What are the solutions of this quadratic equation?
X^2 = 16x – 65

We know that the expression for the population is given by:

We want to know how long it takes to increase the population from 10500 to 13650. This means that we need to find the time it takes for the population to increase 3150; since this does not depends on the initial population but just in the exponential rate we have:

Therefore, it will take 537.01 years to increase the population.

Step-by-step explanation:

x intercept is when y = 0 and y intercept is when x = 0 hence, x intercept is : x = -56 hence (-56, 0) and y intercept is: 4y = -56 y = -14 hence (0, -14)

Topic: coordinate geometry

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Using  cylindrical coordinates ∫∫∫ (r^3cos^2θ) dz dr dθ, where r ranges from 0 to 2, θ ranges from 0 to 2π, and z ranges from 0 to √(36r^2).

To evaluate the integral ∫∫∫ x^2 dV over the solid e, using cylindrical coordinates, we need to express the integral in terms of cylindrical coordinates and determine the appropriate bounds for the variables.

In cylindrical coordinates, the solid e can be defined as follows:

Radius: r ranges from 0 to 2 (from x^2 + y^2 = 4, taking the square root).

Angle: θ ranges from 0 to 2π (full revolution around the z-axis).

Height: z ranges from 0 to the height of the cone, which is determined by z^2 = 36x^2 + 36y^2.

To convert the integral, we need to express x^2 in terms of cylindrical coordinates:

x^2 = (rcosθ)^2 = r^2cos^2θ

The integral in cylindrical coordinates becomes:

∫∫∫ (r^2cos^2θ) r dz dr dθ

Now we can determine the bounds for the variables:

r ranges from 0 to 2.

θ ranges from 0 to 2π.

z ranges from 0 to the height of the cone, which can be determined by setting z^2 = 36r^2.

Substituting the bounds and integrating, we can evaluate the integral to find the desired result.

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All the figures can be proven to be parallelograms by the markings.

The properties of parallelogram are:

Parallel opposite sides

Congruent opposite sides

Diagonals may or may not be congruent

Congruent opposite angles

Based on the above properties, all the figures can be proven to be parallelograms

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The area of Triangle B is 2 times greater than the area of Triangle A.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

Area of the triangle = 1/2 h*b

For Triangle A, the area is:

Area_A = 1/2 * b * h

For Triangle B, the area is:

Area_B = 1/2 * b * 2h = b * h

So, the area of Triangle B is twice the area of Triangle A.

Therefore, the area of Triangle B is 2 times greater than the area of Triangle A.

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Step-by-step explanation:

a. The thickness of a piece of paper increases each time it is folded. When the paper is folded in half, the thickness doubles because the two layers are now stacked on top of each other. If the paper is folded again, the thickness doubles again because there are now four layers. As the number of folds increases, the number of layers and the overall thickness of the paper increases exponentially. Therefore, the thickness in inches, t, is a function of the number of times the paper is folded, n.

b. We can represent the relationship between t and n using the function:

f(n) = 0.004 x 2^n

This function takes the number of folds, n, as input and outputs the corresponding thickness, t, in inches. Each time the paper is folded, the thickness is multiplied by 2, so we raise 2 to the power of n. The initial thickness of the paper is 0.004 inches, so we multiply this by 2^n to get the total thickness after n folds. Therefore, the function f(n) = 0.004 x 2^n represents the relationship between t and n.

The effect that it has on the graph is a shift right of 2 units, so the correct option is the second one counting from the top.

For any function f(x), we can define a horizontal shift of N units as:

y = f(x + N)

where:

In this case, we have.

y = f(x - 2)

so we have N = -2, then we have a shift of 2 units to the right. This means that the correct option will be the second one, counting from the top:

"The graph of y = f(x) will shift right 2 units."

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Answer:

452.39 sq.unit is the area of that circle.

To find the mean, variance, and standard deviation of a random variable X associated with a probability density function (PDF), we need to calculate the following:

Mean (μ):

The mean of a random variable X is given by the integral of x times the PDF over the entire interval. In this case, the PDF is f(x) = (2-2)(6-2) = 4, and the interval is not provided. Therefore, it is not possible to calculate the mean without knowing the interval.

Variance :

The variance of a random variable X is given by the integral of \((x - meu)^2\) times the PDF over the entire interval. Since we don't have the mean μ, we cannot calculate the variance.

Standard Deviation (σ):

The standard deviation of a random variable X is the square root of the variance. Since we cannot calculate the variance, we also cannot calculate the standard deviation.

In summary, without the interval or further information, it is not possible to calculate the mean, variance, or standard deviation of the random variable X associated with the given PDF.

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Answer:

not too sure about it

Step-by-step explanation:

x+5>=10

x>=10-5(collecting like terms)

x>=5☺️

Combining three popular technologies, blockchain: keys for cryptography. a network of peers that uses a shared ledger. a method of computation for storing exchanges and records.

Blockchain technology sets itself apart from conventional networks by offering transparency and integrity.

Integrity: When a user retrieves data from a network, he or she may be sure that the data is accurate and unaffected.

Transparency: Every user on the network may confirm any modifications made to the blockchain technology.

The read, write, create, and update operations to databases are provided by the traditional network, however the blockchain technology only enables users to attach the structure and already stored data cannot be changed.

When a new transaction is created, the blockchain makes sure to record it and perform transaction validation.

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Answer:

1530cm

Step-by-step explanation:

First figure      (9x10)x9=810

Second figure (18x10)x4=720

720+810=1530

Answer:

90 liters

Step-by-step explanation:

please mark me as brainlest

Answer:

44

Step-by-step explanation:

33:11 = 132:44

Answer:

Step-by-step explanation:

true

Answer:

False

Step-by-step explanation:

Answer:

-3x + 8

Step-by-step explanation:

The railroad track moves in a straight path from station A to station B and then from station B to station C.

Let the distance from station A to station C be AC and the distance from station B to station C as BC while the distance from station A to station B be AB the following equation holds:

AC = AB + BC

Given the distance from station A to station C is 3x + 4 and from station B to C is 6x-4, Hence:

AC = 3x + 4 and BC = 6x - 4.

Using the line segment addition postulate:

AC = AB + BC

3x + 4 = AB + (6x - 4)

AB = 3x + 4 - (6x - 4)

AB = 3x + 4 - 6x + 4

AB = 3x - 6x + 4 + 4

AB = -3x + 8

Step-by-step explanation:

Since the initial fee is fixed, we can assume it is a constant and the succeeding mile fee is the variable as it changes for every mile covered.

Let x = distance (mile)

let y = total charge (dollars)

Yellowcab company equation for cost calculation;  3.50 + 2.5x = y

laxicab company equation for cost calculation;  4.54+2.3x = z

the two companies charge the same amount when y = z

; 3.50 + 2.5x = 4.54+2.3x

x = 5.2 miles

COST CALCULATION

;3.50 + 2.5x = ?

if x = 5.2;

; 3.50 + 2.5(5.2) =$16.50

OR

; 4.54+2.3x = ?

; 4.54 + 2.3(5.2) = $16.50

Answer:

A

Step-by-step explanation:

(f*g)(x) = f(x) * g(x)

=(x2+1)(x4-1)=x6-x2+x4-1

Answer:

1288.................

Answer:

92

Step-by-step explanation:

first find the unit rate

8 ÷ 14 = 0.57142857142

0.57142857142/1

multiply that by the number of games (161)

0.57142857142 × 161 = 92

and you get 92 goals!

Answer:

2(t-4)+1

2t-8+1

2t-7

Akash estimate of 700cm of plastic trim is not sensible because he needs more than that.

The diagram of the question is below.

The window is made of a semi circle and a rectangular. More like a composite figure.

Composite figure are 2 dimensional figures that combines two or more two dimensional figures. Therefore, the part the plastic trim was applied are those sharp line region. It's like finding the perimeter of the whole shaded region.

He estimate he will need 700 cm of plastic trim in total. Therefore, let check if his estimate is sensible.

Therefore,

radius = 59 cm

perimeter of the rectangle = 2(113) + 2(118) = 462 cm

perimeter of the semi circle = 3.14 × 59 = 185.26 cm

Two radius = 2(59) = 118 cm

Therefore,

whole perimeter where plastic trim will be applied  = 462 + 185.26 + 118 =  765.26 cm.

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Based on my analysis of the current geopolitical landscape, the probability of the United States and China going to war this century is difficult to predict with certainty.

However, it is essential to understand that a military conflict between two of the world's superpowers would have catastrophic consequences not only for both countries but for the entire global community.

The probability of war between the US and China cannot be entirely ruled out due to several factors, including historical tensions, economic competition, territorial disputes, and geopolitical rivalry. Both countries have shown assertiveness in their foreign policies, and their interests often clash.

However, it is crucial to note that a military confrontation would have significant risks and costs for both countries, as well as the global economy and security. Therefore, it is in the best interest of both countries to avoid any escalation of tensions and to engage in constructive dialogue to address their differences. Diplomacy and cooperation are vital tools to prevent conflicts and build a stable and peaceful world order.

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The output of the Perceptron Learning Algorithm (PLA) with the given weights and bias for input vector (0,0) is -1. The output for input vectors (1,0) and (0,1) is 1, while the output for the input vector (1,1) is -1. The discriminant function for this PLA can be represented by the equation y = sign(w1 * x1 + w2 * x2 - w0), where w1 = 1, w2 = 1, and w0 = -1.5.

The PLA is a binary classification algorithm that determines the output based on a linear combination of the input features (x1, x2) with corresponding weights (w1, w2) and a bias term (w0). In this case, the weights are w1 = 1 and w2 = 1, and the bias is w0 = -1.5. The input vector (0,0) has an output of -1 since the discriminant function y is calculated as y = sign(1 * 0 + 1 * 0 - (-1.5)), which simplifies to y = sign(1.5) = -1.

For the input vectors (1,0) and (0,1), the output is 1. Plugging the values into the discriminant function, we have y = sign(1 * 1 + 1 * 0 - (-1.5)) = sign(2.5) = 1. Similarly, for the input vector (1,1), the output is -1: y = sign(1 * 1 + 1 * 1 - (-1.5)) = sign(1.5) = -1.

The discriminant function for this PLA can be represented by the equation y = sign(w1 * x1 + w2 * x2 - w0), where w1 = 1, w2 = 1, and w0 = -1.5. This equation defines the decision boundary, or discriminant, which separates the input space into two regions corresponding to the two possible outputs (-1 and 1) of the PLA.

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Answer:

y = (2/7)x -12

Step-by-step explanation:

y = mx + b is the standard form of an equation of a straight line in which m is the slope and b is the y-intercept (the value of y when x is zero)..

m=(2/7) and b = -12

y =   mx  + b

y = (2/7)x -12

The probability of getting exactly one head is 1/3.

To find the probability of getting exactly one head when tossing n coins after drawing a ball with number n from the box, we need to consider the possible values of n (0, 1, or 2) and calculate the probability for each case.

Case 1: n = 0

If the ball drawn has number 0, we toss 0 coins and the probability of getting exactly one head is 0 since there are no coins to toss.

Case 2: n = 1

If the ball drawn has number 1, we toss 1 coin and there is only one possible outcome to get exactly one head. The probability of this outcome is 1/2, as there are two equally likely outcomes (head or tail) for a single coin toss.

Case 3: n = 2

If the ball drawn has number 2, we toss 2 coins. There are two possible outcomes to get exactly one head: (head, tail) or (tail, head). Each outcome has a probability of 1/2 * 1/2 = 1/4. Since there are two such outcomes, the total probability is 2 * 1/4 = 1/2.

Therefore, to calculate the overall probability, we need to consider the probabilities for each case weighted by their respective probabilities. Since each case has an equal chance of occurring (1/3 for each case), the final probability is:

(1/3) * 0 + (1/3) * (1/2) + (1/3) * (1/2) = 1/6 + 1/6 = 1/3.

Hence, the probability of getting exactly one head is 1/3.

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Answer:

\(\sqrt{97}\) units

Step-by-step explanation:

Calculate the distance using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = A(- 5, 3) and (x₂, y₂ ) = B(4, - 1)

d= \(\sqrt{(4+5)^2+(-1-3)^2}\)

  = \(\sqrt{9^2+(-4)^2}\)

   = \(\sqrt{81+16}\)

    = \(\sqrt{97}\) ≈ 9.85 ( to 2 dec. places )

Answer:

B

Step-by-step explanation:

definitely b because 6 percent of 2000 is 120 and 120 x 2 is 240 so add that to the 2000 and theres your answer

Answer:

Option D

The Answer is $2,247

Step-by-step explanation:

Alan invested the money in a savings account which increases 6% annually.

2000 × 6 ÷ 100 = $120

Now,

2000 + 120 = $2120

2120 × 6 ÷ 100 = $127

Now,

2120 + 127 = $2247

Thus, Alan's investment worth after two years is $2247

-TheUnknownScientist 72