Answer:
See below
Step-by-step explanation:
Domain would be all the x-values, so this is {3, 8, 8, 9}
Range would be all the y-values, so this is {0, 3, p, q}
a spinner with 10 equally sized slices 4 yellow, 4 red, 2 blue. probability that the dial stops on yellow?
The probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).
Therefore, there is a 40% chance that the spinner will stop on yellow.
To find the probability that the spinner stops on yellow, we need to determine the number of favorable outcomes (yellow) and the total number of possible outcomes.
The spinner has 10 equally sized slices, with 4 yellow, 4 red, and 2 blue.
The number of favorable outcomes (yellow) is 4 because there are 4 yellow slices.
The total number of possible outcomes is 10 because there are 10 slices in total.
Therefore, the probability of the spinner stopping on yellow can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 10
Simplifying this fraction, we get:
Probability = 2 / 5
So, the probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).
Therefore, there is a 40% chance that the spinner will stop on yellow.
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Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
The dependent variable is t.
When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155."
The dependent variable is f(t).
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t.
The independent variable
The correct statements are
The dependent variable is t.
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t. Option A,D,E,F.
Let's analyze each statement to understand why it is true:
A) The dependent variable is t: In the given function, f(t), the value of f depends on the value of t. Therefore, t is the independent variable, and f is the dependent variable.
D) When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced": Here, the value of t is 2, representing the year 2002, and the value of f(t) is 1,323, representing the amount of garbage produced in tons.
E) When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced": Similar to statement D, the value of t is 4, representing the year 2004, and the value of f(t) is 1,458.6, representing the amount of garbage produced in tons.
F) The independent variable is t: As mentioned in statement A, t is the independent variable in the given function. It is the variable that we can change or manipulate, and the value of f depends on the value of t.
Statements B, C, and G are incorrect:
B) When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155": This statement is incorrect because in the given function, t represents the time in years after 2000, not the amount of garbage produced.
C) The dependent variable is f(t): This statement is incorrect because, as mentioned earlier, t is the independent variable, and f is the dependent variable.
G) The independent variable f(t): This statement is incorrect because f(t) represents the amount of garbage produced, which is the dependent variable in the given function.
So Option A,D.E.F. Are correct.
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Note the complete question is
Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
A.) The dependent variable is t.
B.) When f(12) = 2,155, 12 represents "12 tons of garbage produced," and 2,155 represents "the year 2155."
C.) The dependent variable is f(t).
D.) When f(2) = 1,323, 2 represents "the year 2002," and 1,323 represents "1,323 tons of garbage produced."
E.) When f(4) = 1,458.6, 4 represents "the year 2004," and 1,458.6 represents "1,458.6 tons of garbage produced."
F.) The independent variable is t.
G.) The independent variable f(t)
please answer ASAP I will brainlist
Answer:
Below, rises, more, 2, 5
Step-by-step explanation:
Its an positive exponential growth function which means it increases sharply to the right it also is above the x-axis.
The graph is 2 times the graph of 5^x so its steeper or rises more
Plug in 0 to get 1*2=2
Plug in 1 to get 5*1=5
Which table of values represents a function? Step by step.
Answer:
A
Step-by-step explanation:
For a table of values to be a function, all inputs must have one unique output. The only table that doesn't violate this is table A.
Notice that while two different inputs (-4 and 1) have the same output of 7, it is still a function because both outputs of 7 are associated with two different inputs.
Mohammed Corporation's comparative balance sheet for current assets and liabilities was as follows:
Dec. 31, 20Y2 Dec. 31, 20Y1
Accounts receivable $20,900 $20,000
Inventory 61,800 62,500
Accounts payable 19,700 18,600
Dividends payable 24,000 22,000
Adjust net income of $98,500 for changes in operating assets and liabilities to arrive at net cash flow from operating activities.
The net cash flow from operating activities would be $100,800.
What is the net cash flow from operating activities?Change in accounts receivable:
= $20,900 - $20,000
= $900
Change in inventory:
= $61,800 - $62,500
= -$700
Change in accounts payable:
= $19,700 - $18,600
= $1,100
Change in dividends payable:
= $24,000 - $22,000
= $2,000
Change in operating assets and liabilities:
= Change in accounts receivable + Change in inventory - Change in accounts payable - Change in dividends payable
= $900 + (-$700) + $1,100 + $2,000
= $2,300
Net cash flow from operating activities:
= Net income + Change in operating assets and liabilities
= $98,500 + $2,300
= $100,800.
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y = 1/3x -1
x-intercept (3,0)
How did they get this answer? Somebody please help
Answer:
Step-by-step explanation:
x-intercept is where the line cuts the x-axis. That is, when y=0.
Substitute y=0 and we get:
[tex]0=\frac{1}{3} x-1[/tex]
[tex]1=\frac{1}{3} x[/tex]
[tex]x=3[/tex]
So x-intercept is the point (3,0).
Can anyone help me solving this question I forgot how to solve it it’s important
The statement that is correct about the dot plots is that:
A) The distribution for Class M is approximately symmetric
How to identify symmetric distribution?A symmetric distribution in dot plots is defined as a distribution with a vertical line of symmetry in the center of the graphical representation, so that the mean is equal to the median.
A symmetric distribution is one that occurs when the values of a variable occur at regular frequencies, and often the mean, median, and mode all occur at the same point. If we draw a line through the middle of the chart, we can see that the two planes mirror each other.
Now, from the given two dot plots of class M and Class N, it is very clear that class M is very close to being symmetric about the data value 3.
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Please help! :')
Prove that the two circles shown below are similar. (10 points)
Circle X is shown with a center at negative 2, 8 and a radius of 6. Circle Y is shown with a center of 4, 2 and a radius of 3.
A requested task is subject to be reported when:
Answer:
A requested task is subject to be reported when it has been completed according to the instructions provided.
To demonstrate this with chain of thought reasoning:
1. The task requested will have details outlining what needs to be done.
2. To fulfill the request of the task, the instructions outlined must be followed.
3. Once all instructions are met, the task is complete.
4. Completion of the task means it is subject to be reported.
Step-by-step explanation:
Which of the following functions is graphed me below ?
Answer:
[tex]y = |x - 2| + 3[/tex]
The correct answer is C.
Write the correct measurement for A-F (Example 2.2, 5.9, 9)
Answer:
9
Step-by-step explanation:
Question #3
Solve for x
OOO
O 10
07
5
8
6x+8
N
p
U
K
122°
L
M
194°
The calculated value o x in the circle is 7
How to determine the solution for xFrom the question, we have the following parameters that can be used in our computation:
The circle
The value of x can be calculated using teh equation of the intersection of chords
So, we have
122 = 1/2(6x + 8 + 194)
Evaluate
244 = 6x + 202
So, we have
6x = 42
Divide by 6
x = 7
Hence, the solution for x is 7
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Pamela is buying a $242,000 home with a 30-year mortgage. She will make
an 8% down payment. Use the table below to find her monthly PMI payment.
Base-To-Loan %
95.01% to 97%
90.01% to 95%
85.01% to 90%
85% and Under
OA. $96.48
OB. $144.72
OC. $157.30
OD. $151.01
Fixed-Rate Loan
30 yrs. 15 yrs.
0.90% 0.79%
0.78% 0.26%
0.52% 0.23%
0.32% 0.19%
ARM 2% +1 Year Cap
30 yrs.
15 yrs.
n/a
0.92% 0.81%
0.65%
n/a
0.37%
0.54%
0.26%
A building contractor is building a backyard playground and wishes to put down rubber mulch to provide safety from falls. The contractor wishes to put the mulch in a pit in the shape of a rectangular solid 24 feet long, 13 feet wide, and 6 inches deep.
a) Determine the volume, in cubic feet, of mulch the contractor will need.
b) If mulch costs 9$ per cubic foot, what will the cost of mulch be?
Answer:
A= 220.5ft
B= $2425.5
Step-by-step explanation:
A= 220.5ft
B= $2425.5
I dont understand these can someone help?
The corresponding sides and angles of the similar and congruent triangles indicates that we get the following approximate and exact values;
Page 1;
5. [tex]\overleftrightarrow{AC}[/tex] = 4.3. 6. [tex]\overline{BP}[/tex] ≈ 7.5 7. [tex]\overline{YV}[/tex] ≈ 8
Page 2
5. [tex]\overline{DF}[/tex] = [tex]11\frac{1}{4}[/tex], 6. [tex]\overline{ED}[/tex] = 5, 7. [tex]\overline{BC}[/tex] = 22, 8. [tex]\overline{EF}[/tex] = 8
Page 3;
8. m∠ABC = 30°, 9. m∠XYP = 44°, 10. [tex]\overline{AC}[/tex] = 14
What are congruent triangles?Congruent triangles are triangles that have all three corresponding sides of the same length and all three angles of the same measure.
First Page
5. The distance from the vertex B to the line segment [tex]\overleftrightarrow{AC}[/tex] in the triangle ΔABC is the altitude of the triangle, which is 4.3
6. The distance from the vertex B to [tex]\overleftrightarrow{AC}[/tex] = [tex]\overline{BP}[/tex]
Pythagorean theorem indicates that the length of the segment [tex]\overline{BP}[/tex] can be found as follows;
[tex]\overline{BP}[/tex] = √(13.5² - 11.2²) ≈ 7.5
7. The distance from Y to [tex]\overleftrightarrow{XZ}[/tex] is the altitude of the triangle ΔXYZ, which indicates;
The distance from Y to [tex]\overleftrightarrow{XZ}[/tex] = [tex]\overline{YV}[/tex]
The Pythagorean theorem indicates that we get;
[tex]\overline{YV}[/tex] = √(13.34² - 10.67²) ≈ 8
Second page;
5. The scale factor from ΔABC to ΔDEF = 3/4
Therefore, the length of [tex]\overline{DF}[/tex] = (3/4) × 15 = 45/4 = [tex]11\frac{1}{4}[/tex]
6. The scale factor of (1/3) indicates that we get;
[tex]\overline{ED}[/tex] = (1/2) × 10 = 5
7. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 18/9 = 10/5 = 2
The corresponding side to [tex]\overline{BC}[/tex] is [tex]\overline{EF}[/tex]
[tex]\overline{EF}[/tex] = 11, therefore, the length of [tex]\overline{BC}[/tex] = 2 × 11 = 22
8. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 4/6 = 10/15 = 2/3
The corresponding side to [tex]\overline{EF}[/tex] is [tex]\overline{BC}[/tex]
[tex]\overline{BC}[/tex] = 12, therefore [tex]\overline{EF}[/tex] = (2/3) × 12 = 8
Third page;
8. The triangles ΔABV and ΔCVB are congruent triangles by the Leg Hypotenuse congruence theorem.
The angles ∠ABV and ∠CBV are corresponding triangles, therefore;
∠ABV ≅ ∠CBV
m∠CVB = m∠ABV = 15° (Definition of congruent triangles and symmetric and substitution property)
∠ABC = ∠ABV + ∠CBV
Therefore; m∠ABC = 15° + 15° = 30°
9. The angles ∠YXP and ∠YZP are right triangles, therefore;
m∠YXP = m∠YZP = 90°
The right triangles ΔYXP and ΔYZP are congruent by the LH congruence theorem
∠XYP ≅ ∠ZYP (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)
m∠XYP = m∠ZYP (Definition of congruent triangles)
m∠XYZ = m∠XYP + m∠ZYP (Angle addition property)
m∠XYZ = 2 × m∠XYP
2 × m∠XYP = m∠XYZ = 88°
m∠XYP = 88°/2 = 44°
10. The angles ∠ACP and ∠ABP are right angles, according to the indicated markings, therefore;
∠ACP ≅ ∠ABP (All right angles are congruent)
ΔACP ≅ ΔABP by SAA congruence theorem
[tex]\overline{AC}[/tex] ≅ [tex]\overline{AB}[/tex] (CPCTC)
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] (Definition of congruent segments)
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] = 14
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Find the volume of this cylinder give your answer to one decimal place 11height 14 Length
To find the volume of the given cylinder, we need to use the formula of volume of a cylinder which is given by V = πr²h, where V is the volume of the cylinder, r is the radius of the cylinder and h is the height of the cylinder. So, the volume is 1078.1 cubic units.
Given, Length = 14 units, Height = 11 units. Now, we know that the formula for the volume of a cylinder is given as; V = πr²h.
Here, the radius of the cylinder is half the length of the cylinder, which is; Radius = Length/2
Radius = 14/2
Radius = 7 units
Substituting the value of the radius and height, we have; V = π(7)²(11)
V = 1078.1 cubic units. Therefore, the volume of the cylinder is 1078.1 cubic units. Rounded off to one decimal place, the volume is 1078.1 cubic units.
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In rectangle ABCD, AB = x, BC =x + 2, and AC = x +4. Find the value of x.
Answer:
x = 6
Step-by-step explanation:
the diagonal AC divides the rectangle into 2 right triangles.
Consider the right triangle ABC with legs AB , BC and hypotenuse AC
using Pythagoras' identity in right triangle ABC
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
AB² + BC² = AC² ( substitute values )
x² + (x + 2)² = (x + 4)² ← expand factors using FOIL
x² + x² + 4x + 4 = x² + 8x + 16
2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
however , x > 0 , then x = 6
Find the sum of the measures of the angles of a five sided polygon
Answer:540 degrees
The sum of the measures of the angles of a five-sided polygon (pentagon) is 540 degrees123. This can be calculated using the angle sum formula, S = (n − 2) × 180°, where n is the number of sides in the polygon12. Since a pentagon has five sides, the sum of the interior angles is (5 − 2) × 180° = 540°123.
Step-by-step explanation:
Answer:
540°
Step-by-step explanation:
Since a pentagon has n=5 sides, then we have:
[tex]180(n-2)=180(5-2)=180(3)=540^\circ[/tex]
write 718000 in standard form
Answer:
718000
Step-by-step explanation:
718000 is already in standard form
answer the question submitted
The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.
To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:
Step 1: Divide the coefficient of x by 2 and square the result.
(Coefficient of x) / 2 = -28/2 = -14
(-14)² = 196
Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.
g(x) = 4x² - 28x + 49
= 4x² - 28x + 196 - 196 + 49
Step 3: Rearrange the terms and factor the perfect square trinomial.
g(x) = (4x² - 28x + 196) - 196 + 49
= 4(x² - 7x + 49) - 147
= 4(x² - 7x + 49) - 147
Step 4: Write the perfect square trinomial as the square of a binomial.
g(x) = 4(x - 7/2)² - 147
Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.
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The probable question may be:
Rewrite the function by completing the square.
g(x)=4x²-28x +49
g(x)= ____ (x+___ )²+____.
17 students are present in a class. in how many ways ,they can be made to stand in 2 circles of 8 and 9 students
Answer:
24310
Step-by-step explanation:
17 choose 8= 17 choose 9
17 choose 8= 17*16*15*14*13*12*11*10/8!= 24310
d 1 1 logx tanx
dx x
+ + +
The expression you provided appears to be an integral with multiple terms involving logarithmic and trigonometric functions. To solve it, we need to break it down and evaluate each term separately.
Let's examine each term in the given expression:The integral of 1 with respect to x is simply x.The integral of 1/x is ln|x|.
The integral of tan(x) can be evaluated using a substitution or integration by parts technique, depending on the specific limits of integration or any additional context provided.
Without specific limits or further instructions, it's challenging to provide a precise solution or simplify the expression further. However, if you provide more information or clarify the problem statement, I can help you with a more detailed solution.
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please help me asap with this it's getting late
The system B is gotten from system A by operation (d)
How to derive the system B from system AFrom the question, we have the following parameters that can be used in our computation:
x + y = 8
4x - 6y = 2
Also, we have the solution to be (5, 3)
Recall that
x + y = 8
4x - 6y = 2
Multiply the first equation by 6
So, we have
6x + 6y = 48
4x - 6y = 2
Add the equations
10x = 50
This means that the system B from system A is (d)
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Let A be the point (7,4) and D be (-5, -3). What is the length of the shortest path ABCD, where B is a point (x, 2) and C is a point (x,0)? This path consists of three connected segments, with the middle one vertical.
The length of the shortest path ABCD is 7 units.
To find the length of the shortest path ABCD, we need to determine the coordinates of points B and C and then calculate the distances between these points.
Given that B has a y-coordinate of 2, it lies on a horizontal line. Therefore, the y-coordinate of B is 2, and the x-coordinate is the same as the x-coordinate of point A, which is 7. So, B is the point (7, 2).
Similarly, C lies on a vertical line, and its x-coordinate is the same as the x-coordinate of point D, which is -5. So, C is the point (-5, 0).
Now, we can calculate the distances between the points. The distance between A and B can be found using the distance formula:
AB = √[tex]((x2 - x1)^2 + (y2 - y1)^2[/tex])
Substituting the coordinates of A and B, we have:
AB = √[tex]((7 - 7)^2 + (2 - 4)^2) = √(0^2 + (-2)^2[/tex]) = √4 = 2
The distance between B and C is simply the difference in their y-coordinates:
BC = |y2 - y1| = |2 - 0| = 2
Finally, the distance between C and D can be calculated using the distance formula:
CD = √[tex]((-5 - (-5))^2 + (0 - (-3))^2)[/tex] = √[tex](0^2 + 3^2)[/tex] = √9 = 3
Therefore, the length of the shortest path ABCD is the sum of the distances AB, BC, and CD:
Shortest path ABCD = AB + BC + CD = 2 + 2 + 3 = 7
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Please answer ASAP I will brainlist
The solution to the system is (a) a = 4/5, b = 5, c = -4 and d =-4
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The augmented matrix
Where, we have
[tex]\left[\begin{array}{cccc|c}1&0&0&0&4/5\\0&1&0&0&5\\0&0&1&0&-4\\0&0&0&1&-4\end{array}\right][/tex]
From the above, we have the diagonals to be 1
And other elements to be 0
This means that the equation has been solved
So, we have
a = 4/5, b = 5, c = -4 and d =-4
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Prove the following?
The given statement proposition is a that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.
The given statement is a logical proposition involving the concept of induction. Let's break it down and analyze its components.
"If x is inductive..."
This implies that x is a concept or object that possesses the property of being inductive. In mathematics, the term "inductive" typically refers to the property of being a natural number or belonging to the set of natural numbers.
"...then so is (x ∈ X : x = Ф or x = y ∪ {y} for some y)"
Here, we have a set X that consists of elements satisfying a certain condition. The condition states that an element x in X can either be equal to the empty set (Ф) or the union of a set y with itself ({y}). This construction represents a recursive definition, where each element in X is defined in terms of a base case (Ф) and a recursive step ({y}).
"...hence each n ≠ 0 is m + 1 for some m."
This conclusion states that for every natural number n that is not equal to 0, there exists another natural number m such that n can be expressed as m + 1. In other words, any non-zero natural number is the successor of some other natural number.
Overall, the given statement is a proposition that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.
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Use the equation 20x+12y= 24 as an equation in three different linear systems. Write a second equation so that each system has a different number of solutions. Explain what you did for each system.
We have created three different linear systems using the equation 20x + 12y = 24.
System 1 has infinitely many solutions, System 2 has no solution, and System 3 has a unique solution.
Let's create three different linear systems using the equation 20x + 12y = 24 and ensure that each system has a different number of solutions.
System 1:
Equation 1: 20x + 12y = 24 (given)
Equation 2: 40x + 24y = 48
Explanation: In this system, we multiplied both sides of the given equation by 2 to create Equation 2.
By doing so, we have essentially created two equations that are multiples of each other.
Since the equations are equivalent, they represent the same line, and the system has infinitely many solutions.
Any values of x and y that satisfy the first equation will automatically satisfy the second equation as well.
System 2:
Equation 1: 20x + 12y = 24 (given)
Equation 2: 20x + 12y = 48
Explanation: In this system, we changed the constant term in Equation 2 to 48.
By doing so, we have created two parallel lines with the same slope. Since the lines are parallel, they will never intersect, and the system has no solution.
There are no values of x and y that satisfy both equations simultaneously.
System 3:
Equation 1: 20x + 12y = 24 (given)
Equation 2: 40x + 24y = 48
Explanation: In this system, we multiplied both sides of Equation 2 by 2 to create Equation 2.
By doing so, we have created two equations that have the same slope but different y-intercepts.
Since the lines are not parallel and have different y-intercepts, they will intersect at a single point, and the system has a unique solution.
There will be one specific pair of values for x and y that satisfy both equations simultaneously.
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A box contains 240 lumps of sugar. Five lumps are fitted across the box and there were three layers. How many lumps are fitted along the box?
What is the next value?
2 3 E 4 5 I 6 8
options: O 8 M N
Answer:
The correct answer is a.
Step-by-step explanation:
The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.
What is the graph of f(x) = 0.5(4)x (x is an exponent)
It should be a positive graph .