An equation is a mathematical statement showing the equality of two
opposite variables
How to determine the equation of the circle using coordinates?
The equation of a circle is determined by the function r²=(x-x1)² +(y-y1)²
where :
(x1,y1,) marks the centre of the circlex,y marks the points on the circumference of the circumference of the circler marks the radius of the circlethen, the last thing is to write the equation of the circle and input the values of the coordinates to arrive at your answer,
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Write the equation of a line in point slope form that has a slope of 1/3 and passes through the point (6,-2)
The equation of a line in the point-slope form that has a slope of 1/3 and passes through the point (6,-2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex].
What is point-slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point-slope form is used to determine the equation of a line whose slope is "m" and passes through the point ([tex]x_{1}, y_{1}[/tex]). The equation of a straight line can be expressed in various ways, Point slope shape is one of them. The point slope form's equation is as follows:[tex]y-y_{1} =m(x-x_{1} )[/tex]where (x, y) is a chance point on the line that should be treated as a variable when using the formula.A fixed point on the line is ([tex]x_{1}, y_{1}[/tex]).The slope of the line is m.Calculation
[tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-(-2) =\frac{1}{3} (x-6 )[/tex]
[tex]y+2 =\frac{1}{3} (x-6 )[/tex]
Therefore, the equation of a line in the point-slope form that has a slope of 1/3 and passes through the point(6, -2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex]
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Question
A botanist created a linear model to predict plant height from soil acidity (pH level) for a certain type of plant. The slope of the model was 2.5 centimeters per pH level, the standard deviation of the sample of plant heights was 4 centimeters, and the standard deviation of the soil acidities was 1 pH level. What is the value of the correlation coefficient?
The value of the correlation coefficient is 0.625.
What is a correlation coefficient?Correlation coefficients quantify the strength of a relationship between two variables. A correlation coefficient is a number ranging from -1 to 1 that indicates the degree and direction of a relationship between variables. It is a statistical notion that aids in the establishment of a relationship between predicted and actual values collected in a statistical experiment.
In this case, the slope of the model was 2.5 centimeters per pH level, and the standard deviation of the sample of plant heights was 4 centimeters.
The correlation coefficient will be:
= Slope / Standard Deviation
= 2.5 / 4
= 0.625
The coefficient is 0.625.
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What is the area of this triangle?
8cm
6cm
2cm
Answer:
6cm square
Step-by-step explanation:
what is 4x multipied by 7y
Answer:
Step-by-step explanation:
28xy
Principal Interest Rate Time Simple Interest
$12,000 4.25% 5 years
The value of Simple interest for the given data comes as $2550.
Given,
The Principal amount is equal to 12,000 dollars.
The Rate of Interest is stated at 4.25%.
The Total time period given for the question is 5 years.
Let the principal amount be considered as (P), the Rate of Interest per annum be (R), the Time period is (T), and Simple Interest is (S.I).
So, according to the given question,
P = $12,000
R = 4.25%
T = 5 years
We know, Simple interest can be calculated by multiplying the Principal amount with the Rate of Interest as well as the Time period.
If we write it mathematically, the formula will be,
S.I = PRT/100
=> S.I = (12,000* 4.25* 5)/100
=> S.I = (2,55,000)/100
=> S.I = $2550.
Hence, the value of Simple Interest will be 2550 dollars.
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7. The perpendicular bisectors of
AEFG meet at point H. Find HJ.
The distance of the intersection of 3 perpendicular bisectors of a triangle to the 3 vertices are equal.
In other words, HF = HE = HG.
Therefore, we see that 3 isosceles triangles are identified : HFE, HFG, HGF.
We're given HF = 15, therefore HE = 15.
Since HJ is the perpendicular bisector of line EG, JE = JG.
Therefore, JE = 12.
Now, we use the Pythagorean theorem in the right triangle HJE :
[tex]HE^{2} = HJ^{2} + JE^{2} - > HJ = \sqrt{15^{2} - 12^{2} } =\sqrt{81} = 9.[/tex]
Find the area of the square . Units required 18cm
Answer:
324 cm²
Step-by-step explanation:
area of a square = L x L = L²
L = 18cm
(18cm)² = 18cm x 18cm = 324 cm²
e-8/find-the-slope-from-two-points
On two poinICS ZAC
he line that passes through (10, 7) and (3, 1).
wer and write it as a proper fraction, improper fraction, or r
The slop m is ( 2-3).The slope formula, or the ratio of the change in the y values to the change in the x values, is m is equal to subtraction of y2 and y1 and divide by subtraction of x2 and x1 The initial point's coordinates are x1 and y1, respectively.
How to find slop?The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1). The initial point's coordinates are x1 and y1, respectively.
(10, 7) and (3, 1).
m=(y2-y1)/(x2-x1).
3-1 / 7-10= 2/-3
The slop m is ( 2-3)
When determining the slope of a straight line without its equation, there are three steps. The first point's coordinates are x1 and y1. Step one is to locate the line's first two points. Step 2: Decide which will be (x1, y1) and which will be (x2, y2). Step 3: Determine the slope using the slope equation.
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Write the equation of the line parallel to the x-axis passing through
the point (2,5).
Answer:
y=5 .................
how many ways can a president, a vice-president and a secretary be chosen from 17 members of a club assuming that one person cannot hold more than one position?
The three posts can be given in 4080 ways among 17 students.
It is given that the number of people available to choose the posts from is 17.
There are three posts here- president, vice president, and secretary.
Now, if we choose a candidate for President first, there are 17 students available.
Next, if we select a Vice-President, there are 16 ways to select the vice-president, since one student already is the president.
At, last there are 15 students available to choose the secretary from as two students already hold a post.
Hence, the number of ways to select the President, Vice-President, and Secretary are-
17 X 16 X 15 ways
Therefore we get
4080 ways.
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decide whether the following situation is looking for part, the percent, or the whole.
81 of 270 pages in a book
PLEASE HELP quick it would help
81 of 270 pages in a book is a part of the situation.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
81 of 270 pages in a book.
Eighty one of two hundred seventy pages in a book.
In the given situation, A book has 270 pages in that we have taken 81 pages which are part of the book.
We have taken pat of the book,
In the given situation, book is whole and 81 is the part.
Hence 81 of 270 pages in a book is a part of the situation.
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the reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.005 seconds. what is the probability that a reaction requires more than 0.5 seconds?
Answer:0.02275
Normal distribution:
Which is symmetrical about mean.
Mean:
It is the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Complement rule:
When two disjoint sets are meant to occur then the sets are said to be complementary.
Given:
Mean= 0.4 seconds
Standard deviation= 0.005 seconds
Let, X be the reaction time for the driver to view stimulus.
So, distribution of X is given by:
X~ N( 0.4, 0.005)
Where σ= 0.05 and µ= 0.4
Solving this ques by using normal standard deviation and z score given as:
z=\frac{x-µ}{σ}
Applying formula:
P(X>0.5)= P{(x-µ/σ) > (0.5-µ/σ)} P {Z > (0.5-0.4/0.05)}
=P(Z > 2)
By using complement rule we get,
P(Z>2) = 1- P(Z<2)
Using normal standard table we have,
P(Z>2)=1- P(Z<2)
= 1- 0.97725
= 0.02275
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The probability that a reaction requires more than 0.5 seconds is 0.0227
Z-score standardization:
The amount of standard deviations the data point deviates from the mean is shown by the standardized z-score.
• If the z-score increases when it is higher than the mean (0).
• If the z-score is below the mean and takes a negative value (0).
Given that,
Mean = μ =0.4
Standard deviation = σ =0.005
The probability that a reaction requires more than 0.5 seconds is obtained by;
Let X denotes the reaction time of a driver which follows a normal distribution with a mean of 0.4 seconds and a standard deviation of 0.005 seconds.
P(X > 0.5) = 1 - P(X < 0.5)
= 1 - P(0.4 < X < 0.5) (0.5 - 0.4/0.005)
= 1 - P(25.06)
= 1 - P(252)
From the “standard normal table”, the area to the left of is 0.9773.
P(X > 0.5) = 1 - P(252)
= 1 - 0.9773
= 0.0227
Hence, the probability that a reaction requires more than 0.5 seconds is 0.0227
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The area of rectangle abcd is 28 cm a) what is the length of side ab in terms of x? length of ab = 4 cm x cm 6 cm x cm b) if the area of rectangle abcd is 28 cm?, we can show that x2 + ax = b where a and b are integer values. work out the values of a and b. a : (1) b= (1) total marks: 3
The length AB of rectangle in terms of x is (4 + x) and values of a and b are 10 and 4.
The side AB measures (4 + x). Hence, the length of AB in terms of x is (4 + x).
The area of rectangle is calculated by the formula-
Area = length × breadth
Keep the values in formula -
28 = (4 + x) (6 + x)
Performing multiplication of both brackets with each other
28 = 24 + 4x + 6x + x²
Solving and rewriting the equation
x² + 10x = 4
Equation in question - x² + ax = b
Comparing both the equations, we get a = 10 and b = 4.
Thus, length of AB is (4 + x) and value fo a is 10 and b is 4.
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Could someone help me out, please?
Answer:
For x = -2, y would equal -3.
For x = -1, y would equal -2.
For x = 0, y would equal -1.
For x = 1, y would equal 0.
For x = 2, y would equal 1.
Step-by-step explanation:
So what we have to do is plug in the x-values from the table into the equation.
1) y = -2 -1 => y = -3
2) y = -1 - 1 => y = -2
3) y = 0 - 1 => y = -1
4) y = 1 - 1 => y = 0
5) y = 2 - 1 => y = 1
Which of the following equations shows a directly proportionate relationship?
y = -4x
y = 3x - 1
y = 2.75x - 3
y = 7x
Answer:
first and third
Step-by-step explanation:
the equation representing direct proportion is
y = kx ← k is the constant of proportion
y = - 4x is in this form with k = - 4
y = 7x is in this form with k = 7
Write the equation for the absolute value function graphed
Thank you!
The equation for the absolute value function is y = -2lx-4l + 2
An absolute value function is what?
A function that surrounds an algebraic expression in absolute value symbols is called as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The definition of the absolute value parent function is given as follows: f(x)=x if x>00 if x=0 if x0.
Y=a| x+h |+k is the form of the equation for an absolute value function. Also:
The graph's vertex is (h,k).
The range of the graph is y≥k for a>0 and its domain is a set of all real numbers.
The range of the graph is y≤k when a0, and its domain is a set of all real numbers.
X=h is the symmetry axis.
If a>0, it opens up; if a0, it opens down.
The graph of y=a| xh |+k can be created by translating the line graph y=| x | by h units horizontally and k units vertically.
If | a | 1 and if | a | >1, the graph of y=a| x | is wider than the graph of y=| x | and narrower.
So here (h,k)=(4,2)
range of y≤2
and its narrower so a≥1
hence the equation is y = -2 l x-4 l +2
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sarah owns a farm and has lots of dogs on her property. in the table below, she has listed each of her dogs by name and has classified them according to size and color. at random, she picks one of the dogs to take with her to the pet store. what is the probability the selected dog is medium and brown?
The probability the selected dog is medium and brown by Sarah is 6/49.
What is meant by the word probability?A field of mathematics that deals with the exploration of probabilities. The ratio of that number of alternatives in an exhaustive set all equally probable scenarios that cause a specific event to that same total number of conceivable outcomes.Probability = favourable outcome/ total outcome
The table for the given question is attached.
Total dogs owned by Sarah = 7.
Total medium sized dogs = 2.
Total brown coloured dogs = 3
Probability( medium sized ) = 2/7
Probability( brown coloured ) = 3/7
Probability( medium sized and brown coloured ) = (2/7)×(3/7)
Probability( medium sized and brown coloured ) = 6/49
Thus, the probability the selected dog is medium and brown is 6/49.
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Caina earned a scholarship of $6,000 next year. She also expects to receive a grant of $3,200 next year and will make another $400 per month working a part-time job. How much does she anticipate in income next year?
Caina anticipate in income next year $14000.
What is an income?
The amount of money, property, and other value transfers received over a predetermined period of time in return for goods or services is often referred to as income.
We have,
A scholarship of $6000 and a grant of $3200 together are $9200
6000 + 3200 = 9200.
She will make another $400 per month working a part-time job, so for 12 months she will make $400 × 12 = $4800.
All together will be $9200 + $4800 = $14000.
Therefore, She anticipate in income next year $14000.
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Which number is greatest? 24/100 0.3 16%
jake's on 49 tickets to the school are, and jeans sold 12 tickets. what is the ratio, in simplest form, of the number of tickets jeans sold to the number of tickets jake sold?
The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.
Given that,
Jake sold 49 tickets while jeans sold 12 for the school.
In simplest form the ratio of the given case will be;
Simplest form:
A fraction is a number that falls between the whole numbers but is not a whole number. It belongs to the entire. A fraction also consists of a denominator and a numerator. We obtain the fraction in its simplest form when both the numerator and denominator can no longer be independently reduced to any smaller integer.
The ratio we get;
→ 12/49
The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.
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S.
The memory card on Melcher's digital camera can hold about 430 pictures. Melcher used 18% of
the memory card while taking pictures at a family reunion. About how many pictares did
Melcher take at the family reunion? Round to the nearest whole number.
Answer:
Step-by-step explanation:
18% of 430 comes out to 77.4 total pictures taken. After rounding it to the nearest whole number because you cant take a fraction of a picture it would be 77 total pictures taken.
how would you respond to a statement that says that by increasing the sample size, the amount of sampling error will be decreased?
The statement about That by increasing the sample size, the amount of sampling error will be decreased is true.
Given that,
That by increasing the sample size, the amount of sampling error will be decreased
Sampling error is inversely related to sample size. Therefore, if we expand the size of our sample, the likelihood of sampling error is reduced and the results are more trustworthy. The standard error is the term used to describe the sampling error that is most frequently utilized (SE). A measurement of the range of estimations around the "actual value" is the standard error. You get a lower return by increasing the sample size beyond what you already have because the added accuracy won't make much of a difference.
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PLEASE HELP!
Find the y-intercept of the line on the graph.
Enter the correct answer.
008
Clear all
7
DONE
Answer: y intercept is -1
Step-by-step explanation:
Show all of your work and use proper mathematical form and language for full marks.
- A pole 3.8m high casts a shadow 1.3m long. A nearby tree casts a shadow 4.5m long
A. How tall is the tree, correct to one decimal place? Justify your answer.
The height of the tree is 13.2 m.
What is proportional ?
The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.
We can set up a proportion comparing the height of each object to the length of the shadow.
Then , [tex]\frac{h}{s}[/tex].
=> [tex]\frac{3.8}{1.3} = \frac{h}{4.5}[/tex]
=> h = [tex]\frac{3.8*4.5}{1.3}[/tex]
=> 13.2 m.
Hence the height of the tree is 13.2 m.
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Omar is hiring a painting company to paint the interior of his house. The table represents prices the painting company quoted Omar.
Write a two-variable linear equation to represent the total cost, c, given the square feet, s, of the house.
A: c=2.25s+1347.85
B: c=2.25s+2847.85
C: c=2.25s+4047.85
D: c=2.25s+7654.60
The linear equation to represent the total cost c = 2.25s + 1,347.85.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
Using slope
slope= ( 5847. 75 - 4074 . 85)/( 2000- 1200)
slope= 1800 - 800
slope= 2.25
and, slope- intercept form
c - 4047.85 = 2.25 ( s- 1200)
c - 4047.85 = 2.25s - 2700
c = 2.25s - 2700 + 4047.85
c = 2.25s + 1,347.85
Hence, linear equation to represent the total cost c = 2.25s + 1,347.85.
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Look at the figure. Which step should be take. Next to construct a line through point R that is perpendicular to ST?
Extend the compass from point T to little more than the midpoint of ST in such a way the arc drawn touches the point R. Similar is to be done from point S. Draw a line through the cut made by the 2 arcs at R.
Rafael has saved up $650 to buy a new laptop. The laptop he wants is in stores for $749.99 but is on sale for 25% off. After the discount is removed, a tax rate of 5.75% is added on. After Rafael buys the laptop, how much money will he have left over? Remember to round to the nearest hundredth as you go because this is money.
The amount of money left over after buying the laptop is $55.17.
How to calculate the value?From the information, the laptop he wants is in stores for $749.99 but is on sale for 25% off and after the discount is removed, a tax rate of 5.75% is added on.
This will be:
= $749.99 - (25% × $749.99)
= $749.99 - $187.50
= $562.49
The addition of the tax will be:
= $562.49 + (5.75% × $562.49)
= $562.49 + $32.34
= $594.83
The money left over will be:
= $650 - $594.83
= $55.17
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each quiz in a course contains 15 questions. how many different ways could the questions on a given quiz be ordered?
The no. of ways could those question be ordered is 1307674368000 ways A combination is what?
When selecting components from a collection using the combination method, the sequence of selection is unimportant, in contrast to permutations. In simpler scenarios, the number of combinations can be counted.
The act of combining n objects into k groups, one at a time, without repetition Repetition-allowed combinations are usually referred to as k-selection or k-combinations with repetition.
Given
that, Total no of question in quiz is 15 The no. of ways could those question be ordered is 15! ways = 1307674368000 ways The number of possible ways for those questions is 1307674368000.
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I need help asap… Is this relation a function or no ?
Answer:
Step-by-step explanation:
yes, it is a function
Answer: no
Step-by-step explanation: you have -2,-5 and -2,0 you cant have 2 or more x values that are the same.
Anthony say he can evaluate the expression (5+4) x 3-2 without parentheses and get the Same answer. Is Anthony correct? Explain your answer.
Answer:
Step-by-step explanation:
5 + 4 × 3 - 2
9 × 3– 2 =
27–2 = 25
