how many different triangles with sides measuring 3,4, and 5 exist?

The explicit formula an=−4n−1 represents the sequence defined recursively by a1=1 and an=−4an−1 for n≥2.

The given sequence is defined recursively as follows: a1=1 and an=−4an−1 for n≥2.

To find the explicit formula for this sequence, we need to express the nth term of the sequence in terms of n without any reference to the previous terms.

Let's write out the first few terms of the sequence to look for a pattern:

a1=1

a2=−4a1=−4

a3=−4a2=16

a4=−4a3=−64

a5=−4a4=256

It seems that each term is obtained by multiplying the previous term by -4. In general, we can write:

an=−4n−1

This is the explicit formula that represents the given sequence. We can check that it satisfies the recursive formula by substituting it into the recurrence relation:

a n​ =−4a n−1​ = −4(-4^(n-2)) = -4^(n-1) = -4n-1

Therefore, the explicit formula an=−4n−1 represents the sequence defined recursively by a1=1 and an=−4an−1 for n≥2.

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The distance between you and your friend is 61.8 feet.

You let 52 feet of string on your kite. Your friend is standing in an unknown distance from you, with the kite flying on air somewhere between you two. From your friend the angle of elevation is 70 degrees. The angle formed at the kite is 64 degrees.

Therefore, the distance between you and your friend can be calculated as follows:

The situation forms a triangle. The distance between them can be found using sine law.

Hence,

a / sin A = b / sin B = c / sin C

Therefore,

52 / sin 70 = b / sin 64

where

Therefore,

52 / sin 70 = b / sin 64

cross multiply

52 sin 64 = b sin 70

b = 52 sin 64 / sin 70

b = 47.8413539862 / 0.77389068155

b = 61.8175709726

b = 61.8 feet

Therefore,

distance between them = 61.8 feet

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A common control procedure in a group design is b. random assignment of subjects to groups. Random assignment is a crucial step in experimental research designs to ensure that participants have an equal chance of being assigned to different groups. It helps in minimizing the influence of confounding variables and increasing the internal validity of the study.

Random assignment involves assigning participants to different groups (e.g., experimental group and control group) based on chance alone. This process helps ensure that any observed differences between groups after the intervention can be attributed to the independent variable (the variable being manipulated) rather than pre-existing differences between participants.

By randomly assigning participants to groups, researchers can create groups that are statistically equivalent in terms of their characteristics, which allows for better comparison of the effects of the independent variable. Random assignment helps control for potential biases and ensures that any observed differences in the dependent variable (the outcome being measured) can be attributed to the treatment or intervention.

Random assignment also helps reduce the potential for systematic bias, as it minimizes the chances of experimenter bias or self-selection bias influencing the results. It enhances the reliability and generalizability of the findings by providing a more rigorous and unbiased comparison between groups.

Random assignment of subjects to groups is a common control procedure in group designs because it helps ensure the internal validity of the study by reducing confounding variables and increasing the likelihood that any observed differences between groups are due to the treatment or intervention being studied.

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Answer:Roughly Symmetric

Step-by-step explanation:

I'm too lazy

Answer:

23

Also correct 7.32pi

Step-by-step explanation:

Hello,

kᵃ x kᵇ = kᵃ⁺ᵇ

kᵃ ÷ kᵇ = kᵃ⁻ᵇ

7⁹/7² x 7⁹

= 7⁹⁻² x 7⁹

= 7⁷ x 7⁹

= 7⁷⁺⁹

= 7¹⁶

Since the graph of F(x), has the same shape as the graph of G(x) = x³ - x², but it is shifted to the left 1 unit, its equation is: B. F(x) = (x + 1)³ - (x + 1)²

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

On the other hand, the translation a geometric figure or graph upward simply means adding a digit to the numerical value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, we have the following transformation:

(x, y)                               →                  (x - 1, y)

G(x) = x³ - x²                  →        F(x) = (x + 1)³ - (x + 1)²

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Complete Question:

The graph of F(x), shown below, has the same shape as the graph of G(x) = x³ - x², but it is shifted to the left 1 unit. What is its equation?

F(x) =

OA. F(x) = (x-1)3³ -(x-1)²

B. F(x) = (x + 1)³ - (x + 1)²

C. F(x)=x²-x²-1

O D. F(x)=x²-x²+1

Answer: System

Step-by-step explanation:

The question defined a system.

For future reference

Temperature is a measure of the average kinetic energy of molecules

Potential Energy is a measure of how much energy can be turned into kinetic energy (think a ball about to be dropped)

Matter is a term for stuff, everything is made of matter, atoms and molecules

Kinetic energy is energy in motion (think a falling object)

States are the position or form things are in, this is probably going to be used as "states of matter" (solids, liquids, gasses)

Conduction is the transfer of heat or electricity through two objects touching

Energy is "the ability to do work" think of energy like a general term for potential and kinetic energy, undefined if you ill

Hope this helps

A. The distance from the x - axis to the top of the circle is 10.3 feet

B. The equation of the circle is (x - 2)² + (x² - 3)² = 4

C. The equation of the parabola is x = a(y - k)² + h

D. The area of the window is 9.2 ft²

A. (14.6 - x)² + (4.6/2)² = 10.6 { Pythagores theorem"}

(14.6 - x) + 5.29 = 112.36

(14.6-x)² = 112.36 - 5.29

14.6-x)²= 107.07

(14.6 - x)² = 107.07

X= 213.16 - 107.07

x = 106.09

X=10.3 feet

B. The equation of the circle is (x - 2)² + (x² - 3)² = 4

The equation represents a circle centered at the point (2, 3) with a radius of 2 units, as determined by the standard form equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

C. The equation of the parabola is x = a(y - k)² + h

D. The area of the window is determined using the following below:

x = a(y - k)² + h, where a is the horizontal stretch or compression factor.

x = 14.6 (10.1 - 4.6)² + 4.6

x = (147.47 - 67.16)² + 4.6

x = 80.31)² + 4.6

x = 84.37²

x = 9.2 ft

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Answer:

Step-by-step explanation:

You want the solutions to various problems involving ratios, proportions, and scale factors.

The ratio of 15 apples ot 25 oranges can be written several ways, with and without units:

  15 apples to 25 oranges, or 15 to 25.

  Reduced to 3 apples to 25 oranges, or 3 to 5

  15 apples : 25 oranges, or 15 : 25

  Reduced to 3 apples : 5 oranges, or 3 : 5

  15 apples / 25 oranges, or 15/25

  Reduced to 3 apples / (5 oranges), or 3/5

You can solve the proportion ...

  x/9 = 10/12

by multiplying both sides by 9:

  x = 9·10/12 = 90/12

  x = 15/2 = 7.5

If each inch represents 12 ft, then 8 inches represents 8·12 ft = 96 ft.

The actual length of the back wall is 96 feet.

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Answer: B. Food

Step-by-step explanation:

If those two angles are equal (alt exterior angles)  then lines u and v are parallel.

6x + 14 =80

6x = 80-14

6x = 66

x = 11

So when x =11, then lines u and v are parallel.

Given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ).

Given the expression:
sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ))
Let's simplify this expression step by step:
1. First, recognize that cos(θ) * cos(θ) can be written as cos²(θ). So, the expression becomes:
sin(θ) + cos²(θ) * (1 - cos(θ))
2. Next, we'll distribute cos²(θ) to both terms inside the parentheses:
sin(θ) + cos²(θ) - cos³(θ)
At this point, we have simplified the expression as much as possible. The final expression is:
sin(θ) + cos²(θ) - cos³(θ)
In summary, given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ). Remember that this is a general expression and its specific value depends on the angle θ.

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A variable with equal distances between score units and a true meaningful zero is called a ratio variable.

Ratio variables have the properties of interval variables, meaning that the distances between consecutive values are consistent, and they also have an absolute zero point. The true zero allows for meaningful ratios to be calculated between values. For example, if we have a variable representing weight, a value of 0 indicates the absence of weight, and we can make meaningful statements such as "one object is twice as heavy as another."

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The number that Alice is writing is 9,008,352.

We are given that;

Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones

Now,

To find the number that Alice is writing, you need to identify the place value of each digit based on the clues given. You can use a place value chart to help you. You can write your solution as:

Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones

3  

5

8  

2

9    

Therefore, by algebra the answer will be 9,008,352.

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The area of the figure E in terms of x  is x² + 2xy + y²

The figure is added as an attachment

The dimensions of the figures are

A = x by x

B = x by y

C = y by y

D = x by y

So, we have

Area of A = x²

Area of B = xy

Area of C = y²

Area of D = xy

This means that the area of E is

E = x² + 2xy + y²

From the above, we can see that the expression has 3 terms

Also, we have the coefficient of x² to be 1 and the coefficient of x to be 2y

The degree of the expression is 2

This is because the highest power is 2

The name of the algebraic expression is a sum of squares

Lastly, we have

x = 3 and y = 2

This means that

Area = 3² + 2 * 3 * 2 + 2²

Evaluate

Area = 25

Hence, the value of the expression is 25

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Answer:

1.8

Step-by-step explanation:

speed = distance/time

Distance measured in km

Time measures in hours

750m = 0.75

25mins = 0.42 of an hour

0.75/0.42 = 1.8 to 1dp

Answer:

-----------------------

We know that:

Find the speed and convert as below:

Answer:

The true statements about solving equations are:

-You are using inverse operations to isolate the variable.

-Order of operations is often done in reverse order.

Answer: the true statements are. you are inverse operations to isolate the variable. the addition property is usually used first. and Order of operations is often done in reverse order

Step-by-step explanation:

The triangle with segments AB=4cm,BC=6 cm and angle ABC=90° is constructed

We follow the certain steps to construct a triangle ABC

Firstly we have to draw a line segment AB = 4 cm and extend till X

By using Compass draw an arc taking B as center intersecting at P & Q on AB & BX

Increasing compass width slightly taking P as center Draw an arc

Now by keeping the same measurements with compass draw arcs taking Q as center such that it intersects arc drawn in step 3 at R

Now draw a line from B passing through R  and taking length = 3 cm and mark the other end as C

Now join AC

Construct perpendicular  Bisector of AC at O

By taking O as center and radius = OA = OB = OC , draw an circle

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Using a ruler and a pair of compasses only,construct

(i) a triangle ABC ,given AB=4cm,BC=6 cm and angle ABC=90°.

(ii) a circle which passes through the points A,B and C and mark its centre as O.

Answer:

3/10

Their favourite is pizza

Step-by-step explanation:

30% = 30/100

simplified is 3/10

Answer:

3/10

Step-by-step explanation:

1. 30%=3/10

2. The schools favorite lunch is pizza

If Bill has 20 apples and Sarah has 15 apples, and they put them in a big pile and eat half, then There are 17.5 apples left.

Bill has 20 apples and Sarah has 15 apples. When they put them together in a pile, the total number of apples is 20 + 15 = 35. They eat half of the apples, which is equivalent to dividing the total number of apples by 2.

35 / 2 = 17.5

Therefore, there are 17.5 apples left after they eat half of the pile. It's important to note that while the concept of "half an apple" may not be physically possible, we can still express the result as a decimal to represent the fractional amount remaining. In this case, 17.5 represents the remaining apples after dividing the original pile in half.

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The three statements that are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   .......equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

Based on the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

By comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x - 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

Step-by-step explanation:

Evaluating the expression gives:

Therefore, the value of the expression is 1536.

1) Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. 2) The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. 3) trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

1. Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. Therefore, the ratios of the sine, cosine, and tangent of the corresponding angles in similar triangles will also be equal.

2. The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. This means that the sine of an angle is equal to its complement's cosine, and vice versa.

3. Using the appropriate formula based on the given information, trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

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When x = 8, 26 is the right answer.

We have to given that;

A team in a group trivia game receives 5 points for a right response and -2 points for an incorrect one.

In addition, the game has 15 questions.

Since, We know that;

According to the definition of a mathematical expression, it is a grouping of variables and functions that are created using addition, subtraction, multiplication, and division.

Now, We have find the expression as;

For a team, the correct answer is worth 5 points, and the incorrect response is worth -2 points.

In addition, the game has 15 questions.

Hence, We get;

⇒ 5x - 2 (15 - x)

At x = 8;

⇒ 5 × 8 - 2 (15 - 8)

⇒ 40 - 2 × 7

⇒ 40 - 14

⇒ 26

Thus, The correct solution when x = 8 is,

⇒ 26

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The term that describes an event that increases the likelihood of a response being repeated is known as reinforcement.

Reinforcement can be defined as any consequence that strengthens or increases the probability of a behavior occurring again in the future. This can include positive reinforcement, which involves adding a desirable consequence after a behavior, or negative reinforcement, which involves removing an aversive consequence after a behavior. Both types of reinforcement have been shown to be effective in increasing the likelihood of a behavior being repeated.

Overall, understanding the concept of reinforcement is essential in the field of psychology, particularly in the areas of behaviorism and behavior modification. By providing positive consequences after desired behaviors, individuals can be motivated to continue engaging in those behaviors, which can lead to long-term positive changes. Reinforcement can also be used to shape new behaviors or replace unwanted behaviors with more desirable ones.

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Answer:

6 + 13i – (7 – 15i)

= 6 + 13i - 7 + 15i (distribute the negative sign)

= -1 + 28i (combine like terms)

Therefore, the answer is -1 + 28i in the form of a + bi.

Step-by-step explanation:

The most appropriate answer would be option a) "Confounding is likely to be a problem in the interpretation of these results."

Now, let's consider the 95% confidence interval (CI) provided as (0.8, 3.8). A confidence interval is a range of values within which the true population parameter (in this case, the risk ratio) is likely to fall. The lower and upper bounds of the confidence interval in this case are 0.8 and 3.8, respectively.

Confounding refers to the presence of an extraneous factor that is associated with both the exposure and the outcome and can distort the observed association.

In this situation, since the confidence interval includes the null value of 1 (i.e., 1 is within the range), it suggests that the observed association may not be statistically significant.

A statistically significant result means that the observed association is unlikely to have occurred due to chance alone.

Therefore, option a) "Confounding is likely to be a problem in the interpretation of these results" is a reasonable conclusion.

Hence the correct option is (a).

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Complete Question:

What can be said about the situation in a cohort study reporting an adjusted risk ratio of 2.5, with a 95% confidence interval of (0.8, 3.8)

a) Confounding is likely to be a problem in the interpretation of these results,

b) This estimate had a P value that was at or below 0.05.

c) There is a clear and strong association between the exposure and the health outcome understudy.

d) None of the above.

[tex]f(x)=3x^2+5\\g(x)=4x-2\\h(x)=x^2-3x+1\\\\f(x)+g(x)-h(x)=3x^2+5+4x-2-(x^2-3x+1)\\f(x)+g(x)-h(x)=3x^2+4x+3-x^2+3x-1\\f(x)+g(x)-h(x)=2x^2+7x+2[/tex]

[tex]A(x)=4x^2-5x-3x^3+6[/tex]    and   [tex]B(x)=3x^3-5x-4+6x^2[/tex]. Sort the polynomial A(x), B(x) according to the decreasing power of the variable. The final solution for N(x) is;

  [tex]N(x)=10x^2-10x+2[/tex]

To type the polynomials A(x) and B(x) in line with the lowering energy of the variable, we want to arrange the phrases in order that the highest diploma term comes first, observed with the aid of the next maximum diploma time period, and so forth. We also want to mix any like phrases which have identical diplomas. For example, A(x) has two terms with degree 2, so we will upload them collectively. Here is how we kind A(x) and B(x):

[tex]A(x) = -3x^3 + 4x^2 - 5x + 6[/tex]

[tex]B(x)=3x^3+6x^2-5x-4[/tex]

To calculate N(x) = A(x) + B(x), we want to feature the corresponding phrases of A(x) and B(x) which have an equal degree. For example, to locate the coefficient of [tex]x^3[/tex] in N(x), we want to add the coefficients of x^three in A(x) and B(x), which might be -3 and +3 respectively. Here is how we calculate N(x):

[tex]N(x)=(-3+3)x^3+(4+6)x^2+(-5-5)x+(6-4)[/tex]

[tex]N(x)=10x^2-10x+2[/tex]

This is the final solution for N(x).

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