The value of the required probabilities are:
(a) E[X] = 6
(b) E[X|Y=1] = 1/36
(c) E[X|Y=5] = 5/36.
To find the values of P{X=x, Y=1} and P{X=x, Y=5}, we need to understand the concept of conditional probability and the properties of geometric distributions.
First, let's recall some properties of geometric distributions:
The probability of success (rolling a specific number on a fair die) in a single trial is denoted by p, and for a fair die, p = 1/6.
The probability of failure (not rolling the specific number) in a single trial is denoted by q, and for a fair die, q = 1 - p = 5/6.
The geometric distribution is the number of trials required to achieve the first success (rolling the specific number) in a sequence of independent trials.
For the random variable X (number of rolls necessary to obtain a 6), X follows a geometric distribution with parameter p = 1/6.
Now, let's find the values of P{X=x, Y=1} and P{X=x, Y=5}.
(a) E[X]:
The expected value of X (denoted as E[X]) for a geometric distribution is given by E[X] = 1/p. For a fair die, p = 1/6, so E[X] = 1 / (1/6) = 6.
(b) E[X|Y=1]:
This represents the expected number of rolls necessary to obtain a 6 given that the first roll resulted in a 5.
To find E[X|Y=1], we need to consider the conditional probability.
The event "Y=1" represents that the first roll resulted in a 5.
The probability of rolling a 6 in the next roll (X=1) given that Y=1 is P{X=1, Y=1}.
Since the rolls are independent, P{X=1, Y=1} = P{X=1} * P{Y=1}.
The probability of rolling a 6 in a single roll (P{X=1}) is 1/6, and the probability of rolling a 5 in a single roll (P{Y=1}) is also 1/6 (since we want the first roll to be a 5).
So, P{X=1, Y=1} = (1/6) * (1/6) = 1/36.
Now, to find E[X|Y=1], we need to sum the products of the number of rolls (x) and the corresponding probabilities for all possible values of x, given that Y=1:
E[X|Y=1] = ∑(x * P{X=x, Y=1})
Since the geometric distribution is defined over all non-negative integers, we need to consider all possible values of x (0, 1, 2, 3, ...).
E[X|Y=1] = (0 * P{X=0, Y=1}) + (1 * P{X=1, Y=1}) + (2 * P{X=2, Y=1}) + ...
Now, we already know that P{X=1, Y=1} = 1/36. For all other values of x, P{X=x, Y=1} = 0 because we cannot have any rolls beyond the first roll when Y=1 (since Y=1 means the first roll was a 5).
So, E[X|Y=1] = (1 * 1/36) + (0 * 0) + (0 * 0) + ... = 1/36.
(c) E[X|Y=5]:
This represents the expected number of rolls necessary to obtain a 6 given that the first roll resulted in a 5 followed by four rolls that resulted in other numbers (not 6).
Similarly to part (b), we need to consider the conditional probability.
The event "Y=5" represents that the first five rolls resulted in numbers other than 6.
The probability of rolling a 6 in the next roll (X=1) given that Y=5 is P{X=1, Y=5}.
Again, since the rolls are independent, P{X=1, Y=5} = P{X=1} * P{Y=5}.
The probability of rolling a 6 in a single roll (P{X=1}) is 1/6, and the probability of rolling a number other than 6 in a single roll (P{Y=5}) is 5/6 (since we want the first five rolls to be numbers other than 6).
So, P{X=1, Y=5} = (1/6) * (5/6) = 5/36.
To find E[X|Y=5], we need to sum the products of the number of rolls (x) and the corresponding probabilities for all possible values of x, given that Y=5:
E[X|Y=5] = ∑(x * P{X=x, Y=5})
Similarly to part (b), for all values of x other than 1, P{X=x, Y=5} = 0 because we cannot have any rolls beyond the first roll when Y=5 (since Y=5 means the first five rolls were other numbers).
So, E[X|Y=5] = (1 * 5/36) + (0 * 0) + (0 * 0) + ... = 5/36.
Hence, The value of the required probabilities are:
(a) E[X] = 6
(b) E[X|Y=1] = 1/36
(c) E[X|Y=5] = 5/36.
