Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets

Answer:

After five years beyond the initial 20-year stretch, the population of this small community will be 4268.

Step-by-step explanation:

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

The representation of the exponential function is:

p = aeᵏᵗ

where a and k represent constants.

Taking the natural logarithm on both sides:

In p = In aeᵏᵗ

In p = In a + In eᵏᵗ

In p = In a + kt

In p = kt + In a.

We can apply linear regression to model the relationship between In p and t, thereby determining the values of k and In a.

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601

In p = kt + In a.

y = mx + b

Here m corresponds to k and b is In a

By conducting a linear regression on the transformed linear relationship among In p and t and creating a graph of the variables, we derive the regression equation:

y = 0.151x + 4.584

The first image illustrates the equations needed for estimating the parameters of linear regression.

The second image displays the regression calculations alongside the graph of In p versus t.

By comparing

y = 0.151x + 4.584

to

In p = kt + In a.

y = In p

k = 0.151

x = t

In a = 4.584

a = 97.905

Thus, the exponential relationship between p and t is formulated as:

p = 97.905 e⁰•¹⁵¹ᵗ

In order to forecast the population for 5 years ahead from the 20-year mark, we need to find p at t=25 years.

0.151 × 25 = 3.775

p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41, which rounds down to 4268.

Hope this assists!!!

Answer:

17/4 kg

Step-by-step explanation:

Sunita initially has = 10kg of grapes

Amount distributed:

To Reena =3 1/2 kg

7/2 kg

To Anita =2 1/4 kg

9/4 kg

Total grapes given away

7/2+9/4

(14+9)/4

23/4 kg

The remaining grapes after distribution = Total grapes first minus grapes given away

10/1 - 23/4

(40-23)/4

= 17/4 or 4 1/4

Thus, she retains 17/4 kg of grapes

An inverse function will also qualify as a function if the original is a One-to-One function. This means that each y value corresponds to exactly one x value, thus ensuring that the inverse remains a function.

The function shown in option C meets this criteria, as all x values and y values are distinct. Therefore, the inverse of the function in option C will also be a functional relation.

In contrast, other options have repeated y values, indicating they do not exhibit the one-to-one characteristic.

Hence, the correct answer is option C

By expressing the equation in its standard format, we have: ax^2 + bx + c = 0. First, we expand (x + 15)(x) = 100 to get x^2 + 15x - 100 = 0. Next, from (x + 20)(x - 5) = 0, we find the solutions to be x = -20 and x = 5. Hence, the accurate choice is option B. We discard x = -20 since it is not a valid solution.

Answer:

The correct statements are options 1 (E F + F G > E G), 2 (E G + F G > E F), and 5 (E G + E F < F G).

Step-by-step explanation:

We have triangle EFG.

For any triangle with sides a, b, and c, these inequalities hold:

Specifically for triangle EFG:

• 
• 
• 

Thus, the true statements are options 1, 2, and 5.

Statements 3 and 4 are incorrect.