ 0 and y ≥ 0, the situation is infeasible: True.

In Mathematics, these rules are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a coordinate plane:

In this context, we can logically deduce that the given system of inequalities 5x+3y ≤ 15 and y ≥ 6 would not have a feasible solution set if they are subjected to x ≥ 0 and y ≥ 0:

Assuming the ordered pair (1, 2), we have:

y ≥ 6

2 ≥ 6 (False).

5x+3y ≤ 15

5(1) +3(2) ≤ 15

5 + 6 ≤ 15

11 ≤ 15 (True).

Therefore, it is not a feasible solution.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Mary ran the farthest

Step-by-step explanation:

Look at Diagram :)

As the Diagram shows, Mary ran the farthest!

Hope this Helps!

Answer:

VAT = Rs 4,080 and VAT% = 12%.

Step-by-step explanation:

VAT = Rs 38,080 -Rs 34,000

or, VAT = Rs 4,080

now

VAT % = 4,080/34,000×100%

= 12%

A computer costing Rs. 34,000 is sold at Rs. 38080 including VAT. Find the amount of VAT and its percentage.

• Amount of VAT = Rs. 4,080

• VAT % = 12%

→ Amount of VAT = Rs 38080 - Rs 34000 = Rs 4080

→VAT % = \( \frac{4080}{34000} \times 100 = 12\)%

--------------------------------------------------------

[VAT stands for Value Added Tax]

If 40L of gas are used from a gasoline tank that initially contains 45L, 1/9 of the tank remains. This fraction represents the portion of the tank's capacity that is still filled with gas after the 40L is consumed.

To determine the fraction of the gasoline tank that remains after using 40L of gas, we can follow these steps:

Step 1: Calculate the remaining amount of gas in the tank by subtracting the amount used from the initial amount.

Remaining gas = Initial amount - Amount used

Remaining gas = 45L - 40L

Remaining gas = 5L

Step 2: Express the remaining amount as a fraction of the initial amount.

Fraction remaining = Remaining gas / Initial amount

Fraction remaining = 5L / 45L

Step 3: Simplify the fraction if possible.

To simplify the fraction 5/45, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 5 and 45 is 5.

5/45 = (5 ÷ 5) / (45 ÷ 5)

5/45 = 1/9

Therefore, the fraction of the gasoline tank that remains after using 40L of gas is 1/9.

To understand this fraction visually, imagine the gasoline tank divided into nine equal parts. Each part represents 1/9 of the tank's capacity. If 40L of gas are used, only one out of the nine parts will be left, indicating 1/9 of the tank remains.

It's important to note that fractions represent a part-to-whole relationship. In this case, the numerator (1) represents the remaining gas, and the denominator (9) represents the initial gas capacity of the tank.

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The fee with each airline was 35 dollars, and the bag was 7 pounds over the weight limit.

Let w be the weight of the bag in pounds, and let x be the weight over the limit.

The first airline charges 28 + 7x dollars for the bag, and the second airline charges 14 + 9x dollars for the bag.

Since the fees are the same with both airlines, we can set these two expressions equal to each other:

28 + 7x = 14 + 9x

Solving for x, we find that x = 7.

Substituting this value back into either of the original expressions, we find that the fee with each airline is 28 + 7x = 35.

Therefore, the fee with each airline was 35 dollars, and the bag was 7 pounds over the weight limit.

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The point where marginal cost equals $15 is at the production of the 7th pizza. Therefore, the firm should produce 7 pizzas.

The firm's shut-down price is the price at which the firm is indifferent between producing and shutting down.

Using the table provided, we can calculate the missing values:

Variable Cost:

For 0 pizzas, the variable cost is $0.

For 1 pizza, the variable cost is $10.

For 2 pizzas, the variable cost is $12.

For 3 pizzas, the variable cost is $2.

For 4 pizzas, the variable cost is $1.

For 5 pizzas, the variable cost is $2.

For 6 pizzas, the variable cost is $3.

For 7 pizzas, the variable cost is $13.

For 8 pizzas, the variable cost is $16.

For 9 pizzas, the variable cost is $3.

For 10 pizzas, the variable cost is $6.

For 11 pizzas, the variable cost is $4.

Total Cost: To calculate the total cost, we simply add the variable cost and the fixed cost for each level of output. The fixed cost is not given in the table, so we cannot calculate the total cost.

Average Variable Cost:

To calculate the average variable cost, we divide the variable cost by the level of output. For example, the average variable cost for 1 pizza is $10/1 = $10.

Average Fixed Cost:To calculate the average fixed cost, we divide the fixed cost by the level of output.

Average Total Cost: To calculate the average total cost, we add the average variable cost and the average fixed cost. The firm should produce pizzas up to the point where marginal cost equals marginal revenue.

This is the point where the firm maximizes its profit. From the table, we can see that the marginal cost is increasing as output increases, while the marginal revenue remains constant at $15.

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Answer:

35

Step-by-step explanation:

Answer:

-81+9p

Step-by-step explanation:

-9(9-p)

-9×9-9×-p

-81-9×-p

-81-(-9p)

-81+9p

9p-81

This is a 45°-45°-90° triangle, in which the sides occur in a ratio of 1 to 1 to √2. So x = √2.

If you didn't already know that, you can trigonometry. By definition of cosine,

cos(45°) = 1/x

Then

x = 1/cos(45°) = 1/(1/√2)) = √2

Answer:

4.25

Step-by-step explanation:

Shown in photo

The solution to the system of equation is x = -2 and y = -3.

System of equation can be solved using different method such as elimination method, graphical method and substitution method,

here we have,

Therefore, let's solve the system of equation by using substitution method.

-2x+ 7y = 15

6y=x

substitute the value of x in equation(i)

-2* 6y+ 7y = 15

or, -12y + 7y = 15

or, -5y = 15

or, y = -3

so, we get,

x = 6/ -3

or, x = -2

Hence, The solution to the system of equation is x = -2 and y = -3.

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Considering the competition, there are already 32 pizza places in the area. The new pizza place will be the 33rd in the vicinity.

The Pretty Pizza Company plans to open a new pizza place. The company has identified a location that is 0.01 (15 blocks) away. The cost per block for constructing the new pizza place is $221. Additionally, there are already 32 existing pizza places in the area.

To calculate the total cost of opening the new pizza place, we multiply the distance by the cost per block:

Total cost = 0.01 (15 blocks) * $221 = $331.50

Considering the competition, there are already 32 pizza places in the area. The new pizza place will be the 33rd in the vicinity.

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The interpretation of this expression is that the partial derivative of TC w.r.t. x is the rate of change of TC with respect to x, considering all other variables constant. It means if we change one unit of labor, TC will increase by 2e2x - 4 units, considering all other variables remain constant.

T C = 1/2 e2x + ey - 4x - 2ywhere x = units of labor and y = units of human capital, x, y > 0.Calculate:We need to calculate dTC/dx.

Interpretation:First, we need to calculate partial derivative of T C w.r.t. x. We know that partial derivative of a function with respect to one of its variable means to find the derivative of that variable with respect to the function, considering the other variables constant. Hence, it is a rate of change of one variable with respect to other variables considered constant. This is used to find the slope of a surface in a given direction.

The partial derivative of T C w.r.t. x is given as:

∂/∂x (T C)

= 2e2x - 4.∂/∂x (T C)

= 2e2x - 4

The interpretation of this expression is that the partial derivative of TC w.r.t. x is the rate of change of TC with respect to x, considering all other variables constant. It means if we change one unit of labor, TC will increase by 2e2x - 4 units, considering all other variables remain constant.

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Answer:

y = 12x

Step-by-step explanation:

For an equation to be parallel the slopes must be the same.  The slope from the equation is 12.

y = mx + b  is the slope-intercept form of a line'

y = 12x + 3.  The m is the slope and that is 12 ion this equation.

We will use the slope (12), the x (0) and the y (0) to write the new equation.  We need to find the y intercept.  We can see from the ordered pair given that the y - intercept would be zero, but here is another way to check.

y = mx + b

0 = 12(0) + b

0 = 0 + b

0 = b

y = 12x + 0

or

y = 12x

The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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Answer:

4

Step-by-step explanation:

Answer:

D should be right

Step-by-step explanation:

Mr. Wrench would charge $139 for a two-hour repair job for coming out to the house as N dollars and the charge per hour of work as x dollars.

Let's denote the charge for coming out to the house as N dollars and the charge per hour of work as x dollars. We are given the following information:

For a one-hour repair job, the total charge is $97.

For a five-hour repair job, the total charge is $265.

From this, we can set up two equations:

N + 1x = 97 (equation 1)

N + 5x = 265 (equation 2)

To find the charge for a two-hour repair job, we need to solve for N and x in the equations above and substitute the value of x into the equation for a two-hour repair job.

Subtracting equation 1 from equation 2, we get:

(5x - 1x) = (265 - 97)

4x = 168

x = 42

Now we can substitute the value of x into equation 1 to solve for N:

N + 1(42) = 97

N + 42 = 97

N = 97 - 42

N = 55

Therefore, the charge for a two-hour repair job is N + 2x:

55 + 2(42) = 55 + 84

= $139

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To find the minimum value of a quadratic function most efficiently, we would like to see the quadratic function in its vertex form.

The vertex form of a quadratic function is given by:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola, and "a" determines the direction and the "stretch" of the parabola.

If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.

The minimum value of the function occurs at the vertex if the parabola opens upwards (a > 0), and the maximum value occurs at the vertex if the parabola opens downwards (a < 0).

In this case, since we're looking for the minimum value, we would want a quadratic function where a > 0. Once we have the vertex form, we can easily identify the vertex (h, k), and the minimum value of the function will be k.

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The maximum number of guesses necessary to guess correctly a given number between the numbers n and m can be determined by using a binary search algorithm.

In a binary search, you repeatedly divide the search space in half based on whether the target number is greater or smaller than the midpoint. This process continues until the target number is found.

The maximum number of guesses required can be calculated by determining the number of times you need to divide the search space in half until you narrow down to the correct number. This can be expressed as the logarithm (base 2) of the size of the search space.

If the size of the search space (m - n + 1) is a power of 2, the maximum number of guesses will be log2(m - n + 1). Otherwise, if the size of the search space is not a power of 2, the maximum number of guesses will be ⌈log2(m - n + 1)⌉.

Note that this assumes a worst-case scenario where the target number is at the most distant end of the search space. In practice, the actual number of guesses required may be lower if the target number is found earlier during the search process.

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Answer:

Multiple answers in Step-by-step explanation

Step-by-step explanation:

x+y = 10

1 + 9 = 10

2 + 8 = 10

3 + 7 = 10

4 + 6 =10

5 + 5 = 10

x - y = 2

4 - 2 = 2

8 - 6 = 2

10 - 8 = 2

12 - 10 = 2

22 - 20 = 2  

The value of the x is 3.

What is the Exterior Angle Theorem?

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

We have,

∠EGF = 2x + 1

∠EFG = 25

∠GEF = 10x + 2

Exterior Angle Theorem:

The measure of exterior angle = Sum of two opposite interior angles’ measure.

According to the Exterior Angle property of a triangle theorem, the sum of measures of ∠EGF and ∠EFG would be equal to the exterior angle ∠GEF.

∴ ∠EGF + ∠EFG =  ∠GEF

   2x + 1 +  25 = 10x + 2

   2x +  26 = 10x + 2

   26 - 2 = 10x - 2x

   24 = 8x

    x = 24/8

   ∴   x = 3

Hence, the value of the x is 3.

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To find the horizontal asymptotes with square root in denominator, first, we have to divide the numerator and denominator by the highest power of x under the radical.

We need to simplify the expression by multiplying the numerator and denominator by the conjugate of the denominator. Finally, we take the limit as x approaches infinity and negative infinity to find the horizontal asymptotes. If the limit is a finite number, then it is the horizontal asymptote, but if the limit is infinity or negative infinity, then there is no horizontal asymptote.

Here is an example of how to find horizontal asymptotes with square root in denominator: Find the horizontal asymptotes of the function f(x) = (x + 2) / √(x² + 3)

Dividing the numerator and denominator by the highest power of x under the radical gives: f(x) = (x + 2) / x√(1 + 3/x²)

As x approaches infinity, the denominator approaches infinity faster than the numerator, so the fraction approaches zero. As x approaches negative infinity, the denominator becomes large negative, and the numerator becomes large negative, so the fraction approaches zero. Hence, the horizontal asymptote is y = 0.

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The fee paid by the person for a $23.50 payment with a 2% processing fee is $0.47.

As the meal program accepts online payments by the use of a credit card. for every payment processed and the processing fee for the credit card payment is 2% of the payment amount. To calculate the fee if a person made a payment of $23.50, we can multiply the payment amount by 2% or 0.02.

Fee = 23.50 x 0.02 = $0.47

Therefore, the fee paid by the person for a $23.50 payment is $0.47.

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Answer:

$182

Step-by-step explanation:

$54 + $128 = $182.

Hope that helps!

Answer:look at the answer down⬇️ It’s right :)

Step-by-step explanation:

Probability that the number drawn is less than 4 is given by 0.3

The likelihood of an event happening is gauged by probability.

The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

The overall chance of every event in a sample space is 1.

Let random variable X represent the number of the drawn tag.

Since the simple space consists of 10 equally likely events

S = {1,2,3,4,5,6,7,8,9,10}

The formula for probability distribution is given by:

f(x) = { (1/10) for x = 1,2....10,    else 0 elsewhere

since, each number can equally likely occur, therefore

P(x) = 1/10 = 0.1

Probability that the number drawn is less than 4 is given by:

P(x<4) = P(1) + P(2) + P(3)

           = 0.1 + 0.1 + 0.1

           = 0.3

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