Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys?My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?

Answer:

  C.  4² +8² ≠ 10²

Step-by-step explanation:

You want to know why it is not possible for the lengths 4, 8, and 10 to form a right triangle.

The side lengths of a right triangle must satisfy the Pythagorean relation:

  a² +b² = c²

These numbers do not:

  4² +8² = 16 +64 = 80 ≠ 10² = 100

A right triangle is not formed because ...

  4² +8² ≠ 10²

__

Additional comment

The smallest Pythagorean Triple is {3, 4, 5}. Doubling these numbers gives {6, 8, 10}. If the two longest sides are 8 and 10, the shortest must be 6 for a right triangle to be formed.

When the side lengths are reduced to a mutually prime set of numbers, their sum must be even.

   4:8:10 reduces to 2:4:5 which has an odd sum.

The given expression in simplified radical form is  2x⁴ y³  [tex]\sqrt[4]{2y^3}[/tex]

Define Radicals.

The term "radical" is used to represent the square root or nth roots.

Expression with a square root is referred to as a radical expression.

Radicand: The value or phrase contained within the radical symbol.

Given expression is,

[tex]\sqrt[4]{32x^1^6 y^1^5}[/tex]

Rewrite this expression,

we know, 2⁵ = 32

[tex]\sqrt[4]{(2x^4.y^3)^4 .y^3 .2}[/tex]

You see this expression is equal to given expression i.e, [tex]\sqrt[4]{32x^1^6 y^1^5}[/tex]

Take out the term from under the radical,

2x⁴ y³  [tex]\sqrt[4]{2y^3}[/tex]

Hence, the given expression in simplified radical form is  2x⁴ y³  [tex]\sqrt[4]{2y^3}[/tex]

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The mid point of the line segment is (1,9)

The general formula to calculate the midpoint is written as

(x, y) = (x1+x2/2) , (y1 + y2)/2

Where (x1, y1) and (x2, y2) refers the end points.

Here we have given that line segment with endpoints a (-3, 7) and b (1, 11).

And we need to find the midpoint.

While we looking into the given question we have the end point of the line segment

Then the values of (x1, y1) is (-3, 7) and the value of (x2, y2) is (1, 11),

Then the midpoint is calculated by apply the values on the formula, then we get,

=> (1 - 3)/2 , (11 + 7)/2

When we do the appropriate mathematical operation, then we get

=> 2/2 , 18/2

Therefore, the midpoint is (1, 9).

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The density of the drink is 1.04 grams per cm³

Given:

density of grape juice = 1.07 grams per cm³, density of fruit syrup = 1.6 grams per cm³ and density of carbonated water = 0.99 grams per cm³

volume of grape juice = 35 cm³, volume of fruit syrup = 25 cm³ and volume of carbonated water = 310 cm³

First, find the mass of grape juice, fruit syrup and carbonated water using their volume and density:

density = mass / volume

=> mass = density × volume

mass of grape juice = 1.07 × 35 = 37.45 grams

mass of fruit syrup = 1.6 × 25 = 40 grams

mass of carbonated water = 0.99 × 310 = 306.9 grams

Total mass = 37.45 + 40 + 306.9  = 384.35 grams

Total volume = 35 + 25 + 310 = 370 cm³

density of the drink = Total mass / Total volume

density of the drink = 384.35 / 370 = 1.04 grams per cm³

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The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all.

In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.

As per the given numbers in the number line has been drawn below,

The value of a number in the number line is the absolute value without considering the sign.

For example value of -2 is the distance from zero to -2 so it will be 2.

The largest value is 8 among all numbers.

Hence "The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all".

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By using compound interest, it can be calculated that-

A) Deposit is $45544.69

B) Interest = $84455.31

What is compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.

If p is the principal, r is the rate and n is the time in years, then amount is calculated by

[tex]A = p(1 + \frac{r}{100})^n[/tex]

The difference between the amount and the principal is the compound interest

A)Here,

Let the principal be $p

Rate = 6%

Time = 18 years

Amount = $130000

[tex]130000 = p(1 + \frac{6}{100})^{18}[/tex]

[tex]130000 = p(1 + \frac{3}{50})^{18}[/tex]

[tex]130000 = p(\frac{53}{50})^{18}[/tex]

[tex]130000 = p(1.06)^{18}[/tex]

[tex]p = \frac{130000}{1.06^{18}}[/tex]

p = $45544.69

B) Interest = $(130000 - 45544.69)

                  = $84455.31

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Answer:

16.13

Step-by-step explanation:

multiply 10.75 and 1.5 which equals 16.125 so you would round up to 16.13 so your final answer would be $16.13 per hour

The equation in the standard form of a parabola is y = -3x² - 7x - 2

What is the standard form of a parabola?

Another equation that, when graphed, produces a parabola is one written in standard form. Like the letters in the vertex form equation, each letter in the standard form equation provides a nugget of knowledge about the parabola.

Here, we have

The standard equation of a parabola is

y = ax² + bx + c

Substitute the given values in this equation

When x = - 3 and y = -8

-8 = a (-3)² + b (-3) + c

-8 = 9a - 3b + c …. (1)

When x = 0 and y = - 2

-2 = a (0)² + b (0) + c

c = -2....(2)

When x = 2 and y = -28

-28 = a (2)² + b (2) + c

-28 = 4a + 2b + c …. (3)

Equations (1) and (3) can be written as

9a - 3b + c = -8 …. (4)

4a + 2b + c = -28 …. (5)

Multiply equation (4) by 2 and equation (5) by 3 to eliminate 'b'

18a - 6b + 2c = -16

12a + 6b + 3c = -84

Subtracting these equations

30a + 5c = -100

Substitute the value of 'c' here

30a + 5(-2) = -100

30a = -100 + 10

30a = -90

a = -3

Substitute the value of a and c in equation (1)

-8 = 9a - 3b + c

-8 = -27 - 3b -2

-6 = -27 - 3b

3b = -21

b = -7

Here the value of a = -3, b = -7, and c = -2.

Hence, the equation in the standard form of a parabola is y = -3x² - 7x - 2

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Answer:88 i think

Step-by-step explanation:

The required given function is a translation of the parent function by 8 units left and  3 units up.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function, g(x) = (x − 8)³+ 3

Parent function, f(x) = x³

From observation, it is seen that,
The given function is translated function of the parent function as,
As the parent function is translated left on the x-axis by 8 units, and 3 units up on the y-axis.

Thus, the required given function is a translation of the parent function by 8 units left and  3 units up.

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7*2*4 = 56.

7 is the length, 2 is the height, 4 is the widght

Equation for volume is l*h*w

Answer:

√64 = 8

8i

Step-by-step explanation:

i = √-1

but √64 is a positive number which will produce 8i

The equation that represents the total cost you pay for cable television after x months is y = 35 + 29.95x.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Given that a cable operator offers that buy a television at $29.95 per month plus a one-time installation fee.

The total cost that need to pay after 6 months is  $214.70.

Assume that a be the cost one-time installation fee.

Then total cost that need to pay after 6 months is  (6 × 29.95) + a = 179.7 + a

Therefore,

179.7 + a = $214.70

a = 35.

After x month, he needs to pay 35 + 29.95x.

Assume that y represents total cost after x months.

y = 35 + 29.95x

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The monomial that completes the expression is x²

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

36 - 12x + ...

Complete the expression with a variable

So, we have

36 - 12x + y

Rewrite as

y - 12x + 36

The given terms of the expression are factors of 6

By trial and error, we make use the following representation

y - 12x + 36 = (x - 6)²

Expand the expression

y - 12x + 36 = x² - 12x + 16

Evaluate the like terms

y = x²

Hence, the monomial is x²

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The value of the given fraction in mixed numbers is 6, or 36/6.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator.

Here,

=81/6-45/6

=(81-45)/6

=36/6

=6

The value for given fraction in mixed number will be 6 that is 36/6.

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The length of the major arc AB is 15.44 units

Given:  line x + 2y = −5 and circle of radius 5 centered at the origin

The equation of a circle of radius r whose center is the origin O (0, 0) is given by x²+y² = r². Thus:

x²+y² = 5²

x²+y² = 25

To find the points where the line intersects the circle, we can substitute the equation of the circle into the equation of the line.

Substituting this into the equation of the line, we have;

x + 2y = -5

x²+y² = 25

Solving for x, we have

x = (-5 ±√(33))/2

Since the circle is centered at the origin, both of these points are on the circle. Thus, the coordinates of the points A and B are

A: (-5 +√(33))/2, (-5 - √(33))/4

B: (-5 - √(33))/2, (5 - √(33))/4

To find the length of the major arc AB, we can use the formula

length = θ/360 × 2πr

where r is the radius of the circle, and θ is the central angle formed by points A and B. The central angle can be found using the formula

θ= 180 - 2cos⁻¹((AB² + r² - AC²)/(2 × AB × r))

where AB is the distance between the points A and B, and AC is the distance between point A and the center of the circle (which is the origin)

We can use the Pythagorean Theorem to find AB and AC:

AB = √(((-5 + √(33))/2 - (-5 - √(33))/2)² + ((-5 - √(33))/4 - (5 - √(33))/4)²)

     = √(66)

AC = √(((-5 + √(33))/2)² + ((-5 - √(33))/4)²)

    = √(25 + 33)/2

    = √(58)/2

Substituting these values into the formula for θ, we have

θ = 180 - 2cos⁻¹((√(66)² + 5² - (√(58)/2)²)/(2 × √(66) ×5))

  = 180 - 2cos⁻¹((66 + 25 - 29)/(20))

  = 180 -2cos⁻¹(62/20)

  = 180 - 2cos⁻¹(3.1)

  = 180 - 2 × 1.43

  = 180 - 2.86

  = 177.14

Finally, substituting this value into the formula for the length of the major arc, we have

length = 2 × π × 5 × (177.14/360)

           = 2  × π  5 ×  (0.4925)

           = 2 ×  3.14 ×  5 ×  (0.4925)

           = 6.28 × 5 ×  (0.4925)

           = 31.4 ×  (0.4925)

           = 15.44 units

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Answer: Sonya's heart rate increased by 75% after running a mile on the treadmill.

Step-by-step explanation:

To find the percent increase in Sonya's heart rate, we can use the following formula:

Percent increase = (New value - Old value) / Old value * 100

Substituting the given values into the formula, we get:

Percent increase = (133 beats per minute - 76 beats per minute) / 76 beats per minute * 100

Calculating the result, we get:

Percent increase = 57 beats per minute / 76 beats per minute * 100

= 0.75 * 100

= 75%

Therefore, Sonya's heart rate increased by 75% after running a mile on the treadmill.

When the number of machines increased by factor 2 the order would have been finished in 11 hours,

Given that,
All the fudge machines at a chocolate factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Number of hours as of the current number of working machines = 22
The number of machinery now doubled so working hours = 22 / 2 = 11 hours.

Thus, When the number of machines increased by factor 2 the order would have been finished in 11 hours,

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Answer:

x= 1/3rd and 5/3rds

Step-by-step explanation:

9x^2 + 5 = 18x

9x^2-18x+5=0

a=9 b=-18 c=6

x=-b+- the Square root of b^2-4ac all over 2a

so x= 18+- the Square root of -18^2 -4x9x5 all divided by 18

x= 18+- the square root of 144 all over 18

so 18+12 over 18 and 18-12 over 18

this simplifies down to x= 5/3 and 1/3

We can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, the quantity of mixed nuts we need is x pounds.

There are 0.70 pounds of peanuts in this mixture.

3 pounds of peanuts make up the 20% mix, or 0.20*15.

We got the equation:

0.70 x + 3 = 0.40(x + 15)

Now, solve this equation as follows:

0.70 x + 3 = 0.40(x + 15)

0.70 x + 3 = 0.40(x + 15)

0.70x + 3 = 0.40x + 6

0.70x - 0.40x = 6 - 3

0.30x = 3

x = 10 pounds

Therefore, we can add 10 pounds of mixed nuts that contain 20% peanuts by solving equations.

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Answer: centimeters 3

The measures are  NE = 7.5 units, GO = 9 units, AG = 12 units, and the perimeter of the ΔOAG is 36 units.

What is the perimeter of the triangle?

A triangle's perimeter is measured in the same unit as its side lengths. If the lengths of its sides are measured in a different unit, first convert them to that unit.

We have,

OA = (4x + 3)  .............(1)

NE = (2.5x)     .............(2)

RN = 4.5         .............(3)

ER = (2x)         .............(4)

Mid-point segment of the triangle

EN = 1/2(OA)         .............(5)

from equations (1), (2), and (5)

2.5x = 1/2(4x + 3)

5x = 4x + 3

x = 3           .............(6)

OA = 4x + 3 = 15

NE = (2.5x) = 7.5

ER = (2x) = 6

RN = 1/2(GO)

GO = 2 * RN = 2 * (4.5)

GO = 9

ER = 2x = 2*3 = 6

AG = 2(ER) = 2 * 6 = 12

The perimeter of the OAG is OA + AG + GO = 15 + 12 + 9

= 36 units.

