Answer:
(x + 1)² + (y - 3)² = 16
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 1, 3 ) and r = 4 , then
(x - (- 1) )² + (y - 3)² = 4² , that is
(x + 1)² + (y - 3)² = 16
Answer:
(x+1)^2 + (y-3)^2 = 16
Step-by-step explanation:
The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2 = (x+1)^2 + (y-3)^2 = 16.
Can someone help pls
Answer:
x = 0, x = 5
Step-by-step explanation:
x² - 5x = 0 ← factor out x from each term
x(x - 5) = 0
equate each factor to zero and solve for x
x = 0
x - 5 = 0 ⇒ x = 5
B
23. Find the EXACT circumference of the circle
if AB = 2in and BC = 11in.
A
C
a. √117 in
b.
5√5π in
c.
35.1 in
d. 5√5 in
Answer:
C. 35.1
Step-by-step explanation:
First get the length of AC by using the Pythagorean Theorem, that ends up being about 11.18. Then you need to get the radius of the circle so you divide 11.18 by 2 and get 5.59. Then plug 5.59 for r into 2(pi)(r). 2(pi)(5.59) = 5.123
Answer:
Answer B is correct
Step-by-step explanation:
First, let us find the diameter (AC) of the circle using the Phythogerem theorem.
AC² = AB² + BC²
AC² = 2² + 11²
AC² = 4 + 121
AC² = 125
AC = √ 125
AC = 5√5
And now let us find the circumference of the circle.
C = π × d
C = π × 5√5
C = 5√5π in
How many times do you need to divide by ten to get from 0.747 to 0.0747?
Answer:
Step-by-step explanation:
Quick Answer 1
Solution
x = 0.747 / 0.0747
When you do the division, you get 10. That means that you need to divide 0.747 by just 1 ten to get 0.0747
Answer:
Once
Step-by-step explanation:
You have to divide once because if you divide a decimal by 10, you add a zero before the decimal point
construct a quadrilateral
AB=6cm , BC = 5cm, AD = 4CM CD =7cm and BD = 6cm
If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.
What is quadrilateral?
If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.
Given: AB = 6cm , BC = 5cm, AD = 4cm, CD = 7cm and BD = 6cm
Draw a line AB with 6cm with A as the center draw an arc of radius 4 cm. And draw another arc of 6cm to cut the previous arc at D with B as the center draw an arc of radius 5cm. And with D draw another arc of 7cm to cut the previous arc at C. Join the lines of the quadrilateral.
Now ABCD exists as a required quadrilateral.
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Find the area of quadrilateral abcd. [hint: the diagonal divides the quadrilateral into two triangles.]
The area of quadrilateral ABCD exists equivalent to the area of triangle ABD plus the area of triangle ADC
Heron's Formula exists a technique for estimating the area of a triangle when you know the lengths of all three sides.
Therefore, the total area of quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].
How to find the area of quadrilateral abcd?Let a, b, and c be the lengths of the sides of a triangle.
The area is given by:
[tex]$$A = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
where p exists half the perimeter
[tex]$p = \frac{a+b+c}{2}[/tex]
To estimate the area of triangle ABD
we have
a = AB = 2.89 units
b = BD = 8.59 units
c = DA = 8.6 units
To estimate the perimeter
[tex]$p = \frac{2.89+8.59+8.6}{2}[/tex]
= 10.4 units
To estimate the area
[tex]$A = \sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]
[tex]$A = \sqrt{10.04(7.15)(1.45)(1.44)}[/tex]
[tex]$A = \sqrt{149.89}[/tex]
A = 12.24 [tex]$$units^2[/tex]
To estimate the area of the triangle ADC
we have
a = AC = 4.3 units
b = AD = 8.6 units
c = DC = 7.58 units
To estimate the half perimeter p
[tex]$p = \frac{4.3+8.6+7.58}{2}[/tex]
= 10.24 units
To estimate the area
[tex]$A = \sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]
[tex]$A = \sqrt{10.24(5.94)(1.64)(2.66)}[/tex]
[tex]$A = \sqrt{265.35}[/tex]
A = 16.29 [tex]$$units^2[/tex]
To estimate the total area
A = 12.24+16.29 = 28.53 [tex]$$units^2[/tex].
Therefore, the total area of quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].
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Find the results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.
The resultant of subtractions of u = <-8, 4> and v = <2, 7> are
-u-v = <6, -11>,
u-v = <-10, -3>,
and v-u= <10,3>.
What is a vector in simple definition?
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.The resultant of subtractions of u = <-8, 4> and v = <2, 7> are
-u-v = <6, -11>,
u-v = <-10, -3>,
and v-u= <10,3>.
Given that,
The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.
We have to determine,
The value of -u-v, u-v, and v-u.
According to the question,
The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.
The value of -u-v is,
-u -v = - < -8 ,4 > - <2,7>
-u -v = <8, -4> - < 2, 7 >
-u - v = < 8 - 2 , -4 - 7 >
-u -v = < 6 , - 11 >
The value of u-v is,
u -v = < -8 ,4 > - < 2,7 >
u - v = < - 8 - 2, 4 - 7 >
u - v = < 10 ,3>
The value of v - u is,
v - u = < 2 , 7> - < - 8,4 >
v - u = < 2 + 8 , 7 - 4 >
v - 4 = < 10 , 3 >
Hence, The resultant of subtractions of u = <-8, 4> and v = <2, 7> are
-u-v = <6, -11>,
u-v = <-10, -3>,
and v-u= <10,3>.
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Haley and tyler are on the cross country team. tyler can run 1 mile (ata constant speed) in 8 minutes and 20 seconds. haley's distances and times for a training run are given by the equation y=8x where x represent distanse and times in miles and y represents time in minutes. who ran farther in 10 minutes how much farther
Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Tyler can run 1 mile in 8 minutes and 20 seconds.
Time taken = 8 mins + 20 sec (0.33 min) = 8.33 minutes
Speed = distance / time = 1 mile / 8.33 = 0.12 mile per min
In 10 minutes, distance = 0.12 mile per min * 10 min = 1.2 mile
Haler is given by:
y = 8x; where y is time and x is distance.
In 10 minutes, distance = y/8 = 10/8 = 1.25 miles
Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.
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Let f(x) = 8x3 + 18x2 − 10 and g(x) = 4x + 1. Find f of x over g of x.
The value of function f(x) over g(x) is [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]
Given functions are:
f(x)=8[tex]x^{3}[/tex]+18[tex]x^{2}[/tex]-10
g(x)=4x+1
In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions exist everywhere, and they are crucial for constructing physical links in the sciences.
In mathematics, a function is represented as a rule that produces a distinct result for each input x. A function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
[tex]\frac{f(x)}{g(x)}=\frac{8x^{3}+18x^{2} -10 }{4x+1}[/tex]
= [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]
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Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines? cake can be cut into equal parts.
Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines, cake can be cut into 20 equal parts.
This is further explained below.
What are gridlines?Generally, In spreadsheet software, gridlines are the light gray lines that divide the cells, rows, and columns. Gridlines are often used to maintain track of data. Gridlines are widely used in popular spreadsheet programs like Spreadsheet.
In conclusion, If the cuts can only be done along the gridlines, the cake may be divided into 20 equal pieces when cutting along the lines.
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A friend of mine believes that the average GPA at KSU is equal to 3.0. In order to test whether he/she is right, I collect some information from the data. Specifically, I use 100 KSU students to form a sample and find that their sample average GPA is equal to 3.3. In addition, suppose that I also know the population standard deviation of GPA at KSU is 1.5. I decide to use 0.05 as the level of significance for my hypothesis testing. Could you help me with Q1-Q10 below? Q1: What should be my null hypothesis? What should be my alternative hypothesis? Q2: Is this a lower-tailed, upper-tailed or two-tailed case? Q3: Show me how to calculate my test statistic.
Q4: If I use the critical value approach, explain how to derive my critical value(s). Q5: If I use the p-value approach, explain how to derive my p-value. Q6: If I use the confidence interval approach, show me how to derive the confidence interval. Q7: How to make my decision, if I use the critical value approach? Q8: How to make my decision, if I use the p-value approach? Q9: How to make my decision, if I use the confidence interval approach? Q10: Are the decisions in Q7, Q8, and Q9 the same?
The solution of the questions is given as
a)
The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)
b)
This is a case with two separate arguments. (This is a two-tailed case)
c)
Test Statistic is given by:
z= 2.00
d)
Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.
e)
, p-value = 0.0455
f)
CI= (3.006, 3.594)
g)
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
h)
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
i) Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.
j)
The choices you choose in Questions 7, 8, and 9 are identical.
What is the null hypothesis?a)
The null hypothesis states that mu equals 3.0. ( the average GPA at KSU is equal to 3.0) (Claim)
The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)
b)
This is a case with two separate arguments.
c)
Test Statistic is given by:
[tex]z=\frac{\barx-u^0}{σ/Vn}\\\\z=33 - 3.0/1.5/V100[/tex]
z= 2.00
d)
[tex]\alpha = 0.05[/tex]
Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.
e)
Z Score = 2.00
reading from table, p-value = 0.0455
f)
Confidence Interval:
[tex]CI= \barx \pm \frac{ZX\sigma }{\sqrt((n)}[/tex]
[tex]CI =3.3 \pm 1.96 x 1.5 / \sqrt{100}[/tex]
CI= (3.006, 3.594)
g)
The disparity is noteworthy given that the computed value of Z = 2.00 is higher than the crucial value of z = 1.96. Cast doubt on the null hypothesis.
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
h)
The difference may be considered statistically significant since the p-value of 0.0455 is lower than the alpha threshold of 0.05. Cast doubt on the null hypothesis.
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
i)
The difference is statistically significant since the value of 3.0 is not included in the confidence range (3.006 - 3.594). Cast doubt on the null hypothesis.
Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.
j)
The choices you choose in Questions 7, 8, and 9 are identical.
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Nuber 17 pls (question on quadratics)
Considering the equation of the parabola, the coefficients are given as follows: p = 5, q = -20, r = 19.
The graph is the one given at the side of the question.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the turning point is (2,-1), hence h = 2, k = -1, and the equation has the following format:
y = a(x - 2)² - 1
The curve passes through (3,4), that is, when x = 3, y = 4, and we use it to find a.
y = a(x - 2)² - 1
4 = a(3 - 2)² - 1
a = 5.
Hence the equation is:
y = 5(x - 2)² - 1
Placing it into standard form, we have that:
y = 5(x² - 4x + 4) - 1
y = 5x² - 20x + 19
Hence the coefficients are:
p = 5, q = -20, r = 19.
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question down below about linear equations and grapghing.
The system of equations is -x + y = 4 and -2x + y = 0
How to create the system of linear equations?To do this, we make use of the following ordered pairs
(4, 8)
The above point represents April 2008.
Let the system of equations be
mx + ny = 4
2mx + ny = 0
Substitute (4, 8) for x and y in the above equations.
4m + 8n = 4
8m + 8n = 0
Subtract both equations
4m - 8m = 4
This gives
-4m = 4
Divide by 4
m = -1
Substitute m = -1 in 8m + 8n = 0
-8 + 8n = 0
This gives
8n = 8
Divide by 8
n = 1
So, the system of equations is -x + y = 4 and -2x + y = 0
The graph of the system of equationsThe system of equations is -x + y = 4 and -2x + y = 0
See attachment for the graph of the system of equation
Prove that the solution is (4, 8)The above is represented in the (a) part of this solution
Verify that the solution is (4, 8)
We have:
-x + y = 4 and -2x + y = 0
Substitute (4, 8) for x and y in the above equations.
