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The polynomial that gives the interest earned after a year will have variables, exponents and constants that are joined by operators.

Reasons:

The amount Paul has to invest = $900

The annual interest rate from the savings account = 1.8%

The amount the money market account pays per year = 4.2 %

Required: The polynomial for the interest Paul earned by investing x dollars in the savings account.

Solution:

The interest earned is found using the compound interest formula as follows;

[tex]\displaystyle A = \mathbf{P \cdot \left(1 + \frac{r}{n} \right)^{n \cdot t}}[/tex]

Where;

A = The amount in the account after one year

P = The original amount invested = x

r = The interest rate offered on the investment = 1.8% = 0.018

t = The time of the investment = 1 year

n = The number of times of application of the interest per period = Once per year

Which gives;

Interest = Amount earned = A - P

Therefore;

[tex]\displaystyle Interest, \ I = \mathbf{P \cdot \left(1 + \frac{r}{n} \right)^{n \cdot t} - P}[/tex]

Plugging in the values gives;

[tex]\displaystyle I = x \cdot \left(1 + \frac{0.018}{1} \right)^{1 \times 1} - x = x \cdot 1.018^1 - x = 1.018 \cdot x - x = 0.018 \cdot x[/tex]

The polynomial equation is therefore;

Interest, I = 0.018·x

Using the simple interest formula, we have;

[tex]\displaystyle Interest = \mathbf{\frac{P \times r \times t}{100}}[/tex]

Which gives;

[tex]\displaystyle Interest = \frac{x \times 1.8 \times 1}{100} = 0.018 \cdot x[/tex]

Interest earned by investing in the savings account for one year, I = 0.018·x

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Answer:

The discount is $77, and the discount percent is 5%

Step-by-step explanation:

Discount: $1,540 - $1,463 = $77

Discount percent: $1,463 / $1,540 = 0.95, 1.00 - 0.95 = 0.05, 0.05 = 5%

Step-by-step explanation:

option A is correct answer

Answer:

Should be C if not then A

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

There are 5 ways you could choose the group in tennis.

It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

The total no of students is 16,

As there can be only a maximum of 10 students in a group,

If the student in Swimming is 10 then in Tennis it will be 6,

If the student in Swimming is 9 then in Tennis it will be 7,

If the student in Swimming is 8 then in Tennis it will be 8,

If the student in Swimming is 7 then in Tennis it  will be 9,

If the student in Swimming is 6 then in Tennis it will be 10,

Therefore, there are 5 ways you could choose the group in tennis.

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Answer:

Gross Pay for 1 paycheck

Deductions for federal tax, state tax, and city tax hope it helps :)

Step-by-step explanation:

The net monthly income of Jason is $194.68 and the net annual salary is 23324.16.

Gross pay of an employee is basically sum of his basic pay, dearness allowance, any other allowance only. Public providend fund, income tax are not deducted from it.

1) Gross paycheck=2*40*25.5=$2040.

2) Federal tax=2040*21%=$428.4

3) State tax=25=$25

4) City tax=2040*12%=$244.8.

5) Deductions=2040*12.45=$252.96.

6) Net monthly income=2*(Gross pay-federal tax-state tax-city tax-deductions-deductions for F.IC.A. or social security tax)

=2*[2040-428.4-25-244.8-252.96-117]

=1943.68

7) Net annual salary=12* net monthly income.

=1943.68*12  ( 1year= 12 months)

=$23324.16

Hence the net monthly income of Jason is $194.68 and the net annual salary is 23324.16.

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Answer:

3/20

Step-by-step explanation:

3/20 I sure, Just trying this one

Using proportions, it is found that the height of the lighthouse is of 84 ft.

The rule of three is:

5.25 feet - 8 feet

x feet - 128 feet

Applying cross multiplication:

[tex]8x = 5.25(128)[/tex]

[tex]x = \frac{5.25(128)}{8}[/tex]

[tex]x = 84[/tex]

The height of the lighthouse is of 84 ft.

A similar problem, which also uses proportions, is given at https://brainly.com/question/24372153

Btw also found a spelling mistake in the question:instead of newtons you put netwons-      lol-

btw  

Rounded to the nearest thousandth would be 4.444 Newtons (same units you solved for k with)

But anyway here you go:

4a - 5b = 7

substract 4a from both sides

4a - 5b - 4a = 7 - 4a

positive 4a with negative 4a

5b = 7 - 4a

devide both sides by 5

[tex] \frac{5b}{5} = \frac{7 - 4a}{5} [/tex]

[tex]b = \frac{7 - 4a}{5} [/tex]

Answer:

3/4 or 0.75

Step-by-step explanation:

[tex] \frac{3 }{8} + \frac{3}{8} [/tex]

transform the equation

[tex] \frac{3 + 3}{8} [/tex]

calculate

[tex] \frac{6}{8} [/tex]

simplify

[tex] \frac{3}{4} [/tex]

or 0.75

Answer:

x=(m)(7)(6) or x=m*7*6

Step-by-step explanation:

The number is 3947

It should be noted that 36 hundreds will be equal to:

= 36 × 100

= 3600

It should be noted that 34 tens will be:

= 34 × 10

= 340

7 ones will be:

= 7 × 1

= 7.

