Build a binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order (10 marks)
Answers
The binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order is attached.
What is a binary search tree?A rooted binary tree data structure known as a binary search tree, also known as an ordered or sorted binary tree, is one in which each internal node's key is greater than all the keys in the corresponding node's left subtree and less than all the keys in the corresponding node's right subtree
Banana, peach, apple, pear, coconut, mango, and papaya are the given words. Banana is where we begin. This is the first word, and we will then ensign it to the tree's root.
Peach is the next word on the list. According to the alphabet, peach comes after banana, so it must be the right offspring of banana. Apple is the next word on the list. Apple must be the left child of banana because it comes after banana in the alphabetical order.
Pear is the next word on the list. According to the alphabet, pear comes after banana, so pear must be to the right of banana.
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Related Questions
$80 at q $100 at qlet q represent the quantity of output and suppose the price of the good is $125 then the marginal revenue is
Answers
For the given diagram 1. d) all of them are correct, 2. d)none of them are correct and Total Revenue is 3. b. $90,125
1.
Marginal Revenue is
the change in Total Revenue/Change in units of output produced
In the given question the price of the output is fixed at $125.
Hence no matter what the quantity of output sold, every additional output produced will generate an additional revenue of $125.
hence option d) all of them are correct has to be chosen.
2.
Now we already know that if the price has been fixed at $125, the marginal revenue generated cannot be anything but $125.
Hence, option d) None of them are correct.
3.
Total Revenue = Price X Quantity
Here it is given that the Price is $175
Output is 515 units
Hence, the Total Revenue will be $(175 X 515)
= $90125
Hence, option b. $90125 is correct.
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Complete Question
(Image Attached)
sort these items into the order that you would use them in order to calculate the confidence interval for the mean.
Answers
The order of calculate the confidence interval for the mean are as follows:
1. Select sample stat
2. select desired confidence
3. determine margin of error
4. specify upper and lower limits
Now, According to the question:
The order of calculate the confidence interval for the mean are as follows:
1. Select sample stat
2. select desired confidence
3. determine margin of error
4. specify upper and lower limits
Let's know:
What is Confidence Interval?
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.
The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.
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Need Help with this question.
Answers
Answer:
x=5
Step-by-step explanation:
If p and q are parallel, then the two angles in question should be equal to one another.
So,
(3x+15)°=(8x-10)°
(3x+15)°+10°=(8x-10)°+10°
(3x+25)°=(8x)°
(3x+25)°-(3x)°=(8x)°-(3x)°
25°=5x°
5=x
So, the two angles should be (8(5)-10)° and (3(5)+15)°. Both of these expressions equal 30°. This makes sense, as the illustration shows that the two angles are acute.
A customer spends a total of $52.25 at an amusement park. The customer buys a $30.25 ticket to enter the park and 4 game tickets.
If each game ticket costs the same amount, x, which statement is true?
Responses
An equation that can be used to find x is 4(x+30.25)=52.25, and each game ticket costs $5.50.
An equation that can be used to find x is 4 ( x + 30.25 ) = 52.25 , and each game ticket costs $ $ 5.50 .
An equation that can be used to find x is 4(x+30.25)=52.25, and each game ticket costs $18.00.
An equation that can be used to find x is 4 ( x + 30.25 ) = 52.25 , and each game ticket costs $ $ 18.00 .
An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $5.50.
An equation that can be used to find x is 4 x + 30.25 = 52.25 , and each game ticket costs $ $ 5.50 .
An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $18.00.
Answers
Answer: I believe its: An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $5.50.
Step-by-step explanation:
well, 52.25 - 30.25 is 22$
22 divided by 4 is 5.50
4 times x plus 30.25 is 52.25
so 4x+30.25= 52.25
Given f(x) = 4x2 – 4x + 1 and g(x) = 2x – 1, which of the following are expression(s) for f · g? Select all that apply.
A. 6x3 + 6x2 – 6x + 1
B. (2x – 1)3
C. 8x3 – 12x2 + 6x – 1
D. 4x2 – 2x
Answers
The value for the expression, (f * g)(x) is calculated as: C. 8x³ - 12x² - 6x - 1.
How to Evaluate the Expressions of Functions?We are given the following functions,
f(x) = 4x² – 4x + 1 and g(x) = 2x – 1.
To find the value of the expression, (f * g)(x), it means we have to multiply the functions together. See the steps explained below.
(f * g)(x) = f(x) * g(x)
Plug in the values:
(f * g)(x) = f(x) * g(x) = (4x² – 4x + 1)(2x – 1)
(f * g)(x) = 4x²(2x – 1) - 4x(2x – 1) + 1(2x – 1)
Apply the distribution property of equality:
(f * g)(x) = 8x³ – 4x² - 8x² + 4x + 2x – 1
Combine like terms:
(f * g)(x) = 8x³ - 12x² - 6x - 1
Therefore, the answer is: C. 8x³ - 12x² - 6x - 1.
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the student government claims that 70% of all students favor an increase in student fees to buy indoor potted plants for the classrooms. a random sample of 12 students produced 2 in favor of the project.
(a) What is the probability that 2 or fewer in the sample will favor the project, assuming the student government's claim is correct? (Use 3 decimal places.) (b) Do the the data support the student government's claim, or does it seem that the percentage favoring the increase in fees is less than 70%? The data do not give us any indication that the percent favoring the increase in fees differs from 70%. The data seem to indicate that the percent favoring the increase in fees is greater than 70%. The data seem to indicate that the percent favoring the increase in fees is less than 70%. The data seem to indicate that the percent favoring the increase in fees is equal to 70%.
Answers
The probability that 2 or fewer in the sample will favor the project is 4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%
According to the question,
It is given that according to the student's government
The probability that number of students in favor of increment in fees : p = 0.70
The probability that number of students against the increment : q = 0.30
Sample Size : n = 12
Number of students follows Binomial distribution
(a) We have to find the probability that 2 or fewer in the sample will favor the project
P( x ≤ 2) = P(0) + P(1) + P(2)
As we know ,
P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾
=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰
=> P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹ + 12×11/2 × (0.70)²(0.30)¹⁰
=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]
=> P( x ≤ 2) = 5.9×10⁻⁶[0.78]
=> P( x ≤ 2) = 4.368 × 10⁻⁶
Which is very close to zero
(b) The data doesn't support the student government claim.
The data seem to indicate that the percent favoring the increase in fees is less than 70%.
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The implicational rule of inference that permits us to derive a specific instance from a universal statement isa. Existential Generalization.b. Existential Instantiation.c. Universal Generalization.d. Universal Instantiation.
Answers
Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.
It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.
Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.
Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."
∀xA⇒A(x↔a}
for every formula A and every term a, where A(x↔a} is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of
∀xA.
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u (x comma y )space equals space 5 (x plus y )u (x comma y )space equals space 5 y u (x comma y )space equals space 5 x u (x comma y )space equals space 5 x squared plus 5 y squared
Answers
To solve this system of differential equations using the series method, we can assume that the solution can be expressed as a power series in both x and y:
[tex]u(x,y) = a0 + a1x + a2y + a3xy + a4x^2 + a5y^2 + ...[/tex]
Substituting this expression into each of the differential equations and collecting the coefficients of each term gives us the following system of equations:
a0 + 5a0 = 0
a1 + 5a2 = 0
a2 + 5a1 = 0
a4 + 5a4 = 0
a5 + 5*a5 = 0
Solving this system of equations gives us the following values for the coefficients:
a0 = 0
a1 = 0
a2 = 0
a3 = 0
a4 = 0
a5 = 0
Therefore, the power series expansion of the solution is:
u(x,y) = 0
This means that the only solution to the differential equations is the trivial solution u(x,y) = 0.
Note that this method of solving differential equations using power series is only applicable if the differential equations are linear and homogeneous, which means that the coefficients of the terms in the differential equations do not depend on x and y, and the right-hand sides of the equations are all equal to 0. If the differential equations are nonlinear or inhomogeneous, other methods may be required to find their solutions.
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Frank bought two pork roasts. One roast weighed five and seven-eighths pounds and the other roast weighed nine and five-sixths pounds. What is the total weight of the pork roasts?
Answers
Answer:
15[tex]\frac{17}{24}[/tex]
Step-by-step explanation:
5 [tex]\frac{7}{8}[/tex] + 9 [tex]\frac{5}{6}[/tex] We can write the fractions as equivalent fractions with a common denominator of 24
[tex]\frac{7}{8}[/tex] x[tex]\frac{3}{3}[/tex] = [tex]\frac{21}{24}[/tex]
[tex]\frac{5}{6}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{20}{24}[/tex]
5[tex]\frac{21}{24}[/tex] + 9[tex]\frac{20}{24}[/tex]
5 + 9 + [tex]\frac{21}{24}[/tex] + [tex]\frac{20}{24}[/tex]
14 + [tex]\frac{41}{24}[/tex]
14 + [tex]\frac{24}{24}[/tex] + [tex]\frac{17}{24}[/tex] I broke up [tex]\frac{41}{24}[/tex] because [tex]\frac{24}{24}[/tex] is another name for 1
14+1 + [tex]\frac{17}{24}[/tex]
15[tex]\frac{17}{24}[/tex]
1. Which equation describes the line with
slope -4 and y-intercept 2?
A y=-4x+2
B y=-4x-2
C y=4x-2
D y = 4x + 2
Answers
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.
Lisa read 2/5 of her book over the weekend and 1/3 of it on monday. What fraction of the book is left?
Answers
Answer:
4/15
Step-by-step explanation:
To answer this question, we're gonna want to convert the fractions so that they have the same denominator (the number on the bottom of the fraction) and it's easy for us to visualize what's going on. AKA, we need to find the least common denominator (LCD).
We're going to multiply 2/5 and 1/3 by a number so they have the same denominator. In this case, that would mean multiplying them by the other fractions denominator. So multiplying 2/5 by 3 and 1/3 by 5.
2/5x3= 6/15. 1/3x5=5/15.
Now we're viewing the book in 15ths instead of both 5ths and 3rds.
6+5=11, so we know that 11/15 of the book has been read.
15/15-11/15=4/15
4/15 of the book is left to read.
Hope this explanation helped!
5400 dollars is placed in an account with an annual interest rate of 9%. To the
nearest tenth of a year, how long will it take for the account value to reach 15500
dollars?
Answers
Answer:
12.2 years
Step-by-step explanation:
To solve, use the exponential growth formula:
[tex]A_t=A_0(1+r)^x[/tex]
where
[tex]A_t[/tex] = Amount as a function of time ($15500)
[tex]A_0[/tex] = Original amount ($5400)
[tex]r[/tex] = rate (.09)
[tex]x[/tex] = time in years
So,
[tex]15500=5400(1+.09)^x\\15500(\frac{1}{5400})=5400(1.09)^x(\frac{1}{5400})\\2.87=1.09^x\\\log_{1.09}2.87=\log_{1.09}1.09^x[/tex]
Use the logarithmic rules that state [tex]\log_{a}a=1[/tex] and [tex]\log_{a}a^b=b\log_{a}a[/tex]:
So,
[tex]\log_{1.09}2.87=x\\12.24\ years=x[/tex]
the manager of a store increases the price of a popular product the new price x+0.07x
Answers
Answer:
The new price of the product will be 1.07x, where x is the original price.
The manager has increased the price by 0.07x, which is 7% of the original price. This is equivalent to multiplying the original price by 1 + 0.07, or 1.07.
So, the new price of the product is 1.07 times the original price, or 1.07x.
Fully simplify.
(3x^2y^2)^3
(3x
2
y
2
)
3
Answers
Answer:
[tex]27x^6y^6[/tex]
Step-by-step explanation:
The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex]. So,
[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].
Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex]. So,
[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]
On a 3 section math test a student correctly answered 17/20 11/15 20/25 what percentage of questions on the entire test did the student answer correctly
Answers
Step-by-step explanation:
17 of 20
11 of 15
20 of 25
that is in total
17+11+20 = 48
of
20+15+25 = 60
so, he answered 48 of 60 correctly
48/60 = 4/5 = 0.8 = 80%
Answer:
79.44%
Step-by-step explanation:
We are given that there are 3 sections to this test and how the student scored in each of those sections. Let us add all of these fractions together.
[tex]\frac{17}{20} +\frac{11}{15} +\frac{20}{25} =\frac{143}{60} \\[/tex]
We must now divide this amount by 3 to find the average of the three sections. This gives us [tex]\frac{143}{180}[/tex].
These means that the student answered [tex]\frac{143}{180}[/tex] of the questions correctly, or 79.44%.
what is the width of 1 book, if the bookshelf is 3 feet 9 inches wide?
Answers
Answer:
2.5
Step-by-step explanation:
Step-by-step explanation:
Given
Shelf Width = 3ft 9in
Copies = 18
Required
Determine the width of each book
This is calculated by dividing the shelf width by the number of copies.
Width = Shelf Width ÷ Copies
Width = (3 ft 9in) ÷ (18)
[Convert with to inches]
Width = (3 * 12 + 9) ÷ (18)
Width = (36 + 9) ÷ (18)
Width = 45 ÷ 18
Width = 2.5 inches
Let a, b, and c be real numbers where a ≠ b ≠ c ≠ 0. Which of the following functions could represent the graph below?
f(x) = x²(x-a)²(x-b)4(x-c)
f(x) = x³(x-a)³(x-b)(x-c)²
f(x) = x²(x-a)(x-b)³(x-c)³
f(x) = (x-a)^2(x-b)(x-c)^6
Answers
The characteristics of polynomial graphs' intercepts reveal the multiplicity's characteristics. The function is a potential representation of the graph; f(x) = x²·(x - a) (x - a) , ²·(x - b) (x - b),⁴·(x - c) (x - c).
How to find the calculation?The alternative provides a function that can represent a graph;
f(x) = x²·(x - a) (x - a)
²·(x - b) (x - b)
⁴·(x - c) (x - c)
Reason:
The graph's description is as follows:
Three points on the graph deviate from the x-axis.
Therefore;
The first equation is satisfied by the graph's even multiplicity at three places, such as x2, (x - a)2, and (x - b)4.
The graph once almost linearly crosses the x-axis.
Therefore;
The first equation's function contains a single zero or component, such as (x - c), so;
The function is a potential representation of the graph;
f(x) = x²·(x - a) (x - a)
²·(x - b) (x - b)
⁴·(x - c) (x - c).
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The length of four rivers in Africa is shown in the table below.
How is the length of the Zambezi river written in scientific notation?
Move the correct answer to each box. Not all answers will be used.
Answers
The length of the Zambezi river is 838 × 10⁵ or 83.8 × 10⁶ or 8.38 × 10
What is scientific notation?
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
For example, 750,000,000 can be written in scientific notation as 7.5 ✕ 10⁸.
The length of the Zambezi river 83,800,000 feet.
Rewrite 83,800,000:
83,800,000 = 838 × 100000
83,800,000 = 838 × 10⁵ [Since the number of zeros is 5]
Multiply and divide 10:
83,800,000 = 838 × 10⁵ × (10/10)
83,800,000 = (838/10) × 10⁵ × 10
83,800,000 = 83.8 × 10⁵ × 10
83,800,000 = 83.8 × 10⁶
Multiply and divide 10:
83,800,000 = 83.8 × 10⁶ × (10/10)
83,800,000 = (83.8/10) × 10⁶ × 10
83,800,000 = 8.38 × 10⁷
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Which graph represents the solution set of the system of inequalities?
y < -3x-2
y ≤ x-2
Answers
The graph that represents the solution to the system of inequalities is graph (a).
What is system of inequality?
A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem requires a variety of solutions and those solutions must satisfy multiple constraints, systems of inequalities are used.
The given system of inequalities is,
y < -3x - 2
y ≤ x - 2
y < -3x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a dotted line.
y ≤ x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a closed line.
The above highlights means that the shaded region that represent the solution to the system of inequalities will be at the left-hand side
Hence, graph (a) represents the system of inequalities.
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simplify the expression: 6(1+9t)
Answers
Answer:
Hi!
The answer would be: 6 + 54t
I hope this helped you! :)
Step-by-step explanation:
Answer:
54t + 6
Step-by-step explanation:
Simplify the expression. Use the distributive property. The distributive property states that an expression which is given in form of a(b + c) can be solved into (ab) + (ac). Distribute and multiply 6 to all terms within the parenthesis. Then, simplify:
[tex]6(1 + 9t)\\\\=(6 * 1) + (6 * 9t)\\= (6) + (54t)\\ = 54t + 6[/tex]
54t + 6 is your answer.
~
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record the angular velocity w. calculate the total moment of inertia of the cylinder-person system. (hint: treat the person as a single particle.) calculate the total angular momentum of the system.
Answers
For recording the angular velocity we will use
angular velocity, ω = dθ /dt
Angular velocity:
Angular velocity is a vector quantity, expressed as the angular velocity or rotational speed of an object and the rate of change of angular displacement that specifies the axis about which the object rotates. The amount of change in a particle's angular displacement over time is called its angular velocity. The trajectory of the angular velocity vector is usually perpendicular to the plane of rotation in the direction given by the right-hand rule.
Total Moment of Inertia:
The total moment of inertia is the sum of the moments of inertia of the mass elements in the body.
Unlike mass, which is a constant for a given body, the moment of inertia depends on the location of the center of rotation. In general, the moment of inertia is calculated by using integral calculus.
Thin cylindrical shell open at both ends, radius r, mass m.
This formula assumes that the thickness of the shell is negligible. This is a special case of a thick-walled cylindrical tube with r1=r2. A point mass m at the end of a rod of length r has the same moment of inertia and the value r is called the radius of gyration.
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Evaluate the function
f(n) = 4x + 5; Find f(2)
Answers
Answer: 13
Step-by-step explanation: To find f(2), you can put 2 into all of the x spots, thus making the equation 4(2)+5. From there you can do PEMDAS and multiply 4 and 2 to get 8, and then add 5 to get 13.
Suppose that DEF is isosceles with base DE.
Suppose also that mZD=(5x+26)° and mZF = (3x+63)°.
Find the degree measure of each angle in the triangle.
k
D
(5x + 26)
-(3x + 63)°
E
mZD=
mZE=
mZF =
X
O
Answers
The degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
What is an isosceles triangle?
In an isosceles triangle, the two base angles are congruent, or equal in measure.
In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:
m∠D + m∠F + m∠E = 180 degrees
Substituting the given values for the measures of angles D and F, we get:
(5x+26) + (3x+63) + m∠E = 180
Combining like terms and solving for m∠E, we find that:
m∠E = 180 - (5x+26) - (3x+63)
= 180 - 8x - 89
= 91 - 8x
Therefore, the measure of angle E is 91 - 8x degrees.
To find the measure of angles D and F, we can substitute this value back into the equation:
m∠D + m∠F + m∠E = 180
(5x+26) + (3x+63) + (91-8x) = 180
Solving for x, we find that x = 6.
m∠D =5(6) + 26 = 30 + 25 = 56°
m∠F = 3(6) + 63 = 18 + 63 = 81°
m∠E = 91 - 8(6) = 91 - 48= 43°
Therefore, the degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
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The degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
What is an isosceles triangle?
In an isosceles triangle, the two base angles are congruent, or equal in measure.
In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:
m∠D + m∠F + m∠E = 180 degrees
Substituting the given values for the measures of angles D and F, we get:
(5x+26) + (3x+63) + m∠E = 180
Combining like terms and solving for m∠E, we find that:
m∠E = 180 - (5x+26) - (3x+63)
= 180 - 8x - 89
= 91 - 8x
Therefore, the measure of angle E is 91 - 8x degrees.
To find the measure of angles D and F, we can substitute this value back into the equation:
m∠D + m∠F + m∠E = 180
(5x+26) + (3x+63) + (91-8x) = 180
Solving for x, we find that x = 6.
m∠D =5(6) + 26 = 30 + 25 = 56°
m∠F = 3(6) + 63 = 18 + 63 = 81°
m∠E = 91 - 8(6) = 91 - 48= 43°
Therefore, the degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
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AXY is similar to ABC
Which of the following expressions could be used to determine the length of segment AB?
Answers
The expression that could be used to determine the length of segment AB in the triangles given is: A. AB = AX * AC/AY.
What are Similar Triangles?When two triangles are stated to be similar to one another, it means both triangles have equal corresponding angles, but their corresponding sides have proportional lengths or have ratios that are equal.
This means similar triangles have the same shape but different sizes, since their corresponding side lengths have proportional length.
Given that triangle AXY is similar to triangle ABC, it means that:
m<A = m<A
m<X = m<B
m<Y = m<C
AX/AB = AY/AC = XY/BC
To find the length of AB, we could use the following expression derived from the ratios stated above:
AX/AB = AY/AC
Cross multiply:
(AB) * (AY) = (AX) * (AC)
Divide both sides by AY
(AB) * (AY) / AY = (AX) * (AC) / AY
AB = AX * AC/AY
The expression to use is: A. AB = AX * AC/AY
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Find the value of csc for the angle 0 in standard position having 5,-12) on its terminal side
Answers
The cosecant of the angle is 0.2
How to determine the cosecant of the angle?From the question, we have the following parameters that can be used in our computation:
(5,-12)
This means that
(x, y) = (5,-12)
The csc(θ) is calculated as
csc(θ) = 1/x
Substitute the known values in the above equation, so, we have the following representation
csc(θ) = 1/5
Evaluate
csc(θ) = 0.2
Hence, the value of csc(θ) is 0.2
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The Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course. In analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours. Consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed: i. At the 5% level, BAOI can infer that the average time to complete exceeds 60 hours. ii. At the 1% level, BAOI can infer that the average time to complete exceeds 60 hours. What is true about i. and it: O Only (l) is true O There is insufficient information to determine which of the other answers shown here is correct. O Neither (1) nor (ii) is true O Both (1) and (ii) are true O Only ) is true
Answers
As per the given standard deviation, only (i) is true.
The term standard deviation refers the measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Here have given that the Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course.
Here by analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours.
So, let us consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed:
i. For the 5% level, BAOI can infer that the average time to complete exceeds 60 hours.
ii. For the 1% level, BAOI can infer that the average time to complete exceeds 60 hours.
Here we are trying to determine if they should spend at least 480 minutes a day studying.
Now, our knoll is that the mean is 480 and then we are looking for evidence that they are studying less than 480.
Here we don't know the population standard deviation so we're going to use a distribution.
In the given, critical values are going to be a distribution with degrees of freedom.
So, if we look at a chart 11 of freedom, we can see our critical value. I'm going to center to zero if I draw our T.
Therefore, the tail probability of.05 and the rest of it is.95%.
Based on these value we have conform that option (1) is correct.
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7. Evaluate the expression below if a = 64,
b = 9, and c = 5
A. 19
B. 19/2
C. 49/4
D.49/2
Answers
The given expression can be simplified to get the value as 19. The correct option is (A).
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is as below,
[tex](12b - 2^{c}) /\sqrt[3]{a}[/tex]
Substitute a = 64, b = 9 and c = 5 to obtain the value as below,
⇒ (12 × 9 - 2⁵)/∛64
⇒ (108 - 32)/4
⇒ 76/4
⇒ 19
Hence, the value of the given expression is obtained as 19.
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The image of the complete problem is attached here.
A box contains 2 red marbles and 3 black marbles. Two marbles are drawn in succession without replacement. Find the following: a. Find the probability the second marble is red? b. Find the probability that both marbles are the same color? c. Find the probability that the second marble is black given the first marble is red? d. Find the probability that first marble red given that the second marble is red?
Answers
a. The probability that the second marble is red is 2/5, since there are 2 red marbles and a total of 5 marbles.
b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.
c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.
d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.
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Caleb's school is five blocks due north of his home, and is the closest to the straight-line distance from Caleb's s
A) 389 f t
B) 825 f t
C) 1,260 ft
(D) 1,481 ft
Answers
If Caleb's school is five blocks due north of his home, the figure that is closest to the straight-line distance from Caleb's s is (D) 1,481 ft.
What is distance?Distance can be defined as how far an object is from another object.
Using Pythagoreans theorem
Hypotenuse =√Perpendicular² + Base²
Where:
Perpendicular = 275 feet ×5 = 1375ft
Base = 275 feet × 2 = 550ft
Let plug in the formula
Hypotenuse =√ 1375 ft² + 550ft
Hypotenuse =√1,890,625 + 302,500
Hypotenuse =√2,193,128
Hypotenuse = 1,480.9ft
Hypotenuse = 1,481ft (Approximately)
Therefore the correct option is D.
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John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours john’s brother works, and c, the total cost of the project ?
Answers
According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.
What are time and work?A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.
What is work time problem in math?The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.
Briefing:Given that John paid $485 to build a deck.
And he will pay $25 per hour to his brother for building the deck.
one hour of work costs John $25 + $485 .
Total cost of building deck = $25 × h number of hours + $485
3 hour of work costs $25 × 3 = $75 + $485 = $560
8 hour of work costs = $25 × 8 = $200 + $485 = $685
12 hour of work costs = $25 × 12 = $300 + $485 = $785
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The complete question is-
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?
h c
0 485
3 510
8 535
12 560
h c
0 510
3 535
8 560
12 585
h c
0 485
3 560
8 685
12 785
h c
0 510
3 585
8 710
12 810
