Misha’s family bought a large cattle farm. The number of acres of the cattle farm is the cube of the acres they used to own plus 10 acres. If a represents the number of acres the family used to own, which expression represents the number of acres they own now?

Answer:

The explicit formula of the geometric sequence is:

                   [tex]a_n=4\times 5^{n-1}[/tex]

Step-by-step explanation:

The explicit formula is the expression where the nth term is given in terms of the first term of the sequence.

We know that the explicit formula for a geometric sequence is given by:

       [tex]a_n=(a_1)^{r-1}[/tex]

Here we are given:

The second and fifth terms as: 20 and 2500 respectively.

i.e.

[tex]a_2=20[/tex] and  [tex]a_5=2500[/tex]

i.e.

[tex]ar=20\ and\ ar^4=2500[/tex]

Hence,

[tex]\dfrac{ar}{ar^4}=\dfrac{20}{2500}\\\\\\\dfrac{1}{r^3}=\dfrac{1}{125}\\\\\\(\dfrac{1}{r})^3=(\dfrac{1}{5})^3\\\\\\\dfrac{1}{r}=\dfrac{1}{5}\\\\\\r=5[/tex]

Also,

we have:

[tex]ar=20\\\\i.e.\\\\a\times 5=20\\\\i.e.\ a=4[/tex]

Hence, the explicit formula is given by:

         [tex]a_n=4\times 5^{n-1}[/tex]

Answer:

u didn't provide a chart but the dependent variable is the y axis, or the vertical line

Step-by-step explanation:

It's always the y axis (the vertical line)

Answer:

  Two-point

Step-by-step explanation:

"Orthogonal" lines intersect the horizon at two points. This is an example of 2-point perspective.

The correct option is a. 625.

The total number of outcomes in 4 spins of the spinner can be found by multiplying the number of outcomes in one spin by itself 4 times, resulting in 625 outcomes.

The sample space for 4 spins of the spinner can be calculated by raising the number of outcomes in one spin to the power of the number of spins.

In this case, as there are 5 outcomes on the spinner, the total number of outcomes in 4 spins would be 5^4 = 625.

Therefore, the correct option is a. 625.

Answer:

Hence, the model that best represents the data is:

[tex]y=26.9x-1.3[/tex]

Step-by-step explanation:

We are given a table that  shows the estimated number of lines of code written by computer programmers per hour when x people are working.

We are asked to find which model best represents the data?

So for finding this we will put the value of x in each of the functions and check which hold true that which gives the value of y i.e. f(x) as is given in the table:

We are given 4 functions as:

A)

[tex]y = 47(1.191)^x[/tex]

B)

[tex]y=34\times (1.204)^x[/tex]

C)

[tex]y=26.9x-1.3[/tex]

D)

[tex]y=27x-4[/tex]

We make the table of these values at different values of x.

x                  A                 B                C               D

2              66.66          49.3            52.5           50

4             94.57            71.44           106.3         104  

6             134.14           103.57         160.1          158

8             190.27          150.14          213.9         212

10           269.91           217.64         267.7         266

12           382.85          315.5           321.5          320.

Hence, the function that best represents the data is:

Option C.

y=26.9x-1.3

To calculate the selling price with a 75% markup on a $5.50 item, multiply the original cost by 0.75 to find the markup amount and then add it to the original cost. The final selling price is $9.63.

Calculating the Selling Price with a Markup

To determine the selling price of an item with a 75% markup, follow these steps:

Therefore, the selling price for the item with a 75% markup on an original cost of $5.50 is $9.63.

Final answer:

To evaluate the limit of the given function, substitute the value that t is approaching into the expression. In this case, t is approaching -2. Plugging -2 into the function, we get 0.7647.

Explanation:

To evaluate the limit of the given function, we can substitute the value that t is approaching into the expression. In this case, t is approaching -2. Plugging -2 into the function, we get:

lim t → -2 t^4 - 3 / 2t^2 - 3t + 3 = (-2)^4 - 3 / 2(-2)^2 - 3(-2) + 3 = 16 - 3 / 8 + 6 + 3 = 13 / 17 = 0.7647

Therefore, the limit is approximately 0.7647.

sqrt(32) = 5.66

 so it is in section B

Answer:

section B.

YOUR WELCOME

The required probability of the numbers picked of the first three digits of the mobile number is 0.037.

Given that,
Pick 3 digits (0-9) at random without replacement, and write them in the order picked. what is the probability that you have written the first 3 digits of your phone number? assume there are no repeats of digits in your phone number is to be evaluated.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
From 0 to 9 we have 10 numbers,
For the number to be picked,
There must be no repetition,
So the number of ways to 1 pick 1st number is 10,
The number of ways to pick 2nd number is 9
The number of ways to pick 3rd number is 8
Total number of ways = 10 + 9 + 8 = 27
Now probability, that this three-digit  would be a mobile number,

= 1 / 27
= 0.037

Thus, the required probability of the numbers picked of the first three digits of the mobile number is 0.037.

