What is the value of x?
Enter your answer in the box.

Since the interest is compounded, we will have to use the compound interest formula.

We Weill plug 7500 in for A, because that's the amount of money that we want to have at the end of some amount of time.

5000 will go in for P because that's the starting amount.

2.7% will be converted into a decimal percentage form. You can do this by dividing by 100, which you will get .027, and then plug that in for r, the rate.

Since the interest is compounded quarterly, n = 4.

After a bit of number crunching, you will get to the point where you have to solve for an exponent. You can easily do this by using the natural log ln(). One property of logarithm is that you can take the exponent and place it in front of the log. Now you can divide both sides to separate and solve for t.

It take 10.5 years for the investment to grow to $7,500 in the account with a 2.7% annual interest rate compounded quarterly.

Given:

P = $5000

r = 2.7% = 0.027 (as a decimal)

n = 4 (quarterly compounding)

A = $7500

The formula for compound interest:

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

Substituting these values into the formula

[tex]\[ 7500 = 5000\left(1 + \dfrac{0.027}{4}\right)^{4t} \][/tex]

Dividing both sides of the equation by $5000, we have:

[tex]1.5 = (1.00675)^{(4t)[/tex]

Assuming a natural logarithm (ln), we have:

ln(1.5) = [tex]ln((1.00675)^{(4t))[/tex]

Using the logarithm property,[tex]ln(a^b) = b * ln(a)[/tex], simplify the equation:

[tex]ln(1.5) = 4t * ln(1.00675)[/tex]

Now, dividing both sides of the equation by 4 * ln(1.00675):

t = ln(1.5) / (4 * ln(1.00675))

t = 10.5 years.

Therefore, it will take 10.5 years for the investment to grow.

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Answer:

the answer os eleven

Step-by-step explanation:

As oyu see the half way number is 4 higher that 7 and 4 lower than 15.

Answer:

I think it's D

Step-by-step explanation:

Answer:  I think its D

Step-by-step explanation:

Rigid transformation moves a shape without changing the size of the shape.

See attachment for the diagram that shows the position of D'

Answer:

B. A data set can have multiple modes.

D. A data set will never have a mode.

Step-by-step explanation:

reason for B: some data are referred to as multimodal data because they have multiple modes.

reason for D: data can lack a mode if no value appears more than two times, or frequently.

Answer:

b. vertical shrink

Step-by-step explanation:

Answer:

22, 24, 26, 28, 30

Step-by-step explanation:

If the sum of 5 numbers is 130, that means the average of these numbers is 26.

If it is the average then it is the middle, or the third number. The two numbers before it would then be 22 and 24 by subtracting twos, and the two numbers after it would be 28 and 30 by adding twos.

22, 24, 26, 28, 30

Answer:

22,24,26,28,30

Step-by-step explanation:

I call the unknown number x

I write consecutive numbers in terms of x.

x+ (x+2) + (x+4) + (x+6) + (x+8) = 130

5x + 20 = 130

5x = (130 - 20)

5x = 110

x = 22 = smallest even number

x + 2 = 24 = second even number

x +4 = 26

x + 6 = 28

x + 8 = 30

Answer:

866.16??????

Step-by-step explanation:

The amount is 4,494.40 plant earned per man-hour of labor 3 years after it opened.

It is required to find the amount the plant earned per man-hour of labor 3 years after it opened.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. where r is the common ratio between successive terms.

Given:

A manufacturing plant earned 4000 pesos per man-hour of labor.

Rate= 6% per man-hour.

Time=3 years

We can consider the geometric sequence formula

[tex]A_{n} = A_{1} r^{n-1}[/tex]

[tex]A_{1}[/tex]= 4000

r = 1.06/1 = 1.06

n = 3

Substitute:

[tex]A_{3} = 4000(1.06)^{3-1} \\A_{3} = 4000(1.06)^{2}\\A_{3}= 4000(1.1236)\\A_{3} = 4,494.40[/tex]

Therefore, the amount is 4,494.40 plant earned per man-hour of labor 3 years after it opened.

