Find x and then find the measure of the exterior angle

Step-by-step explanation:

explanation is in the attachment

hope it is helpful to you

Answer:

(a) [tex]A = A_0 * e^{kt}[/tex]

(b) There will be 1lb left after 14 hours

Step-by-step explanation:

Solving (a): The equation

Since the substance decomposes at a proportional rate, then it follows the following equation

[tex]A(t) = A_0 * e^{kt}[/tex]

Where

[tex]A_0 \to[/tex] Initial Amount

[tex]k \to[/tex] rate

[tex]t \to[/tex] time

[tex]A(t) \to[/tex] Amount at time t

Solving (b):

We have:

[tex]t = 4.6hr[/tex]

[tex]A_0 = 8[/tex]

[tex]A(4.6) = 4[/tex]

First, we calculate k using:

[tex]A(t) = A_0 * e^{kt}[/tex]

This gives:

[tex]A(4.6) = 8 * e^{k*4.6}[/tex]

Substitute: [tex]A(4.6) = 4[/tex]

[tex]4 = 8 * e^{k*4.6}[/tex]

Divide both sides by 4

[tex]0.5 = e^{k*4.6}[/tex]

Take natural logarithm of both sides

[tex]\ln(0.5) = \ln(e^{k*4.6})[/tex]

This gives:

[tex]-0.6931 = k*4.6[/tex]

Solve for k

[tex]k = \frac{-0.6931}{4.6}[/tex]

[tex]k = -0.1507[/tex]

So, we have:

[tex]A(t) = A_0 * e^{kt}[/tex]

[tex]A(t) = 8e^{-0.1507t}[/tex]

To calculate the time when 1 lb will remain, we have:

[tex]A(t) = 1[/tex]

So, the equation becomes

[tex]1= 8e^{-0.1507t}[/tex]

Divide both sides by 8

[tex]0.125= e^{-0.1507t}[/tex]

Take natural logarithm of both sides

[tex]\ln(0.125)= \ln(e^{-0.1507t})[/tex]

[tex]-2.0794= -0.1507t[/tex]

Solve for t

[tex]t = \frac{-2.0794}{-0.1507}[/tex]

[tex]t = 13.7983[/tex]

[tex]t = 14[/tex] --- approximated

Answer:

(x, y, z) =(1, -1,2)

Step-by-step explanation:

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

Answer:

x = 5q - 15

Step-by-step explanation:

[tex]\frac{7}{7q+21}=\frac{x}{5q^{2}-45}\\\\\frac{7}{7(q+3)}=\frac{x}{5 (q^{2} -9)}\\\\frac{1}{q+3}=\frac{x}{5*(q^{2}-3^{2})}\\\\\frac{1}{q+3}=\frac{x}{5(q+3)(q-3)}\\\\\frac{1}{q+3}*5*(q+3)(q-3)=x\\\\5(q-3)=x\\\\x= 5q-15[/tex]

Answer:

9,16,25,36 neither, 24,18,12 arithmetic, 500,100,20 ,4 geometric

Step-by-step explanation:

1. has no common number

2. goes down by 6 each time

3. is divided by 5 each time

Answer:

2.5 kg

Step-by-step explanation:

2.451

Find the number in the tenth place 4 and look one place to the right for the rounding digit 5.

Round up if this number is greater than or equal to 5 and round down if it is less than 5.

Answer:

Step-by-step explanation:

Answer:

PART A

Given:

f(x) = 0.69(1.03)x

To find:

If the price of the product is increasing or decreasing and by what percentage

Steps:

we know the formula to find the price of Product A per year, so

f(1) = 0.69 * 1.03 * 1

Price = $0.7107

f(2) = 0.69 * 1.03 * 2

Price = $1.4214

Here the Price of Product after 2 years is greater than the price of Product after one year. So the price of the product A is increasing.

Now to find percentage increase,

Percentage increase = [tex]\frac{FV-SV}{SV}*100[/tex]        (FV = final value, SV = starting value)

Percentage increase = [tex]\frac{1.4214 - 0.7107}{0.7107}*100[/tex]

Percentage increase = [tex]\frac{0.7107}{0.7107}*100[/tex]

Percentage increase = 100 %

Therefore, the percentage increase of Product A is 100%

PART B

Given:

Price of product B in 1st year = $10,100

Price of product B in 2nd year = $10,201

Price of product B in 3rd year = $10,303.01

Price of product B in 4th year = $10,406.04

To find:

Which product recorded a greater percentage change over the previous year

Steps:

We need to find the percentage change of Product B and Product A of each year. We know that the percentage change of product A is 100 % for each year, so we only need to calculate for product B

PC of product B from 1st to 2nd year = [tex]\frac{10,201-10,100}{10,100}*100[/tex]

                                                             = [tex]\frac{101}{10,100}*100[/tex]

                                                             = 0.01 * 100

                                                             = 1 %

PC of product B from 2nd to 3rd year = [tex]\frac{10,303.01-10,201}{10,201} *100[/tex]

                                                              = 1%

PC of product B from 3rd to 4th year [tex]=\frac{10,406.04-10,303.01}{10,303.01}*100[/tex]

                                                              ≈ 1%

So, percentage change of product B is 1% per year

Therefore, Product A has greater percentage change

Happy to help :)

If u need more help, feel free to ask

Answer:

A) The price of product A is increasing by 3% per year.

(B) The product A recorded a greater percentage change in price over the previous year.

Step-by-step explanation:

(A)

The function representing the price, in dollars, of product A after x years is:

FA(x)=0.69*(1.03)x

The function  FA(x)can be written as:

FA(x)=0.69*1+(0.03)x

The function FA(x) is similar to the exponential growth function, y=a(1+r)x .

Here r is the growth rate.

Thus, it can be said that the price of product A is increasing by 3% per year.

(B)

Consider the data of product B for the year 3 and 4.

The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.

Compute the percent price change from year 3 to 4 as follows:

10406.04-10303.01/10303.01*100

which is 0.999%

~1%

The price of product B is increasing by 1% per year.

Thus, the product A recorded a greater percentage change in price over the previous year.

Solution :

Given :

X = the number of boys in a family of four children

Families having four children are chosen randomly.

The gender distribution in the four child family are equally probable.

Thus,

 X                P(X)                                          CDF

0             [tex]^4C_0 (1/2)^{4}[/tex]        = 1/16                     [tex]\frac{1}{16}[/tex]

1               [tex]^4C_1 (1/2)^{4}[/tex]       = 1/4                       [tex]\frac{5}{16}[/tex]

2                [tex]^4C_2 (1/2)^{4}[/tex]      = 3/8                      [tex]\frac{11}{16}[/tex]

3                [tex]^4C_3 (1/2)^{4}[/tex]      = 1/4                       [tex]\frac{15}{16}[/tex]

4                  [tex]^4C_4 (1/2)^{4}[/tex]    = 1/16                      1

Answer:

Step-by-step explanation:

Answer:

0.525 = 52.5%

Step-by-step explanation:

Moment generating function ( Mx(t) ) = ( 4 / 4-t)^3

Reimbursement by Insurer = 70%

Determine the expected reimbursement by insurer for policyholder

 d/dx (Mx(t) ) = d/dt ( 4 / 4-t)^3 = d/dt (1 - t/4 )^-3

                                                 = 3/4 ( 1 - t/4 )^-4 =  3/4

as t → 0

Given that the insurer reimburses 70% = 0.7

expected reimbursement = 0.7 * 3/4  = 0.7 * 0.75 = 0.525

Answer:

Radius = 41

Step-by-step explanation:

Diameter/2=radius

82/2 =41

Answer:

Radius=41

Step-by-step explanation:

Preamble

Diameter=82

Radius=?

Formula

Radius=diameter/2

Radius=82/2

reduce the fraction

82/2=82÷2/2÷2=41/1

therefore radius=41

Answer:

46

Step-by-step explanation:

Just multiply 6 by 7 2/3 to get 46.

Answer:

The answer is 46 bags

Step-by-step explanation:

Have a good summer!!!

9514 1404 393

Answer:

  15 in, 36 in, 39 in

Step-by-step explanation:

The Pythagorean theorem tells us that for short side x, the relation is ...

  (2x +9)² = (2x +6)² +x²

  4x² +36x +81 = 4x² +24x +36 +x²

  x² -12x -45 = 0 . . . . . subtract the left-side expression

  (x -15)(x +3) = 0 . . . . factor

  x = 15 . . . . . . . . . . . the positive value of x that makes a factor zero

The side lengths of the triangle are 15 inches, 36 inches, and 39 inches.

Answer: 0.070

Step-by-step explanation:

The question is asking you to estimate how many students completed the English 101 course.

1. Round 99 and 71 to 100 and 70

2. I am not completely sure but I believe the answer is 0.070?

3. Hope it helps! :)

Answer:

c is answer

Step-by-step explanation:

c is ans because it is simple c only serves the need of questions and satisfy it

Answer:

D) 8

Step-by-step explanation:

Liner pair meaning that the angles have a sum of 180. So you add them together to get the equation 16x+52=180 an16x=128 and then you divide both sides by 16 to get x equal to 8. Hope I helped and post more questions :)

Answer: I don't know but i have the formula.

Step by Step: [tex]A=\frac{1}{2}b h[/tex]

Answer:

9 + 10 = 21

Step-by-step explanation:

9 + 10 = 21

Factor out 9 and 10

9 = 3 · 3   10 = 2 · 5

Next multiply 3 by 2

3 × 2 = 6

Then multiply 3 by 5

3 · 5 = 15

Finally add the products

15 + 6 = 21

Answer:

 x ≠ -5

Step-by-step explanation:

The easiest way is to factor the numerator.

x2 + 9x + 20 = (x + 4)(x + 5)

Then

(x2 + 9x + 20)/(x + 5) = (x + 4)(x + 5) / (x + 5) = x + 4,

with the restriction that x ≠ -5

x(x-1)(x+1)(x²+1)=0

Hope it helps you

Answer:

Due to the higher z-score, the regional campus had the more successful year in student recruitment.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The main campus incoming class has a mean of 3,507 and a standard deviation of 375. There were 3,838 incoming students on the main campus.

We have to find Z, considering [tex]X = 3838, \mu = 3507, \sigma = 375[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3838 - 3508}{375}[/tex]

[tex]Z = 0.88[/tex]

Regional campus incoming class has a mean of 740 and a standard deviation of 114. 848 students on the regional campus.

We have to find Z when [tex]X = 848, \mu = 740, \sigma = 114[/tex].

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{848 - 740}{114}[/tex]

[tex]Z = 0.95[/tex]

Which had the more successful year in student recruitment based on z scores?

Due to the higher z-score, the regional campus had the more successful year in student recruitment.

Explanation:

Perimeter is simply the sum of all the edges. The same way 10 can be made of 4+6 or 3+7, the perimeter can be made by many combinations. if you know the 2 must equal 24cm, then we can create numerous combinations.

Answer:

A

Step-by-step explanation:

The product is opposite of the integer

For example

2 * -1 = -2

Answer: K941,200,000

Step-by-step explanation:

From the question, we are to calculate the amount of earning that PNG can make in a year in cocoa export of 400 000 tonnes at K2 353 per tonne.

This will be:

= Number of tonnes × Amount per ton

= 400000 × k2353

= K941,200,000

Therefore, the answer is K941,200,000

Answer:

p > 9

Step-by-step explanation:

First let's note down-

George- has 23$

Total cost of m+p= more than $14

Second, let's subtract 23 and 14 to get what the glue costs.

23 - 14 = 9

So now we can cross out choice A and D.

Third, now earlier I said  more than $14, this is the key part to find what we are going to choose.

more than = >

now we just plug in the variable,

p > 9

Hope this helps!

Please reach out to me if you still don't understand :)