a.
You made a critical assumption in problem 4-56 when you made a probability
area model and multiplied the probabilities.
Blood type is affected by genetic inheritance. What if Zack and Nick were
related to each other? What if they were brothers or father and son? How
could that affect the possible outcomes?
b. What has to be true in order to assume a probability area model will give
an accurate theoretical probability?

An isosceles right triangle is a special type of triangle that has two equal sides and one right angle.

It can be described using the Pythagorean Theorem, which states that the sum of the squares of the two legs of a right triangle are equal to the square of the hypotenuse. Mathematically, this can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two legs, and c is the length of the hypotenuse.

In an isosceles right triangle, two of the sides must be equal, so a=b. This means that the Pythagorean Theorem simplifies to 2a^2 = c^2. Solving for a gives a = sqrt(c^2/2). This is the formula for the sides of an isosceles right triangle.

As an example, consider a triangle with a hypotenuse of length 5. Substituting this into the formula gives a = sqrt(25/2), or a = 5/sqrt(2). This means that both of the legs of the triangle have length 5/sqrt(2).

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When y changes directly as x, the variation constant is 5/4.

In a direct variation, the ratio of two variables; in an inverse variation, the product of two variables. The constant of variation k is used in the direct variation equations = k and y = kx, as well as the inverse variation equations xy = k and y =. A constant of variation (k) is a ratio that shows the connection between the independent and dependent variables (x and y) (y). If both variables have known values, it may be determined by dividing y by x. The constant of variation is the number that connects two variables that are either directly or inversely proportional to each other.

Here,

When one thing varies to another there is always a constant of variation. direct variation it is; y = kx

use the x,y values to find k

5 = 4k

5/4 = k

The constant of variation when y varies directly as x is 5/4.

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Using the provided coordinates and the scaling factor, The answer is option b. B'(-4.5, 0), M'(-4.5, 4.5), S'(4.5, -27).

In mathematics, a transformation refers to a function or a mapping that takes an input and produces an output. The input and output can be geometric shapes, vectors, or functions, and the transformation can change their position, size, or shape. Examples of transformations include translation, rotation, scaling, and reflection. In physics and engineering, transformation also refer to mathematical operations used to change a system's variables from one set of coordinates to another set of coordinates.

Scaling refers to the process of enlarging or reducing an object in size, either uniformly or non-uniformly. In mathematics, scaling is often represented by a scaling factor, which is a number used to multiply the coordinates of the object. Scaling can be applied to geometric shapes, vectors, and functions, and it can be done in one or multiple dimensions. Uniform scaling means that the object is scaled by the same factor in all dimensions. Non-uniform scaling means that the object is scaled by different factors in different dimensions.

B(-1, 0), M(-1, 1), and S(1, -6)

scaling factor (k) = 4.5

after scaling,

B'(-4.5, 0), M'(-4.5, 4.5), S'(4.5, -27)

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The total perimeter of fencing that is needed for the entire animal pen is equal to 48 feet.

In order to determine the feet of fencing that is needed for the entire animal pen, we would have to calculate the third side of this right triangle pen by applying Pythagorean's theorem:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right triangle.

16² + b² = 20²

b² = 400 - 256

b = √144

b = 12 feet.

Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:

Perimeter of a triangle = a + b + c

Where:

a, b, and c represents the length of sides of a triangle.

Perimeter of a triangle = 16 + 20 + 12

Perimeter of a triangle = 48 feet.

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Answer: x = 6.2

Step-by-step explanation: don't ask how I know

Answer:

  6 units

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with legs 5 and √11.

The Pythagorean theorem tells you the relation between the legs a, b, and the hypotenuse c of a right triangle is ...

  c² = a² +b²

  c² = 5² +(√11)²

  c² = 25 +11 = 36

  c = √36 = 6

The length of the third side is 6 units.

Unknown numbers are 68, 31.50, 20, 600, 150, 50, 400%, 25%, 50, and 500 as percentages or rates.

A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.

given

1. percentage

p = base x rate

= 80 x 85%

= 68

2. percentage

= 70 x 45%

= 31.50

3. base

b = percentage ÷ rate

= 7 ÷ 35%

= 20

4. base

= 660 ÷ 110%

= 600

5. base

= 120 ÷ 80%

= 150

6. base

= 125 ÷ 250%

= 50

7. rate

= 64 ÷ 16 x 100

= 400%

8. rate

= 85 ÷ 340 x 100

= 25%

9. base

= 13 ÷ 26%

= 50

10. base

= 2.5 ÷ 0.5%

= 500

Unknown numbers are 68, 31.50, 20, 600, 150, 50, 400%, 25%, 50, and 500 as percentages or rates.

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The distance from the home plate to the 2nd base will be 127.27 ft.

What is Pythagoras theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Now using the Pythagoras theorem we can find out the length of the other wall

b²=h²-p²

The distance from home plate to the 2nd base will be

b²=h²-p²

h² = b²+p²

h² = 2*90²

h² = 2*90²

h² = 2*8100

h² = 16200

h = 127.27

Hence The distance from the home plate to the 2nd base will be 127.27 ft.

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Answer: 72cm i think

Step-by-step explanation: L=6cm, W=2cm, H=6cm

6x2x6=72cm

The formula for finding the area of a triangle with an unknown height is: Area = (Base * Height) / 2. This formula uses the base length of the triangle, multiplied by the height of the triangle, then divided by 2.

The formula for finding the area of a triangle with an unknown height is: Area = (Base * Height) / 2. This formula uses the base length of the triangle, multiplied by the height of the triangle, then divided by 2. To use this formula, start by determining the base length of the triangle. This is the length of any one side of the triangle. Once the base is determined, use the formula to calculate the area. In the formula, the base is multiplied by the height of the triangle. Since the height is unknown, use the Pythagorean Theorem to calculate it. The Pythagorean Theorem states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides. Once the hypotenuse is known, the height can be found by using the formula (Height = Hypotenuse - Base) / 2.

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The meaning of 2n in mathematics is just a simple series that gives us different values when we put the integral values of n.

Oftentimes we come across a special series in the mathematical problems.

This mathematical series can be simplified into a quite simpler and a shorter form.

The given form 2n is also nothing but just yet another example of the mathematical series.

When we put the values of end to be 1,2,3,4,5,6,7,8...

We get the values of the expression to be 2,4,6,8,10...

This mathematical series makes problem easier for us understand and solve.

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Answer: Your answer would be 152 cm

Step-by-step explanation:

Outer part of the shape:

Length  =  18 cm  

width  =  12 cm

Area of large rectangle  =  (18 ⋅ 12)

=  216 cm2------(1)

Inner part of shape:

Length  =  6 cm

width  =  3 cm

Area of small rectangle  =  (8 ⋅ 8)

=  64 cm2------(2)

(1) – (2)

=  (216 – 164) cm2

=   154 cm2

I hope this helps!

On solving the provided question, we can say that equality of given trapezium we find, y=13/10 and x=21

A convex quadrilateral with exactly one pair of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. A quadrilateral is a polygon in Euclidean geometry that has four sides and four vertices.

Since ABCD~PQRS

then, on comparing

5y-3/4 = 7/8

y=13/10

On comparing angle,

3x+24=87°

3x=63°

x=21

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Answer:

325 adults and 612 students entered the school play

Step-by-step explanation:

1st equation: x is the number of adults and y the number of students.

2nd equation: Students times what they payed + adults times what they payed:

1st:          x + y = 937

2nd:       2x + 0.75y = 1109

x = 937 - y

Now let's replace x for (937 - y) in the 2nd equation, to find out the value of y:
2(937 - y) + 0.75y = 1109

1874 - 2y + 0.75y = 1109

1874 - 1.25y = 1109

-1.25y = 1109 - 1874

-1.25y = -765 (multiply -1)

1.25y = 765

y = 765 / 1.25

y = 612

Now that we found the y value, let's replace it in the 1st equation to find out the value of x:

x + 612 = 937

x = 937 - 612

x =  325

If you want to double check it, you can replace both in the 2nd equation, to make sure:
2 * 325 + 0.75 * 612 = 1109

650 + 459 = 1109  (checked)

Answer:

B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

The expression p + 0.08p can be interpreted as "p plus 8% of p". Mathematically, this expression is equal to 1.08p, which is the same as saying "p multiplied by 1.08".

We checked the equation of lines are not parallel to each other.

The two lines when located at the same plane and equidistance from each other are called parallel lines. The properties of parallel lines as shown in equation is that both have same slope but different y intercept.

Two parallel lines never intersect.

equation of line passes through the point (- 3, -3) and (3, 9)

is given by the formula [ y - y₁] = [(y₂- y₁) / (x₂- x₁)] [x - x₁}

                                      [ y- (-3)] = [9 - (-3) / 3- (-3)] [x - (-3)]

                                 (y +3) = [(9+3)/ (3+3)] (x+3)

                                  y+ 3 = 12/ 6 (x+3)

                                  y+3 = 2 (x+3)

                                   y+3 = 2x+6

                                   y = 2x+3 this is the first line.

equation of line passes through (-5, 12) and (1, 0)

                          [y - 12] = [(0 - 12) / 1 - (-5)] [x - (-5)]

                       y -12 = -12/ 6 (x+5)

                         y - 12 = -2 x - 10

                        y = - 2x + 2

the above is the equation of second line.

the above two equation have same slope but different sign. Hence, the lines are not parallel to each other.

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The set of points that represents a relation and a function are given as follows:

A relation represents a function when each input value is mapped to a single output value.

Hence the desired relations are given as follows:

As they both have different inputs, hence each input is mapped to a single output and they are functions.

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Find the rise and run to determine the slope. Look up the y-intercept (the point where the line crosses the y-axis) Insert the value into the formula f(x)=mx+b.

For any input, a function will only have one or no outputs. The equation does not define a function if a given input has more than one output. Each value of x must have a maximum of one output value of y in order to be considered a function. To determine the slope of a graphed function, use the average rate of change formula.

The average rate of change from a to some other value x is what determines the instantaneous rate of change at some time[tex]x_{0} =a[/tex]. The average rate of change from x=a+h to x=a is y x = f(x) f(a) x a                     =f (a + h) f( a ) h if h = 0 and a = f ( a + h ) f (a) h are set.

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a. The person who wrote more words in total will be Hudson.

b. Hudson wrote 80 more words

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Isabelle worked for 55 minutes and wrote an average of 16 words per minute. The total words would be:

= 55 × 16

= 880

Hudson worked for 80 minutes and wrote an average of 12 words per minute. The total words will be:

= 80 × 12

= 960

The difference will be:

= 960 - 880

= 80

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P = 140,000 - 41,000

P = 99,000

The population of Brownsville in 1990 was 99,000 people.

By dividing any number 3 to simplify the expression.

What is simplifying an expression?

To simplify an expression, create a similar expression devoid of any similar terms. Therefore, we will rewrite the expression using the fewest number of terms possible.

When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.

One third is one part of three equal parts. When you split an object or number into thirds, you divide it by three.

Thirds are calculated by dividing by 3.

For example: One third of 24 =1/3 of 24 = 24/3 = 8.

Hence, by dividing any number 3 to simplify the expression.

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The prime factorization of 60 from smallest to largest is  2×2×3×5.

Prime factorization is the technique of expressing a number as the product of prime numbers. The only two components in prime numbers are the number itself and the number itself. Prime numbers include, for instance, 2, 3, 5, 7, 11, 13, 17, 19, and so forth. Any number can be represented as a sum of prime numbers using prime factorization.

The prime factorization of the number 60 is,

60 = 6×10.

60 = 2×3×2×5.

60 = 2×2×3×5.

60 = 2²×3×5.

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The diagram models the expression of option D: (x² + x - 2)/(x - 1) = x + 2.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given image is the dissection of an expression.

From the image it can be obtained that -

The area of the shadow of the fourth quadrant is equal to the width of the first quadrant multiplied by the length of the third quadrant.

So, the expression for the statement will be -

x² + x + x - x - 1 - 1 = (x + 1 + 1)(x-1)

x² + x - 2 = (x + 2) (x - 1)

(x² + x - 2)/(x - 1) = x + 2

Therefore, the expression obtained is (x² + x - 2)/(x - 1) = x + 2

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The zeros of the function y = 2x²+7x+1 are -0.35 and -3.35

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.The zeros are often called the roots, solutions, or x-intercepts of the function.

Therefore when y = 0

2x²+7x+1 = 0

using formula method

a= 2, b= 7 and c = 1

x = (-b ± √b²-4ac )/2a

x= -7± √ -7²-4×2×1)/2×2

x= (-7± √ 49-8)/4

x= (-7± √41)/4

x= (-7+√41)/4 or (-7-√41)/4

x =( -7+6.4)/4

or (-7-6.4)/4

x = -1.4/4 or -13.4/4

x = -0.35 or -3.35

therefore the zeros of the function are -0.35 and -3.35

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Answer:  

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is a variable.

The equations that are quadratic equations are:

(i) x^ 2 + 6 x − 4 = 0

(v) 2 x^ 2 − √ 3 x + 9 = 0

The equations that are not quadratic equations are:

(ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0

(iii) x^ 2 + 1/ x^ 2 = 5

(iv) x − 3/ x = x ^ 2

(vi) x ^ 2 − 2 x − √ x − 5 = 0

(vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3

(viii) x + 1 x = 1

In (ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0 the coefficient of x^2 is not a real number.

In (iii) x^ 2 + 1/ x^ 2 = 5 the equation is not in the form of ax^2 + bx + c = 0

In (iv) x − 3/ x = x ^ 2 the equation is not in the form of ax^2 + bx + c = 0

In (vi) x ^ 2 − 2 x − √ x − 5 = 0 the equation is not in the form of ax^2 + bx + c = 0

In (vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3 both sides are not equal

In (viii) x + 1 x = 1 the equation is not in the form of ax^2 + bx + c = 0

So, the equations that are quadratic equations are (i) and (v).

Step-by-step explanation:

The values of x = 14 and y = 6.

Triangles that resemble one another but may not be exactly the same size are said to be similar triangles. When two objects have the same shape but different sizes, they can be said to be similar. 

If ΔABC and ΔPQR are two similar triangles

=> AB/PQ = BC/QR = AC/PR

Here we have

ΔFGH and ΔIJH are two similar triangles

FG/IJ = GH/JH = FH/HI  

From the given data,

6/3 = 12/y = x/7    

Take 6/3 = x/7      

Do cross multiplication

=> 3x = 42

=> x = 14  

Take 6/3 = 12/y  

Do cross multiplication

=> 6/3 = 12/y  

=> 6y = 36

=> y = 6  

Therefore,

The values of x = 14 and y = 6.

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So on solving the provided question we can say that -  table of 5 are as follows - 5,10,15,20,25,30,35,40,,45,50

What is table?
The definition of a mathematical table is a set of numbers that represents the outcome of a computation with different inputs. Numbers and descriptions that are grouped in rows and columns of data. The table of ten pattern is simple to recall. The numbers are 10, 20, 30, 40, 50, 60, 70, 80, 90, etc. in that order. Relationships between data objects are represented using value tables. In your science lesson, you can make use of the values table. Researchers and scientists use tables of values to record data and hunt for patterns in the data. This pattern may then be applied to forecasting.

table of 5 are as follows  -

5,10,15,20,25,30,35,40,,45,50

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The given number 0.02 can be written in exponential form as [tex]2 \times 10^{-2}[/tex] , because to express small number in exponential form power of 10 notation is used .

To write the number 0.02 to exponential form ,

the first step is to move the decimal point to right until it is after the first non zero digit.

In this number we move the decimal point to move two spaces to right.

So , the number becomes ; [tex]\frac{2}{100}[/tex] ;

Now , we multiply the number 2 we created by 10 having exponent of -2. we know that , Whenever decimal point moves to right, the exponent of 10 will be a negative exponent.

The number after the decimal point is always equal number of spaces  decimal point moves.

So , the final exponential form of 0.02 is [tex]2 \times 10^{-2}[/tex] .

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You can conclude that it took you less time on Tuesday to run to and from the playground than it did on Monday.

Distance is defined as the product of speed and time.

To compare the times it took to go to and from the playground each day, you need to calculate the total time for each day.

On Monday, it took 22 minutes to run to the playground and 25 minutes to run back home, for a total time of 47 minutes.

On Tuesday, you ran the entire 4 1/2 miles at a constant speed of 6 1/4 miles per hour, so you can use the formula:

distance / speed = time.

In this case, 4.5 miles / 6.25 mph = 0.72 hours or 43.2 minutes.

Therefore, you can see that it took you 47 minutes on Monday, and 43.2 minutes on Tuesday to run to and from the playground.

Hence, you can conclude that running to and from the playground took you less time on Tuesday than it did on Monday.

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