cos(a+b) x cos(a-b)/cos^2(a)x cos^2(b)=1-tan^2(a)xtan^2(b)

Transitional forms in the fossil record, including Archaeopteryx, provide evidence for the pattern of evolution known as "gradualism."

This pattern suggests that species change over time through a slow and continuous process of accumulation of small, incremental changes. Transitional fossils like Archaeopteryx exhibit characteristics that are intermediate between two different groups of organisms, indicating a gradual transition from one form to another.

The presence of transitional fossils supports the idea that species do not undergo abrupt transformations but instead evolve gradually over long periods of time.

These fossils provide a tangible link between different groups of organisms, such as dinosaurs and birds in the case of Archaeopteryx, and offer evidence for the gradual transformation of one group into another. This supports the broader concept of evolution as a slow and continuous process of change in populations over generations.

Learn more about fossil here : brainly.com/question/31419516

#SPJ11

The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.

Given that,

Jake sold 49 tickets while jeans sold 12 for the school.

In simplest form the ratio of the given case will be;

Simplest form:

A fraction is a number that falls between the whole numbers but is not a whole number. It belongs to the entire. A fraction also consists of a denominator and a numerator. We obtain the fraction in its simplest form when both the numerator and denominator can no longer be independently reduced to any smaller integer.

The ratio we get;

→ 12/49

The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.

To learn more about simplest form click here:

brainly.com/question/290068

#SPJ4

The predicted population of Tanzania 5.5 years ago is approximately 46.1 million. This estimation is based on the current population, the population growth rate, and the formula for exponential population growth.

To predict the population of Tanzania 5.5 years ago, we need to use the population growth rate and the current population.

The formula for exponential population growth is:

P = P0 * e^(rt)

Where:

P = population after time t

P0 = initial population

r = growth rate (expressed as a decimal)

t = time in years

e = Euler's number (approximately 2.71828)

Given information:

Current population (P0) = 50.3 million

Growth rate (r) = 2.14% per year

Time (t) = -5.5 years (5.5 years ago)

Converting the growth rate to decimal form:

r = 2.14% = 0.0214

Substituting the values into the formula:

P = 50.3 million * e^(0.0214 * -5.5)

Calculating the exponential growth:

P = 50.3 million * e^(-0.1177)

P ≈ 46.1 million

Rounding the answer to one decimal place and expressing it in millions, the predicted population of Tanzania 5.5 years ago is approximately 46.1 million.

Learn more about predicted population visit:

https://brainly.com/question/32860951

#SPJ11

Answer: x = 2.4

Hope this helps. Other formats of the answer would be 12/5 or 2 2/5

Answer:

x=12/5

Step-by-step explanation:

5x-4=8

5x=8+4

5x=12

x=12/5

thanks.

The maximum length of the remainder has 15 bits. The generator polynomial of a cyclic code determines the number of check bits, the minimum Hamming distance, and the maximum length of the remainder.

The degree of the generator polynomial in binary BCH codes corresponds to the number of check bits in the code. Furthermore, the length of the code is determined by the generator polynomial and is given by (2^m)-1 where m is the degree of the generator polynomial.Let the generator polynomial be X16+1 and we are to determine the maximum length of the remainder. For this polynomial, the degree is 16 and the length of the code is (2^16)-1 = 65535. We know that the maximum length of the remainder is equal to the degree of the generator polynomial minus one, i.e. 15.So, the maximum length of the remainder has 15 bits.

To know more about  cyclic code visit:

brainly.com/question/4545055

#SPJ11

Answer:

  see attached

Step-by-step explanation:

You want the given triangle reflected over the line y = -1/2x +1.

The transformation for reflection over the line y = mx +b is ...

  (x, y) ⇒ (x(1-m²) +y(2m) -2mb, x(2m) +y(m²-1) +2b)/(1+m²)

Using m=-1/2 and b=1, this transformation becomes ...

  (x, y) ⇒ ((3x -4y +4)/5, (-4x -3y +8)/5)

Then for the vertex points, we get ...

  (1, 3) ⇒ ((3·1 -4·3 +4)/5, (-4·1 -3·3 +8)/5) = (-5/5, -5/5) = (-1, -1)

  (1, 8) ⇒ (3·1 -4·8 +4)/5, (-4·1 -3·8 +8)/5) = (-25/5, -20/5) = (-5, -4)

  (6, 3) ⇒ (3·6 -4·3 +4)/5, (-4·6 -3·3 +8)/5) = (10/5, -25/5) = (2, -5)

The line of reflection is the perpendicular bisector of the segments connecting each point with its image. This fact can be used to find the reflection graphically.

The given line has slope -1/2, so a perpendicular line will have slope -1/(-1/2) = 2. A line with slope 2 can be drawn through each vertex point. The reflected point will be the same distance along that line on the other side of the line of reflection. The dashed lines in the attached figure show the idea.

Answer:

20

Step-by-step explanation:

Total no of plants in a garden = 36

The ratio of tomato plants to cucumber plants to be 4:5.

Let tomato plants are 4x and cucumber plants is 5x.

ATQ,

4x+5x=36

9x = 36

x = 4

For cucumber plant, 5x = 5(4) = 20

So, there are 20 cucumber plants will be in Reggie's garden

The remainder when x³ - 1 is divided by (x + 3) is  -28

The functions are given as

x 3 1 is divided by x 3

Rewrite them as

f(x) = x³ - 1 is divided by (x + 3)

Set the divisor to 0

So, we have

x + 3 = 0

Determine the value of x

This gives

x = -3

By the remainder theorem

Substitute x = -3 in the function f(x)

So, we have

f(-3) = (-3)³ - 1

Evaluate the expression

f(-3) = -28

By the remainder theorem, this represents the remainder

Read more about remainder at

brainly.com/question/14130807

#SPJ1

Answer:

2 centimeters

Step-by-step explanation:

volume = 125.6 cubic centimeters

heigh = 10 cubic centimeters

volume of cylinder formula and obatin the radius value:

π \(R^{2}\) h

r = radius of the cylinder & h is the height of cylinder

π is constant has value 3.14 of pi

\(3.14 * r^{2} * 10\) = 125.6

Then again: \(R^{2} = \frac{125.6}{31.4}\)

Then \(R^{2}\) = 4

Square root it:

r = \(\sqrt{4}\)

r = 2

2 is the answer

The equation of the circle with center (-6,0) and containing the point (-12,-√13) is: \(x^2 + 12x + y^2 = 13\)

What is equation of a circle?

The equation of a circle with center (h, k) and radius r is given by:

\((x - h)^2 + (y - k)^2 = r^2\) where (x, y) is any point on the circle. This equation represents all points (x, y) that are at a fixed distance r from the center (h, k).

The distance between the center and the given point is the radius:

\(r = \sqrt{[(x2 - x1)^2 + (y2 - y1)^2}\\r = \sqrt{ [(-12 - (-6))^2 + (-√13 - 0)^2}\\r = \sqrt{36 + 13}\\r = \sqrt{49}\\r = 7\)

Substituting the center and radius into the equation of the circle, we get:

(x + 6)^2 + y^2 = 7^2

Simplifying, we get:

\(x^2 + 12x + 36 + y^2 = 49\)

Hence, The equation of the circle with center (-6,0) and containing the point (-12,-√13) is: \(x^2 + 12x + y^2 = 13\)

Learn more about equation of a circle, by the following link.

https://brainly.com/question/1506955

#SPJ1

a) Sample size 13:(43.614, 44.386)

b) Sample size 1300:(43.9663, 44.0337)

The weight of the screws is normally distributed and has a variance of 0.64g^2. In a sample, the mean of the screws was 44g. The following are the two-sided (symmetrical) confidence intervals with a 95 percent confidence level for the expected value of the weight:Option a) Sample size 13:For a sample size of 13, the standard error of the mean is calculated as follows:SE = σ/√nwhere SE is the standard error, σ is the variance, and n is the sample size.In this case, SE = √(0.64)/√(13) = 0.1772.The t-distribution should be used to calculate the confidence interval since the population's standard deviation is unknown.The t-value corresponding to the 95% confidence interval with 12 degrees of freedom (df = n – 1) is 2.179. Therefore, the confidence interval can be calculated as follows:44 ± 2.179(0.1772)= 44 ± 0.386= (43.614, 44.386)The expected weight of the screws in the population is estimated to be between 43.614 g and 44.386 g.Option b) Sample size 1300:For a sample size of 1300, the standard error of the mean is calculated as follows:SE = σ/√nwhere SE is the standard error, σ is the variance, and n is the sample size.In this case, SE = √(0.64)/√(1300) = 0.0172.The z-distribution should be used to calculate the confidence interval since the sample size is large enough to assume that the sample mean is approximately normally distributed.The z-value corresponding to the 95% confidence interval is 1.96. Therefore, the confidence interval can be calculated as follows:44 ± 1.96(0.0172)= 44 ± 0.0337= (43.9663, 44.0337)The expected weight of the screws in the population is estimated to be between 43.9663 g and 44.0337 g.

