An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 1300 meters, and Plane B was at an altitude of 1092 meters. Plane A is gaining altitude at 17 meters per second, and Plane B is gaining altitude at 21 meters per second. Let x be the number of seconds passed

Answer:

4

Step-by-step explanation:

8/2=4

To sketch the curve of the function y = (x^2 + 12)/(x - 2) and determine the equation of the slant asymptote, we follow the guidelines provided:

Guideline D states that if the degree of the numerator is exactly one more than the degree of the denominator, there is a slant asymptote. In this case, the degree of the numerator (2) is exactly one more than the degree of the denominator (1), indicating the presence of a slant asymptote. To find the equation of the slant asymptote, we perform polynomial long division between the numerator and denominator. Dividing x^2 + 12 by x - 2, we get:

markdown

Copy code

      x + 2

___________________

x - 2 | x^2 + 0x + 12

- (x^2 - 2x)

2x + 12

- (2x - 4)

16

The quotient is x + 2 and the remainder is 16. Therefore, the slant asymptote is the equation y = x + 2.

When graphing the function, we plot points on the curve, noting the vertical asymptote at x = 2 and the slant asymptote y = x + 2. We can also identify key points such as the y-intercept (0, 6) where x = 0, and the horizontal asymptote y = 0, which is the x-axis. Considering the behavior of the function, as x approaches positive or negative infinity, the value of y also tends to positive or negative infinity, respectively. The graph would exhibit a "U" shape, approaching the slant asymptote and the vertical asymptote as x increases or decreases. By following these guidelines and understanding the characteristics of the function, we can sketch the curve and accurately depict the slant asymptote and other key features of the graph.

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Answer: -2/11

Step-by-step explanation:

The slope of line from the points given is 1

The slope of a line is a measure of how steep the line is and the direction it is going. In mathematical terms, it is defined as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. Slope is often represented by the letter "m". If (x₁, y₁) and (x₂, y₂) are two points on the line, the slope can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

In this problem, we can take the two points and calculate the slope.

m =  (y₂ - y₁) / (x₂ - x₁)

Substituting the values into the formula to find the slope;

m = -5 - 1 / -8 - (-2)

m = 1

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Complete Question; Calculate the slope of the line (-2, 1) and (-8, -5)

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

1/8

The probability of getting a head or a tail when flipping a coin is 1/2.  

Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.

The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.

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The probability is= 1/665,280 in fraction in simplest form.

The idea of probability describes the possibility of an event happening.

We frequently have to make forecasts about the future in real life.

We may or may not be aware of the outcome of an event.

When this happens, we declare that there is a chance the event will take place.

In summary, probability has a wide range of fantastic applications in entertainment, business, and this recently expanding branch of artificial intelligence.

The probability formula can be used to determine the likelihood of an event by only dividing the favorable number of possibilities by the entire number of p-ossible outcomes.

According to our question-

P(n, r) = n! / (n - r)!

P(12, 7) = 12! / (12 - 7)!

12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

5! = 5 × 4 × 3 × 2 × 1

1/665,280

Hence,  The probability is= 1/665,280 in fraction in simplest form.

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Home plate to second base is located at a distance of 90√2 feet.

A square is a rectangle in which each side is the same length. The distance separating the square's opposing vertices is known as the diagonal. The Pythagoras Theorem can be used to compute the diagonals:

Diagonal² = Side² + Side²

Diagonal² = 2 Side²

Diagonal = √2 Side

The answer to the question is that it is 90 feet from home plate to first base.

This is the length of the side that makes up the baseball diamond's square shape. The diagonal of the square is the distance from home plate to second base.

Diagonal = √2 Side

Diagonal = 90√2

Hence, home plate to second base is located at a distance of 90√2 feet.

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The question is incomplete. The complete question will be -

"A baseball diamond is square. The distance from home plate to first base is 90 feet. In feet, what is the distance from home plate to second base?"

Answer:

Domain: (-∞,∞), Range: [2,∞)

1) The provided stirrups are greater than the minimum amount of transverse reinforcement.

2) The shear strength provided by concrete Vc, using Equation (a) in ACI Table 22.5.5.1, is [insert value] kips.

