Solve the following using the quadratic formula:


\(x^{2} - 9x - 45 = 0\)

The average water level in Boston Harbor over the 24-hour period is 7.2 feet.

To find the average water level in Boston Harbor over the 24-hour period, we need to calculate the average value of the function H(t) over the interval [0, 24]. The Mean Value Theorem for Integrals states that if f(x) is continuous on the interval [a, b], then there exists a number c in the interval (a, b) such that the average value of f(x) over [a, b] is equal to f(c).

In our case, the function H(t) = 4.8 sin[(π/6)(t - 10)] + 7.6 is continuous over the interval [0, 24]. To find the average value, we integrate H(t) over the interval [0, 24] and divide by the length of the interval.

Let's calculate the integral first:

∫[0,24] H(t) dt = ∫[0,24] (4.8 sin[(π/6)(t - 10)] + 7.6) dt

Using the antiderivative of the sine function and evaluating the integral over the interval [0, 24], we get:

= [-9.6 cos[(π/6)(t - 10)] + 7.6t] evaluated from 0 to 24

= (-9.6 cos[4π] + 7.6 * 24) - (-9.6 cos[0] + 7.6 * 0)

= (-9.6 + 182.4) - (-9.6)

= 172.8

The length of the interval [0, 24] is 24 - 0 = 24.

Therefore, the average water level over the 24-hour period is:

Average = (1/(24 - 0)) * ∫[0,24] H(t) dt

= (1/24) * 172.8

= 7.2

To determine the times of the day when the water level equals the average, we need to find the values of t that satisfy H(t) = 7.2. We can solve this equation:

4.8 sin[(π/6)(t - 10)] + 7.6 = 7.2

Simplifying the equation, we have:

4.8 sin[(π/6)(t - 10)] = 7.2 - 7.6

4.8 sin[(π/6)(t - 10)] = -0.4

Dividing by 4.8, we get:

sin[(π/6)(t - 10)] = -0.4/4.8

sin[(π/6)(t - 10)] = -1/12

To find the values of t, we can take the arcsine (inverse sine) of both sides:

(π/6)(t - 10) = arcsin(-1/12)

Solving for (t - 10), we have:

(t - 10) = (6/π) * arcsin(-1/12)

Finally, solving for t:

t = (6/π) * arcsin(-1/12) + 10

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Answer:

your answer would be 3/10.

Step-by-step explanation:

you divide both 9/30 by 3

Answer:

3/10

Step-by-step explanation:

The first step is to find the greatest common factor, in this case it's 3.

Then divide the 9 by 3, which is 3.

Next you divide 30 by 3 which is 10

When simplifying a fraction you don't flip the numerator and denominator, so you put the simplified values in their places and you get 3/10.

The discount of 20.25% on a Cadbury chocolate which cost $18.99 is $3.85

Discounted price is the reduction in actual price of an item and this often comes in percentage. When we subtract the discounted price from the original price, we will get the sale price of the item.

The discount percent in this item is 20 1/4% which is 20.25%. We can proceed to find the discount by solving 20.25% of 18.99

This becomes 0.2025 * 18.99 = 3.845 ≅ $3.85

The discounted price of the chocolate is $3.85

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To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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Answer:

231

Step-by-step explanation:

So the tiny 2 above the 15 means 15 is squared

15 squared = 225

225 + x(2)

If x = 3, then simply plug that into the equation

225 + 3(2)

225 + 6

231 is your answer

Answer:

231

Step-by-step explanation:

I put the equation as 15^2+2(3) I'm guessing the x was suppose to be after the 2 because it doesn't make sense putting x in front of the two....

separateAnswer:

A) x = 4/3

Step-by-step explanation:

Multiply each term by 7 so you get

-7x + 3 = 14x - 25

Take the x's and the integers to seperate sides

3 + 25 = 14x + 7x

28 = 21x

Divide the 21 to get the x alone

28/21 = x

Simplify; x = 4/3

The variable x in the equation \(-x+\frac{3}{7} =2x-\frac{25}{7}\) is 4 / 3.

Variables are numbers represented by letters in an equation. Therefore, let's find the variable x in the equation.

\(-x+\frac{3}{7} =2x-\frac{25}{7}\)

add x to both sides of the equation

-x + x + \(\frac{3}{7} = 2x+x-\frac{25}{7}\)

Therefore,

\(\frac{3}{7} =3x-\frac{25}{7}\)

add 25 / 7 to both sides of the equation

\(\frac{3}{7} +\frac{25}{7}=3x\)

\(\frac{3 + 25}{7} = 3x\)

\(\frac{28}{7}=3x\)

cross multiply

28 = 7 × 3x

21x = 28

x = 28 / 21

x = 4 / 3

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Mr. Red's salary is an illustration of an arithmetic sequence

The explicit rule of Mr. Red's salary is an = 500n + 29500

Mr. Red's salary is an arithmetic sequence with the following parameters:

First term, a1 = 30000

Common difference, d = 500

The explicit rule is calculated as:

an = a1 + (n - 1) * d

This gives

an = 30000 + (n - 1) * 500

Evaluate the product

an = 30000 - 500 + 500n

This gives

an = 29500 + 500n

Rewrite as:

an = 500n + 29500

Hence, the explicit rule of Mr. Red's salary is an = 500n + 29500

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A is an n x n diagonal matrix with rank r , where rsn  and the statement (a)"O is an eigenvalue with algebraic muitiplicity n-r "  about A is true

Since A is an n x n diagonal matrix with rank r, the number of non-zero entries on the diagonal is r. This means that there are n - r zero entries on the diagonal.

For any diagonal matrix, the eigenvalues are simply the entries on the diagonal. Since there are n - r zero entries, the eigenvalue O has a geometric multiplicity of n - r.

Therefore, the correct statement is that O is an eigenvalue with geometric multiplicity n - r.

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The value of X from the similar triangles above would be = 4. That is option B.

To determine the value of X from the missing part of the similar triangles, the formula that should be used is given below as follows:

VR/VU = VQ/VT

Where;

VR = 33

VU = 44

VQ = 8x-2

VT = 40

That is;

33/44 = 8x-2/40

33×40 = 44(8x-2);

1320 = 352x-88

1320+88 = 352x

1408 = 352x

X = 1408/352

= 4.

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To find out the sales tax rate we must do a division between the sales tax and the cost before tax, then:

But we want to find it in percentage, then we must multiply it by 100 at the end!

Now we have the formula, we can just apply it and do the calculus!

Hence, the sales tax rate is 7%

The proportion of defective circulators can be calculated by weighting the defect rates of each company by their respective proportions in the contractor's inventory. Thus, the proportion of defective circulators can be expected to be 0.0065 (0.60*0.005 + 0.40*0.010).Plugging in these values, we get P(B|A) = (0.005*0.60)/0.0065 = 0.046, or approximately 4.6%.

To calculate the probability that a defective circulator came from the first company, we can use Bayes' theorem.

Let A denote the event that a circulator is defective, and let B denote the event that the circulator came from the first company.

We want to find P(B|A), the probability that the circulator came from the first company given that it is defective.

This can be calculated using the formula P(B|A) = P(A|B)*P(B)/P(A), where P(A|B) is the probability of a defective circulator given that it came from the first company (0.005),

P(B) is the probability that a circulator came from the first company (0.60), and P(A) is the overall probability of a defective circulator (0.0065).

Plugging in these values, we get P(B|A) = (0.005*0.60)/0.0065 = 0.046, or approximately 4.6%.

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If a function f has an inverse and f(-3) = 6, then we can conclude that

\(f^-1(6) = -3\)

which means that if we plug in 6 as the input value to the inverse function

\(f^-1\)

we get -3 as the output value.

If a function f has an inverse, it means that for every output value of f, there exists a unique input value that produces that output value. The inverse function of f, denoted as

\(f^-1\)

takes an output value of f and returns the input value that produced it.

Given that f(-3) = 6, we know that the input value -3 produced an output value of 6. We can say that

\(f^-1(6) = -3\)

This means that if we plug in 6 as the input value to the inverse function

\(f^-1\)

we get -3 as the output value.

To see why this is true, we can think of it in terms of reversing the process of the original function f. If we start with an input value of -3, the function f produces an output value of 6. If we then take this output value of 6 and plug it into the inverse function

\(f^-1\)

we should get back our original input value of -3.

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Answer:

x = ±3 sqrt(2)

Step-by-step explanation:

x^2 = 18

Take the square root of each side

sqrt(x^2) = sqrt(18)

x = ± sqrt(18)

x =±sqrt(9*2)

x = ±sqrt(9) sqrt(2)

x = ±3 sqrt(2)

Answer:

just kill the heavy scientists with f1s(rust mentality(

Step-by-step explanation:

Answer:

A) 315/1005

Explanation:

Total choices: 120 + 255 + 35 + 60 + 200 + 110 + 75 + 150 = 1005

Favorable choices: 255 + 60 = 315

probability:

favorable choices/total choices

315/1005

21/67

Answer:

Pr(Cb) & Pr(cost $15) = 15(Ncb)/(T1×T3)

Step-by-step explanation:

Classification of the book in to 3

First let's assign terms to each probability

Let:

T1= total number of type of Reader's group

T2 = total number of Type of book

T3 = total number of type of Cost

Probability of child's book and cost $15= Pr(Cb) & Pr(cost $15)

Then find probability of child's book and cost separately:

Pr of child's book = Pr(Cb)

Pr(Cb) = (number of child's book)/ total number of type of group

Ncb = number of child's book

Pr(Cb) = Ncb/T1

Pr (cost $15) = $15 book/total number of cost

Pr (cost $15) = 15/T3

probability of child's book and cost $15 = Pr(Cb) × Pr (cost $15)

= Ncb/T1 × 15/T3

Pr(Cb) & Pr(cost $15) = 15(Ncb)/(T1×T3)

On factorizing the polynomial 3m²-9 we get 3(m²-3).

The factor of polynomial is defined as the process of expressing the polynomial as a product of two or more polynomials.

For Example : the factors of x²-16 are (x+4)(x-4).

In the given question we need to factor

3m²-9

here 9 can be written as 3*3

rewriting the above equation we get

3m²-3*3

As both the terms contain 3 we can take 3 common from both the terms ;

taking 3 common from each term we get ,

=3(m²-3)

Therefore , On factorizing 3m²-9 we get 3(m²-3) .

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The translation from preimage P(9. 1.5) to image P'(12, 1)) in ordered pair is (3, -0.5)

Translation refers to a type of transformation that involve a straight line movement.

The type of movements related to translation includes

The up and down movements are on the vertical direction controlled by the y coordinate. In the question, the preimage moved form 1.5 to 1

hence we say

The left right movement is controlled by the x coordinate. The preimage moved from 9 to 12 ⇒ 9 + 3. Hence we say that

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The given expression is:
5m^2 + 9n^3 - mn^2 + 2m^3

This expression is a polynomial. The correct answer is option c.

It consists of four terms:

5m^2: This term is a monomial with a coefficient of 5 and a single variable, m, raised to the power of 2.

9n^3: This term is a monomial with a coefficient of 9 and a single variable, n, raised to the power of 3.

-mn^2: This term is a monomial with a coefficient of -1 and two variables, m raised to the power of 1 and n raised to the power of 2.

2m^3: This term is a monomial with a coefficient of 2 and a single variable, m, raised to the power of 3.

Therefore, The expression 5m^2 + 9n^3 - mn^2 + 2m^3 is a ploynomial. which is option c

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The probable question may be:

What is 5m^2+9n^3-mn^2+2m^3

choose the correct answer

a) monomial

b) binomial

c) polynomial

Answer: 25°

Step-by-step explanation:

So we know that the right angle equals 90°.

And we know that all the angles of a triangle have to add up to 180°.

Also angle x and the exterior angle that is 115° are supplementary, so they have to add up to 180°. So we have to subtract 180 - 115 = 65.

So our equation for y is:

y + 65 + 90 = 180

y + 155 = 180

y = 25

So y = 25°

Hope this helps!!! :)

Answer:

B ) 2 g + 12

Step-by-step explanation:

The probability of winning the game is 0.5.

