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1. Using the Pythagoras theorem, the area of the rectangle RSTW is 168 units².

2. Using the Pythagoras theorem, the measure of line segment ST is 48 units.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The diagonal SW measures = 25 units

The breadth ST measures = 24 units.

Applying the Pythagoras theorem -

(Hypotenuse)² = (Base)² + (Perpendicular)²

Substituting the values in the equation -

(SW)² = (ST)² + (WT)²

(25)² = (24)² + (WT)²

(WT)² = (25)² - (24)²

(WT)² = 625 - 576

(WT)² = 49

WT = √49

WT = 7 units

The length WT measures = 7 units

The formula for the area of the rectangle is -

Area = Length × Breadth

Area = WT × ST

Area = 7 × 24

Area = 168 units²

Therefore, the area of the rectangle is obtained as 168 units².

The line segment SZ measures = 25 units

According to the properties of rectangle the diagonals bisect each other.

So, the measure of SW = 2(SZ) = 50 units

The length WT measures = 14 units

Applying the Pythagoras theorem -

(Hypotenuse)² = (Base)² + (Perpendicular)²

Substituting the values in the equation -

(SW)² = (ST)² + (WT)²

(50)² = (ST)² + (14)²

(ST)² = (50)² - (14)²

(ST)² = 2500 - 196

(ST)² = 2304

ST = √2304

ST = 48 units

Therefore, the breadth ST measures = 48 units.

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A function that represents the transformation include the following: B. g(x) = (x + 4) + 3.

In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.

Conversely, the translation a geometric figure or graph upward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

By translating the pre-image vertically upward by 3 units and horizontally left by 4 units, the function becomes;

f(x) = x

f(x) → g(x) = (x + 4) + 3.

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The volume of the cylinder is

V = 2πr ∫ x h(x) dx.

Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.

The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.

I first found what x=1 would be in terms of y.

y=(2)3=8

And in terms of y, the original equation becomes:

y=x3x=y13

See the image as the answer is given in the image down below.

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The volume of the cylinder is V = 2πr ∫ x h(x) dx.

Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.

The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.

I first found what x=1 would be in terms of y.

y=(2)3=8

And in terms of y, the original equation becomes:

y=x3x=y13

See the image as the answer is given in the image down below.

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Answer:

Step-by-step explanation:

it is simply factorized.

as we have 2x³-x²-2x+1

we will take common number and variable from it

So as we can see that in this polynomial we can take x-1 common

we will take x-1 common and write the rest polynomial

As we will multiply x-1 with 2x²+x-1    

it will give the previous answer or nmber

Answer: a) 8:6

              b) 8:14

Step-by-step explanation:

You got the answer correct for a but you have to switch the numbers around because the ratio of red apple to green apples is 8:6

Considering the figure, the value of x is calculated using adjacent angles concept and it is solved to be

The angle at PSR is 90 degrees

Also, angle PSQ and angle QSR are adjacent angles hence

angle PSQ + angle QSR = angle PSR = 90

90 = (5x − 12)∘ + (10x − 3)

opening the parenthesis

90 = 5x − 12 + 10x − 3

collecting like terms

90 + 12 + 3 = 5x + 10x

105 = 15x

isolating x by dividing through by 15

15x / 15 = 105 / 15

x = 7

hence the value of x is 7

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The dimensions of the tennis court are 42 feet by 114 feet.

Let the width of the tennis court be x feet.

We can use the formula for perimeter to solve this problem. The perimeter of a rectangle is equal to 2 times the length plus 2 times the width.

2(2x + 30) + 2x = 228

4x + 60 = 228

4x = 168

x = 42

The length of the tennis court is 2x + 30 = 2(42) + 30 = 114 feet.

The dimensions of the tennis court are 42 feet by 114 feet.

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The solutions are 150, 2.5, 39 and 101. The solutions have been obtained using the arithmetic operations.

What are arithmetic operations?

In all, there are four basic mathematical operations which are applicable for all the real number. The operations are as follows:

1.Addition(‘+’) operation which gives the sum of the numbers.

2.Subtraction(‘-’) operation which gives the difference of the numbers.

3.Multiplication(‘×’) operation which gives the product of the numbers.

4.Division(‘÷’) operation which gives the quotient of the numbers.

1. The sum of 6 and the square of 12

The square of 12 = 12*12 = 144

Sum of 6 and 144 = 6 + 144 = 150

2. The quotient of 30 and the sum of 5 and 7

The sum of 5 and 7 = 5 + 7 = 12

The quotient of 30 and 12 = 30 ÷ 12 = 2.5

3. The difference of 4 cubed and 25

The cube of 4 = 4*4*4 = 64

The difference of 64 and 25 = 64 - 25 = 39

4. 5 more than the product of 12 and 8

The product of 12 and 8 = 12*8 = 96

5 more than 96 = 5 + 96 = 101

Hence, the solutions are 150, 2.5, 39 and 101.

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Answer:

40% decrease

Step-by-step explanation:

since it is 100 it is easy to convert to a percentage. 100-60=40 so you have a 40% decrease

The ratios that are equivalent to 12:6 are (a) 10 : 5 and (b) 18 : 9

From the question, we have the following parameters that can be used in our computation:

Ratio = 12 : 6

Divide both sides of this ratio by 6

So, we have the following representation

Ratio = 2 : 1

Multiply the ratio by 9

Ratio = 18 : 9

Multiply the ratio by 5

Ratio = 10 : 5

Hence, the equivalent ratios are 10:5 and 18:9

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Each cut piece measures 6.25 meters in length.

One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.

One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.

Given

The thread was divided into 4 equal pieces after being cut at 25 meters.

= 25/4 \s = 6.25.

The thread was divided into 4 equal pieces after being cut at 25 meters.

= 25/4 \s = 6.25.

Each cut piece measures 6.25 meters in length.

The complete question is,

A 25 meter distance. Cindy cut the string into four equal pieces. each component's quality.

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The angle ∠G will be 140° for the given curve.

An arc is a section of a circle's or curve's boundary in mathematics. It is additionally known as an open curve. The circumference also referred to as the perimeter, is the measurement around a circle that defines its edge.

Given that the angle ∠I is equal to 70°. The value of angle G will be calculated by the angle of the arc theorem.

One-half the size of the central angle is the size of an angle that is inscribed in a circle. Congruent inscribed angles are those that intersect the same arc.

∠I = ( 1 / 2 ) x ∠G

∠G = 2 x ∠I

∠G = 2 x 70

∠G = 140

Hence, the angle ∠G will be 140.

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Answer:

72ft

Step-by-step explanation:

Area of one square = 54ft^2/6 = 9ft^2

The side of the square is the square root of the area, so the side length of one square is

√9ft^2 = 3ft.

each square has a perimeter of

4*3ft = 12ft.

So the perimeter of all six squares is

12ft * 6 = 72ft

By Linear Function f(x) = -4 + 2 and g(x) = x - 3 this we get the Value -2.

The slope-intercept form or the point-slope form are used to find a linear function.

With the aid of an example, the procedure for determining a linear function is the same as determining a line's equation.

When "m" and "b" are real numbers, then a function has the form f(x) = mx + b.

Examples :

f(x) = -4 + 2,g(x) = x - 3: -2

Steps

Find  f ° g given f(x) = -4 + 2, g(x) = x - 3

f ° g = f(g (x))

Constant function results in a constant

f (x )  = -4 + 2

-4 + 2 = -2

Answer = -2.

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Regression toward the mean is most likely to account for the higher scores. So the option 2 is correct.

The answer to this query is based on a long-term investigation. An observational study that tracks the same people across time, sometimes from birth to death, is called a longitudinal study.

The right response is regression to the mean. When a sample point for a random variable is extreme, regression toward the mean is the phenomena that results, with subsequent measurements, in a point that is closer to the mean or average.

This is your response with justification. You can find me in the comments section if you have any questions or doubts about the question or the answer, though.

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The complete question is:

In a flight simulation test, a particular pilot among a group of pilots receives a very low score. However, when he takes the test after six months, he performs considerably better and his scores are closer to the average of the group. Which of the following is most likely to account for the higher scores?

1. instrument decay

2. regression toward the mean

3. carryover effects

4. fatigue effects

Answer: 149 cm^3

To find the volume for a cube, the formula is V = a^3, where a = length of one side.

Smaller cube:

a = 3

(3)^3, or 3 x 3 x 3

= 27 cm^3

Larger cube:

a = 5

(5)^3, or 5 x 5 x 5

= 125 cm^3

To find the volume of the entire sculpture, add the volumes of each of the cubes.

27 + 125

= 149 cm^3

Answer:

(f-g)x is the same as f(x)-g(x)

(f-g)x= 4x^3+7x^2+8x-(7x^2-7x)

= 4x^3+7x^2-7x^2+8x+7x

=4x^3+0+15

=4x^3+15

(f-g)0= 4(0)^3+15

=0+15

=15

The surface area of the interior of the box is the total area of the interior walls of the box.

This can be calculated by subtracting the area of the 5 unit square removed from the total area of the original 20 by 30 unit rectangular sheet of cardboard. This gives us an area of 450 units. To calculate the area of the interior walls, we need to multiply the length and width of the remaining rectangle. This gives us a length of 15 units and a width of 25 units, which gives us a total area of 375 units. Therefore, the surface area of the interior of the box is 375 square units. We can calculate this using the formula A = L x W, where A represents the area, L represents the length and W represents the width.

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Answer:

a) To estimate the probability that the server will earn at least $800 in tips, we need to use the cumulative distribution function (CDF) of the normal distribution, since the mean and standard deviation of the tips are given. The CDF of the normal distribution with mean μ and standard deviation σ is given by F(x) = P(X <= x) = (1/2)(1 + erf((x-μ)/(σ * sqrt(2)))

We can use this formula to find the probability that the server will earn at least $800 in tips. We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the CDF of the normal distribution with μ = $10.70 and σ = $6.70.

P(X >= 800) = 1 - P(X <= 800) = 1 - F(800)

b) To find out how much the server earns on the best 10% of such weekends, we need to find out what the 90th percentile of the distribution is. We can use the inverse cumulative distribution function (ICDF) of the normal distribution to find this. The ICDF of the normal distribution with mean μ and standard deviation σ is given by x = μ + σ * sqrt(2) * erf^-1(2F(x) - 1)

We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the ICDF of the normal distribution with μ = $10.70 and σ = $6.70.

Then we can find the 90th percentile: x = $10.70 + $6.70 * sqrt(2) * erf^-1(2*0.1 - 1)

Please note that the above calculation required erf^-1(inverse error function) which is not a standard function on most calculators, you may need to use a software/programming language to find it.

Answer: The set {x|−7 < x} can be written in interval notation as (-infinity, -7) < x.

This set represents all real numbers greater than -7. The interval notation uses the less-than symbol (<) to represent that all values of x greater than -7 are included in the set. The interval notation uses the infinity symbol to represent the fact that there are no limits on the lower end of the interval.

It's important to note that the interval notation includes the endpoint values when it is in the form of (a,b) or [a,b) but it does not include endpoint values when it is in the form of (a,b] or [a,b].

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

2/3 4/6

Note that in the above problem where a marine biologist uses the triangles shown in the diagram to measure the width of an oil spill in the bay from a safe distance on shore, note that the width of the oil spill is 20m. See the proof below.

In ΔABC and ΔDEC, Note that since

DC = BC; and

EC = AC

It means that ∠DCE = ∠ACB (Diagonal Equality)

⇒ ΔABC ≅ ΔDEC

Therefore:

DE = AB

Since AB = 20m,

DE is also = 20m.

Thus, it is correct to state that the width of the oil spill is 20m.

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The new coordinate of Q after a rotation of 90° is (10, -5)

Rotation simply means turning

In order to answer this question, you need to know the rotation rule  for  90° about the origin.

If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x).

From the graph, the initial coordinate of Q is (-5, -10).

Thus, the new coordinate of Q will be (10, -5)

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The distance of the town from the base of the cliff  is; 62.42 ft

The 6 trigonometric ratios are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/ adjacent

sec θ = 1/cos θ

cosec θ = 1/sin θ

cot θ = 1/cot θ

We are given the angle of depression as 10 degrees. By definition of alternate angles, the angle the hypotenuse formed will make with the base of the town is 10 degrees.

Since the height from the cliff to the town is 354 ft, then we can use trigonometric ratio to find the distance of the town from the base of the cliff as;

354/adjacent = tan 10

adjacent = 354 * tan 10

adjacent = 62.42 ft

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Answer:

To solve the equation Z - 2/5=1/3, we need to get Z alone on one side of the equation.

First we add 2/5 to both sides of the equation to get

Z - 2/5 + 2/5 = 1/3 + 2/5

Z = 1/3 + 2/5

To combine the fractions on the right side of the equation, we need to find a common denominator.

The common denominator of 1/3 and 2/5 is 15

So we can convert 2/5 to 9/15

Z = 1/3 + 9/15

Now we can add the fractions

Z = 12/15 + 9/15

Z = 21/15

So the solution to the equation is Z = 21/15

Step-by-step explanation:

The level of measurement of the data can be given as follows:

Interval or ratio.

There are four levels of measurement for the data, given as follows:

The measures of central tendency for each level are given as follows:

For this problem, we have the arithmetic mean, meaning that the level of measurement can be either interval or ratio.

The problem asks for the level of measurement of the data.

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Answer:

Step-by-step explanation:

5

The composition with rotation to map ΔABC to ΔA'B'C' is;

Reflection across the y-axis and 270 degrees counterclockise rotation about the origin

A rotation is defined as a type of transformation that takes each point in a figure and rotates it to a specific number of degrees around a given point.

Now, the coordinates of triangle ABC from the graph are;

A(-8, -2)

B(-6, 3)

C(-5, -1)

The coordinates of triangle A'B'C' from the graph are;

A(-2, -8)

B(3, -6)

C(-1, -5)

Now, the transformation rule for reflection across the y -axis is (x, y) → (-x, y) .

Finally rotation 270 degrees counterclockwise will produce;

(-x, y) → (y, x)

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The coordinates of the image of the point Q is Q'(3, 6).

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

From the given graph, we have point Q(-4, 4).

Here the point is translated.

After translation, the original figure is shifted from a place to another place without affecting it's size.

The rule of translation is given as the point (x, y) is translated as (x + 1, y + 2).

So the given point is (-4, 4).

(-4, 4) after translation becomes by the definition (-4 + 1, 4 + 2).

So the required point is (-3, 6).

Hence the image of point Q is (-3, 6).

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Your question is incomplete, Probably, the correct graph for the question is given below.

Answer:

Choice C. is the answer

Step-by-step explanation:

greetings !!

just following the series the

If any questions and unclear ideas tag on comment box.

Hope it helps!!!