a) The vectors a and b are collinear when compa b=compb a. This means that they have the same direction, so that they're pointing in the same direction or opposite directions. In other words, if the angle between them is 0° or 180°, then they are collinear.
b) The vectors a and b are orthogonal when proja b=proj b a. This means that they are perpendicular to each other, so that the angle between them is 90°. Furthermore, it means that the projection of one vector onto the other is equal to zero.
This is because the projection of a vector onto itself is equal to the magnitude of the vector, while the projection of a vector onto a vector orthogonal to it is equal to zero.
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Question 4 of 17:
Select the best answer for the question
4. Demand for winter holiday decorations is at an all-time high in late December. What may you consider after the holidays to make room for new spring
merchandise?
A. maintain an accurate count of all inventories
O B. all answers are correct
C. sell the holiday decorations at a discounted price
D. store decorations in the warehouse until next winter
Mark for review (Will be highlighted on the review page)
OO
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PAR
Answer:
Step-by-step explanation:
we will maintain an accurate count of all inventories.
so A is correct.
describe whether your percent yield for the product was high or low. if it was either high or low, explain what might have caused the high/low percent yield.
A product-focused process is commonly used to produce: high-volume, low-variety products.
There are other types of processes. This process is completely developed around the product, it is considered a continuous process with high volume of products that have low variety. It presents a high facility utilization (this is considered an advantage), organized by product, which receives a high-fixed price, but the variable cost is low.
Product focused prodction is one that focuses on improving the product by arranging sets of people into production lines to increase efficiency of production.
Equipment and people are grouped based on products being produced. For example in a manufacturing plant assembly lines are formed that focuses on one product.
This tends to be used for products that have low differentiation and are to be produced on high volume.
Example automobile plants, clothing factories, and food factories.
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A spinner with 7 equal sections
labeled A-G is spun 84 times. How
many times would you expect it to
land on a vowel?
Answer:
24 vowels
Step-by-step explanation:
A B C D E F G
two out of 7 are vowels....you would expect to get 2/7 ths of 84 spins to be vowels
2/7 * 84 = 24 vowels
Geometry Dilation
Please help!!!!
Answer:
C' (-2, -2)
D' (-2, 2)
E' (2, 0)
F' (0, -2)
Step-by-step explanation:
A dilation of factor k about the origin is a transformation that enlarges a figure by a factor of k, while keeping the origin fixed.
It means that each point (x, y) on the pre-image is transformed to a new point (kx, ky) in the dilated figure.
Therefore, the rule for a dilation of 2 about the origin is:
(x, y) → (2x, 2y)From inspection of the given diagram, the vertices of the pre-image are:
C = (-1, -1)D = (-1, 1)E = (1, 0)F = (0, -1)Applying the dilation rule (x, y) → (2x, 2y):
C' = (2 · -1, 2 · -1) = (-2, -2)D' = (2 · -1, 2 · 1) = (-2, 2)E' = (2 · 1, 2 · 0) = (2, 0)F' = (2 · 0, 2 · -1) = (0, -2)[BRAINLIEST] The first two terms of a geometric sequence are 27 and 9. What is the fourth term?
The required Fourth term of the given geometric sequence is 1.
What is geometric sequence?Similar to how the word arithmetic series denotes that each phrase is the arithmetic mean of its two neighbors, the name geometric series denotes that each term is the geometric mean of its two neighbours.
A geometric sequence always multiplies (or divides) by the same number to move from one term to the next. Therefore, 1, 2, 4, 8, 16,... is geometric since each step is a multiple of two; 81, 27, 9, 3, 1, 31... is geometric since each step is a multiple of three.
According to question:Sequesnce; 27 , 9
Common ratio(r) = 9/27 = 1/3
Then, we know that
[tex]a_{n}=ar^{n-1}[/tex]
So,
a₄ = 27(1/3)³
a₄ = 27/27 = 1
a₄ = 1
Thus, fourth term of the sequence is 1.
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Answer:
1
Step-by-step explanation:
1 is the correct one i got it right on test
Matt sells used books on the internet. The cost of using the website is $7.50 per week and he earns 1.50 on each book he sells Matt uses the linear model y=1.5x to figure his weekly earnings what is the rate of Change of this situation
Answer:
$1.5 per book
Step-by-step explanation:
Since y=1.5x, the rate of change is 1.5/1. Rate of change: y/x. Hence, the rate of change is 1.5/1 since y=1.5 and x=1.
