Write a function with a slope of 4 that includes the point (−1, 3)

a) The earnings of Portfolio 1 are given as follows: $679.5.

b) The Portfolio with the greatest earnings is: Portfolio 1.

The earnings are found by the sum of the multiplication of the equivalent decimal of the return by the investment.

The equivalent decimals are given as follows:

Then the earnings of the Portfolio 1 are given as follows:

0.028 x 1425 - 0.0155 x 1380 + 0.117 x 3400 + 0.0849 x 3100 = $679.5.

The earnings of the Portfolio 2 are given as follows:

0.028 x 4500 - 0.0155 x 3600 + 0.117 x 2150 + 0.0849 x 1980 = $489.86.

Hence Portfolio 1 earned the most, as 679.5 > 489.86.

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its a shirt................

Answer:

a Shirt

Step-by-step explanation:

of course

Answer:

393.27 rounded to the nearest hundreth

Step-by-step explanation:

Answer:

Step-by-step explanation:

circumference of  a circle (c) = 2πr

where

c = 2471 in

find radius (r)

2471 = 2 π  r

r = 2471 / (2 π)

r = 393.27 in

The statements provided can be rewritten as follows: 1. If n is an odd integer, then there exist integers a and b such that n = a^2 - b^2. 2. n is an odd integer if and only if 3n + 5 is of the form 6k + 8 for some integer k. 3. n is an even integer if and only if 3n + 2 is of the form 6k + 2 for some integer k.

Let's analyze these statements:

1. If n is an odd integer, then there exist integers a and b such that n = a^2 - b^2.

  This statement is true and can be proven using the concept of the difference of squares. For any odd integer n, we can express it as the difference of two perfect squares: n = (a + b)(a - b), where a and b are integers. This shows that n can be written as the difference of two squares.

2. n is an odd integer if and only if 3n + 5 is of the form 6k + 8 for some integer k.

  This statement is not true. Consider the counterexample where n = 1. In this case, 3n + 5 = 8, which is not of the form 6k + 8 for any integer k.

3. n is an even integer if and only if 3n + 2 is of the form 6k + 2 for some integer k.

  This statement is true. For any even integer n, we can express it as n = 2k, where k is an integer. Substituting this into the given equation, we get 3n + 2 = 3(2k) + 2 = 6k + 2, which is of the form 6k + 2.

In conclusion, statement 1 is true, statement 2 is false, and statement 3 is true.

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Answer:

Part A: yes it is a function because every input value (x) produces only one output value (y).

Note: It is still a function if different x values produce the same y value, in this case, x=1 and x=-1 produce the same y value 1, but it is NOT a function if y=1 and y=-1 have the same x value x=1.  

Part B: when x=30: f(30)=17*30+50=560

if means that the cost of renting the truck for 30 hours is 560 dollars.

this help?

212345678901234567890

Answer:

120

Step-by-step explanation:

The number of ways the gold can be awarded is 6

The number of ways the silver can be awarded is 5

And the number of ways the bronze can be awarded is 4

6 * 5 * 4 = 120

The pressure above the water is 15 lb/in^2 and for every 10 ft, the pressure rises 4.54 lb/in^2

The equation would be:

If x = 0, the pressure in the surface is 15 lb/in^2, for each 10 ft of x, the pressure rises 4.54 lb/in^2

Now to solve when the pressure is 80 lb/in^2, we subtitute in the equation:

And solve for x:

Then the answer to question 2 is 1.43ft

This is basically a linear equation. The slope is the 4.54lb/in^2 for each 10ft. Then we need to adjust the 10ft of x, to reprensents each step of 10 ft for x. And we need to add the 15lb/in^2 for the surface pressure. With all this, we can construct the function of the pressure dependant of the deepness x.

Andrea arrived 5 minutes past 11:00 am, or at 11:05 am. Adding the 8 minutes indicated on her card, we get 11:13 am as the time Andrea arrived.

Let x be the number of minutes past 11:00 am that Andrea arrived. Then, Zach arrived (x + 15) minutes past 11:00 am. Two minutes ago (i.e., at 11:28 am), Andrea had been waiting for (28 - x) minutes, and Zach had been waiting for (13 + x) minutes. Three minutes from now (i.e., at 11:33 am), Andrea will have been waiting for (33 - x) minutes, and Zach will have been waiting for (18 + x) minutes. Since Andrea and Zach have waited for the same amount of time, we can set up the equation:

Solving for x, we get:

2x = 10

x = 5

Therefore, Andrea arrived 5 minutes past 11:00 am, or at 11:05 am. Adding the 8 minutes indicated on her card, we get 11:13 am as the time Andrea arrived.

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This can be expressed in this form:

1/2x - 18.

The exponential function \(f(x) = 2^x\) after a vertical stretch by a factor of 5 is defined as follows:

\(f(x) = 5(2)^x\)

The parent function for this problem is defined as follows:

\(f(x) = 2^x\)

Due to the vertical stretch by a factor of 5, the definition of the function is multiplied by 5, hence it is given as follows:

\(f(x) = 5(2)^x\)

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2 is the only prime number that is even. Therefore, this is the only counter example for the problem. 2 is a prime number because the only factors is 2 and itself (2n = 2*1 = 2).

Best of Luck!

Answer:

22

Step-by-step explanation:

the absolute value function always give a positive value , that is

| - a | = | a | = a

given

5 | 3x - 11 | + 2 ← substitute x = 5

= 5 | 3(5) - 11 | + 2

= 5 | 15 - 11 | + 2

= 5 | 4 | + 2

= 5 × 4 + 2

= 20 + 2

= 22

Since, the length of the three sides of a triangle are consecutive odd integers. The middle of the three side lengths is 2120 inches.

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

The perimeter of a triangle is defined as the total length of its boundary. A triangle is a polygon with 3 sides and it can be classified into different types based on the measure of its sides and angles

Now, according to the question:

If the middle of the three consecutive odd integers is n, then the smallest is n +1 , the largest is n+2 and we have:

The perimeter of the triangle is as follows;

Therefore, Perimeter = n + (n + 1) + (n + 2)

⇒ 6363 = 3n + 3

⇒ 6363 - 3 = 3n

⇒ 6360 = 3n

⇒ n = 2120 inches

Therefore, the value of middle of the three side of length is 2120 inches.

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The coordinates of R′ for the dilation centered at P with scale factor 0.5 are R' (-1, -0.5).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 0.5 centered at the point P (-3, -3) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate R, we have;

Coordinate R = (1, 2)  →  (0.5(1 - (-3)) + (-3), 0.5(2 - (-3)) + (-3))

Coordinate R = (1, 2)  →  (0.5(1 + 3) - 3, 0.5(2 + 3) - 3)

Coordinate R = (1, 2)  →  (0.5(4) - 3, 0.5(5) - 3)

Coordinate R' = (1, 2)  →  (-1, -0.5)

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115.

The point estimate for the average IQ score of the population of 3000 college students based on a simple random sample of 150 students with an average IQ score of 115 and a standard deviation of 10 is 115.

Therefore, the correct option is 115.

A point estimate is an estimate of a population parameter based on a single value or point. It is obtained by using statistics collected from a sample to infer population values. It can be a single value or a range of values that best represents the unknown population parameter.

Based on the given information, a simple random sample of 150 students is drawn from a population of 3000 college students.

Among sampled students, the average IQ score is 115 with a standard deviation of 10. The point estimate, in this case, is the average IQ score of the population, which is estimated to be 115 based on the sample data.

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Answer:

153.938 sq in.

Step-by-step explanation:

7 x 7 = 49

49 x pi = 153.938

pi = 3.14

Answer:

Step-by-step explanation:

By the Pythagorean Theorem

c^2=a^2+b^2 ( where c is the hypotenuse and a and b are the legs of a right triangle)

c^2=15^2+8^2

c^2=225+64

c^2=289

c=17 feet

Answer:

3.5 m

Step-by-step explanation:

PQ = 5/(5+5) × 7

= 5/10 × 7

= 3.5 m

Answer:

The number of terms in the sequence is 9

Step-by-step explanation:

We want to get the number of terms

Mathematically, we have the formula for the sum of terms in an arithmetic sequence as

\(sn = \frac{n}{2} (a + 1)\)

a represents the first terms, and i represent the last term

\(423 = \frac{n}{2} (15 + 79) \\ \\ 423 \times 2 = 94(n) \\ \\ 94n = 846 \\ \\ n = \frac{846}{94} \\ \\ n = 9\)

The present value of the annuity is $4,813.52.

To calculate the present value of the annuity, we can use the formula for the present value of an increasing annuity:

PV = C * (1 - (1 + r)^(-n)) / (r - g)

Where:

PV = Present Value

C = Payment amount at time t=1

r = Interest rate

n = Number of payments

g = Growth rate of payments

In this case:

C = $300

r = 8% or 0.08

n = Number of payments = Last payment amount - First payment amount / Growth rate + 1 = ($1000 - $300) / $50 + 1 = 14

g = Growth rate of payments = $50

Plugging in these values into the formula, we get:

PV = $300 * (1 - (1 + 0.08)^(-14)) / (0.08 - 0.05) = $4,813.52

Therefore, the present value of this annuity is $4,813.52. This means that if we were to invest $4,813.52 today at an interest rate of 8%, it would grow to match the future cash flows of the annuity.

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Answer:49

Step-by-step explanation:

A rational equation with a vertical asymptote at x=2 and a hole at x=-1 can be represented by the equation y = (x+1)/(\(x^{2}\)-3x-2).

To create a rational equation with a vertical asymptote at x=2 and a hole at x=-1, we need to construct a fraction that has a denominator that becomes zero at x=2 and x=-1. The vertical asymptote occurs when the denominator of the fraction equals zero but the numerator doesn't. A hole occurs when both the numerator and denominator become zero at a certain x-value, but they can be factored out.

In this case, we can start by factoring the denominator of the rational equation. The quadratic equation \(x^{2}\)-3x-2 can be factored as (x-2)(x+1). We want the denominator to equal zero at x=2, so we include the factor (x-2) in the denominator. However, we want to remove the common factor (x+1) from both the numerator and denominator to create the hole at x=-1. By canceling out the common factor, we get the final rational equation: y = (x+1)/(\(x^{2}\)-3x-2).

This equation satisfies the given conditions: x=2 is a vertical asymptote because the denominator becomes zero at x=2, and x=-1 is a hole because both the numerator and denominator become zero at x=-1 but can be canceled out.

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Answer:

The y-intercept of this line is (0, 4)

Step-by-step explanation:

Given that the slope of this line is -3, we know the general form of its equation is y = -3x + b.  Arbitrarily choosing the first point, (-2, 10), and substituting -2 for x and 10 for y, we find the y-intercept as follows:

10 = -3(-2) + b, or

10 = 6 + b, or

b = 4  (Answer C)

The y-intercept of this line is (0, 4)

Answer:

Step-by-step explanation:

4

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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The position of the mass when \(\(t = a\) is \(x(a) = \frac{1}{10}\sin(3a)\)\) and the amplitude of vibrations after a very long time is\(\(A_p = \sqrt{\left(\frac{9}{4}c_1^2 + \frac{9}{4}c_2^2 + \frac{1}{100}\right)}\)\).

The equation of motion for the system is given by:

\(\(4x'' + 36x = \cos(3t)\)\)

Dividing the equation by 4, we have:

\(\(x'' + 9x = \frac{1}{4}\cos(3t)\)\)

Let's substitute \(\(y = x\)\), then the equation becomes:

\(\(y'' + \frac{9}{4}y = \frac{1}{4}\cos(3t)\)\)

The complementary function (homogeneous solution) for \(\(y'' + \frac{9}{4}y = 0\)\) is:

\(\(y_C = c_1\cos\left(\frac{3}{2}t\right) + c_2\sin\left(\frac{3}{2}t\right)\)\)

To find the particular integral, let's assume:

\(\(y_p = A\cos(3t) + B\sin(3t)\)\)

Substituting this into the differential equation, we get:

\(\(A = 0\), \(B = \frac{1}{10}\)\)

Therefore, the particular integral is:

\(\(y_p = \frac{1}{10}\sin(3t)\)\)

The general solution of the differential equation is:

\(\(y = c_1\cos\left(\frac{3}{2}t\right) + c_2\sin\left(\frac{3}{2}t\right) + \frac{1}{10}\sin(3t)\)\)

Now, let's find the values of \(c_1\) and \(c_2\) using the initial conditions:
\(\(x_0 = y(0) = 0\)\)

\(\(v_0 = y'(0) = 0\)\)

The solution becomes:

\(\(y = \frac{1}{10}\sin(3t)\)\)

Hence, the position of the mass when \(\(t = a\)\) is:

\(\(x(a) = y(a) = \frac{1}{10}\sin(3a)\)\)

b) The amplitude of vibrations after a very long time is given by:

Amplitude = \(\(A_p\)\)

\(\(A_p = \sqrt{c_1^2 + c_2^2}\)\)

\(\(A_p = \sqrt{\left(\frac{9}{4}c_1^2 + \frac{9}{4}c_2^2 + \frac{1}{100}\right)}\)\)

Thus, the position of the mass when \(\(t = a\) is \(x(a) = \frac{1}{10}\sin(3a)\)\) and the amplitude of vibrations after a very long time is\(\(A_p = \sqrt{\left(\frac{9}{4}c_1^2 + \frac{9}{4}c_2^2 + \frac{1}{100}\right)}\)\).

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Answer:

Medical Insurance

Step-by-step explanation:

Answer:

Medical Insurance

Step-by-step explanation:

serious car accident and broke both wrists.

The total number of extra points earned is approximately 214 using Simpson's Rule.

Simpson's rule is a technique of numerical integration that approximates the value of a definite integral of a function by using quadratic functions. Here, you are supposed to create a spreadsheet to estimate the total number of extra points earned on the exam using Simpson's rule.Here is the table provided:

Number of hours of study, x1 2 3 4 5 6 7 8 9 10 11

Rate of extra points 4 8 14 11 12 16 22 20 22 24 26 earned on exam, f(x) OCIED

We first calculate h and represent it as follows:  

h = (b-a)/nwhere b = 11, a = 1, and n = 10.

 Therefore, h = (11-1)/10 = 1.

Substituting the values into the Simpson's Rule formula, we have:

∫ba{f(a) + 4f(a+h) + 2f(a+2h) + 4f(a+3h) + ... + 2f(b-h) + 4f(b-2h) + f(b)} / 3n

We have 10 intervals. Thus we have:

∫1111 {4 + 4(8) + 2(14) + 4(11) + 2(12) + 4(16) + 2(22) + 4(20) + 2(22) + 4(24) + 26} / 30≈ 214.0

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Answer:

c. x=1,000

Step-by-step explanation:

log x = 3

Imagine that it's log10 x = 3

So, x =  10^3 (10 to the third power)

x = 10 * 10 * 10

x = 1,000

Answer:

no solution

Step-by-step explanation:

Given

2(x - 3) = 2x + 5 ← distribute parenthesis on left side

2x - 6 = 2x + 5 ( add 6 to both sides )

2x = 2x + 11 ( subtract 2x from both sides )

0 = 11 ← not possible

This indicates the equation has no solution