3. (3 points) We toss n coins, and each one shows heads with probability p, independently of each of the others. Each coin which shows heads is tossed again. What is the PMF of the number of heads resulting from the second round of tosses
Answers
The PMF of the number of heads resulting from the second round of tosses can be summarized as follows P(X = n) = p^n.
The PMF (Probability Mass Function) represents the probability distribution of a discrete random variable. In this scenario, we are interested in finding the PMF of the number of heads resulting from the second round of tosses, given that we initially tossed n coins and each coin shows heads with probability p.
To determine the PMF, we need to consider the possible outcomes and their associated probabilities. Let's denote the number of heads resulting from the second round as X.
If none of the n coins show heads in the first round:
The probability of this event is (1-p)^n since each coin shows heads with probability p.
In this case, the number of heads in the second round will be 0.
If exactly k coins show heads in the first round (0 ≤ k ≤ n):
The probability of this event is given by the binomial distribution: C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the binomial coefficient.
In this case, the number of heads in the second round will be k, as all k coins that showed heads in the first round will be tossed again.
If all n coins show heads in the first round:
The probability of this event is p^n.
In this case, all n coins will be tossed again, resulting in n additional heads.
Therefore, the PMF of the number of heads resulting from the second round of tosses can be summarized as follows:
P(X = 0) = (1-p)^n
P(X = k) = C(n, k) * p^k * (1-p)^(n-k) for 0 ≤ k ≤ n
P(X = n) = p^n
Here, P(X = x) represents the probability that the number of heads in the second round is x, where x takes values from 0 to n.
It's important to note that this PMF assumes that the coins are tossed independently and that the probability of each coin showing heads remains constant throughout the tosses.
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Related Questions
what is the length and width of a basketball court
Answers
The length of a standard basketball court is 94 feet (28.65 meters), and the width is 50 feet (15.24 meters).
A standard basketball court is rectangular in shape and follows certain dimensions specified by the International Basketball Federation (FIBA) and the National Basketball Association (NBA). The length and width of a basketball court may vary slightly depending on the governing body and the level of play, but the most commonly used dimensions are as follows:
The length of a basketball court is typically 94 feet (28.65 meters) in professional settings. This length is measured from baseline to baseline, parallel to the sidelines.
The width of a basketball court is usually 50 feet (15.24 meters). This width is measured from sideline to sideline, perpendicular to the baselines.
These dimensions provide a standardized playing area for basketball games, ensuring consistency across different courts and facilitating fair play. It's important to note that while these measurements represent the standard dimensions, there can be slight variations in court size depending on factors such as the venue, league, or specific regulations in different countries.
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On average, 4 customers per hour use the public telephone in the sheriff's detention area, and this use has a Poisson distribution. The length of a phone call varies according to a negative exponential distribution. with a mean of 5 minutes. The sheriff will install a second telephone booth when an arrival can expect to wait 3 minutes or longer for the phone
a. By how much must the arrival rate per hour increase to justify a second telephone booth?
b. Suppose the criterion for justifying a second booth is changed to the following: install a second booth when the probability of having to wait at all exceeds 0.6 Under this criterion, by how much must the arrival rate per hour increase to justity a second booth?
Answers
A. The arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone boothe.
B. The arrival rate per hour must increase by at least 1.6 customers per hour to justify a second telephone booth under the new criterion.
How to calculate arrival rateTo get the how much arrival rate must increase, we must get the expected waiting time for a customer.
Assuming;
X is the number of customers who arrive per hour
Y is the length of a phone call in minutes.
Then, X follows a Poisson distribution with λ = 4 (since 4 customers per hour use the phone on average)
Y follows a negative exponential distribution with mean μ = 5 (since the mean length of a phone call is 5 minutes).
Total time is given as sum of waiting time and length of call;
T = W + Y
The waiting time W is the difference between the time a customer arrives and the time that the phone becomes available. waiting time follows a uniform distribution where mean= 1/λ (since the arrivals follow a Poisson process);
Then we have;
E(W) = 1/(2λ) = 1/8 hours
The expected total time T that a customer spends at the phone booth is:
E(T) = E(W) + E(Y) = 1/8 + 5/60 = 11/48 hours
For a second telephone booth to be justifiable, new customer that arrives must wait 3 minutes or longer for the phone.
E(W) ≥ 1/20
To get λ,
1/(2λ) ≥ 1/20
λ ≤ 10
This means that, the arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone booth.
b. Getting how much the arrival rate per hour must increase to justify a second telephone booth under the new criterion,
we need to find the probability that a customer has to wait at all.
Let P(W > 0) be the probability that a customer has to wait.
P(W > 0) = 1 - P(W = 0)
The waiting time W follows a uniform distribution with mean 1/λ, so we have:
P(W = 0) = 1 - λ/4
The length of a phone call Y follows a negative exponential distribution with mean 5 minutes = 1/12 hours, so we have:
P(Y > t) = e^(-μt) = e^(-t/12)
The probability that a customer has to wait is given as;
P(W > 0) = 1 - P(W = 0) = λ/4
To justify a second telephone booth, the probability of having to wait at all must exceed 0.6. so we have;
P(W > 0) > 0.6
λ > 2.4
The arrival rate per hour must increase by at least 2.4 - 4 = 1.6 customers per hour to justify a second telephone booth under the new criterion.
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Write in slope-intercept form an equation of the line that passes through the given points.
(1, 2) , (-2, -1)
Answers
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (1, 2) and (x2, y2) = (-2, -1). Substituting these values, we get:
m = (-1 - 2) / (-2 - 1) = -1/3
Now we can use the point-slope form of the equation of a line to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) = (1, 2) and m = -1/3. Substituting these values, we get:
y - 2 = (-1/3)(x - 1)
Simplifying this equation, we get:
y = (-1/3)x + 7/3
Therefore, the equation of the line in slope-intercept form that passes through the points (1, 2) and (-2, -1) is y = (-1/3)x + 7/3.
Based on the information marked in the diagram, triangle PQR and triangle STU must be congruent
A. True
B. False
Answers
Answer:
A. True
Step-by-step explanation:
Given points A(-1,4) and B(x,7), determine the value(s) of x if AB=5cm
Answers
The value of x is either 3 or -5 based on the distance formula.
What is a co-ordinate system?
In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.
Main body:
according to question
Given points A(-1,4) and B(x,7)
Also AB = 5 cm
Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)
here by using points ,
5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)
taking square on both side ,'
25 = \((x+1)^{2} +3^{2}\)
25-9 = (x+1)²
16 = (x+1)²
taking square root on both sides,
x+1= ±4
x = 4-1 = 3 or x = -4-1 = -5
Hence value of x is either 3 or -5.
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What single transition does the same job as <4, -2> followed by <2, -3>?
Answers
A transition mutation is a point mutation that transforms one nucleotide from one type of purine to another (A to G) or from one type of pyrimidine to another (C to T). G and C are substituted for A and T, respectively, and G is a different purine and C is a different pyrimidine.
What does mutational transition mean?A transition mutation is a point mutation that transforms one nucleotide from one type of purine to another (A to G) or from one type of pyrimidine to another (C to T). G and C are substituted for A and T, respectively, and G is a different purine and C is a different pyrimidine.The transition that should be used with each single-property transition is described (or the special values all and none ). The property to which the transition should apply is represented by a value of 0 or 1.When a CSS property switches from one value to another over time, a transition takes place. Four CSS properties are condensed into the transition property: transition-property,duration, timing function, and delay during transitions.To learn more about Transition mutation refer to:
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15-16 find the domain of each function.
15. (b) \(f(x)=\frac{1+x}{e^{\cos x}}\)
Answers
The domain of a function represents all the possible input values for which the function is defined and meaningful.
What is the set of valid input values for the function?
Determining the domain of a function involves identifying any restrictions or limitations on the input values that would make the function undefined or result in an invalid output. It is crucial to consider the nature of the function and any mathematical operations or expressions involved.
Without a specific function provided in the question, it is challenging to determine the exact domain. However, in general, common restrictions may include:
Denominators cannot be zero: If the function involves a fraction, the denominator should not be zero. Therefore, any values that would make the denominator zero must be excluded from the domain.
Square roots of negative numbers: If the function contains a square root, the radicand (expression under the square root) must be non-negative. Otherwise, complex or imaginary numbers would result, which might not be applicable in certain contexts.
Logarithms of non-positive numbers: If the function includes a logarithm, the argument (input value) must be strictly positive since the logarithm of zero or a negative number is undefined.
To determine the precise domain of a specific function, it is necessary to analyze the function's properties, rules, and any given restrictions explicitly provided. Consulting mathematical principles and applying algebraic manipulations can help identify the valid input values for the function.
Learn more about:
Understanding the domain of a function is fundamental in mathematics as it ensures that the function is well-defined and can produce meaningful outputs for certain inputs. By carefully examining the nature of the function and considering any limitations or restrictions, mathematicians can establish the set of values over which the function is defined. Analyzing the domain allows for accurate mathematical modeling, problem-solving, and interpretation of real-world phenomena.
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The domain of the function is all real numbers.
The given function is \(\(f(x) = \frac{1+x}{e^{\cos x}}\)\). To determine its domain, we need to identify any restrictions on the values of (x) that would make the function undefined.
In this case, the function involves basic arithmetic operations (addition and division) and exponential functions. Both addition and division can be performed for any real numbers, and the exponential function is defined for all real numbers as well.
Therefore, there are no restrictions or conditions on the values of (x) that would make the function undefined.
The domain of the function (f(x)) is the set of all real numbers.
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I forgot how to solve these.
Answers
Step-by-step explanation:
4x + 16 = 2x + 34
4x - 2x = 34 - 16
2x/2 = 18/2
x = 9
2(9) + 34
= 18 + 34
= 52
52 x 2
= 104
360 - 104
= 256
256/2
= 128
Therefore angle 1 is 128°
aldosterone stimulates the reabsorption of sodium while enhancing potassium secretion.
a. true b. false
Answers
I believe that may be false
Answer:
Step-by-step explanation:
True.
Aldosterone is a hormone produced by the adrenal gland that plays an important role in regulating electrolyte and water balance in the body. It acts on the cells of the distal tubules and collecting ducts of the kidneys to increase the reabsorption of sodium ions and the secretion of potassium ions.
This helps to increase blood volume and blood pressure by retaining more sodium and water in the body while getting rid of excess potassium. Aldosterone release is regulated by the renin-angiotensin-aldosterone system, which is activated in response to low blood pressure or low sodium levels in the blood.
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How does the experimental probability of choosing a yellow tile compare with the theoretical probability of choosing a yellow tile
Answers
Answer:
The experimental probability is the same as the theoretical probability.
Step-by-step explanation:
The given data is:
color observed frequency relative frequency
Red 15 3/10
Blue 12 6/25
Green 8 4/25
Yellow 10 1/5
Purple 5 1/10
The experiment was repeated 50 numbers of times.
Solution:
Theoretical probability is basically what is expected to happen without experimenting and experimental probability is what actually happens as a results of an experiment.
Theoretical probability = favorable outcomes / all possible outcomes
Experimental probability = no. of times outcome occurs / no. of times
experiment is performed The experimental probability and theoretical probability are same i.e. 1/5
This can be seen from the table:
Experimental probability = 1/5
As the experiment is performed 50 times and the outcome (yellow tile) occurs 10 times so using the formula of experimental probability:
10/50 = 1/5
Now as given, there are 5 number of tiles (red,blue,green,yellow,purple) so number of possible outcomes is 5. Yellow tile among these 5 tiles is 1. So the favorable outcomes is 1. So looking at the given formula of theoretical probability:
1/5
So
experimental probability = 1/5
theoretical probability = 1/5
Hence the experimental probability is the same as the theoretical probability.
Answer: A
Step-by-step explanation: it’s A for the lazy people
if 2x+5y=180 and 3x+3y=180
what are the x and y values?
Answers
Answer:
x=40,y=20
Step-by-step explanation:
a{2x+5y=180
b{3x+3y=180
b-a
x-2y=0
x=2y
substitute:
2×2y+5y=180
9y=180
y=20
substitute:
x=2y
x=2×20
=40
Consרider the following. (Round your answers to four decimal places.)
f(x,y)=xcos(y)
(a) Evaluate f(6,5) and f(6.1,5.05) and calculate Δz.
f(6,5)=
f(6.1,5.05)=
Δz=
(b) Use the total differential dz to approximate Δz.
dz=
Answers
The evaluated values of the given problem are:
(a) f(6, 5) ≈ 4.2185; f(6.1, 5.05) ≈ 4.2747 and Δz ≈ 0.0562
(b) dz ≈ 0.0715
(a) To evaluate f(6,5) and f(6.1,5.05) and calculate Δz, we substitute the given values into the function f(x, y) = x * cos(y).
Substituting x = 6 and y = 5:
f(6, 5) = 6 * cos(5) ≈ 4.2185
Substituting x = 6.1 and y = 5.05:
f(6.1, 5.05) = 6.1 * cos(5.05) ≈ 4.2747
To calculate Δz, we subtract the initial value from the final value:
Δz = f(6.1, 5.05) - f(6, 5)
Δz ≈ 4.2747 - 4.2185 ≈ 0.0562
Therefore:
f(6, 5) ≈ 4.2185
f(6.1, 5.05) ≈ 4.2747
Δz ≈ 0.0562
(b) To approximate Δz using the total differential dz, we can use the formula:
dz = ∂f/∂x * Δx + ∂f/∂y * Δy
where ∂f/∂x represents the partial derivative of f with respect to x, and ∂f/∂y represents the partial derivative of f with respect to y.
Taking the partial derivative of f(x, y) = x * cos(y) with respect to x gives us:
∂f/∂x = cos(y)
Taking the partial derivative of f(x, y) = x * cos(y) with respect to y gives us:
∂f/∂y = -x * sin(y)
Substituting the given values Δx = 0.1 and Δy = 0.05 into the formula, we get:
dz = cos(5) * 0.1 + (-6 * sin(5) * 0.05)
≈ 0.0872 - 0.0157
≈ 0.0715
Therefore:
dz ≈ 0.0715
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Point A is at-4 and point B is at 6. Which describes one way to find the point that divides AB into a 3:2 ratio?
A
B
-54-3 -2 -1 0 1 2 3 4 5 6 7 8
O For a ratio of 3:2, divide AB into 3 equal parts. Each equal part is 3 units, so the point that divides AB into a 3:2
ratio is 0.
O For a ratio of 3:2, divide AB into 3 equal parts. Each equal part is 3 units, so the point that divides AB into a
3:2 ratio is 3.
O For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a
3:2 ratio is 1.
O For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a
3:2 ratio is 2
Answers
The point that divides AB into a 3:2 ratio is calculated by (d) for a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2
How to determine the ratio?The given parameters are:
A = -4
B = 6
Start by calculating the length AB using:
AB = |B - A|
This gives
AB = |6 -(-4)|
Evaluate
AB = 10
Next, the length is divided into 5 parts.
So, the length of each part is:
Length = 10/5
Length = 2
The point on the location 3 : 2 is then calculated as:
Point = A + 3 * Length
This gives
Point = -4 + 3 * 2
Evaluate
Point = 2
The above computation is represented by option (d)
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Anyone know how to do this pleaseee?
Answers
Answer:
It should be 384^2
Step-by-step explanation:
Answer:
384 unit^2
Step-by-step explanation:
SA = 2(lw + wh + hl)
= 2(8x8 + 8x8 + 8x8)
= 2(64 + 64 + 64)
= 2(192)
= 384
Hope it helps!
If your insurance plan is $15,000 and you pay for 20%, how much do you
pay monthly? *
2 poir
$250
$3,000
$57.69
$300
Answers
Answer: 250
Step-by-step explanation:
20% of 15,000 is 3,000
3,000/12=250
Answer:
$3000 Per Month
Step-by-step explanation:
Hi there,
How I like to solve these is first take the total number (15,000) and divide it by 100 to then find how much 1% of 15,000 is.
So :
15,000 / 100
=
150
Now we know :
1% = $150
We need to find 20% now so all we do is multiply.
150 x 20
($150 x 20%)
= $3,000 Per Month
I hope this helps!
If you have any questions or concerns be sure to comment or message me ! :)
EDIT : The other person is most likely right. I am 17 and dont have insurance yet Lol
Amaya used these steps to solve the equation 8x+4=9+4(2x−1)
. Which choice describes the meaning of her result, 4=5?
the choices are :
Amaya made a mistake because 4
is not equal to 5
.
No values of x
make the equation true.
.
All values of x
make the equation true.
.
The solution is x=4
or 5
.
Answers
Amaya made a mistake because 4 is not equal to 5. She incorrectly wrote 4=5 in the final step of solving the equation 8x+4=9+4(2x-1). So, the correct answer is A).
In step 1, Amaya sets up the equation 8x+4=9+4(2x-1).
In step 2, she simplifies the right side of the equation to 9+8x-4=5+8x.
In step 3, she subtracts 8x from both sides of the equation to get 4=5.
In step 4, she simplifies the equation to 4=9-4.
In step 5, she mistakenly writes that 4=5, which is incorrect.
Therefore, the correct choice is that Amaya made a mistake because 4 is not equal to 5. So, the correct option is A).
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125+s is greater than or equal to 2300 in words
Answers
125 is greater than 23.
Given the question is to explain 125 > 23.
Here we have two numbers which are 125 and 23.
Inequalities:
Whenever we check the number which is greater or lesser by taking the difference between those two numbers we conclude which is greater or lesser.
If the difference between the numbers gets a positive number then the first number is greater than the second.
If the difference between the numbers gets a negative number then the first number is lesser than the second.
If the difference between the numbers gets zero value then the two numbers are equal.
So the difference between the given two numbers are
= 125 - 23
= 102
positive
So 125 is greater than 23.
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Your question is incomplete. Please find the complete question below
.Find 125 is greater than 23. Write about it in words.
Vladas believes that an equation with a squared term is never a function of x. Which equation can be used to show vladas that his hypothesis is incorrect?.
Answers
The equation that shows that his hypothesis is wrong is:-
x²+ y²= 25
What is an equation in math?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
How do we solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Vladas said that the equation with a squared term is never a function of x.
According to the Pythagorean Theorem, the square of two natural numbers is the third number. When these numbers are used to create a triangle, a right-angled triangle is formed, with a 90° angle between the two smaller sides.
Among the four provided hypotheses:
Option (C) is true since x2+y2=25.
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MathWiz wya? I need some help with this...show your work <3
Answers
Answer:
(4i+1)^2
4i^2 + 2(4i) + 1
16(-1) + 8i + 1
-15+8i
8i-15
(x+1) + (x-2)(x+3)
(x+1) + (x^2-2x+3x-6)
(x+1)+x^2+x-6
x+1+x^2+x-6
x^2+2x-5
Let me know if this helps!
A boutique is offering a 15% discount for
cash. Calculate the cash price for a dress
with a marked price of $12500.
Answers
$12500 - 30%
=
$8750
Step-by-step explanation:
10% of $12500 = $1250
10% × 3 = 30% = $1250 × 3 = $3750
30% = $3750
$12500 - $3750 = $8750
What is an equation of the line that passes through the point (-4, 5) and is
perpendicular to the line 4x +y = 72
Submit Answer
attempt 1 out of
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Copyright ©2022 DetaMath.com All Rights reserved
Answers
Answer:4(-4)+5=72
Step-by-step explanation:
in the context of rm and range safety mitigation of risk is the ability
Answers
In the context of Range Safety and Risk Mitigation, the ability to detect, assess, and respond to potential hazards is essential.
Range safety and risk mitigation involve identifying and minimizing potential hazards associated with range operations, such as the launch or test of rockets, missiles, or unmanned aerial vehicles. To ensure safety, it is critical to have the ability to detect and assess potential hazards, such as debris, vehicle or equipment malfunctions, and human error. Once hazards have been identified and assessed, the next step is to develop and implement appropriate safety measures to mitigate the risk associated with those hazards. These measures may include the use of safety protocols, engineering controls, or administrative procedures to ensure that all personnel and equipment are protected. In summary, the ability to detect, assess, and respond to potential hazards is critical for effective range safety and risk mitigation. By implementing appropriate safety measures and protocols, the risks associated with range operations can be minimized, ensuring the safety of personnel and equipment.
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What can you see in this form of the linear equation? 6x+2y=13
Answers
The given equation 6x+2y=13 is a linear equation in two variables. In this equation, x and y are variables while 6 and 2 are their respective coefficients, and 13 is a constant term. The equation can be represented as a straight line on a graph. The slope of this line is -3, and it intersects the y-axis at the point (0, 13/2).
In this equation, if we substitute x=0, then y=13/2, and if we substitute y=0, then x=13/6. These are the two points that the line passes through the x and y-axis.
A linear equation is a polynomial equation that is of the first degree, meaning the variables in the equation are not raised to any powers other than one. This equation is in the standard form where the variables are in the first degree. 6x + 2y = 13 is the form of the given linear equation. x and y are the two variables, and 6 and 2 are their respective coefficients. The equation can be represented as a straight line on a graph. The slope-intercept form of this equation is y = -3x + 13/2. The equation is also in standard form.
When x = 0, the equation becomes 2y = 13. This means that the point of intersection is (0, 13/2) when y = 0, the equation becomes 6x = 13, and the point of intersection is (13/6, 0). The slope of the line is -3. When x increases by 1, y decreases by 3.
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Given the following, find A"B"C"D" if A(3, -4), B (0, -3), C(-1, -8), and D(-4,-9).
A. Translated along the vector (7, 0)
B. 90 degree counterclockwise rotation about (3, -2)
Answers
The vertices of A"B"C"D" are A"(-4, -3), B"(3, -2), C"(2, -7), and D"(-1, -8).
Given that, the coordinates are A(3, -4), B (0, -3), C(-1, -8), and D(-4,-9).
A. Given that, translated along the vector (7, 0).
The translation of vector A, B, C, and D along the vector (7, 0) will result in the points given by A'(10, -4), B'(7, -3), C'(6, -8), and D'(3, -9).
B. Given that, 90 degree counterclockwise rotation about (3, -2).
90 degree counterclockwise rotation about (3, -2) will result in the points given by A"(-4, -3), B"(3, -2), C"(2, -7), and D"(-1, -8).
Therefore, the vertices of A"B"C"D" are A"(-4, -3), B"(3, -2), C"(2, -7), and D"(-1, -8).
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The equation 4x2 8x 15 = 0 is being rewritten in vertex form. fill in the missing step. given 4x2 8x 15 = 0 step 1 4(x2 2x ___) 15 ___ = 0 step 2 ✔ step 3 4(x 1)2 11 = 0 4(x2 2x 1) 15 − 4 = 0 4(x2 2x 1) 15 − 1 = 0 4(x2 2x 2) 15 − 2 = 0 4(x2 2x 4) 15 − 4 = 0
Answers
Answer:
a) is the correct answer
Question 18 (2 points)
A triangle has vertices at F(-7,3) G(2,6) and H(3,5). What are the coordinates of each vertex of the image if the triangle is reflected
over the line y=x?
a
O b
ос
Od
F(-3,7) G'(-6,-2) H'(-5,-3)
F(7,-3) G'(-2,-6) H'(-3,-5)
F(-7,-3) G'(-2,6) H'(-3,5)
F(3,-7) G'(6,2) H'(5,3)
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The coordinates of each vertex of the given triangle FGH, if the triangle is reflected over the line y = x, are F'(3, -7), G'(6, 2), and H'(5, 3).
What is the rule for the reflection of a shape across the line y = x?The rule for the reflection across the line y = x is
(x, y) ⇒ (y, x)
Here the coordinates are shuffled or interchanged among themselves for a reflection and form an image.
Calculation:The given triangle has vertices at F(-7, 3), G(2, 6), and H(3, 5).
When it is reflected across the line y = x, the image of the triangle forms at the vertices
F(-7, 3) → F'(3, -7)
G(2, 6) → G'(6, 2)
H(3, 5) → H'(5, 3)
The reflection across the line y = x is shown in the graph below.
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solve the systems of equations via graphing then check the solution in each equation: 4x+6y=18, (y+2)=1/3(x+2)
Answers
Answer:
(4 1/3, 1/9)Step-by-step explanation:
Given system
4x + 6y = 18(y + 2) = 1/3(x + 2)Solution is the intersection point:
(4 1/3, 1/9)Simplify the first equation:
2x + 3y = 93y = -2x + 9y = -2/3x + 3Check:
1/9 = -2/3*4 1/3 + 91/9 = -26/9 + 91/9 = (27 - 26)/91/9 = 1/9Simplify the second equation:
y + 2 = 1/3x + 2/3y = 1/3x + 2/3 - 2y = 1/3x - 4/3Check:
1/9 = 1/3*13/3 - 4/31/9 = (13 - 12)/91/9 = 1/9
Answer:
see belowStep-by-step explanation:
to understand thisyou need to know about:linear equationgraphing linear equationPEMDASgiven equation:4x+6y=18......(I)
(y+2)=1/3(x+2).......(ii)
let's solve using graph:the picture is attached
got from the picture
\(x = 4 \frac{1}{3} \\ y = \frac{1}{9} \)
let's justify the (I) equation
\(4(4 \frac{1}{3}) + 6( \frac{1}{9} ) = 18\)
\(4( \frac{13}{3} ) +6 (\frac{1}{9}) = 18\)
\( \frac{52}{3} + \frac{2}{3} = 18\)
\( \frac{52 + 2}{3} = 18\)
\( \frac{54}{3} = 18\)
\(18 = 18\)
provenlet's justify the ii equation:\( \frac{1}{9} + 2 = \frac{1}{3} ( \frac{13}{3} + 2)\)
\( \frac{19}{9} = \frac{1}{3} \times \frac{19}{3} \)
\( \frac{19}{9} = \frac{19}{9} \)
proven
An initial population, p, of 1000 bacteria grows according to the equation p(1) 1000(1 + 4t 12+ 50), where t is in hours. Find the rate at which the population is growing after 1 h and after 2 h.
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The problem involves finding the rate at which the population of bacteria is growing after 1 hour and after 2 hours, given initial population of 1000 bacteria and growth equation p(t) = 1000(1 + 4t + 12t^2 + 50t^3).
We need to calculate the growth rate at these specific time intervals.To find the rate at which the population is growing after a certain time, we need to calculate the derivative of the growth equation with respect to time.
Taking the derivative of p(t) = 1000(1 + 4t + 12t^2 + 50t^3) with respect to t gives us the growth rate function:
p'(t) = 400 + 24t + 150t^2
To find the growth rate after 1 hour, we substitute t = 1 into the growth rate function:
p'(1) = 400 + 24(1) + 150(1)^2
p'(1) = 400 + 24 + 150
p'(1) = 574
Therefore, after 1 hour, the population is growing at a rate of 574 bacteria per hour.Similarly, to find the growth rate after 2 hours, we substitute t = 2 into the growth rate function:
p'(2) = 400 + 24(2) + 150(2)^2
p'(2) = 400 + 48 + 600
p'(2) = 1048
Therefore, after 2 hours, the population is growing at a rate of 1048 bacteria per hour.
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4. Which must be true of a scale factor of a dilation if the image is
smaller than the pre-image?
a. The scale factor is negative.
b. The scale factor is between – 1 and 0.
C. The scale factor is between 0 and 1.
d. The scale factor is greater than 1.
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I took the test
Barney and betty buy a home. They plan to make a down payment and carry a $101,000 mortgage. Closing costs are $3,750 and are added to the loan amount. What is the new amount being financed?.
Answers
Answer:
$104,750
Step-by-step explanation:
we just add 101,00 and 3,750 together since they are both being financed
Hopes this helps please mark brainliest