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Natasha_Volkova [10]

2 years ago

14

Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a com

puter. The original cost of the computer is $750.00. The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price. After purchasing the computer, how much does Hakim have left in his bank account? Show your work.

1 answer:

sdas [7]2 years ago

6 0

I believe that he would have $111 left in his account.

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The product of 3 and an unknown number diminished by eight

Sindrei [870]

Answer:

3x-8

Step-by-step explanation:

7 0

3 years ago

Kameryn types 75 words per minute and is just starting to write a term paper. Joe already has 510 words written and types at a s

AnnZ [28]

Answer:

Kameryn will have more words typed than Joe when the number of minutes exceeds 34.

Step-by-step explanation:

Let

x -----> the number of minutes

y ----> the total words typed

we know that

<em>Kameryn</em>

$y=75x$ -----> equation A

<em>Joe</em>

$y=60x+510$ -----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for x

$75x=60x+510$

$75x-60x=510$

$15x=510$

$x=34\ minutes$

That means

For x=34 minutes

The amount of words written by Kameryn and Joe are the same.

therefore

For x > 34 minutes

Kameryn will have more words typed than Joe when the number of minutes exceeds 34.

6 0

3 years ago

Using the binomial theorem , obtain the expansion of :

andrezito [222]

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1 6 15 20 15 6 1

Decreasing powers of 1 from $1^{6}$ to $1^{0}$

Increasing powers of 3x from $(3x)^{0}$ to $(3x)^{6}$

$1+3x)^{6}$

= 1. $1^{6}$ $(3x)^{0}$ + 6. $1^{5}$ $(3x)^{1}$ + 15. $1^{4}$ $(3x)^{2}$ + 20. $1^{3}$ $(3x)^{3}$ + 15.1² $(3x)^{4}$ + 6. $1^{1}$ $(3x)^{5}$ + 1. $1^{0}$ $(3x)^{6}$

= 1 + 18x + 135x² + 540x³ + 1215 $x^{4}$ + 1458 $x^{5}$ + 729 $x^{6}$

--------------------------------------------------------------------------------------

$(1-3x)^{6}$

= 1. $1^{6}$ $(-3x)^{0}$ + 6. $1^{5}$ $(-3x)^{1}$ + 15. $1^{4}$ $(-3x)^{2}$ + 20. $1^{3}$ $(-3x)^{3}$ + 15.1² $(-3x)^{4}$ + 6. $1^{1}$ $(-3x)^{5}$ + 1. $1^{0}$ $(-3x)^{6}$

= 1 - 18x + 135x² - 540x³ + 1215 $x^{4}$ - 1458 $x^{5}$ + 729 $x^{6}$

----------------------------------------------------------------------------------

Collecting like terms from both expressions

$(1+3x)^{6}$ + $(1-3x)^{6}$

= 2 + 270x² + 2430 $x^{4}$ + 1458 $x^{6}$

----------------------------------------------------

(2)

Using Pascal's triangle with n = 5

1 5 10 10 5 1

Decreasing powers of 1 from $1^{5}$ to $1^{0}$

Increasing powers of 2x from $(2x)^{0}$ to $(2x)^{5}$

$(1+2x)^{5}$

= 1. $1^{5}$ $(2x)^{0}$ + 5. $1^{4}$ $(2x)^{1}$ + 10. $1^{3}$ $(2x)^{2}$ + 10. $1^{2}$ $(2x)^{3}$ + 5. $1^{1}$ $(2x)^{4}$ + 1. $1^{0}$ $(2x)^{5}$

= 1 + 10x + 40x² + 80x³ + 80 $x^{4}$ + 32 $x^{5}$

8 0

3 years ago

Which of the following could NOT be the lengths of the sides of a triangle?

Furkat [3]

Given:

Sides of triangles in the options.

To find:

Which could NOT be the lengths of the sides of a triangle.

Solution:

Condition for triangle:

Sum of two smaller sides of a triangle must be greater than the longest side.

In option A,

$5+5=10>5$

Sides 5 in, 5 in, 5 in are the lengths of the sides of a triangle.

In option B,

$10+15=25>20$

Sides 10 cm, 15 cm, 20 cm are the lengths of the sides of a triangle.

In option C,

$3+4=7>5$

Sides 3 in, 4 in, 5 in are the lengths of the sides of a triangle.

In option D,

$8+5=13$

Since, the sum of two smaller sides is less than the longest side, therefore the sides 8 ft, 15 ft, 5 ft are not the lengths of the sides of a triangle.

Therefore, the correct option is D.

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2 years ago

Which of the following scatterplots do not show a clear relationship and would not have a trend line?

docker41 [41]

Answer:

the second one

Step-by-step explanation:

it is not going in any general direction

5 0

2 years ago