Answers
Here
A=B=1 and C=-1Q(2,6) is the pointDistance
\(\\ \rm\Rrightarrow \dfrac{|Ax+By+C|}{\sqrt{A^2+B^2}}\)
\(\\ \rm\Rrightarrow \dfrac{|1(2)+1(6)-4|}{\sqrt{1+1}}\)
\(\\ \rm\Rrightarrow \dfrac{8-4}{\sqrt{2}}\)
\(\\ \rm\Rrightarrow \dfrac{4}{\sqrt{2}}\)
\(\\ \rm\Rrightarrow 2\sqrt{2}units\)
Related Questions
-2(3x - 4) + 7
divided by 3
Answers
Answer:
-6x+31/3
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all fractions 2x+6y=−24
Answers
Answer:
The slope is -1/3 and the y-interept is -4 or (0, -4)
Step-by-step explanation:
Solving for y will put this equation into slope-intercept form.
Dividing both sides by 6, we get: (1/3)x + y = -4
Now solve this result for y Subtract (1/3)x from both sides:
y = -(1/3)x - 4 This is the equation in slope-intercept form. The slope is -1/3 and the y-interept is -4 or (0, -4)
When Louis Brandeis graduated from Harvard Law School, he immediately established a
reputation in Boston as an attorney who would accept cases
Later appointed
Answers
Solve the equation on the
interval [0, 2π).
√2 cos x - 1 = 0
Answers
Answer:
Step-by-step explanation:
\(\sqrt{2} cos x-1=0\\cos x=\frac{1}{\sqrt{2} } =cos (\frac{\pi }{4} ),cos (2\pi -\frac{\pi }{4} )\\cos x=cos(2n\pi +\frac{\pi }{4} ),cos(2n\pi +\frac{7\pi }{4} )\\x=2n\pi +\frac{\pi }{4} ,2n\pi +\frac{7\pi }{4} \\n=0\\x=\frac{\pi }{4} ,\frac{7\pi }{4}\)
The perimeter of a rectangular field is 274 yards. If the length of the field is 82 yards, what is its width?
Answers
The width of the rectangular field is 55 yards.
Let's assume that the width of the rectangular field is "w" yards.
We know that the perimeter of a rectangle is given by the formula:
P = 2(l + w)
where "l" is the length and "w" is the width of the rectangle.
Substituting the given values, we get:
274 = 2(82 + w)
Simplifying the above equation, we get:
137 = 82 + w
Subtracting 82 from both sides, we get:
w = 137 - 82 = 55
Therefore, the width of the rectangular field is 55 yards.
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Baker Jack baked 160 cakes. 55% of them were walnut cakes and the rest were almond cakes. After selling some of the walnut cakes, the percentage of the walnut cakes become 40%.
Answers
After selling some of the walnut cakes, the number of walnut cake remaining is 48. The number of walnut cake sold is 40.
How to find the number of walnut cakes?Baker Jack baked 160 cakes. 55 percent of them were walnut cakes and the rest were almond cakes.
Therefore,
the number of walnut cakes = 55% of 160
the number of walnut cakes = 55 / 100 × 160
the number of walnut cakes = 8800 / 100
the number of walnut cakes = 88
Therefore,
the number of almond cakes = 160 - 88 = 72
After selling some of the walnut cakes, the percentage of the walnut cakes become 40%.
Therefore, the number of walnut cakes after sales is as follows:
let
x = number of walnut cake sold
40% of (88 - x + 72 ) = 88 - x
40 / 100 (160 - x) = 88 - x
6400 - 40x / 100 = 88 - x
cross multiply
6400 - 40x = 8800 - 100x
6400 - 8800 = -100x + 40x
-2400 = -60x
x = 2400 / 60
x = 40
Therefore,
number of walnut cake remaining = 88 - 40 = 48
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{x|x is an odd counting number between 8 and 16} find n(a) for the sets of 3-6
Answers
Answer:
vsdddddddddddddddd
Step-by-step explanation:
888iiiiiiiiiiiiit3jjgfifhhh
Real estate ads suggest that 62% of homes for sale have garages 28% have swimming pools and 18% have both features. If a home for sale has a garage what’s the probability that it has a pool too?
Answers
Answer:
Step-by-step explanation:
The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool
You get GPS units from two manufacturers, A and B. You get 43% of your units from A and 57% of your units from B. In the past, 2% of the units from A have been defective, and 1.5% of the units from B have been defective. Assuming this holds true, if a GPS unit is found to be defective what is the probability that it came from manufacturer A (think Bayes Theorem AND round to two decimal places)
Answers
Answer:
0.5015 = 50.15% probability that it came from manufacturer A.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which
P(B|A) is the probability of event B happening, given that A happened.
\(P(A \cap B)\) is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: From manufacturer A.
Probability a unit is defective:
2% of 43%(from manufacturer A)
1.5% of 57%(from manufacturer B). So
\(P(A) = 0.02*0.43 + 0.015*0.57 = 0.01715\)
Probability a unit is defective and from manufacturer A:
2% of 43%. So
\(P(A \cap B) = 0.02*0.43 = 0.0086\)
What is the probability that it came from manufacturer A?
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0086}{0.01715} = 0.5015\)
0.5015 = 50.15% probability that it came from manufacturer A.
Please answer immediately I beg.
A pyramid and a cone have the same base area and height. The volume
of the pyramid is 175m³. What is the volume of the one? Explain your answer.
Answers
The volume of cone is 175 m³
Firstly,
Volume of Pyramid.
The volume (V) of a pyramid is
V = ⅓Ah
Data:
V = 175m³
Calculation:
175 = ⅓× A× h
Ah = 175*3
Ah = 525m³
Secondly,
The volume (V) of a cone is
V = ⅓Ah
Data:
Ah = 525 m³
Calculation:
V = ⅓ A× h
V = 175 m³
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Given the two functions, which statement is true? f(x) = 3x, g(x) = 3x + 5 Question 12 options: g(x) is translated up 5 units compared to f(x) g(x) is translated left 5 units compared to f(x) g(x) is translated down 5 units compared to f(x) g(x) is translated right 5 units compared to f(x)
Answers
The correct statement is: g(x) is translated up 5 units compared to f(x).
The correct answer is A.
To determine the translation between the two functions, we can observe that the only difference between them is the constant term.In f(x) = 3x, there is no constant term, so the graph of f(x) passes through the origin (0, 0).In g(x) = 3x + 5, there is a constant term of 5 added to the function. This means that the graph of g(x) is shifted vertically upward by 5 units compared to the graph of f(x).Therefore, g(x) is translated up 5 units compared to f(x).The correct answer is A.
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Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answers
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
Answers
The required coefficients are:4, -1, -11, and 7.
Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.
In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.
In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.
We need to consider the polynomial:
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:
4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2
Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn
Taking the coefficients of the constant terms6 + 2 - 1 = 7
Therefore, the required coefficients are:4, -1, -11, and 7.
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(3a to 3rd power - 5b to 3rd power) + ? 3/a + ? b to the 3rd power = (3/a + b to the 3rd power)
Answers
The simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³
How to solve Algebraic Fractions?
We want to solve the algebraic fraction equation given as;
3a³ - 5b³ + (3/a) + b³
Rearranging the algebra to get;
(3a³ + (3/a)) + b³ - 5b³
Factorizing out 3/a and simplifying gives;
(3/a)(a⁴ + a) - 4b³
This is the final part for the simplification of the given algebraic fraction. Thus, we can conclude that the simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³
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Please help- I cannot get this wrong
Answers
Answer:
Top left table
Step-by-step explanation:
It increases at a constant rate of 2 in the y for every 2 in the x so its slope is 1.
Answer:
Top left corner.
Step-by-step explanation:
2, 7
4, 9
6, 11
8, 13
The coordinates increase at a proportional rate.
the sum of two consecutive natural number is 36 find the number
Answers
So, simply if we add 18 to itself comes 36.
A baseball player had batting average of 0.298 what the probability of him getting exactly 4 out of 10 times he was up at bat
Answers
The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.
To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.
The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of getting exactly k hits
n is the total number of trials (in this case, the player's 10 times at bat)
k is the number of successful trials (in this case, 4 hits)
p is the probability of success in a single trial (in this case, the player's batting average, 0.298)
(1 - p) is the probability of failure in a single trial
Plugging in the values:
P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)
Using the combination formula C(n, k) = n! / (k! * (n - k)!):
P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)
Calculating the values:
P(X = 4) ≈ 0.161
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In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even. (Round your answer to four decimal places.) (b) What is the probability that a subject would guess more than 20 correct in a series of 36 trials?
Answers
The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001
How to find the pobability that a subject would guess more than 20 correct in a series of 36 trialsIn a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.
Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.
The probability of guessing more than 20 correct is:
P(X > 20) = 1 - P(X ≤ 20)
Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).
Therefore: P(X > 20) = 1 - 0.9999 = 0.0001
So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).
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Ajay works in a department store selling clothing. He makes a guaranteed salary of
$450 per week, but is paid a commision on top of his base salary equal to 15% of his
total sales for the week. How much would Ajay make in a week in which he made
$375 in sales? How much would Ajay make in a week if he made x dollars in sales?
Answers
= $56.25
Total earnings = 450 + 56.25
= $506.25
Total earnings when selling $x = 450 + (15% x X)
Why is it
sufficient to graph this function in the
upper right quadrant only? How far can
Rick drive on 2.5 gallons of gasoline?
Answers
Answer:
a) see attachment
b) negative values for miles or gallons are not possible
c) 45 miles
Step-by-step explanation:
a)See the attachment for a graph
__
b)Graphing in the first quadrant is all that is necessary, because the number of gallons and the number of miles cannot be negative.
__
c)Use 2.5 for g and evaluate:
d = 18(2.5) = 45
Rick can drive 45 miles on 2.5 gallons of gas.
.
Five more than the product of a number and 8 equals 9.
Use the variable b for the unknown number.
Answers
The unknown number, represented by the variable b, is 1/2, which satisfies the equation "Five more than the product of a number and 8 equals 9."
To solve the equation "Five more than the product of a number and 8 equals 9" using the variable b for the unknown number, we can express this statement as an equation:
8b + 5 = 9
To solve for b, we need to isolate the variable on one side of the equation. Let's simplify the equation step by step:
Subtract 5 from both sides to get rid of the constant term:
8b + 5 - 5 = 9 - 5
8b = 4
Divide both sides of the equation by 8 to solve for b:
8b/8 = 4/8
b = 1/2
Therefore, the solution to the equation is b = 1/2. This means that when we substitute b = 1/2 into the equation, the equation will hold true:
8(1/2) + 5 = 9
4 + 5 = 9
Both sides of the equation are equal, confirming that b = 1/2 is the solution.
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___ planning is the process of identifying long-term organizational goals, strategies, and resources.
a. Opportunity b. Preliminaryc. Strategicd. Vertical
Answers
Strategic planning is an essential process for any organization that wants to succeed and achieve long-term success. It involves identifying long-term organizational goals, strategies, and resources that will help the organization reach its objectives.
Option C. Strategic planning is the process of identifying long-term organizational goals, strategies, and resources.Strategic Planning: Achieving Long-Term Organizational GoalsThis process requires a comprehensive assessment of the organization's current and future needs, including its strengths and weaknesses, opportunities and threats, and the external environment. Once identified, the organization must develop and implement a plan to achieve its goals and objectives. This involves setting objectives, developing and implementing strategies and tactics, and allocating resources in a way that will maximize the organization's chances of success.
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Katrina is building a wall around her backyard using bricks that are 18 inches long. The wall needs to be 36 feet, or 432 inches, long.
Answers
Katrina will need 24 bricks to build the wall around her backyard.
We have,
To determine the number of bricks needed for the wall, we need to divide the total length of the wall (432 inches) by the length of each brick (18 inches):
So,
Number of bricks = Total length of the wall / Length of each brick
Number of bricks = 432 inches / 18 inches
Number of bricks = 24 bricks
Therefore,
Katrina will need 24 bricks to build the wall around her backyard.
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The complete question:
Katrina is building a wall around her backyard using bricks that are 18 inches long. The wall needs to be 36 feet, or 432 inches, long.
Find the number of bricks needed to build around he backyard.
write 0.000001705 in scientific notation
Answers
Round to the nearest hundred
Answers
To the nearest hundredths place: 29.03 kg
PLZ HELP I'LL GIVE BRAINLY IF RIGHT What is the slope of the line passing through the points (0, -5) and (4, 2)?
Answers
Answer:
7/4
Step-by-step explanation:
The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of the dinner for two at a local Chinese restaurant. The dinner is valued at $35. Since the fortune cookies were donated to the club, we can ignore the cost of the cookies. The club sold 743 cookies before the drawing.
(a) Lisa bought 12 cookies. What is the probability she will win the dinner for two? (Round your answer to three decimal places.)
What is the probability she will not win? (Round your answer to three decimal places.)
(b) Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? (Round your answer to two decimal places.)$
How much did she effectively contribute to the hiking club? (Round your answer to two decimal places.)$
Answers
Answer:
a)
- the probability she will win the dinner for two is 0.016
- the probability she will not win the dinner for two is 0.984
b)
- Lisa's expected earnings is $0.57
- Money she effectively contributed to the hiking club is $11.43
Step-by-step explanation:
Given the data in the question;
fortune cookies; $1 per cookies
club sold 743
a) Lisa bought 12 cookies. What is the probability she will win the dinner for two?
P( she will win ) = Number of cookies bought / Total number of cookies
P( she will win ) = 12 / 743
P( she will win ) = 0.01615 ≈ 0.016
Therefore, the probability she will win the dinner for two is 0.016
P( she will not win ) = 1 - P( she will win )
P( she will not win ) = 1 - 0.016
P( she will not win ) = 0.984
Therefore, the probability she will not win the dinner for two is 0.984
b) Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? (Round your answer to two decimal places.)$
given that value of dinner = $35
P( she will win ) = 0.01615
so
Lisa's earning = $35 × 0.01615
Lisa's earning = $0.57
Therefore, Lisa's expected earnings is $0.57
- How much did she effectively contribute to the hiking club? (Round your answer to two decimal places.)$
Lisa's contribution = Money she paid for cookies - money from expected earnings
Lisa's contribution = ( 12 × $1 ) - $ 0.57
Lisa's contribution = $12 - $0.57
Lisa's contribution = $11.43
Therefore, Money she effectively contributed to the hiking club is $11.43
Show that (fof-1) (x)=x and (F-1 of)(x) = x for the following pair of functions.f(x) = 5-4x, f'(x) =5-754Show that (fof-1)(x) = x.(fof- ')(x) = 0Write the expression for the composition.= x(Do not simplify. Type an exact answer, using radicals as needed.)
Answers
To obtain the expression for the composition of the function of the inverse function of x, the following steps are necessary:
Step 1: Write out the expression for the function of x and the inverse function of x, as below:
\(\begin{gathered} f(x)=\sqrt[5]{5-4x} \\ ^{}f^{-1}(x)=\frac{5-x^5}{4} \end{gathered}\)Step 2: Write out the expression for the composition of the function of the inverse function of x, as below:
\((f^{-1}Of))(x)=^{}\frac{5-(\sqrt[5]{5-4x})^5}{4}\)Thus, the above is how the expression for the composition of the function of the inverse function of x is to be written out
what is the correct ordering, from smallest to largest, of the following: $\dfrac{7}{6},$ $\dfrac{17}{15},$ $\dfrac{28}{25}\,?$
Answers
So, the correct ordering from smallest to largest is 17/15, 7/6, 28/25.
When comparing fractions, one way to determine which fraction is larger or smaller is by finding a common denominator and then comparing the numerators. A common denominator is a multiple of both denominators. The least common denominator (LCD) is the smallest common denominator.
In this case, the least common denominator for the fractions 7/6, 17/15, 28/25 is 30.
This is because 30 is the smallest multiple of 6 and 15 that is also a multiple of 25
So, 7/6 = 35/30, 17/15 = 17/15 and 28/25 = 84/75
The numerators of the fractions are 35, 17, and 84 respectively. Since 17 is the smallest numerator and 84 is the largest numerator, we can conclude that 17/15 is the smallest fraction and 84/75 is the largest fraction.
Therefore, the correct ordering from smallest to largest is 17/15, 7/6, 28/25.
In summary, to compare fractions, we can find a common denominator, then compare the numerators. In this case, we used the least common denominator 30, and then compared the numerators 35, 17, 84, which allowed us to order the fractions in an increasing order.
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Does anyone know this?
Answers
Answer:
i think c or b I D K
Step-by-step explanation: