Mrs. Johnson borrows $1400 with an interest rate of 5.5%. How much interest does she pay if she pays off the debt in 8 months?

Answer: 8

Step-by-step explanation:

A Geometric sequence can be used:

To Model this sequence you need to use this formula

A (subscript n) = Ar(n-1)

a = value of the first term

n = the # of the term you want to find (For example, if you want to find the term number 3, it is 12)  

r = the common ratio, this is obtained by dividing the second term in the sequence by the first.

So the value of r is = 2/3 because 27 times 2/3 = 18 which is the second term

n = 4 since you want to find the 4th term in the sequence

Plug it in and results are

4th term = 27(2/3)^(4-1)  = 8

Sample Response:

There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.

Answer:

The answer is below

Step-by-step explanation:

We need to prove that:

(Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A.

Firstly, 1 / cos A = sec A, 1 / sin A = cosec A and tanA = sinA / cosA.

Also, 1 + tan²A = sec²A; sec²A - 1 = tan²A

[tex]\frac{\sqrt{secA-1} }{\sqrt{secA+1} } +\frac{\sqrt{secA+1} }{\sqrt{secA-1} } =\frac{(\sqrt{secA-1)}(\sqrt{secA-1})+(\sqrt{secA+1)}(\sqrt{secA+1}) }{(\sqrt{secA+1})(\sqrt{secA-1}) } \\\\=\frac{secA-1+(secA+1)}{\sqrt{sec^2A-secA+secA-1} } \\\\=\frac{2secA}{\sqrt{sec^2A-1} } \\\\=\frac{2secA}{\sqrt{tan^2A} } \\\\=\frac{2secA}{tanA} \\\\=\frac{2*\frac{1}{cosA} }{\frac{sinA}{cosA} }\\\\= 2*\frac{1}{cosA}*\frac{cosA}{sinA}\\\\=2*\frac{1}{sinAA}\\\\=2cosecA[/tex]

Answer:

7*6543=45801

Step-by-step explanation:

We have the digits 34567 and must arrange them into a product with the largest possible value.

It's clear that we must place the largest digits to the left, so they represent larger numbers to multiply.

Let's try with:

7654*3=22962

765*43=32895

76*543=41268

7*6543=45801

This last combination definitely produces the largest product

Answer: 7*6543=45801

Answer:

-4x^4-9x^3+4x^2-7x-7

Step-by-step explanation:

Answer:

Ziad is 30 years old.

Marc is 10 years old.

Step-by-step explanation:

We will use m to represent Marc's age this year, and z to represent Ziad's age this year.

This year:

z = 3m

To show their relative ages in ten years time:

z + 10 = 2(m+10)

We can rearrange this to make m the subject.

z + 10 = 2m + 20

z = 2m + 10

We also know that m = 3z. We can substitute this value into our equation.

3m = 2m + 10

m = 10

Use z = 3m to find that z = 30.

Answer: s = 16

2(s - 10) = 12

distribute the 2

2s - 20 = 12

add 20 to both sides

2s = 32

divide both sides by 2

s = 16

you can then check your work by putting in the 16

2 (16-10) = 12

2 (6) = 12

12 = 12

Answer:

Kindly check explanation

Step-by-step explanation:

Let :

Original commute time = x

Commute time due to road construction = 150% of original commute time

Hence, commute time due to road construction :

(150 / 100) * x

0.15x

Hence, the implication of the road construction in progress means that it will now take additional half of the usual time it takes them on a Monday morning.

For instance, an individual whose usu commute time is 10 minutes in the morning will now take :

1.5x = 1.5(10) = 15 minutes commute time on a Monday morning.

Answer:

its b

Step-by-step explanation:

Time interval 6:53 a.m to 8:53 a.m, the average rate of change per hour the greatest.

Given,  

Time          Temperature (°F)  

5:53 a.m.       60.1

6:53 a.m.       60.1

8:53 a.m.       66.9

11:53 a.m        75.2

3:53 p.m.        78.1

From 5:53 a.m. to 6:53 a.m. the temperature is constant. So average rate of change per hour is 0.

From 6:53 a.m to 8:53 a.m. the temperature is increasing from 60.1 to 66.9 or 6.8 in 2 hours . So average rate of change per hour is [tex]\frac{6.8}{2} =3.4[/tex].

From 8:53 a.m. to 11:53 a.m the temperature is again increasing from 66.9 to 75.2 or 8.3 in 3 hours. So average rate of change per hour is [tex]\frac{8.3}{3} =2.76[/tex].

From 11:53 a.m to 3:53 p.m. the temperature is again increasing from 75.2 to 78.1 or 2.9 in 4 hours. So average rate of change per hour is [tex]\frac{2.9}{4}=0.725[/tex].

Now clearly from the above points time interval 6:53 a.m to 8:53 a.m, the average rate of change per hour the greatest.

For more details on temperature scale follow the link:

https://brainly.com/question/15819503

Answer:

Gracias generous mane •‿•

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

Answer:

w times t

Step-by-step explanation:

Answer:

1.25t+5

Step-by-step explanation:

period

The equation representing the situation is c = 3.5b

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Harold can buy 2 pounds of bananas for $7.

Since, he can buy 2 pounds in $7 so, 1 pound in = 7/2 = $3.5

So, when he will buy b pounds of bananas he will spend = $3.5b

So, if c is the total cost for b pounds of bananas, then the equation representing the total cost for b pounds of bananas will be,

c = 3.5b

Hence, c = 3.5b is the equation that represent the cost, c, for b bananas.

