Evaluate the function.

Given:

The function is:

[tex]f(x)=2.9646(1.0170)^x[/tex]

To find:

Rewrite the exponential equation given above using base e.

Solution:

The exponential models is:

[tex]f(x)=P(1+r)^x[/tex]         ...(i)

Where P is initial values, r is the rate of interest and x is the time period.

The exponential models using base e is:

[tex]f(t)=Pe^{rt}[/tex]           ...(ii)

Where, P is initial values, r is the rate of interest and t is the time period.

The given function is:

[tex]f(x)=2.9646(1.0170)^x[/tex]

It can be written as:

[tex]f(x)=2.9646(1+0.0170)^x[/tex]        ...(iii)

On comparing (i) and (iii), we get

[tex]P=2.9646[/tex]

[tex]r=0.0170[/tex]

Putting [tex]P=2.9646[/tex] and [tex]r=0.0170[/tex] in (ii), we get

[tex]f(t)=2.9646e^{0.0170t}[/tex]

Therefore, the correct option is D.

Answer:

n=10.

Step-by-step explanation:

[tex]\frac{45}{n^{2}-3n-4 }[/tex] - [tex]\frac{3}{n-4}[/tex] = [tex]\frac{2}{n+1 }[/tex]

[tex]\frac{45}{n^{2}-3n-4 }[/tex] -  [tex]\frac{3(n+1)}{(n+1)(n-4)}[/tex] = [tex]\frac{2(n-4)}{(n+1)(n-4) }[/tex]

[tex]\frac{45}{n^{2}-3n-4 }[/tex] -  [tex]\frac{3n+3}{n^{2} -3x-4}[/tex] = [tex]\frac{2n-8}{n^{2} -3x-4 }[/tex]

45-3n-3=2n-8

45-3+8=5n

n=50/5=10

Answer:

120in. ezy

Step-by-step explanation:

Answer:

48 square. Units

Step-by-step explanation:

Given that :

Triangle and rectangle have the same base, b and height, h

AREA of triangle = 0.5 * base * height

48 = 0.5 bh

bh = 0.5 * 48

bh = 96

Total area of section 1 & 2 :

bh = area of triangle + x

X = bh - area of triangle

X = 96 - 48

Area of se tion 1&2 = 48

Answer:

50

Step-by-step explanation:

To answer this we need to use the PEMDAS strategy, first solve any questions in parentheses, next solve all multiplication and division problems from left to right. Next, solve all addition and subtraction problems from left to right.

36 + (12 - 8) + 2 × 5​

36 + 4 + 2 x 5

36 + 4 + 10

40 + 10

50

Answer:

[tex]50[/tex]

Step-by-step explanation:

Follow the PEMDAS order of operations:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction.

Calculate the Parentheses- (12-8)

This will equal 4.

[tex]36+4+2x5[/tex]

(x= times)

Multiply and divide, left to right.

[tex]2x5=10[/tex]

[tex]36+4+10=50[/tex]

Answer:

4y² + 5y - 3

roots are:  (-5 ± [tex]\sqrt{73}[/tex]) / 8

Step-by-step explanation:

8y + 4y² - 3y - 3

4y² + 5y - 3

roots are:  (-5 ± [tex]\sqrt{73}[/tex]) / 8

Answer:

4^2 + 5 − 3

Step-by-step explanation:

you multiply those numbers, add these and those, combine these and that. and BOOM. you have your answer UwU

Answer:

Step-by-step explanation:

a = 1

b = 6

c = 6

axis of symmetry =  -(6) / 2*1

= -6 /2

= -3

vertex = ( -3,  -3 )   :)

Answer:

Step-by-step explanation:

a = 1 because if is not written what x^2 multiply, it means that x^2 multiply 1

b = 6  b is the term that multiply x

c = 6  c is the therm without x

axis of symetry = -6/2 = -3

the x of vertex is same of the axis of the symmetry so it is -3

if we subistute x with this value we can find the y of vertex

(-3)^2 + 6(-3) + 6 = 9 -18 + 6 = -3

Vertex (-3, -3)

Answer: 2 units long

Answer:

444 :) (angel number, haha)

Step-by-step explanation:

it needs 74 times 2 mm which is 148 I think, which will also be the length since 148 is 2 times more than 74

so it's : 74 + 74 + 148 + 148 which is basically just 148 times three, so the answer is 444!

Son el B el C y el E

Answer:0.4813042802

Step-by-step explanation:

Answer:

z = 8

Step-by-step explanation:

All angles inside a triangle add up to 180 so:

90 + 40 + 5z + 10 = 180

5z + 140 = 180

5z = 40

z = 8

Answer:

Is there a picture?

