The mode is the number in the set that appears the most.
In the given data set, the number 45 is listed twice while all the other numbers are only listed once.
The mode is 45.
Answer:
45
Step-by-step explanation:
The value which appears most often or has the highest frequency in a data set is said to be the mode.
Here we are given the following data set:
{41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}
For this data set, we can see that the number / element 45 has occurred the most often which is twice. So the mode of this data set will be 45.
Last August we had 729 7th grade students. This august we started with 1084 7th grade students. what was the percent increase in 7th grade enrollment from august 2017 to august 2018?
Answer:
The percent increase was 48.7.
Step-by-step explanation:
The absolute increase in enrollment is 1084 - 729 = 355. This corresponds to a relative increase of 355/729=0.487 (relative to Aug 2017). The proportion 0.487, expressed in percent: 48.7%
Depending on your current method to exercise, you could solve this using the proportionality method: 355/729 = x/100, then cross-multiply and solve for x. Same thing.
will mark brainlest
Find the constant of proportionality for the table and write in the form y = kx.
A) y = 1
15
x
B) y = 10x
C) y = 15x
D) y = 150x
Divide y by x:
150/10 = 15
135/9 = 15
30 /2 = 15
They all equal 15
This means the constant of proportionality would be y = 15x
The answer is C.
Answer:
Option C is correct
y = 15x
Step-by-step explanation:
Direct variation states that:
[tex]y \propto x[/tex] ......[1]
then, the equation is in the form of:
[tex]y=kx[/tex], where k is the constant of variation.
From the given table :
consider any points;
x = 9 and y = 135
Substitute these in [1] we have;
[tex]135 = 9k[/tex]
Divide both sides by 9 we have;
15 = k
or
k = 15
then, the equation we have; y = 15x
Therefore, the constant of proportionality for the table and write in the form y = kx is, y = 15x
The table below shows Britney's distance, in miles, from her destination after different time intervals in hours: Time (hours) (x) 2 4 1 3 6 5 7 Distance from destination (miles) (y) 1,000 880 1,060 940 760 820 690 What is the correlation coefficient for the data, and what does it represent? 0; it represents no correlation between x and y 0.999; it represents a linear positive correlation between x and y −0.999; it represents a linear negative correlation between x and y 0.999; it represents a linear negative correlation between x and y
Answer:
r = -0.9997
Step-by-step explanation:
A statistics calculator gives the value
r = -0.9997
You can see in the graph below that it represents an excellent negative correlation between x and y.
Every point appears to be exactly on the regression line .
It represents a linear positive correlation between x and y −0. 999.
Given
The table shows Britney's distance, in miles, from her destination after different time intervals in hours:
Time (hours) (x) 2 4 1 3 6 5 7
Distance from destination (miles) (y) 1,000 880 1,060 940 760 820 690
What is the correlation coefficient?A number between +1 and −1 is calculated so as to represent the linear interdependence of two variables or sets of data.
Then,
The correlation coefficient for the data, and what does it represent is;
It represents no correlation between x and y.
0.999; Represents a linear positive correlation between x and y.-0.999; represents a negative correlation between x and y.0.999; it represents a negative correlation between x and y.Hence, it represents a linear positive correlation between x and y −0. 999.
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PLEASE HELP ILL MARK BRAINLIEST AND THANK YOU, 100 POINTS!!!!!!!
19. Graham's class raise $200 in a coin drop for a school fundraiser. The total for the entire school campus was 4.8 * 10^3 how many times greater was the total amount raised by the school compared to grahams class? Express your answer in scientific notation.
Answer:
2.4 * 10^1
Step-by-step explanation:
Divide the two numbers. 4.8 * 10^3 = 4800
4800/200 = 24
Put into scientific notation
24 = 2.4 * 10^1
4.8 * 10^3 is 24 (2.4*10^1) times greater than 200
The total amount raised by the school is 24 times greater than the amount raised by Graham's class.
Explanation:The amount raised by Graham's class is $200.
The total amount raised by the school is [tex]4.8 * 10^3.[/tex]
To find the number of times greater the total amount raised by the school is compared to Graham's class, we need to divide the total amount raised by the school by the amount raised by Graham's class.
So, we divide 4.8 * 10^3 by 200 to find the number of times greater the total amount raised by the school is compared to Graham's class.
Therefore,
[tex]= 4.8 * 10^3/ 200[/tex]
[tex]= 2.4 * 10^1.[/tex]
Therefore, the total amount raised by the school is 24 times greater than the amount raised by Graham's class.
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#2. Find the missing side. Round to the nearest tenth.
5.3
Step-by-step explanation:The mnemoic SOH CAH TOA reminds you that ...
... Tan = Opposite/Adjacent
... tan(24°) = x/12
Then multiplying by 12 gives ...
... 12·tan(24°) = x = 5.34274 ≈ 5.3
Which of the following ordered pairs is a solution to y = 2^x?
(3, 8)
(3, 9)
(3,27)
Answer:
(3, 8)
Step-by-step explanation:
For x = 3,
. . . y = 2^x
. . . y = 2^3 = 2·2·2 = 8
This is represented by the ordered pair (x, y) = (3, 8).
Answer:
(3,8)
Step-by-step explanation:
Since the answer choices are given we can plug the "x" value and see if it returns the y-value given in the ordered pair (x,y) and so:
[tex]y=2^x[/tex]
Let's use the ordered pair (3,8) meaning that when x=3 y =8 and so:
[tex]y=2^3=2\times2\times2=8[/tex]
[tex]y=8[/tex]
This is correct and so this is a solution, since the solution is unique when x=3 y is always going to return an 8.
Solve for x I the equation x^2+14x+17=-96
Answer:
x=-7+8ı ,-7-8ı
Step-by-step explanation:
Move all terms to one side
x²+14x+17+96=0
Simplify x²+14x+17+96 to x²+14x+113
x²+14x+113=0
Use the quadratic Formula
x= -14+16/2 , -14-16ı/2
Simplify Solutions
x=-7+8ı ,-7-8ı
In the figure, what is the area of the shaded region?
Answer:
30 units ^2
Step-by-step explanation:
To find the area of the shaded region, we find find the area of the large triangle and subtract the area of the unshaded triangle.
A of large triangle = 1/2 b*h
height = (6+3) = 9
The base is found by using the pythagorean theorem c^2 = a^2 + b^2
We need to find b^2
c^2 -a^2 = b^2
taking the square root on each side
sqrt(c^2 -a^2) = sqrt(b^2)
the base = sqrt(c^2 -a^2)
= sqrt( 15^2 - 9^2)
= sqrt(225-81)
= sqrt(144)
=12
Now that we know the base and the height, we can find the area
A of large triangle = 1/2 b*h
= 1/2 * 12 * 9
= 6*9 = 54
Using the rule of similar triangles
9 6
---- = ----------
12 base
We can use cross products to find the base of the smaller triangle
9* base = 12*6
9* base = 72
Divide by 9 on each side
base = 72/9 = 8
Now we can find the area of the smaller triangle
base = 8 and height = 6
A of smaller triangle = 1/2 b*h
= 1/2 *8 * 6
= 4*6 = 24
Area of the shaded region = Area large triangle - Area of small triangle
= 54-24
= 30
please help with this and show work
9. AM ≅ AT
10. x=3, y=5
AH being the perpendicular bisector of MT means MH ≅ TH. Then ΔAHM ≅ ΔAHT by SAS, and by CPCTC.
... SAS — side-angle-side: if two adjacent sides and the included angle of a triangle are congruent to their corresponding sides and angles in another triangle, the two triangles are congruent.
... CPCTC — Corresponding Parts of Congruent Triangles are Congruent
___
Using the result of problem 9 as a guide, you can say that ...
... 2x = x+3 ⇒ . . . . (subtract x from both sides)
... y +4 = 2y -1 ⇒ . . . . (add 1-y to both sides)
((− 1/2 )y^4)^3·(–16y^2)
one half of y to the power of four to the power of three times sixteen y squared
Answer:
2y^14
Step-by-step explanation:
= (-1/2)^3 · (y^4)^3 · (-16) · y^2
= (-1/8)·(-16) · (y^(4·3) · y^2) . . . . . simplify some
= 2 · y^(12 +2) . . . . . simplify more
= 2y^14
1.) (7.RP.3) Tracy started a savings account that is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. Tracy invests $5,000 at 4.5%, what is the total simple interest accumulated in the checking account after 2 years? Show your work. *
$4.50
$45
$450
$4,500
$45,000
2. (7.RP.3) Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest. What rate of interest did the certificate pay? *
$450
Step-by-step explanation:Each year, the amount of interest earned is ...
... 4.5% × $5000 = $225
After 2 years, a total of ...
... $225 × 2 = $450
has been transferred.
_____
Comment on percentages
Of course, you know that 4.5% = 4.5/100 = 45/1000 = 0.045.
You can think of the % symbol as a fancy (shorthand) way to write /100. (Likewise, the ‰ symbol means /1000.)
PLZ HELP ASAP WILL MARK BRAINIEST
Which graph represents the inequality:
-6 x 2
Attachment
QUESTION 32
4 is a solution of x < -5
True
False
QUESTION 33
Solve for x: x + 3 > 5
x > 2
x > 8
x > 1
x > 3
Answer:
31) Second number line
32) False
33) x>2
Step-by-step explanation:
31) Since -6<x has only < sign but no = sign, it will be an open dot on top of -6.
Since x≤2 has = sign, it will be a closed dot on top of 2.
So, second number line is the correct option.
32) x < -5 represents all the numbers to the left of -5 on a number line like -6,-7,-8,-9 etc.
Since 4 is on the right side of -5 on the number line, it won't be a solution of the inequality x < -5.
33) x+3 > 5
Subtracting 3 from both the sides of the inequality, we have
x + 3 -3 > 5 - 3
Cancelling out the +3 and -3 from the left side, we have
x > 2
1. The 2nd number line represents the inequality.
Explanation:
In words, the inequality reads "negative six is less than x, which is less than or equal to two". On the number line, the open circle at negative six means that -6 is not a solution to the inequality: -6 < x. The point at positive two means that positive two is a solution to the inequality: x ≤ 2. Therefore, all numbers greater than -6 and less than or equal to +2 are solutions to the inequality. This is shown on the second number line.
2. False
Explanation:
In words, the inequality reads "x is less than negative five". This means that all numbers less than -5 are solutions to the inequality. Positive four is not less than negative five, so it is not a solution to the inequality.
3. x > 2
Explanation:
To solve the inequality, we have to move all the terms that do not contain x to one side. This inequality is simple because it only requires one step: subtraction.
Solve for x: x + 3 > 5
1. Subtract 3 from both sides to get x by itself:
x + 3 - 3 > 5 - 3
2. Simplify
x > 2
The graph shown represents an inequality. The solid line that forms the boundary tells you that ______.
The graph is correct.
The inequality is correct.
The inequality has no equal sign in it.
The inequality has an equal sign in it.
Answer:
D. The inequality has an equal sign it
Step-by-step explanation:
We use solid lines whenever the inequality contains [tex]\leq[/tex] or [tex]\geq[/tex]. That means it contains an equal sign which means the boundary line is inclusive.
On the other hand when the inequality does not have an equal sign in it we use a dashed line to indicate that all values on the boundary line are not inclusive.
That is we use a dashed or broken line for the boundary line of an inequality whenever it contains [tex]\:<\: or \:>\:[/tex].
The correct answer is D
Analyze the diagram below and complete the instructions that follow.
Find m < 0
A.
49
B.
59
C.
63
D.
78
Answer:
A. 49°
Step-by-step explanation:
∠O is the other base angle (along with ∠Q) of the isosceles triangle OPQ. Base angles of an isosceles triangle have the same measure.
At a farm, there are two huge pits for storing hay. 90 tons of hay is stored in the first pit, 75 tons in the second pit. Then, three times as much hay was removed from the first pit as was removed from the second pit. After that, there was half as much hay in the first pit as there was now in the second pit. How many tons of hay was taken from the first pit?
Answer:
63 tons
Step-by-step explanation:
The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.
The amount remaining in the first pit is 90-x.
The amount remaining in the second pit is 75 -x/3.
Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...
... 90 -x = (1/2)(75 -x/3)
... 180 -2x = 75 -x/3 . . . . multiply by 2
... 105 - 2x = -x/3 . . . . . . subtract 75
... 315 -6x = -x . . . . . . . . multiply by 3
... 315 = 5x . . . . . . . . . . . add 6x
... 63 = x . . . . . . . . . . . . . divide by 5
63 tons of hay were taken from the first pit.
_____
Check
After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.
Please answer ASAP will give brainliest
1. Work out the expression -2.5(1 - 2n) - 1.5n using both the Distributive Property and Combining Like Terms
2. Can we subtract -2.5 - 3.5n?
3. Can we add -2.5 + 3.5n?
4. Can we subtract -2.5 - 6.5n?
someone help pls need help on this one
Answer:
[tex]\dfrac{2}{3x^5y}[/tex]
Step-by-step explanation:
A negative exponent in the numerator is the same as a positive exponent in the denominator, and vice versa.
... a^-b = 1/a^b . . . . . for any value of b, positive or negative
The exponent of a product is the sum of the exponents:
... (a^b)(a^c) = a^(b+c)
___
Applying these rules, you have
... = 2/(3x^4·x·y) = 2/(3x^(4+1)·y) = 2/(3x^5·y)
What would be the answers for the three boxes please help
Look at the prime factorization. If all the factors have powers that are multiples of 6, then the number is a square and a cube. If they are multiples of 3, then a cube; if multiples of 2, then a square.
1000 = 2³·5³ . . . . a perfect cube
4 = 2² . . . . a perfect square
120 = 2³·3·5 . . . . none of the above (not a square or a cube)
36 = 2²·3² . . . . a perfect square
100 = 2²·5² . . . . a perfect square
49 = 7² . . . . a perfect square
125 = 5³ . . . . a perfect cube
25 = 5² . . . . a perfect square
The price of a gallon of gasoline has increase, on average from $2.50 in 2006 to $4.00 in 2008. What is the percentage of increase?
Answer:
60% increase
Step-by-step explanation:
Percentage increase = (new - old)/ old * 100
We know the new = 4.00
old = 2.50
Lets substitute the values in
Percentage increase = (4-2.5)/2.5 *100
= 1.5/2.5 * 100
=.6*100
=60%
Which rectangular prism has the greatest volume?
Answer: First prism has the greatest volume.
Step-by-step explanation:
Since we have given that
Volume of prism = Length × Breadth × Height
So, we need to find the greatest volume, for which we find volumes of all figures:
1) Volume of prism would be
[tex]5\times 7\times 5\\\\=175\ cm^3[/tex]
2) Volume of prism would be
[tex]10\times 3\times 4\\\\=120\ cm^3[/tex]
3) volume of prism would be
[tex]7\times 7\times 3\\\\=147\ cm^3[/tex]
4) Volume of prism would be
[tex]5\times 3\times 7\\\\=105\ cm^3[/tex]
Hence, first prism has the greatest volume.
The volume of the prism with the Greatest volume is 250cm³
The volume of a prism is calculated by multiplying the prism's base area by its height. Mathematically expressed as
V = Base Area×Height
, it represents the space enclosed within the prism.
Since the prism is a cuboid, then
V = l × w × h
Where h is the height , l is the length and w is the width.
V = 5 × 5 × 10
V = 250 cm³
The volume of the prism is 250cm³
Simplify 4 square root of 2 end root plus 7 square root of 2 end root minus 3 square root of 2
2 square root of 8
8 square root of 2
8 square root of 6
6 square root of 8
Answer:
8√2
Step-by-step explanation:
4√2 + 7√2 - 3√2 = (√2)(4 + 7 - 3) = 8√2
Recognize that √2 is a common factor and simply add its coefficients.
[tex]4\sqrt2+7\sqrt2-3\sqrt2=(4+7-3)\sqrt2=\boxed{8\sqrt2}\\\\Answer:\ \boxed{\text{8\ square root of 2}}[/tex]
Ana took Ali out for lunch. Their lunches cost $13.28 and $14.25, including tax and tip. Ana paid with two $20 bills. How much change did Ana receive?
Answer:
$12.47
Step-by-step explanation:
The total charge was ...
... $13.28 +14.25 = $27.53
The change from 2 $20 bills is ...
... 2 × $20 - 27.53 = $40.00 -27.53 = $12.47
The total cost of lunch is $27.53. Ana paid with two $20 bills, which equals $40.00. After Ana gave the two $20 bills, she received $12.47 in change.
Explanation:The subject area of this question is mathematics, specifically arithmetic involving decimal numbers. To solve this, we first add together the costs of the two lunches, which are $14.25 and $13.28, that result in $27.53. Ana initially pays with two $20 bills, which sums up to $40.00. Now, we subtract the total cost of the lunches from the amount Ana paid with. So, $40.00 - $27.53 gives us $12.47. This tells us that Ana received $12.47 in change back after paying for lunch.
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graph the function. please help asap
Answer:
See the attached
Step-by-step explanation:
A graph of almost any exponential function quickly goes off-scale. The attachment shows a short table of values.
Find the measurement of one interior angle in each polygon. Round your answers to the nearest tenth if necessary.
Find the measure of one exterior angle in each polygon. Round your answer to the nearest tenth if necessary.
1–4: The interior angle of an n-sided regular polygon is (n-2)/n times 180°. For n ∈ {5, 6, 11, 4}, this is {3/5, 4/6, 9/11, 2/4} · 180°, or {108°, 120°, 147.3°, 90°}
5–8: The exterior angle of an n-sided regular polygon is 360°/n. For n ∈ {5, 9, 7, 4}, this is 360°/{5, 9, 7, 4}, or {72°, 40°, 51.4°, 90°}
What is the measure of ∠BCD? Enter your answer in the box. ° quadrilateral A B C D with side A B parallel to side D C and side A D paralell to side B C. angle B is 103 degrees.
Answer:
77°
Step-by-step explanation:
Angles B and C are adjacent angles of a parallelogram, so are supplementary.
... ∠C = 180° -∠B = 180° -103° = 77°
The measure of ∠BCD in a parallelogram with ∠B given as 103° is also 103° because opposite angles in a parallelogram are equal.
Explanation:The measure of ∠BCD in a parallelogram can be found by using the property that opposite angles in a parallelogram are equal.
To find the measure of angle BCD, we can use the fact that angles in a quadrilateral sum up to 360 degrees.
We know that angle B is 103 degrees.
Since quadrilateral ABCD has sides AB and DC parallel, as well as sides AD and BC parallel, it is a parallelogram.
Given that ∠B is 103°, the measure of ∠BCD is also 103° because it is the angle opposite ∠B.
Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution.
3x+6y=18
3y=-3/2x+9
please help just looking for the answer
For this case, we have that by definition:
Let "x" be an angle of any vertex of a right triangle.
[tex]Sin (x) = \frac {Cathet \ opposite} {hypotenuse}[/tex]
So, if we want to find the sine of angle A:
[tex]Sin (A) = \frac {3} {5}[/tex]
Thus, the sine of angle "A" is[tex]\frac {3} {5}[/tex]
Answer:
[tex]\frac {3} {5}[/tex]
Option A
Use the graph below to write 5 conic section equations that create it. Use Desmos to check if your equations produce this picture. Hint: 3 circles, 1 ellipse and 1 parabola
1.The head(red circle)
2. The Left Eye (Blue Circle)
3. The Right Eye (Green Circle)
4. The Mouth (Purple Ellipse)
5. The Body (Black Parabola)
Answer:
See below for the graph.
Step-by-step explanation:
A circle or ellipse can be defined using the same sort of equation. Here, we have chosen to use the formulation ...
... ((x -a)/p)^2 +((y -b)/q)^2 -1 = 0
This will be the general form of the equation for an ellipse with center (a, b) and semi-axes p and q, in the x- and y-directions, respectively. When the axes are the same length, the ellipse is a circle.
By defining the function ...
... c(a, b, p, q, x, y) = ((x -a)/p)^2 +((y -b)/q)^2 -1
we can use the same function for all of the circles/ellipses in the figure. The parabola has vertex (0, -6) and a vertical scale factor of -1, so it can be formulated using the vertex form:
... y = k(x -a)^2 +b . . . . . for vertex (a, b) and vertical scale factor k.
_____
The equations
(x/6)² +(y/6) -1 = 0(x+2)² +(y-2)² -1 = 0(x-2)² +(y-2)² -1 = 0(x/3)² +(y+2)² -1 = 0y = -x² -6Parabola is a plane curve. The iconic character can be made with the following equation as given below,
[tex](x-0)^{2}+(y-0)^{2}=6^{2}[/tex][tex](x+2)^{2}+(y-2)^{2}=1^{2}[/tex][tex](x-2)^{2}+(y-2)^{2}=1^{2}[/tex][tex](\dfrac{x}{3})^{2}+(y+2)^{2}-1=0[/tex][tex]y=-(x-0)^{2}-6[/tex]
We need to draw 3 circles, an ellipse and a parabola, in order to get the desired digram.
For a circle, we only need to know the radius of the circle and the center of the circle,
1. The head(red circle)
The head of the circle is drawn from the origin of the coordinate, while the radius can be found by dividing the length between the points where the circle cuts the x-axis.
[tex]Radius =\dfrac{6-(-6)}{2} = 6[/tex]
Equation of the circle face,
[tex]\text{Equation of the circle face} => {(x-0)^2+(y-0)^2} = 6^2[/tex]
2. The Left Eye (Blue Circle)
3. The Right Eye (Green Circle)
Similarly for the eyes of the diagram,
The right eye = [tex](x-2)^{2}+(y-2)^{2}=1^{2}[/tex]
The left eye = [tex](x+2)^{2}+(y-2)^{2}=1^{2}[/tex]
4. The Mouth (Purple Ellipse)
The equation of the parabola can be written as,
(x/3)² +(y+2)² -1 = 0
5. The Body (Black Parabola)
The parabola can be made using the equation,
Equation of a parabola
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Therefore, the equation for the body,
Equation of the parabola = [tex]y = -(x-0)^2 -6[/tex]
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The beginning checkbook balance of Gregory Co. was $3,045.58. Their bank statement indicated a balance of $4,262.92. The bookkeeper of Gregory Co. discovered a $220.05 deposit not reflected on the statement and checks numbered 478 and 492 in the amounts of $325.50 and $497.65 still outstanding. The bank credited Gregory’s account for $651.84 for a note that they had collected. The bank charged their account $37.60 for printed checks. Their reconciled balance was (Remember: To reconcile the bank balance with the checkbook balance means to compare the two, make the necessary adjustments (debits and credits) and ensure that the two amounts are equal.)
$3,569.82. $3,659.28. $3,659.82. $6,359.82.
Answer:
$3,659.82
Step-by-step explanation:
Adding to the checkbook those debits and credits not already there brings its balance to ...
... $3045.58 +651.84 -37.60 = $3659.82
Adjusting the bank's balance by the deposits and checks not already there brings its balance to ...
... $4262.92 +220.05 -325.50 -497.65 = $3659.82
Thus, the reconciled accounts will agree on the balance $3659.82.
The reconciled balance for Gregory Co. was $3,659.82 after accounting for all transactions including deposits, outstanding checks, credited note, and bank charges.
The question involves reconciling the checkbook balance with the bank statement balance for Gregory Co. To reconcile the bank balance with the checkbook balance, we need to account for any transactions that have not been reflected in one or the other. We start with the bank statement balance and adjust it for outstanding checks and deposits not reflected on the statement.
Starting balance: $3,045.58Add outstanding deposit: $220.05Subtract outstanding checks: $325.50 + $497.65Add credited note: $651.84Subtract bank charges: $37.60Reconciled balance calculation: $3,045.58 + $220.05 - $325.50 - $497.65 + $651.84 - $37.60 = $3,659.82Why is -0.45, 5/12, 0, 247 rational or an irrational number.
All are rational.
Step-by-step explanation:Any number you can write exactly and completely, or any repeating decimal is a rational number. Any number that can only be written exactly using a symbol, such as π or √2, is an irrational number. Something like √6.25 is rational, because it can be written exactly as 2.5, without the symbol.
The idea of "rational" means the number can be expressed as the ratio of two integers. Any integer can be expressed as the ratio of itself and 1.
All of your numbers can be expressed as the ratio of integers:
... -0.45 = -45/100 . . . . any terminating decimal can be expressed as a ratio of integers by making use of the place value multipliers
... 5/12 . . . . is the ratio of integers
... 0 = 0/1
... 247 = 247/1