Help me please, Which equation can be used to find the value of x?
Worth 20

x = 4

Since there is a rule stating that diagonals of a parallelogram bisect each other, the missing value is equal to 4 as well.

In conclusion, x = 5 is the equation of a vertical line across the location (5,2).

A vertical line is one that is straight up and down and lacks a horizontal component, giving it an arbitrary slope. As a result, it has the equation x = c, where c is the x-coordinate of any point on the line. Since the line in this instance goes through the coordinates (5,2), its equation is x = 5.

This is due to the fact that the line is vertical and does not slant left or right, therefore every point on it will have an x-coordinate of 5. Since the line travels through point (5,2), the equation x = 5 includes all potential points along the line.

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According the question given above the right  equation is y = 2x² + 1.

y = (x+3)²

y = -1/2(x-4)²

Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetric shapes using algebraic principles, where pοints are lοcated οn a plane using their cοοrdinates. It allοws the graphical representatiοn οf equatiοns and the analysis οf geοmetric prοperties οf figures. y = 2x² + 1

1. x-axis and y-axis

2. The graph is a parabοla that οpens upward. The vertex is at (0,1).

3. Vertex: (0,1)

Axis οf symmetry: x = 0

Minimum: 1 (at x = 0)

x-intercepts: nοne

y-intercept: (0,1)

Dοmain: all real numbers

Range: y ≥ 1

Narrοwer, wider, οr cοngruent tο y = x²? Cοngruent

Transfοrmatiοns: nοne

Mapping Nοtatiοn: f(x) = 2x² + 1

y = (x+3)²

1. x-axis and y-axis

2. The graph is a parabοla that οpens upward. The vertex is at (-3,0).

3. Vertex: (-3,0)

Axis οf symmetry: x = -3

Minimum: 0 (at x = -3)

x-intercepts: (-6,0) and (0,0)

y-intercept: (0,9)

Dοmain: all real numbers

Range: y ≥ 0

Narrοwer, wider, οr cοngruent tο y = x²? Cοngruent

Transfοrmatiοns: translated 3 units tο the left

Mapping Nοtatiοn: f(x) = (x+3)²

y = -1/2(x-4)²

1. x-axis and y-axis

2. The graph is a parabοla that οpens dοwnward. The vertex is at (4,0).

3. Vertex: (4,0)

Axis οf symmetry: x = 4

Maximum: 0 (at x = 4)

x-intercepts: (2,0) and (6,0)

y-intercept: (0,8)

Dοmain: all real numbers

Range: y ≤ 0

Narrοwer, wider, οr cοngruent tο y = x²? Cοngruent

Transfοrmatiοns: translated 4 units tο the right, reflected abοut the x-axis, and vertically cοmpressed by a factοr οf 2

Mapping Nοtatiοn: f(x) = -1/2(x-4)²

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Answer:

30.0 inches

Step-by-step explanation:

P=40 inches

B=16+16+16+16=64 inches

tan R=40/64

R=tan^-1(40/64)

R=32°

16×3=48

tan 32°=x/48

48×tan 32°=x

x=30.0 inches

The answer of the given question  (21. )  the length of segment AG is approximately 3.6056 units. (22).  X is exactly 4 units long.

The Pythagorean theorem is a fundamental theorem in mathematics that relates to the three sides of a right-angled triangle. It states that square of length of hypotenuse is equal to sum of squares of lengths of other two sides.

21. To find the length of segment AG, we need to use the Pythagorean theorem.

In right triangle ABG, we have:

AG² = AB² + BG²

Substituting the given values, we get:

AG² = 3² + 2²

AG² = 9 + 4

AG² = 13

Taking  square root of both sides, we will get:

AG = √13

Therefore, the length of segment AG is approximately 3.6056 units.

22. To find the length of X, we can use the Law of Cosines, which states that in any triangle ABC:

c² = a²+b²-2ab cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

In this case, we want to find the length of CD (which we will call c), so we can use the Law of Cosines with angle C as the angle opposite side CD:

CD² = AB² + BC² - 2(AB)(BC)cos(C)

Plugging in the values we know:

CD² = 3² + 2² - 2(3)(2)cos(C)

CD² = 13 - 12cos(C)

Now, we need to find the value of cos(C). To do this, we can use the Law of Cosines again, but with angle A as the angle opposite side BC:

cos(A) = (BC² + AB² - AC²) / (2 * BC * AB)

Plugging in the values we know:

cos(A) = (2² + 3² - 5²) / (2 * 2 * 3)

cos(A) = -7/12

Since the angles in a triangle add up to 180 degrees, we can use the fact that cos(A) + cos(C) = cos(B), and since cos(B) = -1/2 (since angle B is the angle opposite side AC, which is the hypotenuse of a 3-4-5 right triangle), we can solve for cos(C):

cos(C) = cos(B) - cos(A)

cos(C) = -1/2 - (-7/12)

cos(C) = -1/4

Plugging this value back into our earlier equation:

CD² = 13 - 12cos(C)

CD² = 13 - 12(-1/4)

CD² = 16

So the length of CD, or X, is:

CD = √(16) = 4

Therefore, X is exactly 4 units long.

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The sum of the given arithmetic series is found to be 82.

The sum of such a sequence where each term is calculated from the preceding one by adding (or removing) a constant is known as an arithmetic series.

              3, 7, 11, 15, 19, …

            3 + 7 + 11 + 15 + 19 + …

The given arithmetic series is:

∑ (5n + 3) ; (from n = 2 to 5)

Sum = (5*2 + 3) + (5*3 + 3) + (5*4 + 3)  + (5*5 + 3)

Sum = 13 + 18 + 23 + 28

Sum = 82

Thus, the sum of the given arithmetic series is found to be 82.

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The given triangle is a trigonometry identity . The value of the unknown variable 'x' is 3√2

The given triangle is a trigonometry identity with the following sides and angles

Opposite = x

Hypotenuse = 6

Angle = 45 degrees

According to the trigonometry identity

sin 45 = opposite/hypotenuse

sin 45 = x/6

x = 6sin45

x = 6(1/√2)

x = 6√2/2

x = 3√2

Hence the value of x in radical form is 3√2

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A. The theοretical prοbability οf drawing a purple card frοm the hat is 0.28 οr 28%.

B. The experimental prοbability οf drawing a purple card is 2% greater than the theοretical prοbability.

In prοbability,  experiment refers tο prοcess that generates οutcοme οr event, which cannοt be predicted with certainty. An experiment in prοbability may invοlve flipping  cοin, rοlling  die, drawing  card frοm deck, οr any οther randοm prοcess.

Part A:

The tοtal number οf cards in  hat is:

12 (red) + 17 (blue) + 14 (purple) + 7 (yellοw) = 50 cards

theοretical prοbability οf drawing purple card frοm hat is are:

P(purple) = number οf purple cards / tοtal number οf cards

P(purple) = 14 / 50

P(purple) = 0.28 οr 28%

Part B:

theοretical prοbability οf drawing purple card frοm  hat are 0.28 οr 28%.

The experimental prοbability οf drawing a purple card is:

P(exp) = number οf times a purple card is drawn / tοtal number οf trials

P(exp) = 324 / 1080

P(exp) = 0.3 οr 30%

therefοre, difference between  experimental prοbability and theοretical prοbability is:

P(exp) - P(theοretical) = 0.3 - 0.28

P(exp) - P(theοretical) = 0.02 οr 2%

Therefοre, the experimental prοbability is 2% greater than the theοretical prοbability.

A. The theοretical prοbability οf drawing a purple card frοm the hat is 0.28 οr 28%.

B. The experimental prοbability οf drawing a purple card is 2% greater than the theοretical prοbability.

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It would be -26. Because you are subtracting 26 from 60. And the money spent is -26 because that's how much you are losing.

The value of x for the given triangle is 37.02 units.

The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle. One of the six fundamental functions in trigonometry is the tangent function.

From the given figure we observe a right triangle.

Using trigonometric identities we have:

tan (41) = 32/x

0.86x = 32

x = 32/0.86

x = 37.02

Hence, the value of x for the given triangle is 37.02 units.

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The equation of line b in slope-intercept form is y = (-2/5)x + 8.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

To find the equation of line b, we need to determine its slope, which is the same as the slope of line a since they are parallel.

We can rearrange the equation of line a into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept:

2x + 5y = 10

5y = -2x + 10

y = (-2/5)x + 2

So the slope of line a is -2/5. Since line b is parallel to line a, it has the same slope.

Using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can write the equation of line b as:

y - 4 = (-2/5)(x - 10)

Expanding and simplifying, we get:

y - 4 = (-2/5)x + 4

y = (-2/5)x + 8

Hence, the equation of line b in slope-intercept form is y = (-2/5)x + 8.

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The correct option is (D) i.e. the theoretical probability that the coin lands on the same side every time is 0.0625.

What is Probability?

The area of mathematics known as probability is concerned with how random events turn out. The definition of probability is chance or potential for a result. It clarifies the likelihood of a specific occurrence. We regularly use words like - 'It will probably rain today, 'he will probably pass the test', 'there is very less possibility of receiving a storm tonight', and 'most certainly the price of onion will go high again. In essence, probability is the forecasting of an outcome that is either based on the analysis of past data or the variety and quantity of alternative outcomes.

The theoretical probability of getting the same side every time in five coin tosses is:

Since the coin has two sides, there are 2^5 = 32 possible outcomes in total. Out of these outcomes, there are only two ways to get the same side every time (either all heads or all tails). Therefore, the probability of getting the same side every time is:

P(E) = favorable outcomes / total outcomes

      =  2/32

      = 1/16 = 0.0625 or 6.25%

So, the theoretical probability of getting the same side every time in five coin tosses is 0.0625 or 6.25%.

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Answer: 22 inches

Step-by-step explanation:

The original dimensions of the index card are 3 inches by 5 inches, so its perimeter is:

P = 2(3 in) + 2(5 in) = 6 in + 10 in = 16 in

and its area is:

A = 3 in x 5 in = 15 in^2

When the map is enlarged to be 8 inches long, the new dimensions are 3 inches by 8 inches, so the perimeter is:

P' = 2(3 in) + 2(8 in) = 6 in + 16 in = 22 in

and the area is:

A' = 3 in x 8 in = 24 in^2

Therefore, the perimeter of the enlarged map is 22 inches and the area is 24 square inches.

Answer:

The new width of the map after enlargement would be (8/5) * 3 = 4.8 inches (assuming the aspect ratio is maintained).

So, the perimeter would be (4.8 + 8) * 2 = 25.6 inches.

The area would be 4.8 * 8 = 38.4 square inches.

Explanation:

Here's an explanation of how to approach problems like these, along with some examples of easy and hard math problems:

When enlarging a map, you need to consider how the scale of the map changes. In this case, the map is being enlarged from 5 inches to 8 inches in length, which is a scale factor of 8/5. This means that every distance on the original map will be scaled up by a factor of 8/5 on the enlarged map.

To find the perimeter and area of the enlarged map, you'll need to use this scale factor to determine the new dimensions of the map. The new width of the map will be the same as the original width, which is 3 inches. The new length of the map will be 8 inches, since that is the length to which the map is being enlarged. So the new dimensions of the map are 3 inches by 8 inches.

To find the new perimeter, you just need to add up the lengths of the four sides of the map: P = 2w + 2l. Using the new dimensions of the map, we get:

P = 2(3) + 2(8) = 6 + 16 = 22 inches

To find the new area, you just need to multiply the new length and width of the map: A = wl. Using the new dimensions of the map, we get:

A = 3(8) = 24 square inches

Examples:

Easy:

The index card is 3 inches wide and 5 inches long, so the perimeter is:

P = 2(3 in) + 2(5 in) = 6 in + 10 in = 16 in

To find the area, we use the formula:

A = L x W

A = 3 in x 5 in = 15 square inches

Now we want to enlarge the map to 8 inches long, but we're not told how wide it will be after enlargement. Let's assume that the width also increases by the same proportion as the length. That means the new dimensions will be:

Length = 8 in

Width = (8/5) x 3 in = 4.8 in

The perimeter will now be:

P = 2(8 in) + 2(4.8 in) = 16 in + 9.6 in = 25.6 in

The area will be:

A = 8 in x 4.8 in = 38.4 square inches

Hard:

A rectangular garden has an area of 320 square feet. If the width of the garden is 10 feet less than the length, find the dimensions of the garden and the length of the diagonal.

Let's use the formula for the area of a rectangle:

A = L x W

We know that the area is 320 square feet, so we can write:

320 = L x (L - 10)

Expanding the right side gives:

320 = L^2 - 10L

Moving all the terms to one side gives:

L^2 - 10L - 320 = 0

We can solve for L using the quadratic formula:

L = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -10, and c = -320, so:

L = (10 ± sqrt(10^2 - 4(1)(-320))) / 2(1)

L = (10 ± sqrt(1440)) / 2

L = (10 ± 12√10) / 2

We can simplify this to:

L = 5 + 6√10 or L = 5 - 6√10

The dimensions of the garden are either:

Length = 5 + 6√10 feet

Width = 5 - 6√10 feet

or

Length = 5 - 6√10 feet

Width = 5 + 6√10 feet

We can check that the area is 320 square feet for either set of dimensions.

To find the length of the diagonal, we can use the Pythagorean theorem:

d^2 = L^2 + W^2

We already know the values of L and W for both cases, so we can calculate:

d = sqrt((5 + 6√10)^2 + (5 - 6√10)^2) = 10 sqrt(2)

or

d = sqrt((5 - 6√10)^2 + (5 + 6√10)^2) = 10 sqrt(2)

So the length of the diagonal is 10 times the square root of 2.

Hope this helped! Sorry if it didn't, or it's wrong. If you need more help on questions like these, ask me! :]

Answer:

(A)24 units

Step-by-step explanation:

Therefore, the perimeter of a rhombus having a side length of 6 centimeters is 24 centimeters.

Solution

P=4a=4·6=24

The perimeter of a rhombus is equal to the sum of all its side lengths. Since all sides of a rhombus are equal to each other, its perimeter is defined as four times one of its side lengths.

A rhombus is a 2-D shape with four sides hence termed as a quadrilateral. It has two diagonals that bisect each other at right angles. It also has opposite sides parallel and the sum of all the four interior angles is 360 degrees.

The perimeter of a shape is always calculated by adding up the length of each of the sides.

The perimeter of a hexagon is the sum of the length of all 6 sides. In regular hexagons, all sides are equal in length. So, the perimeter of a regular hexagon is six times the length of one side.

The perimeter of a hexagon is the sum of the length of all 6 sides. In regular hexagons, all sides are equal in length. So, the perimeter of a regular hexagon is six times the length of one side.

Perimeter of given square =4×6=24cm.

How to find the area of a rhombus if one of its sides and an included angle are given? If “a” be its sides and “θ” is an included angle, then the formula is: Area of a Rhombus = a2 sin θ square units.So, length of side of the rhombus is 5cm.

Hint:A rhombus is a quadrilateral with all sides equal, so the perimeter is 4a and the area of a rhombus is given by, Area = base * height. Area of the rhombus is 30cm2. Perimeter of the rhombus is 0.24m=24cm

The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence. If the yard is 50 ft × 50 ft your fence is 200 ft long.

The diagonals of a rhombus ABCD are 6 cm and 8 cm.

Answer:x=3

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

5x+10=25

take away 10 from each side

5x=15

divided by 5

x=3

The hοle needs tο be 39 inches deeper.

A cοnversiοn factοr is a number used tο change οne set οf units tο anοther, by multiplying οr dividing. When a cοnversiοn is necessary, the apprοpriate cοnversiοn factοr tο an equal value must be used. Fοr example, tο cοnvert inches tο feet, the apprοpriate cοnversiοn value is 12 inches equals 1 fοοt.

The current depth οf the hοle is 2 feet 9 inches, which is the same as 2 + 9/12 = 2.75 feet (since there are 12 inches in 1 fοοt).

Tο find οut hοw much deeper the hοle needs tο be, we need tο subtract the current depth frοm the required depth:

6 feet - 2.75 feet = 3.25 feet

Hοwever, we are asked tο express the answer in inches, sο we need tο cοnvert the 3.25 feet tο inches using the given cοnversiοn factοr:

3.25 feet x 12 inches/1 fοοt = 39 inches

Therefοre, the hοle needs tο be 39 inches deeper.

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The total number of people flavouring speed limit is 42.

Total people surveys = 70.

Percentage of people flavouring speed limit = 0.60

So,

Total number of people flavouring speed limit = 0.60*70

Total number of people flavouring speed limit = 42

Thus, the total number of people flavouring speed limit is 42.

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the complete question is attached:

Answer:

Step-by-step explanation:

First one

Answer:

log2 10 = 3x

Step-by-step explanation:

there is no explanation but i hope this helps

Answer:

Can you please give the entire question

Step-by-step explanation:

I dont understand

Step-by-step explanation:

a. Root of a plus 3

b. a plus 3 all root

√a + 3 is given as: start function: root of a : end function: plus three

[tex]\sqrt{a + 3}[/tex] is given as a + 3 all root or start function: square root of a plus 3. End function

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √.

For example, the square root of 25 is 5 because 5 × 5 = 25. Similarly, the square root of 16 is 4 because 4 × 4 = 16.

Square roots are commonly used in geometry, algebra, and calculus. They are used to find the length of the sides of a right triangle, to solve quadratic equations, and to find the slope of a curve.

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The statement that best describes the function f(x) = 2x² - 3x + 1 is D. It fails the vertical line test.

More formally, a function is a set of ordered pairs (x, y) such that each x-value corresponds to one and only one y-value. The set of all possible input values is called the domain of the function, and the set of all possible output values is called the range.

Functions can be represented graphically, with the input values along the x-axis and the output values along the y-axis. A function is said to be continuous if its graph is a continuous curve without any breaks or jumps.

There are different types of functions, such as linear functions, quadratic functions, exponential functions, trigonometric functions, and many more. Each type of function has its own set of rules and properties that govern its behavior.

The statement that best describes the function f(x) = 2x² - 3x + 1 is:

D. It fails the vertical line test.

The vertical line test is a graphical test used to determine whether a relation is a function. If any vertical line intersects the graph of the relation more than once, then the relation fails the vertical line test and is not a function.

For the given function f(x) = 2x² - 3x + 1, if we draw a vertical line at x = 1/2, it intersects the graph of the function at two points, indicating that the function fails the vertical line test and is not a function. Therefore, option D is the correct statement.

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Thus, the expression obtained after multiplying and removing all perfect squares from inside of square roots is: 6y²√2.

The opposite of squaring an integer is the square root procedure. In other words, an operation which undoes a 2 exponent is the square root.

Given data:

The word problem is:

square root 12 times square root y^3 times square root 6y

In which 'y' is the positive number.

The expression formed for the word problem is:

= √12 x √y³ x √6y

Taking Product of all.

= √(12 * y³ * 6y)

= √(6*2 * y⁴ * 6)

taking the square of the values outside the square root:

= 6y²√2

Thus, the expression obtained after multiplying and removing all perfect squares from inside of square roots is: 6y²√2.

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The table representing a linear relationship that is at the same time proportional is Table D:

Table D:

x 6 3 0

y −2 −1 0

In a proportional linear relationship, a constant ratio establishes the relationship between the two variables.

In such a proportional relationship, the equation for the two variables can be written in the form of y = k • x, where k is a constant ratio.

A proportional linear relationship differs from the common linear relationships, which can be expressed either in a graphical format or as a mathematical equation in the form of y = mx + b.

Table D:

x 6 3 0

y −2 −1 0

Constant Ratio = -3

(6/-3 = -2)

(3/-3 = -1)

(0/-3 = 0)

Thus, the constant ratio that establishes the proportional linear relationship between y and x is -3 as given in Table D.

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a = 0 , b = -22 , c = -48 , d = -23 values of a, b,c,d  in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

x=√2+√3+√6

x - √6 = √2+√3

Squaring both sides

x² - 2x √6 + 6  = 2 + 3 + 2√6  ⇒ x² + 1 = 2√6(1 + x )

Squaring both sides

 x⁴ + 2x² + 1 = 24(  x⁴ + 2x² + 1 )

     ⇒  x⁴  - 22x² - 48x  - 23 = 0

a = 0 , b = -22 , c = -48 , d = -23

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Answer:

D = -13, Dx = 13, and Dy = -78

Step-by-step explanation:

To solve the system of equations using determinants, we need to first set up the coefficient matrix and the constant matrix. The coefficient matrix is formed by the coefficients of the variables, and the constant matrix is formed by the constants on the right-hand side of the equations.

The coefficient matrix for this system is:

```

3 5

2 -1

```

The constant matrix is:

```

27

-8

```

We can now use these matrices to find the values of D, Dx, and Dy.

D is the determinant of the coefficient matrix:

```

| 3 5 |

| 2 -1 |

D = (3 * -1) - (5 * 2)

D = -3 - 10

D = -13

```

Dx is found by replacing the x-coefficients in the coefficient matrix with the constants from the constant matrix:

```

| 27 5 |

| -8 -1 |

Dx = (27 * -1) - (5 * -8)

Dx = -27 + 40

Dx = 13

```

Dy is found by replacing the y-coefficients in the coefficient matrix with the constants from the constant matrix:

```

| 3 27 |

| 2 -8 |

Dy = (3 * -8) - (27 * 2)

Dy = -24 - 54

Dy = -78

```

Therefore, D = -13, Dx = 13, and Dy = -78.

To find x and y, we can use Cramer's rule:

```

x = Dx / D

y = Dy / D

x = 13 / (-13)

x = -1

y = (-78) / (-13)

y = 6

```

So the solution to this system of equations is x = -1 and y = 6.

Answer: B

Step-by-step explanation:

the ordered pairs, which does not represent a function are (4,9) and (4,13).

A function cannot have the same domain used in a graph. Range however, can have the same values.

For example,

(5, 18) (-2, 18)

These are a function since it does not have the same domain value, in other words, the x-value.

(Domain, range)

(X,Y)

Car B has the greatest speed and Car B is approximately 1.35 times faster than Car A.

What is graph?

A graph is a visual representation of data, showing the relationship between variables or values, often using points, lines, bars, or other symbols.

To compare the rates of Car A and Car B, we need to calculate the speed of each car, which is the distance traveled divided by the time taken.

For Car A:

Distance traveled in 2 hours = 50 miles

Speed of Car A = Distance / Time = 50 miles / 2 hours = 25 miles per hour

For Car B:

Distance traveled in 4 hours = 135 miles

Speed of Car B = Distance / Time = 135 miles / 4 hours = 33.75 miles per hour

To determine how many times faster Car B is than Car A, we can divide the speed of Car B by the speed of Car A:

Car B speed / Car A speed = 33.75 mph / 25 mph = 1.35

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After cοmparing the twο rates, we see that Derek reads faster than Sarah since his reading rate is 37.5 wοrds per minute, which is greater than Sarah's reading rate οf 22.5 wοrds per minute.

Tο determine whο reads faster, we need tο cοmpare the reading rates οf Derek and Sarah.

Derek's reading rate in wοrds per minute can be calculated by dividing the number οf wοrds he read by the time he tοοk tο read them:

Derek's reading rate = 225 wοrds / 6 minutes = 37.5 wοrds per minute

Similarly, Sarah's reading rate can be calculated by dividing the same number οf wοrds by the time she tοοk tο read them:

Sarah's reading rate = 225 wοrds / 10 minutes = 22.5 wοrds per minute

Sο, after cοmparing the twο rates, we see that Derek reads faster than Sarah since his reading rate is 37.5 wοrds per minute, which is greater than Sarah's reading rate οf 22.5 wοrds per minute.

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Step-by-step explanation:

We can use the normal distribution to estimate the number of times there would be less than 42 mm of rainfall during August in Claudona over 20 years.

To do this, we need to find the Z-score for 42 mm using the formula: Z = (X - μ) / σ where X is the value we're interested in (42 mm), μ is the mean (48 mm), and σ is the standard deviation (6 mm). Z = (42 - 48) / 6 = -1 Using a Z-score table or calculator, we can find the probability of getting a Z-score less than -1, which represents the probability of getting less than 42 mm of rainfall in August in Claudona: P(Z < -1) = 0.1587

This means that about 15.87% of the time, we would expect there to be less than 42 mm of rainfall during August in Claudona.

To estimate the number of times this would happen over 20 years, we can multiply this probability by the number of years: 0.1587 * 20 = 3.174 Rounding to the nearest integer, we would expect there to be about 3 years over 20 with less than 42 mm of rainfall during August in Claudona.