-4 + 8 = 4 --- true
-2*4 + 8 = 0 --- true
Both equations are true
Hence, the system of equations have been verified
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Algebra 3, in the excercise size the graphs to determine the functions domain and range, x and y intercepts if any, and the functions values indicated below the graphs
Answer:
Read Explanation
Step-by-step explanation:
The domain is a list of all possible x-values, this graph starts at 0 and proceeds to positive infinity, making the domain:
[0,∞)
The range is a list of all possible y-values, this graph starts at -1 and proceeds to positive infinity, making the range:
[-1,∞)
x-intercepts Are where the line crosses the x-axis, in this graph the line only crosses the x-axis at x of 2. Making its only x-intercept 2.
y-intercepts Are where the line crosses the y-axis, in this graph the line only crosses the y-axis at y of -1. Therefore its y-intercept is -1.
In function notation when a question asks for f(x) its asking for the y values at the given x-values. At x of 3 the y value equals 1.
Select the correct answer. what is the completely factored form of this expression? 3x2 − 17x − 28 a. (3x 4)(x 7) b. (3x 4)(x − 7) c. 3x2 − 17x − 28 d. (3x2 4)(x − 7)
Answer:
A. (3x + 4)(x-7)
Step-by-step explanation:
3x times x = 3x^2
3x times -7 = -21x
4 times x = 4x
4 times -7 = -28
-21x + 4x = -17x
3x^2 - 17x - 28
1)Find the L.C.Mof the following set of numbers by prime factorization method:
a)6 and 9
b)16 and 24
c)24,48 and 64
2)Find L.C.M of the following set of numbers by division method:
a)6 and 15
b)25,30 and 75
Note: Answer must have proper explanation
Answer:
a) 18
b) 48
c) 192
a) 30
b) 150
Step-by-step explanation:
Answer:
1
a ) 18
b ) 48
c ) 144
2
a ) 30
b ) 150..
[tex]...[/tex]
The sum of three numbers is 134. The second number is 8 less than the first. The third number is 4 times the second. What are the numbers?
Answer:
29, 21, 84
Step-by-step explanation:
Let the first number be x.
The second number is x - 8.
The third number is 4(x - 8).
Their sum is 134.
x + (x - 8) + 4(x - 8) = 134
x + 5(x - 8) = 134
x + 5x - 40 = 134
6x = 174
x = 29
x - 8 = 29 - 8 = 21
4(x - 8) = 4(29 - 8) = 4(21) = 84
A basketball is shot into the air. its height is represented by the polynomial equation h(t) = –16t2 35t 5, where h is the height of the basketball at t seconds. what is the height of the basketball at 0.5 seconds?
The height of the basketball at 0.5 seconds will be = 26.5
What is a polynomial equation?A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.
Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.
According to the given equation if we put value in it we will follow the following steps -
[tex]h(t) = - 16t^{2} + 35t+ 5\\ h(0.5) = -16(0.5)^{2} + 35(0.5) + 5\\h(0.5) = -16(0.25) + 17.5 + 5\\h(0.5) = 4 + 17.5 + 5\\h(0.5) = 26.5\\[/tex]
Therefore, the height of the basketball at 0.5 s will be 26.5
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Answer:
Is the question supposed to be (1.5), if so then the answer would be 21.5
Step-by-step explanation:
ht=-16t^2+35t+5
h(1.5)=-16(1.5)^2+35(1.5)+5
=21.5
A 164 ft^2
B 1233 ft^2
C 1395 ft^2
D 1557 ft^2
Answer:
B 1233 ft^2
Step-by-step explanation:
I hope this is right
A football is kicked toward the goal. the height of the ball is modeled by the function h(t) = −16t2 64t, where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. what is the axis of symmetry, and how does it relate to the time the ball is in the air? t = 2; it takes the ball 2 seconds to reach the maximum height and 2 more seconds to fall back to the ground. t = 2; it takes the ball 2 seconds to reach the maximum height and 4 more seconds to fall back to the ground. t = 4; it takes the ball 4 seconds to reach the maximum height and 4 more seconds to fall back to the ground. t = 4; it takes the ball 4 seconds to reach the maximum height and 8 more seconds to fall back to the ground.
The function [tex]H(t) = -16t^2 + 64t[/tex] exists in a parabola.
The axis of symmetry of a parabola exists at the midpoint between the two real roots.
The roots exist the solutions of H(t) = 0
To estimate the roots equation exists [tex]-16t^2 + 64t = 0[/tex]
Factor t(-16t + 64) = 0
t = 0 and -16t + 64 =0
-16t + 64 = 0
t = 64 / 16 = 4
t = 4
Then the two roots are t = 0 and t = 4, and the axis of symmetry exists
t = (0+4)/2 = 4/2 = 2
How to estimate the axis of symmetry?The axis of symmetry exists at t = 2.
It represents the time at which the ball is at the higher point, the maximum height.
You can find the maximum height replacing t = 2 in the function H(t)
[tex]H(t) = -16(2^2) + 64(2)[/tex]
= 64 feet.
And you can also deduce that the second part of the flight will take 2 seconds, for a total flight time of 4 seconds.
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Answer:
answer is a
Step-by-step explanation:
it takes 2 seconds for the ball to reach maximum height and 2 seconds to fall on the ground.
t = 2; it takes the ball 2 seconds to reach the maximum height and 2 more seconds to fall back to the ground
Took the FLVS test!
This pattern follows the rule add 14. What other features do you observe?
13, 27, 41, 55
please help meeeeee
The above pattern follows an arithmetic sequence with a common difference of 14 and first term of 13
How to solve a pattern?The pattern can be represented as follows:
13, 27, 41, 55
The first term of the sequence is 13 and the common difference is 14.
The above pattern is an arithmetic sequence.
Therefore, the following can be used to find the nth term.
nth term = a + (n - 1)d
where
n = number of termd = common differencea = first termTherefore,
a = 13
d = 27 - 13 = 14
Let's find the next term
5th term = 13 + (5 - 1)14
5th term = 13 +(4)14
5th term = 13 + 56
5th term = 69
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Find the output, y, when the input, x, is -5.
The output, y, when the input, x, is -5 is -2
How to determine the value of the output y?The input is given as:
-5
This means that
x = -5
This is so because x represents the input
From the graph, we have the following highlight
The line of the graph passes through the point x = -5
On the graph;
When x = -5, the value of y is -2
This means that the output, y, when the input, x, is -5 is -2
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A group of 65 baseball players were surveyed about which hand they favor for batting. The data from the survey are shown in the Venn diagram.
Determine the value for each variable in the two-way table.
The value of each variable in the two-way table is:
a = 7
b = 31
c = 28
d = 13
e = 65
What are the value of the variables?A Venn diagram uses circles that overlap each other to show the relationship between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.
a = females that favor the left. Looking at the Venn diagram, this number is 7.
b = total number of females : 24 + 7 = 31
c = males that favor the right = total number of males - males that favor the left34 - 6 = 28
d = Total number of people who favor the left = 7 + 6 = 13
Total number of baseball players = 65
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Use a calculator to find the mean of the data. {211, 226, 186, 221, 181, 228, 207, 215, 203, 203, 204, 196, 226, 212, 212, 201, 219, 191, 191, 185, 193, 231}
The mean of the given data is 206.5.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."It is the total (sum) of all the values in a set of data, such as numbers or measurements, divided by the number of values in the list. Add up all of the values in the set to find the mean. Then divide the total by the number of possible values.To find the mean of the given data:
Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542
Number of values = 22
Mean = 4,542 ÷ 22 = 206.5
Therefore, the mean of the given data is 206.5.
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Answer:
Step-by-step explanation:
I need some help with this
Answer:
5.09 years
Step-by-step explanation:
The formula for the future value of an investment can be filled with the given values and solved for time.
FormulaThe future value of a one-time investment P earning interest at annual rate r compounded n times per year for t years is ...
FV = P(1 +r/n)^(nt)
ApplicationUsing this formula with the given values, we have an expression for t:
7300 = 5000(1 +0.075/4)^(4t)
Dividing by 5000, we have ...
1.46 = 1.01875^(4t)
Taking logarithms gives the linear equation ...
log(1.46) = 4t·log(1.01875)
Dividing by the coefficient of t, we find ...
t = log(1.46)/(4·log(1.01875)) ≈ 5.0929
The time required for the value to reach $7300 is about 5.09 years.
