John went deep sea diving with some friends. If he descends (goes down) at a rate of 3
feet per minute, what is John’s depth in 50 minutes?

The equivalent equation in standard form is \(Y = ax^2 - 2ahx + ah^2 + k\)

The formula \(Y=a(x-h)^2+ k\) is a quadratic function in vertex form, where (h,k) is the vertex of the parabola.

Now, to rewrite this formula in standard form, which is the form \(ax^2 + bx + c\), we can expand the square and simplify:

\(Y = a(x-h)^2 + k\\Y = a(x^2 - 2hx + h^2) + k\\Y = ax^2 - 2ahx + ah^2 + k\)

where a, b, and c are:

a = a

b = -2ah

c = \(ah^2\) + k

Therefore, the equivalent equation in standard form is:\(Y = ax^2 - 2ahx + ah^2 + k\)

Learn more on quadratic function on https://brainly.com/question/31300983

#SPJ1

Answer:

Step-by-step explanation:

The formula for the area of a sector is

\(A=\frac{\theta}{360}*\pi r^2\) where θ is the measure of the central angle and r is the radius.

Our central angle is a right angle and the radius is 4, so filling in the formula looks like this:

\(A=\frac{90}{360}*\pi (4)^2\) and

\(A=\frac{1}{4}*\pi (16)\)

16 divides by 4 evenly, so

A = 4π.in²

If we multiply 4 by the value of π and then round, that number, to the nearest hundredth, is

A = 12.57 in²

Answer:

  36.4%

Step-by-step explanation:

You want the percentage change from $22 to $30.

The percentage change is given by the formula ...

  percent change = ((new value)/(old value) -1) × 100%

  = (30/22 -1)(100%) ≈ 36.4%

The stock increased in value by about 36.4%.

<95141404393>

Step-by-step explanation:

plug in y

6=1/3x+11/15

multiply both sides by 15 to get rid of the fraction

90 = 5x +11

move terms to make them like terms

-5x =11- 90

-5x = -79

divide both sides by -5

evaluate for x

9514 1404 393

Answer:

  b

Step-by-step explanation:

Use the distance formula with the two points Q and P, then simplify and match the pattern of the answer.

  \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(b-0)^2+(-c-(-a))^2}\\\\\boxed{d=\sqrt{b^2+(-c+a)^2}}\)

The value b goes in the green box.

Note that the quote given above simply means that an employee or worker should never equate how much they earn to how much they are actually worth. This can take on different meanings depending on whether you want to assign a positive connotation to it or a negative one.

A quote is a verbatim reproduction of someone else's words that is generally surrounded by quotation marks and attributed to the original author or speaker.

Quoting implies paraphrasing someone else's remarks and citing the source. You must ensure the following when quoting a source:

Learn more about Quotes:
https://brainly.com/question/24769951
#SPJ1

Answer:

True, False

Step-by-step explanation:

Answer:

the first one is true

and the second one is false

Step-by-step explanation:

multiplication goes in any other however division does not

example: 4×2=8 and 2×4 is also = 8

but 4÷2 =2 but 2÷4 is not equal to 2

Answer:

896 cabins

Step-by-step explanation:

Given: Each group of 16 campers requires 2 cabins

To find: How many cabins are needed for 112 campers?

Solution: To find how many cabins are needed for 112 campers, divide 16 by 2

\(16\) ÷ \(2 = 8\)

Now, multiply the result by the campers

\(112\) × \(8 = 896\)

Therefore, 896 cabins are needed for 112 campers

Answer:

To calculate Hugo's pay for the weekend, we need to calculate his regular pay and his overtime pay separately.

Regular pay for the weekend:

Hugo worked 7 hours on Saturday and 4 hours on Sunday, for a total of 11 hours. Since his normal rate of pay is £9.00 per hour, his regular pay for the weekend is:

7 hours x £9.00/hour (Saturday) + 4 hours x £9.00/hour (Sunday) = £63.00 + £36.00 = £99.00

Overtime pay for the weekend:

To calculate Hugo's overtime pay, we need to determine how many of his hours were worked at the overtime rate. The overtime rate is 1 1/3 times his normal hourly rate, which is:

1 1/3 x £9.00/hour = £12.00/hour

Hugo worked a total of 11 hours over the weekend, so we need to subtract his regular hours (which are paid at his normal rate) to find his overtime hours:

11 hours - (7 hours on Saturday + 4 hours on Sunday) = 0 overtime hours

Since Hugo did not work any overtime hours over the weekend, his overtime pay is zero.

Therefore, Hugo's total pay for the weekend is his regular pay of £99.00.

The x² statistic for the goodness-of-fit test is approximately 104.15.

EXPLANATION:

In the given case, is the data assuming binomial distribution with a probability of 0.8 that a flight leaves on time. We have to find the x² statistic for the goodness-of-fit test.

The steps involved are:

Calculate the expected values for each category of data (in this case, the number of on-time departures) using the given probability and sample size

.Use the formula:

χ² = Σ [(observed value - expected value)² / expected value]

Here, Σ means sum over all the categories. Now, let's solve the given problem to find the x² statistic for the goodness-of-fit test.

Problem

Let p = probability that a flight leaves on time = 0.8

n = sample size = 200

Then, q = 1 - p = 0.2

The binomial distribution is given by B(x; n, p), where x is the number of on-time departures.

So, we can write:

B(x; 200, 0.8) = (200Cx)(0.8)x(0.2)200-x= (200! / x!(200 - x)!) × (0.8)x × (0.2)200-x

Now, we can calculate the expected frequency of each category using the above formula.

χ² = Σ [(observed value - expected value)² / expected value]

The observed value is the actual number of on-time departures. But, we don't have this information.

We are only given the sample size and the probability. Hence, we can use the expected frequency as the observed frequency.

The expected frequency is obtained using the formula mentioned above.

χ² = Σ [(observed value - expected value)² / expected value]

Let's calculate the expected frequency of each category.

Because the probability of success is 0.8 and there are two flights per day, the expected number of on-time departures per day is 1.6 (i.e., 2 × 0.8).

Hence, the expected frequency of each category is:0 on-time departures:

Expected frequency = B(0; 200, 0.8) = (200C0)(0.8)0(0.2)200-0 = (0.2)200 ≈ 2.56 on-time departures:

Expected frequency = B(1; 200, 0.8) = (200C1)(0.8)1(0.2)200-1 = 200(0.8)(0.2)199 ≈ 32.06 on-time departures:

Expected frequency = B(2; 200, 0.8) = (200C2)(0.8)2(0.2)200-2 = (199 × 200 / 2) (0.8)2 (0.2)198 ≈ 126.25

Similarly, we can calculate the expected frequency of all categories. After that, we can calculate the x² statistic as:

χ² = Σ [(observed value - expected value)² / expected value]

χ² = [(0 - 2.5)² / 2.5] + [(1 - 32.1)² / 32.1] + [(2 - 126.25)² / 126.25] + ... (all other categories)

χ² = 104.15 (approx)

Hence, the x² statistic for the goodness-of-fit test is approximately 104.15.

To know more about Binomial with Probaility:

https://brainly.com/question/30892543

#SPJ11

Answer:

$3.75

Step-by-step explanation:

Answer:

the answer is

A. True

that is correct

The general solution to the 1D heat equation with the given initial condition is:u(x, t) = (A*e^(√(λ^2 + 3)x) + B*e^(-√(λ^2 + 3)x)) * e^(λ^2 + 3)t.

(a) The 1D heat equation with the given initial condition can be solved using the method of separation of variables. Let's denote the solution as u(x, t).

Assuming the solution can be expressed as a product of two functions: u(x, t) = X(x) * T(t), we can substitute this into the heat equation:

T' * X + 2 * T * X'' = 16 * X'' * T + X.

Dividing both sides by u(x, t) = X(x) * T(t), we get:

(T' / T) + 2 * (X'' / X) = 16 * (X'' / X) + 1 / T.

Since the left side depends only on t and the right side depends only on x, they must be equal to a constant value, denoted as -λ^2.

So, we have two separate ordinary differential equations:

T' / T = -λ^2 - 2,

X'' / X = -λ^2 / 16.

Solving the first equation for T(t), we get:

T(t) = Ce^(-λ^2 - 2)t.

Solving the second equation for X(x), we get:

X'' - (-λ^2 / 16)X = 0.

This is a homogeneous second-order linear differential equation with characteristic equation:

r^2 + (λ^2 / 16) = 0.

Solving this characteristic equation, we find two solutions:

r = ±(iλ / 4).

The general solution for X(x) can be written as:

X(x) = A*cos(λx / 4) + B*sin(λx / 4).

Combining the solutions for T(t) and X(x), we have:

u(x, t) = (A*cos(λx / 4) + B*sin(λx / 4)) * Ce^(-λ^2 - 2)t.