For more references on equations, click;

https://brainly.com/question/29657983

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Answer:

x= 7/2

2(x+1)=9

x+1=9/2

x=9/2 - 1

x=7/2

Answer:

x=7/2 x=3.5

Step-by-step explanation:

divide both sides by 2

(x+1)(2)/2=9/2

simplify

x+1=9/2

subtract 1 from both sides

x+1-1=9/2-1

simplify

x=7/2

Answer:

It is NOT possible to construct a quadrilateral from any 4 given measurements of its sides.

Step-by-step explanation:

We are asked to tell whether it is possible to construct a quadrilateral from any 4 given measurements of its sides.

Well, in order to construct a quadrilateral from any 4 given measurements of its sides, we need at least five dimensions.

With only 4 given measurements of its sides, we won't know any of its angles.

Thus, it is NOT possible to construct a quadrilateral from any 4 given measurements of its sides.

Answer:

100%

Step-by-step explanation:

percentage change is

(new price - old price) / old price

2 - 1 / 1

1 * 100% = 100%

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All of the points on the graph could represent rational numbers. (-1, 0, 1, 4.5)

Answer:

B

Step-by-step explanation:

A: false, point C isn't a rational number

B: True, Every negative integer is a negative rational number, like point A

C: false, point D is a fraction, therefore, point D is a rational number

D: false, like said in A, point C isn't a rational number

Answer:

The answer is -5

Step-by-step explanation:

−11−(−6)

=−11−(−6)

=−11+6

=−5

The answer is C. 6 blocks.

Answer:

C. 6 blocks is correct. I took the test and got that right :)

Step-by-step explanation:

Answer:

Equation- 50+40h=210

Answer- h=4

Step-by-step explanation:

Just simplify the equation :)

50+40h=210

40h=160

h=4

The electrician worked for 4 hours.

Happy holidays!

Answer:

5280

Step-by-step explanation:

Answer:

5280x=y

Step-by-step explanation:

5280(8) = 42240

Answer:

Brainliest are always appreciated :)

Step-by-step explanation:

For Number 1, just make a graph. (THE LINE WILL BE STRAIGHT)

For Number 2:

Proportional is when quantities have the same relative size. In other words they have the same ratio. The cocoa has an equivalent ratio which is why its proportional. This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.

Answer:

7 divided 2 is another way of saying 7/2 since division and fractions are alike.

Step-by-step explanation:

Answer:

because youre still dividing it either way;

Step-by-step explanation:

an improper fraction (7/2) you would have to see how many times the 2 goes into the 7 to get a proper fraction. its the same way with division, just less complicated and in a different format.

Answer:

the turning point is (-2,-1)

i dont know the turning point but i hope this helps

Step-by-step explanation:

Answer:

a) (-2 , -1)

b) (-1 , 0) and (-3 , 0)

Step-by-step explanation:

For part a)

We can find the coordinates of the turning point by seeing at the graph where it turns the other way or in simpler words the axis of symmetry so if see the graph the axis of symmetry is the line x = -2 so that means the turning point is (-2 , -1).

For finding the turning point mathematically we compare the equation to its standard form which is:

[tex]x^2+4x+3=a(x-h)^2+k[/tex]

where h is the x coordinate  and k is the y coordinate of the turning point of the equation (h , k) = (x , y).

so just solve the left side,

[tex]a(x-h)^2+k\\a((x)^2-2(x)(h)+(h)^2)+k\\a(x^2-2xh+h^2)+k\\\\ax^2-2ahx+ah^2+k=x^2+4x+3\\[/tex]

and so we compare the coefficients of x^2 on the right and left side we get

[tex]a=1[/tex]

if we compare the coefficients of x on the right and left side we get

[tex]-2ah=4\\-2(1)h=4\\-2h=4\\h=\frac{4}{-2}\\\\h=-2[/tex]

now we compare the constants on the right and left side we get

[tex]ah^2+k=3\\(1)(-2)^2+k=3\\(1)(4)+k=3\\4+k=3\\k=3-4\\k=-1[/tex]

so the turning point is (-2 , -1) proven mathematically and graphically as well

For part b)

Roots of the equation are also called as x-intercepts which means where the graph intersects/cuts the x-axis so if see the graph it cuts the x-axis at 2 points  firstly at -3 and then at -1 so the roots of the equation would be (-1 , 0) and

(-3 , 0) the y coordinate is zero when the points lies on the x-axis.

for mathematically solving the equation we would equate the equation to zero

[tex]y=x^2+4x+3\\x^2+4x+3=0[/tex]

Now solve it by either factorizing or by using the quadratic formula we would get two values for x those are the roots of the equation

we solve it by factoring

[tex]x^2+4x+3=0\\x^2+3x+x+3=0\\x(x+3)+1(x+3)=0\\(x+3)(x+1)=0\\x=-3\ ,\ x=-1\\[/tex]

proven mathematically as well as graphically.

Answer:

4

Step-by-step explanation:

divide by 2 and you will have your answer

Answer:

-12

Step-by-step explanation:

× x 2 = 2x

2x/3= -8x3/2

x = -12

Answer:

7.24 * 10^-5

Step-by-step explanation:

I think it's (3,4) but I am not confident so please be understanding

Answer:

(3, 1 )

Step-by-step explanation:

The centre of the circle is at the midpoint of the diameter.

Given endpoint (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = (9, 7) and (x₂, y₂ ) = (- 3, - 5 ) , then

midpoint = ( [tex]\frac{9-3}{2}[/tex], [tex]\frac{7-5}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex], [tex]\frac{2}{2}[/tex] ) = (3, 1 )

Thus centre of circle = (3, 1 )