Help with this exponential function!

A species of animal is discovered on an island. Suppose that the population size P (t) of the species can be modeled by the following function, where time t is measured in years.

Find the population size after 6 years and after 8 years.
Round your answers to the nearest whole number as necessary.

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{67 + x = 90^\circ}[/tex]

[tex]\mathsf{x+ 67 = 90^\circ}[/tex]

[tex]\large\textsf{SUBTRACT 67 to BOTH SIDES}[/tex]

[tex]\mathsf{x + 67 - 67 = 90^\circ - 67}[/tex]

[tex]\large\textsf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = 90 - 67}[/tex]

[tex]\mathsf{x = 23}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{x = 23}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

In this problem, we're given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.

Remember! SOH-CAH-TOA

We are given a 26 degree angle, looking from which we have the adjacent side and the hypotenuse. As such, we should use the cosine function.

cos(26) = x / 69

x = cos(26) * 69

x = 62.0168

x = 62.0

Hope this helps!

Step-by-step explanation:

Answer: 26

Step-by-step explanation:

to solve this series, we should find a pattern first.

if we look at the differences of each number, we can see that

4-1=3

8-4=4

13-8=5

19-13=6

to find the next number in the series, it would be 7 more than 19, since are counting upwards from 3.

Answer: 26

1 to 4 is 3

4 to 8 is 4

8 to 13 is 5

13 to 19 is 6

the next number should be 26

Answer:

c. a[b(b + 6)+7(a²-2)]

Step-by-step explanation:

look at the pic

The equivalent expression of the expression ab² + 6ab + 7a³ - 14a is

C. a [b (b + 6) + 7 (a² - 2)]

Option C is the correct answer.

We have,

To find the expression that is equivalent to ab² + 6ab + 7a³ - 14a, we can factor out common terms from the given expression.

The common terms in the expression are "a" and "(b + 7)".

Step 1:

Factor out "a" from the expression:

ab² + 6ab + 7a³ - 14a = a(b² + 6b + 7a² - 14)

Step 2:

Factor the quadratic expression inside the parenthesis:

b² + 6b can be factored as b(b + 6)

7a² - 14 can be factored as 7(a² - 2)

Step 3:

Putting it all together, the equivalent expression is:

a [b (b + 6) + 7 (a² - 2)]

Now let's check which option matches this expression:

a. (b + 7)(b + 6)(a² - 2) - Not equivalent

b. b(b + 6) + 7(a^2 - 2) - Not equivalent

c. a[b(b + 6) + 7(a² - 2)] - Equivalent

d. a[(b + 6)(b + 7a² - 14)] -Not equivalent

Thus,

The equivalent expression is

C. a [b (b + 6) + 7 (a² - 2)]

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Answer: Options 2, 3, 6

Step-by-step explanation:

Option 2: Correct because both sides are multiplied by 6.

Option 3: Correct because the distributive property is used on the left.

Option 6: Correct because 4 is subtracted from both sides.

The answer to the question has to be filled into the blank as

This is described as the likelihood of the test correctly rejecting the null hypothesis on the basis that the alternative hypothesis is correct.

This question requires us to fill in the blank with the details that we have been given.

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Answer:

Step-by-step explanation:

given:f(x)=x/x+6

let, f(x)=y

y=x/x+6

interchanging the roles of x and y

or, x=y/y+6

or, xy+6x=y

therefore,inverse of f is xy+6x

The dimensions of the circular cylinder of maximum volume inscribed in  sphere is r = 20.4 cm , h = 28.86 cm.

A sphere is a three dimensional round shaped figure , It has no vertices and the distance form the centre to any point on the sphere is same.

It is given that

A right circular cylinder is inscribed in a sphere

The circular cylinder has the maximum volume

Radius of the sphere is 25 cm.

Dimensions of the cylinder = ?

As it is a right cylinder.

The Pythagoras theorem can be applied

r² + (h/2)² = 25²

r² = 625 - h²/4

volume of the cylinder

=  πh(625 - h²/4)

= π(625 h - h³/4)

As the volume is maximum ,

so the derivative of the expression = 0

π(625 - 3h²/4) = 0

so h =  50 /√ 3

so r² = 625 - 2500 / (3 *4 )

r = 20.4 cm

h = 28.86 cm

Therefore the dimensions of the circular cylinder of maximum volume inscribed in a sphere is r = 20.4 cm , h = 28.86 cm.

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The lower class boundary for the third class is 0.50.

The lower class boundary of a class can be determined by calculating the average the upper limit of the previous class and the lower limit of the given class.

The lower class boundary = ( 1296 - 1295) / 2 = 0.50

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How to determine whether or not the paired t test is appropriate for a two-sample hypothesis is: The  two samples are independent.

Two-sample hypothesis can be defined as  a test that is conducted on two samples  so as to determine whether the two samples are independent.

A  paired t-test is appropriate when the scores are of  equal subject or  equal variances.

Therefore how to determine whether or not the paired t test is appropriate for a two-sample hypothesis is: The  two samples are independent.

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Answer:

the area of a square garden 3136cm what is the length of one side

Answer:

12

Step-by-step explanation:

First solve the inside brackets.

[tex]3[6-(+2)]=3[6-2]\\\\=18-6\\\\=12[/tex]

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

The amount or the strength of force is called its magnitude.

Step-by-step explanation:

The amount or the strength of force is named magnitude.

Force is that the push or pull on an object with mass that causes it to alter its velocity. Force is an external agent capable of adjusting the state of rest or motion of a selected body. it's a magnitude and a direction.

The term which is true is magnitude. The magnitude of a force is expressed within the SI unit of force called Newton. 1 Newton is that the force which might make an object of 1 kilogram mass to  at a speed of 1 meter per second. Magnitude is essentially the most extent of size and also the direction of an object. Magnitude is employed as a typical think about vector and scalar quantities. Magnitude of earthquake is measured by Richter scale.

Hence the number or the strength of force is named its magnitude.

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The perimeter of the hexagon is 180 ft.

The area of the hexagon is 2338.3 ft

The perimeter of the polygon can be found as follows:

The polygon is a regular hexagon.

Therefore,

perimeter of the hexagon = 30 × 6 = 180 ft

Area of the hexagon = 3√3 / 2 × s²

where

Therefore,

Area of the hexagon = 3√3 / 2 × 30²

Area of the hexagon =  3√3 / 2 × 900

Area of the hexagon = 450 × 3√3

Area of the hexagon = 2338.26859022

Area of the hexagon = 2338.3 ft

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Answer:

y = 20°

x = 35°

Explanation:

Equation's:

   1) 2y + x + 105° = 180°

   2) 3x + x + 2y = 180°

Make y subject in equation 2

3x + x + 2y = 180

4x + 2y = 180

2y = 180 - 4x

y = 90 - 2x

Insert this into equation 1

2(90 - 2x) + x + 105° = 180°

180 - 4x + x + 105 = 180

-3x = -105

x = 35°

Find value of y

y = 90 - 2x

y = 90 - 2(35)

y = 20°

Using the normal distribution, it is found that there is a 0.3192 = 31.92% probability that 20 customers will wait an average of less than 21 minutes to be seated.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The parameters for this problem are given as follows:

[tex]\mu = 23.8, \sigma = 6, n = 20, s = \frac{6}{\sqrt{20}} = 1.3416[/tex]

The probability that 20 customers will wait an average of less than 21 minutes to be seated is the p-value of Z when X = 21, hence:

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

By the Central Limit Theorem:

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

[tex]Z = \frac{21 - 23.8}{6}[/tex]

Z = -0.47

Z = -0.47 has a p-value of 0.3192.