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This question is solved using translation concepts, and doing this, it is found that the equation of the new graph is:

[tex]y = |x - 3|[/tex]

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

When a function f(x) is translated a units to the left, we get f(x - a).

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

In this question:

The original function is [tex]y = |x|[/tex]

Point (1,1) is moved to (4,1), that is, 3 is added to the x-coordinate, meaning that the function was shifted 3 units to the left.

Thus, the new equation is:

[tex]y = g(x) = f(x - 3) = |x - 3|[/tex]

A similar question is given at https://brainly.com/question/23602866

Answer:

Answer:

associative

Step-by-step explanation:

Answer:

the answer is 1 and 1/2

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

Given: Lines J and H are parallel lines. O intersects both lines equally.

Since two angles equal 180, that will be what  (4y + 12) and 64 will be equal to.

(4y + 12) + 64 = 180

76 + 4y = 180

-76          -76

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

    4y = 104

      y = 26

x and y is both 26 because they are vertical angles.

Hope this helped.

Answer:

25(6+x) = (25×6) + (25×x)

= 150+25x

Step-by-step explanation:

i hope it helps

⇛25(6 + x)

⇛150 + 25x

[tex] [/tex]

Answer:

1441.08in^3

Step-by-step explanation:

Answer:

1. x²-2x+15

This can't be factored, I've tried multiple ways now, but it just can't be factored.

2. y²-19y+90​

Let's factor y^2−19y+90

y^2−19y+90

The middle number is -19 and the last number is 90.

Factoring means we want something like

(y+_)(y+_)

Which numbers go in the blanks?

We need two numbers that...

   Add together to get -19

   Multiply together to get 90

Can you think of the two numbers?

Try -9 and -10:

   -9+-10 = -19

   -9*-10 = 90

Fill in the blanks in

(y+_)(y+_)

with -9 and -10 to get...

(y-9)(y-10)

Answer:

(y−9) (y−10)

Answer:

answer is 6

Step-by-step explanation:

f(x) = x2 - 4x

f(-3)= -3*2-4*-3

      =-6-(-12)

      =6

Answer:

50 bags

Step-by-step explanation:

1 kg = 1000 grams

10 kg * 1000g/ 1kg = 10000 g

Divide 10000 grams by 200 g

10000g / 200g = 50

Answer:

Option C, 93.6 mi³

Step-by-step explanation:

Volume of the triangular prism,

(8×3.9/2)×6

= 93.6 mi³

Answer: I think it would be C

Step-by-step explanation:

Answer:

the correct answer is C because its the only polygon with a caved in feature

Answer:

False

Step-by-step explanation:

If an angle is congruent, it means that the angle is equal to the first angle which is 56 degrees, in theory, it would be false because 56 degrees is an acute angle and not obtuse.

Answer:

d = 1.1 units

Step-by-step explanation:

Since the x- coordinates of the 2 points are equal, both 3, then they lie on a vertical line. The distance between the 2 points is the difference in the y- coordinates, that is

d = | 2.4 - 1.3 | = | 1.1 | = 1.1 units

Answer:

Answer is "1.1"

Step-by-step explanation:

.......................

Answer:

x= 8

Step-by-step explanation:

Right angled triangle :

Use Pythagorean theorem,

Base² + altitude² = hypotenuse²

x² + ( 2x - 1)² = (2x +1)²

(2x + 1)² - (2x-1)²  -x² = 0

[tex]\boxed{(a+b)^{2}-(a-b)^{2}=4ab}[/tex]       {here, a = 2x and b = 1}}

4*2x*1 - x²= 0

8x - x² = 0

x(8 - x) =0

x = 0  {Ignore}  or 8 - x= 0

                  -x = -8

                   x = 8

x = 8

Answer:

A

Step-by-step explanation:

Let's say we need x pounds of one-dollar-a-pound coffee . The coffee must average out to 84 cents a pound, and the formula for average is

sum of cost of coffee / number of pounds of coffee, so we have

0.84 = total cost of coffee / (x+80) . The total cost of coffee can be found to be the sum of the cost of $1 coffee and 70 cent coffee, so we have

0.84 = (cost of $1 coffee + cost of 70 cent coffee) / (x+80)

The cost of $1 coffee can be found by adding $1 for each pound of one dollar coffee, or $1 * x. Similarly, the cost of 70 cent coffee is equal to 0.70 * 80, so we have

0.84 = (1*x+0.7*80)/(x+80)

0.84 = (x+56)/(x+80)

multiply both sides by (x+80) to remove a denominator

0.84(x+80) = x+56

0.84x + 67.2 = x+56

subtract both sides by 56 and 0.84x to isolate the x and its coefficients

11.2 = 0.16 x

divide both sides by 0.16 to isolate x

11.2/0.16 = x = 70

The number of pounds of a constituent in a mixture given the cost of the

mixture and the cost and mass of the other constituent can be calculated

by using an equation to model the system

The correct option for the number of pounds of one-dollar- pound coffee needed is option A

(A) 70 pounds

The procedure for arriving at the correct option is as follows:

The given parameters are;

The cost of the the coffee for which the mass in the mixture is to be determined = One-Dollar a pound = 100 ¢ a pound

The mass of the coffee 70¢ a pound coffee to be mixed = 80 pounds

The cost per pound of the mixture = 84 ¢ a pound

The required parameter;

The number of pounds of the one-dollar-a-pound (100 ¢ a pound) coffee in the mixture

Method:

Let x (pound) represent the number of pounds of the one-dollar-a-pound coffee in the mixture, we have;

Mass of mixture = Mass of the one-dollar-a-pound in the mixture, x + Mass of 70 ¢ a pound in the mixture, 80

∴ Mass of mixture in pounds = x + 80

Cost = Cost per pound × Number of pound

Find solution by applying the equation;

Cost of the constituents = Cost of the mixture

Where;

Cost of the constituents = $1 × x + 70 ¢ × 80 = 100 ¢ × x  + 70 ¢ × 80

Cost of the mixture = 84 ¢ × (x + 80)

Therefore;

100 ¢ × x  + 70 ¢ × 80 = 84 ¢ × (x + 80)

The above can be expressed as 100·x + 70×80 = 84 × (x + 80)

Expanding, evaluating and collecting like terms gives;

100·x + 5,600 = 84·x + 6,720

100·x - 84·x = 6,720 - 5,600 = 1,120

16·x = 1,120

x = 1,120/16 = 70

The number of pounds of one-dollar- pound coffee needed, x = 70 pounds

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Answer:

So the sqrt(46) is between 6 and 7

Step-by-step explanation:

sqrt(46)

5*5 = 25

6*6=36

7*7=49

So the sqrt(46) is between 6 and 7

Answer:

= -2

Step-by-step explanation:

-2 -(-7)

= 5

Answer:

I think it would be

A .39

I hope that it helps you

Answer:

( x - 11 )^2 + ( y - 5 )^2 = 4^2

Step-by-step explanation:

The general form of equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2.

h and k are the co-ordinates of the center of circle and r is the radius

We have,

r=4

(h,k)=(11,5)

( x - h )^2 + ( y - k )^2 = r^2

or, ( x - 11 )^2 + ( y - 5 )^2 = 4^2

If you simplify,

x^2-22x+121+y^2-10y+25=16

or, x^2+y^2-22x-10y+146-16=0

or,x^2+y^2-22x-10y+130=0

Answer:

( x - 11 )^2 + ( y - 5 )^2 = 4^2

Step-by-step explanation:

Cost price is Rs600 and marked price is Rs780.

Must click thanks and mark brainliest