For these problems, please show your algebraic work using logarithms. 1. Determine the doubling time for each situation listed below. a. A population is growing according to P = P_0e^0.2t b. A bank account is growing by 2.7% each year compounded annually.

Answer:

The total compound interest is $37,147.24.

Step-by-step explanation:

I could be wrong

The example of a sequence of rational numbers is 1/1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1, 1/4, 4/3, 3/5, 5/2, 2/5, 5/3, 3/4, ….

The term rational number in math is defined as  a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.

Here we have given that {xₙ} n > 0 is a sequence of reals.

Here we need to find the definition of sequence and the example for the sequence of rational numbers.

As per the given definition we all know that the rational number is the number that can be expressed as the quotient or fraction

Here first we have to identify the definition of sequence that is none other than a group of numbers in an ordered way following a pattern and it is also known as Series which means that it is a sum of the elements of the sequence.

And the example for sequence of rational number is written as 1/1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1, 1/4, 4/3, 3/5, 5/2, 2/5, 5/3, 3/4, ….

Here we have given that the value must be greater than 0, so we have taken only the positive values.

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Answer:

x = 15

Step-by-step explanation:

the segment inside the triangle is an angle bisector and divides the side opposite the bisected angle into segments that are proportional to the other two sides, that is

\(\frac{x}{21-x}\) = \(\frac{25}{10}\) ( cross- multiply )

10x = 25(21 - x)

10x = 525 - 25x ( add 25x to both sides )

35x = 525 ( divide both sides by 35 )

x = 15

Answer:

Step-by-step explanation:

m<7=3x-10

m<3=2x+5

we know that from corresponding angle axiom that

m<7=m<3

3x-10=2x+5

3x-2x=10+5

x=15

m<7=45-10=35,  

m<7=m<1=35

1. The function f that determines the height of the beanstalk is \(h(t) = 7 * (1.15)^t\)

2. f(1)/f(0) = 1.15.

3. f(2)/f(1) = 1.149.

Let h be the height of the beanstalk in inches after t days. Then we can write: \(h(t) = 7 * (1.15)^t\) where 1.15 is the factor by which the height increases each day.

i. To compute f(1)/f(0), we need to substitute t = 1 and t = 0 into the function f and divide:

f(1)/f(0) = [7 * (1.15)^1] / [7 * (1.15)^0]

f(1)/f(0) = 1.15/1

f(1)/f(0) = 1.15

ii. To compute f(2)/f(1), we need to substitute t = 2 and t = 1 into the function f and divide:

f(2)/f(1) = [7 * (1.15)^2] / [7 * (1.15)^1]

f(2)/f(1)= (1.3225) / (1.15)

f(2)/f(1) = 1.149

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The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Here, we just need to add x and y and subtract it from 180.

x + y = 91 + 42 = 133.

180 - 133 = 47.

Hence, z = 47 degrees.

Answer:

Step-by-step explanation:

straight line = 180° we remove the angles x and y and find z

180 - 91 - 42 =

47°

Answer:

66789

Well you never told to explain :/

Not tryna be smart just saying

Answer:

66789

Step-by-step explanation:

3 times 3 is 9, 3 times 4 is 12 carry the 1, 3 times 5 is 15 plus the 1 is 16

Add a 0 underneath the other numbers, 2 times 3 is 6, 2 times 4 is 8, 2 times 5 is 10

Add  two 0's 1 times 3 is 3, 1 times 4 is 4, 1 times 5 is 5

Add all of them and you get 66789

Answer:

28.07°

Step-by-step explanation:

use SohCahToa

in this case we use tan^-1 to get the angle x°

tan^-1(8/15)=28.07248694

to the nearest hundredth

=28.07°

Using relations in a right triangle, the secant of angle θ is given by:

D. 5/4.

The relations in a right triangle are given as follows:

Using the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 9² + 12²

h = sqrt(9² + 12²)

h = 15.

The secant of an angle is 1 divided by the cosine, hence:

Which means that option D is correct.

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Answer:

you didn't post a picture :/

Answer: 0.62

Step-by-step explanation: I got the answer

The probability that the next customer will pay with cash is 0.62

"It is finding out the possibilities of the occurrence of an event."

"P(A) = n(A) / n(S)

where, n(A) is the number of favorable outcomes of an event A

n(S) is the total number of outcomes for an experiment"

For given example,

in the last week 80 customers paid cash, 45 customers used a debit card, and 4 customers used a credit card.

