I resolved this problem for a test already but it looks like the graph it’s not ok can you help me?
Answers
SOLUTION
The function given is
[tex]f(x)=2x+1[/tex]To obtain the slope, we compare the equation above with the standard form of a slope intercept form.
Hence,, slope intercept is given as
[tex]\begin{gathered} y=mx+c \\ \text{Where m=slope.c=intercept on y (0,c)} \end{gathered}[/tex]Comparing with the function given, we have
[tex]\begin{gathered} M=2,c=1 \\ \text{Hence } \\ \text{slope}=2,\text{ y-intercept=(0,1)} \end{gathered}[/tex]Therefore
The slope = 2 and the y-intercept= (0,1 )
The graph of the functionis given in the image below
Related Questions
Please ANSWER this
The table shows the parts of gelatin and water used to make a dessert.
Boxes of Gelatin Powder (oz) Water (cups)
3 9 6
7
At this rate, how much gelatin and water will Jeff use to make 7 boxes?
Jeff will use 14 oz of powder and 21 cups of water to make 7 boxes of gelatin.
Jeff will use 13 oz of powder and10 cups of water to make 7 boxes of gelatin.
Jeff will use 27 oz of powder and 18 cups of water to make 7 boxes of gelatin.
Jeff will use 21 oz of powder and 14 cups of water to make 7 boxes of gelatin.
Answers
Jeff needs 21 oz of gelatin and 14 cups of water to make 7 boxes
How to determine the amount of gelatin and water needed to make 7 boxes?The table of values is given as
Boxes Gelatin Powder (oz) Water (cups)
3 9 6
From the above table, we can see that
Gelatin Powder = 3 * Boxes
Water = 2 * Boxes
When there are 7 boxes, the equations become
Gelatin Powder = 3 * 7
Water = 2 * 7
Evaluate the products in the above equation
So, we have
Gelatin Powder = 21
Water = 14
Hence, the amount of gelatin and water needed to make 7 boxes are 21 oz and 14 cups respectively
Read more about proportions at
https://brainly.com/question/16828793
#SPJ1
Answer: D: jeff will use 21 oz of powder and 14 cups of water
Step-by-step explanation:
the chart says there are
3 boxes of gelatin ) 9 oz of powder ) 6 cups of water
that equals the same as
1 box of gelatin ) 3 oz of power ) 2 cups of water
so for every box of gelatin, there is 3oz of powder and 2 cups of water
if he wants to make 7 boxes.....
7x3oz=21 oz
7x2cups=14 cups
so the Answer is D
i need help with this question
Answers
The side AB = BD
7x + 10 = 9x - 2
SImplify for x :
Subtract 7x from both side :
7x + 10 - 7x = 9x - 7x - 2
10 = 2x - 2
Add 2 on both side :
10 + 2 = 2x - 2 + 2
12 = 2x
divide both side by 2 :
2x/2 = 12/2
x = 6
What is the probability that a randomly selected oar was purchased in the 2010s given that the oar was made from ash wood?Simplify any fractions
Answers
P (A) = probability of a car purchased in 2010's
P (B) = probability of the car being made from ash wood
P (A and B) = 4
P (B) = 4 +3 = 7
Conditional probability:
P (B/A) = P (A and B ) / P (B) = 4 / 7 = 0.5714
Select your answer to the question below: * AABC is shown below. Suppose the triangle is translated 5 units to the right and 7 units down. What are the coordinates of the image of vertex B after this transformation? : Y 6 B'C 2 A C. 8 G 2 4 A (8-6) B (2-6) c (-3.-6) D (2.0)
Answers
From the given graph,
The coordinates of point B are (-3, 7)
The triangle ABC has translated 5 units to the right and 7 units down
That means the x coordinate of B must add by 5 and the y-coordinate must subtract by 7
The rule is (x + 5, y - 7)
The image of point B is B'
B' = (-3 + 5, 7 - 7)
B' = (2, 0)
The image of point B is (2, 0)
Rewrite the equation by completing the square. x^2 + 4x − 21 = 0
( x + _ )^2 = _
Answers
[tex] {x}^{2} + 4x + ( \frac{4}{2} )^{2} - 21 = 0 + ( \frac{4}{2} )^{2} \\ {x }^{2} + 4x + 4 = 4 + 21 \\ (x + 2)(x + 2) = 25 \\ {(x + 2)}^{2} = 25[/tex]
ATTACHED IS THE SOLUTION
is 11.22497 a rational or irrational number
Answers
11.22497 is a rational number
First we need to undertsand what rational and irrational numbers are:
Rational numbers are numbers that can be written as a ratio of two numbers. it is the division of two integers.
Integers are numbers with no fraction.
irrational numbers cannot be written as a fraction of two integers.
The number 11.22497 can be written as a fraction of two ingers:
[tex]11.22497\text{ =}\frac{1122497}{100000}[/tex]Therefore, it is a rational number.
The mean of a population is 100, with a standard deviation of 15. The mean of
a sample of size 100 was 95. Using an alpha of .01 and a two-tailed test, what do
you conclude?
O Accept the null hypothesis. The difference is not statistically significant.
Reject the null hypothesis. The difference is statistically significant.
Accept the null hypothesis. The difference is statistically significant.
Reject the null hypothesis. The difference is not statistically significant.
Answers
We conclude that Reject the null hypothesis. The difference is statistically significant.
Define integers.The symbol used to represent integers is the letter (Z). A positive integer can be 0 or a positive or negative number up to negative infinity. The three elements that make up an integer are zero, the natural numbers, and their additive inverse. It can be shown on a number line, but without the fractional portion. Z stands for it.
A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043
Given,
The mean of a population is 100, with a standard deviation of 15. The mean of a sample of size 100 was 95.
z = [tex]\frac{95-100}{15/10}[/tex]
z = 3.333
Using the p value technique, the value of p is 0.0009, and since p = 0.0009 0.01 the null hypothesis is rejected, the conclusion is made.
Reject the null hypothesis. The difference is statistically significant.
To learn more about integers, visit:
https://brainly.com/question/15276410
#SPJ13
Given the functions f(x) = x ^ 2 + 3x - 1 and g(x) = - 2x + 3 determine the value of (f + g)(- 2)
Answers
Start by finding (f+g)(x)
[tex](f+g)(x)=(x^2+3x-1)+(-2x+3)[/tex]simplify the equation
[tex]\begin{gathered} (f+g)(x)=x^2+(3x-2x)-1+3 \\ (f+g)(x)=x^2+x+2 \end{gathered}[/tex]then, replace x by -2
[tex]\begin{gathered} (f+g)(-2)=(-2)^2+(-2)+2 \\ (f+g)(-2)=4-2+2 \\ (f+g)(-2)=4 \end{gathered}[/tex]Which inequalities are shown on the graph?Find your inequalities in the grid below. Check the ONE box that pairs the two correct inequalitiesY-3-1 y>-**-172-**-1 y<-**-1<3+3y>+3y< <+3y2 ++3D D D DOOOO"OOOOPreviousPauseO Search for anything0-
Answers
From the graph we could see that y = x + 3 for the first line . The shaded line is where y is less than or equals to x + 3.
For the second line we can see that y = x - 1 . The shaded line is where y is greater than or equals to x - 1 . Therefore, the inequalities are as follows
[tex]\begin{gathered} y\leq x+3 \\ y\ge x-1 \end{gathered}[/tex]Coronado co. sells product p-14 at a price of $52 a unit. the per unit cost data are direct materials $16, direct labour $12, and overhead $12 (75% variable) Coronado has no excess capacity to accept a special order for 38,700 units at a discount of 25% from the regular price. Selling costs associated with this order would be $3 per unit. Indicate the net income/loss
Answers
The net loss from accepting the special order at a discount of 25% from the regular price, without the existence of excess capacity is $38,700.
How is the net loss determined?Since Coronado Co. lacks the excess capacity for special orders, it implies that it will incur fixed costs per unit of the special order in addition to the variable costs.
Therefore, the company will incur a per unit cost of $40 ($16 + $12 + $9 + $3) while generating a revenue of $39 per unit.
This results in a loss of $1 per unit.
Selling price per unit = $52
Unit Costs:
Direct Materials = $16
Direct Labor = $12
Variable Overhead = $9 (75% of $12)
Total variable cost per unit = $37
Fixed Overhead = $3 (25% of $12)
Special order price per unit = $39 ($52 x 1 - 75%)
Contribution margin per unit = $2 ($39 - $37)
Total contribution margin = $77,400 ($2 x 38,700)
Fixed Overhead without excess capacity = $116,100 ($3 x 38,700)
Net loss = $38,700 ($77,400 - $116,100)
Thus, without excess capacity, it is inadvisable for Coronado to accept the special order at a total loss of $38,700.
Learn more about accepting special orders at https://brainly.com/question/28124882
#SPJ1
The population of a town is decreasing at a rate of 1% per year. In 2000there were 1300 people. Create a function to find the populationin 2008.
Answers
Given that;
The population of a town is decreasing at a rate of 1% per year.
[tex]\text{Rate r = 1\% = 0.01}[/tex]In 2000 there were 1300 people.
[tex]P_o=1300[/tex]To find the population in 2008;
[tex]P_8[/tex]The time taken is;
[tex]\begin{gathered} t=2008-2000 \\ t=8\text{ years} \end{gathered}[/tex]We can calculate the population of the town in 2008 by applying the formula;
[tex]P_8=P_o(1-r)^t[/tex]Substituting, the given values;
[tex]\begin{gathered} P_t=1300(1-0.01)^t \\ P_t=1300(0.99)^t \end{gathered}[/tex]Above is a functon for calculating the population of the town at time t years after 2000.
The population of the town in the year 2008 is;
[tex]\begin{gathered} P_8=1300(0.99)^8 \\ P_8=1,199.568 \\ P_8\approx1,200 \end{gathered}[/tex]Therefore, the population of the town in 2008 is approximately 1,200 people.
We can also write the equation as;
[tex]y=1300(0.99)^8[/tex]Where y is the population of the town in year 2008.
Find the volume of the given prism. Round to the nearest tenth if necessary.A.2,511.5 yd^3B.1,255.7 yd^3C.1,025.3 yd^3D.1,450.0 yd^3
Answers
Given:
The sides of an equilateral triangle base are 10 yds. The height of the prism is 29 yds.
To find:
The volume of the prism.
Solution:
The formula of the volume of the triangular prism is given by:
[tex]V=\text{ (area of base)}\times\text{ (height of the prism)}[/tex]It is known that the area of the equilateral triangle is given by:
[tex]A=\frac{\sqrt[]{3}}{4}(side)^2[/tex]So, the area of the base of the triangular prism is:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(10)^2 \\ =\frac{1.732}{4}\times100 \\ =\frac{173.2}{4} \\ =43.30 \end{gathered}[/tex]Now, the volume of the given triangular prism is:
[tex]\begin{gathered} V=43.30\times29 \\ =1255.7\text{ yad\textasciicircum{}3} \end{gathered}[/tex]May I please get help with this. For I have tried multiple times but still can’t get the right answer or the triangle after dilation?
Answers
Solution:
Given the triangle ABC as shown below:
To draw the image,
step 1: Determine the coordinates of the vertices of the triangle.
In the above graph,
[tex]\begin{gathered} A(6,7) \\ B(9,9) \\ C(8,6) \end{gathered}[/tex]step 2: Evaluate the new coordinates A'B'C' of the triangle after a dilation centered at the origin with a scale factor of 2.
After a dilation centered at the origin with a scale factor of 2, the iniatial coordinates of the vertices of the triangle are multiplid by 2.
Thus,
[tex]\begin{gathered} A(6,7)\to A^{\prime}(12,14) \\ B(9,9)\to B^{\prime}(18,18) \\ C(8,6)\to C^{\prime}(16,12) \end{gathered}[/tex]step 3: Draw the triangle A'B'C'.
The image of the triangle A'B'C' is as shown below:
Find the x-intercept and y-intercept of the line.
5x-9y=-12
Answers
The x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
What is termed as the x and y intercepts?An intercept is a y-axis point that the slope of a line passes. It is the y-coordinate of the a point on the y-axis where a straight line or even a curve intersects. This is represented by the equation for a straight line, y = mx+c, where m is the slope and c seems to be the y-intercept. There are two types of intercepts: x-intercept and y-intercept.For the given question,
The equation of the line is 5x-9y=-12.
For the x intercept, Put y = 0.
5x-9×0=-12.
x = 12/5
x intercept = (12/5, 0)
For y intercept, put x = 0.
5×0-9y=-12
y = -12/9
y = -4/3
y intercept = (0, -4/3)
Thus, the x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
To know more about the x and y intercepts, here
https://brainly.com/question/24609929
#SPJ13
the answers to questions 4 & 5 please!!
Answers
The height of the cone is (c) 5 cm.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.So, the volume of a cone is: V = 1/3πr²h
V is 83.73 and r is 4.Now, calculate the height of the cone as follows:
V = 1/3πr²h83.73 = 1/3π4²h83.73 = 1/3π16h3(83.73) = 3.14(16)h251.19 = 50.24hh = 251.19/50.24h = 4.9999Rounding off: 5 cm
Therefore, the height of the cone is (c) 5 cm.
Know more about cones here:
https://brainly.com/question/1082469
#SPJ13
if two angles measure 90 and are complementary and congruent, the measure of each angle is
Answers
Leonardo, the answer is
45 degrees.
I need help with this kind of math please. I have tried doing it but I’m so lost and confused
Answers
GF < GE < EF
Explanation:The given angles:
∠G = 74°
∠F = 65°
∠G + ∠F + ∠E = 180° (sum of angles in a triangle)
74 + 65 + ∠E = 180
139 + ∠E = 180
∠E = 180 - 139
∠E = 41°
The size of the side length of the triangles corresponds the size of the angles.
The higher the angle, the higher the side length and viceversa
∠E corresponds to side GF
∠F corresponds to side GE
∠G corresponds to side EF
∠E = 41 is the lowest, followed by ∠F = 65, highest is ∠G = 74
From least to greatest:
GF < GE < EF
Find the lateral surface area and volume of the object in picture below
Answers
So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:
[tex]\frac{(6^{\prime}+5^{\prime})}{2}\cdot2.1^{\prime}=11.55in^2[/tex]Then the total lateral surface is:
[tex]11.55in^2\cdot4=46.2in^2[/tex]Then we need to find the volume of the truncated pyramid. This is given by the following formula:
[tex]\frac{1}{3}h(a^2+ab+b^2)[/tex]Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:
[tex]\frac{1}{3}\cdot2^{\prime}\cdot(5^{\prime2}+6^{\prime}\cdot5^{\prime}+6^{\prime2})=60.7in^3[/tex]In summary, the lateral surface is 46.2in² and the volume is 60.7in³.
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the equation. (3, 7); y=3x+7
Answers
The linear equation parallel to y= 3x + 7 is:
y = 3x - 2
How to find the linear equation?A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two lines are parallel only if the lines have the same slope and different y-intercepts.
So a line parallel to y = 3x + 7 will be of the form:
y = 3x + c
To find the value of c we use the point (3, 7) which must belong to the line, replacing the values in the linear equation:
7 = 3*3 + c
7 = 9 + c
7 - 9 = c
-2 = c
The linear equation is y = 3x - 2
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
what is the slope of the line that passes through the points of (5,3) (5.-9)
Answers
Answer:
undefined
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-9 - 3)/(5 - 5)
slope = -12/0
Since the slope calculation involves division by zero, this line has undefined slope. The two points have the same x-coordinate, so the line is vertical. The slope of a vertical line is undefined.
Find the solutions to the following quadratic equation negative 3X squared plus 4X plus one equals zero (-3x^2 + 4x + 1 = 0)
Answers
Answer:
Explanation:
Given:
[tex]-3x^2+4x+1=0[/tex]To find:
the value of x using the quadratic formula
The quadratic formula is given as:
[tex]$$x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$[/tex]where a = -3, b = 4, c = 1
[tex]\begin{gathered} x\text{ = }\frac{-4\pm\sqrt{(4)^2-4(-3)(1)}}{2(-3)} \\ \\ x\text{ = }\frac{-4\pm\sqrt{16+12}}{-6} \\ \\ x\text{ = }\frac{-4\pm\sqrt{28}}{-6} \end{gathered}[/tex][tex]undefined[/tex]I need help with this math problem
Answers
Answer: [tex]s=4f[/tex]
Step-by-step explanation:
The scaled copy has a side length four times of the original figure, so the equation is [tex]s=4f[/tex].
Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down. A′(−4, −1), B′(0, 1), C′(−2, −4) A′(−4, 7), B′(0, 9), C′(−2, 4) A′(0, 3), B′(4, 4), C′(3, 0) A′(−8, 7), B′(−4, 9), C′(−6, 4)
Answers
Given:
The triangle is ABC
Vertices of ABC is
[tex]\begin{gathered} A=(-4,3) \\ \\ B=(0,5) \\ \\ C=(-2,0) \end{gathered}[/tex]Find-:
The vertex after 4 units down
Explanation-:
The triangle is down, which means changing the coordinates of the y-axis
The y axis reduce by 4 units, then coordinates is
[tex]\begin{gathered} A=(-4,3) \\ \\ A\rightarrow A^{\prime} \\ \\ A^{\prime}=(-4,(3-4)) \\ \\ A^{\prime}=(-4,-1) \end{gathered}[/tex]The B' is
[tex]\begin{gathered} B=(0,5) \\ \\ B^{\prime}=(0,(5-4)) \\ \\ B^{\prime}=(0,1) \end{gathered}[/tex]The C' is
[tex]\begin{gathered} C^{\prime}=(-2,(0-4)) \\ \\ C^{\prime}=(-2,-4) \end{gathered}[/tex]So, the new coordinates are
[tex]\begin{gathered} A^{\prime}(-4,-1) \\ \\ B^{\prime}(0,1) \\ \\ C^{\prime}(-2,-4) \end{gathered}[/tex]Drag and drop the correct value next to its equivalent expression number maybe use ones are not at all.
Answers
Solution:
Expression:
[tex]\begin{gathered} \frac{2}{3}\times42=2\times14 \\ \frac{2}{3}\times42=28 \end{gathered}[/tex]Expression:
[tex]\begin{gathered} \frac{5}{12}\times26=\frac{5}{6}\times13 \\ \\ \frac{5}{12}\times26=\frac{65}{6} \\ \\ \frac{5}{12}\times26=10\frac{5}{6} \end{gathered}[/tex]ANSWER:
[tex]\frac{5}{12}\times26=10\frac{5}{6}[/tex]Expression:
[tex]\begin{gathered} \frac{11}{15}\times20=\frac{11}{3}\times4 \\ \\ \frac{11}{15}\times20=\frac{44}{3} \\ \\ \frac{11}{15}\times20=14\frac{2}{3} \end{gathered}[/tex]ANSWER:
[tex]\frac{11}{15}\times20=14\frac{2}{3}[/tex]Expresion:
[tex]\begin{gathered} \frac{3}{8}\times54=\frac{3}{4}\times27 \\ \\ \frac{3}{8}\times54=\frac{81}{4} \\ \\ \frac{3}{8}\times54=20\frac{1}{4} \end{gathered}[/tex]ANSWER:
[tex]\frac{3}{8}\times54=20\frac{1}{4}[/tex]If triangular pyramid P and triangular pyramid D are similar, which of the following statements must be true?
Answers
When two figures are similar, the relation or proportion between same measures is the same. So answer is option d.
A very large bag contains more coins than you are willing to count. Instead, you draw a random sample of coins from the bag and record the following numbers of eachtype of coin in the sample before returning the sampled coins to the bag. If you randomly draw a single coin out of the bag, what is the probability that you will obtain apenny? Enter a fraction or round your answer to 4 decimal places, if necessary.Quarters27Coins in a BagDimes21Nickels24Pennies28
Answers
Given:
The number of quarters = 27
The number of dimes = 21
The number of Nickels = 24
The number of Pennies = 28
Required:
Find the probability to obtain a penny.
Explanation:
The total number of coins = 27 + 21 + 24 +28 = 100
The probability of an event is given by the formula:
[tex]P=\frac{Number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]The number of penny = 28
[tex]\begin{gathered} P(penny)=\frac{28}{100} \\ P(penny)=0.28 \end{gathered}[/tex]Final Answer:
The probability of obtaining Penny is 0.28.
Use the Pythagorean Theorem to find the missing side length. *A. 12B. 144C. 10D. 24
Answers
We use the Pythagorean theorem formula to find the missing side length.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the sides} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=x \\ b=16 \\ c=20 \end{gathered}[/tex][tex]\begin{gathered} a^{2}+b^{2}=c^{2} \\ x^2+16^2=20^2 \\ x^2+256=400 \\ \text{ Subtract 256 from both sides} \\ x^2+256-256=400-256 \\ x^2=144 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ \sqrt{x^2}=\sqrt{144} \\ x=12 \end{gathered}[/tex]AnswerThe length of the missing side is 12.
Hi, can you help me to solve this problem please!
Answers
We have the following function
[tex]f(x)=7+6x[/tex]Now, we must replace the variable x by the given value, that is,
[tex]f(10)=7+6(10)[/tex]which gives
[tex]\begin{gathered} f(10)=7+60 \\ f(10)=67 \end{gathered}[/tex]Therefore, the answer is f(10)=67
Lesson 4-2: Relations VA Name the ordered pair for each point. C С 1.A 2.B DI 3.C 4.D e е )
Answers
Assign the pair of coordinates for each point (use the graph)
A. (1,4)
B. (-2,-4)
C. (-2,2)
D. (4,-2)
A media company wants to track the results of its new marketing plan, so the video production manager recorded the number of views for one of the company's online videos. The results of the first 5 weeks are shown in this table. Write an equation to model the relationship between the number of weeks, x, and the number of views, f(x). Enter the correct answer in the box by replacing the values of a and b.
Answers
ANSWER
[tex]f(x)=5120\cdot1.25^x[/tex]EXPLANATION
We want to write an equation that models the relationship between the number of weeks (x) and the number of views, f(x).
From the table, we see that the relationship of the two terms (number of views and number of weeks) is exponential.
The general form of an exponential function is given as:
[tex]f(x)=a\cdot b^x[/tex]where a = initial value
b = exponential factor
We have to find a and b.
We do this by replacing x and f(x) in the function with values from the table.
Let us use the first set of values:
[tex]\begin{gathered} 5120=a\cdot b^0 \\ \Rightarrow5120=a\cdot1 \\ \Rightarrow a=5120 \end{gathered}[/tex]We have found the value of a, now we can find the value of b by using another set of values from the table.
That is:
[tex]\begin{gathered} 6400=5120\cdot b^1 \\ 6400=5120\cdot b \\ \text{Divide both sides by 5120:} \\ b=\frac{6400}{5120} \\ b=1.25 \end{gathered}[/tex]Now, we have found a and b.
Therefore, the equation that models the relationship between number of views and number of weeks is:
[tex]f(x)=5120\cdot1.25^x[/tex]