A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $504. What was the simple interest rate of the bonds? Do NOT round off a decimal answer.

multiply 5.5 cm by 11.5 km

5.5 * 11.5 = 63.25

 rounded to nearest tenth = 63.3 km

For two trains with speeds given as 50 mph and 55 mph and a 30-minute head start for the first, the second train overtakes the first after 5 hours, based on their relative speed.

Here's how to solve a similar problem based on the given examples:

Let the first train's speed be 50 mph and the second train's speed be 55 mph.

The first train has a 30-minute head start, which at 50 mph means it has traveled 25 miles before the second train departs (since 50 miles/hour * 0.5 hours = 25 miles).

The second train travels 5 mph faster than the first, so the relative speed is 55 mph - 50 mph = 5 mph.

Now calculate the time it takes for the second train to catch up by dividing the head start distance by the relative speed: Time = Distance / Relative Speed, which is Time = 25 miles / 5 mph = 5 hours.

So, the second train will overtake the first train after 5 hours.

Answer: i did the test and i got B and i was right so its B

Step-by-step explanation:

The complete expression for the given equation is x^2 - 6x + 9= -13 +9

Given the quadratic expression x^2 - 6x = -13

In order to complete the square, we will follow the steps

Coefficient of x is -6

Half of the coefficient. = (-6/2) = -3

Square of the result = (-3)^2 = 9

Add 9 to both sides of the equation

x^2 - 6x + 9= -13 +9

Hence the complete expression for the given equation is x^2 - 6x + 9= -13 +9

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x-5>-2

x> -5+2

X>3

 Answer is: {x | x R, x > 3}

I believe that the correct word here is correlation. Correlation is the term that we use when we want to say that something is strong related to the other. Correlation must be however differentiated from causality. Correlation is when two things occur at the same time. Causality is when one results in the occurrence of the other.

Correlation coefficient has a maximum value of 1 which indicates strong relationship.

Answer:

Speed of current = 5 mph

Step-by-step explanation:

Let u be the speed of boat and v be the speed of current.

A boat makes a 120-mile trip downstream in 3 hours.

120 = 3(u+v)

u + v = 40

It makes the return trip in 4 hours.

120 = 4(u-v)

u - v= 30

Adding both equations

u + v + u - v = 40+30

2u = 70

u = 35 mph

35 + v = 40

v = 5 mph

Speed of current = 5 mph

he pays 29.59 a week

 multiply that by 52 weeks in a year

29.59 * 52 = 1538.68 a year

 Answer is A

Answer:

The graph has local maximum at (0,0) and minimum at  (-2,-4) and (2,-4).

Step-by-step explanation:

Consider the provided graph.

it is not always possible to find maximum or minimum for the whole function, but locally it is.

To find the local maximum and minimum we need to choose an interval first.

Local maximum: f(c) ≥ f(x) for all x in the interval

Local minimum: f(c) ≤ f(x) for all x in the interval

For better understanding refer the figure 1

Now consider the provided graph:

The graph of the function at (-2,-4) and (2,-4) shows the minimum value that is -4.

Because at x = -2 and 2 the value of function f(x)≥f(c) for every x in the domain.

Also the graph of the function has local maximum at (0,0) as at x = 0

The value of function f(x)≤f(c) for every x in the domain.

Hence, the graph has local maximum at (0,0) and minimum at  (-2,-4) and (2,-4).

Answer:

It's three. Look at 11 on the Y axis (computers) and count how many dots are at  11. There's a total of three computers based on the dots at 11.

Step-by-step explanation:

A scatter plot is a set of points plotted on horizontal and vertical axes.

It shows the relationship between two sets of data.

The number of offices that have 11 computers is 3.

A scatter plot is a set of points plotted on horizontal and vertical axes.

It shows the relationship between two sets of data.

We have,

Horizontal axes =  number of desks

Vertical axes = number of computers

Each dot in the scatter plot indicates offices.

Number of offices = 12 dots = 12

We need to find the number of dots that is with 11 computers.

We see that there are 3 dots with 11 computes so there are 3 offices that have 11 computers.

Thus the number of offices that have 11 computers is 3.

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Answer:

[tex]x^2+x-1-\frac{6}{x+4}[/tex]

Step-by-step explanation:

Rational expression form : [tex]\frac{a(x)}{b(x)}=q(x)+\frac{r(x)}{b(x)}[/tex]

a(x) = dividend

b(x) = divisor

q(x) = quotient

r(x) = remainder

Given expression : [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex]

We know that [tex]Dividend = Divisor \times Quotient+Remainder[/tex]

So, [tex]x^3+5x^2+3x-10 =x+4 \times (x^2+x-1)-6[/tex]

Thus a(x) = dividend =  [tex]x^3+5x^2+3x-10 [/tex]

b(x) = divisor= [tex]x+4[/tex]

q(x) = quotient=[tex]x^2+x-1[/tex]

r(x) = remainder=-6

Substitute the value in the rational form.

[tex]\frac{x^3+5x^2+3x-10}{x+4}=x^2+x-1-\frac{6}{x+4}[/tex]

Hence the rational expression [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex] in the form of [tex]q(x)+\frac{r(x)}{b(x)}[/tex] is  [tex]x^2+x-1-\frac{6}{x+4}[/tex]

I assume that we want to find the minimum distance between the point A(-1, 7) and the line y = 3x.

We will get that the distance is 3.22

So first, let's see how to get the distance between two points (x₁, y₁) and (x₂, y₂). We just use the general formula:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Now we want to find the distance between (-1, 7) and a point on the line y = 3*x, that can be written as (x, 3x)

That distance is:

[tex]d = \sqrt{(-1 - x)^2 + (7 - 3x)^2}[/tex]

Now we want to minimize this, which is equivalent to minimize d^2, then we can define:

D = d^2

and write:

[tex]D = (-1 - x)^2 + (7 - 3x)^2\\\\D = 1 - 2x + x^2 + 49 - 42x + 9x^2\\\\D = 10x^2 - 44x + 50[/tex]

Now we need to minimize this, which is a parabola, so the minimum will be at the vertex of the parabola (we know this because the leading coefficient is positive, thus the parabola opens upwards).

Remember that for a parabola like:

a*x^2 + b*x + c

The vertex is at:

x = -b/2a

Then for our parabola, the vertex will be at:

x = -(-44)/(2*10) = 44/20 = 2.2

Thus the minimum distance is given by:

[tex]d = \sqrt{(-1 - 2.2)^2 + (7 - 3*2.2)^2} = 3.22[/tex]

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The quotient of  4+2i/6-i is (11/4-4i)/*1/5.

Quotient is a result obtained by dividing one quantity by another.

explanation;

(4-2i)/(6-i)

Multiply and divide by the denominator = (6+i)

=>(4-2i)/(6-i)/(6+i)(6+i)

=> (4*6 + 4i - 12i - 2i^2)/[6^2 - (2i)^2]

=>  (24 - 8i -2)/ [36 + 4]                            [since i^2 = -1]

=> (22-8i) /40

=> 22/40 - 8i/40

=> 11/20 - i/5

Hence, the quotient of 4+2i/6-i is (11/4-4i)/*1/5.

A ratio is an ordered pair of numbers a and b, written a / b in which b does no longer identical zero. A proportion is an equation wherein ratios are set equal to each other. The share components is used to depict if two ratios or fractions are same. we can find the lacking fee by dividing the given values. the proportion formula can be given as a: b::c : d = a/b = c/d wherein a and d are the acute terms and b and c are the mean phrases.

The quantitative relation among two quantities showing the number of times one cost consists of or is contained inside the other. The indicated quotient of two mathematical expressions. b : the connection in quantity, quantity, or size among  or more matters.

A ratio can be defined as the connection or assessment among two numbers of the same unit to check how larger is one variety than the alternative one. as an instance, if the quantity of marks scored in a take a look at is 2 out of 5, then the ratio of marks received to the total range of marks is written as 2:5.

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The equation of the line that passes through the point (-1,5) and has a slope of 3 in point-slope form is y = 3x + 8.

The subject of this question relates to Mathematics, specifically algebra and line equations. The line equation in point-slope form is given by y - y1 = m(x - x1). In this equation, (x1, y1) represents the point that the line passes through and m represents the slope of the line. In our case, we know that the line passes through the point (-1,5) and has a slope of 3.

By substituting these values into the point-slope formula, we get the following:y - 5 = 3(x - (-1)), or, after simplifying, y - 5 = 3x + 3. So, the equation of the line that passes through (-1,5) and has a slope of 3 is y = 3x + 8.

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