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PLEASE HELP I WILL DO ANYTHING
Find the constant of proportionality for the proportional relationship shown on the graph.
graph of a line going through 0 comma 0 and one half comma 8
p = 0.5
p = 0.625
p = 16
p = 8
The proportionality constant of the given graph is k = 16.
How to find the proportionality constant of a graph?The proportionality constant of a graph is the ratio of the y-coordinates to the x-coordinates.
Thus, it is written as k = y1/x1 = x2/y2 = ... = yn/xn
Calculation:The given graph has the coordinates as
x = 0; y = 0 i.e., (0, 0)
x = 0.5; y = 8 i.e., (0.5, 8)
x = 1; y = 16 i.e., (1, 16)
x = 1.5; y = 24 i.e., (1.5, 24)
and so on.
Then, the ratio of y - coordinate to the x - coordinate is
k = 8/0.5 = 16
or
k = 16/1 = 16
or
k = 24/1.5 = 16
and so on.
So, the proportionality constant for the given graph is k = 16.
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A baker sells boxes of cookies for $5 each. She has a total of 20 boxes of cookies to sell, and each box contains 12 cookies. The bakers total sales, in dollars, is a function of the number of boxes of cookies she sells, as shown by the
graph below
The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A pastry specialist sells boxes of treats for $5 each. She has a sum of 20 boxes of treats to sell, and each crate contains 12 treats.
Let 'x' be the number of boxes of cookies and 'y' be the total cost. Then the equation is given as,
y = 5x
The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.
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If x = 2 and y = –1, what is the difference between 1 + 2x + 5y2 and 4x + 3y?
Answer:
55
Step-by-step explanation:
if you do the calculations it is 55*5=uy66
Karen makes 5 dollars per hour babysitting and 12 dollars per hour giving music lessons. One weekend, she worked a total of 18 hours and made 139 dollars. How many hours did she babysit that weekend
Answer:
15.06
Step-by-step explanation:
Substituting this value into the first equation gives us b + 2.94 = 18, so b = 15.06 hours. Since Karen can only work whole hours, she must have worked 15 hours babysitting and 3 hours giving music lessons.
At the local bunny-hop, Mr. Meyering jumps 20 inches on his first jump and then 10 inches with his second jump. If the distances form a geometric sequence, what is the total distance Mr. Meyering jumps if he completes infinitely many jumps?
Hint: Use S= a1/1- r and remember that |r| must be less than 1.
Using sum of infinite series in a geometric progression, the total number of jumps is 40 inches
What is Geometric ProgressionA geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term.
The jumps are infinite and to find the total distance, we can use the equation given;
S = a(1 / 1 - r)
a = first termr = common ratioThe first term (a) = 20 in
The common ratio = 10 / 20 = 1/2 = 0.5
Substituting the values into the equation;
S = 20(1 / 1 - 0.5)
S = 20(1 / 0.5)
S = 20 * 2
S = 40 in
The total distance is 40 inches
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select every definite integral below that can be evaluated using the fundamental theorem of calculus (there may be more than one).
The basic theorem of calculus states that the function must be differentiable throughout the specified limit interval. So all options are correct.
In the given question, we have to select every definite integral below that can be evaluated using the fundamental theorem of calculus (there may be more than one).
The given integrals are:
[tex]\int_{-\pi}^{\pi}sin^7(4x)cos^8(3x)dx[/tex][tex]\int_{-5}^{12}(x\text{In}x+2x-1)dx[/tex][tex]\int_{0}^{4}(12x^{16}-5x^{11}+81x^{8}-208432x^{2}+x-2)dx[/tex][tex]\int_{-1}^{1}\frac{1}{x}dx[/tex][tex]\int_{1}^{9}|x|dx[/tex]As we know that,
A definite integral is a formal estimate of the area beneath a function. Integrals can reflect a region's (signed) area, the total value of a function that changes over time, or the amount of a given thing given its density.
The basic theorem of calculus states that the function must be differentiable throughout the specified limit interval.
Within the specified limit interval, the integral in the supplied option is differentiable.
Therefore, each choice is valid.
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the questions in this activity refer back to prelab 0, which would be a good place to look if you need any help. in test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again calculate mean, standard deviation, and standard error.