Hence, the asked measures are  NE = 7.5 units, GO = 9 units, AG = 12 units, and the perimeter of the ΔOAG is 36 units.

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Answer: y-3 = -4/5(x+0)

Step-by-step explanation:

formula

y-y1=m(x-x1)

y = y coordinate of the second point

y1 = y coordinate of point one

m = slope

x = x coordinate of the second point

x1 = x coordinate of point one

slope formula

y2-y1/x2-x1

-1-3/5-0

slope = -4/5

the 2 points on the graph are (0,3) (5,-1)

substitute and solve

y-3 = -4/5(x+0)

y-3=-4/5x

The Cramer rule can be applied to solve the system of equations and the value of x₂ is x₂ = 12.

For a given system of equations ax + by = c ; px + qy =r, if the determinant of the coefficient matrix [tex]A = \begin{bmatrix}a&b\\p&q\end{bmatrix}[/tex] is non-zero, then as per the Cramer rule, the solution to the system of equations is:

[tex]x=\frac{ \begin{vmatrix}c&b\\r&q\end{vmatrix}}{\begin{vmatrix}a&b\\p&q\end{vmatrix}}\quad\text{and}\quad y=\frac{ \begin{vmatrix}a&c\\p&r\end{vmatrix}}{\begin{vmatrix}a&b\\p&q\end{vmatrix}}[/tex]

The given system of equations is:

-2x₁ - x₂ = 2

-3x₁ - 2x₂ = -3

The coefficient matrix of the system of equations is:

[tex]A = \begin{bmatrix}-2&-1\\-3&-2\end{bmatrix}[/tex]

Now, find the determinant of the coefficient matrix:
[tex]A = \begin{vmatrix}-2&-1\\-3&-2\end{vmatrix}\\A = 4-3\\A =1[/tex]

Since the determinant of the coefficient matrix is non-zero, the Cramer rule can be applied.

According to the Cramer rule, it follows:

[tex]x_2=\frac{\begin{vmatrix}-2&2\\-3&-3\end{vmatrix}}{\begin{vmatrix}-2&-1\\-3&-2\end{vmatrix}}\\\\x_2=\frac{6-(-6)}{1}\\\\x_{2}=12[/tex]

Hence, the Cramer rule can be applied to solve the system of equations and the value of x₂ is x₂ = 12.

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Answer: 28 inches

Hope this helps!!! :)

On solving the question, we that when focus is (0,4) and a directrix y is -4 coordinate is (0,0).

Parabola is the name of the graph of the quadratic function. Another way to think of this is the collection of all points whose distance from the focal point is equal to the distance from the line.

Focus (0,4) ,

the directrix y is (-4)

The vertex (h ,k) - halfway between the,

directrix and focus.

y = [y coordinate of focus + directrix] / 2.

The x coordinate will be the same as the x coordinate of the focus.

[tex]\frac{(0, 4-4)}{2} \\(0,0)[/tex]

Focus of (3,0),

a directrix of x = -3

The vertex (h , k) is halfway

between the directrix

and focus.

x = [x coordinate of focus + directrix] / 2.

The x coordinate will be the same as the y coordinate of the focus.

[tex]\frac{3-3,0}{3} \\(0,0)[/tex]

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the percent of change in the average cost of a gallon from year one to year two is 5.8%

The term "average cost" refers to the production cost per unit, which is determined by dividing the overall production cost by the overall number of units produced.

The overall cost of production can also be divided into fixed and variable costs. Since total fixed costs often remain constant, changes in total variable costs are the main cause of changes in average costs.

The average cost of a gallon of gas in year one was $2.95

The average cost of a gallon of gas in year two was $2.78

The change in the average cost of a gallon from year one to year two is

$2.95 - $ 2.78

⇒$0.17

So percent of change in the average cost of a gallon from year one to year two is

($0.17/$2.95) * 100%

⇒ 0.0576 * 100%

⇒ 5.76%

⇒ 5.8%

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Step-by-step explanation:

[tex]2x + 3y = 5[/tex]

[tex]2x = 5 - 3y[/tex]

[tex]x = \frac{5 - 3y}{2} \\ [/tex]

Answer: Add 3y to both sides of the equation. 2x=5+3y Divide each term in 2x=5+3y by 2 and simplify.