The coordinate of the image of the point (-3/2, -1/2) under reflection in the x-axis is (-3/2, 1/2).
What is image of a point ?When we want to reflect a point with respect to x-axis, the value of ordinate is negated. Reflection with respect to x-axis does not alter the value of abscissa but the ordinate value changes.
(i) The image coordinates of the point (2, -5) under reflection in the x-axis are (2, 5). This signifies that the point's x-coordinate remains constant while its y-coordinate changes sign (from negative to positive).
(ii) The image of the point (-3/2, -1/2) under reflection in the x-axis has the coordinates (-3/2, 1/2). This signifies that the point's x-coordinate remains constant while its y-coordinate changes sign (from negative to positive).
(iii) The image coordinates of the point (-7, 0) under reflection in the x-axis are (-7, 0). This signifies that the point's x-coordinate remains constant while its y-coordinate remains constant (zero).
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The complete question is: 1. Find the co-ordinates of the images of the following points under reflection in the x- axis:
(i) (2, -5)
(ii) (-3/2, -1/2)
(iii) (-7, 0)
Select all the expressions that are equivalent to -2/5(15-20d+5c).
1: -30+40d-10c
2: -6+8d-2c
3: -2c+8d-6
4: 6-8d+2c
5: -2(3-4d+c)
Please help
The equivalent expressions are;
-6+8d-2c-2c+8d-6-2(3-4d+c)The correct answer choice is option B, C and E
Which expressions are equivalent?-2/5(15 - 20d + 5c)
open parenthesis
= -30/5 + 40/5d - 10/5c
= - 6 + 8d - 2c
Check:
-6+8d-2c
True
-2c+8d-6
rearrange
= -6 + 8d - 2c
-2(3-4d+c)
open parenthesis
= -6 + 8d - 2c
Hence, the equivalent expression to -2/5(15 - 20d + 5c) are -6+8d-2c, -2c+8d-6 and -2(3-4d+c)
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Unit 8 Right triangles and trigonometry Homework 3
The value of x for each triangle are:
x = 6√7x = 11.6x = 21.3x = 3√29; y = 6.46; z = 2.4Please note that I only answer the circled number and please refer to the attached picture for any additional annotations.
Note that each triangles are a right angled triangle. We use phytagoras theorem to find any unknown side of a triangle.
Triangle 1x² = 14² + y²
a² = y² + 4²
x² + a² = 18²
x² + a² = 18²
(14² + y²) + (y² + 4²) = 18²
14² + 2y² + 4² = 18²
196 + 2y² + 16 = 324
2y² = 112
y² = 56
x² = 14² + y²
x² = 196 + 26
x² = 252
x = 6√7
Triangle 2(x + 28)² = a² + b²
a² = 28² + 18²
b² = x² + 18²
(x + 28)² = a² + b²
(x + 28)² = (28² + 18²) + (x² + 18²)
x² + 56x + 784 = 1432 + x²
56x = 648
x = 11.6
Triangle 3a² = b² + (x - 12)²
b² = 16² - 12²
x² = 16² + a²
x² = 16² + a²
x² = 16² + (b² + (x - 12)²)
x² = 16² + [(16² - 12²) + (x - 12)²]
x² = 256 + 112 + (x - 12)²
x² = 368 + x² - 24x + 144
24x = 512
x = 21.3
Triangle 4x² = 15² + 6²
x² = 261
x = 3√29
(15 + z)² = x² + y²
y² = z² + 6²
(15 + z)² = x² + y²
(15 + z)² = 261 + (z² + 6²)
225 + 30z + z² = 261 + z² + 36
225 + 30z + z² = 297 + z²
30z = 72
z = 2.4
y² = z² + 6²
y² = 36 + 5.76
y² = 41.76
y = 6.46
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Madison starts with a population of 1,000 1 , 000 amoebas that triples in size every hour for a number of hours, ℎ h . She writes the expression 1,000(3ℎ) 1,000 ( 3 h ) to find the number of amoeba after ℎ h hours. Tyler starts with a population of 1 1 amoeba that increases 30% 30 % in size every hour for a number of hours, ℎ h . He writes the expression (1+0.3)ℎ 1 + 0 . 3 h to find the number of amoeba after ℎ h hours. Use the drop-down menus to explain what each part of Madison’s and Tyler’s expressions mean.
The population is increasing at a constant rate, which can be represented by a simple exponential function.
Madison's expression: 1,000(3ℎ)
1,000 - This represents the starting population of amoebas, which is 1,000.
3 - This represents the rate of increase in size, which is a tripling of the original size every hour.
ℎ - This represents the number of hours for which the population is increasing.
So, the entire expression 1,000(3ℎ) means the number of amoebas after ℎ hours, where the population is tripling every hour.
Tyler's expression: (1+0.3)ℎ
1 - This represents the starting population of amoebas, which is 1.
0.3 - This represents the rate of increase in size, which is a 30% increase in size every hour.
ℎ - This represents the number of hours for which the population is increasing.
So, the entire expression (1+0.3)ℎ means the number of amoebas after ℎ hours, where the population is increasing by 30% every hour.
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Write an equation of the parabola in vertex form. Round any decimal to the nearest thousandth.
The required form of a parabola in vertex form is y = a(x - h)² + k.
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation.
Here,
The standard form of a parabola in vertex form is:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and a determines the direction of opening (a > 0 for an upward-facing parabola and a < 0 for a downward-facing parabola). The coefficient also determines the shape and steepness of the parabola.
Thus, the required form of a parabola in vertex form is y = a(x - h)² + k.
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I need to find x and y, help pls
How to do Surface Area and Volume.?
Answer:
Surface Area : find the area of each face and add them together.
Volume : multiplying height, width, and depth.
5-6. For the next school year, the soccer team will need to come up with $600.
b. Jeff is a member of a new sports team. His dad owns a bakery. to help raise money for the team, jeff's dad agrees to provide the team with cookies to sell at the concession stand usually sells about 60 to 8- baked goods per games. Using your answer from part (a), determine a percent markup for the cookies the team plans to sell at next year's opening game. Justify your answer.
The markup is of amount $97.5
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
P = $500
i = 0.5%
n= 1
Using the formula
F = P + P x i x n
F= 500 + 500 x 0.005 x 1
F= 500+ 2.5
F= $502.5
So, the team need to raise
= 600- 502.5
= $97.4
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A wire that is 40 cm long is bent into the shape of a rectangle whose width is x cm.
(i) Find an expression, in terms of x, for the area, A cm², of the rectangle. Find the x-intercepts on the graph of A against x.
(ii) Find the x-intercepts on the graph of A against x.
(iii) Find the maximum area that can be formed.
(iv) Show that this maximum area is only possible if the shape formed is a square.
How do I solve (iii) and (iv)? Thank you!
Answer:(iii) To find the maximum area of the rectangle, we can use the formula for the area of a rectangle, A = lw, where l is the length and w is the width. Since the wire is 40 cm long, we have l = 40 cm - x cm = 40 - x cm. The maximum area occurs when the length and width are equal, so we set l = w and solve for x:
40 - x = x
2x = 40
x = 20
So, the maximum area of the rectangle is A = lw = (40 - x)x = (40 - 20) * 20 = 20 * 20 = 400 cm².
(iv) To show that the maximum area is only possible if the shape formed is a square, we use the result from part (iii) that the maximum area occurs when the width x = 20 cm. If the width is less than 20 cm, the length will be greater than 40 - x, and the area will be smaller. If the width is greater than 20 cm, the length will be less than 40 - x, and the area will be smaller. So, the maximum area is only possible if x = 20 cm, which means the rectangle is a square.
Step-by-step explanation:
a. what's the probability that she chooses to teach both classes? b. what are the odds in favor of her choosing to teach both classes?
The odds of an event are calculated by taking the number of positive outcomes and dividing it by the number of negative outcomes.the odds in favor of her teaching both classes are 15:85 or 1:5.5.
a. The probability that she chooses to teach both classes is 15%.
b. The odds in favor of her choosing to teach both classes are 1:5.5.
a. The probability of an event is calculated by taking the number of positive outcomes and dividing it by the total number of outcomes. In this case, the professor has a 50% chance of teaching the first class and a 30% chance of teaching the second class. Therefore, the probability of her teaching both classes is 0.5 x 0.3 = 0.15 or 15%.
b. The odds of an event are calculated by taking the number of positive outcomes and dividing it by the number of negative outcomes. In this case, there is a 15% chance of her teaching both classes and an 85% chance of her not teaching both classes. Therefore, the odds in favor of her teaching both classes are 15:85 or 1:5.5.
The complete question is :
A professor is deciding whether to teach two classes. There is a 50% chance that she will teach the first class and a 30% chance that she will teach the second class.
a. What's the probability that she chooses to teach both classes?
b. What are the odds in favor of her choosing to teach both classes?
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three points x1, x2, x3 are selected at random on a line l. what is the probability that x2 lies between x1 and x3?
By applying permutation formula, it can be concluded that the probability that x₂ lies between x₁ and x₃ is 1/3
Permutation is rearranging a collection of objects in a different order from the original order.
P(n,r) = n! / (n-r)! where
n = number of objects
r = number of object selected
We have three points x₁, x₂, and x₃ are selected at random on line L.
Number of points = 3.
Now we can calculate the number of ways of arranging 3 points:
P(3,3) = 3! / (3 - 3)!
= 3!
= 6
There are two arrangements that x₂ lies between x₁ and x₃.
Thus, the probability that X₂ lies between X₁ and X₃ = 2 / 6 = 1/3
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from 6 positive and 8 negative numbers, 4 numbers are chosen at random (without replacement) and multiplied together. what is the probability that the product is a positive number?
Let's say event A is the selection of four positive numbers, event B the selection of four negative numbers, and event C the selection of two positive and two negative numbers.
Since four numbers are chosen without replacement, n(A) = 6 × 5 × 4 × 3 = 360 n(B) = 8 × 7 × 6 × 5 = 1680. In event C, four numbers are to be chosen without replacement such that two numbers are positive and two numbers are negative.
This can be done in following ways: + + – – OR + – + – OR + – – + OR – + – + OR – – + + OR – + + – ∴ n(C) = 6 × 5 × 8 × 7 + 6 × 8 × 5 × 7 + 6 × 8 × 7 × 5 + 8 × 6 × 7 × 5 + 6 × 5 × 8 × 7 + 8 × 6 × 5 × 7 = 6 × (8 × 7 × 6 × 5) =10080 Here, total number of numbers = 14 ∴ n(S) = 14 × 13 × 12 × 11 = 24024
Since A, B, C are mutually exclusive events,
Required probability = P(A) + P(B) + P(C)
= n(A)/n(S) + n(B)/n(S)+ n(C)/n(S)
= 360+1680+10080/24024
= 505/1001
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Cost and revenue functions. The operating cost of
a company can be approximately modelled as
C(x) = 17- 8x - 2x², where x is the time in years.
Given that its revenue function is R(x) = 5 - 3x,
find the number of months during which the
company is not making a profit.
The number of months for which the company made no profit is 18 months.
What is profit?Generally speaking, a product's profit is defined as the sum received from sales, which should exceed the product's cost price. It is the gain from any type of commercial activity. In other words, if a product's selling price (SP) is higher than its cost price (CP), there has been a gain or profit. It explains the monetary gain realised if the revenue from the company activity is greater than the costs, such as taxes and expenses, involved in maintaining the business activity.
The cost function is given as: C(x) = 17- 8x - 2x²
The revenue function is given as: R(x) = 5 - 3x
Profit = Revenue - Cost
For no profit the equation becomes:
5 - 3x - 17 + 8x + 2x² = 0
2x² + 5x - 12 = 0
2x² + 8x - 3x - 12 = 0
2x(x + 4) - 3(x + 4) = 0
2x - 3 = 0 and x + 4 = 0
x = 3/2 and x = -4
Since, month cannot be a negative quantity we have x = 3/2.
That is 3/2 (12) = 18 months.
The number of months for which the company made no profit is 18 months.
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izzy computes each players batting average by dividing the numbers of base hits by the number of at bats. A players batting average is recorded as a decimal number
Step-by-step explanation:
HOPE IT HELPS I AM NOT SURE
Consider the function g(x)=^3√x-1
What is the range of this function's inverse?
The range of the inverse of g(x) = √(x³ - 1) is [0, ∞).
How to find the range of the function's inverse?The range of a function's inverse is the set of all possible values that the inverse function can take. To find the range of the inverse of a function, we need to find the inverse function first and then determine the set of all possible values it can take.
For the function g(x) = √(x³ - 1), we first need to find its inverse. To do this, we need to switch the roles of x and y in the original function and solve for x.
g(x) = y
y = √(x³ - 1)
x³ - 1 = y²
x³ = y² + 1
x = ∛(y² + 1)
since x = g⁻¹(y) = ∛(y² + 1)
Thus, g⁻¹(x) = ∛(x² + 1) (Replace y with x)
This is the inverse of g(x). To find the range of g⁻¹(x) we need to find the set of all possible values of x that the inverse function can take. Since the square root of a real number is always non-negative, the range of the inverse function will be all non-negative real numbers.
So, the range of the inverse of g(x) = √(x³ - 1) is [0, ∞).
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assuming that the failure of a server is independent of the other servers, what is the probability that one or more of the servers is operational? (round your answer to 6 decimal places.)
The probability that one or more of the servers is operational is 0.898994.
The probability that one or more of the servers is operational is calculated as the complement of the probability that all servers fail. If the failure of each server is independent and has a probability of 0.1, the probability that all servers fail is 0.1 * 0.1 * ... (10 times) = 0.1^10 = 1e-10. The probability that one or more servers is operational is calculated as 1 - 1e-10 = 0.9999999999, which can be rounded to 0.898994. In other words, the probability of at least one server being operational is almost 90%.
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What are the domain and the range of function f?
The domain and the range of function f are given as follows:
Domain: (-∞, -3) U (-3, 6) U (6, ∞).Range: (-∞, 0) U (0, 1/9) U (1/9, ∞).How to obtain the domain and the range of a function?The domain of a function is the set that contains all the input values that can be assumed by the function.
The function in this problem is a fraction, meaning that the denominator must assume values different of zero, hence the values outside the domain are:
x² - 3x - 18 = 0.
(x - 6)(x + 3) = 0
Hence:
x + 3 = 0 -> x = -3.x - 6 = 0 -> x = 6.Hence the domain is:
(-∞, -3) U (-3, 6) U (6, ∞).
The range of a function is the set that contains all the output values that can be assumed by the function.
The x - 6 term can be canceled, hence the output value that the function will never assume is of:
1/(6 + 3) = 1/9.
And also y = 0, as it would assume a value of zero at x = 6 but the denominator would also be zero.
Hence the range is of:
(-∞, 0) U (0, 1/9) U (1/9, ∞).
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b. Measure the length of the side DF.
c. Measure the height of the triangle, XF.
d. Describe in words the locus of the point that is 2cm from E and draw this onto your diagram.
e. Use compasses to bisect the angle D. You must leave your construction arcs in.
Answer:
C and D
Step-by-step explanation:
HELPPP
1) Among the sets, P = {3,4,5,6} , Q = {0,1,2,3} , R = {5,6,7,8,9}
i) write a pair of disjoint sets
ii)name a pair of equivalent sets
2) Out of the students in the class, 3/7 are girls. If there are 24 boys in the class, find the total number of students in the class.
Answer:
Question 1:
i) A pair of disjoint sets from the given sets are P and Q. Since there are no common elements between the sets P and Q, they are disjoint.
ii) A pair of equivalent sets from the given sets is Q and {0,1,2,3}. They contain the same elements and have the same number of elements.
Question 2:
The number of girls in the class is 3/7 * number of students in the class. Let's say there are n students in the class. Then, 3/7 * n = 3/7 * (24 + n) = 3 girls.
Solving for n, we get n = 84, which is the total number of students in the class.
Step-by-step explanation:
A fast-food worker works Monday through Friday, 8 hours per day. Daily, the worker receives a -hour break in the morning, a -hour break for lunch, and a -hour break in the afternoon. How many hours of break time does the worker receive per day? 1 1
The fast-food worker receives 3 hours of break time per day.
This breaks down to a one-hour break in the morning, one hour for lunch, and one hour in the afternoon.
Mathematically, this can be expressed as
1 hour + 1 hour + 1 hour = 3 hours.Additionally, the worker works 8 hours per day, Monday through Friday. This can be expressed as 5 days x 8 hours = 40 hours per week. The worker then receives 3 hours of break per day, which can be expressed as 40 hours - (5 days x 3 hours of break) = 25 hours of work per week.
Therefore, the fast-food worker receives three hours of break time per day and 25 hours of work time per week.
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how many grades do u have to fail to get held back in 7th grade?
Answer:about 3
Step-by-step explanation:
A rectangle has a length of 12 inches and a width of 5 inches whose sides are
changing. The length is increasing by 9 in/sec and the width is growing at 2 in/sec.
What is the rate of change of the area?
The rate of change of the area of the rectangle as required in the task content is; 87 in²/sec.
By what rate if the area of the Rectangle changing?It follows from the task content; The length is increasing by 9 in/sec which represents 75% of the initial length and the width is growing at 2 in/sec which represents 40% of the initial width.
Since the area of a rectangle is; A = l × w
A (initial) = 60in².
Therefore, the new area of the rectangle after every second is;
Area (new) = 1.75l × 1.4w
Area (new) = 2.45 lw
This therefore translates to the fact that the area of the rectangle is increasing by a factor of 1.45 which is equivalent to 145% of initial Area.
Therefore, the area is increasing by 1.45 × 60 = 87in²/sec.
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Heather's school is selling tickets to the annual talent show. One the first day of ticket sales the school sold 3 senior citizen tickets and 4 child tickets for
a total of $46. The school took in $48 on the second day by selling 4 senior citizen tickets and 2 child tickets. What is the price of each ticket type?
The price of a child ticket is $4 and the price of a senior citizen ticket is $10
Let's call the price of a senior citizen ticket "x" and the price of a child ticket "y".
On the first day, the school sold 3 senior citizen tickets and 4 child tickets for a total of $46, so we can write the equation:
3x + 4y =46
On the second day, the school took in $48 by selling 4 senior citizen tickets and 2 child tickets, so we can write another equation:
4x + 2y = 48
Now that we have two equations, we can use substitution or elimination to find the value of x and y.
For substitution, we can solve one equation for one variable and then substitute that expression into the other equation. For example, let's solve the first equation for x:
x = (46 - 4y)/3
Then, we can substitute this expression for x into the second equation:
4((46 - 4y)/3) + 2y = 48
Expanding the left side of the equation:
(184 - 16y)/3 + 2y = 48
Multiplying both sides by 3:
184 - 16y + 6y = 144
Combining like terms on the left side:
184 - 10y = 144
Subtracting 184 from both sides:
-10y = -40
Dividing both sides by -10:
y = 4
So the price of a child ticket is $4. To find the price of a senior citizen ticket, we can substitute this value back into the equation we solved for x:
x = (46 - 4y)/3 = (46 - 4 * 4)/3 = (46 - 16)/3 = 30/3 = $10
So the price of a senior citizen ticket is $10.
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(4x + 2)(x -1)(3x)(2x + 3) = 194 meters squared
what is the value of X
Answer:
x ∈ {−2.18723509003, 1.68723509003}
Step-by-step explanation:
You want the value of x that satisfies the equation (4x +2)(x -1)(3x)(2x +3) = 194.
QuarticThe fact that 194 is not divisible by 3 means the real solutions will not be integer values, likely irrational. A graphical solution and some iterations tell us the solutions are ...
x = −2.18723509003
or
x = 1.68723509003
__
Additional comment
The product has units of square meters, so we presume these dimensions come in pairs of factors. It appears that both the positive and negative values of x will give factors pairs that have a positive product.
Any rational solutions would be multiples of 1/24. These solutions are not rational.
Solve the equation and check your solution: x + 4 = -2 +
Answer:
x = -6
Step-by-step explanation:
Solving an equation:x + 4 = -2
Subtract 4 from both sides,
x + 4 - 4 = -2 - 4
x = -6
[tex]\boxed{\bf x = -6}[/tex]
Check: Substitute x = -6 in the LHS of the equation,
LHS = x +4
= -6 + 4
= -2 = RHS
what 2848x4848x495948+3858 / 384
if your still awake doing school stuff, take a break if you want you can talk with me in ch.at
The result of the expression 2848 × 4848 × 495948 + 3858 / 384 is equal to 684,114,389,002.05 approximately to 2 decimal place using PEDMAS
What is PEDMASP – Parentheses First: B – Brackets First
E – Exponents
D – Division
M – Multiplication
A – Addition
S – Subtraction
The expression 2848 × 4848 × 495948 + 3858 / 384 can be simplified as follows:
2848 × 4848 × 495948 + 3858 / 384
(2848 × 4848) × 495948 + (3858 / 384)
13807104 × 495948 + 10.0469
6811753718272 + 10.0469
684,114,388,992 + 10.0469
684,114,389,002.05
Therefore, the result from applying the right order of mathematics operations for the expression 2848 × 4848 × 495948 + 3858 / 384 is equal to 684,114,389,002.05 approximately to 2 decimal place using PEDMAS.
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kevin has four red marbles and eight blue marbles. he arranges these twelve marbles randomly, in a ring. determine the probability that no two red marbles are adjacent.
To determine the probability that no two red marbles are adjacent, we can calculate the number of arrangements of the 12 marbles such that no two red marbles are next to each other, and divide that by the total number of arrangements of the 12 marbles.
One way to do this is to place the red marbles first, and then the blue marbles. If we place the red marbles randomly, there are 5 gaps between the red marbles where we can insert the blue marbles. Thus, there are 5! = 120 ways to arrange the blue marbles.
Next, we need to determine the number of ways to arrange the red marbles. If we think of the red marbles as a sequence of R's and B's (where B represents a gap between red marbles), we have 4 R's and 5 B's. To avoid adjacent R's, we need to arrange the R's and B's such that no two R's are next to each other. One way to do this is to use the concept of combinations.
There are C(9,4) ways to arrange 4 R's and 5 B's in a sequence of 9 elements. This number can be calculated using the formula for combinations: C(n,k) = n! / (k! (n-k)!). In this case, C(9,4) = 126.
Finally, we divide the number of arrangements of the red marbles by the total number of arrangements of the 12 marbles to obtain the desired probability. The total number of arrangements of the 12 marbles is 12!. Thus, the desired probability is:
P = 126 / (120 * 12!) =
126 / (120 * 479001600)
= approximately 0.0000026
So, the probability that no two red marbles are adjacent is approximately 0.0000026.
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need help asap cause its my next class in 10 minutes
Answer: 6) 33° , 7) x=3°
Step-by-step explanation:
The sum of the three angles of any triangle is equal to 180 degrees.
6) ∡SUT= 180-102 = 78 Linear Pair
∴ ∡UTS=180-(69+78)
=180-147
= 33°
7) ∡DBC=180-123=57 Linear Pair
57+25x+2+15x+1=180
60+40x=180
40x=180-60
=120
x=120/40=3°
∴ ∡D=77
∡C=46
how would you compute the minimum number of semesters it would take a student to take all of the courses?
The math equation for this example would be 12 courses divided by 4 courses = 3 semesters.
The formula for computing the minimum number of semesters it would take a student to take all of the courses is calculated by dividing the total number of courses by the number of courses that can be taken in a semester. For example, if a student needs to take 12 courses, and the maximum number of courses that can be taken in a semester is 4, then the minimum number of semesters it would take the student to take all of the courses is 3 semesters. The math equation for this example would be 12 courses divided by 4 courses = 3 semesters. In order to determine the exact number of semesters it would take a student to take all of the courses, the total number of courses must be divided by the number of courses that can be taken in a semester.
The formula for calculating the minimum number of semesters it would take a student to take all of the courses is Total Number of Courses divided by Number of Courses that can be taken in a semester. For example, if a student needs to take 12 courses, and the maximum number of courses that can be taken in a semester is 4, then the minimum number of semesters it would take the student to take all of the courses is 3 semesters. The math equation for this example would be 12 courses divided by 4 courses = 3 semesters.
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i toss a coin and pick a card. what is the probability that i get a head in the coin toss and a letter card (a, q, k, or j)? there are 52 cards in a standard deck of cards.
The probability that I get a head in the coin toss and a letter card is 2/ 13.
Therefore the answer is 2/ 13.
There are 4 As, 4Qs, 4Ks and 4 Js, so there are 16 choices. The probability of getting a head in a coin toss is 1/2, and the probability of picking a letter card is 16/ 52 = 4/ 13. So
P(heads) = 1/ 2
P(letter card) = 4/ 13
To find the joint probability of both events happening (getting a head and picking a letter card), you multiply the individual probabilities:
P(heads and letter card) = P(heads) * P(letter card)
= (1/ 2) * (4/ 13)
= 2/ 13
So the probability of getting a head and picking a letter card is 2/13.
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At what point does the line given by the following equation cross the y-axis?
y = -2x + 3
The given line y = -2x + 3 will cross the y-axis at (0, 3).
Coordinate plane:A coordinate plane is a two-dimensional plane that consists x-axis and a y-axis. These are perpendicular to each other and will be intersected at the point called the origin.
The coordinates of the point that lies on the y-axis are (0, y), Similarly, the coordinates of the point that lies on the x-axis are (0, x).
Here we have
The equation of the line is y = -2x + 3
To find the required point take x = 0
=> y = -2(0) + 3
=> y = 0 + 3
=> y = 3
Therefore,
The given line y = -2x + 3 will cross the y-axis at (0, 3).
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