Why can it help to line up the decimal
points before comparing and ordering
numbers with decimals?

Answer:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=[3-(-2)]^2+(9-4)^2

d^2=(5)^2+(5)^2

d^2=25+25

d^2=50

d= [tex]\sqrt{50}[/tex]

d=7.07 units

The probability that washing dishes will take time between 14 and 16 minutes is equal to 25%.

This type of probabilty can be termed a uniform probability in which all the outcomes or results are equally likely.

The lower limit can be represented as a and in this problem is 12 minutes and the upper limit can be considered b and in this problem is 20 minutes.

The equation to find probability, in this case, can be given as:

P ( c ≤ X ≤ d ) = d - c / b - a

Here c = 14 and d = 16 as we have to find the probability that washing dishes will take between 14 and 16 minutes.

Therefore;

P ( 14 ≤ X ≤ 16 ) = 16 - 14 / 20 - 12 = 2 / 8 = 0.25

Converting it into percentage:

0.25 = 0.25 × 100 = 25%

Therefore, the probability that washing dishes will take her between 14 and 16 minutes is calculated to be 25%.

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We can show that x² + 5x = 3 given the dimensions of the rectangle that has an area of 9 cm² as explained below.

To find the area of a rectangle, use the formula given below:

Area of a rectangle = (length)(width).

Given the parameters:

To show that x² + 5x = 3, plug in the values into the formula for the area of a rectangle:

(x + 3)(x + 2) = 9

Apply the distributive property of equality

x(x + 2) + 3(x + 2) = 9

x² + 2x + 3x + 6 = 9

Combine like terms:

x² + 5x + 6 = 9

Add -6 to both sides of the equation

x² + 5x + 6 - 6 = 9 - 6 [subtraction property of equality]

x² + 5x = 3

Thus, if the area of the rectangle with the given dimensions is 9 cm², then we can show that, x² + 5x = 3 as explained above.

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For given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13

In this question, we have been given two functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x²

We need to find f(x) - g(x)

We need to subtract function g(x) from function f(x)

= f(x) - g(x)

= 3x² - 8 - (5 - 2x - 2x²)

= 3x² - 8 - 5 + 2x + 2x²

= 3x² + 2x² + 2x - 8 - 5

= (3 + 2)x² + 2x - (8 + 5)

= 5x² + 2x - 13

Therefore, for given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13

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The probability that the first applicant with advanced training in programming is found on the third interview is  0.0469

Let X denote the number interviewed until 1 has advanced training and follows a geometric distribution with parameter 75%, so

Geometric distribution is: (1-75%)

                                        =0.75

The density function of geometric distribution is,

[tex]P(X=x)=p(1-p)^{x-1}[/tex], for all x = 1,2,3,....

Now, we calculate the probability that the first applicant with advanced training in programming is found on the third interview:

P(X=3) =[tex]0.75(1-0.75)^{3-1}[/tex]

          =[tex]0.75(1-0.75)^{2}[/tex]

          =0.75×0.0625

          =0.0469

Hence, the required probability is 0.0469

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Answer:

Below in bold.

Step-by-step explanation:

10% = 0.10 as a decimal fraction.

After t years:

Amount = 6000(1 + 0.10)^t

Answer:

True???

Step-by-step explanation:

Is this a true or false question?

P+12=even number

Examples...

12+12=24

16+12=28

66+12=78

Answer:

YES

Step-by-step explanation:

even + even = even

always and forever

Answer:

x= x1.5  y = x1.5

E' = E dilated by 1.5

Step-by-step explanation:

-1 x 1.5 =-1.5  -3 x 1.5 = -4.5  (-1.5,-4.5)

0 x 1.5 =0  1 x 1.5 = 1.5  (0,1.5)

3 x 1.5 = 4.5   -2 x 1.5 =-2  (4.5.-3)

Answer:

Answer:

x = 15

Step-by-step explanation:

Let's start by copying down the equation.

6 + 4x + 3 = 6x - 21

Let's simplify this equation and we get,

4x + 9 = 6x - 21

Now, we can add 21 to both sides to isolate 6x on one side. Then, we get...

4x + 30 = 6x

Now, we minus 4x from both sides to get rid of it.

Then we get...

2x = 30

Thus, x = 15

6 + 4x + 3 = 6x - 21

We minus (4x+3) on both side.

6 + 4x + 3 - (4x+3) = 6x - 21 - (4x + 3)

6 = 2x - 24
2x = 30
x = 15.

Recheck : 6 + 60 + 3 = 90 - 21
69 = 69 (nice.)

The system of Inequality for the given graph is;

2x + 3y ≥ 12

3x - 5y ≥ 15

Inequalities that use < or > symbols are always plotted with a dashed line while Inequalities that use ≤ or ≥ symbols are always plotted with a solid line.

Now, if the shaded portion is above a dashed line, the the symbol is > but if it is shaded above a solid  line, then the symbol is ≥. In this question, a solid line is used for both equations and shaded above the lines and so we will use ≥.

Equation of Line 1;

x-intercept = 6

y intercept = 4

Slope = -2/3

Thus, using the general equation of slope of line, the equation of this inequality is; 2x + 3y ≥ 12

Similarly, the equation of the second line will be;

3x - 5y ≥ 15

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Answer:

Non-linear

Step-by-step explanation:

Because the line is not straight.

Answer:

05/20 is not an equivalent fraction

Step-by-step explanation:

1) Write each fraction in its simplest form. To do this divide the numerator by the denominator.

04/12 becomes 1/3

07/21 becomes 1/3

05/20 becomes 1/4

09/27 becomes 1/3

2) all the fractions simplify to the same number except 05/20. So, we can conclude that 05/20 is not an equivalent fraction

The correct option B. It is a one-to-one function; for the given graph.

For the given question;

As, in the given graph for the function, for each value of the domain (the value of x), there is only one value of range (y).

Thus, the given graph shows the one-to-one function.

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The rational equivalent to 0.86 can be written as 43/50.

A rational number may be defined as the number which can be expressed in the form of p/q where p and q are integers, and the term q cannot be equal to zero. It can be either positive or negative or both. We can also say that any fraction which does not have zero in the denominator is called a rational number. Zero can also be regarded as a rational number as it can also be represented as a fraction. For example, 0/2, 0/5.  In order to write 0.86 as a rational number, we have to convert it in fraction form. In fraction form it can be written as

0.86 = 86/100

This is also a rational number, but we simplify it further and we get

86/100 = 43/50 which is a rational number.

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Answer:

Greater.

Step-by-step explanation:

The in the function , the square root term has to give a real number if is to be real. This can only happen if because if then will give a complex number and therefore will not be real.

Thus, the domain for f(x) is all real numbers greater than or equal to 2.

Answer:

The domain for f(x) is all real numbers greater than or equal to 2.

Step-by-step explanation:

Given function:

[tex]f(x)=2x^2+5 \sqrt{x-2}[/tex]

The domain of a function is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken:

[tex]\implies x-2\geq 0[/tex]

Therefore:

[tex]\implies x-2+2\geq 0+2[/tex]

[tex]\implies x\geq 2[/tex]

Therefore, the domain of the given function is greater than or equal to 2.

Answer: x = -21/2

Step-by-step explanation:

2x/2 = -21/2

x = -21/2

Divide both sides by 2.

-21 is not divisible by 2, so -21/2 is improper in simplest form.

The solution for the expression x² = 12 will be x = ±2√3.

The expression is given in the form of square of a variable x which is equal to 12. This expression does not form a perfect square as the constant term is not a perfect square number. A perfect square is a number which is expressed as the square of whole number, or a number multiplied by itself twice. Here, we are given that x² = 12. We take square root of the expression on both the sides then,

√x² = √12

x = √(2×2×3)

x = ±2√3

We use the sign '±' because any number which when expressed in variable form comes out of the square root then it can be positive or negative,

Thus, the value of x is ±2√3.

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Answer:

That means the sum of the first 99 positive integers is 49(100) + 50 = 4900 + 50 = 4950. 2.

The order of the rotational pentagon is 6.

The amount of times a form may be turned in a full circle without losing its appearance is known as its order of rotational symmetry. The only time the triangle appears the same after being rotated a full 360 degrees is when it returns to its original beginning position. It only has one rotational symmetry order, which is the initial position. A form can only have one rotational symmetry order.

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The longest side of a quadrilateral with length of consecutive even integers is 26 feet.

The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers.

A quadrilateral is a polygon with 4 sides.

Therefore, the sides are consecutive even numbers.

Hence,

smallest side = x

Therefore, perimeter is the sum of the whole sides of the quadrilateral.

x + x + 2 + x + 4 + x + 6 = 92

4x + 12 = 92

4x = 92 - 12

4x = 80

x = 80 / 4

x = 20

Therefore, the longest side of the quadrilateral is 20 + 6 = 26 ft.

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Brian will have 46.90 miles to his destination after 41 minutes of driving.

In the question ,

it is given that

Brian has 69 miles left to his destination after 15 minutes of driving

let x denotes the driving time ( in minutes)

and y denote the remaining distance ( in miles )

so the point is represented by (15,69)  

and given that

Brian has 58.8 miles to his destination after 27 minutes of driving

so the second point is (27,58.8).

Since the relationship is given to be linear , hence it will represent a line .

the equation of line passing through the two points (15,69) and (27,58.8) is given by

(y-69)=(58.8-69)/(27-15) * (x-15)

y-69 = -10.2/12 * (x-15)

y-69 = -0.85(x-15)

y-69= -0.85x+12.75

y = -0.85x + 81.75

So , the linear relationship between remining distance and driving time is given by y = -0.85x + 81.75 .

to find miles will he have to his destination after 41 minutes of driving

Substituting x=41 we get

y = -0.85(41) + 81.75

y = -34.85 + 81.75

y = 46.90 .

Therefore , Brian will have 46.90 miles to his destination after 41 minutes of driving.

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The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 [tex]y = \frac{3}{2}x+1[/tex] i.e because they have same slope(rate of change )

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 i.e [tex]y = \frac{3}{2}x+1[/tex]

because they have same slope(rate of change )

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Answer:

(3,2)

Step-by-step explanation:

since -3 + 9 =6

6 ÷ 2 =3

2 + 2 = 4

4 ÷ 2 = 2

therefore (3,2)

Ellie needs 1.5 gallon of milk (that is 24 cups).

we are given 2 cup = 1 pint

we have 24 cup which will be equal to 24/2 i.e. 12 pint.

we are given 2 pint = 1 quart

we have 12 pint which will be equal to 12/2 i.e. 6 quart

we are given 4 quart = 1 gallon

we have 6 quart which will be equal to 6/4 i.e. 1.5 gallon.

Hence, we know 24 cups of milk is equivalent to 1.5 gallon of milk

what are conversions in maths?

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. When a conversion is required, the right conversion factor to an equivalent value must be applied. For instance, 12 inches equals 1 foot when converting between inches and feet.

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answer step by step:

hope this helps

_

Average of given n numbers X1,X2,.........,Xn is x= £xi/n

Let the my number be x

Given:- The average of 3,15,x is 40

£xi/n =40

3+15+x/3=40

Multiplying 3 both side

18+x=120

x=120-18

x=102

Hence, my number is 102