How much interest is gained if $250 is deposited in your bank account at the end of the year for each of the next 7 years? savings account pays 8% compounded annually?

use Pythagorean Theorem

2.5^2 + 6^2 = x^2

6.25 +36 = 42.25

x= sqrt(42.25) = 6.5 miles

Answer:

2:1

Step-by-step explanation:

The ratio is 2:1 and the new value can also be 8/4= 2/1

Answer:

1.2675 x 10^37

Step-by-step explanation:

you would have to first multiply 3.9 x 3.25 =12.675. It is not in scientific notation so you would have to change the decimal 1.2675 x 10^37

The ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]

The rate of energy is given as:

[tex]Rate = 3.9 * 10^{33}\[/tex] radiant energy per second

The time is given as:

[tex]Time = 3.25 * 10^3[/tex] seconds

The amount of radiant energy produced in this time is:

[tex]Energy = Rate * Time[/tex]

So, we have:

[tex]Energy = 3.9 * 10^{33} * 3.25 * 10^3[/tex]

Multiply

[tex]Energy = 12.675* 10^{36}[/tex]

Rewrite as:

[tex]Energy = 1.2675* 10^{37}[/tex]

Approximate

[tex]Energy = 1.3* 10^{37}[/tex]

Hence, the ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]

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Answer:

The answer is Savings account B

Savings account A offers a higher APY because it compounds quarterly, which is more frequent than savings account B which compounds semiannually. More compounding periods per year lead to interest being earned on interest more often, resulting in a higher effective yield.

Annual Percentage Yield (APY) given that both accounts offer the same Annual Percentage Rate (APR) of 7%, but one compound quarterly and the other semiannually. The APY is a measure of how much interest an account will earn in a year, taking into account the effect of compounding.

Compounding more frequently results in a higher yield because interest is earned on interest more often. Account A compounds quarterly, meaning it does so four times a year, while Account B compounds semiannually, meaning it does so twice a year. As the frequency of compounding increases, so does the APY, because the money earns interest on the interest that has been added to the account more frequently.

Therefore, the correct answer is A. Savings account A, because it has more compounding periods per year, which means it will have a higher APY compared to savings account B which compounds less frequently.

The solution is False

The slope of a vertical line is given by the equation Slope m = undefined

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the line be represented as A

Now , the line A is a vertical line

So , the equation of line will be represented as y = mx + c

where m is the slope of the line

And , Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of a vertical line is infinite or undefined as it has no y-intercept

Because , the change is x is 0

So , the denominator of the fraction is 0 and division by 0 is undefined

Slope m = ( y₂ - y₁ ) / 0

Hence , the slope m is undefined

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Answer:

Joint variation.

Step-by-step explanation:

There are four types of variation,

Direct variation : When a variable varies directly as another variable,

Example : y varies directly with x ⇒ y = kx,

Where, k is the constant of variation,

Inverse variation : When a variable varies inversely as another variable,

Example : y varies inversely with x ⇒ [tex]y=k\frac{1}{x}[/tex]

Joint variation : When a variable varies directly with two or more than two variables,

Example : y varies directly with both x and z ⇒ y = kxz

Combined variation : When a variable varies both directly and indirectly as another variables,

Example : y varies directly with x and inversely with z ⇒ [tex]y=k\frac{x}{z}[/tex]

Now, here the given expression,

y = 4mt,

Where, y, m and t are variables and 4 is the constant of variation,

⇒ y varies directly as both m and t,

⇒ y = 4mt is an example of joint variation.

A binomial distribution is an experiment where there are two outcomes; Success and failure. In here, you are given n = 128 and p = 0.27. The formula for the variance of a binomial distribution is n*p(1 – p) or n*p*q*. They are equivalent because q = 1- p. We will use the first equation.

Variance = n*p*(1 – p)

Variance = 128*0.27*(1 – 0.27)

Variance = 25.23

To get the standard deviation, find the square root of the variance.

Standard deviation = sqrt (Variance)

Standard deviation = sqrt (25.23)

Standard deviation = 5.02

The distance between two points can be found using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2).

The distance between two points can be found using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2). To find the distance between the two points represented by p1 and p2, we substitute the x and y coordinates of p1 and p2 into the formula:

distance = sqrt((p2.x - p1.x)^2 + (p2.y - p1.y)^2).

perimeter = add all 3 sides 13+13+10 = 36 cm

 for area you need to find the height of the triangle, which is the red dotted line

to do that use the Pythagorean Theorem

a^2 + B^2= c^2

a^2 = height

a^2 +5^2 = 13^2

a^2 +25 = 169

a^2 = 169-25 = 144

a=square root(144) = 12

 so the height is 12

area = 1/2 h x b = 1/2 x 12 x 10 = 1/2x 120 = 60

area = 60 cm^2

 cost is $4 per square cm

 there is 60 square cm in the triangle so multiply 60 x 4 = $240

270 =60 + 0.50(x-40)

270 =60 + 0.50x -20

210 =0.50x -20

230=0.50x

x=230/0.50 = 460 miles

check:

460-40 = 420

420*0.50=210 +60=270

 she can drive 460 miles total

Final answer:

The vector function r(t) representing the curve of intersection of the surfaces z = 7x² + y² and y = 3x² is r(t) = it + 3t²j + (7t² + 9t´)k.

Explanation:

Finding a Vector Function for a Curve of Intersection

To find the vector function r(t) that represents the curve of intersection of the surfaces z = 7x² + y² and y = 3x², we can parameterize the variables using a suitable parameter, commonly denoted as t. We can set x = t, which imminently provides y as y = 3t² by substituting t into the equation of the parabolic cylinder. Then, substituting both x and y into the equation of the paraboloid gives us z = 7t² + (3t²)² = 7t² + 9t´. Therefore, the vector function is:

r(t) = it + j3t² + k(7t² + 9t´).

This function r(t) represents all points (x, y, z) on the curve where the two surfaces intersect. Since the curve lies on both surfaces simultaneously, z must be equal for both equations when x and y from the curve are substituted into them.

The decrease in Carmen's account was $1961, which is 26.5% of her original investment of $7400. Hence, by subtracting this decrease from the original investment, we find that Carmen had $5439 left at the end of the year.

The decrease in Carmen's account over the year is 26.5% of the original investment of $7400. In mathematical terms, we can calculate this value by multiplying the original investment by the percentage decrease, using the formula: Decrease = Original Amount * Percentage Decrease.

In Carmen's case, this would be $7400 * 0.265 (converted from 26.5%). Upon calculating, we find that the decrease is $1961.

Now, to find how much money Carmen had at the end of the year, we subtract this decrease from the original amount invested. Again, using the formula: Final Amount = Original Amount - Decrease, we plug in the numbers to get $7400 - $1961, which equals $5439. This is how much Carmen had left in her account at the end of the year after the decrease.

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The Golden Ratio is a mathematical relationship that exists in art, shapes, nature and the human body. The golden ratio can be present in your body, from the length of your arms and legs when compared to your torso. Fingers is another example because the length of our fingers, each section from the tip of the base to the wrist is larger than the preceding.

The measurement of the human navel to the floor and to the top of the head to the navel is also the Golden ratio. Plastic surgeons and dental surgeons use it to reconstruct the human face. It also appears in everything around us like in the nature and science. It appears on in flower petals because it is believed that each petal is placed to so that each petal gets the best exposure to sunlight. Dolphins, starfish, sea urchins and honeybees also exhibit the proportion like humans. DNA molecules measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral, these two number are successive numbers. I think that the Golden Ratio is just a freak coincidence that happened.

We are given that:

a x^2 + b x + c = 0

Divide all terms with c/ a:

x^2 + (b / a) x + (c / a) = 0

Subtract c from both sides:

x^2 + (b / a) x + (c / a) – c / a = 0 – c / a

x^2 + (b / a) x = - c / a

Add a constant k to complete the square:

where k = ((b / a) / 2)^2 = (b /2a)^2

x^2 + (b / a) x  + k = - c / a + k

x^2 + (b / a) x + (b/2a)^2 = - c / a + (b /2a)^2

So the perfect square trinomial is:

(x + b/2a)^2 = - c / a + (b /2a)^2

Taking the square root of both sides:

x + b/2a = sqrt [- c / a + (b /2a)^2]

x = sqrt [(-c/a) + (b /2a)^2] – (b/2a)

Answer:

My equation is 3x^2 + 12x + 24 = 0. When I divide all of the terms by 3, the equation becomes x^2 + 4x + 8 = 0. When I subtract both sides by the constant, 8, the equation is x^2 + 4x = -8. When I add a constant to create the perfect square, the equation now becomes x^2 + 12x + 36 = 28. Finally, the equation simplified equals (x + 6)= the square root of 28.

Step-by-step explanation:

The equation in standard form is y = x^2 - 8x + 38

The vertex form of the equation is given as':

y = (x - 4)^2 + 22

Expand the equation

y = x^2 - 8x + 16 + 22

Evaluate the sum

y = x^2 - 8x + 38

Hence, the equation in standard form is y = x^2 - 8x + 38

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