Learn more about Sample size

brainly.com/question/25894237

#SPJ4

Answer: y = -2x + (insert any number you want here)

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1, so m x m = -1.

1/2 x -2 = -1

Make the y-intercept whatever you want.

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

Read more about rate of change at

https://brainly.com/question/17131025

#SPJ1

Take into account that the formula for the area of a triangle is:

A = b·h/2

where b is the base, h is the height h = 7.2 cm and A is the area A = 28.8 cm²

Solve for b in the previous formula, and replace the values of A and h, as follow:

b = 2·A/h

b = 2(28.8 cm²)/(7.2 cm)

b = 8 cm

Hence, the length of the base of the triangle is 8 cm

Answer: 170

Step-by-step explanation:

t r is 90 and 82 and it = 172 just round that and you have 170

Graph option B is the correct answer.

Graphical representation refers to the use of charts and graphs to visually display, analyse, clarify, and interpret numerical data, functions, and other qualitative structures.

Given are function,

y = x+1 ≤0 and y = 3x

The best demonstration of these functions can be seen in graph 2.

Hence, Graph option B is the correct answer.

For more references on graphical representation, click;

https://brainly.com/question/22070598

#SPJ1

Answer: help woth what?

Step-by-step explanation:

I dont see anything?

Step-by-step explanation:

I think you may have forgotten to put the picture..

(a) The probability that all 4 missiles will fire is 0.2098 and (b) The probability that at most 2 will not fire is 0.0099.

Here we need to use the concept of combinations to get our required answer.

Here we have been given that 4 out of 14 missiles are defective.

Hence 10 missiles are working.

A sample of 4 missiles was chosen

Hence the simple can be chosen in ¹⁴C₄ ways

a)

The probability that all 4 missiles will fire is

¹⁰C₄/¹⁴C₄

= 0.2098

b)

The probability that at most 2 will not fire is

1 - the probability of including all three defective missiles

= 10³C₃/¹⁴C₄

= 0.0099

To learn more about Probability visit

https://brainly.com/question/30034780

#SPJ4

(a) Probability all 4 fire: 0.3297. (b) Probability at most 2 not fire: 0.9591.

(a) To track down the chance that all of the 4 rockets will fire, we actually need to do not forget the quantity of methods we can select 4 operating rockets out of the eleven that are not unsuitable, isolated by the all out range of approaches we will select four rockets out of the whole component.

The amount of ways of selecting four operating rockets out of the eleven that aren't improper is given by way of the combination recipe:

C(eleven,four) = 330

The absolute quantity of methods of selecting four rockets out of the entire part is given via:

C(14,4) = 1001

Subsequently, the chance that each one of the four rockets will hearth is:

P(all four hearth) = C(11,four)/C(14,4) = 330/1001 ≈ zero.3297

(adjusted to 4 decimal spots)

(b) To find the likelihood that at most 2 rockets might not fire, we need to remember every one of the potential conditions in which 0, 1, or 2 poor rockets are selected, and afterward song down the likelihood of every case and upload them up.

Case 1: No defective rockets are selected

The amount of ways of selecting four working rockets out of the eleven that are not faulty is given through the mixture recipe:

C(11,four) = 330

Subsequently, the chance of choosing no defective rockets is:

P(0 inadequate) = C(eleven,4)/C(14,four) ≈ 0.3297

Case 2: One defective rocket is chosen

The quantity of ways of selecting three operating rockets out of the eleven that are not poor is given with the aid of the combo equation:

C(eleven,three) = 165

The amount of ways of selecting 1 damaged rocket out of the three that are available is given through the mix equation:

C(three,1) = 3

Subsequently, the all out number of approaches of selecting 1 insufficient and three running rockets is:

C(eleven,three) × C(3,1) = 495

Thusly, the probability of choosing one deficient rocket and three running rockets is:

P(1 deficient) = C(eleven,three) × C(three,1)/C(14,4) ≈ 0.4655

Case three: Two poor rockets are selected

The amount of approaches of choosing 2 poor rockets out of the three which might be handy is given through the combination recipe:

C(3,2) = 3

The amount of ways of choosing 2 running rockets out of the 11 that aren't faulty is given via the mix recipe:

C(11,2) = 55

In this way, the all out number of methods of selecting 2 broken rockets and 2 working rockets is:

C(3,2) × C(eleven,2) = one hundred sixty five

Subsequently, the chance of choosing two incorrect rockets and two operating rockets is:

P(2 insufficient) = C(3,2) × C(11,2)/C(14,four) ≈ 0.1638

Subsequently, the likelihood that at maximum 2 rockets might not fireplace is:

P(at maximum 2 don't fire) = P(zero imperfect) + P(1 blemished) + P(2 deficient) ≈ 0.9591

(adjusted to 4 decimal spots).

To learn more about probability, refer:

https://brainly.com/question/1581511

#SPJ4

Answer: Credit cards are safer to carry than cash and offer stronger fraud protections than debit.

Answer:

- \(\frac{3}{5}\) i

Step-by-step explanation:

Given

\(\frac{3}{5i}\)

Multiply numerator/ denominator by i

= \(\frac{3i}{5i^2}\) [ i² = - 1 ]

= \(\frac{3i}{-5}\)

= - \(\frac{3}{5}\) i

Answer:

Already answered but oh well

It's -4

Answer:

n =22

Step-by-step explanation:

12-5=7

15-5=10

20-5=15

n-5=17

collect like terms

n=17+5

n=22

Answer:

Looking at the rule we can see that our x value is always 5 more than our y value.  So to get our n we just take the y value of 17 and add 5 and we get 22.  So our n is equal to 22.

The value of rate per toppings is, A = $ 0.50

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that;

The cost of 2 toppings = $ 3.99

The cost of 4 toppings = $ 4.99

Let the cost of the toppings be represented as A

Now , The equation will be;

The cost of 2 toppings = $ 3.99

So , 2A = 3.99  ..(1)

And, The cost of 4 toppings = $ 4.99

⇒ 4A = 4.99   .. (2)

Subtracting equation (1) from equation (2) , we get;

4A - 2A = 4.99 - 3.99

On simplifying the equation , we get

2A = 1.00

Divide by 2 on both sides of the equation , we get

A = $ 0.50

Therefore , The value of rate is, $0.50

Hence , The cost of one toppings = $ 0.50

Learn more about equations visit:

brainly.com/question/19297665

#SPJ1

Answer:

24% increase

Step-by-step explanation:

percent change = (new value - old value)/(old value) × 100%

A positive percent change is a percent increase.

A negative percent change is a percent decrease.

In this problem:

new value = 31

old value = 25

percent change = (31 - 25)/(25) × 100%

percent change = 24%

Since the percent change is positive, the percent change is a

24% increase

The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the an 24% increase in the puppy's weight in 1 month.

The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.

To explain this further, let's look at an example. If a puppy weighed 25 pounds at 4 months, and it gained 6 pounds over the course of the following month, it would weigh 31 pounds at 5 months. To calculate the percentage increase, take the difference in weight (6 pounds) and divide it by the starting weight (25 pounds). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight.

To calculate the percentage decrease, use the same steps as above, but subtract the starting weight from the final weight instead. For example, if a puppy weighed 25 pounds at 4 months and lost 6 pounds over the course of the following month, it would weigh 19 pounds at 5 months. The percentage decrease would be calculated as (25 - 19)/25 = 0.24, or a 24% decrease in the puppy's weight.

In summary, the percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.

See more about percentage change at: https://brainly.com/question/1053881

#SPJ11

Answer:

Division property of equality

Step-by-step explanation:

What she did was ;

\(\frac{-3x}{-3} =\frac{3}{-3} \\\\x =-1\)

Answer:

Grams

Step-by-step explanation:

Edg. 2020 :D

Answer:

grams

Step-by-step explanation:

Step-by-step explanation:

the answer to the question is C. 64.

Answer:

yes

Step-by-step explanation: