Write each expression as a single logarithm.
log 7 +log 2

The amount after 10 years is $11,842.43

In continuous compounding the number of times by which compounding occurs tends to infinity.

In order to calculate the amount use the following formula

A= Pe^rt

where P represents the initial amount, e is the mathematical constant having value 2.7182, r is the rate of interest and t is the time period

Here the principal amount is $6000, r is 6.8 and time period t is 10 years

A = $6000 x 2.718⁽¹⁰ ˣ ⁶·⁸ %⁾

A = 6000 x 2.718⁽¹⁰ ˣ ⁶·⁸÷¹⁰⁰⁾  

A = 6000 x 2.718 x 0.68

A = $ 11,842.43

Therefore the total amount calculated after 10 years is $ 11,842.43

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

y = 7x , that is y = 7x + 0 ← in slope-intercept form

with gradient 7 and y- intercept (0, 0 )

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

y = 6x - 8 ← is in slope- intercept form

with gradient 6 and y- intercept (0, - 8 )

Answer:

28 points

Step-by-step explanation:

Answer: 161+7n

Explanation: Let the number be n.

7(23+n)

=161+7n

Hope this helps you! Have a great day!!!!! :) :D

The result of the linear expression [tex]5-\frac{t}{3}[/tex] is 1.

What is linear expression?

An algebraic expression that uses either a constant or a variable raised to the first power for each term is known as a linear expression. This means that none of the exponents can be greater than 1.

Given [tex]5-\frac{t}{3}[/tex]

Also given that t = 12

Substitute the value of t and we get

[tex]5-\frac{12}{3}\\=5-4\\=1[/tex]

Therefore, the result of the linear expression [tex]5-\frac{t}{3}[/tex] is 1.

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Answer: 78

Step-by-step explanation: multiply 44 by 2 because there are two sides on the rectangle and then you add 5 and 5 because yet again there are two sides so when you get your answer subtract 10 from the 88 and then you get 78 there is your explanation and equation

Rectangle with perimeter 44 ft has its length and breadth 13 ft and 9 ft respectively.

Dimension of rectangle : 13 × 9

Given, that perimeter of rectangle is 44 ft .

Now, perimeter of rectangle is given by:

P = 2(l + b)

l = Length of rectangle .

b = Breadth of rectangle.

Let the breadth of rectangle be 'x' m.

Then length will be (2x -5) ft.

Substitute the values in the perimeter formula,

[tex]44 = 2(x + 2x -5)\\22 = 3x -5\\x = 9[/tex]

Thus the breadth of rectangle is 9 ft .

Length of rectangle is 5 ft less than twice its breadth.

Length = 2(9) - 5

Length = 13 .

Therefore the dimensions of rectangle is 13 × 9.

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x=3.4

Im writing this bc the app says the answer is too short

Answer:

If 0.65 is a decimal, then as a fraction it would be 65/100. This can be simplified though. 65 and 100 are both divisble by 5.

100 divided by 5 is 20 and 65 divided by 5 is 13. This is as simplified as it can go, so the answer is 13/20.

For clarification the answer is

13/20

Step-by-step explanation:

We need to know about logarithm to solve this problem. The greatest integer that is less than the value of log 5 is 0.

Logarithm is the exponent that is raised to a base to get a certain number. There are a few rules of algorithm, log a+ log b can be written as log ab, log a -log b can be written as log a/b, when a number whose logarithm is being calculated is raised to a certain power then the power can be directly multiplied to the log itself. Logarithm when written as log has a base of 10, the logarithm of a number that is same as it's base is always 1, the log of 1 is always zero, because any nonzero number raised to 0 is 1.We will find the value of log 5 first and then choose the nearest integer that is less than log 5.

log 5=log 10/2 =log 10-log 2=1-0.30=0.7

Therefore the greatest integer that is less than the value of log 5 is 0.

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Answer:

12

Step-by-step explanation:

Area of a triangle = 1/2*b*h

[tex]144=(\frac{1}{2})*(2x)*(x)\\12=x[/tex]

Answer:

Step-by-step explanation:

True

TRUE   AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

It will take 4.63 years to double the principal.

The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously after t years is-

A = P[tex]e^{rt}[/tex]

Here r = 6.5%

= 0.065

Let the principal amount be P,

then the amount after t years = 2P

A = P[tex]e^{rt}[/tex]

2P = P[tex]e^{rt}[/tex]

2P/P = [tex]e^{rt}[/tex]

2 = [tex]e^{0.065t}[/tex]

Taking log on both sides-

Log 2 = log [tex]e^{0.065t}[/tex]

Log 2 = 0.065t log e

Log 2 = 0.065t

0.65t = Log 2t

= log 2/ 0.065t

= 0.301/ 0.065 t

= 4.63

Thus, it will take 4.63 years to double the principal.

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Answer:20

Step-by-step explanation:

Answer:

-21/8

Step-by-step explanation:

3 (3/8) * -7/3

= 9/8 * -7/3

= 3/8 * -7

= -21/8

Answer/Step-by-step explanation:

f(6) = 3x² - 5

f(6) = 3(6)² - 5

f(6) = 3(36) - 5

f(6) = 108 - 5

f(6) = 103

(x, y) = (6, 103)

I hope this helps!

The volume of the tepee is 100.48 feet³

The formula for the volume of tepee is same as the volume of cone which is given as :

               V = 1/3 πr²h        (1)

where V = volume

           r = radius of the tepee

           h = height of the tepee

According to the question we have been given that

            radius = 4 feet

             height = 6 feet

Putting the required values in equation (1) we get

                V = 1/3 π (4)²(6)

                   = 1/3 (3.14)(96)

                   = 301.44/3

                   = 100.48 feet³

Hence the volume of the tepee is  100.48 feet³

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Option c is correct i.e., |81 - ( -29)|

On January 1, the high temperature was 81 F in Kona and the low temperature was - 29 F in Barrow.

We have to find the difference between the two temperatures.

So the difference between is

    = 81 - (- 29)

    = 81 + 29

    = 110

Therefore the difference the two temperatures is 110.

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The equation that shows how the total number of loads done, y, depends on how many weekdays have passed, x will be y = 3 + x.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario. It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

In this case, Cohen family desperately needs to catch up on doing laundry. Over the weekend, Mr. and Mrs. Cohen got 3 loads done. Now, during the week, they plan to do 1 load per day.

The equation that shows how the total number of loads done, y, depends on how many weekdays have passed, x will be:

y = 3 + 1(x)

y = 3 + x

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Answer:

M(-3;3/2)

Step-by-step explanation:

substitute in this formula of finding midpoint coordinate:M(x1+x2÷2;y1+y2÷2)

The respective prices are given below as

The price of the sandwich is 20/3 dollars.

The salad may be purchased for a price of $16/3.

There is a fee of $2 for the drinks.

Let's say that the price of the sandwich is x.

Allow the price of salad to equal y.

Allow the price of drinks to equal z.

The new total for this meal is $46. It includes three sandwiches, three beers, and two salads. Thus;

3x + 3y + 2z = 40 ——- (eq 1)

The price of $29 covers two sandwiches, two drinks, and one salad.

Thus;

2x + 2y + z = 26 ——-(eq 2)

It will cost you $54 for four sandwiches, one drinks, and three salads. Thus;

4x + y + 3z = 38 ———-(eq 3)

The following are the results of concurrently solving the three equations:

x = 20/3

y = 16/3

z = 2

Therefore, the following is how much each item costs:

There is a charge of $20/3 for the sandwich.

The salad may be purchased for a price of $ 16/3.

There is a fee of $2 for the drinks.

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Answer: x  ≤ 4.5

Step-by-step explanation:

Since the inequality goes left and has a closed circle it would be x  ≤ 4.5

Graham drove 32.58 miles in one hour and it took 1.84 minutes to drive a mile

Miles Graham drove in 13 hours = 423 miles

Unitary method: A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. It is a technique that we employ for the majority of math calculations.

Part a:

Miles driven in one hour = Total miles driven/Total no. of hours taken

= 423/13 = 32.58 miles

Part b:

Hours took to drive a mile = Total no. of hours taken/ Total miles driven

= 13/423  = 0.030 hours or 1.84 minutes

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After solving the equation, x = 3/2 is the value of x in 2x = 3.

⇒ 2x = 3

⇒ x = 3/2

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

[tex] \rightarrow \sf \: −31[/tex]

Step-by-step explanation:

[tex] \rightarrow \sf \frac{1}{4} (4)-5(6)-2[/tex]

[tex] \rightarrow \sf \: \frac{1}{4} \times \frac{4}{1} - 30 - 2[/tex]

[tex] \rightarrow \sf \: 1 - 30 - 2[/tex]

[tex] \rightarrow \sf \: - 31[/tex]

Answer: 118728

Step-by-step explanation:

You can just simply find this answer using a calculator.

The answer after simplification is 48[tex]\sqrt{2}[/tex]

We are required to simplify two values in square root form

Given values are :

4[tex]\sqrt{32}[/tex]+4[tex]\sqrt{128}[/tex]

4([tex]\sqrt{32}[/tex]+[tex]\sqrt{128)}[/tex]

Now we know that

32= [tex]2^{5}[/tex]

128=[tex]2^{7}[/tex]

Putting these values inside the square root,

we know that square root is to the power 1/2

our equation becomes

4([tex]\sqrt{2^{5} } +\sqrt{2^7[/tex])

removing the square root,
4([tex]2^{5/2}+2^{7/2}[/tex])

Now we know that 4 is 2 to the power 2 , and taking 2^5/2 as common, we get:

[tex]2^{2}*2^{5/2}(1+2^{2/2})[/tex]

16[tex]\sqrt{2}[/tex](3)

=48[tex]\sqrt{2}[/tex]

The answer after simplification is 48[tex]\sqrt{2}[/tex]

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