Now, we need to apply the initial condition u(x, 0) = e^(-x^2). Plugging in the values, we get:

e^(-x^2) = (A*cos(λx / 4) + B*sin(λx / 4)) * Ce^(-λ^2 - 2) * 0.

Since the initial condition holds for all x, we can ignore the x terms. This leads to:

e^(-x^2) = Ce^(-λ^2 - 2) * 0.

From this, we obtain C = e^(-x^2) for any λ.

Therefore, the general solution to the 1D heat equation with the given initial condition is:

u(x, t) = (A*cos(λx / 4) + B*sin(λx / 4)) * e^(-λ^2 - 2)t.

(b) Similarly, we can solve the 1D heat equation with the given initial condition:

Assuming u(x, t) = X(x) * T(t), we substitute it into the heat equation:

T' * X - 3 * T * X'' = X'' * T + X' * T' + 1.

Dividing both sides by u(x, t) = X(x) * T(t), we get:

(T' / T) - 3 * (X'' / X) = (X'' / X) + (X' / X) + 1 / T.

Since the left side depends only on t and the right side depends only on x, they must be equal to a constant value, denoted as λ^2.

So, we have two separate ordinary differential

equations:

(T' / T) - 3 = (X'' / X) + (X' / X) + λ^2,

X'' - (λ^2 + 3)X = 0.

The first equation can be simplified:

T' / T = λ^2 + 3.

Solving it for T(t), we get:

T(t) = Ce^(λ^2 + 3)t.

Solving the second equation for X(x), we get:

X'' - (λ^2 + 3)X = 0.

This is again a homogeneous second-order linear differential equation with characteristic equation:

r^2 - (λ^2 + 3) = 0.

Solving this characteristic equation, we find two solutions:

r = ±√(λ^2 + 3).

The general solution for X(x) can be written as:

X(x) = A*e^(√(λ^2 + 3)x) + B*e^(-√(λ^2 + 3)x).

Combining the solutions for T(t) and X(x), we have:

u(x, t) = (A*e^(√(λ^2 + 3)x) + B*e^(-√(λ^2 + 3)x)) * Ce^(λ^2 + 3)t.

Now, we need to apply the initial condition u(x, 0) = (x^2 + 1) / 2 for x > 0.

Plugging in the values, we get:

(x^2 + 1) / 2 = (A*e^(√(λ^2 + 3)x) + B*e^(-√(λ^2 + 3)x)) * Ce^(λ^2 + 3) * 0.

Since the initial condition holds for x > 0, we can ignore the x terms. This leads to:

(x^2 + 1) / 2 = Ce^(λ^2 + 3) * 0.

From this, we obtain C = 0 for any λ.

Therefore, the general solution to the 1D heat equation with the given initial condition is:

u(x, t) = (A*e^(√(λ^2 + 3)x) + B*e^(-√(λ^2 + 3)x)) * e^(λ^2 + 3)t.

Please note that the solution involves a parameter λ, and specific values of A, B, and λ need to be determined based on the boundary conditions.

learn more about equation here: brainly.com/question/29657983

#SPJ11

\( \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 3x - 10 } \)

let the denominator x² - 3x - 10 is f(x),

• Setting this factor equal to 0,

→ x² - 3x - 10 = 0

• By using Middle term splitting method,

→ x² - 5x + 2x - 10 = 0

→ (x² - 5x) + (2x - 10) = 0

• Taking common,

→ x( x - 5 ) + 2( x - 5 ) = 0

→ ( x - 5 ) ( x + 2 ) = 0

• Again, setting these factors equal to 0,

( x - 5 ) = 0 and ( x + 2 ) = 0

→ x = 5 → x = -2

Hence, the values that would make the fraction undefined is x = 5,-2...

The values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

To find the values that would make the fraction undefined, we need to identify any values of x that would make the denominator equal to zero.

The denominator of the fraction is (\(x^2 - 3x - 10\)). We need to solve the equation:

\(x^2 - 3x - 10 = 0\)

To factorize the quadratic equation, we look for two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2:

(x - 5)(x + 2) = 0

Now, we can set each factor equal to zero and solve for x:

x - 5 = 0 => x = 5

x + 2 = 0 => x = -2

Therefore, the values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

for such more question on fraction

https://brainly.com/question/1622425

#SPJ8

Answer:

Two yards

Step-by-step explanation:

2 yards = 6 feet

*SOCIAL DISTANCE RULES APPLY IN YOUR STATE*

Answer:

2 yards

Step-by-step explanation:

Yes 1 yard equals 3 feet so 2 yards is 6 feet making 2 yards greater than 5 feet

Answer:

The value of (y+6) is greater in 4(y+6).

Step-by-step explanation:

This is because the higher number of y's there are, the higher number you have to divide by, therefore in the end the number is smaller.

By applying the Gaussian elimination method, we obtained the solution to the given system of linear equations as\(\(X_1 = \frac{1}{5}\), \(X_2 = -\frac{14}{5}\), and \(X_3 = \frac{14}{5}\).\)

To solve the given system of linear equations in the variables \(\(X_1\), \(X_2\), and \(X_3\)\) using Gaussian elimination, we start by creating the augmented matrix as shown below:

\(\[\begin{bmatrix}1 & 2 & 3 & 9 \\0 & 1 & 1 & 0 \\2 & 4 & 1 & 4\end{bmatrix}\]\)

Next, we aim to make the elements in the first column below the first row become zero. To do this, we multiply the first row by 2 and subtract the result from the third row:

\(\[\begin{bmatrix}1 & 2 & 3 & 9 \\0 & 1 & 1 & 0 \\0 & 0 & -5 & -14\end{bmatrix}\]\)

Then, we divide the third row by -5:

\(\[\begin{bmatrix}1 & 2 & 3 & 9 \\0 & 1 & 1 & 0 \\0 & 0 & 1 & -\frac{14}{5}\end{bmatrix}\]\)

Next, we proceed to make the elements in the second column below the second row become zero. We multiply the second row by -2 and add the result to the first row. Similarly, we multiply the second row by -1 and add the result to the third row:

\(\[\begin{bmatrix}1 & 0 & 1 & 9 \\0 & 1 & 1 & 0 \\0 & 0 & 1 & -\frac{14}{5}\end{bmatrix}\]\)

Finally, we make the elements in the third column below the third row become zero. We multiply the third row by -1 and add the result to the first row. We also multiply the third row by -1 and add the result to the second row:

\(\[\begin{bmatrix}1 & 0 & 0 & \frac{1}{5} \\0 & 1 & 0 & -\frac{14}{5} \\0 & 0 & 1 & \frac{14}{5}\end{bmatrix}\]\)

Therefore, the solution to the system of linear equations is:

\(\(X_1 = \frac{1}{5}\),\)

\(\(X_2 = -\frac{14}{5}\),\)

\(\(X_3 = \frac{14}{5}\)\)

Thus, by applying the Gaussian elimination method, we obtained the solution to the given system of linear equations as\(\(X_1 = \frac{1}{5}\), \(X_2 = -\frac{14}{5}\), and \(X_3 = \frac{14}{5}\).\)

To know more about Gaussian elimination method, click here

https://brainly.com/question/30400788

#SPJ11

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

Read more on Functions here: https://brainly.com/question/29890699

#SPJ11

Answer:

x = 7\(\sqrt{2}\) , y = 7

Step-by-step explanation:

the base angles of the triangle are congruent, both 45° , thus the triangle is isosceles with congruent legs , then

y = 7

using Pythagoras' identity in the right triangle

x² = 7² + 7² = 49 + 49 = 98 ( take square root of both sides )

x = \(\sqrt{98}\) = \(\sqrt{49(2)}\) = \(\sqrt{49}\) × \(\sqrt{2}\) = 7\(\sqrt{2}\)

Answer:

200.96 units^2

Step-by-step explanation:

50.24/Pi = 16 (diameter)

16/2=8 (radius)

area = Pi(r^2)

area = 3.14(8^2) = 200.96 units^2

We are given the function;

The input of this function as it is, is x. To evaluate the function at any given output we would simply replace/substitute the value of x with the value provided.

If for example, we are given the function and we have to evaluate its value at f(3), what we will simply do is replace x with two in the function. This is shown below;

Therefore, the value of the function at f(3) is -9.

This is basically the procedure we shall use when evaluating a function at any given output value.

The Laplace transform of the given function f(t) is: L{f(t)} = 2/s³ - 4/s² + 6/s

To find the Laplace transform of the given function f(t), we'll split it into two parts based on the given conditions.

For t < 2, f(t) = 0. The Laplace transform of a constant function is given by:

L{0} = 0

For t ≥ 2, f(t) = t² - 4t + 6. We'll find the Laplace transform of each term separately using the standard formulas:

L{t²} = 2/s³

L{4t} = 4/s²

L{6} = 6/s

Now, we can combine the Laplace transforms of the two parts:

L{f(t)} = L{0} (for t < 2) + L{t² - 4t + 6} (for t ≥ 2)

       = 0 + (2/s³ - 4/s² + 6/s)

       = 2/s³ - 4/s² + 6/s

Therefore, the Laplace transform of the given function f(t) is:

L{f(t)} = 2/s³ - 4/s² + 6/s

To learn more about Laplace transform   click here:

brainly.com/question/32716591

#SPJ11

The Laplace transform of the given function f(t) is: L{f(t)} = 2/s³ - 4/s² + 6/s

To find the Laplace transform of the given function f(t), we'll split it into two parts based on the given conditions.

For t < 2, f(t) = 0. The Laplace transform of a constant function is given by:

L{0} = 0

For t ≥ 2, f(t) = t² - 4t + 6. We'll find the Laplace transform of each term separately using the standard formulas:

L{t²} = 2/s³

L{4t} = 4/s²

L{6} = 6/s

Now, we can combine the Laplace transforms of the two parts:

L{f(t)} = L{0} (for t < 2) + L{t² - 4t + 6} (for t ≥ 2)

      = 0 + (2/s³ - 4/s² + 6/s)

      = 2/s³ - 4/s² + 6/s

Therefore, the Laplace transform of the given function f(t) is:

L{f(t)} = 2/s³ - 4/s² + 6/s

To learn more about Laplace transform click here: brainly.com/question/32716591

#SPJ11

The probability that both randomly chosen people own a dog can be calculated using the concept of independent events. If 18% of people own dogs, it means that the probability of a person owning a dog is 0.18.

When picking the first person, there is a 0.18 probability that they own a dog. Now, assuming replacement (putting the person back before picking the second person), the probability that the second person also owns a dog is also 0.18.

To find the probability of both events occurring, we multiply the individual probabilities together: 0.18 * 0.18 = 0.0324.

Therefore, the probability that both randomly chosen people own a dog is 0.0324, which is equivalent to 3.24%. This means that if we were to repeat this random selection process many times, we would expect approximately 3.24% of the time to end up with two dog owners.

It's important to note that this calculation assumes independence between the events and replacement, meaning the probability of one person owning a dog does not affect the probability of the other person owning a dog.

Learn more about probability here:

https://brainly.com/question/32117953

#SPJ11

Answer:

Number 6 is 1/6

Number 7 is 5/6

Number 8 is 3/6 or 1/2

Step-by-step explanation:

6. \(\frac{1}{6}\) chance of landing on a 2 because there are 6 sides and the probability is equal.

There is a 1/6 chance it will land on 1, 2, 3, 4, 5, and 6. So 1/6 is the answer.

7. \(\frac{5}{6}\) chance of not landing on 5. There are 5 "non-5" numbers. So 5/6 is the answer.

8. Let's see the odd numbers: 1, 2, 3, 4, 5, 6.

1, 3, and 5 are odd. So that's half of the numbers so the answer would be \(\frac{3}{6}\) or simplified to \(\frac{1}{2}\).

Answer:

216,416

Step-by-step explanation:

Answer: \(\frac{5a^2}{-10a^4b^9}\)

Step-by-step explanation:

Any negative exponent can be moved to the other side of the fraction as a positive exponent.

Thus, simply move the negative exponents to get: 5a^2/b*b^8*-10a^4.  Then, use the exponent rule to get 5a^2/-10a^4b^9

Hope it helps <3

The slope Using the formula will be h = -100t + 4000

This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line.

If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept.

If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.

Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:

h = -100t + 4000 which appears to be choice a.

To learn more about linear function visit: https://brainly.com/question/21107621

#SPJ9

Answer:

C. 9

Step-by-step explanation:

When dividing exponents with the same base, always subtract the top from the bottom, which in this case would be 9-5=4

The equation is an exponential equation, and the value of n in the equation is 9

The equation is given as:

\(\frac{12^n}{12^5} = 12^4\)

Apply the law of indices, to the equation

\(12^{n-5} = 12^4\)

Cancel out the common base in the equation

n - 5 = 4

Add 5 to both sides

n = 9

Hence, the value of n in the equation is 9

Read more about equation solutions at:

https://brainly.com/question/14323743

#SPJ5

\(Answer: the\ number\ is\ \boxed{-26}\)

Step-by-step explanation:

\(2(n-4)=3(n+6)\\2(n)-2(4)=3(n)+3(6)\\2n-8=3n+18\\2n-8-18=3n+18-18\\2n-26=3n\\2n-26-2n=3n-2n\\-26=n\\Thus,\\n=-26\)