1) Which of the following statements is the most likely description of the comparison of the standard deviations found in Test A and Test B? o The standard deviations found in Test A and Test B will be about the same. o The standard deviation found in Test A will about be twice as big as the standard deviation found in Test B. o The standard deviation found in Test A will about be four times as big as the standard deviation found in Test B. o The standard deviation found in Test B will about be twice as big as the standard deviation found in Test A. o The standard deviation found in Test B will about be four times as big as the standard deviation found in Test A. Submit 2) Which of the following statements is the most likely description of the comparison of the standard errors found in Test A and Test B? o The standard errors found in Test A and Test B will be about the same. o The standard error found in Test A will about be twice as big as the standard error found in Test B. o The standard error found in Test A will about be four times as big as the standard error found in Test B. o The standard error found in Test B will about be twice as big as the standard error found in Test A. o The standard error found in Test B will about be four times as big as the standard error found in Test A. Submit 3) This question and the next one refer to a hypothetical experiment in which you slide red and green blocks down an identical ramp to see how far they go before stopping. After doing three trials of each case you find that the best estimate of the distance slid by red blocks is 15 + 3 feet and that the best estimate of the distance slid by green blocks is 25 + 4 feet. Find the t' parameter for the comparison of the distance slid by red and green blocks. o t' = 2.0 o t' = 2.5 o t' = 3.0 o t' = 3.5 o t' = 4.0 Submit 4) Suppose the experiments described in Question 3 are testing the claim that the distance slid by a block does not depend on the color of the block. Which of the following conclusions regarding this claim is most consistent with your data? o The claim is true. o The claim is false. o The claim might be true or it might be false.
The value of the standard deviation does not change and remains the same.
Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.
The mean μ = 82.4
The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]
we have to find the variance,
We now add a constant k to each data value and calculate the new mean μ'.
μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k
We now calculate the new mean standard deviation σ'.
σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]
Note that x + k - μ' = x + k - μ - k = x - μ
also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ
Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ
If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.
Hence, the standard deviation does not change.
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Triangles EFG and QRS are similar. The length of the sides of EFG are 144, 128, and 112. The length of the smallest side of QRS is 280, what is the length of the longest side of QRS? (draw a diagram and solve)answer choices360240290340
The length of the sides of EFG are 144 cm, 128 cm and 112 cm. And length of the longest side of QRS is 360 cm.
A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is represented as ΔABC.
In Euclidean geometry, any three points, if not collinear, define a unique triangle and, at the same time, a unique plane (that is, two-dimensional Euclidean space). That is, there is only one plane containing this triangle, and all triangles are contained in one plane. If all geometries were just Euclidean planes, there would be only one plane and all triangles would be in it. But this is not the case in high dimensional Euclidean space. This article is about triangles in Euclidean geometry, specifically the Euclidean plane, unless otherwise stated.
According to the question:
Triangles EFG and QRS are similar
So EF/QR = FG/RS = EG/QS
Therefore,
The length of the sides of EFG are 144 cm, 128 cm and 112 cm.
Here, 112 is smallest side of triangle EFG
Let, the smallest side of EFG be EF so QR is also the smallest side of triangle QRS i.e. QR = 280 cm & other sides be assumed "x" & "y"
Now,
112/280 = 144/x = 128/y
⇒ 2/5 = 144/x = 128/y
Taking first two, we get
x = 360 cm
Now,
Taking first and third , we get ,
y = 320 cm
So others two sides of triangle QRS are 320 cm & 360 cm.
And length of the longest side of QRS is 360 cm.
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ind the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4x3, y = 4x, x20; about the x-axis
The Volume of the solid formed by the curves y = 4x³ , y = 4x, x ≥ 0 ; about the x axis is 64π/21 .
In the question ,
it is given that ,
the given curves are y = 4x³ , y = 4x, x ≥ 0 ,
we have to find the volume about x axis ,
the region formed by the given curves about x axis is shown below in the figure .
So , the Volume of the required region is
V = [tex]\int\limits^1_0 {\pi [(4x)^{2} - (4x^{3} )^{2} }] \, dx[/tex]
On simplification ,
we get ,
V = [tex]\pi \int\limits^1_0 { [16x^{2} - 16x^{6} }] \, dx[/tex]
V = π[ x³/3 - x⁷/7 ]¹₀
= 16π( 1/3 - 1/7 - 0 - 0)
= 16π((7 - 3)/21)
= 64π/21
Therefore , the required Volume is 64π/21 .