The problem requires us to find the probability of winning the game, which is 0.411. To approach this problem, we can use the formula for conditional probability which says that the probability of A given B is equal to the probability of A and B divided by the probability of B. This method allows us to define certain events like A, B, and C to find the probabilities of each event.

Event A represents both cards being of the same suit, and its probability is P(A) = 1/4 because there are four suits, and we need two cards of the same suit. Event B represents neither of the first two cards being the same suit, and its probability is P(B) = 3/4 * 2/3 = 1/2 since the first card can be any suit, but the second card must be a different suit. Event C represents the third card matching the suit of one of the first two cards. If both cards are of the same suit, any third card will match. Therefore, the probability of C given A is P(C|A) = 1. If the first two cards are not the same suit, there will be two suits left that can match one of the first two cards, making the probability of C given B as P(C|B) = 1/2.

Now, we can calculate the probability of winning by adding the probabilities of events A and B multiplied by the probability of event C given B. So, P(A) + P(B)P(C|B) = 1/4 + (1/2)(1/2) = 1/4 + 1/4 = 1/2. Therefore, the probability of winning the game is 0.5.

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Answer:

9

Step-by-step explanation:

6      x

-   =   -

8      12

the relationship from 8 to 12 is divided by.666666666666

So, we do the same for 6

We get 9.

Answer:

answers B and E are true.

Step-by-step explanation:

(5,0) means x=5, y=0

the point of origin is (0,0) with x=0, y=0

therefore, A is wrong. yes, the point is 5 units to the right of the origin, but 0 (no) units up. and not 1.

B is therefore true.

C is therefore wrong.

D is wrong, because the point is to the right of y-axis (the vertical axis) and not on it.

E is true, because we go only to the right of the origin, but neither up or down. so, we stay on the x- axis (horizontal axis).

Answer:

-3 + 9i

Step-by-step explanation:

The conjugate of -3i is - 3 - i.

(- 3 i) × (- 3 - i)

Multiply both terms.

-3 + 9i

The multiplication of the complex number -3i and it’s conjugate 3i is 9.

A complex number is characterized by an ordered pair of numbers, the real and imaginary parts. It can be represented in multiple ways such as Standard form(rectangular form), Polar form, Exponential form.

For the given situation,

The complex number is -3i.

The conjugate of a complex number a+bi is a-bi.

So, the conjugate of a complex number \(-3i\) is \(3i\)

Now multiply -3i and 3i, we get

⇒ \((-3i)(3i)\)

⇒ \(-9(i^{2} )\)

⇒ \(-9(-1)\)               [∵ \(i^{2}=-1\)]

⇒ \(9\)

Hence we can conclude that the multiplication of the complex number -3i and it’s conjugate 3i is 9.

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Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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Confidence intervals and hypothesis testing share the characteristic that they are both inferential techniques

Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution.

What is confidence interval?

Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. It is possible that occasionally, when the hypothesis produces a non-significant result, the confidence interval will exclude the value specified under the null hypothesis because the standard error used to calculate the confidence interval is different from the standard error used in hypothesis testing.

We use the standard error of the mean to show the degree of uncertainty surrounding the estimation of the mean measurement. Most helpful for calculating a confidence interval is the standard error.

Hence , Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution.

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Answer:

55%

Step-by-step explanation:

We can infer a few things here and come to a logical conclusion.

$9 is not exactly half of 20 right?

So this tells us that our answer needs to be over 50% because a 50% discount would make the bookbag $10.

If we look at the answers only 1 of them is over 50% and that is 55%.

However, let's check our work

First we multiply 20 by .55 (when multiplying a percent we move the decimal over twice)

\((20) *(.55) = 11\)

We got 11 out of this, the next thing we do is subtract that 11 from the overall 20:

\(20-11= 9\)

Therefore we see that 55% is the answer!

Hope this helps!!

- Kay

Step-by-step explanation:

we see that 55% is the answer

Answer: the answer is 0=0

Step-by-step explanation: