Under his cell phone plan, Mason pays a flat cost of $51.50 per month and $4 per gigabyte, or part of a gigabyte. (For example, if he used 2.3 gigabytes, he would have to pay for 3 whole gigabytes.) He wants to keep his bill under $65 per month. What is the maximum whole number of gigabytes of data he can use while staying within his budget?

Answer: The answer is 4cm

Step-by-step explanation:

64x1/4 = 16cm2

x2=16

x=4

so the answer is 4cm

hope this helps:)

The price of 1 hamburger is $4.6 and 1 fish sandwich is $5.2

Let 1 hamburger be x

Let 1 fish sandwich be y

Thus, we have:

3x + 2y= 24.20...... eq 1

4x + y= 23.60........ eq 2

Let's use the substitution method here:

Make y the subject formula in eq 2

y= 23.60 - 4x......... eq 3

Put the value of y into eq 1

3x + 2(23.60 - 4x) = 24.20

3x + 47.2 - 8x = 24.20

-5x + 47.2 = 24.20

Exchange values to eliminate the negative symbol

5x = 47.2- 24.20

5x= 23

x= 4.6

Put the value of x into eq 3

23.60- 4(4.6)

y= 23.60-18.4

y= $5.2

Therefore, the price of 1 hamburger is $4.6 and 1 fish sandwich is $5.2

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a) reflection in the line x = -2 is P'Q'R' is shown.

b) The coordinates of image P'Q'R' are

(-12, 0), (-18, -9), R(-5,-5) respectively.

Part a) reflection in the line x = -2

When the triangle PQR with the coordinates P(-4, 0), Q(-6, -3), and R(-5,-5) made a reflection along the x = -2, the coordinates of the image are obtained as;

See the graph; image triangle P'Q'R';

P' = (0, 0)

Q' = (2, -3)

R' = (1, -5)

Part b) dilation with scale factor of 3 using (-1, -4) as the center.

Let the coordinates are;

(x, y) ---> (kx, ky); where k is the scale factor i.e, 3.

This can be written as; (3x, 3y).

For the point  P(-4, 0).

The image of P' = (-4×3, 0×3) = (-12, 0)

For the point  Q(-6, -3)

The image of Q' = (-6×3, -3×3) = (-18, -9)

For the point R(-5,-5)

The image of P' = (-5×3, -5×3) = (-15, -15)

Therefore, the image with the dilation of scale factor of 3 is P'Q'R' are

(-12, 0), (-18, -9), R(-5,-5) respectively.

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The square root of 3 is not greater than the square root of 10/2.  

This is because the square root of 3 is 1. 73 and the square root of 10/2 is 2. 24

The square root of a number can be defined as the factor that when multiplied by itself gives the original number.

The square root is represented with the symbol " √"

From the information given, we are to determine which is greater between the square root of 3 and the square root of 10/2

The expression is represented as;

√ 3

√10/2

Now, let's simply the square root

√3

Find the square root

= 1. 73

√10/2

Find the quotient of 10/2 first, then substitute the value to find the square root, we have;

10/ 2

5

Find the square root of 5

√5 = 2. 24

We can see that the square root of 3 is not greater than the square root of 10/2

Thus, the square root of 3 is not greater than the square root of 10/2

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The solution to the inequality expression 1/5 p > -10 is p > -50

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

1/5 p > -10

Multiply both sides of the inequality by 5

So, we have

5 * 1/5 p > -10 * 5

Evaluate the product

So, we have:

p > -10 * 5

Evaluate the product

So, we have:

p > -50

Hence, the solution to the inequality expression 1/5 p > -10 is p > -50

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Based on the fact that there are 52 cards in the standard deck and you are dealt a 7 card hand, the number of possible hands containing 3 clubs and 4 diamonds is 204,490.

The possibility of selecting a hand with 3 clubs and 4 diamonds is 0.001529.

The number of possible hands can be found as the combination of picking 3 clubs from 13 club cards and 4 diamonds from 13 diamonds card.

This gives us:

= C (13, 3) x C (13,4)

=(13! /(3! x (13 - 3 )!) x (13! / (4! x (13 - 4)!)

= 204,490 hands

The possibility of selecting a hand with 3 clubs and 4 diamonds is:
= Number of possible hands with 3 clubs and 4 diamonds / Number f possible hands from 52 card deck

= 204,490 / 133,784,560

= 0.001529

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The total price of the financed is $7,973

The total finance charges are $2,272.31

The monthly payment if the vehicle is financed for 3 years is $284.59

What is the impact of trade-in allowance on selling price?

The trade-in allowance on the car's selling price reduces the total amount the car dealer would charge a tax of 8% on.

selling price net of trade in allowance=$8850-$1500

selling price net of trade-in allowance=$7,350

the selling price plus sales tax=$7350*(1+8%)

the selling price plus sales tax=$7,938.00

total cost including title fee =$7,938+$35

total cost including title fee=$7,973

finance charges for 3 years=$7,973*9.5%*3

finance charges for 3 years=$2,272.31

monthly payment=($7,973+$2,272.31)/36

monthly payment=$284.59

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The order of numbers from least to greatest :

0.0099998 < 0.059 < 0.09 < 0.11 < 0.111 .

Given, numbers  0.059 , 0.11 , 0.09 , 0.0099998 , 0.111 .

Ascending order : When the set of numbers are to be arranged in least to greatest order.

Descending order : When the set of numbers are to be arranged in greatest to least order.

Now the numbers are to be arranged in ascending order.

Least number : 0.0099998

Second least number : 0.059

Third least number : 0.09

Fourth least number : 0.11

Greatest number : 0.111

Thus the order of numbers in ascending order will be least to greatest .

0.0099998 < 0.059 < 0.09 < 0.11 < 0.111

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Answer:

12x

Step-by-step explanation:

12(5-4x)=60-48x

=12x

Answer:

The top right and left are function.  The top middle is not.  

The bottom left is not a function and the bottom middle and bottom right are functions.

Step-by-step explanation:

To be a function every input can only have one output.  

The top middle is not a function because the input -7 cannot have an output of 5 and 4.

the bottom right is not a function because the input-3 cannot have the output 11 and 19.

Answer:

  (a)  -6x⁴y-2x³y² + 9x²y³ - 3xy + y⁵

Step-by-step explanation:

You want the difference of polynomials (-2x³y² + 4x²y³ - 3xy) - (6x⁴y-5x²y³ -y⁵).

The difference expression is simplified by using the distributive property and combining like terms.

  (-2x³y² + 4x²y³ - 3xy) - (6x⁴y-5x²y³ -y⁵)

  = -2x³y² + 4x²y³ - 3xy - 6x⁴y + 5x²y³ + y⁵ . . . . distribute the minus sign

  = -6x⁴y -2x³y² +(4x²y³ +5x²y³) -3xy +y⁵ . . . . . group like terms

  = -6x⁴y -2x³y² +(4 +5)x²y³ -3xy +y⁵ . . . . . . . . combine like terms

  = -6x⁴y -2x³y² +9x²y³ -3xy +y⁵

__

Additional comment

The terms here are written in "lexicographical" order. All terms with x are listed before any terms that do not have x. If they were listed in "standard form," terms of the same degree would be listed in lexicographical order, and terms of lower degree would be listed later. That would have the effect of interchanging the last two terms.

The difference of the value of polynomials is -6x⁴y -2x³y² +9x²y³ -3xy +y⁵

A polynomial is an expression in mathematics that consists of indeterminates (also known as variables and coefficients) and only uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an illustration of a polynomial of a single indeterminate x. x3 + 2xyz2 yz + 1 is an illustration with three variables.

Numerous branches of mathematics and science make use of polynomials. For example, they are used to define polynomial functions, which appear in contexts ranging from basic chemistry and physics to economics and social science, and they are used to approximate other functions in calculus and numerical analysis.

Polynomial equations are used to encode a wide range of problems, from simple word problems to complex scientific problems.

Lets simply the polynomials

⇒ (-2x³y² + 4x²y³ - 3xy) - (6x⁴y-5x²y³ -y⁵)

= -2x³y² + 4x²y³ - 3xy - 6x⁴y + 5x²y³ + y⁵

= -6x⁴y -2x³y² +(4x²y³ +5x²y³) -3xy +y⁵

= -6x⁴y -2x³y² +(4 +5)x²y³ -3xy +y⁵

= -6x⁴y -2x³y² +9x²y³ -3xy +y⁵

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Answer: 12-(15/3)-3 = 4

Step-by-step explanation:

12-(15/3)-3 = 4

The graph to determine an equation of the circle in

(a) center radius form

(b) general form

 (x -3)² +(y -1)² = 4 . . . . center-radius form

 x² +y² -6x -2y +6 = 0 . . . . general form

The "center-radius" form is

 (x -h)² +(y -k)² = r² . . . . . . . circle with center (h, k) and radius r

The graphed circle has its center at (3,1) and a radius of 2. Putting these numbers into the above form gives the equation

 (x -3)² +(y -1)² = 4 . . . . center-radius form

Expanding the parentheses, we get

 x² -6x +9 +y² -2y +1 = 4

Subtracting 4, and putting in general form, the equation becomes ...

 x² +y² -6x -2y +6 = 0 . . . . general form

a graph (inclusive of a sequence of one or greater factors, strains, line segments, curves, or areas) that represents the variant of a variable in assessment with that of one or greater other variables. the gathering of all factors whose coordinates fulfill a given relation (inclusive of a function)

A graph of a function is a unique case of a relation. within the modern foundations of mathematics, and, generally, in set theory, a function is clearly same to its graph. however, it is regularly useful to look functions as mappings, which consist no longer best of the relation among enter and output, but additionally which set is the domain, and which set is the codomain. as an instance, to mention that a characteristic is onto (surjective) or not the codomain have to be taken under consideration

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[tex] \large \bf \implies{15 \:minutes}[/tex]

In this question speed remain same

[tex] \bf \longrightarrow{Apply \: \frac{d_1}{d_2} = \frac{t_1}{t_2} }[/tex]

[tex] \bf \longrightarrow{\frac{6}{5400} = \frac{1}{t_2} }[/tex]

[tex] \bf \longrightarrow{t_2 = 900 \: second}[/tex]

Convert this second into minutes

[tex] \bf \longrightarrow{1min = 60sec} \\ \bf \longrightarrow{1sec = \frac{1}{60} min} \\ \bf \longrightarrow{ \frac{900}{60} = 15min}[/tex]

Answer:

70

Step-by-step explanation:

if the number Is less than 5 it's takes a 0 if the number is more that 5 it rounds off to the next ten

Answer:

45°

Step-by-step explanation:

59 + x + 80 + 49 + x = 180  the sum of the interior angles of a triangle equal 180  Combine the like terms

2x + 188 = 180  Subtract 1588 from both sides

2x = -8  divide both sides by 2

x = -4  Now plug this in for A

49 + x

49 -4 = 45

Star B is roughly 12 billion years old as star A.

In the situation given in the question where start A is 12 billion years old and star B is from the same cluster as star B.

Therefore, star B is roughly 12 billion years old.

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Answer:

[tex]\boldsymbol{\boxed{\dfrac{6}{11} }}[/tex]

Step-by-step explanation:

According to the classical definition of probability:

[tex]P(A) = \dfrac{m}{n}[/tex]

A - event

m - number of favorable outcomes

n - number of adverse outcomes

According to the task:

A - choose a student

m - 6 students

n - 11 students

[tex]\boldsymbol{\boxed{P(A) = \dfrac{6}{11} }}[/tex]

Answer:

$2.14 per pound

Step-by-step explanation:

To find this: do 6.42 divided by 3, will give you the unit price

In first diagram;

The value of x is 25.

In second diagram;

The value of x is 35.

In third diagram;

The value of x is 29.

In fourth diagram;

The value of x is 400.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, In first diagram;

The pattern is given as;

2 × 3 + 4 × 1 = 10

5 × 2 + 3 × 2 = 16

Hence, The value of x = 3 × 5 + 5 × 2

                                  = 15 + 10  

                                  = 25

In second diagram;

The pattern is given as;

1 × 2 × 3 = 6

4 × 4 × 5 = 80

Hence,  The value of x = 1 × 5 × 7

                                    = 35

In third diagram;

The pattern is given as;

4 × 9 + 2 = 38

8 × 6 + 3 = 51

Hence,  The value of x = 4 × 6 + 5

                                    = 29

In fourth diagram;

The pattern is given as;

5 × 2 = 10 and 10 × 10 = 100

3 × 2 = 6 and 6 × 6 = 36

Hence,  The value of x = 4 × 5 = 20 and 20 × 20 = 400

So,  In first diagram;

The value of x is 25.

In second diagram;

The value of x is 35.

In third diagram;

The value of x is 29.

In fourth diagram;

The value of x is 400.

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The digits for the missing number are 1, 2, 3, 4.

The difference between her vault score and her uneven bar score is 0.367

The floor score must be higher than 15.133 and lower than 15.500

The missing digit must be an integer.

Then all the possible scores are: 15.166 , 15.266 , 15.366 and 15.466

Because 15.166 > 15.133 and 15.466 < 15.500

Then all the possible digits are 1 , 2 , 3 , 4

The difference between her vault score and her uneven bar score is  

= 15.500 - 15.133

= 0.367

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Ana’s gymnastics scores were posted on the scoreboard in order from highest to lowest score. One digit in her floor score is not visible. List all the possible digits for the missing number.

Vault- 15.500

Floor- 15._66

Uneven Bars- 15.133

Beam- 14.200

What is the difference between her vault score and her uneven bar score?

The value of the expression given as [tex]-4\frac 23 - 7\frac 34[/tex] is [tex]-12\frac5{12}[/tex]

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

Simplify negative 4 and 2 over 3 minus 7 and 3 over 4.

Rewrite the above expression properly as follows:

Simplify -4 2/3 - 7 3/4

Using LaTeX, the above expression can be further represented as

[tex]-4\frac 23 - 7\frac 34[/tex]

Rewrite the above fractions and express it as improper fractions

[tex]-\frac{14}3 - \frac{31}4[/tex]

Rewrite the above fractions and take the LCM

[tex]\frac{-14 * 4 - 31 * 3}{12}[/tex]

Evaluate the difference of product in the above expression

[tex]-\frac{149}{12}[/tex]

Rewrite the above expression as a mixed fraction

[tex]-12\frac5{12}[/tex]

Hence, the value of the expression given as [tex]-4\frac 23 - 7\frac 34[/tex] is [tex]-12\frac5{12}[/tex]

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Answer:

Each person would get 1/12 of the original pie

Step-by-step explanation:

3×4=12 1/3÷4=1/12

If a person from this group is selected at random, the probability that this person has type AB blood is 0.0928

From the question we have the total number of persons that there blood types have been collected as 700.

The number of people that have the AB blood type is given as 65.

Hence the probability would be

65 / 700

= 0.0928.

This is the term that is used in the field of mathematics to refer to the likelihood of something occurring. It tells us of the chances that may be present that would show that a certain phenomenon would occur.

Hence the probability is 0.0928

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Answer:

O 2.5%

Step-by-step explanation: