Evaluate ƒ(x) when x = -10

16
No solution
-7
-24

PART A) the initial value of the function is 150 at 0 weeks, that means that there are still 150 songs to be downloaded at the beginning.
The rate of change is -30 songs each week, that is because the amount of songs left to be downloaded decrease by 30 each week.

PART B:
lets use 2 points of the graph p1(0, 150), p2(1, 120)
calculate the slope:
m = (y2- y1)/(x2 - x1) = (120 - 150)/(1 - 0)
m = -30
and now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 150 = -30(x - 0)
y = -30x + 150

The slope is -30/1 or -30

The equation is y = -30x + 150

Solving this problem is just pretty straight forward. All we simply have to do is to plug in the value of t (in days) in the function, solve then we get the number of susceptible people.

A. At the beginning of the epidemic
t = 0

f(x) = 15000 e-^(0.05 * 0)

f(x) = 15000

B. After 14 days

t= 14

f(x) = 15000 e-^(0.05 * 14)

f(x) = 7,448.78 = 7,449

C. After 21 days

t = 21

f(x) = 15000 e-^(0.05 * 21)

f(x) = 5,249

D. After 5 weeks

t = 5 * 7 = 35

f(x) = 15000 e-^(0.05 * 35)

f(x) = 2,606.61 = 2607

To find the number of susceptible people during an epidemic at various time intervals, we apply the given exponential function for t=0, 14, 21, and 35 days. This yields 15,000 susceptible individuals at the start, approximately 7439 after 14 days, about 5141 after 21 days, and around 2430 after 5 weeks.

The student asks about the number of susceptible people during an epidemic at various points in time, given by the function f(t) = 15000e-0.05t, where t is time in days. To find the number of susceptible people, we substitute the given times into the function:

This exponential function represents the number of people who remain susceptible as the epidemic progresses, assuming no one gains immunity other than through infection (no vaccination, and disease-induced immunity only).

Answer:

A, C, and E

Step-by-step explanation:

The exterior angles are ∠2, ∠3, ∠4 and ∠6.

The correct options are E, F, A, and C.

Based on the information provided, we can identify the exterior angles by their positions outside the triangle. From the given options, the exterior angles are: ∠2, ∠3, ∠4 and ∠6.

Exterior angles are formed by extending one side of the triangle outward, and they lie outside the triangle itself. In this case, angles ∠1 and ∠5 are interior angles because they are inside the triangle, while angles ∠2, ∠3, ∠4 and ∠6 are exterior angles as they extend beyond the sides of the triangle.

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8 1/4 = 33/4

33/4 / 3/4 =

33/4 * 4/3 = 132/12

132/12 = 11

 he will have 11 servings

Answer: 11 servings

Step-by-step explanation:

To get the number of servings, all we need to do is divide 8 1/4 by 3/4

converting 8 1/4 to improper fraction will yield 33/4

8 1/4 ÷ 3/4

=33/4 ÷ 3/4

= 33/4 ÷ 4/3

The 4 at the numerator will cancel the 4 at the denominator. we will be left with;

=33/3 =11

Therefore, there will be 11 servings.

Answer:

you just  need to make your math to right a little more math

Step-by-step explanation:

The distance between the two soccer players positioned at (-7, 5) and (7, 5) in a Cartesian coordinate system is 14 units, calculated using the difference in x-coordinates.

The question is focused on understanding the Cartesian coordinate system and calculating distances between points on this grid. To determine the distance between two points on a soccer field, one can apply the distance formula derived from the Pythagorean theorem. If the positions of the two players are (-7, 5) and (7, 5), the players are aligned horizontally and share the same y-coordinate. Therefore, their distance apart is simply the difference in their x-coordinates, which can be calculated by subtracting the x-coordinate of player 1 from that of player 2 or vice versa. The result is the absolute value of the difference, |7 - (-7)| = 14 units, which is their horizontal separation on the field.

The measure of arc arc [tex]AC[/tex] will be [tex]90^0[/tex] .

Arc is the part or segment of the circumference of a circle which is drawn between two points and an angle. And length of arc is known as arc length.

i.e.  Arc length [tex](L)=\frac{\theta}{r}[/tex]

And "The measure of an arc is equal to the measure of the central angle that intercepts it".

We have,

[tex]\theta = 90^0[/tex]

So,

From the above mentioned statement i.e.,

"The measure of an arc is equal to the measure of the central angle that intercepts it".

We can say that,

The measure of arc [tex]AC=90^0[/tex]

Hence, we can say that the measure of arc arc [tex]AC[/tex] is [tex]90^0[/tex].

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60* 2/3 = 60/1 x 2/3 =120/3

 120/3 = 40

he spent $40

Answer:

The function is a growth function when [tex]r>0[/tex].

Step-by-step explanation:

We are given,

The exponential function is [tex]A(x)=P(1+r)^x[/tex], where P= initial value and r= rate of change.

Now, we know,

1. The function is an exponential growth if their is positive rate of change.

2. The function is an exponential decay if their is negative rate of change.

Since, it is required to make the function a growth function.

We need the positive rate of change for the function A(x),

That is, [tex]r>0[/tex]

Hence, the function is a growth function when [tex]r>0[/tex].

The next term for the given series will be equal to a(5)  = -4.

When there is a constant between the two successive numbers in the series then it is called a geometric series.

This is a geometric sequence with a common ratio of -1/3 and an initial term of -324.  Any geometric sequence can be expressed as:

a(n)   =    [tex]ar^{n-1}[/tex], in this case a=-324 and r=-1/3 so

a(n)   =  -324(-1/3)[tex].^{n-1}[/tex]  so the 5th term will be

a(5)   =  -324(-1/3)⁴

a(5)   =  -324/81

a(5)   =   -4

Therefore the next term for the given series will be equal to a(5)  = -4.

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Answer:

B is the lowest price per ounce

Step-by-step explanation:

choice A is 14 cents per ounce, and choice B  is 12 cents per ounce.

153/9 = x/13

153 x 13 = 1989

1989/9=221

x = 221

The surface area of the right cone with a radius of 8 and slant height of 15 is,

SA = 184π units³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Radius of cone = 8

Slant height = 15

Since, The surface area of the right cone is,

SA = πr (r + l)

where,

r is the radius of the cone

l is the slant height of the cone.

Hence, We get;

SA = π × 8 (8 + 15)

SA =  π × 184

SA = 184π units³

Thus, The surface area of the right cone with a radius of 8 and slant height of 15 is,

SA = 184π units³

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3.2362

To solve this, we are going to use the trig identity: [tex]csc(x)=\frac{1}{sin(x)}[/tex]

We know that our problem that [tex]sin(x)=0.3090[/tex], so let's replace the value in our identity:

[tex]csc(x)=\frac{1}{sin(x)}[/tex]

[tex]csc(x)=\frac{1}{0.3090}[/tex]

[tex]csc(x)=3.2362[/tex]

We can conclude that the approximate value of [tex]csc(x)[/tex] is 3.2362.

The approximate value of csc(x) is 3.2362

since  sin x = 0.3090

Therefore,

1 / sin x  = csc x

Then

csc x = 1 / 0.3090

csc x = 3.23624595469

csc x ≈ 3.2362

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