1.5 / 1 = 1.5
Hence, the rate of change is 1.5.
But what's 1.5 represent?
1.5 is the number of dollars earned per book sold.
Hence, the rate of change is $1.5 per book.
how many square feet of wallpaper will be used to cover a wall measuring 9 feet by 18 1/4 feet?
The area covered by the wallpaper will be 164.25 square feet.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
Given, A wallpaper measures 9 feet by 18 1/4 feet.
Therefore, The area of the wallpaper will be,
= (9×73/4) square feet.
= 164.25 square feet.
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The number e is named after
?
f(x)=x^4-4x^3 5 estimate local extrema of each function and estimate the intervals on which the function is increasing and decreasing
The local extrema is at point (3, -22).
The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).
Now, According to the question:
The function is :
[tex]f(x)=x^4-4x^3 +5[/tex]
Graphing Functions:
In order to graph a function, we first need to know the characteristics of that given function. On the other hand, we also need to simplify first the given function or rewrite it in general form for easier graphing.
Now, Graphing the function, we have
From the graph, the local extrema is at point (3, -22).
The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).
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Is it
1.A
2.B
3.C
4.D
Answer:
26 R 1
Step-by-step explanation:
how to show that the real exponetial sequence for f[k]=f[kt] is f[k]b^k
The real exponential sequence for f[k]=f[kt] is f[k]=b^k.
What is exponential sequence ?
The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers.
The real exponential sequence for f[k]=f[kt] can be shown to be f[k]=b^k by using the definition of exponential functions. If f[k]=f[kt], then f[k]=f[k-1]t and f[k-1]=f[k-2]t, and so on. By substitution, we have:
f[k]=f[k-1]t
f[k-1]=f[k-2]t
f[2]=f[1]t
f[1]=f[0]t
So we can write:
f[k]=f[k-1]t=f[k-2]t^2=...=f[1]t^(k-1)=f[0]t^k
Next, we can define b as f[0] and substitute it into the above equation:
f[k]=b^k
Therefore, the real exponential sequence for f[k]=f[kt] is f[k]=b^k.
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Choose all the expressions that equal 36.
Responses
A (14⋅32)2−28open paren 1 fourth times 32 close paren squared minus 28
B 23 + (58−54)2 + 122 3 + ( 58 - 54 ) 2 + 12
C 92 − (43 + 32) + 3005092 − ( 4 3 + 3 2 ) + 300 50
D 124 + (82 − 42) − 99124 + ( 8 2 − 4 2 ) − 99
E 53 − (2. 5 × 30) − 20
The expressions that equal 36 is:
E) 53 − (2. 5 × 30) − 20
Calculation of Algebra ExpressionEvaluated the mathematical expressions in each response to see if they equal 36.
A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.
B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.
C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.
D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.
Thus, only the expressions listed in my previous answer equal 36.
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In 2009 the average weekly wage of men exceeded that of a woman by $162. The um of their average wage equaled $1476. Write and olve a ytem of equation to determine the average wage of men and of women in 2009
The average wage of men is $819 and of women is $657 in 2009
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Information about the problem:
M = W + 162M + W = 1476M = average wage of menW = average wage of womanTo solve this problem we must establish the equations according to the given data and solve the operations:
M = W + 162 (1)
M + W = 1476 (2)
We have two equations with two unknowns, substituting the value (M) in the second equation, we have:
M + W = 1476
W + 162 + W = 1476
162 + 2W = 1476
2W = 1476 - 162
2W = 1314
W = 1314/2
W = 657
Substituting (W) into one of the equations (M) we have:
M = W + 162
M = 657 + 162
M = 819
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suppose winston's loud music externalizes a cost onto his neighbor, chloe. suppose winston and chloe decide to solve this problem using the coase theorem. if they are successful, what is a possible result of the execution of this theorem?
The Coase theorem states that if property rights are well-defined and transaction costs are low, then the allocation of resources will be efficient, regardless of the initial allocation of property rights.
If Winston and Chloe successfully apply the Coase theorem to solve the problem of Winston's loud music externalizing a cost onto Chloe, they may reach a mutually beneficial agreement. This could result in either Winston reducing the volume of his music or compensating Chloe for the cost of the externalization, or a combination of both.
The goal is to reach a solution where the costs and benefits are more efficiently allocated between the two parties.
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(x + 1) is a factor of x145 + 3x45 – 4.
True or False
(x + 1) is not a factor of the polynomial,
x¹⁴⁵ + 3x⁴⁵ - 4.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
We have a polynomial,
x¹⁴⁵ + 3x⁴⁵ - 4.
If (x + 1) is a factor.
Then x = -1 is a zero of polynomial.
Now,
(-1)¹⁴⁵ + 3(-1)⁴⁵ - 4
= -8
Therefore, (x + 1) is not a factor.
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show that 2 mn = 1 m (m n 2 ) 1 n (m n 2 ) and use this identity to obtain the unit fraction decompositions of 2 7, 2 35, and 2 91 as given in the 2/n table in the rhind mathematical papyrus.
The fractions found in the 2/n table in the Rhind Mathematical Papyrus.
2/7 = (m n 2 ) 1 n (m n 2 )
= (2 7 2 ) 1 7 (2 7 2 )
= (14 2 ) 1 7 (14 2 )
= 7 1 7 + 7 1 14
2/35 = (m n 2 ) 1 n (m n 2 )
= (2 35 2 ) 1 35 (2 35 2 )
= (70 2 ) 1 35 (70 2 )
= 35 1 35 + 35 1 70
2/91 = (m n 2 ) 1 n (m n 2 )
= (2 91 2 ) 1 91 (2 91 2 )
= (182 2 ) 1 91 (182 2 )
= 91 1 91 + 91 1 182
Using the identity (m n 2 ) 1 n (m n 2 ) we can decompose the fractions 2/7, 2/35, and 2/91 into unit fractions. For 2/7, we obtain the decomposition 7 1 7 + 7 1 14, for 2/35 the decomposition 35 1 35 + 35 1 70, and for 2/91 the decomposition 91 1 91 + 91 1 182. This matches the fractions found in the 2/n table in the Rhind Mathematical Papyrus.
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Write the equation of the line that passes through the points (−1,−7) and (1,7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
HELP ME PLEASE I DONT UNDERSTAND!!!!!
what percentage smoke something (cigars, cigarettes or both)? b. what percentage smoke neither cigars nor cigarettes? c. what percentage smoke cigars but not cigarettes? d. what is the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars?
Percentage is a concept used to express a fraction as a part of 100. It is typically expressed as a fraction with a denominator of 100 and is written as a number followed by the percent sign (%). For example, the fraction 3/20 can be expressed as 15%, which means 15 out of every 100. Percentage is a useful concept when comparing two or more values, as it provides a way to measure the relative size of each value. For example, if one group of people has 25% of the total number of votes, this means that they have more votes than the other groups, whose percentages are lower.
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Complete question:
A total of 28% of Americans smoke cigarettes, 7% smoke cigars and 5% smoke both cigarettes and cigars
a. What percentage smoke something (cigars, cigarettes or both)?b. What percentage smoke neither cigars nor cigarettes?c. What percentage smoke cigars but not cigarettes?d. What is the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars?list five vectors in span{1, 2 }. for each vector, show the weights on 1 and 2 used to generate the vector. do not make a sketch. V1 = ( 3 1 2 ) , V2 = ( −4 0 1 )
The five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)
We are given that two vectors
v1 = ( 3 1 2 ) and v2 = ( −4 0 1 )
We have to list five vectors in the span {v1, v2}
Let us choose five sets of weights as:
w = {0, 0}, {1, 0}, {0, 1}, {1, 1}, {1, -1}
So, the five vectors are:
V1 = 0 (v1) + 0 (v2) = (0 0 0)
V2 = 1 (v1) + 0 (v2) = (3 1 2)
V3 = 0 (v1) + 1 (v2) = (-4 0 1)
V4 = 1 (v1) + 1 (v2) = (3-4 1+0 2+1) = (-1 1 3)
V5 = 1 (v1) - 1 (v2) = (3+4 1-0 2-1) = (7 1 1)
Hence, the five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)
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(Lesson 2.9: Jointly Distributed RVs.) YES or NO? Suppose X and Y have joint p.d.f. f(x, y) = cxy/(1+x² + y² ) for 0 < x < 1, 0 < y < 1, and whatever constant c makes the nasty mess integrate to 1. Are X and Y independent? a. Yes b. No
Suppose X and Y have joint p.d.f. f(x, y) = cxy/(1+x² + y² ) for 0 < x < 1, 0 < y < 1, and whatever constant c makes the nasty mess integrate to 1 is No as well as x and y are not independent
What is variables?
Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle kind.
The joint p.d.f of X and Y is f(x, y)
f(x,y) = cxy/ 1+[tex]x^{2}[/tex]+[tex]y^{2}[/tex] for 0 < x < 1 and 0 < y < 1
marginal p.d.f of x = f(x):
f(x) = {1y_of(x,y)dy
= {1y=0 /cxy/ 1+x+[tex]y^{2}[/tex] dy
Cx/2 ( {1y=0 /2y/1+ [tex]x^{2}[/tex] + [tex]y^{2}[/tex] dy)
Take substitute 1+[tex]x^{2}[/tex]+ [tex]y^{2}[/tex] = t⇒2y dy=dt
Lower limit: y = 0⇒t=1+[tex]x^{2}[/tex]
Upper limit: y=1➡t=1+[tex]x^{2}[/tex]+1
F(x) = cx/2
f 1y= 0 2y
=0 1+2+[tex]y^{2}[/tex]dy)
=Cx/2({1+[tex]x^{2}[/tex]+1dt/t
=1+[tex]x^{2}[/tex]t)
=cx/2(In(t) - ln(1+[tex]x^{2}[/tex])/1[tex]x^{2}[/tex])
=cx/2 (In (1+[tex]x^{2}[/tex]+1))-In(1+[tex]x^{2}[/tex]))
=cx/2 (In (1+[tex]x^{2}[/tex]+1/1+[tex]x^{2}[/tex]))
=Cx (In(1+1/1+[tex]x^{2}[/tex]))
marginal p.d.f of y = f(y):
f(y) = {1x
=0(x,y)dx
= F1x
=0/cxy/ 1+[tex]x^{1}[/tex][tex]y^{2}[/tex]=dx
= cy/2({1x)
=0/2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]dx}
Take substitute 1 + [tex]y^{2}[/tex] + [tex]x^{2}[/tex] = t 2x dx = dt
Lower limit: x = 0
t = 1 + [tex]y^{2}[/tex]
Upper limit: x =1
=t + [tex]y^{2}[/tex] + 1
F(y)=cy/2({1x=0 2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]/dx)
=cy({1+[tex]y^{2}[/tex]+1dt/t
=1[tex]y^{2}[/tex]t/)
=Cy/2((In(t))1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex])
=cy(In(1+[tex]y^{2}[/tex]+1) – In( 1+[tex]y^{2}[/tex]))
=cy(In(1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex]))
=cy/2(In(1+1/1+y2))
Now we have to check for independence.
F(x,y)= cxy/1+[tex]x^{2}[/tex]+[tex]x^{2}[/tex] for0<x<1 and 0<y<1
F(x) = cx/2( In(1+1/1+[tex]x^{2}[/tex])) for 0<x<1
F(y)=cy/2(In(1+1/1+[tex]y^{2}[/tex])) for < y <1
=f(x)*f(y)
=c2xy/4 ( In ( 1+1/1+[tex]x^{2}[/tex] ) *In( 1+1/1+[tex]y^{2}[/tex])) #f(x,y)
F(x,y) #f(x)* f(y) for all x and y
=x and y are not independent.
no is correct answer.
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formulas used to calculate the free cash flow to firm (fcff)?
(OCF): OCF = Net Income + Depreciation & Amortization - Changes in Working Capital, (CapEx): CapEx = Investment in Property, Plant & Equipment + Investment in Intangible Assets. therefore, (FCFF): FCFF = OCF - CapEx
The Free Cash Flow to Firm (FCFF) is a measure of a company’s cash flow available for distribution to shareholders and debt holders. To calculate FCFF, the following three steps are taken:
1. Calculate Operating Cash Flow (OCF): OCF is calculated by taking net income, adding back depreciation and amortization, and subtracting any changes in working capital.
2. Calculate Capital Expenditures (CapEx): CapEx includes investments in property, plant, and equipment, as well as any investments in intangible assets.
3. Calculate Free Cash Flow to Firm (FCFF): FCFF is calculated by subtracting CapEx from OCF. This figure represents the cash flow available for distribution to shareholders and debt holders.
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The formula V = 1/3 πr²h gives the volume V of a cone with height h and base radius r.
Solve the formula for h.
Then find h when r = 2 inches and V = 45 cubic inches.
height = 10.74 inches
for steps refer attachment
The volume of a cone = (1/3) πr2h cubic units
Therefore, the volume of a cone = 20.93 cubic units
What is cone and formula?A cone has only one face, which is the circular base but no edges. A cone has only one apex or vertex point. The volume of the cone is ⅓ πr2h. The total surface area of the cone is πr(l + r) The slant height of the cone is √(r2+h2)Basically, the volume is equal to the product of the area and height of the shape. Volume = Base Area x Height. For shapes having flat surfaces such as cubes and cuboids, it is easy to find the volumeTo calculate the volume of a box, you need to know its height, width, and depth. You can find the volume by multiplying these three dimensions togetherTo learn more about cone refers to:
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Which could be the scale factor of the following similar figures? (1 point)
The first triangle's sides are 9,9,12
The second triangles sides are 6,6,8
A.) 2/3
B.) 3/4
C.) 1
D.) 3/2
E.) 4/3
Answer:3/2
Step-by-step explanation: just did the test
As all sides have grown by 2/3 times, The scale factor is 2/3. Thus, option A is correct.
What is scale factor?In its simplest form, a scale factor is the proportion between the model measurement and the actual measurement. The scale factor, as opposed to a scale ratio, does not contrast various measurement units. A model car that is scaled at one-twentieth of its real-world counterpart is said to be that size. The car is also 20 times bigger than the model, according to this statement.
16 feet is the length of a fence. The fence is depicted as being 4 inches tall on a map. Write a ratio comparing the two quantities before attempting to calculate the scale factor of the drawing to the actual fence.
Given triangle side are 6, 6, 8 and scaled triangle is 9,9,12
The corresponding sides are
6/9, 6/9, 8/12
When you simply, we get
2/3, 2/3, 2/3
As all sides have grown by 2/3 times, The scale factor is 2/3. Thus, option A is correct.
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Identify the values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20.
(5,y1) and (x2,2)
The correct values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20 are,
⇒ y₁ = - 1
⇒ x₂ = 10
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.
We have to given that;
The equation is,
⇒ 3x - 5y = 20
Now, If (5, y₁) is the solution of above equation, then it satisfy the equation.
⇒ 3x - 5y = 20
⇒ 3 × 5 - 5y₁ = 20
⇒ 15 - 5y₁ = 20
⇒ 15 - 20 = 5y₁
⇒ - 5 = 5y₁
⇒ y₁ = - 1
And, If (x₂, 2) is the solution of above equation, then it satisfy the equation.
⇒ 3x₂ - 5y = 20
⇒ 3x₂ - 5×2 = 20
⇒ 3x₂ - 10 = 20
⇒ 3x₂ = 20 + 10
⇒ 3x₂ = 30
⇒ x₂ = 10
Thus, The correct values that create ordered pairs that are solutions to the solutions to the equation are,
⇒ y₁ = - 1
⇒ x₂ = 10
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Work out
(√6 +√12)²
Give your answer in the form
c+d√2
where c and d are integers.
Answer:
[tex]18 + \sqrt[12]{2} [/tex]
= 34.97056
Justin Wallace started a business to offer development of online stores for small businesses. Record the following transactions in the journal of the business. Include an explanation with each journal entry
September 1 Wallace invested $32,000 cash in a business bank account to start his business. The business received the cash and gave Wallace owner's equity in the business
September 2 Purchased computer equipment on account, $9,800.
September 2
Paid cash for September's office rent of $3,900.
September 3 Recorded $6,400 revenue for services rendered to clients on account
Begin with the investment that Justin Wallace deposited in a business bank account.