3) The shear strength provided by concrete Vc, using Equation (b) in ACI Table 22.5.5.1, is [insert value] kips.

4) The shear strength provided by concrete Vs is [insert value] kips.

5) The design shear strength ϕVn, using the Vc value from Question (2), is [insert value] kips.

1) To determine if the provided stirrups exceed the minimum amount of transverse reinforcement, we need to calculate the area of transverse reinforcement Av and compare it to the minimum required area Av,min. The area of four No. 3 stirrups spaced at 8 inches on centers can be calculated, and if it is greater than Av,min, the requirement is satisfied.

2) The shear strength provided by concrete Vc can be calculated using Equation (a) in ACI Table 22.5.5.1. This equation considers the size and strength of the beam and the concrete compressive strength. By plugging in the appropriate values, we can determine Vc.

3) The shear strength provided by concrete Vc can also be calculated using Equation (b) in ACI Table 22.5.5.1. This equation incorporates the size, strength, and reinforcement of the beam, as well as the concrete compressive strength. By inputting the relevant values, we can calculate Vc.

4) The shear strength provided by concrete Vs can be calculated using the formula Vs = 2Asfy/d, where As is the area of the longitudinal reinforcement and d is the effective depth of the beam.

5) The design shear strength ϕVn can be determined using the value of Vc calculated in Question (2). The design shear strength is given by the equation ϕVn = Vc, where ϕ is the strength reduction factor.

Note: Please provide the necessary values and equations for a more accurate calculation of the shear strengths and design shear strength.

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Exercise regularly.

Do not smoke or use tobacco products.

Get plenty of rest.

Eat a balanced diet.  

Wayne's Actual ACT score is 19.2 where mean is 21, standard deviation is 5 and the Z - score is -0.6.

Standard Deviation:

Standard deviation is  a measure of the dispersion of a set of numerical values from their mean.

The general form of the standard deviation is,

\(SD=\sqrt{\frac{\sum (x_i-\bar{x})}{n} }\)

where

xi is each value in the data set,

x-bar is the mean, and

n is the number of values in the data set.

Given,

Mean = 21.

Standard deviation = 5

Wayne's standardized score on the act = −0.6 .

Here we need to find the Wayne's Actual ACT score.

Let x be the Wayne's Actual ACT score.

So,
=> z-score = (x - mean)/SD

Apply the values on it,

=> -0.6 = (x - 21) / 3

=> -1.8 = x - 21

=> x = 21 - 1.8

=> x = 19.2

Therefore, Wayne's Actual ACT score is 19.2

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Answer:

200 sq cm

Step-by-step explanation:

Lateral surface area is the surface area without the bases, or without the top and bottom. So, you just add up the area of the 4 sides.

The front and back are both 10 x 20, so 200 each = 400

The left and right are 5 x 20, so 100 each = 200

The lateral surface area is 200 sq. cm.

Answer:

option 2 : 754 in³

Step-by-step explanation:

diameter = 8 => radius, r = 4 inches , h = 15 inches

\(volume = \pi r^2 h\)

          \(=\pi \times 4^2 \times 15 \\\\=753.9 \ in^3\\\\= 754 \ in^3\)

Step-by-step explanation:

volume of cylinder = πr²h

its yr ans.

hope it helps

According to the given points, the equation of the slope-intercept form for the line is:

\(\sf \boxed{\bold{y = \dfrac{3}{2x} + -18}}\)

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

From the information in the question,

Firstly, find the value of b,

\(\sf -3 = \dfrac{3}{2}(10) + b\)

\(\sf -3 = (15) + b\)

\(\sf \bold{b = -18}\)

Now, let's write the equation,

\(\sf \bold{y = \dfrac{3}{2x} + -18}\)

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The possible formula for P(x) would be \(P(x)=x^5+x^4-5x^3+3x^2\).

What is a polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The polynomial of degree 5.

Each root corresponds to a linear factor, so we can write:

        \(P(x) = x^2(x-1)^2(x+3)\\\\P(x)=x^2(x^2-2x+1)(x+2)\\\\P(x)=x^5+x^4-5x^3+3x^2\)

Hence, the possible formula for P(x) would be \(P(x)=x^5+x^4-5x^3+3x^2\).

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Answer:

 the answer is repeating

Step-by-step explanation:

I hope this helps you :)

Answer: Repeating decimal

Step-by-step explanation:

Thus the hydrogen ion concentration is 1.67 * 10^-10 M.

The molar concentration refers to the concentration in mole per liter. Now we know that the pOH has to do with the concentration of the hydroxide ion concentration.

We know that;

pH = 14 - 4.223 = 9.777

Now

[H^+] = (Antilog -9.777)

[H^+] = 1.67 * 10^-10 M

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Answer:

2pi

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

Required

Explain how 3 * 65 could be used for (0.03) * (0.65)

0.03 is to 2 decimal places and 0.65 is also to 2 decimal places

In total, we have: \(2 + 2 = 4\)

So, to get (0.03) * (0.65) from 3 * 65.

Simply calculate the product: 3 * 65

Then divide by 10 to the power of the sum of the decimal places i.e. 4

This is shown below

(0.03) * (0.65)

Express as fraction

\((0.03) * (0.65) = \frac{3}{100} * \frac{65}{100}\)

\((0.03) * (0.65) = \frac{3*65}{100*100}\)

\((0.03) * (0.65) = \frac{3*65}{10^2*10^2}\)

\((0.03) * (0.65) = \frac{3*65}{10^4}\)

Height of cylinder is 5 units

Define Cylinder

               ⇒ V = (π × radius²) × h

We have given,

Slant height of cylinder = √29

Radius is = 2 units

Now, we to have to calculate the height for that we have the formula

h = √l² - r²

where, l = slant height

            r = radius of the circular base

            h = height of the cylinder

Now, for the sake of simplicity

h = √l² - r²

h² =  l² - r²

Now, plug in the values

h² = (√29)² - 2²

h² = 29 - 4

h² = 25

h = 5

Hence, the height of cylinder is 5 units

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Answer:

5

Step-by-step explanation:

Step-by-step explanation:

\( \frac{137}{24} \)

or

\( \frac{137}{24} or \: 5 \frac{17}{24} \)

hope that helps you

Answer:

78 !!!!

Step-by-step explanation:

Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

Answer:

Step-by-step explanation:

Given series:

We can see that:

Each number starting from the third term is the sum of previous two

So the next term is:

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The number of ways in which the 8 teams finish found by permutation is 1st, 2nd, 3rd is 336.

A permutation would be a mathematical computation of the number of possible arrangements of a given set, in which the sequence of the arrangements is important.

Now, according to the question,

We have ten teams and want to understand number of times PERMUTATIONS OF 3 are possible.  For only a PERMUTATION, we want to consider how several positions we are selecting and how many options are available for each of those positions.

So, given three options are;

(# of choices for first) x (# of choices for second) x (# of choices for third)

If there are originally 8 teams to pick from, then first place has 8 alternatives. When one of those is chosen for first, there are only 7 alternatives for second, and only 6 choices for third... and so on.

8 × 7 × 6 = 336

Therefor, here are 366 possible methods to choose first, second, and third place from the original eight teams.

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The average pay-per-hour of the year for Elise will be 13.73 pounds.

From the information, in 2016 she earned £2100 and in 2017 she was awarded a 3% increase on her monthly salary.

Therefore, the new salary will be:

= 2100 + 3%(2100)

= 2100 + 63

= 2163

Now she worked for 42 hours per week for 45 weeks. This will be:

= 42 × 45

= 1890 hours

Therefore, the total earnings for the year will be:

= 2163 × 12 months

= 25956

The average pay-per-hour of the year will be:

= Total amount / Number of hours

= £25956 / 1890

= £13.73

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Answer:

30 cm

Step-by-step explanation:

Make sure all units are the same!

P = Perimeter

A = Area

Formula used for similar figures:

\(\frac{A_{1}}{A_{2}} = (\frac{l_{1}}{l_{2}})^{2}\) —- eq(i)

\(\frac{P_{1}}{P_{2}} = \frac{l_{1}}{l_{2}}\) ———— eq(ii)

Applying eq(ii):

∴\(\frac{25}{P_{2}} = \frac{10}{12}\)

Cross-multiplication is applied:

\((25)(12) = 10P_{2}\)

\(300 = 10P_{2}\)

\(P_{2}\) has to be isolated and made the subject of the equation:

\(P_{2} = \frac{300}{10}\)

∴Perimeter of second figure = 30 cm

We have obtained three equations:

59x2 + 19x3 + 22x4 = -84 (equation 6)

-62x2 + 2x3 - 28x4 = -6 (equation 7)

x1 + 2x2 + 2x3 + x4 = 7 (equation 1)

To solve the system of equations:

x1 + 2x2 + 2x3 + x4 = 7

x1 - 3x2 + x3 - x4 = 2

3x1 - x2 + x3 + x4 = 0

2x1 + 2x3 = 8

We can use the method of elimination to eliminate variables one by one.

First, let's eliminate x1 from equations 2 and 3. Multiply equation 2 by 3 and equation 1 by -1, then add them together:

-3(x1 - 3x2 + x3 - x4) + (x1 + 2x2 + 2x3 + x4) = -6 + 7

-3x1 + 9x2 - 3x3 + 3x4 + x1 + 2x2 + 2x3 + x4 = 1

-2x1 + 11x2 - x3 + 4x4 = 1 (equation 4)

Now, let's eliminate x1 from equations 3 and 4. Multiply equation 4 by 3 and equation 3 by 2, then subtract them:

3(-2x1 + 11x2 - x3 + 4x4) - 2(3x1 - x2 + x3 + x4) = 3 - 0

-6x1 + 33x2 - 3x3 + 12x4 - 6x1 + 2x2 - 2x3 - 2x4 = 3

-12x1 + 35x2 - 5x3 + 10x4 = 3 (equation 5)

Now, we have a system of three equations:

x1 + 2x2 + 2x3 + x4 = 7 (equation 1)

-2x1 + 11x2 - x3 + 4x4 = 1 (equation 4)

-12x1 + 35x2 - 5x3 + 10x4 = 3 (equation 5)

We can solve this system of equations using various methods such as substitution or matrix operations. However, since the system is already reduced, we can proceed to find the values of the variables directly.

From equation 5, we can express x1 in terms of the other variables:

x1 = (35x2 - 5x3 + 10x4 - 3) / -12

Substituting this expression into equations 1 and 4, we can find the values of x2, x3, and x4.

Substituting x1 into equation 1:

(35x2 - 5x3 + 10x4 - 3) / -12 + 2x2 + 2x3 + x4 = 7

Simplifying and combining like terms:

35x2 - 5x3 + 10x4 + 24x2 + 24x3 + 12x4 = -84

Combining like terms again:

59x2 + 19x3 + 22x4 = -84 (equation 6)

Substituting x1 into equation 4:

-2((35x2 - 5x3 + 10x4 - 3) / -12) + 11x2 - x3 + 4x4 = 1

Expanding the expression and simplifying further:

(-2 * (35x2 - 5x3 + 10x4 + 3) / -12) + 11x2 - x3 + 4x4 = 1

Multiplying through by -12 to eliminate the fractions:

2 * (35x2 - 5x3 + 10x4 + 3) + (-12 * (11x2 - x3 + 4x4)) = -12

Simplifying and combining like terms:

70x2 - 10x3 + 20x4 + 6 - (132x2 - 12x3 + 48x4) = -12

Simplifying further:

70x2 - 10x3 + 20x4 + 6 - 132x2 + 12x3 - 48x4 = -12

Combining like terms:

-62x2 + 2x3 - 28x4 - 6 = -12

Rearranging the equation:

-62x2 + 2x3 - 28x4 = -6

Now we have a new equation:

-62x2 + 2x3 - 28x4 = -6 (equation 7)

We have obtained three equations:

59x2 + 19x3 + 22x4 = -84 (equation 6)

-62x2 + 2x3 - 28x4 = -6 (equation 7)

x1 + 2x2 + 2x3 + x4 = 7 (equation 1)

To solve this system of equations, we can use various methods such as substitution, elimination, or matrix operations. By solving these equations, we can determine the values of x1, x2, x3, and x4.

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