Learn more about probability here:

brainly.com/question/14290572

#SPJ5

Final answer:

There can be 900,000 unique 6-digit numbers formed using the digits 0-9 with repetitions allowed, considering the first digit cannot be 0.

Explanation:

Calculating 6-Digit Numbers with Repetitions

The question pertains to the number of unique 6-digit combinations that can be made from the digits 0-9 when repetitions are allowed. Since the first digit of a 6-digit number cannot be 0 (as it would make the number a 5-digit number), there are 9 possibilities for the first digit (1-9). For each of the five remaining positions, all 10 digits (0-9) are possibilities because we are allowing repetitions. Therefore, the total number of combinations is calculated by multiplying the possibilities for each digit place.

The solution is as follows: 9 possibilities for the first digit times 10 possibilities for each of the second, third, fourth, fifth, and sixth digits.

9 (first digit) * 10 (second digit) * 10 (third digit) * 10 (fourth digit) * 10 (fifth digit) * 10 (sixth digit) = 900,000 unique 6-digit numbers that can be formed.

Answer:

x-3

Step-by-step explanation:

I believe the problem ask for s which is the standard deviation. We must recall that the formula for z statistic is stated as:

z = (x – x over bar) / s

Where,

z = z statistic = 2.5

x = sample value or sample score = 102

x over bar = the sample mean or sample average  = 100

s = standard deviation = unknown

Rewriting the equation in terms of s:

s = (x – x over bar) / z

Substituting the given values into the equation:

s = (102 – 100) / 2.5

s = 0.8  

Therefore the standard deviation s is 0.8

area of the ceiling = 55 x 55 = 3025 square feet

 3025/275 = 11 cans

Segment AB has slope 0. Segment DE, with midpoints of AC and BC, also has slope 0. Thus, DE is parallel to AB.

To prove that segment DE is parallel to segment AB, we need to show that the slopes of both segments are equal.

The slope of segment AB, denoted as [tex]\( m_{AB} \)[/tex], can be calculated using the coordinates of points A and B:

[tex]\[ m_{AB} = \frac{{y_B - y_A}}{{x_B - x_A}} \][/tex]

Given that point A is at (0, 0) and point B is at [tex]\((x_2, 0)\)[/tex], the slope [tex]\( m_{AB} \)[/tex] is:

[tex]\[ m_{AB} = \frac{{0 - 0}}{{x_2 - 0}} = 0 \][/tex]

Now, let's find the coordinates of points D and E.

Point D lies on segment AC, so it is at the midpoint of segment AC. Therefore, the coordinates of point D, denoted as [tex]\((x_{D}, y_{D})\)[/tex], are the average of the coordinates of points A and C:

[tex]\[ x_{D} = \frac{{x_1 + 0}}{2} = \frac{{x_1}}{2} \][/tex]

[tex]\[ y_{D} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]

Similarly, point E lies on segment BC, so it is at the midpoint of segment BC. Therefore, the coordinates of point E, denoted as [tex]\((x_{E}, y_{E})\)[/tex], are the average of the coordinates of points B and C:

[tex]\[ x_{E} = \frac{{x_1 + x_2}}{2} \][/tex]

[tex]\[ y_{E} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]

Now, let's calculate the slope of segment DE, denoted as [tex]\( m_{DE} \)[/tex]:

[tex]\[ m_{DE} = \frac{{y_{E} - y_{D}}}{{x_{E} - x_{D}}} \][/tex]

Substituting the coordinates of points D and E:

[tex]\[ m_{DE} = \frac{{\frac{{y_1}}{2} - \frac{{y_1}}{2}}}{{\frac{{x_1 + x_2}}{2} - \frac{{x_1}}{2}}} \][/tex]

[tex]\[ m_{DE} = \frac{0}{{\frac{{x_1 + x_2 - x_1}}{2}}} \][/tex]

[tex]\[ m_{DE} = 0 \][/tex]

Since the slopes of segments AB and DE are both equal to 0, we can conclude that segment DE is parallel to segment AB.

Part A

months = m

 since birds decrease by 7%, there will be 93% left. 93% = 0.93
birds: 975 x 0.93^m
trees: 350 - 7m

Part B
birds: 975 x 0.93^12 = 408
trees: 350-7(12) = 266

Part C

350 - 7m = 0.93^m(975)

We have intersection points at approximately 22.21 and 44.4781. round off to whole numbers, we have 22 and 44 months.

Answer:

A.15^2 x π (APEX)

Step-by-step explanation:

82% = 0.82

823/4% = 0.8275