The radius of a circle with equation is x² + y² + 8x - 6y + 21 = 0 is 2 units .
In the question ,
it is given that ,
the equation of circle is ⇒ x² + y² + 8x - 6y + 21 = 0 ,
we know that the general equation of the circle is x²+y²+2fx+2gy+c=0
so , the radius of the circle is calculated using the formula ,
radius = √(f² + g² - c)
On comparing the given equation with general equation
we get , the values of f as 4 and g as -3 .
So after substituting the values of f , g and c in the radius formula ,
we get ,
radius = √(16 + 9 - 21)
= √(16 + 9 - 21)
= √(25 - 21)
= √(4) = 2 .
Therefore , the radius of given circle is 2 units .
The given question is incomplete , the complete question is
What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 ?
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the task of framing a building has been estimated to take an average of 25 days with a standard deviation of 4 days. what duration should be used if there is to be a 90% confidence that the duration will not be exceeded? what is the probability that the duration will actually exceed 23 days?
The required probability that the duration will actually exceed 23 days is 22.66%.
What is Probability distribution?A probability distribution is a factual capability that depicts every one of the potential qualities and probabilities for an irregular variable inside a given reach.
According to question:We have,
μ = 25, σ = 4,
For 90% confidence interval, Z = 1.645
Then,
Z =( x -μ )/σ =(x - 25)/4
1.645 = (x - 25)/4x
x = 4(1.645) + 25 = 31.58 days
when duration increase by 3 days
So, Z = 3/4 = 0.75
Probability = 22.66%
Thus, required probability is 22.66%.
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What shape is the king of the quadrilaterals?
Square is consider as the king of all the quadrilaterals.
Explanation:
Quadrilaterals are four sided geometrical shape with four vertices, four sides, and four angles enclosed in it.There are six types of quadrilaterals namely trapezium, parallelogram, rectangle, rhombus, square, and kite.Square is consider as the king of all the quadrilaterals:
Square have all four sides congruent, opposite pair of sides parallel to each other, and measure of each angle is 90 degree.Each of these properties represents different types of quadrilateral.Each angle 90 degree represent rectangle.Opposites are parallel to each other represent parallelogram.All sides are congruent represents rhombus.Square consists property of parallelogram, rectangle, and rhombus.Therefore, square shape is consider as the king of all the quadrilaterals.
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Find a low-rank approximation Compute the optimal rank-2 approximation of the symmetric matrix 3.75 -1.25 0.25 -1.75 -1.25 3.75 -1.75 0.25 A= given that the columns of 0.25 -1.75 3.75 -1.25 -1.75 0.25 -1.25 3.75 of A are eigenvectors A2 = Save & Grade 10 attempts left Save only Additional attempts available with new variants
Previous question
Answer: 53.213
Step-by-step explanation:
pls answer this fast
Answer:
dark blue
Step-by-step explanation:
The organizers of a school playestimate that half the students who attend will bring an adult guest. If s represents the number of students expected to attend the play, which expression represents the total expected attendance
Answer: 1/2s + s = total expected attendance.
Step-by-step explanation: If s is the number of expected students and half of them are estimated to bring a guest than you would find half of s and add it to s to get the total expected attendance.
how many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 14?
Because of this, we need to choose 15 integers in such a way that we can ensure that when they are divided by 14, at least two of them will provide the same residual.
In order to be sure that at least two of them have the same remainder when divided by 14.
Generally, If you divide a number by 14, the result is a fraction. There are 14 remainders that might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and, 13.
So if we pick a number and divide it by 14, the remainder can be one of 14 (0 memory 13). So if we select 14 numbers, we have the option to select 14 unique memories ranging from 0 to 13.
Finally, if we choose another integer, we will have the same reminders according to the drawer principle, because there are only 14 reminders and 15 > 14.
Therefore, we should choose the number of 15 so that at least two numbers have the same remainder when divided by 14.
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order these from smallest to largest
0.13 ,3/20 ,12% ,1/10, 0.09
Answer:
0.09, 1/10, 121%, 0.13, 3/20
Step-by-step explanation:
0.13 = 0.13
3/20 = 0.15
12% = 0.12
1/10 = 0.10
0.09 = 0.09
0.09, 0.10, 0.12, 0.13, 0.15
Answer: 0.09, 1/10, 121%, 0.13, 3/20
What does 1/2 of a number mean?
1/2 of a number means one - half of a number.
The irreducible fraction that results from dividing one by two or from dividing any number by its double is known as a half (plural: halves).
Conversely, division by one-half is equivalent to multiplication by two, or "doubling," while multiplying by one-half is equivalent to division by two, or "halving."
In measurements, recipes, equations, etc., one half is frequently used. One part of something that is divided into two equal pieces is said to be divided in half.
For instance, a triangle's S-area is calculated.
S = base / 2 * perpendicular height.
The typical decimal extension of one half is 0.5, and it frequently appears as 0.49999999. In any even base, it has a similar pair of expansions.
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What is the LCD of
17x/(x+1)(x+1) and x² /x² -1
Answer:
To find the least common denominator (LCD) of two fractions, we need to find the least common multiple of the denominators of the fractions. The first fraction is 17x / (x + 1)(x + 1), and the second fraction is x² / x² - 1. The denominators of these fractions are (x + 1)(x + 1) and x² - 1, respectively.
To find the least common multiple of (x + 1)(x + 1) and x² - 1, we need to first factor each denominator. The denominator (x + 1)(x + 1) can be factored as (x + 1)², and the denominator x² - 1 can be factored as (x + 1)(x - 1). The least common multiple of these two denominators is (x + 1)², which is the LCD of the two fractions. Therefore, the LCD of 17x / (x + 1)(x + 1) and x² / x² - 1 is (x + 1)².
Step-by-step explanation:
Please help me with part B
Answer:
To find the zeros ( roots ) of f(x). Put f(x) = 0.
We have :
[tex]0 = 10 - \sqrt{8 - x \\ } \\ \sqrt{8 - x} = 10 \\ 8 - x = 100 \\ 8 - 100 = x \\ x = - 92[/tex]
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the bone density test scores that can be used as cutoff values separating the lowest 3% and highest 3%, indicating levels that are too low or too high, respectively.
The bone density scores are -1.88, 1.88
What is Standard Normal Deviation ?A normally distributed deviation is a standard normal deviate. A standard normal random variable is a realization of a random variable with an expected value of 0 and a variance of 1.
The z score for the lowest 3%(0.03) calculated from the standard normal table = -1.88
X1 = 0+1× (-1.88 ) = -1.88
Similarly, The z score for the highest 3%(0.03) calculated from the standard normal table = +1.88
X2 = 0+1× (1.88 ) = +1.88
So
The bone density scores are -1.88, 1.88
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Tia began filling the bathtub at a constant rate.
She then turned off the water for a while and some of the water drained out of the bathtub.
Tia turned the water back on at the same rate as before until the bathtub was full.
Which graph best represents Tia filling the bathtub?
The 1st graph best represents Tia filling the bathtub
How to determine which graph best represents Tia filling the bathtub?(Consider the image I attached)
At point 1, Tia began filling the bathtub at a constant rate until the water in the bathtub reached point 2
She then turned off (point 2) the water for a while and some of the water drained out of the bathtub. That, the water level dropped from point 2 to point 3
Tia turned the water back on(point 3) at the same rate as before until the bathtub was full (point 4). As you can see there is an increase from point 3 to point 4.
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a sporting goods store manager was selling a kayak set for a certain price the manager offered markdowns 10 percent, and 30 percent marking the one-day sale price as 328 find the original selling of the kayak
Using percentages, we know that $515.87 approx is the purchase price at the start.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
Although "pct," "pct," and occasionally "pc" are also employed as acronyms, the percent symbol "%" has been most usually used to denote it.
A% is a number that has neither dimensions nor a specified unit of measurement.
For example, if you properly completed 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
So, in mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Let x represent the initial asking price ( in dollars ),
After 10% is deducted, 10% of x less the new selling price, or x - 0.1x, equals 0.9x.
Having reduced the price by 30%,
The final selling price equals 90% less than 90%.
= 0.9x - 0.3 × 0.9x
= 0.9x - 0.27x
= 0.63x
The answer to the query is:
0.63x = 325
x = 325/0.63
x = 515.87
Therefore, using percentages, we know that $515.87 approx is the purchase price at the start.
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Correct question:
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $325. Find the original selling price of the ski set. It was marked down 10% and 30%
Directions: Use the formula Sn =a (1 - rn ) ÷ (1 – r) to find the sum Sn for each of the geometric series, given the value for a, r, and n.
1. a = -1, r = -2, n = 8
2. a = ½, r = -1/3, n = 6
3. a = 4, r = 3, n = 5
4. a = -9, r = -3, n =4
5. a = 6, r = 3, n =4
6. a = 4, r = ¼, n = 4
7. a = 3, r = -2, n = 7
8. a = -2, r = 3, n = 5
The required sum Sn for each of the given geometric series is illustrated in the solution.
The sum of a geometric series is given by the formula Sn = a(1 - r^n) / (1 - r), where a is the first term of the series, r is the common ratio, and n is the number of terms in the series.
As per the given question, the required solution would be as:
1. a = -1, r = -2, n = 8:
Sn = (-1)(1 + 2⁸) / (1 + 2) = -1023 / 3
2. a = 1/2, r = -1/3, n = 6:
Sn = (1/2)(1 + (-1/3)⁶) / (1 + (-1/3)) = (1/2)(1 + 1/729) / (4/3) = 728/2187
3. a = 4, r = 3, n = 5:
Sn = (4)(1 + 3⁵) / (1 + 3) = 1792 / 4
4. a = -9, r = -3, n = 4:
Sn = (-9)(1 + (-3)⁴) / (1 + (-3)) = -729 / 2
5. a = 6, r = 3, n = 4:
Sn = (6)(1 + 3⁴) / (1 + 3) = 3456 / 4
6. a = 4, r = 1/4, n = 4:
Sn = (4)(1 + (1/4)⁴) / (1 + (1/4)) = 256 / 5
7. a = 3, r = -2, n = 7:
Sn = (3)(1 + (-2)⁷) / (1 + (-2)) = -769 / 3
8. a = -2, r = 3, n = 5:
Sn = (-2)(1 + 3⁵) / (1 + 3) = -1792 / 4
Thus, the required sum Sn for each of the given geometric series is illustrated in the above solution.
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Write 14/5 as a mixed number
Answer:
2 4/5
Step-by-step explanation:
14 = 10 + 4
10/5 = 2
4/5
3. Simplify 5/1 divided by 7/2
To divide fractions, remember this.
Keep change flip.
Keep one of the fractions.
Change the sign to multiplication.
Flip the other fraction.
[tex]\frac{5}{1} /\frac{7}{2} =\frac{5}{1} *\frac{2}{7} = \frac{10}{7}[/tex]
Answer is 10/7
Hope this helps :)
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- Jeron
How can the triangles be proven similar by the SSS?
Answer:If the corresponding sides are known then they can be calculated.
Step-by-step explanation:If the measures of corresponding sides are known, then their proportionality can be calculated.
(11-5)² + (15/3)
It’s 15 divided by 3
Help
Answer: 41
Step-by-step explanation: First, you subtract 11-5 to get 6 then you square 6 (2nd power) to get 6 x 6, which equals 36. Then, you divide 15 by 3 to get 5, then add, then you should get 41. I hoped this answered this question.
Answer:
41
Step-by-step explanation:
11-5 = 6 .
6 to the second power is 36.
15/3 =5
36+5=41
(11-5)² + 15/3
6. + 15/3
36 + 5. =41
Hope this helps!
max earns £18000 a year he gets a 3.5% pay rise how much more does max earn per month
Answer: I don't really understand what £ means but the answer is 0.35
What is the value formula?
The value formula is: Value = Place Value × Face Value
We know that the value in mathematics is nothing but the worth of each digit depending on where it lies in the number.
We calculate the value of number by multiplying the place value and face value of the digit.
The value formula is:
Value = Place Value × Face Value
Place value is the value of the column in which the number is. Each column in a number holds a different place value.
For exa., consider a number 456. Here, the place value of the digit 5 is tens and the place value of 4 is hundreds.
The face value of any digit is the same digit.
For a number 120 , the face value of 1 is 1, face value of 2 is 2.
Therefore, the formula for the Value = Place Value × Face Value
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What shape is the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base?
A triangle shape is formed by the cross-section of a triangular pyramid sliced by a plane that is perpendicular to its base
A triangular pyramid is a geometric solid having a triangle for a base and three triangles with the same vertex on each side. That is, the triangular pyramid is made up of four triangles. Pyramids made of triangles might be straight or inclined. It resembles a pyramid with four triangular faces that meet at one vertex and a triangular base.
Let's first draw the triangular pyramid. Now, mark the base. Then, denote the plane passing perpendicular to the base. From the diagram we can tell, the plane cuts this pyramid to form a triangle cross-section.
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PLEASE HELP 35 POINTS MATH
Answer:
31
Step-by-step explanation:
-4+16+19=31
solve this math 1-1=?
Serious question or not the answer is zero
Answer:
0
Step-by-step explanation:
One minus one is zero.
You have a surfboard at the store you work at that has a price tag of $800.
You were told that it will cost $745 when it goes on sale this Friday.
You are asked to make a poster describing the sale. They want the poster to say
Surfboards
____% off
Today only!
Calculator the % of sale.
Answer:
Hope this is helpful
Step-by-step explanation:
50% off Today Only!
which expression factors to 8(x + 2)?
The factors of 8(x + 2) are 2, 4, 8, (x+2)
What is factor of an expression?
In mathematics, an integer m that can be multiplied by another integer to create n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.
Given expression is
8(x+2)
The factorization of 8 is 2 × 2 × 2.
Putting 8 = 2 × 2 × 2 in the given expression:
= 2 × 2 × 2 (x+2)
= 2 × 4 (x+2)
The factor of 8(x+2) are 2, 4, 8, 2(x+2), 4(x+2), 8(x+2).
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0.36 as a fraction in its simplest form
Answer:
0.36 can be expressed as 9/25 in the form of a fraction.
Step-by-step explanation:
hoped this helped:)
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How do you draw a 1 1 scale bar?
To draw a figure with 1 : 1 scale, draw the the figure in actual size
The scale factor can be defined as the ratio between the original size of the figure and the new size of the figure.
While scale factoring the shape of the object will be same but the size changes
Here the given ratio = 1 : 1
The means the scale factor = 1/1
= 1
When the scale factor is equal to one, the the size of the original object and the size of the new object will be same
Therefore, 1 : 1 scale bar is the drawing with actual size of the object
I have solved the question in general, as the given question is incomplete
The complete question is
How do you draw a figure with 1 : 1 scale bar ?
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a baseball league has nine teams. during the season, each of the nine teams plays exactly three games with each of the other teams. what is the total number of games played?
The total number of game played are 108.
What is baseball?
In the bat-and-ball game of baseball, two teams of nine players each alternate between batting and fielding. When the umpire indicates to the pitcher that the ball is now in play, either verbally or physically, the game is in progress.
9 teams means each team will play 8 other teams 3 times (totaling 24). 24 games times 9 teams is 216.
However, when you count the first 24 games for team 1, you are counting the 3 games played against team 2.
When you add the games for team 2, you can’t also add the games played against team 1, or you’d be doubling the games counted.
This continues for each team. Team 3 can’t count it’s games against teams 1 or 2. Team 4 can’t count it’s games against teams 1, 2, or 3.
Continuing this and adding the total gets you 108.
Also, taking the first total of 216, you can simply divide by 2 and get the same number.
Hence, the total number of game played are 108.
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correlation and regression are two closely related topics in statistics. for each of the following statements, indicate whether the statement is true of correlation, true of regression, true of both correlation and regression, or true of neither correlation nor regression.
Outliers can have an impact on correlation and regression, which may result in the calculation of inaccurate parameters.
Given that,
In statistics, correlation and regression are frequently used interchangeably.
Regression models the impact of one variable on another, whereas correlation assesses the strength of the link. The following is the solution:
Correlation
Correlation and Regression
Correlation
The degree and type of the association between variables, which cannot be deduced from the regression equation, can be determined using the correlation coefficient.
Both Outliers can have an impact on correlation and regression, which may result in the calculation of inaccurate parameters.
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consider the angle the bottom of the ladder makes with the ground. how fast is the angle changing (in radians) when the ladder is 5.4 feet away from the house?
The angle is changing 0.05136 radians when the ladder is 5.4 feet away from the house.
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Here, we have
The angle the bottom of the ladder makes with the ground.
d∅/dt = d∅/dx × dx/dt.....(1)
bur, x = 24cos∅
dx/d∅ = -24sin∅
d∅/dx = 1/(-24sin∅)
Now, equation (1) becomes,
d∅/dt = 1/(-24sin∅)× dx/dt
If the ladder is 5.4 feet away from the house then,
sin∅ = √24² - 5.4²/24
d∅/dt = -1/√24² - 5.4² ×0.12
d∅/dt = 0.05136 radian
Hence, the angle is changing 0.05136 radians, when the ladder is 5.4 feet away from the house.
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