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

9514 1404 393

Answer:

  ∠CBE = 59°

Step-by-step explanation:

Adjacent angles of a parallelogram are supplementary.

  ∠BCD +∠CDE = 180°

  ∠BCD +∠CDB +∠BDE = 180°

  (21x -5) +34 +(4x+1) = 180

  25x +30 = 180

  25x = 150

  x = 6

∠CBE = ∠CDE = 34 +(4x +1) = 4x +35 = 4(6) +35

∠CBE = 59°

Hi there!

[tex]\large\boxed{\text{Average rate = 1}}[/tex]

We can calculate the average rate of change using the following:

[tex]ARC = \frac{f(b)-f(a)}{b-a}[/tex]

Thus, we can plug in the endpoints of -4 and -2. Find the corresponding y-values for these x-values:

f(-2) = -(-2)² - 5(-2) + 8  = -4 + 10 + 8 = 14

f(-4) = -(-4)² - 5(-4) + 8 = -16 + 20 + 8 = 12

Plug in the solved for values into the ARC equation:

[tex]ARC(slope) = \frac{14-12}{-2(-4)} = \frac{2}{2} = 1[/tex]

Answer:

The National Health and Nutrition Examination Survey reported that the proportion of U.S. adults with high blood pressure is 0.3. A sample of 38 U.S. adults is chosen. a. Is it appropriate to use the normal approximation

Step-by-step explanation:

Mean number of tickets sold by boys =

Total Number of tickets sold / Number of boys

=

[tex] \frac{(1 \times 4) + (2 \times 3) + (4 \times 1) + (12 \times 1) + (13 \times 1) + (15 \times 3) + (14 \times 2}{4 + 3 + 1 + 1 + 1 + 3 + 2} \\ = \frac{4 + 6 + 4 + 12 + 13 + 45 + 32}{15} \\ = \frac{116}{15} \\ = 7.73(nearest \: hundredth)[/tex]

Answer:

B should be the correct answer.

Step-by-step explanation:

15 + 11 + 9 + 12 + 6 + 11 = 64

64<90

Answer:

15 red out of 64 total markers

15 / 64 = .234375

90 x .234375 = 21.09375

so she will pick a red marker about 21 times

Step-by-step explanation:

Answer:

y = 6

Step-by-step explanation:

y varies directly with x

y = k*x

Where,

k = constant of variation

Find y when x = 2 and constant of variation,k =3

y = k*x

y = 3 * 2

y = 6

Check:

if y = 6 and x = 2, find k

y = k*x

6 = k*2

6 = 2k

k = 6/2

k = 3

Answer:

the second one

Step-by-step explanation:

Answer:

15 + 4x = 40

Step-by-step explanation:

To construct this equation, we'll list all the values we will include first.

The total fee equals $40, so we'll put 40 on one side of the equation.

On the other side, we have to put the values that make up the total. The fee is made with the project cost plus the hourly rate. The first part of this is the beginning cost, $15. Added to this is the hourly cost, $4, times the number of hours spent. So, the other side of the equation is 15 (the starting cost) plus 4 (the rate) times x (the unknown number of hours).

So, our equation is 15 + 4x = 40.

Good luck ^^

Answer:

13:5

Step-by-step explanation:

Messy played 65 minutes while the substitute played 25 minutes. This ratio is 65:25 and can be simplified to 13:5.

Answer:

24,150

Step-by-step explanation:

7% of 345,000 = 24,150

Answer:

y = 2x

Step-by-step explanation:

Total distance walked = y

Number of trips = x

Lily walks 2 kilometers during each trip to school

Equation that shows the

relationship between the number of trips x and the total distance walked y:

y = 2x

For example, if the number of trips (x) is 3

Total distance walked,y = 2(3)

y = 6 kilometers

Answer:

4xy

Step-by-step explanation:

(x+y) (x+y) - (x-y) (x-y)​

(x² + xy + xy + y²) - (x² - xy - xy + y²)

(x² + 2xy + y²) - (x² - 2xy + y²)

x² + 2xy + y² - x² + 2xy - y²

x² - x² + 2xy + 2xy + y² - y²

4xy

Answer:

that could literally be anything, as long as the first sum is greater then the second.

example;

(2+4) (3+5) - (6+1) (5+2)

(or, 6+8 = 14, 7+7 = 14, 14 - 14 = 0)

hope this helped :)

Answer:

X equals -0.5 in decimal and in fraction it would be negative one half. Im not 100% sure of the answer also I dont know what angle that is...