So, the total number of customers:

⇒ n(S) = 80 + 45 + 4

⇒ n(S) = 129

Let event A: the next customer will pay with cash

n(A) = 80

So, the probability that the next customer will pay with cash would be,

⇒ P(A) = n(A)/n(S)

⇒ P(A) = 80/129

⇒ P(A) = 0.62

Therefore, the probability that the next customer will pay with cash is 0.62

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Answer:

i don't know

i want to know

please tell

me guys

to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.

\(\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4\)

Let's make a diagram to visualize the problem.

First, let's find angle A.

Then, we use the law of sines to find AB.

Let's find the slope

So it is an undefined slope.

Answer:

Step-by-step explanation:

it is Negative

Answer:

Step-by-step explanation:

BC=\(\sqrt{5^2+5^2}\)

x   =\(\sqrt{50}\)

x   = 5\(\sqrt{2}\)

tan theta= 5/5

      theta= tan^-1 (5/5)        

                =45°

Step-by-step explanation:

BC=\sqrt{5^2+5^2}52+52

x   =\sqrt{50}50

x   = 5\sqrt{2}2

tan theta= 5/5

      theta= tan^-1 (5/5)        

                =45°

Answer:

276,108 < x < 271,680

Step-by-step explanation:

*Hope this helped*

answer= the lcm of 11,8a d 12 is 264

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

B.

Step-by-step explanation:

Hope this helps!!

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$790\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &5 \end{cases} \\\\\\ 790=P(0.04)(5)\implies \cfrac{790}{(0.04)(5)}=P\implies \boxed{3950=P}\)

Answer:

The mean absolute deviation is 2. Hope this helps

Step-by-step explanation:

7+2+8+9+9+5+6+8+1=5.5

7-5.5=1.5

5.5-2=3.5

8-5.5=2.5

9-5.5=3.5

9-5.5=3.5

5.5-5=0.5

6-5.5=1.5

8-5.5 2.5

5.5-1=4.5

1.5+3.5+2.5+3.5+3.5+0.5+1.5+2.5+4.5=2

Answer is 2.

I hope this can help!

Have a nice day :)

~Amy

Answer: Suppose there exists a positive rational number r such that r^2 < 2. Then we have 2 - r^2 > 0. Let h = (2 - r^2)/4. Then h > 0 because r^2 < 2.

Consider the number rh = r + h. We have:

(rh)^2 = (r + h)^2 = r^2 + 2rh + h^2 = r^2 + 2(2 - r^2)/2 + (2 - r^2)/16

= r^2 + 2 + (2 - r^2)/16

< 2 + 2 + (2 - 2)/16 = 2.

Thus, for any positive rational number r such that r^2 < 2, there exists a larger positive rational number rh = r + h such that (rh)^2 < 2.

Step-by-step explanation:

Answer:

for  n =  3

       \(Z(3) = 0.26\)  

for  n =  10

       \(Z(3) = 0.028\)

Step-by-step explanation:

from the question we are that

  The  number of applicant is n

  The  number of  people on the committee is \(N = 3\)

Generally given that the applicant ranking is random the probability of a candidate being accepted is mathematically represented as

       \(Z(n) =  N  *  \frac{1}{n} *  \frac{1}{n}  *  \frac{n-1}{n}  + \frac{1}{n} *  \frac{1}{n} * \frac{1}{n}\)

Now  for  n =  3

       \(Z(3) =  3  *  \frac{1}{3} *  \frac{1}{3}  *  \frac{3-1}{3}  + \frac{1}{3} *  \frac{1}{3} * \frac{1}{3}\)      

         \(Z(3) = 0.26\)            

Now  for  n =  10

       \(Z(3) =  3  *  \frac{1}{10} *  \frac{1}{10}  *  \frac{10-1}{10}  + \frac{1}{10} *  \frac{1}{10} * \frac{1}{10}\)      

         \(Z(3) = 0.028\)

Answer:

In step by step explanation

Step-by-step explanation:

a) Normal distribution N( 0, 1 )

If the sample size is equal n = 16 we have to use t-student distribution since     n < 30.

In the case n = 36 we should use normal distribution (z tables)

b) We can´t use the  standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 in the first case n < 30 .

We can calculate that  probability in the case of the second sample

Answer:

i belive its d or c

Step-by-step explanation:

Can you be a little more specific?