Looking at the graph,would you agree that the boa constrictor population would become a problem?

The solution is, the nth term of the sequence is: an = 250 * 0.4(n-1)

To find a formula for the nth term of the sequence 250, 100, 40, we need to first determine the pattern or rule that generates the sequence. If we divide each term by the previous term, we get the following ratios:

100/250 = 0.4

40/100 = 0.4

We can see that each term is obtained by multiplying the previous term by the common ratio of 0.4.

So, the formula for the nth term of the sequence is:

an = a1* r(n-1)

where a1= 250 is the first term, r = 0.4 is the common ratio, and n is the term number.

The solution is, the nth term of the sequence is: an = 250 * 0.4(n-1)

To learn more about sequence here:

brainly.com/question/30262438

#SPJ1

compplete question:

What is a formula for the nth term of the given sequence 250,100,40

Answer:

Answer is 36 1/8

Step-by-step explanation:

8x4 is 36. 1/2 x 1/4 is 1/8

Answer:

36 1/8

Step-by-step explanation:

8 1/2 = 17/2 x 17/4 = 289/8 = 36.125 = 36 1/8

The correct statement is: c. Median is less than or equal to [tex]18[/tex].

Let's analyze the given range of values, which is [tex]5 \ to \ 18[/tex], and evaluate the statements:

a. Mean is less than [tex]6[/tex]:

To determine if the mean is less than [tex]6[/tex], we need to find the average of the given range.

The mean can be calculated as:

[tex]\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \][/tex]

In this case, the sum of the values is [tex]5 + 6 + 7 + \ldots + 18[/tex], and the number of values is [tex]18 - 5 + 1[/tex] (inclusive).

b. Range is greater than [tex]18[/tex]:

The range is the difference between the maximum and minimum values in a dataset. In this case, the range is [tex]18 - 5 = 13,[/tex] which is less than 18.

c. Median is less than or equal to [tex]18[/tex]:

The median is the middle value in a dataset when the values are arranged in ascending order. In this case, since the range starts from [tex]5[/tex] and ends at 18, the median is less than or equal to [tex]18[/tex].

d. IQR is greater than or equal to [tex]6[/tex]:

The interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset. Since we don't have the actual dataset or specific values beyond the range, we cannot determine if the IQR is greater than or equal to [tex]6[/tex].

Therefore, based on the given range, the correct statement is:

c. Median is less than or equal to [tex]18[/tex].

For more such questions on median : https://brainly.com/question/26177250

#SPJ11

The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1  using synthetic division is x³ +  2x² - 2x  + 7  and the remainder is 13

From the question, we have the following parameters that can be used in our computation:

x⁴ - 3x³ + 9x + 6 ÷ x + 1

The synthetic set up is

-1  |   1  3  0   9   6

    |__________

Bring down the first coefficient, which is 1 and repeat the process

-1  |   1  3  0   9   6

    |__-1_-2_-2_7____

       1  2  -2  7  13

This means that the quotient is

x³ +  2x² - 2x  + 7  

And the remainder is 13

Read more about synthetic division at

https://brainly.com/question/31664714

#SPJ1

Complete question

Find the quotient and remainder using synthetic division.

x^4-3x^3+9x+6/x+1

The quotient is

The remainder is

Answer:

Step-by-step explanation:

To use synthetic division, we need to set up the coefficients of the dividend polynomial in decreasing order of powers of x, including any missing terms with zero coefficients.

So we have:

Dividend: x^4 - 3x^3 + 9x + 6

Divisor: x + 1

We can represent the divisor as (x + 1) and set up the synthetic division table as follows:

-1 | 1 -3 9 0 6

| -1 4 -13 13

|___________________

| 1 -4 13 -13 19

The numbers on the first row of the table are the coefficients of the dividend polynomial in decreasing order of powers of x. The -1 on the left of the table is the opposite of the divisor, x + 1.

The first number in the second row is always 0, and we get it by bringing down the first coefficient, which is 1. To get the next number in the second row, we multiply the divisor, -1, by 1, and add the result to the second coefficient, which is -3. This gives us -1 x -3 = 3, which we write under -3 in the first row.

We repeat this process for the next numbers in the second row, always multiplying the divisor by the last number in the second row, and adding the result to the next coefficient in the first row. We continue until we reach the last coefficient in the first row.

The last number in the second row, 13, is the remainder of the division. The other numbers in the second row are the coefficients of the quotient polynomial in decreasing order of powers of x. So the quotient is:

x^3 - 4x^2 + 13x - 13

And the remainder is:

13

Therefore, the quotient is x^3 - 4x^2 + 13x - 13, and the remainder is 13.

The common difference is -3, and the terms are 17, 14, 11, 8, 5 and the formula is a(n) = 17 - 3(n - 1)

From the question, we have the following parameters that can be used in our computation:

a20 = -40

a37 = -91

An arithmetic sequence is represented as

a(n) = a + (n - 1) * d

Where

d = common difference

Using the given terms, we have

a + 19d = -40

a + 36d = -91

So, we have

17d = -51

Divide

d = -3

This also means that

a + 19(-3) = -40

So, we have

a  = 17

Calculating the first five terms, we have

17, 14, 11, 8, 5

This also means that the nth term is a(n) = 17 - 3(n - 1)

Read more about sequence at

https://brainly.com/question/30499691

#SPJ1

Answer:

BC is 32 cm

Step-by-step explanation:

Answer: attached in image, look at both

Step-by-step explanation:

Hello!

1 book => [tex]1^{\frac{3}{8} }[/tex]

14 books => [tex]14*1^{\frac{3}{8} }[/tex]

[tex]14*1^{\frac{3}{8} }\\\\= 14 * 1\\\\ \boxed{=14}[/tex]

The answer is 14 inches thick.

The number of pounds of 40% alloy and 61% alloy required to make the third alloy containing 46% aluminum is 16.29 pounds and 40.71 pounds respectively.

Let

[tex]\sf x + y = 57[/tex]

[tex]\sf 40x + 61y = 46\times57[/tex]

[tex]\sf x + y = 57[/tex]

[tex]\sf 40x + 61y = 2622[/tex]

Solve simultaneously

From (1)

[tex]\sf x = 57 - y[/tex]

Substitute into (2)

[tex]\sf 40x + 61y = 2622[/tex]

[tex]\sf 40(57-y) + 61y = 2622[/tex]

[tex]\sf 2280 -40y+61y = 2622[/tex]

[tex]\sf -40y+61y = 2622-2280[/tex]

[tex]\sf 21y = 342[/tex]

[tex]\sf y = \dfrac{342}{21}[/tex]

[tex]\sf y = 16.29 \ pounds[/tex]

Substitute y = 16.29 pounds into (1)

[tex]\sf x + y = 57[/tex]

[tex]\sf x + 16.29 = 57[/tex]

[tex]\sf x = 57 - 16.29[/tex]

[tex]\sf x = 40.71 \ pounds[/tex]

So therefore, the number of pounds of 40% alloy and 61% alloy is 16.29 pounds and 40.71 pounds respectively.

Read more on simultaneous equation:

brainly.com/question/16863577

The critical value for a confidence level of 98% with a sample size of 32 is given as follows:

t = 2.4528.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.

(df is one less than the sample size).

More can be learned about the t-distribution at https://brainly.com/question/27701525

#SPJ1

The solution of the equation, | x + 10 / 2x + 1 | = 20 is x = 10 / 39 or x = -30 / 41.

The absolute equation can be solved as follows:

| x + 10 / 2x + 1 | = 20

Therefore,

x + 10 / 2x + 1 = 20  or  x + 10 / 2x + 1 = - 20

cross multiply

x + 10 / 2x + 1 = 20

x + 10 = 20(2x + 1)

x + 10 = 40x + 20

x - 40x  = 20 - 10

-39x = -10

x = 10 / 39

x + 10 / 2x + 1 = - 20

cross multiply

x + 10 = -20(2x + 1)

x + 10 = -40x - 20

x + 40x = -20 - 10

41x = -30

divide both sides of the equation by 41

x = - 30 / 41

Therefore, x = 10 / 39 or x = -30 / 41

learn more on equality here: https://brainly.com/question/9070018

#SPJ1

The proof that the value of x is 38° is shown below

From the question, we have the following parameters that can be used in our computation:

ABDE is a parallelogram.

The measure of the angle opposite the vertex x is

Angle = 180 - 68

Evaluate the like terms

So, we have

Angle = 112

Also, we have

B = 68

AB = AC

So, we have

y = 180 - 68 - 68

y = 44

Using the above as a guide, we have the following:

x + 44 = 82

So, we have

x = 82 - 44

Evaluate

x = 38

Hence, we have shown that the value of x is 38°

Read more about parallelogram at

https://brainly.com/question/970600

#SPJ1

The value of f(4) for the piecewise function f(x) is found to be 23, hence, option A is correct answer.

The given function is a piecewise function which means it is defined by different formulas for different intervals of x. We need to evaluate f(4) using the formula that applies for the interval that contains 4. Since 4 is in the interval -3 ≤ x ≤ 4, we use the formula f(x) = 2x² - 9 for f(4). To find f(4), we substitute 4 for x in the formula,

f(4) = 2(4)² - 9

Evaluating 2(4)²,

f(4) = 2(16) - 9

Simplifying 2(16) - 9:,

f(4) = 23

Therefore, f(4) = 23. So, the correct answer is Option A.

To know more about piecewise function, visit,

https://brainly.com/question/27262465

#SPJ1

Complete question - Determine f(4) for A piecewise function

f(x) = x³ ____ x<-3

f(x) = 2x²-9 ____ -3 ≤ x≤ 4

f(x) = 5x+ ____ when x>4

A. 23

B. 24

C. 41

D. 64

The probability of someone being a right-handed chess player is 0.962, or approximately 0.96

Now, We have to given that;

The probability of being right-handed (R) is 0.9 and the probability of playing chess (C) given that someone is left-handed (L) is 0.6.

And, We are also told that dominant hand and playing chess are independent, so this means that the probability of playing chess is the same regardless of whether someone is left-handed or right-handed.

Hence, the probability of someone being a right-handed chess player, we can use the following formula:

P(R and C) = P(R) x P(C)

We know that P(R) = 0.9,

and since playing chess is independent of handedness,

P(C) = P(C|L) + P(C|R) = 0.6 + P(C|R).

We want to find P(C|R), the probability of playing chess given that someone is right-handed.

We can use the fact that the probabilities must add up to 1 to solve for P(C|R):

P(C|R) = 1 - P(not C|R)

We know that;

P(not C|R) = 1 - P(C|R),

so we can substitute to get:

P(C|R) = 1 - (1 - P(C|R)) = 2P(C|R) - 1

Now we can substitute this back into the original formula and solve for P(R and C):

P(R and C) = P(R) x P(C) P(R and C) = 0.9 x (0.6 + P(C|R))

P(R and C) = 0.54 + 0.9P(C|R)

Finally, we use the fact that the probabilities must add up to 1 to solve for P(C|R):

P(C|R) = 1 - P(not C|R) P(C|R)

= 1 - P(no C and R) / P(R) P(C|R)

= 1 - P(R and not C) / P(R) P(C|R)

= 1 - (0.1 x 0.4) / 0.9

P(C|R) = 0.5333

Now we can substitute this back into the equation for P(R and C) to get:

P(R and C) = 0.54 + 0.9(0.5333...)

P(R and C) = 0.962

Therefore, the probability of someone being a right-handed chess player is 0.962, or approximately 0.96

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].

Option D is the correct answer.

We have,

The expression:

2/5 - 15 + 8 - 1/5 + 3

Now,

To make the simplification easier,

We combine the fraction and like terms together.

So,

[2/5 + (-1/5)] + [8 + 3 + (-15)]

This can be seen as applying the properties of commutative and associative.

Thus,

The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The values of a is 2, b is -6 and c is 7 from the quadratic equation  2x² - 6x + 7 = 0

The given quadratic equation is 2x² - 6x + 7 = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

When we compare the given quadratic equation with standard form we get the values of a , b and c

a=2

b=-6

c=7

Hence, the values of a is 2, b is -6 and c is 7 from the quadratic equation  2x² - 6x + 7 = 0

To learn more on Quadratic equation click:

https://brainly.com/question/17177510

#SPJ1

Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.

If Keenan earns 1 mile for every $8 he spends, then he would need to spend 8 times as much money to earn the same number of miles as he did before.

In other words, he would need to spend $8 to earn 1 mile instead of $1 to earn 1 mile under the old program.

To calculate the new amount of money Keenan needs to spend to earn the miles for his trip, we would need to multiply the old amount by 8.

For example, if under the old program, Keenan needed to spend $10,000 to earn 25,000 miles for his trip, under the new program he would need to spend:

$10,000 x 8 = $80,000

So under the new program, Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.

To learn more about multiplication;

https://brainly.com/question/19634536

#SPJ1

Answer:

Angle B measures 70°, so angle C measures 110°.

20° + B = 90°, so B = 70°.

70° + C = 180°, so C = 110°.

The value of m∠ECD is 50°

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

In the right triangle, m∠B = 90°, hence:

m∠A + m∠B + m∠C = 180° (sum of angles in a triangle)

40 + 90 + m∠C = 180

m∠C = 50°

Also:

m∠C = m∠ECD (opposite angles are equal)

m∠C = m∠ECD = 50°

m∠ECD is 50°

Find out more on volume at: https://brainly.com/question/27710307

#SPJ1

Step-by-step explanation:

She walks the entire CIRCUMFERENCE of the circle

circumference = pi X diameter

                       = pi X 14 ft = 43.98 ft  = ~ 44 ft (rounded)

The exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]

Given that the population is expected to decrease by a factor of 1/4 each decade, we know that the common ratio, b, is 1/4.

Since the most recent estimate is about 115,000 sage grouse, we can assign this value to the initial population, a.

Therefore, the exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]

Learn more about exponential equation at https://brainly.com/question/12940982

#SPJ1

Answer:

The area is 44

Step-by-step explanation:

If you add the numbers that across from each other you would get 12+12+2+2+8+8= 44

Answer:

[tex] \frac{3( {5}^{8} - 1) }{5 - 1} = 292968[/tex]

The scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex] where 10 raised to an exponent (-2).

In scientific notation, a number is expressed as the product of a coefficient and a power of 10.

To write the number 0.08 in scientific notation, it as a decimal number multiplied by a power of 10.

So, 0.08 can be written in scientific notation as 8 x [tex]10^{(-2)[/tex].

In scientific notation, the number is written as the product of a coefficient (8) and a power of 10 raised to an exponent (-2), indicating the decimal's position relative to the coefficient.

Therefore, the scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex].

Learn more about Scientific notation here:

https://brainly.com/question/19625319

#SPJ6

The correct answer is Add all of the numbers, then divide.

Given that we need to determine which choice demonstrates the process for calculating the mean,

We know that the mean is calculated by,

You must add up all the values in a dataset and divide the total by the overall number of values in order to determine the mean, also known as the average.

The following steps should be followed to determine the mean:

Add up all the figures.

Subtract the amount from the overall value set.

In order to determine the mean, the option "Add all of the numbers, then divide" is the proper course of action.

Hence the correct answer is Add all of the numbers, then divide.

Learn more about mean click;

https://brainly.com/question/31101410

#SPJ1

Answer:

True

False
True

Answer:

B

Step-by-step explanation:

[tex]tan^{2}\alpha (sec^{2} \alpha + cosec^{2} \alpha )\\\frac{sin^{2}\alpha}{cos^{2}\alpha} (\frac{1}{cos^{2}\alpha}+\frac{1}{sin^{2}\alpha})\\ \frac{sin^{2}\alpha}{cos^{2}\alpha} (\frac{1}{cos^{2} \alpha . sin^{2}\alpha} )\\\frac{1}{cos^{4}\alpha}\\= sec^{4}\alpha[/tex]

Answer: There are 32,760 color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options.

Step-by-step explanation: To determine the number of color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options, we need to calculate the number of permutations.

Since each room is assigned a different color, we can arrange the colors in a specific order. The number of ways to arrange 15 colors in 4 distinct positions is given by the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of options (15 colors) and r is the number of positions (4 rooms).

Using the formula, the number of color arrangements possible is:

P(15, 4) = 15! / (15 - 4)!

= 15! / 11!

= (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)

= 32,760

After considering the given data we conclude that the area of the given figure is 62.2 cm², under the condition that x = 5 cm

Since the given figure comprises of two right angled triangle and one rectangle we can split them and calculate their area separately then apply summation at the ending.
Let us proceed with the triangle
Let us first name the whole figure, ABCD is the whole diagram out of which first we will deal with triangle CDG,
In triangle CDG
The height length (DG) = 7.5 cm
The base  length ( CG) = 2.4 cm
Then the area of the triangle CDG
[tex]Area =1/2 * base *height[/tex]
= 1/2 × 2.4 ×7.5
= 1/2 × 18
= 9 cm²
Now moving on to the other triangle ABE
The height length (AE) = 7.5 cm
The base  length (EB) = 4.2 cm
Then the area of the triangle ABE
[tex]Area =1/2 * base *height[/tex]
= 1/2 × 4.2 × 7.5
=1/2 × 31.5
= 15.7 cm²
Finally moving onto the rectangle AEGD,
Given
Length of the rectangle (DG) = 7.5 cm
Breadth of the rectangle ( GE) = x = 5 cm
Placing the values in the formula
[tex]Area = length * breathe[/tex]
Area = 7.5 × 5
Area = 37.5 cm²

Now applying summation to evaluate the total area of the quadrilateral ABCD
Area of CDG + Area of ABE + Area of AEGD
= ( 9 + 15.7 + 37.5)
= 62.2 cm²
To learn more about triangle
https://brainly.com/question/29782809
#SPJ1