Laura is a chemist working with liquids and solutions. She has two large cylindrical barrels that can hold up to 2,000 liters each. The first barrel contains 900 liters of solution, and the second barrel contains 100 liters of solution. Laura begins draining the first barrel at a rate of 36 liters per minute at the same time she begins filling the second barrel. Laura fills the second barrel with 44 liters of solution every minute. Which inequality represents the seconds, s, when the second barrel contains a greater or equal amount of solution than the first barrel?

Answer:

x=12

Step-by-step explanation:

tangent forms 90° with the touch point at circle

(x+8)^2 = 256+x^2

x^2 + 16x + 64 = 256 + x^2

16x = 192

x= 12

Answer:

D.2xn

Step-by-step explanation:

From the given information provided, the average stopping distance is 316 feet for car travelling at 65mph on dry level pavement.

The average stopping distance of a car traveling at 65 mph on dry, level pavement depends on various factors, such as the condition of the pavement, the condition of the tires, the weight of the car, and the efficiency of the braking system.

However, as a general estimate, the average stopping distance of a car traveling at 65 mph on dry, level pavement is about 316 feet. This includes both the reaction time of the driver and the braking distance of the car. It's important to note that this is an average estimate and actual stopping distance can vary depending on the conditions mentioned above. It's always best to drive at a safe speed and maintain a safe distance from other vehicles to avoid accidents.

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When performing a hypothesis test on the population mean (μ) when the population standard deviation (σ) is known, the null hypothesis (H0) can never be rejected if the sample mean falls within the acceptance range determined by the chosen significance level and the critical values.

In hypothesis testing for the population mean when the population standard deviation is known, the null hypothesis (H0) represents the claim or assumption that the population mean is equal to a specific value. The alternative hypothesis (Ha) states that the population mean is not equal to the specific value.

To determine whether to reject or fail to reject the null hypothesis, we compare the sample mean to the expected value under the null hypothesis. If the sample mean falls within the acceptance range determined by the chosen significance level and the critical values, we do not have sufficient evidence to reject the null hypothesis. The acceptance range is defined by the margin of error around the expected value, and it indicates the range of values that can be considered reasonably close to the expected value.

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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).

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Answer:

First quartile: the lowest 25% of numbers.

Step-by-step explanation:

you're welcome.

Answer:

a. 3.904×10^7

Step-by-step explanation:

I hope this helps.

The domain of the function is `R` and the y-intercept is `(0, -3)`

Given, `y = log4(2x + 1) - 3`.

To determine the domain of the function,

we should look for all values of `x` that would make the given function undefined.

There are no real values of `x` that would make the function undefined.

Therefore, the domain of the function is all real numbers or `R`.

To determine the y-intercept, substitute `x = 0` in the given function.`

y = log4(2(0) + 1) - 3 = log4(1) - 3 = 0 - 3 = -3`

Therefore, the y-intercept of the function is `(0, -3)`.

Hence, the domain of the function is `R` and the y-intercept is `(0, -3)`.

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Answer:

The required range is \(7<C<23\).

Step-by-step explanation:

Consider the provided information.

Let the side A = 15 and the side B = 8

Theorem 1: For a triangle with sides A, B, and C the sum of the lengths of any two sides of a triangle must be greater than the third side:

\(A+B>C\) ....(1)

\(B+C>A\)  ...(2)

\(A+C>B\)  ....(3)

By using equations 1 and 2.

Therefore, \(A-B<C<A+B\)

\(15-8<C<15+8\)

\(7<C<123\)

Hence, the required range is \(7<C<23\).

The method that is invoked when an object is created is known as a constructor method.

Constructor in C++ is a special method that is invoked automatically at the time of object creation. It is used to initialize the data members of new objects generally.

The constructor in C++ has the same name as the class or structure. Constructor is invoked at the time of object creation. It constructs the values i.e. provides data for the object which is why it is known as constructors.

Constructor does not have a return value, hence they do not have a return type.

The prototype of Constructors is as follows:

<class-name> (list-of-parameters);

Constructors can be defined inside or outside the class declaration:-

The syntax for defining the constructor within the class:

<class-name> (list-of-parameters) { // constructor definition }

The syntax for defining the constructor outside the class:

<class-name>: :<class-name> (list-of-parameters){ // constructor definition}

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The measure of the supplementary angles is:

∠X = 117°

∠Y = 63°

Here we know that angles ∠X and ∠Y are supplementary angles. Remember that two angles are supplementary if their measures add up to 180°.

Here we know that the measures are:

∠X = 3n − 18

∠Y = 2n − 27

We can write:

∠X + ∠Y = 180°

(3n - 18) + (2n - 27) = 180

Then we can solve that for n.

3n + 2n - 18 - 27 = 180

5n = 180 + 45

n = 225/5 = 45

Then the measures of tha angles are:

∠X = 3n − 18 = 3*45 - 18 = 117°

∠Y = 2n − 27 = 2*45 - 27 = 63°

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Answer:

a=4

Step-by-step explanation:

3a=12

a=12/3

a=4

b+3.3=8.9

b=8.9-3.3

b=5.6

1=14c

1/14=14c/14

1/14=c

512=d+14

512-14=d

498=d

2e=6.4

2e/2=6.4/2

e=3.2

The solution to the given equation is x = 3.To solve the equation, we will simplify and solve for x step by step.

Starting with the given equation: 2(x - 3) + x = 7(x + 1) We first distribute the 2 and the 7 on their respective terms: 2x - 6 + x = 7x + 7 Combining like terms: 3x - 6 = 7x + 7 Next, we move the variables to one side of the equation and the constants to the other side: 3x - 7x = 7 + 6

Simplifying further: -4x = 13 Finally, we solve for x by dividing both sides of the equation by -4: x = 13 / -4 This simplifies to: x = -13/4

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9514 1404 393

Answer:

  a.  0.81

  b.  v = 28000(0.81^n)

  c.  2757.36

Step-by-step explanation:

a. The growth factor is 1 more than the growth rate. Here, the growth rate is -19% (per year), so the growth factor, the multiplier, is ...

  1 -0.19 = 0.81

__

b. The equation sets value equal to the original value multiplied by the growth factor to the power of the number of years:

  value = (original value) × (growth factor)^n

  v = 28000(0.81^n)

__

c. For n=11, this is ...

  v = 28000(0.81^11) ≈ 2757.36

The value of the truck after 11 years is about $2757.

Answer:

The probability of event B given event A has occurred is 1/3.

Step-by-step explanation

Using the formula for conditional probability, we have:

P(B/A) = P(A∩B) / P(A)

P(A) = number of elements in sample space for event A / total number of elements in sample space

= 6/36

= 1/6

P(A∩B) = number of elements in sample space for event A∩B / total number of elements in sample space

= 2/36

= 1/18

Therefore,

P(B/A) = (1/18) / (1/6)

= 1/3

Hence, the probability of event B given event A has occurred is 1/3.

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The red sweaters at the store are made of pure wool = 50

What is Relation ship between store and sweater?

It is assumed that you reside in a region with harsh winters. We'll have to let our Vancouver pals use a little of their imagination.

The supply and demand for premium, warm winter sweaters is seen in the graph below.

When I first saw it in December, the sweater we desire costs 300. It's warm, lovely, and black, but costs more than  like to spend. I am hoping for a price reduction before it gets too cold in January because the weather has been mild.

When January finally arrives, the weather is unusually pleasant. When I go back to the store, the sweater is now 25% discounted. That's 225, hmm. It's still pricey, and the weather isn't all that chilly. I wait in the hopes of getting a better deal.

Concept:

Of the 800 sweaters in a certain store, 150 are red. We can also infer from the stem that 650 are not red

a) 320 of the sweaters at the store are neither red nor made of pool wool. We can infer that 330 are wool but not red

b) 100 of the red sweaters at the store are not made of pure wool.

From this, we can infer that 50 are both red and wool

see the attachment for the solution of the table a & b

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Answer:In order to write an equation for a line when we are only given 2 points it passes through, we first need to determine the slope of the line. The slope of the line is found by dividing the difference in the y-coordinates of the 2 points by the difference in the x-coordinates of the 2 points. (mathematically known as rise over run), (you may remember hearing this in class)

Step-by-step explanation:

y1-y2  / x1-x2 is the formula we will use to find the slope.

Pick one of the coordinates to be 1 and let the other be 2. We will let (3, 8) be 1 and (1, 0) be 2 because it has a 0 and subtracting 0 is easier.

Remember - whichever point contains y1, must also contain x1.

Our slope is found by substituting

(8 - 0) / (3 - 1) =

8 / 2 = 4. So the slope is 4.

Our equation for the line must be in the form of

y = mx + b (m is the slope and be is the y-intercept, where the line crosses the y-axis)

Again, choose a point and we will finish the equation. Let's use (1, 0). Always easier to use when there is a 0.

We will substitute our coordinates into the equation -

y - y1 = m(x - x1)

y - 0 = 4(x - 1)

y = 4x - 4 - your equation.

You can check your work by using the other point, (3, 8)

y = 4x - 4

8 = 4(3) - 4

8 = 12 - 4

Because this equation is true, your equation for the line is correct.

Hope this helps.

Answer:

$345

Step-by-step explanation:

Cp= $300

MP= 115%×$300

=$345

Answer:

Given that AB is the diameter of the circle, we have ∠ACB = 90°, and similarly ∠ADB = 90°.Since ABCD is a cyclic quadrilateral, we have ∠AEB + ∠CED = 180°.Also, since AC and BD are diagonals of the quadrilateral, they intersect at point E.Consider the tangent to the circle at point C. Since PC is also a tangent to the circle, we have ∠CAB = ∠PCB.

Answer: 6.20$

Step-by-step explanation:

Answer:

3 solutions

Step-by-step explanation:

x = 0; x = 2; x = -6

As we are given with an equation as follows :

\({:\implies \quad \sf x^{2}(x+2)(x+6)=0}\)

As product of these three factors is equal . So , any of these factor can be 0 as product is 0 only when one of the expressions which are multiplied is 0. So , 3 cases arises as follows ;

\({:\implies \quad \sf x^{2}=0}\)

On raising ½ power to both sides we have ;

\({:\implies \quad \sf x=\pm \: 0}\)

Now , as +0 and -0 have no difference in them . So , it's simply 0

\({:\implies \quad \sf So\quad x=0}\)

\({:\implies \quad \sf x+2=0}\)

\({:\implies \quad \sf So\quad x=-2}\)

\({:\implies \quad \sf x+6=0}\)

\({:\implies \quad \sf So\quad x=-6}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{Hence \:\: x\in \{0,\: -6,\: -2\}}}}\)

Answer:

whats the question

Step-by-step explanation:

Answer:

I don't see a question to answer

Step-by-step explanation:

Answer: 3(x+4)<-12 and x+4<4

Step-by-step explanation:

3|x+4| - 5 < 7

The two inequalities which is used to find the solution to this absolute value inequality 3 |x + 4| - 5 < 7 are;

⇒ x - 4 < 4

And, x - 4 > - 4

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 3 |x - 4| - 5 < 7

Now,

Since, The inequality is,

⇒ 3 |x - 4| - 5 < 7

Solve as;

⇒ 3 |x - 4| - 5 + 5 < 7 + 5

⇒ 3 |x - 4| < 12

⇒ |x - 4| < 4

This gives two solution as;

⇒ x - 4 < 4

And, x - 4 > - 4

Thus, The two solutions are;

⇒ x - 4 < 4

And, x - 4 > - 4

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Answer:

30 by 500

Step-by-step explanation:

is y

The value of function f(x) at point x = -2 is f(-2) = -13/4.

What is value of function?

The objective function's value at a solution is given by the value function of an optimization problem, which only depends on the problem's parameters.

Function value can mean: The result of applying a function to an argument in mathematics.

Consider, the given function

\(f(x) = \frac{x^2-5x-1}{x-2}\)

We have to find value of function f(x) at point x = -2.

Plug x = -2 in the above equation, we get

\(f(-2) = \frac{(-2)^2 - 5(-2)-1}{-2-2} \\f(-2) = \frac{4 + 10 - 1}{-4}\\f(-2) = \frac{13}{-4} \\f(-2) = -\frac{13}{4}\)

Hence, the value of function f(x) at point x = -2 is f(-2) = -13/4.

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Answer:

Never

Step-by-step explanation:

You are both running at the same speed in the same direction and start at the same time. You will always be 8 miles behind your friend and you will never catch up with him/her