The given question is incomplete , the complete question is
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4x³ , y = 4x, x ≥ 0 ; about the x-axis .
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(10, y) and (3,4) ;m = 2/7
The value of the y such that the slope associated with both points is 2/7 will be 6.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The slope could be positive or negative.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
As per the given points,(10, y) and (3,4) and slope m = 2/7
2/7 = (4 - y)/(3 - 10)
4 - y = -7(2/7)
4 - y = -2
y = 4 + 2 = 6
Hence "The value of the y such that the slope associated with both points is 2/7 will be 6".
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Domain and Range of Functions with Examples, Problems, and Solutions
The function is f(x)=2x
The domain is {1,2,3}
Then the range will be {2,4,6}
Given that,
We have to find what is domain and range of the function.
We know that,
The components of a function are its domain and range. The domain of a function is the set of all possible input values, whereas the range of a function is its potential output. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A⇒ B exists that maps every element of A to an element in B. The representation of an element 'a' under a relation R is given by 'b', where (a,b) R. The range of the function is the set of photos. In general, a function's domain and range are denoted as follows: Range(f) = {f(x): x ∈domain(f)} and domain(f) = {f(x): x ∈R}
So,
The function is f(x)=2x
The domain is {1,2,3}
Then the range will be {2,4,6}
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Which of the following is equivalent to the expression below?
5x + 2(3x - 1) - 5x
Pilihan jawaban
6x - 2
6x + 2
16x - 2
16x + 2
The expression 6x - 2 is equivalent to 5x + 2(3x - 1) - 5x. Option (1) is Correct.
Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
The equality (=) sign is used to denote equivalent phrases. Since the values of both expressions are constant for all values of x, 3(x + 2) and 3x + 6 are equal expressions. 3x + 6 = 3 × 4 + 6 = 18.
Here the expression is : 5x + 2(3x - 1) - 5x ...... (1)
let x=1 put in equation 1
then we get,
=5(1)+2(3(1)-1)-5(1)
=5+6-2-5
=4
now verify with all Options: put x =1
6x - 2 = 6(1) -2
=6-2
=4 (Correct value)
Option 2:
6x + 2
=6(1)+2
=8 (wrong Option)
Option 3:
16x - 2
=16-2
=14 (wrong Option)
Option 4:
=16x + 2
=16+2
=18 (wrong Option)
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Correct Question:
Which of the following is equivalent to the expression below?
5x + 2(3x - 1) - 5x
1. 6x - 2
2. 6x + 2
3. 16x - 2
4. 16x + 2
What is Y=2000(1.25)^12
Answer:
y+29103.83045673370361328125
−7x − 2y = −13
x − 2y = 11
Put the steps in order that are used to solve the following systems of equations by substitution.
The solutions of the systems of equations are x = 3 and y = − 4.
Solving the systems of equations by substitution:The substitution technique is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions.
This method entails determining the value of the x-variable in terms of the y-variable from the first equation and then replacing the value of the x-variable in the second equation.
Here we have
−7x − 2y = −13 ----- (1)
x − 2y = 11 ----- (2)
Do (2) - (1)
=> −7x − 2y − (x − 2y) = −13 − 11
=> −7x − 2y − x + 2y = − 24
=> −8x = − 24
=> 8x = 24
=> x = 3
Now substitute x = 3 in (2)
=> 3 − 2y = 11
=> − 2y = 8
=> y = − 4
Therefore,
The solutions of the systems of equations are x = 3 and y = − 4.
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Answer:
The steps are listed below.
10. Noel is doing some back to school shopping and there are sales EVERYWHERE. a. First she finds a pair of earrings for 15% off and saves $3. What was the original cost of the earrings?
I
By using the concept of discount, it can be calculated that
a) Original cost of earrings is $20
b) Discount = $30
c) 30% discount has been given.
What is discount?
Discount is the price that is reduced from the original price of an article to sell that article at a cheaper cost during a sale.
a) Let the original cost of earrings be $x
Rate of discount = 15%
Discount given = $ [tex]\frac{15}{100}\times x[/tex] = $[tex]\frac{3x}{20}[/tex]
By the problem,
[tex]\frac{3x}{20} = 3\\x = \frac{3 \times 20}{3}\\[/tex]
x = $20
Original cost of earrings is $20
b) Cost of mom jeans = $50
Rate of discount = 60%
Discount = [tex]\frac{60}{100}\times 50 =[/tex] $30
c) Cost of Vintage rock t-shirt = $40
Let the percentage discount be x%
Discount = [tex]\frac{x}{100} \times 40[/tex]
By the problem,
[tex]\frac{x}{100}\times 40 = 12\\x = \frac{12 \times 100}{40}\\[/tex]
x = 30%
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the director of a baseball camp estimates that 100 students will enroll if the tuition is $250. for each $20 increase in tuition, eight fewer students will enroll. determine a linear function that will predict the number of students (y) who will enroll at a given tuition (x).
Answer:
Below
Step-by-step explanation:
y = 100 - ( x-250)/20 *8 for every 20 above 250 eight fewer students from the 100 who would enroll at 250 level ( this is for x >= 250...the question says nothing about enrollment change from lowering the price BELOW 250)
Suppose that 14 inches of wire costs 84 cents. At the same rate, how many inches of wire can be bought for 42 cents
HELPPPP!!! 30 POINTS!!!!
Which of the following correlation coefficients would represent the strongest correlation?
A. -0.9
B. 0.04
C. -0.16
D. .78
Answer:
D
Step-by-step explanation:
i did this before trust me
FILL IN THE BLANK. validity is the extent to which findings may be generalized, while___validity refers to the ability to infer that there is a causal relationship between variables.
Validity is the extent to which findings may be generalized, while Internal validity validity refers to the ability to infer that there is a causal relationship between variables.
"Information available from the question",
In the question:
Validity is the extent to which findings may be generalized, while___ validity refers to the ability to infer that there is a causal relationship between variables.
To fill up the blank space:
Now, According to the question:
Let's Know:
Internal and external validity are two ways of testing cause-and-effect relationships.
Internal validity refers to the degree of confidence that the causal relationship being tested is trustworthy and not influenced by other factors or variables.
External validity refers to the extent to which results from a study can be applied (generalized) to other situations, groups, or events.
Now, According to the above statement is:
Hence, Validity is the extent to which findings may be generalized, while Internal validity validity refers to the ability to infer that there is a causal relationship between variables.
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Please help! It’s really hard
suppose the cost of a car produced in the united states is $20,000. the current exchange rate is us$1= €0.85. What is the cost of the car in euros?
The cost of the car in euros is 17,000 euros
Given that,
Let's say an automobile made in the United States costs $20,000. At this time, one US dollar is worth 0.85 euros. A automobile made in the United States costs $20,000 to construct.
To find : that the car's price in euros ?
The information provided lets us know that,
The car's price in euros= 20,000 * 0.85
= 17,000 euros
Therefore, the car's price in euros is 17,000 euros.
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-9/7 greater than -11/8
To compare two fractions, we need to find a common denominator and then compare the fractions using the numerators. In this case, we can find a common denominator by finding the least common multiple (LCM) of 7 and 8. The LCM of 7 and 8 is 56.
We can then rewrite both fractions using a denominator of 56:
-9/7 = -36/28
-11/8 = -44/28
Now we can compare the fractions using their numerators:
-36/28 < -44/28
Therefore, -9/7 is less than -11/8.
Why does it have the name "denominator"?The Latin word "nomen" (which also appears in words like "nominate" and "nomenclature"), which meaning "name," is the root of the word "denominator." And that is essentially what the denominator of a fraction does: it "names" or specifies the kind of fraction that is specified by the numerator (the top part).
The denominator formula is what?The numerator of a fraction, which determines how many parts are being taken into account, is equal to the number of equal parts that make up the total. You can think of a fraction as being composed of p parts, which is the numerator of an item, and q equal parts, which is the denominator.
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I need help fast with this question.Thank you
The proportion is 135 : 5 : : A : 8 and the value of A is 216 minutes
The time required for Erica to cook her 8 pound roast is 216 minutes
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the time required by Erica to roast 8 pound be = A
Now , the equation will be
Total amount of roast = 5 pound
The time required for Erica to roast 5 pound = 135 minutes
So , the proportion will be
Time required for Erica to roast 5 pound : 5 = Time required by Erica to roast 8 pound : 8
Substituting the values in the equation , we get
135 / 5 = A / 8
Multiply by 8 on both sides of the equation , we get
The value of A = ( 135 x 8 ) / 5
The value of A = 27 x 8
The value of A = 216 minutes
Therefore , the value of A is 216 minutes
Hence , The proportion is 135 : 5 : : A : 8 and the value of A is 216 minutes
The time required for Erica to cook her 8 pound roast is 216 minutes
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Which number sentence is true?
A.
B.
C.
D.
Answer:
you forgot the sentences dude
A can of beans has surface area 366 cm?. Its height is 10 cm. What is the radius of the circular top?
The radius of circular top will be 4.125cm. It can be find out using formula for surface area of cylinder.
What is the surface area?
The surface area of a solid object is a measure of total area that the surface of the object occupy.
The surface area of a cylinder is 2*pi*r^2 + 2*pi*r*h.
where pi = 3.14 , r = radius , h = height.
In the statement we are given that surface area = 366cm^2.
And height ,h = 10cm
So, putting values in above formula we get,
366 = 2*3.14*r^2 + 2*3.14*r*10
366 = 2*3.14 (r^2 + r*10)
366/6.28 = r^2 + 10r
r^2 + 10r - 58.28 = 0
i.e. quadratic equation of form ax^2 + bx + c = 0
where a = 1, b = 10 , c = -58.28
And solution for this equation = (-b ±√b²-4ac)÷2a
by reducing this equation using above values
we get r = 4.125cm.
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Find the measures of HAB and CAB
Answer:
<HAB = 48° and <CAB = 72°
Step-by-step explanation:
Looking at the graph these two angles (<FAD = 20° and <DAH = ?) are complementary which means those two angles add up to 90°
Solve for <DAH.
<FAD = 20° + <DAH = ? = 90
Subtract <FAD = 20° to both sides leaving <DAH = ?
<DAH = 70°
Now that we have that angle we can solve for measured angles <HAB and <CAB. These three angles add up to 180°
<DAH + <HAB + <CAB = 180
Plug in our variables.
70° + 2x + 3x = 180°
Solve our x.
(2x + 3x) = 180° - 70°
5x = 120°
x = 24°
Now substitute x into the x to have our measured angle <HAB and <CAB.
<HAB = 2x = 2*24° = 48°
<HAB = 48°
<CAB = 3x = 3*24 = 72°
<CAB = 72°
Find the distance between the two points rounding to the nearest tenth (if necessary). (1,−6) and (−8,−4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.2[/tex]
Flying against the wind an airplane travels 7360 kilometers in 8 hours. Flying with the wind the same plane travels 6100 kilometers in 5 hours what is the rate of the plane in still air and what is the rate of the wind
Which derivation rule justifies the following argument? If n is a multiple of 8, then n is even. However, n is not even. Therefore, n is not a multiple of 8. O double negation O simplification De Morgan's Laws O modus ponens O modus tollens
If n is a multiple of 8, then n is even, according to commutativity. However, n is not an even number. As a result, n is not a multiple of 8.
Commutativity is a mathematical term that explains sums that can be shifted about and still produce the same solution.
'Commutative' is derived from the term 'commute,' which means to move and go around; thus, commutative equations feature integers that can be moved within the equation.
In mathematics, commutative law is one of two laws relating to number operations of addition and multiplication that are symbolically written as
a + b = b + a and ab = ba.
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When finding f(g(x)) what do you need to know about the domains and ranges
of f(x) and g(x)? Explain
All x-values that are within the scope of both f and g make up the domain of the (f g)(x).
How can the domain of f/g)(x be determined?All x-values that are within the scope of both f and g make up the domain of the (f g)(x). In this case, f has a domain of "x | x 0" and g has a domain of "all real numbers," thus (f g)(x) also has a domain of "x | x 0" since these values of x fall within both f and g's domains.Utilizing graphs is another method for determining the domain and range of functions. The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.To learn more about Domain refer to:
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