Therefore, the sum will be:

= 3600 + 340 + 7 = 3947

Answer:

3947

Step-by-step explanation:

Answer:

You're answer is B. All answers except -6

Step-by-step explanation:

did the test

A parallelogram is a figure which has its opposite sides to be equal and parallel. The missing reason in the proof is:

B. Substitution Angle Angle Postulate.

A parallelogram is a type of quadrilateral that has its opposite sides to be equal and parallel. The sum of its internal angles is [tex]360^{o}[/tex].

To prove that ∠ BAD ≅ ∠ DCB, we have:

Given parallelogram ABCD;

<BAC ≅ <ACD (alternate angle theorem)

<DAC ≅ <ACB (alternate angle theorem)

<BAC + <DAC = <BAD

Also,

<BCA + <DCA = <BCD

Therefore,

<BAD ≅ <DCB (Substitution Angle Angle Postulate)

Thus, the missing reason in the partial proof is:

option B. Substitution Angle Angle Postulate

A sketch is attached to this question for more clarifications.

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Answer:

parallel, perpendicular are opposite

Answer:

PARALLEL PERPENDICULAR

Step-by-step explanation:

Answer:

12 books

Step-by-step explanation:

25% is the same as 1/4

3=25%=1/4

if you multiply 3 by 4 you get 100% or 12

You can also do this by adding 9, aka 3*3, to 3 to get 3*4=12.

Answer:

B 2x+2 I don't know whether is correct or not

Answer:

A=2, B=28

Step-by-step explanation:

A:6:7

8:24:B

A=8÷4

 =2

B=7×4

 =28

Answer:A=2

B=28

Step-by-step explanation:

Answer:

w>-20

Step-by-step explanation:

Answer:

Proof below.

Step-by-step explanation:

Let f(n)=10+ n^2 - (n - 2)^2.

We want to prove f is even for integer n > or = 1.

Let's show f is even for the base case, n=1.

f(1)=10+1^2-(1-2)^2

f(1)=10+1-(-1)^2

f(1)=11-(1)

f(1)=10

f(1) is even.

Let's assume the for some integer k > or = 1 , we have f(k) is even. This means there is some integer m so that f(k)=2m.

Note: f(k)=10+ k^2 - (k - 2)^2.

We want to show f(k+1) is even.

f(k+1)=10+ (k+1)^2 - ([k+1] - 2)^2

f(k+1)=10+ (k+1)^2 - (k-1)^2

f(k+1)=10+ ((k+1)^2 - (k-1)^2)

That difference is a difference of squares. Let's try factoring it.

f(k+1)=10+ (k+1-[k-1])(k+1+[k-1])

f(k+1)=10+ (2)(2k)

Multiply:

f(k+1)=10+4k

Turns out we didn't even need to use our induction hypothesis since 10+4k is 2(5+2k) which makes f(k+1) even given the factor of 2 present.

This proves for all integers n>=1 that f(n) is even.

We could have this without induction then. Let's do that here below this line.

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

10+ n^2 - (n - 2)^2

10+[n^2 - (n - 2)^2]

Factor difference of squares:

10+(n-(n-2))(n+(n-2))

Simplify:

10+(2)(2n-2)

Factor:

2[5+(2n-2)]

Because of the factor of 2, the given expression is always even for integer n.

Answer:

The answer would be -7/12

Step-by-step explanation:

Use math.way itll help you tremendously :)

Answer:

(cost ---> length)

35 ---> 5

49 ---> 7

56 ---> 8

70 ---> 10

Answer:

x-2y=12

Solve for y

x-2y=12

Subtract x on both sides

-2y=-x + 12

Divide both sides by -2

y=\frac{1}{2}x - 6y=21x−6

the domain is {-3,-1,0,2,5}

Domain are the set of x values

Range are the set of y values

We are given with domain x, we need to find out y values using the equation y=\frac{1}{2}x - 6y=21x−6

when x=-3 , y=\frac{1}{2}(-3)-6=\frac{-15}{2}=-7.5y=21(−3)−6=2−15=−7.5

when x=-1 , y=\frac{1}{2}(-1)-6=\frac{-13}{2}=-6.5y=21(−1)−6=2−13=−6.5

when x=0 , y=\frac{1}{2}(0)-6=-6y=21(0)−6=−6

when x=2 , y=\frac{1}{2}(2)-6=-5y=21(2)−6=−5

when x=5 , y=\frac{1}{2}(5)-6=\frac{-7}{2}=-3.5y=21(5)−6=2−7=−3.5

Range is {-7.5, -6.5, -6 , -5, -3.5}

Step-by-step explanation:

solve the equation ? 1 equation with 2 variables ? that is not possible.

what you mean is probably find the range.

x - 2y = 12

-2y = -x + 12

2y = x - 12

y = (x - 12)/2 = (1/2)x - 6

x = -3

y = 1/2 × -3 - 6 = -1.5 - 6 = -7.5

x = -1

y = 1/2 × -1 - 6 = -0.5 - 6 = -6.5

x = 0

y = 1/2 × 0 - 6 = -6

x = 2

y = 1/2 × 2 - 6 = 1 - 6 = -5

x = 5

y = 1/2 × 5 - 6 = 2.5 - 6 = -3.5

so, the corresponding range of the function is

{-7.5, -6.5, -6, -5, -3.5}

Answer:

Yes

Step-by-step explanation:

20 needed to get 80 %. You got one more than that so you got slightly more. So yes you did. You can also make 25 to 100 and 21 x4 so  that gives you 84 % . So you scored %84.

Good job