September 1: Wallace invested $32,000 cash in a business bank account to start his business. The business received the cash and gave Wallace owner's equity in the business. Record the entry. (Record debits
first, then credits. Select the explanation on the last line of the journal entry table. Leave unused cells blank.)
Debit
Date
September 1:
Accounts :
Debit:
Credit:
On September 1 the debit and cash is as follows
Debit: Cash $32,000
Credit: Owner's Equity $32,000
How can we explain each statement?On September 1, Justin Wallace invested $32,000 cash into the business to start the business. This transaction increases the business's Cash account and increases the Owner's Equity account, which represents the owner's investment in the business.
September 2:
Debit: Accounts Payable $9,800
Credit: Cash $9,800
On September 2, the business purchased computer equipment on account for $9,800. This transaction increases the Accounts Payable account, which represents the business's obligation to pay the supplier, and decreases the Cash account.
September 2:
Debit: Cash $3,900
Credit: Rent Expense $3,900
On September 2, the business paid cash for September's office rent of $3,900. This transaction decreases the Cash account and increases the Rent Expense account, which represents the cost of renting office space.
September 3:
Debit: Service Revenue $6,400
Credit: Accounts Receivable $6,400
On September 3, the business recorded $6,400 revenue for services rendered to clients on account. This transaction increases the Service Revenue account, which represents the business's revenue from providing services, and increases the Accounts Receivable account, which represents the business's right to receive payment from clients for services rendered.
What is mensuration?Mensuration is the branch of mathematics that deals with the measurement of geometric shapes and figures, such as length, area, and volume. It typically includes the study of geometric shapes, such as circles, triangles, and polygons, and their properties, such as perimeter, area, and volume. Mensuration is used in many fields, including engineering, physics, and computer graphics.
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an octahedron consists of two square-based pyramids glued together along their square bases to form a polyhedron with eight faces. imagine an ant that begins at the top vertex and walks to one of the four adjacent vertices that he randomly selects and calls vertex a. from vertex a, he will then walk to one of the four adjacent vertices that he randomly selects and calls vertex b. what is the probability that vertex b will be the bottom vertex? express your answer as a common fraction.
The probability that vertex b will be the bottom vertex will be 1/16
The ant has four equally likely possibilities for his initial step from the top vertex, each heading to one of the four vertices close to the top vertex.
When the ant reaches vertex A, he has four equally likely next steps, each heading to one of the vertices next to vertex A.
Only one of these possibilities, however, will send him to the bottom vertex: the one that brings him straight to the bottom vertex.
As a result, the ant's chance of reaching the bottom vertex after two steps is 1/4 * 1/4 = 1/16.
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In the triangle below,
x= [? ]°. Round to the nearest
tenth.
9 cm
90⁰
17 cm
19
After solving the equation the triangle given in question the 63.8°.
What is triangle?A triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry and is very versatile as it can be used to create many other shapes and structures. Triangles are generally classified by the length of their sides, which can be equal (an equilateral triangle), longer in one side than the other two sides (an isosceles triangle) or different in length on all three sides (a scalene triangle). They can also be classified by their angles, which can be acute (the angles are all less than 90 degrees), right (one angle is exactly 90 degrees) or obtuse (one angle is greater than 90 degrees).
x = 63.8°
Using the Law of Cosines, we can calculate the value of x:
x² = 17² + 9² - 2(17)(9)cos(90°)
x² = 289 + 81 - 306
x² = 64
x = √64
x = 8
Therefore, x = 63.8° (rounded to the nearest tenth).
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Suppose that 15 inches of wire costs 75 cents.
At the same rate, how much (in cents) will 9 inches of wire cost?
Answer: 45 cents.
Step-by-step explanation: We can find the cost per inch of wire by dividing the total cost by the total length of wire:
75 cents / 15 inches = 5 cents/inch
Now that we know the cost per inch, we can find the cost of 9 inches of wire by multiplying the cost per inch by 9:
5 cents/inch * 9 inches = 45 cents.
Answer:45 cents for 9 inches of wire
Step-by-step explanation:
Per every 5 incheses is 0.25 cents 0.75/15=$0.25 and then taking 0.25/5=$0.05 cents. So 1 inch costs 0.05 cents. So multiply 0.05×9=$0.45 cents. 45 cents
