In a scientific study, the monarch butterfly population in a southern city appears to be growing. The study initially observed seven butterflies. After one month of observations, there were twenty-one. In the second month, sixty-three butterflies where identified. If this pattern continues, what type of growth best describes this situation? How do you know?

Answer:

47%

Step-by-step explanation:

Total number of males=14

Total number of females =16

Total number of students =16+14

=30

Probability of a selecting a male student

\( = \frac{number \: of \: male \: students}{total \: number \: of \: students} \\ = \frac{14}{30} \\ \frac{7}{15} \\ to \: the \: nearest \: whole \: percent \\ = \frac{7}{15} \times 100 \\ = 46.66 \)

=47%

Answer:

It mostly depends on the question

Step-by-step explanation:

To calculate the annualized rate of return, we can use the formula for compound interest. The correct answer is 11.66%.

The formula for compound interest is given by: A = P(1 + r)^t, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

In this case, the initial investment (P) is BD 14,000, the final amount (A) is BD 52,600, and the time (t) is 12 years. We need to solve for the annual interest rate (r).

\(BD 52,600 = BD 14,000(1 + r)^{12}\)

By rearranging the equation and solving for r, we find:

\((1 + r)^{12} = 52,600/14,000\)

Taking the twelfth root of both sides:

\(1 + r = (52,600/14,000)^{(1/12)}\\r = 0.1166 / 11.66 \%\)

Therefore, Areej has earned an annualized rate of approximately 11.66% on this investment.

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Answer:

10

Step-by-step explanation:

To prove the identity cos(x + y) + cos(x - y) = 2 cos(x) cos(y), we can use the sum and difference of angles formulas for cosine.

We start by applying the sum of angles formula for cosine, which states that cos(a + b) = cos(a) cos(b) - sin(a) sin(b). Applying this formula to the first term of the equation, we have cos(x + y) = cos(x) cos(y) - sin(x) sin(y).

Next, we apply the difference of angles formula for cosine, which states that cos(a - b) = cos(a) cos(b) + sin(a) sin(b). Applying this formula to the second term of the equation, we have cos(x - y) = cos(x) cos(y) + sin(x) sin(y).

Now, substituting these results back into the original equation, we have cos(x + y) + cos(x - y) = (cos(x) cos(y) - sin(x) sin(y)) + (cos(x) cos(y) + sin(x) sin(y)).

Simplifying this expression, we get 2 cos(x) cos(y), which proves the given identity.

Therefore, we have successfully proved that cos(x + y) + cos(x - y) = 2 cos(x) cos(y) using the sum and difference of angles formulas for cosine.

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Cookies sold by Billy are 10 and by Betty are 5;

Total cookies sold by Billy and Betty are 15;

Let the cookies sold by Billy be 'C₁' and by Betty be 'C₂';

what is Permutation?

In mathematics, permutation relates to the act of arranging all of the contributors of a hard and fast into a few sequence or order. In other words, if the set is already ordered, then the rearranging of its elements is called the process of permuting. diversifications occur, in extra or less prominent methods, in almost every place of arithmetic. They regularly stand up whilst one of a kind orderings on positive finite sets are considered.

what's a combination?

The mixture is a manner of selecting objects from a collection, such that (not like permutations) the order of selection does now not matter. In smaller instances, it is feasible to be counted the wide variety of combinations. combination refers back to the mixture of n things taken ok at a time with out repetition. to consult combos in which repetition is authorized, the terms k-choice or k-mixture with repetition are regularly used.

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Therefore, the Super Happy Fun Ball will not bounce before its rebound is less than 1 foot.

To determine the number of times the Super Happy Fun Ball will bounce before its rebound is less than 1 foot, we can set up a geometric sequence.

The height of each bounce can be represented as a sequence of terms: 13, 10.11(13), (10.11)^2(13), (10.11)^3(13), ...

The rebound distance decreases by a factor of 10.11 with each bounce.

We want to find the first term in the sequence that is less than 1 foot (12 inches).

Let's set up the inequality:

\((10.11)^n * 13 < 12\)

Simplifying:

\((10.11)^n < 12/13\)

To find the value of n, we can take the logarithm of both sides:

n * log(10.11) < log(12/13)

Dividing both sides by log(10.11):

n < log(12/13) / log(10.11)

Using a calculator, we can calculate the right side of the inequality:

n < -0.202

Since the number of bounces cannot be negative, we round down to the nearest whole number:

n = 0

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The mean of the given frequency distribution is 587.12.

What is frequency distribution?

In frequency tables or charts, frequency distributions are displayed. The actual number of observations that fall into each range can be seen in frequency distributions, as well as the proportion of observations that do.

We are given a frequency distribution table.

We know that the mean is the average of sum of all the values.

So, we first get the values as :

⇒ 610 * 12 = 7320

⇒ 537 * 6 = 3222

⇒ 597 * 10 = 5970

⇒ 572 * 14 = 8008

⇒ 590 * 9 = 5310

⇒ 606 * 6 = 3636

Now, on adding all the values, we get

⇒ 7320 + 3222 + 5970 + 8008 + 5310 + 3636

⇒ 33466

So,

⇒ Mean =  33466 ÷ 57

⇒ Mean = 587.12

Hence, the mean of the given frequency distribution is 587.12.

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Answer:

-11 degrees Fahrenheit.

Step-by-step explanation:

the higher the negative number is, the colder it gets <D

The slope of the line is represented by the word m which is obtained as 0.5.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

To determine a line's inclination or steepness, use the slope formula. Calculating the ratio of the change in the y-axis to the change in the x-axis may be used to calculate the slope of any line.

From the graph, the data is observed as,

(x₁,y₁)=(0,1)

(x₂,y₂) = (-2,0)

The slope of the line is found as,

\(\rm m =\dfrac{0-1}{-2-0} \\\\ m = 0.5\)

Thus, the slope of the line is represented by the word m which is obtained as 0.5.

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Answer:

He would need to walk the dog 6 more times because 8 times 11 is 88 and if he has already walked the dog 5 times you would subtract that from 11 to get 6. So the answer would be 6

Step-by-step explanation:

8·11= 88

11-5= 6

Answer:

sec²x

Step-by-step explanation:

Using the trigonometric identity

tan²x + 1 = sec²x

9514 1404 393

Answer:

  sec² x

Step-by-step explanation:

It is a trig identity that ...

  tan² x + 1 = sec² x

_____

If you like, you can convince yourself of this using the usual equivalents for tan and sec:

  tan² x + 1 = sin² x/cos² x +1 = (sin² x + cos² x)/cos² x = 1/cos² x = sec² x

Answer:

64 in^2.

Step-by-step explanation:

The surface consists of 4 congruent triangles and a square base.

Area of 1 triangle = 1/2 * 4*6  = 12.

Area of the base = 4*4 = 16.

So the required surface area

= 4*12 + 16

= 64 in^2.

Answer:

Step-by-step explanation:

150 giri

Answer:

5x - 40

Step-by-step explanation:

x = 1

the position the 5 is in makes it a multiplication. multiply x(aka 1) by 5. you get 5x

multiply 5 by 8, giving you 40.

therefore, if my algebra is right, the answer is 5x-40

Answer:

5x-40

Step-by-step explanation:

5(x – 8)

Use the distributive property

5*x - 5*8

5x-40

For her to have 5 green beads, 6 red beads, and 7 white beads in each bracelet, she will make 151 bracelets.

From the given question total numbers of beads of different colors are:

Green beads = 1,012

Red beads = 998

White beads = 1,057

Each bracelet should have number of beads

Green beads = 5

Red beads = 6

White beads = 7

Number of bracelets made with green beads = Total number of green beads/ one bracelet have green bead

Number of bracelets made with green beads = 1,012/ 5

Number of bracelets made with green beads = 202.4 bracelets

Number of bracelets made with red beads = Total number of red beads/ one bracelet have red bead

Number of bracelets made with red beads = 998 / 6

Number of bracelets made with red beads = 166.3 bracelets

Number of bracelets made with white beads = Total number of white beads/ one bracelet have white bead

Number of bracelets made with white beads = 1,057 / 7

Number of bracelets made with white beads = 151 bracelets

For her to have 5 green beads, 6 red beads, and 7 white beads in each bracelet, she will make 151 bracelets.

This is because, if the number of bracelets she makes is more than 151, then she won't have white beads use for it.

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Answer:

d

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

Answer:

No it is not a collection of well defined and distinct objects

Hope this helps <3

Answer:

i think ¹27 yea i ththatthats the answer hope it is

Answer: 6m+4n=32

Step-by-step explanation:

m=4

n=2

From this, we can deduce that m+n=32.

6*4=24 and 4*2=8. 24+8=32

So, 6m+4n=32. Hope this was what you were looking for!

(A) The change-of-basis matrices are

\(M_{C}\) < -B = | 1 -1 2 | | 0 1 1 | | 0 0 -2 |

\(M_{B}\)  < -C = | 2 -2 0 | | 1 1 1 | | -1 1 0 |

(B)The matrix repre- sentations of T with respect to B and C.

\(T_{B}\) = | 0 | | 1 | | 2 |

\(T_{C}\) = | 0 | | 2 | | 4 |

(a) The change-of-basis matrices \(M_{C}\) < -B and \(M_{B}\) < -C, we need to determine how the basis vectors in B and C can be expressed in terms of each other.

We have the basis B = (1, x + 2, x² + 2x + 3) and the basis C = (x², (x + 1)², (x - 1)²).

\(M_{C}\) < -B, we express the vectors in basis C as linear combinations of the vectors in basis B:

x² = (x² + 2x + 3) - (x + 2) + 2(1) (x + 1)²

= (x² + 2x + 3) + (x + 2) (x - 1)²

= (x² + 2x + 3) - 2(1)

Writing these expressions as matrices, we have:

\(M_{C}\) < -B = | 1 -1 2 | | 0 1 1 | | 0 0 -2 |

\(M_{B}\) < -C, we express the vectors in basis B as linear combinations of the vectors in basis C:

1 = 2(x²) + (x + 1)² - (x - 1)²

x + 2 = -2(x²) + (x + 1)² + (x - 1)²

x² + 2x + 3 = (x + 1)² + (x - 1)²

Writing these expressions as matrices, we have:

\(M_{B}\)  < -C = | 2 -2 0 | | 1 1 1 | | -1 1 0 |

(b) The matrix representation of T with respect to B and C, we apply the derivative operation T to each basis vector and express the results in terms of the basis vectors.

T(1) = 0

T(x + 2) = 1

T(x² + 2x + 3) = 2x + 2

Writing these expressions as matrices, we have:

\([T]_{B}\) = | 0 | | 1 | | 2 |

\(T_{C}\), we express the derivative vectors in terms of the basis C:

0 = 0(x²) + 0((x + 1)²) + 0((x - 1)²)

1 = 0(x²) + 2((x + 1)²) + 2((x - 1)²)

2x + 2 = 2(x²) + 4(x + 1) + 4(x - 1)

Writing these expressions as matrices, we have:

\(T_{C}\) = | 0 | | 2 | | 4 |

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Answer:

(x + 10)(x + 2)

Step-by-step explanation:

x² + 12x +20

(x + 10)(x + 2)

Answer:

(x+2)(x+10)

Step-by-step explanation:

The given trinomial needs to be factorised. On the basis of degree of power of polynomial it can also be called a quadratic polynomial . General form is ax² + bx + c .

= x² + 12x + 20

= x² + 10x + 2x + 20

= x ( x + 10 ) + 2( x + 10 )

= ( x + 2)( x +10)

The probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

To find the probability of selecting a red six or a black king from a 52-card deck, we need to determine the number of favorable outcomes (red six or black king) and divide it by the total number of possible outcomes (52 cards).

There are 2 red sixes (hearts and diamonds) and 2 black kings (spades and clubs) in a deck.

Since we want to select either a red six or a black king, we can add these numbers together to get a total of 4 favorable outcomes.

Since there are 52 cards in a deck, the total number of possible outcomes is 52.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 4 / 52 Probability = 1 / 13

Therefore, the probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

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The five-number summary of the data set given is:

The five-number summary can be defined as a set of descriptive statistics that gives you an idea how your data looks like.

The five-number summary include the following:

The interquartile range is a measure of the spread of a data set, which is: IQR = Q3 - Q1

Given the data set, 48, 50, 54, 54, 62, 68, 70, 72, 75, 77, 78, 80:

Minimum = 48

First Quartile (Q1) = (54 + 54)/2 = 54

Median = (68 + 70)/2 = 69

Third Quartile (Q3) = (75 + 77)/2 = 76

Maximum = 80

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Answer:

32.170 or 32.17

Step-by-step explanation:

so when you look at the number:

32.169857883

           ^

look at the place value behind the number in the thousandths. if the number is bigger then five it rounds up. so the number eight would round up to 9 then you can guess from there hope t helps if you need more help ask me! feel free

The given decimal number is rounded to the nearest thousandth as 32.170.

The given decimal number is 32.169857883.

We need to round off the given decimal number to the nearest thousandth.

If that digit is less than 5, round down the thousandth digit. If that digit is greater than or equal to 5, round up the thousandth digit.

Now, in the given number 32.169857883, the digit next to the thousandths place is 8 which is greater than 5.

Then the decimal number rounded to  32.170

Therefore, the given decimal number is rounded to the nearest thousandth as 32.170.

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Answer:

y = 2x + 16

Step-by-step explanation:

slope is parallel and equal to y = 2x + 6

y intercept = 16

Answer:

b - y=2x+16

Step-by-step explanation:

y=y1+m(x+x1)

(-4,8)

y=8+2(x-4)

y=8+2x-8

add 8 on both sides

y=2x+16

Answer:

Look at Step by step for answer.

Step-by-step explanation:

5. Subtract greatest number by the lowest number so 7 - (-10) which gets 17.

6. 8x - 5 + 2x = x - 14

       10x = x - 9

         9x = - 9

           x = -1

7. Add all numbers together and divide by 6 to get 1.3.