mr. smith has two children. at least one of them is a boy. what is the probability that both children are boys?

Answer:

(a + 7)(a² + 15a + 59) + 0 = a³ + 15a² + 59a + 12

Step-by-step explanation:

To solve this problem, we can use the long division method.

First, we need to divide the first term of the dividend, which is a³, by the first term of the divisor, which is a. This gives us a quotient of a² with a remainder of 0. We write this as follows:
a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

Next, we multiply the divisor by the quotient and subtract it from the dividend, giving us a new dividend of 15a² + 59a + 12. We write this as follows:

a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

 -  |

a²  | 15a² + 59a + 12

Next, we divide the first term of the new dividend, which is 15a², by the first term of the divisor, which is a. This gives us a quotient of 15a with a remainder of 0. We write this as follows:
a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

 -  |

a²  | 15a² + 59a + 12

   |

   | 15a | 0

Next, we multiply the divisor by the quotient and subtract it from the dividend, giving us a new dividend of 59a + 12. We write this as follows:

a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

 -  |

a²  | 15a² + 59a + 12

   |

   | 15a | 0

    -  |

   15a | 59a + 12

Finally, we divide the first term of the new dividend, which is 59a, by the first term of the divisor, which is a. This gives us a quotient of 59 with a remainder of 0. We write this as follows:
a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

 -  |

a²  | 15a² + 59a + 12

   |

   | 15a | 0

    -  |

   15a | 59a + 12

      |

      | 59 | 0

Since the remainder is 0, this means that the expression (a³ + 15a² + 59a + 12) is divisible by (a + 7). Therefore, the quotient is:

a³ + 15a² + 59a + 12

a + 7

—————

a² + 15a + 59

We can check our answer by multiplying the divisor by the quotient and adding the remainder (which is 0), and verifying that the result is equal to the original dividend
(a + 7)(a² + 15a + 59) + 0 = a³ + 15a² + 59a + 12

Answer: c, 84

Step-by-step explanation:

Answer:

Step-by-step explanation:

66 minutes

The correct statement is:

x= 125, 180 - (63+62) =55 and 180-55=125

What are interior angles?

An Interior Angle is an angle inside a shape.

The basic polygonal shape of a triangle has three sides and three interior angles. It is one of the fundamental shapes in geometry . It has three connected vertices. Triangles can be divided into a variety of categories according on their sides and angles.

The sum of the diagonal internal angles in a triangle determines its outer angle.

And also,

In a triangle, the sum of the interior angles is always 180°.

So, x= 125 ( Because 63+62=125 ) , 180 - (63+62) =55 and 180-55=125

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The equation of a line whose slope is 3/6 and passes through (8, 4) is y- 4 = 3/6(x -8).

The equation of a line:

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, and y to form an algebraic equation, which is referred to as an equation of a line.

Here we have to find the equation of a line.

Data given:

The slope (m) = 3/6

The point = (8,4)

The general formula for the equation of a line:

y - y1 = m( x - x1)

Where (x1, y1) is the point on the line.

As it is given that the point is ( 8, 4) and the slope is 3/6, so we have,

y - 4 = 3/6(x - 8)

Therefore the equation of a line is y-4 = 3/6(x -8).

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Answer:

Option C is the correct answer

C) 150 m

Step-by-step explanation:

Speed = Distance ÷ Time

Distance = Speed × Time

d = 10 × 15

d = 150 m

Thus, The speed of the object is 150 m.

Answer:

d=150m

Step-by-step explanation:

Speed = Distance /Time 

10= d/155

d= 150m

The missing terms will be 0.5, 2, and 7.5 respectibily.

What is equivalent ratio?

The concept of a ratio in mathematics is the divisional comparison of two quantities, the antecedent and consequent. As an illustration, each ingredient must be added according to a ratio during cooking. So, we may argue that a ratio is employed to represent one quantity as a portion of another. The ratio can be written as a fraction as well. If the ratio a:b is a fraction, its form is a/b. As a result, it is simple to compare two or more equivalent ratios expressed as equivalent fractions.

1st ratio is 8:16 = 1/2

So the following terms will be 1:0.5

For 4 it will be 4:2.

For15 it will be 15:7.5.

Hence, The missing terms will be 0.5, 2, and 7.5 respectibily.

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Answer:

1428.33333 yards

Step-by-step explanation:

1 foot = 0.33333 yards

4285 feet = 4285*0.33333 = 1428.33333 yards

Answer:

     [tex]\frac{16}{25}[/tex]

Step-by-step explanation:

[tex]\frac{5*(\frac{4}{5})^{2}*\frac{3}{5} }{3}[/tex]

= [tex]\frac{\frac{5}{1} *\frac{16}{25}*\frac{3}{5} }{3}[/tex]

= [tex]\frac{\frac{5*16*3}{1*25*5} }{3}[/tex]

= [tex]\frac{\frac{240}{125} }{3}[/tex]

= [tex]\frac{\frac{48}{25} }{3}[/tex]

= [tex]\frac{48}{25} /\frac{3}{1}[/tex]

= [tex]\frac{48}{25} *\frac{1}{3}[/tex]

= [tex]\frac{48*1}{25*3}[/tex]

= [tex]\frac{48}{75}[/tex]

= [tex]\frac{16}{25}[/tex]

The measure of each of the acute angles of the right triangle is 32° and 58°.

A right triangle is a kind of triangle which has a right angle (90°) and two acute angles (less than 90°).

Let x = measure of one of the acute angles

If the measure of one acute angle of a right triangle is 6 less than twice the measure of the other acute angle, then

measure of the other acute angle = 2x - 6

The sum of all the angles of any triangle is equal to 180°. Hence,

90° + x + 2x - 6 = 180°

Solve for the value of x.

3x = 96

x = 32

Solve for the measure of the other acute angle.

2x - 6 = 2(32) - 6 = 58

Hence, the two angles are 32° and 58°.

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Answer:

Step-by-step explanation:

Train D I believe

The equivalent fraction is defined below and the few equivalent fractions of 1/2 are 2/4 , 3/6... .

In the question ,

it is given that the fraction is 1/2 .

The Equivalent Fractions are defined as the fractions that have different numerators and denominators but are equal to same value  and

A fraction is a part of the whole ; Equivalent fractions represent the same portion of that whole.

the fraction is 1/2 ,

to find the equivalent fraction , we multiply numerator and denominator by 2 ,

we get , 2/4

on multiplying by 3 , we get

= 3/6 .

Therefore , the equivalent fractions of 1/2 are 2/4 , 3/6 ...

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A function is a mathematical expression that describes the relationship between an input and an output.

The function table is a visual, graded table with cells for input and cells for output that are organized into rows and columns.

Function tables have three variables components. There is the input, the function and the output. Function tables are created so that one of the three components is unknown and the other two serve as the clues to solving the table.

The rule of a function table is the mathematical operation that describes the relationship between the input and the output. The rule must be consistently applied to all input/output parts.

A traditional function table is made using two rows, with the top row being the input cells and bottom row being the ouput celss. Each column represents a signal input/output relationship.

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Answer:

false

Step-by-step explanation:

5²+6²=61.

>

Square root of 61 is 7.81 and not 12 so the points will not meet

According to the given statement, there were 58 children, 29 adults and 64 students.

Algebraically speaking, an equation is indeed a statement that establishes the equivalence of two mathematical equations.

Let there be x number of children, y number of students and x/2 number of adults. Forming the first equation based on number of students -

x + y + x/2 = 151 : Equation 1

Multiply equation 1 with 2

2x + 2y + x = 302 : Equation 2

3x + 2y = 302 : Equation 3

y = (302 - 3x)/2 : Equation 4

Forming second equation based on cost -

5x + 7y + 12x/2 = 1086 : Equation 5

Rewriting this equation

5x + 7y + 6x = 1086 : Equation 6

11x + 7y = 1086 : Equation 7

Keep the value of y from equation 4 in equation 7

11x + 7(302 - 3x)/2 = 1086

11x + (2114 - 21x)/2 = 1086

22x + 2114 - 21x = 2172

x = 2172 - 2114

x = 58

Now,

y = (302 - 3x)/2

y = (302 - 3×58)/2

y = 128/2

y = 64

Number of adults = 58/2

Number of adults = 29

Thus, there were 58 children, 29 adults and 64 students.

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Answer

Step by step explanation

The y - intercept of a linear function is (0, -4).

What is intercepts?

A y-intercept, also known as a vertical intercept, is a point in analytical geometry where the graph of a function or relation intersects the y-axis of the coordinate system, using the convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Thus,

x = 0 is satisfied at these points.

y - intercept is the point which crosses the y - axis.

Since y - intercept is when x = 0

From the table the first point is x = 0.

Hence, the y - intercept of a linear function is (0, -4).

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The solution is Option C.

Number of squares n in a size number s is given by the equation n = 4s + 1

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

Let the number of squares be = n

Let the size number be = s

Now ,

Figure 1 :

The size number s = 1

The number of squares in the figure 1 is = 5 squares

So , the equation will be n = 4s + 1

n = 4 x 1 + 1 = 5 squares

Figure 2 :

The size number s = 2

The number of squares in the figure 2 is = 9 squares

So , the equation will be n = 4s + 1

n = 4 x 2 + 1

n = 8 + 1 = 9 squares

Figure 3 :

The size number s = 3

The number of squares in the figure 2 is = 13 squares

So , the equation will be n = 4s + 1

n = 4 x 3 + 1

n = 12 + 1 = 13 squares

Hence , The equation is given by n = 4s + 1 , where n is the number of squares and s is the size number

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Answer:

It takes 38.5 years for money to quadruple when invested at an annual interest rate of 1.8% compounded continuously.

Answer: 112.64 mL

Step-by-step explanation:

     To find the number of milliliters of liquid in the beaker then, we will add all of the given values together.

      79.89 mL + 32.7 mL + 0.05 mL = 112.64 mL

The verbal expression of 0.25r+0.6s is 0.25 multiplied by r plus 0.6 multiplied by s

An algebraic expression can be described as an expression that is made up of coefficients, factors, terms, constants and variables.

These expressions are also known to be made up of some arithmetic and mathematical operations, which includes;

Examples of algebraic expressions:

2x + y

3x + 7

4z + 1

Given the expression:

0.25r+0.6s

It is written in words as;

0.25 multiplied by r plus 0.6 multiplied by s

Hence, algebraic expressions are made up of constants and terms

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Complete question:

0.25r+0.6s. What is the verbal expression

The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The quadratic equation is given below.

x² - 8x + 16 = 0

The value of the discriminant is given as,

D = b² - 4ac

D = (-8)² - 4(1)(16)

D = 64 - 64

D = 0

The roots of the equation are calculated as,

x² - 8x + 16 = 0

x² - 4x - 4x + 16 = 0

x(x - 4) - 4(x - 4) = 0

(x - 4)(x - 4) = 0

x = 4, 4

The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.

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Answer: 1/4

Step-by-step explanation:

We know the equation is a/b, and a = 6 when b=24, so we just need to plug the number in the spot of the variable.

6/24 = 1/4

On rolling a standard die , the probability of getting a even number and less than 4 is  1/6 .

In the question ,

it is given that ,

a standard die is rolled ,

the total outcomes is {1 , 2 , 3 , 4 , 5 , 6} .

the even numbers are {2,4,6} .

and the outcome that are less than 4 is only {2} .

so , the number of favorable outcome is only 1 .

and total number of outcome is 6 ;

So , the probability is = (favorable outcome)/(total outcome)

Substituting the value from above ,

we get ,

probability is = 1/6 .

Therefore , the required probability is  1/6 .

The given question is incomplete , the complete question is

You roll a standard die. What is the probability of getting a even number and less than 4 ?

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The transformations that map the strip pattern onto itself is a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°. Option A is the correct option.

The strip pattern can be mapped onto itself in two different ways.

Hence, the transformations that map the strip pattern onto itself can be achieved through a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°.

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Answer:

1.963%

Step-by-step explanation:

Use the equation for compound interest

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

[tex]5400 = 4800(1 + \frac{r}{365})^{(365)(6)}\\5400/4800 = 4800(1 + \frac{r}{365})^{(365)(6)}/4800\\1.125 = (1 + \frac{r}{365})^{2190}\\\sqrt[2190]{1.125} = \sqrt[2190]{ (1 + \frac{r}{365})^{2190}} \\1.0000537836544 = 1 + \frac{r}{365} \\1.0000537836544 -1 = 1 + \frac{r}{365} -1\\.0000537836544 = \frac{r}{365}\\(.0000537836544)(365) = ( \frac{r}{365})(365)\\.019631 = r[/tex]

Yes, the given expressions are equivalent.

What is the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

We have,

9(4 - x)

and 36 - 9x

Are these equivalent expressions?

9(4 - x) = 36 - 9x

36 - 9x = 36 - 9x

So, LHS = RHS = 36 - 9x

Therefore, the expression 9(4 - x) and 36 - 9x  are equivalent expressions.

Hence, yes the given expressions are equivalent.

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Answer:

w(3n)=12n+2

Step-by-step explanation:

. Explanation: to evaluate w(3n) substitute n=3n into w(n). ⇒w(3n)=4(3n)+2=12n+2.