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3 years ago

If the simple interest on $6,000 for 9 years is $3,240 , then what is the interest rate?

Mathematics

1 answer:

igor_vitrenko [27]3 years ago

8 0

Rate of interest is 6 %

Solution:

Given in question that,

simple interest = $ 3240

number of years = 9 years

principal sum = $ 6000

To find: interest rate

The simple interest is given as:

$S.I = \frac{pnr}{100}$

Where, "p" is the principal

"r" is the rate of interest

"n" is the number of years

Substituting the values in above formula,

$3240 = \frac{6000 \times 9 \times r}{100}\\\\3240 = 60 \times 9 \times r\\\\3240 = 540 \times r\\\\r = \frac{3240}{540}\\\\r = 6$

Thus rate of interest is 6 %

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B ^ 2 - 4b - 14 = 0

Blizzard [7]

Simplifying
b2 + -4b + -14 = 0

Reorder the terms:
-14 + -4b + b2 = 0

Solving
-14 + -4b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -4b + 14 + b2 = 0 + 14

Reorder the terms:
-14 + 14 + -4b + b2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -4b + b2 = 0 + 14
-4b + b2 = 0 + 14

Combine like terms: 0 + 14 = 14
-4b + b2 = 14

The b term is -4b. Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4b + 4 + b2 = 14 + 4

Reorder the terms:
4 + -4b + b2 = 14 + 4

Combine like terms: 14 + 4 = 18
4 + -4b + b2 = 18

Factor a perfect square on the left side:
(b + -2)(b + -2) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting
(b + -2) equal to 4.242640687 and -4.242640687. b + -2 = 4.242640687

Simplifying
b + -2 = 4.242640687

Reorder the terms:
-2 + b = 4.242640687

Solving
-2 + b = 4.242640687

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + b = 4.242640687 + 2

Combine like terms: -2 + 2 = 0
0 + b = 4.242640687 + 2
b = 4.242640687 + 2

Combine like terms: 4.242640687 + 2 = 6.242640687
b = 6.242640687
Simplifying
B = 6.242640687

Subproblem 2
b + -2 = -4.242640687

Simplifying
b + -2 = -4.242640687

Reorder the terms:
-2 + b = -4.242640687

Solving
-2 + b = -4.242640687

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + b = -4.242640687 + 2

Combine like terms: -2 + 2 = 0
0 + b = -4.242640687 + 2
b = -4.242640687 + 2

Combine like terms: -4.242640687 + 2 = -2.242640687
b = -2.242640687

Simplifying
b = -2.242640687

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3 years ago

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At a local high school football game, 150 randomly selected people were surveyed about the location of the concession stand. 108

Nesterboy [21]

Answer:

Option B

The best point estimate of the proportion of people attending the game who believe that the concession stand should be closer to the stands is:

p = 0.72.

Step-by-step explanation:

We want to estimate the proportion of people who feel that the stand should be closer to the stands.

We have a sample of 150 people, of which 108 think that the stand should be closer to the stands.

A point estimator for the proportion p is $p\¨$ .

Where

$p\¨ = \frac{x}{n}$

Where n represents the size of the sample and represents the number of favorable cases.

We know that $n = 150$ and $x = 108$ .

Then we can estimate p by the estimator $p\¨$

$p\¨= \frac{108}{150}$

$p\¨ = 0.72$

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rodikova [14]

Answer:

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15(r−s)

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Point M is located at (4,6) on a coordinate grid. Point M is translated 8 units to thr left and 9 units down to create point M'.

nata0808 [166]

Well, i would use the distance formula to find the distance between the two points. Only issue- you do not have the other point, so lets find it!

We have the point 4,6. 4 is the x, and 6 is the y.

Lets start with 4 since the x works with the left and right aspect of the location. It says M has been translated 8 units to the left, meaning we go back 8. So if we are at 4, and we go back (A.K.A. Subtract) 8, we will be at -4.

Now lets move onto the y, which works with the up and down aspect of the location. It says M has been translated 9 unites down, meaning the point will be heading down and getting smaller. So if we are at 6, and we go down (A.K.A. subtract) 9, then we will be at -3.

So now we have the coordinates of point M (4,6) and point M' (-4,-3) so we can now complete the distance formula!

The distance formula helps determine the distance between two points. It looks like this: D = √(x₂-x₁)²+(y₂-y₁)²

Though it does not matter which order you use the coordinates in, i am choosing to use M and then M'.

So, starting with the X, X₂ will be -4 and X₁ will be 4.
Again, starting with the Y, Y₂ will be -3 and Y₁ will be 6.

So, the formula plugged in will look like this: d = √(-4 - 4)² + (-3 - 6)²

Solving it out, we first need to work within the parenthesis. Can you solve it?

Our outcome will be this: -8² + -9². But, since we are squaring (And a negative times a negative equals a positive) you can just write 8² + 9²

8²= 64
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So, the distance between point M and point M' would be 145 units

Hope this helps!

If it does not, please let me know so i can try to help!

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Answer:

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Step-by-step explanation:

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