__
Additional comment
The attachments show different calculator solutions. They give the same value for t.
The TVM Solver uses P/Y = 1 so the value of N is in years.
The graphical solution recasts the problem to f(x) = 0. It finds the value of t that makes the difference between the investment value and $7300 be zero.
determine what type of model best fits the given situation: An Internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. After a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result.
A. none of these
B. quadratic
C. linear
D. exponential
The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.
According to the statement
we have given that:
Monthly Rate = $20, Number of customers = 5000
If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.
And we have to find that The type of model that best fits the given situation.
So, according to the linear representation model
Monthly Rate = $20, Number of customers = 5000
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19, Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18, Number of customers = 5500 + 500 = 6000
Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.
We have 2 pair of values here,
x = 20, y = 5000
x = 19, y = 5500
Let us write the equation in slope intercept form:
y = mx + c
And Slope of a function is
m = y₂ - y₁ / x₂ - x₁
Then
m = 5500 - 5000 / 19 - 20
m = -500
So, the equation become
y = -500x +c
And find the value of by putting the values.
So, c = 15000
And the equation become
y = -500x + 15000.
According to this linear model is perfect for this situation.
So, The linear representation model is best for this situation.
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Find the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0).
The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and
r(1, 1, 0) is x + y + z = 2 .
According to the question
Let the points
p(0, 1, 1) = (x1,y1,z1)
q(1, 0, 1)= (x2,y2,z2)
r(1, 1, 0)= (x3,y3,z3)
now,
The equation of the plane through the points
i.e
The formula of equation of a plane passing through three non collinear points
[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0[/tex]
by substituting the values in the formula of equation of a plane
[tex]\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0[/tex]
[tex]\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0[/tex]
x(1) - (y-1)(-1) + (z-1)(1) = 0
x + y - 1 + z - 1 = 0
x + y + z = 2
Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2 .
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Hazing has been reported all across america. What percentage of students say they have witnessed hazing and did not report it?.
percentage of students say they have witnessed hazing and did not report it are = 95%
What is Hazing?No matter how voluntarily a person is to take part, hazing, initiation or deposition are all actions that are demanded of someone when they join or participate in a group and which humiliate, degrade, abuse, or imperil them.
involves humiliating a person or group. involves making fun of someone or something. involves or includes the deliberate destruction of or removal of private or public property for the purpose of affiliation with, initiation into, or as a requirement for continuing membership in an organization.
What is an example of hazing?Paddling, beating, or other types of attack. Branding. consumption of disgusting substances or mixtures under duress or force.
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Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y29=1
The Jacobian for this transformation is
[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}[/tex]
with determinant [tex]|J| = 12[/tex], hence the area element becomes
[tex]dA = dx\,dy = 12 \, du\,dv[/tex]
Then the integral becomes
[tex]\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv[/tex]
where [tex]R'[/tex] is the unit circle,
[tex]\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1[/tex]
so that
[tex]\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv[/tex]
Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.
[tex]\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}[/tex]
Then
[tex]\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}[/tex]
Express 60 as a product of its prime factors
Answer:
The actual prime factors of 60 are 2, 3, and 5.
Step-by-step explanation:
Greetings !
Use a factor tree to express 60 as a product of prime factors. So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2² × 3 × 5.
In regression, the difference between the confidence interval and prediction interval formulas is ________
In regression, the difference between the confidence interval and the prediction interval formula is "The addition of 1 to the quantity under the radical sign i.e., standard error".
What are the formulas for the confidence interval and prediction interval?
The formula for the confidence interval is
[tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE([tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))
The formula for prediction interval is
Prediction interval = Sample estimate ± (t multiplier × standard error)
[tex]y_{new}[/tex] = [tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE(1 + [tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))
Where μ = x bar.
What is the difference between the confidence interval and the prediction interval?From the above, the prediction interval has one additional MSE term in the standard error calculation. But in the confidence interval, only one term is used.
So, the difference between them occurs in the standard error value.
The formula shows it by adding 1 to the quantity under the radical sign.
Thus, the difference is in the standard error.
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