Find the lateral area of a regular prism with height h if the base of the prism is a square with side 2cm and h=125mm

There are 70 ways to split 8 people into two teams of 4. There are 1680 ways to split 9 people into 3 teams of 3. There are 945 ways to choose 2 teams of 4 from 10 prospects.

To find the number of ways to split 8 people into two teams of 4, we can first choose the first team in $\binom{8}{4} = 70$ ways, and the second team will be the remaining 4 people.

To split 9 people into 3 teams of 3, we can first choose the first team in $\binom{9}{3} = 84$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{3} = 20$ ways. The final team will be the remaining 3 people.

To choose 2 teams of 4 from 10 prospects, we can first choose the first team in $\binom{10}{4} = 210$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{4} = 15$ ways. However, since the order in which we choose the two teams does not matter, we must divide by 2 to get the final answer of $\frac{210 \cdot 15}{2} = 945$.

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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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The best interpretation of a 90% confidence interval is that if we were to take 1000 repeated samples of the same size and compute the confidence interval for each sample, approximately 950 of these intervals would contain the true population mean, while approximately 50 would not.

A confidence interval is a range of values within which we are confident that the population parameter (such as the mean) lies. The confidence level refers to the percentage of intervals, computed from repeated samples, that would include the true population parameter.

A 90% confidence interval means that we are 90% confident that the true population parameter falls within the computed interval. Therefore, if we were to take 1000 repeated samples and compute the confidence interval for each sample, we would expect approximately 900 of these intervals to contain the true population parameter (since 90% of the intervals would be expected to contain the true parameter), while approximately 100 intervals would not contain the true parameter.

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Answer:

Step-by-step explanation:

Evaluating the expression gives:

Therefore, the value of the expression is 1536.

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:

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:

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:

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:

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.

Answer:Roughly Symmetric

Step-by-step explanation:

I'm too lazy

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 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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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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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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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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Answer:

Step-by-step explanation:

You want the areas of a kite and a rhombus, given certain segment lengths.

The area of a quadrilateral in which the diagonals cross at right angles can be found from ...

  A = (1/2)(d1·d2) . . . . . where d1 and d2 are the lengths of the diagonals.

The vertical diagonal is 6m +10m = 16m. The horizontal diagonal is 8m +8m = 16m.

The area is ...

  A = (1/2)(16m)(16m) = 128 m²

The area of the kite is 128 square meters.

Each triangle is a right triangle, so the missing half-diagonal length is ...

  d2 = √(13² -5²) = √144 = 12

The area is ...

  A = (1/2)(2·5 cm)(2·12 cm) = 120 cm²

The area of the rhombus is 120 square centimeters.

__

Additional comment

You can save the trouble of using the Pythagorean theorem to find the missing rhombus diagonal if you remember the Pythagorean triple {5, 12, 13}. That triple, along with {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, and (9, 40, 41} are among those commonly seen in algebra, trig, and geometry problems.

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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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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.

The value of x which is the radius of the circle in the image above, is calculated to the nearest tenth as: x = 14.3.

The circle that is shown above has a radius whose length is represented as x. Since the segment that is drawn from the center of the circle intercepts the chord and is perpendicular to the chord, therefore, it bisects the chord into equal segments.

Thus, the perpendicular segment and half of the segment of  the chord will form a right triangle with the radius of the circle.

Therefore, using the Pythagorean Theorem, we have:

x = √(13² + 6²)

x = 14.3 [to the nearest tenth].

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[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]

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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Answer:

Since each of the four sides of a rhombus has an equal length, the perimeter of a rhombus may be calculated using the formula, Perimeter = 4a, where 'a' denotes the length of the side of a rhombus.

Step-by-step explanation:

The perimeter of a rhombus is calculated by multiplying one of its four equal sides by four 4. Four times the length of one the sides is applied to determine the perimeter of a rhombus.

Answer:

23

Also correct 7.32pi

Step-by-step explanation:

The Surface area of the rectangular prism is 1232 square inches

To find the surface area of a rectangular prism, we need to find the areas of all six faces and add them together.

The two faces that have dimensions of 14 inches by 16 inches have a combined area of 2(14 in)(16 in) = 448 square inches.

The other four faces are all rectangles with dimensions of 14 inches by 14 inches, giving us a total area of 4(14 in)(14 in) = 784 square inches.

Therefore, the surface area of the rectangular prism is:

448 + 784 = 1232 square inches.

So the surface area of the rectangular prism is 1232 square inches.

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The coordinates of the midpoint of AB is (2, 4)

If the line y = x+2 meets the curve y² = 4(2x+1) at A and B. Then we can say:

(x + 2)² = 4(2x+1)

Let's solve for x:

(x + 2)² = 4(2x+1)

x² + 4x + 4 = 8x + 4

x² + 4x -8x + 4 - 4 = 0

x² - 4x = 0

x (x - 4) = 0

x = 0, x - 4 = 0

x = 0, x = 4

when x = 0, y = 2

When x = 4, y = 6

Thus, the coordinates of the two points are:

A(0, 2) and B(4, 6)

midpoint of AB = ((0+4)/2 , (2+6)/2)

                          = (2, 4)

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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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To find the domain of the function f(x, y) = ln(16 − x^2 − 16y^2), we need to determine the values of x and y for which the function is defined.

The natural logarithm function ln(x) is defined only for positive values of x. Therefore, for the given function to be defined, the expression inside the logarithm (16 − x^2 − 16y^2) must be greater than zero.

Setting 16 − x^2 − 16y^2 > 0, we can solve for the values of x and y that satisfy this inequality:

16 − x^2 − 16y^2 > 0

-x^2 − 16y^2 > -16

x^2 + 16y^2 < 16

This is the inequality of an ellipse centered at the origin with semi-major axis length 2 and semi-minor axis length 1. Therefore, the domain of the function f(x, y) is the interior of this ellipse.

To sketch the domain, draw the ellipse centered at the origin and shade the interior of the ellipse. The shaded region represents the domain of the function.

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