0.3192 = 31.92% probability that 20 customers will wait an average of less than 21 minutes to be seated.

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Answer:

[tex]1024x^{40}[/tex]

Step-by-step explanation:

So the first step is to add like terms since you can simplify the numerator by adding the two values sine they have the same variable and degree.

Add like terms:

[tex][\frac{8x^9}{2x}]^5[/tex]

Divide by 2x (divide coefficient by 2, subtract coefficient degrees)

[tex][4x^8]^5[/tex]

Multiply exponents and raise 4 to the power of 5

[tex]1024x^{40}[/tex]

The reason you multiply exponents is because you can think about it like this:

(4 * x * x * x * x * x * x * x * x) (this has one 4 and 8 x's because x is raised to the power of 8. Now if you do that 5 times which is what the exponent is doing you're going to have 40 x's and 8 4's. So it's essentially

(4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x). If you group like terms you'll get (4 * 4 * 4 * 4 * 4) *  (x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x). Which simplifies to 4^5 * x ^ (8 * 5) which further simplifies to the answer 1024x^40

Answer:

1024x^40

Step-by-step explanation:

Apply exponent rule: (a/b)^c = a^c / b^c = (5x^9 + 3x^9)^5 / (2x)^5

Simplify:

(5x^9 + 3x^9)^5: 32768x^45

= 32768x^45 / (2x)^5

Simplify:

(2x)^5: 32x^5

= 32768x^45 / 32x^5

Divide the numbers: 32768 / 32 = 1024

= 1024x^45 / x^5

Apply exponent rule: x^a / x^b = x^a - b

x^45 / x^5 = x^45 - 5

= 1024x^45 - 5

Subtract the numbers: 45 - 5 = 40

= 1024x^40

The amount of pounds of chlorine needed is 62. 5 pounds. Option D

WE have the perimeter of a rectangle to be;

Volume = l × h × w

L = length = 50 meters

w = width = 25 meters

height = 3 meters

Substitute into the formula

Volume = [tex]50[/tex] × [tex]25[/tex] × [tex]3[/tex]

Volume = [tex]3750[/tex] cubic meters

If 0. 25 pounds of chlorine is in 15 cubic meters of water

x pounds would be 3750 cubic meters

Cross multiply

0. 25 × 3750 = 15x

937. 5 = 15x

x = [tex]\frac{937. 5}{15}[/tex]

x = 62. 5 pounds

Thus, the amount of pounds of chlorine needed is 62. 5 pounds. Option D

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The solution to the expression [tex]3(5-\frac{1}{6} x)+\frac{1}{8}(32+6x)+7.3x -5*0.05x[/tex] is 27.03

An equation is an expression that shows the relationship between two or more variables and numbers.

The expression is given as:

[tex]3(5-\frac{1}{6} x)+\frac{1}{8}(32+6x)+7.3x -5*0.05x\\\\When \ x=1\frac{1}{10}=\frac{11}{10} \\\\=3(5-\frac{1}{6} *\frac{11}{10} )+\frac{1}{8}(32+6(\frac{11}{10} ))+7.3(\frac{11}{10} ) -5*0.05(\frac{11}{10} )\\\\=27.03[/tex]

The solution to the expression [tex]3(5-\frac{1}{6} x)+\frac{1}{8}(32+6x)+7.3x -5*0.05x[/tex] is 27.03

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The numeric value of the expression for [tex]x = 1\frac{1}{10} = \frac{11}{10} = 1.1[/tex] is: 27.03.

To find the numeric value of an expression, we replace all instances of x by the desired value.

In this problem, the expression is:

[tex]3\left(5 - \frac{x}{6}\right) + \frac{1}{8}(32 + 6x) + 7.3x - 5(0.05x)[/tex]

The value of x is:

[tex]1\frac{1}{10} = \frac{11}{10} = 1.1[/tex]

Hence the numeric value of the expression is:

[tex]3\left(5 - \frac{1.1}{6}\right) + \frac{1}{8}(32 + 6(1.1)) + 7.3(1.1) - 5(0.05(1.1)) = 27.03[/tex]

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Answer:

slope = -2

Step-by-step explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. Since the given equation is not in the exact slope-intercept form, we need to rearrange it to identify the slope.

y + 2x = 5                         <----- Given equation

y = -2x + 5                       <----- Subtract 2x from both sides

Now, we can see that in the "m" position, there is a value of -2. This makes the slope = -2.

Answer:

[tex]82 = 525y2 \times 6112 =[/tex]

Answer:

b

Step-by-step explanation:

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Find the point-slope equation of the line, with the info given

[tex]\Large\maltese\underline{\textsf{This problem has been solved}}[/tex]

Formula used, [tex]\bf y-y1=m(x-x1)[/tex]

[tex]\bf y-5=13(x-0)}[/tex] | result

[tex]\rule{300}{1.7}[/tex]

[tex]\boxed{\bf aesthetic\not101}}[/tex]

Answer:

[tex]\huge\boxed{\sf y = -2x - 3}[/tex]

Step-by-step explanation:

m = -2

y = mx + c

(x,y) = (-5,7)

So, x = -5, y = 7

To find c, Put the values of x, y and m in the slope-intercept form.

7 = (-2)(-5) + c

7 = 10 + c

7 - 10 = c

-3 = c

c = -3

Now, put the values of m and c in the slope intercept form.

y = -2x - 3

[tex]\rule[225]{225}{2}[/tex]

The coordinates of B is (-2, 3).

In geometry, translation is the movement of a point or shape from one position to another.

Here, The translation from ΔABC to ΔA'B'C' is (x, y) → (x + a, y + b)

Now, given coordinate

A ≡ (5, 1)      ⇒       A' ≡ (6, -2)

                             A' ≡ (1+5, 1 - 3)

                      On comparing this coordinate with translation coordinate

                       (x + a, y + b), we get

                          a = 1 and b = -3

Now translation coordinates is (x + 1, y - 3),

Now, Another coordinate;

B' ≡ (-1, 0)                   and the coordinate of B ≡ (x, y)

B' ≡ (-2+1, 3-3)

On comparing this coordinate with translation coordinate (x + 1, y - 3), we get

x = -2 and y = 3

Thus, the coordinates of B is (-2, 3).

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Answer:

710

Step-by-step explanation:

Numeration of pages goes from 1.

9 pages with 1-digit numbers, from 1 to 9.

90 pages with 2-digit numbers, from 10 to 99.

So,  2*90 + 9 = 189 digits are just used to numerate 9 + 90 = 99 pages.

The rest of numbers are 3-digit.

   [tex]\frac{(2022-189)}{3}[/tex] = 611  pages with 3-digit numbers.

Total pages = 9 + 90 + 611 = 710.

The effective elements to include in the introductions are statement of the topic, a relevant anecdote and a surprising fact about the topic. Therefore the option 1st, 2nd and 6th options are correct.

Introduction is the starting line or the opening hook or portion that attracts the readers attention which carries the relevant background of the information.

It is the statement which represents the main point of the following argument or the paragraphs.

There are many elements that included in the introductory part some of them are as follows:-

Therefore the option 1st, 2nd and 6th options are correct.

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Answer:

The first two, the fourth, and the last one are correct

Step-by-step explanation:

it just is.... so yeah

Hi !

[tex]f(x) = \frac{4}{x - 9} [/tex]

[tex]x-9[/tex] must be different from 0.

[tex]x -9 \ne0 \\ x \ne9[/tex]

[tex] = = > \: D_f=\mathbb{R}-\{9\}[/tex]

Have a nice day ;)

The standard deviation is 3.807.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

Given:

variance= 14.5

standard deviation = √variance

                               = √14.5

                              = 3.807

Hence, the standard deviation is 3.807.

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