f(0) = 2. f(n) = f(n-1)+4
The relationship represented is -
A linear
B exponential
C neither

Answer:

59.9%

Step-by-step explanation:

100/30 = 3.3

3.3*18 = 59.9%

Answer:

8

Step-by-step explanation:

40 divided by 5 is 8 :D

Answer: A. 8 km/hr/sec

Step-by-step explanation:

You divide 40 by 5

40/5

which you'll get

8

The number of possible outcomes exists 21952. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Probability exists a branch of mathematics that deals with numerical representations of the likelihood of an event happening or of a proposition being true. The probability of an event exists a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

Given:

A 28-sided die is rolled 3 times.

28 × 28 × 28 = 21952.

Therefore, the number of possible outcomes exists 21952.

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Answer:

what's the full question...?

Step-by-step explanation:

Answer:

x = 135

Step-by-step explanation:

Cross multiply (Multiplicacao cruzada)

\(\frac{30}{x}=\frac{2}{9}\)

2x = 270

(Now just divide both sides by X) So dividir os 2 lados por 2x

x = 135

Ace

The probability that all five customers do not go above $300 in unusual activity in a month is approximately 0.95

Let X be the dollar value of unusual activity for a customer in a month. Then X follows a normal distribution with mean μ = $250 and variance σ^2 = $391.

We want to find the probability that all five customers do not go above $300 in unusual activity in a month. Let Y be the total dollar value of unusual activity for the five customers in a month. Then Y = X1 + X2 + X3 + X4 + X5, where Xi is the dollar value of unusual activity for customer i.

The total dollar value Y is also normally distributed with mean μY = μX1 + μX2 + μX3 + μX4 + μX5 = 5μ = $1250 and variance σ^2Y = σ^2X1 + σ^2X2 + σ^2X3 + σ^2X4 + σ^2X5 = 5σ^2 = $1955.

To find the probability that all five customers do not go above $300 in unusual activity in a month, we need to find the probability that Y ≤ $1500, since $1500 is the total dollar value of unusual activity for the five customers if each of them has $300 or less in unusual activity.

Using the standard normal distribution, we can standardize Y as follows

Z = (Y - μY) / sqrt(σ^2Y) = (Y - $1250) / sqrt($1955)

Then we can find the probability that Z ≤ (1500 - $1250) / sqrt($1955) = 1.60 using a standard normal distribution table or calculator. This probability is approximately 0.95

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Answer:

$1.25

Step-by-step explanation:

5 dollars for four pounds

one pound = $5 / 4 = $1.25

Answer: 80 cents

Step-by-step explanation: Divide 4 & 5 and get 0.8

To check your answer just multiply 0.8 and 5 which equals 4

So 1 lb cost 80 cents

Natural selection and genetics are intrinsically linked as they both play crucial roles in the process of evolution.

Natural selection is the mechanism by which certain heritable traits become more or less common in a population over generations. It acts on the genetic variation present within a population, favoring individuals with advantageous traits that increase their fitness and survival. These advantageous traits are often the result of genetic variations or mutations that confer a selective advantage. Genetics, on the other hand, is the study of heredity and the variation of genes within populations. Genes are segments of DNA that contain the instructions for the development and functioning of organisms. Genetic variations arise through processes such as mutation, recombination, and gene flow.

Natural selection acts upon the genetic variation present in a population. Individuals with beneficial genetic variations are more likely to survive, reproduce, and pass on their genes to the next generation, increasing the frequency of those favorable traits within the population. Over time, this leads to the accumulation of adaptations and the evolution of populations. Genetics provides the foundation for understanding the inheritance of traits and the mechanisms by which genetic variations arise and are transmitted from one generation to the next. It helps explain how variations within genes can result in phenotypic differences and how these variations can be subject to selective pressures in natural environments.

Overall, genetics provides the raw material for natural selection to act upon, and natural selection, in turn, shapes the genetic composition of populations over time. The interplay between natural selection and genetics is fundamental to our understanding of how species evolve and adapt to changing environments.

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Answer:

7800

Step-by-step explanation: :)

A yield sign measures 24 inches on each of its three sides ( equilateral )then the area of the sign is 249.4

Given,

24 inches on each of its three side. (See in attached picture)

Consider ADB,

As it is an equilateral triangle, BD = BC/2 = 12 inches

By Pythagoras theorem,

AB^2 = BD^2 + AD^2

24^2 = 12^2 + AD^2

24^2 – 12^2 = AD^2

576-144 = AD^2

432= AD^2

20.78= AD

Area = ½ (base * height)

       = ½ (24*20.78)

       = 249.4

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Answer:

Step-by-step explanation:

Known:

What to find = x

Exterior angle = 142

Right angle = 90

Unknown:

what unknown value is = ?

Interior angle = ?

1. Find the angle of the interior angles.

180 - 142 = 38

2. Add the two known angles

38 + 90 = 128

3. Subtract from 180

180 - 128 = 52

Hope this helped,

Kavitha Banarjee

Answer: If 50% of the 8 espressos sold were single-shot, that means the other 50% must have been double-shot.

To find out how many single-shot espressos were sold, we can calculate 50% of 8, which is:

0.5 x 8 = 4

So the cafe sold 4 single-shot espressos.

To find out how many double-shot espressos were sold, we can calculate the other 50% of 8, which is also 4.

Therefore, the cafe sold 4 single-shot espressos and 4 double-shot espressos in total.

Step-by-step explanation:

Answer:

Y=2

Step-by-step explanation:

If x=3 we can see that every two lines is 1 number up then the last

same for y access. Y=-2

Answer:

-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2

Apply this particular rule of logs:

log a - log b = log a/b

Therefore, log2 (3) - log2 (12) = log2 (3/12) = log2 (1/4)

This last result simplifies to  log2 1 - log2 4 = 0 - 2 = -2

Answer:

-2

Step-by-step explanation:

\(log_2(3)-log_2(12)\)

~Simplify using log properties

\(log_2(\frac{3}{12})\)

\(log_2(\frac{1}{4})\)

~Apply log rules

\(-log_2(4)\)

~Rewrite

\(-log_2(2^2)\)

~Apply log rules

\(-2log_2(2)\)

~Apply log rules

-2 * 1

~Simplify

-2

Best of Luck!

Answer:

Step-by-step explanation:

Given three elements A, B and C related together according to the expression A(B+C), according to distributive property, the element A will be distributed to the rest of the element as shown;

A(B+C) = A(B)+A(C)

A(B+C) = AB + AC (Law of distributivity)

Given the expression according to the question (1−2g+4h)⋅5, in order to use the distributive law to find the equivalent expression, we will use the concept above as shown;

= (1−2g+4h)⋅5

= 5.(1−2g+4h)

= 5(1)-5(2g)+5(4h)

= 5 - 10g + 20h

Hence the equivalent expression using the distributive property is 5 - 10g + 20h

Answer:

5 - 10g + 20h

\(g(x) = 3^x + 4\) is a parallel shift of f(x) upwards by 4 units. \(h(x) = (1/4)^x - 4\) is a parallel shift of f(x) downwards by 4 units and has a steeper graph. \(j(x) = 3^{(x + 6)} - 2\) is a horizontal shift of f(x) to the left by 6 units and a vertical shift downwards by 2 units.

\(g(x) = 3^x + 4:\)

The function \(g(x) = 3^x + 4\) is obtained by shifting the graph of \(f(x) = 3^x\) upwards by 4 units. This means that the graph of g(x) will lie entirely above the graph of f(x) and will be parallel to it. The y-values of g(x) will be 4 units higher than the corresponding y-values of f(x) for any given x.

\(h(x) = (1/4)^x - 4:\)

The function \(h(x) = (1/4)^x - 4\) is obtained by shifting the graph of \(f(x) = 3^x\) downwards by 4 units. This means that the graph of h(x) will lie entirely below the graph of f(x) and will be parallel to it. The y-values of h(x) will be 4 units lower than the corresponding y-values of f(x) for any given x. Additionally, the base of the exponential function changes from 3 to 1/4, causing the graph to be steeper.

\(j(x) = 3^{(x + 6)} - 2:\)

The function \(j(x) = 3^{(x + 6)} - 2\) is obtained by shifting the graph of \(f(x) = 3^x\) horizontally to the left by 6 units and then shifting it downwards by 2 units. This means that the graph of j(x) will have the same shape as f(x) but will be shifted to the left by 6 units and down by 2 units. The y-values of j(x) will be 2 units lower than the corresponding y-values of f(x) for any given x.

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Answer:

Option D

Step-by-step explanation:

The triangle ABJ is equitorial

So area

Then mBJ is a arc which is 1/6th of circle

Area.

So area of unshaded region

Answer:

\(\textsf{d.} \quad r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\)

Step-by-step explanation:

To find the area of the unshaded region, subtract the area of ΔJGB from the area of sector JGB.

The measure of an arc is equal to its corresponding central angle measure.  Therefore, the central angle of sector JGB is 60°.

As the two sides of ΔJGB adjacent the central angle are the radii of the circle (and therefore equal in length), ∠GJB = ∠GBJ.  

Interior angles of a triangle sum to 180°.  Therefore, all interior angles of ΔJGB are 60° which makes it an equilateral triangle.

Area of an equilateral triangle:

\(\sf A=\dfrac{\sqrt{3}}{4}a^2 \quad \textsf{(where a is the side length)}\)

As the side length of the given equilateral triangle is the radius (r):

\(\implies \sf Area\:of\:triangle=\dfrac{\sqrt{3}}{4}r^2\)

To find the area of the sector, first convert degrees to radians by multiplying the degrees by π/180 :

\(\implies 60^{\circ}=60 \times \dfrac{ \pi}{180}=\dfrac{\pi}{3}\:\:\sf radians\)

Area of a sector of a circle

\(\textsf{A}=\dfrac12 r^2 \theta \quad \textsf{(where r is the radius and the angle }\theta \textsf{ is in radians)}\)

Substituting the angle in radians, the area of the sector is:

\(\implies \sf A=\dfrac{1}{2}r^2\left(\dfrac{\pi}{3}\right)\)

\(\implies \sf A=\dfrac{\pi}6}r^2\)

Area of the unshaded region:

\(\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\\\& = \dfrac{\pi}{6}r^2 - \dfrac{\sqrt{3}}{4}r^2\\\\& = r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\end{aligned}\)

Therefore, the solution is option D.

Answer:

X side of the triangle in the diagram is the hypotenuse because it's side is long than other side

Answer:

Step-by-step explanation:

Answer:

1 1/15

Step-by-step explanation:

16/15

=1 1/15

......

....

..

.

The order of measurements from greatest to least is:

2 1/4 feet > 45 inches > 6 yards.

The measurements are given as 45 inches, 6 yards, and 2 1/4 feet.

First, we need to convert all the measurements to the same unit.

6 yards = 18 feet

2 1/2 feet = 30 inches

So, the three measurements are:

45 inches, 18 feet, 30 inches

Converting everything to inches:

45 inches, 18 feet = 216 inches, 30 inches

Ordering from greatest to least:

216 inches, 45 inches, 30 inches

Therefore, the order of measurements from greatest to least is:

2 1/4 feet > 45 inches > 6 yards.

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Answer:

∠FDE or ∠GDA

Step-by-step explanation:

The adjacent angle refers to the angle which lies right next to an angle, and the sum of the angles is 180, meaning they are supplementary.

Here, in this diagram, there are 2 adjacent angles for ∠FDG :

In Japanese criminal trials, approximately 95% of the defendants are found guilty, while in the United States, about 60% of defendants are found guilty, according to "The Book of Risks" by Larry Laudan.

The statistics provided indicate a stark contrast in conviction rates between Japanese and American criminal trials. In Japan, the overwhelming majority of defendants, around 95%, are found guilty. This suggests a high degree of confidence in the prosecution's ability to prove guilt. On the other hand, in the United States, about 60% of defendants are found guilty, implying a comparatively lower conviction rate. This discrepancy could be due to several factors, such as differences in legal systems, standards of proof, evidence presentation, and judicial practices. It is essential to note that these statistics provide a general overview and may vary depending on specific circumstances and cases within each country's legal system.

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True. The linear regression model is commonly used for descriptive purposes, such as identifying and quantifying relationships between variables.

True. While a linear regression model can be valuable for descriptive purposes, such as understanding relationships between variables, its predictive value can be limited. This is because linear regression models make assumptions about the linearity of the relationship between variables and may not capture more complex patterns in the data. Additionally, factors like outliers, multicollinearity, and overfitting can negatively impact the model's predictive accuracy. Therefore, it is important to consider these limitations when using a linear regression model for prediction purposes. However, its predictive value is limited as it assumes a linear relationship between variables and does not account for complex interactions or non-linearities in the data. Other predictive models, such as machine learning algorithms, may be more effective in predicting outcomes.

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The vector that starts at point A(7, -28, 12) and ends at point B(6, 6, -11) is AB = <-1, 34, -23>. This vector represents the direction and magnitude of the displacement from point A to point B. Vectors are important in mathematics and physics because they represent both magnitude (length) and direction.

To find the vector that starts at point A(7, -28, 12) and ends at point B(6,6,-11), we need to subtract the coordinates of point A from the coordinates of point B. This will give us a vector that starts at the origin (0, 0, 0) and ends at point B - A.

So, the vector that starts at point A and ends at point B is (6-7, 6-(-28), -11-12), which simplifies to (-1, 34, -23). Vectors are important in mathematics and physics because they represent both magnitude (length) and direction.

In this case, the vector (-1, 34, -23) represents the direction from point A to point B. Understanding vectors and their properties can help solve a variety of problems in physics, engineering, and many other fields.

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1.a The probability of throwing at most 2 heads in 5 throws is more probable.

1.b A total of 2^4 = 16 outcomes.

1.c The probability of selecting a black ball, a red ball, and then another black ball is 5/56.

1a. Probability of throwing exactly 15 heads in 20 throws

Probability of getting a head is p = 0.65, and the probability of getting tails is q = 1 - 0.65 = 0.35.

Let X be the random variable which counts the number of heads in 20 throws.

Then X follows the binomial distribution B(20, 0.65).P(X = 15) = 20C15 * 0.65^15 * 0.35^5= 0.16

Probability of throwing at most 2 heads in 5 throws

Let Y be the random variable which counts the number of heads in 5 throws.

Then Y follows the binomial distribution B(5, 0.65).P(Y ≤ 2) = P(Y = 0) + P(Y = 1) + P(Y = 2)

                                                                                                  = 0.01 + 0.08 + 0.25

                                                                                                  = 0.34

Therefore, the probability of throwing at most 2 heads in 5 throws is more probable.

1b. Suppose we flip a fair coin 4 times.

For what combination(s) do there exist exactly 3 permutations?

There are a total of 2^4 = 16 outcomes.

The combinations that exist in exactly 3 permutations are HTTH, HTHT, THHT, THTH, and HHTT.

1c. Probability of selecting a black ball, a red ball, and then another black ball We want to compute the probability of pulling out 3 balls, without replacement, from a box with 5 red balls and 3 black balls.

The total number of ways of pulling out 3 balls is 8C3.

The probability of pulling out a black ball on the first draw is 3/8.

The probability of pulling out a red ball on the second draw is 5/7.

The probability of pulling out another black ball on the third draw is 2/6 = 1/3.

So, the required probability is (3/8) * (5/7) * (1/3) = 5/56.

Therefore, the probability of selecting a black ball, a red ball, and then another black ball is 5/56.

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