a) The pet shelter has 40% cats (20% black, 5% adopted), and 60% dogs (10% black, 10% adopted). 50% are adopted in non-black cats and dogs, b) 0.45, c) 0.19, d) 0.15, e) 0.375, f) 0.6.
a) The probability tree would seem like this:
P(Cat) = 40%
P(Black Cat) = 20%
P(Adopted Black Cat) = 5%
P(Not Adopted Black Cat) = 95%
P(Not Black Cat) = 80%
P(Adopted Not Black Cat) = 50%
P(Not Adopted Not Black Cat) = 50%
P(Dog) = 60%
P(Black Dog) = 10%
P(Adopted Black Dog) = 10%
P(Not Adopted Black Dog) = 90%
P(Not Black Dog) = 90%
P(Adopted Not Black Dog) = 50%
P(Not Adopted Not Black Dog) = 50%
b) P ( Adopted & Not Black Dog ) = P(Not Black Dog) x P(Adopted | Not Black Dog) = 0.90 * 0.50 = 0.45
c) P(Not Adopted & Black Cat) = P(Black Cat) x P(Not Adopted | Black Cat) = 0.20 * 0.95 = 0.19
d) P(Adopted) = P(Adopted Black Cat) + P(Adopted Not Black Cat) + P(Adopted Black Dog) + P(Adopted Not Black Dog) = 0.05 + 0.50 + 0.10 + 0.50 = 0.15
e) P(Adopted | Cat) = P(Adopted & Cat) / P(Cat) = (0.05 + 0.50) / 0.40 = 0.375
f) P(Cat | Adopted) = P(Cat & Adopted) / P(Adopted) = (0.05 + 0.50) / 0.15 = 0.6.
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If there is a ratio of 150 students to 18 teachers what would be the maximum number of students the school can add if it wants to maintain a ratio of student to teachers 20:1?
The maximum number of students the school can add if it wants to maintain a ratio of student to teachers 20 : 1 is 210.
What does a Ratio define?Ratio defines the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
Ratio of student to teachers now = 150 : 18
Ratio of student to teachers to maintain = 20 : 1
For 1 teacher , number of students needed = 20
For 18 teachers, number of students needed = 20 × 18 = 360
Present number of students for 18 teachers = 150
Maximum number of students who can be added = 360 - 150 = 210
Hence school can add a maximum of 210 students in order to maintain a ratio of student to teachers 20:1.
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You roll a die and pick a card. How many outcomes are possible?
567
8
The number of possible outcomes when you roll the die would be 6
How to solve for the possible outcome in a dieA die is known to have only 6 faces. The 6 faces are numbered from number 1 to number 6
Such that the sample space that we would have would be given as
SS = {1, 2, 3, 4, 5, 6}
Hence the number of outcomes that we would be able to have from one die would be given as 6
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8 4 (x, y, z) = 3x²y-y³z², find grad & at the Paint (1, -2, -1).
donuts at "hole-in-one" donut shop cost $1.20 each. how many donuts can jade purchase if she has $6.00 in her wallet?
Answer:
5
Step-by-step explanation:
6/1.2=5
Which process will create a figure that is congruent to the figure shown
The process that will create a congruent figure is a translation of four units up, followed by a rotation (option B).
What is the meaning of congruent?A figure is said to be congruent with another if they both have the same shape and the dimensions are the same. This means the figures are almost identical, although it is allowed that they are a reflection or that they are placed in the opposite direction.
Based on this, to create a congruent figure you need to translate the original figure and rotate it but not change its size (option B).
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of 2: Determine the domain and range of the graph below
The range of the graph is,
⇒ Range = { y | - 1 < y < 3 }
The domain of the graph is,
⇒ Domain = { x | - 4 < x < 2 }
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The graph is shown in figure.
Now, We know that;
The range of the graph is the value of y where the function of graph is defined.
Hence, The range of the graph is,
⇒ Range = { y | - 1 < y < 3 }
And, The domain of the function is defined the value of y where the function of graph is defined.
Hence, The domain of graph is,
⇒ Domain = { x | - 4 < x < 2 }
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A model is being built of a car. The car is 12 feet long and 6 feet wide if the length of the model is 4 inches how wide should the model be.
please hurry
The model would be 2 inches wide.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
A model is being built of a car.
The car is 12 feet long and 6 feet wide.
The length of the model is 4 inches.
The scale factor x is,
= 4/12
= 1/3
The width of the model is,
= 6 x 1/3
= 2 inches.
Therefore, the width is 2 inches.
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The charge is distributed uniformly throughout the volume of an infinitely long solid cylinder of radius R. (a) Show that, at a distance r from the cylinder axis,
E= rhor/ 2ϵ 0 where rho is the volume charge density. (b) Write an expression for E when r>R.
(a) A distance r from the cylinder axis is pr/2∈₀ and (b) expression for E when r > R is πR²lρ/2πϵ₀
(a) Consider a Gaussian surface in the form of a cylinder with radius r and length A, coaxial with the charged cylinder. An “end view” of the Gaussian surface is shown as a dashed circle. The charge enclosed by it is
q = ρV = πr²lp
V = volume of cylinder
If ρ is positive, the electric field lines are radially outward, normal to the Gaussian surface, and distributed uniformly along with it. Thus, the total flux through the Gaussian cylinder is Φ = E(2πrl). Now, Gauss’ law leads to :
2π∈₀rlE = πr²lp
E = pr/2∈₀
(b) ) Next, we consider a cylindrical Gaussian surface of radius r > R. If the external field [tex]E_{ext}[/tex] then the flux is Φ=2πϵ₀[tex]E_{ext}[/tex]
The charge enclosed is the total charge in a section of the charged cylinder with length A. That is, q=πR²lρ. In this case, Gauss’ law yields :
2πϵ₀[tex]E_{ext}[/tex] = πR²lρ
[tex]E_{ext}[/tex] = πR²lρ/2πϵ₀
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The distribution of the number of transactions per day at a certain automated teller machine (ATM ) is approximately normal with a mean of 80 transactions and a standard deviation of 10 transactions. Which of the following represents the parameters of the distribution?
The mean (μ) and standard deviation (σ) represent the parameters of a normal distribution, so in this case, the parameters of the distribution are: μ = 80 transactions and σ = 10 transactions
A normal distribution, also known as a Gaussian distribution, is a continuous probability distribution that has a bell-shaped curve. This type of distribution is often used to model real-world phenomena that are expected to be distributed in a symmetrical fashion around a central value.
The central value of a normal distribution is the mean (μ), which represents the average of all the observations in the distribution. The spread or dispersion of the distribution is measured by the standard deviation (σ), which indicates how much the observations deviate from the mean.
In the given problem, the distribution of the number of transactions per day at an ATM is assumed to be normal with a mean of 80 transactions and a standard deviation of 10 transactions.
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The director of a hospital pharmacy chooses at random 100 people age 60 or older from each of three surrounding counties to ask their opinions of a new prescription drug program.
The kind of sample described in the given information is a stratified random sample.
What is stratified random sample ?
A stratified random sample is a type of probability sampling method used to obtain a representative sample of a population by dividing the population into smaller, more homogeneous groups called strata, and then selecting a random sample from each stratum.
This method is used when the population has certain characteristics or subgroups that are of interest to the researcher, and the goal is to ensure that the sample accurately represents each subgroup in proportion to its size in the population.
The process of selecting a stratified random sample involves dividing the population into strata based on some relevant characteristic, such as age, gender, education level, income, or geographic location. Then, a random sample is selected from each stratum, using a simple random sampling method. The sample size from each stratum is proportional to the size of that stratum in the population.
The advantage of a stratified random sample is that it can provide a more accurate representation of the population than other types of sampling methods, as it ensures that each subgroup is adequately represented in the sample.
According to given information :
The population of interest is people age 60 or older from the three surrounding counties. To obtain a representative sample of the population, the director of the hospital pharmacy has divided the population into three strata (i.e., the three surrounding counties) and selected a random sample of 100 people age 60 or older from each stratum. This ensures that the sample includes a proportionate number of participants from each county, which should help to reduce the potential for sampling bias that might result from selecting participants from only one county.
Therefore, this is an example of a stratified random sample.
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If
2tan x/1-tan² x= 1, then x can equal:.
A. x =
B. x=
C. x=
K|0
D. x=
8
+ NIT
77
37
+ 27
+ NIT
-57 +1
NIT
SUBMIT
The value of x is x= π/8
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
2tan x/1-tan² x= 1
We know that tan π/4= 1
So, 2tan x/1-tan² x= tan π/4
Also, we know that tan 2x= 2tan x/1-tan² x
Again, 2tan x/1-tan² x= tan π/4
tan 2x= tan π/4
Now comparing we get
2x= π/4
x= π/8
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Which angles are adjacent to each other?
2
3
1
4
6 7
5 8
11
10
12
9
Answer:Angle 6 and Angle 5, Angle 3 and Angle 2
100% correct don't worry ;)
Step-by-step explanation:
Find the equation of a line perpendicular to y = x + 1 that passes through the
point (8,-3).
The Equation of line perpendicular to line y = x + 1 and passes through (8,-3) is y= -x+ 5.
What is Slope?A line's b is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Equation: y= x+ 11
Now, the slope of perpendicular have the slope equal to negative reciprocal so that the product of slope of perpendicular line is -1.
Then, the slope of perpendicular line is, m= -1.
As, line passes through (8, -3) then the slope intercept form
y= mx+ b
-3 = (-1)(8)+ b
-3 = -8 +b
b= 5
Thus, the Equation of line is y= -x+ 5.
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Please answer fully and find y in the given triangle
The value of y is 45.
What are similar triangles?Those triangles look the same but are different in size.
And in similar triangles,
the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.
Given:
The shape of the triangle is given in the image.
Assuming the shape is ABC.
And the segment that is parallel to the base side of the triangle is DE.
BC II DE.
So, the triangle ΔADE is similar to ΔABC.
So, the corresponding sides have a constant proportion.
So, y/15 = (20 + 10)/10
y = 15 x 3
y = 45.
Therefore, y = 45.
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Write an equation for the nth term of the arithmetic sequence 4,7,10,13
The solution is, the nth term of the arithmetic sequence 4,7,10,13 is 1 + 3n.
What is Arithmetic progression?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.
The nth term of AP : a_n = a + (n – 1) × d
here, we have,
the arithmetic sequence 4,7,10,13
so. we get,
1st term = 4 = a
common difference = 3 = d
i.e. the nth term of the arithmetic sequence is, a_n = 4+(n-1)3
=1+3n
Hence, The solution is, the nth term of the arithmetic sequence 4,7,10,13 is 1 + 3n.
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I will give brainliest and ratings if you get this correct
[tex]D(x)=\frac{f(x)}{g(x)}[/tex]
[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex]
What is quotient formula of differentiation?Quotient rule in calculus is method finding the derivative of the differentiable functions which are in the division form
There are different methods to prove the quotient rule formula, given as,
Using derivative and limit propertiesUsing implicit differentiationUsing chain ruleHere, we are using implicit differentiation method to solve this quotient rule,
Let us take a differentiable function ,
[tex]D(x)=\frac{f(x)}{g(x)}[/tex]--------(1)
So, [tex]f(x)={D(x)}*{g(x)}[/tex]
Using the product rule we get,
[tex]f'(x)= D'(x).g(x)+g'(x).D(x)[/tex] solving for [tex]D'(x)[/tex] we get,
[tex]\frac{f'(x)-g'(x).D(x)}{g(x)} = D'(x)[/tex]------(2)
substitute for D(x) sub (1) in (2)
[tex]D'(x) =\frac{f'(x)-g'(x).\frac{f(x)}{g(x)} }{g(x)}[/tex]
⇒[tex]D'(x) =\frac{f'(x)g(x)-g'(x){f(x)} }{(g(x))^{2} }[/tex]
Hence,[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex] proved.
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Given: ⊙O with central angles ∠AOC ≅ ∠BOD Prove: AC ≅ BD Circle O is shown. Line segments O A, O C, O B, and O D are radii. Line segments connect points A and C and points B and D to form 2 triangles inside of the circle. Angles A O C and B O D are congruent. Complete the missing parts of the paragraph proof. Proof: We know that central angles are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because . Then by the congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because .
The missing statements and reasons in the two column proof are;
1. AOC and BOD.
2. All radii of a circle are congruent
3. SAS congruency theorem
4. CPCTC
How to complete two column proofs?A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons that we know those statements are true.
The two column proof of the angles is;
Statement 1: Central angles ∠AOC and ∠BOD are congruent
Reason 1: Given
Statement 2: The segments AO, CO, BO, and DO are congruent
Reason 2: All radii of a circle are congruent
Statement 3: Triangle AOC is congruent to triangle BOD
Reason 3: SAS congruency theorem
Statement 4: Chord AC is congruent to chord BD
Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
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How many liters of pure water should be mixed with a 11-L solution of 60% acid to produce a mixture that is 90% water?
Answer:
55 L of water
Step-by-step explanation:
11-L of 60% acid contains 0.6 × 11 L = 6.6 L acid
Let x = amount of pure water.
Let y = total amount produced of 90% water solution.
A 90% water solution is a 10% acid solution.
Amounts of solutions:
x + 11 = y
Amounts of acid:
6.6 = 0.1y
y = 66
x + 11 = 66
x = 55
Answer: 55 L of water
55 L water has 0 acid.
11 L 60% acid solution has 6.6 L acid.
66 L of 10% acid solution has 6.6 L acid
The table represents a quadratic function f(x). x f(x) −10 24 −9 17 −8 12 −7 9 −6 8 −5 9 −4 12 If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?
Answer:
the value of b is 12.
Step-by-step explanation:
To find the value of b, we can use the vertex form of a quadratic function, which is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Since we know the vertex of this parabola from the table, we can use that information to write the equation in vertex form: f(x) = a(x + 6)^2 + 8
Expanding this, we get f(x) = a(x^2 + 12x + 36) + 8
Comparing this with the standard form, we see that a = 1, b = 12, and c = 8.
Therefore, the value of b is 12.
are the following statements true or false? [true or false]1. if the augmented matrix has a pivot position in every row, then the system is inconsistent. [true or false]2. a vector is a linear combination of the columns of a matrix if and only if the equation has at least one solution. [true or false] 3. if the columns of an matrix span , then the equation is consistent for each in [true or false]4. any linear combination of vectors can always be written in the form for a suitable matrix and vector . [true or false]5. if the system is inconsistent, then is not in the column space of . [true or false]6. the equation is referred to as a vector equation. [true or false]7. if is an matrix and if the equation is inconsistent for some in , then the rref of cannot have a pivot position in every row. [true or false]
From the following statements: statement 1 and statement 6th is false, rest are true about matrix and vector.
1. if the augmented matrix has a pivot position in every row, then the system is inconsistent, this statement is false.
2. a vector is a linear combination of the columns of a matrix if and only if the equation has at least one solution, this statement is true.
3. if the columns of an matrix span , then the equation is consistent for each in b in R^m, this statement is true.
4. any linear combination of vectors can always be written in the form Ax for suitable matrix A and vector x, this statement is true.
5. if the system Ax = b is inconsistent, then b is not in the column space of A, this statement is true.
6. The equation Ax = b is referred to as a vector equation, this statement is false.
7. if A is an matrix and if the equation Ax = b is inconsistent for some in , then the RRef of A cannot have a pivot position in every row, this statement is true.
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write as an expression as a square of a monomial 0.16x^2y^2
The square of the monomial 0.16x^2y^2 can be expressed as:
(0.16x^2y^2)^2 = 0.16^2 * x^2 * y^2 * x^2 * y^2 = 0.0256x^4y^4
hope it helps
Write the percent as a fraction in simplest form and as a decimal. 2315%
Answer:
23:15 as a decimal and 23 3/20
Step-by-step explanation:
Just divide by 100 to get decimal. For the fraction divide by 100 and simplify
This problem relates to the QDA model, in which the observations within each class are drawn from a normal distribution with a class- specific mean vector and a class specific covariance matrix. We con- sider the simple case where p = 1; i.e. there is only one feature. Suppose that we have K classes, and that if an observation belongs to the kth class then X comes from a one-dimensional normal dis- tribution, X ~ N(uk, o?). Recall that the density function for the one-dimensional normal distribution is given in (4.16). Prove that in this case, the Bayes classifier is not linear. Argue that it is in fact quadratic. Hint: For this problem, you should follow the arguments laid out in Section 4.4.1, but without making the assumption that oỉ = ... o^2k =
In the case of a one-dimensional normal distribution with K classes, the Bayes classifier is not linear but is in fact quadratic.
We begin by noting that the Bayes classifier for the one-dimensional normal distribution is given by:
[tex]h(x) = argmaxk P(Ck|x) = argmaxk P(x|Ck)P(Ck)[/tex]
We can rewrite this as:
[tex]h(x) = argmaxk (1/√2πσk) exp(-1/2σ2k(x-uk)2) P(Ck)[/tex]
We can see that this is a quadratic equation in the form: ax2 + bx + c = 0. We can illustrate this by substituting the values for a, b, and c:
[tex]a = -1/2σ2k[/tex]
b = 0
[tex]c = ln(P(Ck)) - 1/2σ2k u2k[/tex]
We can see that this equation is not linear and is instead quadratic. Therefore, we can conclude that in the case of a one-dimensional normal distribution with K classes, the Bayes classifier is not linear but is in fact quadratic.
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couple has 4 children. find each probability. 1) all boys. 2) all girls. 3) exactly 3 boys. 4) at least 1 boy. 5) at most 3 girls.
1) All boys: Probability = 1/16 , 2) All girls: Probability = 1/16, 3) Exactly 3 boys: Probability = 5/16, 4) At least 1 boy: Probability = 15/16, 5) At most 3 girls: Probability = 15/16.
1) All boys: There are 16 possible combinations of 4 children, with each gender combination having an equal probability of 1/16. Therefore, the probability of all boys is 1/16.
2) All girls: Similarly, the probability of all girls is also 1/16.
3) Exactly 3 boys: To find the probability of exactly 3 boys, we need to consider all the cases with 3 boys and 1 girl. There are 4 possible combinations of 3 boys and 1 girl, so the probability of exactly 3 boys is 4/16, or 5/16.
4) At least 1 boy: To find the probability of at least 1 boy, we need to consider all the cases with 1, 2, 3, or 4 boys. There are 15 possible combinations with at least 1 boy (1 boy, 2 boys, 3 boys, and 4 boys), so the probability of at least 1 boy is 15/16.
5) At most 3 girls: To find the probability of at most 3 girls, we need to consider all the cases with 0, 1, 2, or 3 girls. There are 15 possible combinations with at most 3 girls (0 girls, 1 girl, 2 girls, and 3 girls), so the probability of at most 3 girls is 15/16.
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Instructions: Solve the following real world problem.
You and your sister are selling cookies to help raise money for
your field trip. You start out with $24 and sells each bag of
cookies, c, for $3. Your sister doesn't start out with any money but
sells her bags of cookies for $5 each. How many bags of cookies
must they sell in order for them to raise the same amount of
money?
Equating the mathematical expressions, we can determine that the siblings need to sell 12 bags of cookies for them to raise the same amount of money.
What are mathematical expressions?Mathematical expressions are the combination of variables, constants, numbers, and values using mathematical operands like addition and subtraction.
Mathematical expressions are also described as algebraic expressions.
The initial amount that you have = $24
Your selling price per bag of cookies, c, = $3
The total amount you will make is given by Expression 1: 24 + 3c
Your sister's selling price per bag of cookies, c, = $5
The total amount your sister will generate is given by Expression 2: 5c
To determine the number of bags of cookies you must sell to raise the same amount of money between the two siblings, we equate the two expressions as follows:
24 + 3c = 5c
24 = 2c
12 = c
Check:
5c = 60 (5 x 12)
24 _ 3c = 60 (24 + 36)
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select the expression that is equivalent to (x + 6)^2
Answer:
The answer to the expression, (x + 6)^2 is [tex]x^2+12x+36[/tex].
Step-by-step explanation:
How can we solve this?We can solve this problem by breaking (x + 6)^2 into (x + 6) (x + 6). Now, we can use FOIL to figure out the expression that is equivalent to the problem.
(x + 6) (x + 6)
First, we multiply the Xs together.
[tex]x*x=x^2[/tex]
Next, is the Outer values.
[tex]x*6=6x[/tex]
Third, we multiply the Inner values.
[tex]6*x=6x[/tex]
Finally, we can multiply the Last values.
[tex]6*6=36[/tex]
Now, we can put it all together.
[tex]x^2+6x+6x+36[/tex]
We still have one more step left. Add like terms.
[tex]x^2+12x+36[/tex]
The answer is [tex]x^2+12x+36[/tex].
Use the sketch to find the range of values of x for which 2x² + 3x 2≤0
Using the sketch, the possible range of values of x for which 2x² + 3x - 2≤0 is [-2, 0.5].
What is the domain of a function?The domain of a function is a possible set of values of the independent variable. Based on the domain of a function, the codomain and range are determined.
Take the inequality as 2x²+3x-2≤0.
Solve the inequality.
2x²+3x-2≤0
(2x-1)(x+2)≤0
→ -2≤x≤0.5
The inequality is sketched in the graph and the area is also shaded for which 2x²+3x-2≤0. The range values of x mean the set of all points in the inequality -2≤x≤0.5, that is, [-2, 0.5].
Therefore, the obtained answer is [-2, 0.5].
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find invertible matrices such that is invertible. choose so that (1) neither is a diagonal matrix and (2) are not scalar multiples of each other.
To choose that a matrix is neither a diagonal matrix and are not scalar multiples of each other. The matrices will be as:
A = [ 2 1 ; 1 2 ]
B = [ -2 1 ; 1 2 ]
The matrices shown above can be used to find invertible matrices. The sum of A and B is [0 2; 2 4], which has a non-zero determinant and is therefore invertible. This choice of A and B satisfies the given conditions because they have different eigenvalues, ensuring they are not scalar multiples of each other, and are also not diagonal matrices.
The key idea behind this choice was to use matrices with the same trace and determinant, which guarantees that their sum will have the same determinant as well. This method allows us to construct examples of invertible matrices that satisfy the given conditions.
The complete question is provided in the image below.
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Please help me solve this last question
The length of the line QR is 3 units. Options A
What are the properties of a pentagon?
The properties of a pentagon is expressed as;
The number of sides is 5The number of vertices is 5The sum of the Interior angle is 540°The sum of the exterior angle is 360°The Area is ½ × perimeter x apothem (a)Perimeter is expressed as 5 × side.Pentagons are convex, cyclic, equilateral, isogonal, isotoxalFrom the image shown, we have that;
The point from Q to R are (-8, -5)
To determine the distance, we have that;
-8-(-5)
-8 + 5
Add the values
-3
Hence, the number is 3
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