The axis of symmetry of the equation f(x) = - 3x ^ 2 + 13x + 10 is
x = 13/6How to find the axis of symmetryThe axis of symmetry is calculated
= -b / 2a
The quadratic equation is an equation of the form
ax^2 + bx + c
Comparing the given equation f(x) = - 3x^2 + 13x + 10 with ax^2 + bx + c the values of the axis of symmetry is
x = -b / 2a
x = -13 / 2(-3)
x = -13 / -6
x = 13/6
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mark spent a total of $12.33 on 9 oranges and a packet of strawberries. if the packet of strawberries costs $2.88 how much did each orange cost
Answer: $1.05 per orange
Step-by-step explanation:
12.33 - 2.88 = 9.45
9.45 ÷ 9 = 1.05
Write the equation of the line that passes through the points (-5, 9) and (8,-9).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
Answer:
y - 9 = -18/13(x + 5)
Step-by-step explanation:
A local deli makes turkey sandwiches and salami sandwiches at a weekly ratio of 2 salami sandwiches for every 5 turkey sandwiches. If the deli makes 60 turkey sandwiches this week, how many salami sandwiches did they make?
1. 5 salami sandwiches
2. 16 salami sandwiches
3. 30 salami sandwiches
4. 24 salami sandwiches
Please answer :)
Answer:
1.5
Step-by-step explanation:
Which of these relations is a function?
The fourth figure is a function as it passes the vertical line test.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
By vertical line test which is drawing a vertical line anywhere in a graph of a function if it only intersects only at one point, it is a function.
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Please help asap now !!!!!
Answer: I need the Problem?
Step-by-step explanation:
develop a class shapes 2d to represent all 2d geometric shapes excluding line. class should represent the name of the object (a string) the color of the objects (color) and methods that all subclasses should implement (abstract methods) including:
This is the UML diagram for the development of the program, in which Shapes 2D is the superclass and Circle, Square, Triangle, Rectangle, Rhombus, and Parallelogram are subclasses.
This is the program in C++ demonstrating the above classes.
#include<iostream>
using namespace std;
class shapes
{
public:
string name;
string color;
virtual void getAttributes()=0;
};
class Circle: public shapes
{
public:
float radius;
Circle(string n,string c, float r)
{
name=n;
color=c;
radius=r;
}
float getPerimeter()
{
return(2*(3.142)*radius);
}
float getArea()
{
return((3.142)*(radius*radius));
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Square:public shapes
{
public:
float side;
Square(string n,string c, float s)
{
name=n;
color=c;
side=s;
}
float getPerimeter()
{
return(4*side);
}
float getArea()
{
return(side*side);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Triangle:public shapes
{
public:
float base;
float height;
float side1;
float side2;
float side3;
Triangle(string n,string c)
{
name=n;
color=c;
}
float getPerimeter()
{
cout<<"Enter side1\n";
cin>>side1;
cout<<"Enter side2\n";
cin>>side2;
cout<<"Enter side3\n";
cin>>side3;
return(side1+side2+side3);
}
float getArea()
{
cout<<"Enter base\n";
cin>>base;
cout<<"Enter height\n";
cin>>height;
return((0.5)*base*height);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Rectangle:public shapes
{
public:
float length;
float breadth;
Rectangle(string n,string c, float l,float b)
{
name=n;
color=c;
length=l;
breadth=b;
}
float getPerimeter()
{
return(2*(length+breadth));
}
float getArea()
{
return(length*breadth);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Rhombus:public shapes
{
public:
float diagonal1;
float diagonal2;
float side;
Rhombus(string n,string c)
{
name=n;
color=c;
}
float getPerimeter()
{
cout<<"Enter Side\n";
cin>>side;
return(4*side);
}
float getArea()
{
cout<<"Enter diagonal 1\n";
cin>>diagonal1;
cout<<"Enter diagonal 2\n";
cin>>diagonal2;
return((0.5)*diagonal1*diagonal2);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Parallelogram:public shapes
{
public:
float base;
float height;
Parallelogram(string n,string c, float b,float h)
{
name=n;
color=c;
base=b;
height=h;
}
float getPerimeter()
{
return(2*(base+height));
}
float getArea()
{
return(base*height);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
int main()
{
int choice;
while(1)
{
cout<<"\n\nEnter your choice :";
cout<<"\n1 for Circle\n";
cout<<"2 for Square\n";
cout<<"3 for Triangle\n";
cout<<"4 for Rectangle\n";
cout<<"5 for Rhombus\n";
cout<<"6 for Parallelogram\n";
cin>>choice;
system("cls");
switch(choice)
{
case 1:
{
float r;
cout<<"Enter radius\n";
cin>>r;
Circle c("Circle","Yellow",r);
c.getAttributes();
cout<<"Perimeter : "<<c.getPerimeter()<<endl;
cout<<"Area : "<<c.getArea()<<endl;
}break;
case 2:
{
float side;
cout<<"Enter side\n";
cin>>side;
Square s("Square","Red",side);
s.getAttributes();
cout<<"Perimeter : "<<s.getPerimeter()<<endl;
cout<<"Area : "<<s.getArea()<<endl;
}break;
case 3:
{
Triangle t("Triangle","Green");
t.getAttributes();
cout<<"Perimeter : "<<t.getPerimeter()<<endl;
cout<<"Area : "<<t.getArea()<<endl;
}break;
case 4:
{
float l,b;
cout<<"Enter Length and breadth\n";
cin>>l>>b;
Rectangle r("Rectangle","Blue",l,b);
r.getAttributes();
cout<<"Perimeter : "<<r.getPerimeter()<<endl;
cout<<"Area : "<<r.getArea()<<endl;
}break;
case 5:
{
Rhombus r("Rhombus","Purple");
r.getAttributes();
cout<<"Perimeter : "<<r.getPerimeter()<<endl;
cout<<"Area : "<<r.getArea()<<endl;
}break;
case 6:
{
float b,h;
cout<<"Enter base\n";
cin>>b;
cout<<"Enter height\n";
cin>>h;
Parallelogram p("Parallelogram","Pink",b,h);
p.getAttributes();
cout<<"Perimeter : "<<p.getPerimeter()<<endl;
cout<<"Area : "<<p.getArea()<<endl;
}break;
}
}
}
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Sort the following polygons in order of increasing area
The area of the polygons sorted in ascending order of area is:
Rectangle = 4
Triangle = 12
Square = 13
What is a polygon?In geometry, a polygon is a planar shape defined by a restricted number of straight line segments linked to form a closed polygonal chain.
Area of the triangle is:
[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2
Where Ax and Ay are the x and y coordinates of A's vertex. The same is true for the x and y notations of the B and C vertices.
Given,
A(-4-3), B(1, -3), C(-1,2)
We have
[-4(-3-2) + (1(2-(-3)) + (-1(-2-(-3))]/2
= 24/2
= 12
As a result, the area of the triangle is 12.
We use the distance formula to calculate the area of the rectangle. The equation is as follows:
d² = (x₂ - x₁)² + (y₂-y₁)²
Where (x₁, x₂) are the first point's coordinates and (y₁, y₂) are the coordinates of the second point.
Assuming that the vertices are labeled as follows:
A(7,9), B(6,9), C(6,5), D(7,5), then
AB² = (6-7)² + (9-9)²
AB² = 1 + 0
AB = 1
BC² = (6-6)² + (5-9)²
BC² = 0² + -4²
BC = 4
CD² = (7-6)² +(5-5)²
CD² = 1² + 0²
CD = 1
DA² = (7-7)² + (9-5)²
DA² = 0² +4²
DA = 4
As is typical of a rectangle, we can deduce that AB = CD and BC = DA
Since the Area of the rectangle is AB x CD OR BC x DA
The area of the rectangle =4 x 1 = 4
We may also calculate the length of the square's sides using distance methods.
We only need the length of one side because the area of a square is provided as L2.
Hence,
AB = 3.60555
Hence the area of the square =3.60555²
= 12.9999908025
Area of the square is 13
Thus, the polygons are placed in increasing area order as follows:
Rectangle = 4
Triangle = 12
Square = 13
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Rico-Guevara’s feeders take pictures of the birds’ tongues sticking out as they sip nectar. A hummingbird’s beak is b millimeters long and its tongue sticks out t millimeters past its beak. Write an expression to find out the total length of its beak and tongue that sticks out. 4B. Evaluate it: A Rufous-tailed hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters
The expression to find out the total length of its beak and tongue that sticks out is b+t.
When Rufous-tailed hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters, the length is 28 millimeters.
What is an expression to find the total length?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information illustrated, Guevara’s feeders take pictures of the birds’ tongues sticking out as they sip nectar.
A hummingbird’s beak is b millimeters long and its tongue sticks out t millimeters past its beak.
The expression to find out the total length will be:
= Length of beak + Length of tongue
= b + t
The length when the hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters is:
= 20 + 8
= 28 millimeters
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Rewrite the expression as an equivalent ratio of logs using the indicated base. log13(58.875) to base 10
Answer:
log 58.875/ log 13
Step-by-step explanation:
log 58.875/ log 13
which inequality has –12 in its solution set?abcdx + 6 less-than negative 8x + 4 greater-than-or-equal-to negative 6x minus 3 greater-than negative 10x + 5 less-than-or-equal-to negative 4abcd
The inequality contain -12 in its solution is x + 5 ≤ -4.
What is inequality?
The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things.
We have to find from the given inequalities which inequality has -12 in its solution.
Consider, the given inequalities
(1) x + 6 < -8
⇒ x < - 8 - 6
⇒ x < -14
This inequality does not contain -12 in its solution.
(2) x + 4 ≥ - 6
⇒ x ≥ -6 - 4
⇒ x ≥ - 10
This inequality does not contain -12 in its solution.
(3) x - 3 > -10
⇒ x > -10 + 3
⇒ x > -7
This inequality does not contain -12 in its solution.
(4) x + 5 ≤ -4
⇒ x ≤ - 4 - 5
⇒ x ≤ -9
This inequality contain -12 in its solution.
Hence, the inequality contain -12 in its solution is x + 5 ≤ -4.
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what does it mean to say that two variables are negatively associated?what does it mean to say that two variables are negatively associated?
When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.
Express the term negative correlation?When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.
The correlation coefficent, which expresses correlation on a scale from +1 to -1, is used. Values less than 0 indicate a negative connection. An increase in one variable confidently foretells a drop in the other when there is a perfect negative correlation, with a coefficient of -1. An rise or decrease inside one variable consistently forecasts the same directional shift for the second variable, according to a perfect positive correlation that has a coefficient of +1. Non-zero coefficients between -1 and +1 are used to show lower degrees of connection.Zero denotes the absence of a correlation: There is no propensity is for variables to change simultaneously.
Thus, when two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.
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Complete the program so that it takes in 4 integers (a, b, c, and d) as arguments, stores them in the 2D array nums, and then prints their row, column, and total sums. The program should print the integers according to this formula:
(a) (b) (a+b)
(c) (d) (c+d)
(a+c) (b+d) ((a+b)+(c+d)+(a+c)+(b+d))
// (a+b) is the first row's sum
// (c+d) is the second row's sum
// (a+c) is the first column's sum
// (b+d) is the second column's sum.
// ((a+b)+(c+d)+(a+c)+(b+d)) is the total sum of all rows and columns
The program should print the integers according to this formula is
nums[0][0]=a;
nums[0][1]=b;
nums[1][0]=c;
nums[1][1]=d;
nums[0][2]= nums[0][0] + nums[0][1]; //a+b
nums[1][2]= nums[1][0] + nums[1][1]; //c+d
nums[2][0] = nums[0][0] + nums[1][0]; //a+c
nums[2][1] = nums[0][1] + nums[1][1]; //b+d
//sum = (a+b) + (c+d) + (a+c) + (b+d)
nums[2][2] = nums[0][2] + nums[1][2] + nums[2][0] + nums[2][1];
The nums array is 2 dimensional as shown below.
row, column column 0 column 1 column 2
row 0 a b a+b
row 1 c d c+d
row 2 a+c b+d (a+b)+(c+d)+(a+c)+(b+d)
The first index of an array always starts from 0.
Thus, nums[rows][columns] is used to access each element of the array.
The sum of first row elements is to be stored in the last index of row0, that is in nums[1][2].
Thus we equate nums[0][2] = nums[0][0] + nums[0][1]
Similarly, for 2nd row; nums[1][2] = nums[1][0] + nums[1][1]
The sum of first column is to be stored in last index of column0.
Thus, nums[2][0] = nums[0][0] + nums[1][0]
and for 2nd column,
nums[2][1] = nums[0][1] + nums[1][1].
Thus, the answer is--
-------------------------------------------------------------------------------------------------------------------------------------
nums[0][0]=a;
nums[0][1]=b;
nums[1][0]=c;
nums[1][1]=d;
nums[0][2]= nums[0][0] + nums[0][1]; //a+b
nums[1][2]= nums[1][0] + nums[1][1]; //c+d
nums[2][0] = nums[0][0] + nums[1][0]; //a+c
nums[2][1] = nums[0][1] + nums[1][1]; //b+d
//sum = (a+b) + (c+d) + (a+c) + (b+d)
nums[2][2] = nums[0][2] + nums[1][2] + nums[2][0] + nums[2][1];
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The sum of the elements in a tuple can be recursively calculated as follows: the sum of the elements in a tuple of size 0 is 0 otherwise, the sum is the value of the first element added to the sum of the rest of the elements write a function named sum that accepts a tuple as an argument and returns the sum of the elements in the tuple.
The following is a code in python.
What is Python and why it is used?Python is a popular computer programming language used to create software and websites, automate processes, and analyze data. Python is a general-purpose language, which means it can be used to make many different types of programs and isn't tailored for any particular issues.
What are the advantages of Python?One of Python's biggest benefits is the variety of libraries and frameworks it offers. Everything from data visualization, machine learning, data science, natural language processing, and complex data analysis uses the Python Library, from NumPy to TensorFlow.
#Specify the function in
DefinedSum(tu)
# Verify whether the tuple contains 0
if len(tu) == 0
#Then, give back 0
return 0
#Otherwise
else:
#invoke the recursive function.
return tu[0]+Sum (tu[1:])
Set a variable of the tuple type
tu=(2,5,1,8,10)
#print, then invoke the function.
print("The total of tuple is:"), sum(tu),
Output:
The sum of tuple is: 26
Here, we define the method "sum()" and send the parameter "tu" to the function, which saves the value of the tuple type.
If the length of the tuple is 0, then the if conditional expression should verify the condition and return 0.
If not, invoke the function, return the tuple's total (which is determined recursively), and exit.
Last but not least, initialize the "tu" variable of the tuple type, print, then run the sum function.
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A classroom has seven blue chairs five green chairs 18 red chairs and yellow nine chairs if a chair is selected at random which color is the least likely to be chosen
Answer:
green
Step-by-step explanation:
green
I’ll give you points and brainlest answer if you answer with a legit answer!
answer:
(1/y)^3(1/z)^4
step-by-step explanation:
negative exponents just move the number to the denominator. so all you have to do is move the y & z to the denominator to change the exponents to positive. hope that helps!
a local aquarium found that if the price of admission was $11$11, the attendance was about 20002000 customers per week. when the price of admission was dropped to $7$7, attendance increased to about 26002600 per week. write a linear equation for the attendance in terms of the price, p
The linear equation for the attendance in terms of the price, p is
2600= -150p + 3650
A =m*p + b
where A= attendance , m = slope , b = y-intercept and p = price
When p=11 then A=2000 , i e , (11, 2000).
When p= 7 , then A=2600, i .e , (7 , 2600).
m= (b-d)/(a-c)
=> m = (2600-2000)/(7 - 11)
= -150
Therefore , 2600= -150p + b
To get the value of b,
putting the value of p in the obtained equation,
we get,
2600= -150 * 7+ b
2600 = -1050 + b
b = 3650
Hence , our equation becomes
2600= -150p + 3650
Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on
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how many arrangements of the 26 different letters are there that (a) contain either the sequence ""the"" or the sequence ""aid""?
1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
Given that,
We have to find how many different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
We know that,
Total number of arrangements of 26 different letters= 26!
Let A be the number of arrangements that contains 'the' = 24! ( Total no. Of alphabet= 26 subtract the number That contains 'the' i.e, 3 and add one for 'the' 26-23+1=24)
Let B be the number of arrangements that contains 'aid' = 24! (Total no. Of alphabet minus number of letter in 'aid' and add 'aid' as an alphabet i.e, 26-23+1= 24)
Total no. Of arrangements that contains either sequence 'the' or 'aid'
A or B= (A)+(B)- (A intersection B)
24! +24! -22! = 1.239x10²⁴
Therefore, 1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
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Help with these two questions, 100 points!!
Answer:
15. x = 4
16. x = 7
Step-by-step explanation:
15.
CD/ ED = DG / DF
48 / (5x - 2) = 40 / (2x + 7)
48 (2x + 7) = 40 (5x - 2)
96x + 336 = 200x - 80
200x - 96x = 336 + 80
104x = 416
x = 4
16.
ST / PL = TU / LM
(x + 1) / 72 = (2x - 3) / 99
99 (x + 1) = 72 (2x - 3)
99x + 99 = 144x - 216
144x - 99x = 99 + 216
45x = 315
x = 7
Answer:
15. x = 4
16. x = 7
Step-by-step explanation:
Similar Triangles
In similar triangles, corresponding sides are always in the same ratio.
Question 15If ΔCDG ~ ΔEDF then:
CD : ED = DG : DF = CG : EFFrom inspection of the given diagram:
CD = 48ED = 5x - 2DG = 40DF = 2x + 7Therefore:
[tex]\implies \sf CD : ED = DG : DF[/tex]
[tex]\implies 48 : (5x-2) = 40 : (2x+7)[/tex]
[tex]\implies \dfrac{48}{(5x-2)} = \dfrac{40}{(2x+7)}[/tex]
[tex]\implies 48(2x+7)=40(5x-2)[/tex]
[tex]\implies 96x+336=200x-80[/tex]
[tex]\implies 416=104x[/tex]
[tex]\implies x=\dfrac{416}{104}[/tex]
[tex]\implies x=4[/tex]
Question 16If ΔSTU ~ ΔPLM then:
ST : PL = TU : LM = SU : PMFrom inspection of the given diagram:
ST = x + 1PL = 72TU = 2x - 3LM = 99PM = 70Therefore:
[tex]\implies \sf ST : PL = TU : LM[/tex]
[tex]\implies (x+1) : 72 = (2x-3) : 99[/tex]
[tex]\implies \dfrac{(x+1)}{72}= \dfrac{(2x-3)}{99}[/tex]
[tex]\implies 99(x+1)=72(2x-3)[/tex]
[tex]\implies 99x+99=144x-216[/tex]
[tex]\implies 315=45x[/tex]
[tex]\implies x=\dfrac{315}{45}[/tex]
[tex]\implies x=7[/tex]
The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
A shooter has a 27.92% chance of hitting the target at least 13 times.
What does binomial distribution mean?Let X become a random variable and represent the number of times the target gets hit.15 shots are fired, hence 10 trials ("n") are conducted as a result.The likelihood of success is represented by "p" in a binomial distribution, and the likelihood of failure is represented by "q" (where q = 1 - p).p = 0.89 with q = 0.11 because the target has a 0.89 chance of being hit.This probability mass function in this type of binomial distribution is the quantity of successes ("x").
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
The required number of wins is five since we are concerned with the likelihood that target will be hit exactly five times.(i.e., x = 13).
P(X = 13) = ¹⁵C₁₃. (0.89)¹³ (0.11)²
P(X = 13) = 0.2792
P(X = 13) = 27.92%
Therefore, there is a 27.92% chance that a shooter will hit its target at the very most 13 times.
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Scale: 4 inches = 21 miles If the drawing length is 13 inches, what is the actual length?
Answer:
Step-by-step explanation:
do 21 ÷ 4 = 5.25
Now we have 5.25 miles for each inch. So all we have to do is multiply 5.25 by 13 to find the answer:
5.25 × 13 = 68.25
Let me know if this helped!
For a fully discrete whole life insurance of 1000 issued to (x), you are given:
2Ax = 0.08
Ax = 0.2
The annual premium is determined using the equivalence principle.
S is the sum of the loss-at-issue random variables for 100 such independent policies. Calculate the standard deviation of S. (Ans 2500)
The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.
Given that:
2Ax = 0.08
Ax = 0.2
A fully discrete whole life insurance issued to (x) is 1000.
Firstly we have to find out the value of variance S.
Variance S = (insurance issued)^2 * [2Ax - Ax^2]/(1- Ax)^2
Variance S = (1000)^2 * [0.08 - 0.2^2]/(1- 0.2)^2
Variance S = (1000)^2 * [0.04]/.64
Variance S = (1000)^2 * .0625
Variance S = 62500
Standard deviation of S = (insurance issued) * [[tex]\sqrt{2Ax - Ax^2}[/tex]]/(1- Ax)
Standard deviation = 1000 * [[tex]\sqrt{0.08 - 0.2^2}[/tex]]/(1- 0.2)
Standard deviation = 1000 * 0.2/0.8
Standard deviation = 1000 * 1/4 = 250
The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.
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A line with a slope of –1/4 passes through the point (3,3). What is its equation in point-slope form? Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
The equation of the line is y = -1/4x + 15/4
How to determine the equation of the line?From the question, we have the following parameters that can be used in our computation:
Slope = -1/4
Point = (3, 3)
The equation of a line is calculated using
y = m(x - X) + Y
Where
m = Slope = -1/4
(x, y) = Point = (3, 3)
Substitute the known values in the above equation, so, we have the following representation
y = -1/4(x - 3) + 3
So, we have
y = -1/4x + 3/4 + 3
Evaluate
y = -1/4x + 15/4
Hence, the equation is y = -1/4x + 15/4
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Scientists have found a relationship between the temperature and the height above a distant planet's surface. T(h), given below, is the temperature in Celsius at a height h kilometers above the planet's surface. The relationship is as follows:
T(h)=41−1.25h.
Let T^−1 be the inverse function of T. Take x to be the output of the function T.
a) Explain the meaning of T^−1(x).
b) Find T−1(x).
c) Find T−1(30)
.
a) The inverse function is obtained by rearranging the variables for temperature and height in the given equation.
b) T⁻¹(x) =41-x/1.25
c) T⁻¹(30) =8.8
The given function is T(h)=41- 1.25h, so the inverse of a function is just obtained by rearranging the variables for height and temperature, the variable of temperature is replaced by height and vice versa. for the second
T(h)=41- 1.25h, considering h= x
=>T(x)=41- 1.25x
setting T(x)=x and x= T(x), we get
41- 1.25T(x) =x
=>1.25T(x) =x -41
=>T(x) =x- 41/ 1.25
now setting T(x)= T⁻¹ (x) we get : T⁻¹ (x) =41-x/1.25
For T⁻¹(30) =41-30/1.25= 11/1.25 =8.8
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a rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches (see figure). find the dimensions of the package of maximum volume that can be sent. (assume the cross section is square.)
The dimensions of the package of maximum volume that can be sent are 20 inches by 40 inches.
Let us represent the length of the square cross-section of the postal package with x, and the width of the package with y.
So, the perimeter is given by the equation -
y + 4x = 120
y = 120-4x -----------(1)
the volume will be
V = [tex]x^{2} y[/tex] -----------(2)
Now, substitute (1) in (2), and we get,
V = [tex]x^{2}[/tex] (120-4x)
V = 120[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]
Differentiating with respect to x, we get,
V' = 240x - 12[tex]x^{2}[/tex]
V'=0
hence, 240x - 12[tex]x^{2}[/tex] = 0
12[tex]x^{2}[/tex] = 240x
dividing by 120x on both sides,
hence, x=20
Now, we know that,
y = 120 - 4x
y = 120-4(20)
y = 120-80
y=40
Hence, the dimensions that maximize the volume of the package are 20 inches by 40 inches.
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he radius of a circle is 12 m. Find its circumference in terms of pi
Answer:
24π m
Step-by-step explanation:
r = 12 m
C = 2πr
C = 2 × π × 12 m
C = 24π m
Two blueberry farms are similar in shape. the ratio of the side lengths of the farms is 6 : 7, and the smaller farm has a perimeter of 360 yards. the cost to dig a trench is $0.75 per yard. what is the cost to dig a trench around the larger blueberry farm?
Two blueberry farms are similar in shape. the ratio of the side lengths of the farms is 6 : 7 then $337.50 is the cost to dig a trench around the larger blueberry farm
The farms are sized with a ratio of 4:5 which means that the perimeter of the larger farm can be found by subtracting the perimeter of the smaller farm from that of the total of both farms which can be found by the following formula where it is assumed to be x.
4/(4+5) * x = 360 yards
4x = 360 * 9
x = (360 * 9) / 4
x = 810 yards
Size of larger farm = 810 - 360 = 450 yards
If it costs $0.75 to dig a trench per yard, the total cost for the larger farm is;
= 450 * 0.75
= $337.50
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(t/f) since we are sampling from a skewed-right distribution, with sample size 80, the sampling distribution of the sample mean should also be a skewed-right distribution.
True, With an 80-person sample size, we are selecting from a skewed-right distribution, hence the sampling distribution mean should likewise be skewed-right.
80 people make up the sample that was taken from the population distribution with a right skew. We may infer that the sampling distribution of the sample means would be close to normalcy given the size of the sample.
In general, the distribution is normal.
The central limit theorem states that as sample size increases, the sample mean distributions become normal, with standard deviations equaling n and mean values approximating the population mean, regardless of the underlying distribution's form. In other words, the sample means sampling distribution turns roughly normal.
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Find the coordinates of the circumcenter of the triangle with the given vertices.
2. R(-2,5), S(-6, 5), T(-2,-1)
P(4, 7.25) are the coordinates of circumcentre of the triangle
How to find the coordinates of the circumcenter of a triangle
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect
Given: The vertices R(-2,5), S(-6, 5), T(-2,-1)
Let P(x,y) be the circumcentre of triangle. Then,
PR = PS = PT
PR² = PS²
(x-(-2))² + (y-5)² = (x-(-6))² + (y-5)²
(x+2)² + (y-5)² = (x+6)² + (y-5)²
x²+4x+4 + y²-10y+25 = x²+12x+36 + y²-10y+25
12x-4x = 36 -4
8x = 32
x = 32/8 = 4
Also, PS² = PT²
(x-(-6))² + (y-5)² = (x-(-2))² + (y-(-1))²
(x+6)² + (y-5)² = (x+2)² + (y+1)²
x²+12x+36 + y²-10y+25 = x²+4x+4 + y²+2y+2
12x-4x-10y-2y = 4+2-36-25
8x-12y = -55 .......(1)
put x= 4 into (1):
8x-12y = -55
8(4)-12y = -55
32 -12y = -55
-12y = -55-32
-12y = -87
y = 7.25
Therefore, the coordinates of circumcentre of the triangle are P(4, 7.25)
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longobardi corporation bases its predetermined overhead rate on the estimated labor- hours for the upcoming year. at the beginning of the most recently completed year, the corporation estimated the labor-hours for the upcoming year at 46,000 labor- hours. the estimated variable manufacturing overhead was $6.25 per labor-hour and the estimated total fixed manufacturing overhead was $1,026,260. the actual labor- hours for the year turned out to be 41,200 labor-hours. the predetermined overhead rate for the recently completed year was closest to:______.
The predetermined overhead rate for the recently completed year was closest to $28.56 par labor - hour.
What is Labor - hour?
4 to 8 hours or more are typical for active labor. Your cervix will expand on average at a rate of 1 cm per hour. What you can do: Seek encouragement and support from your labor partner and your medical team. To ease your discomfort, try deep breathing and relaxation exercises.
Given:
Longobardi corporation bases its predetermined overhead rate on the estimated labor- hours for the upcoming year.
At the beginning of the most recently completed year, the corporation estimated the labor-hours for the upcoming year at 46,000 labor- hours.
The estimated variable manufacturing overhead was $6.25 per labor-hour and the estimated total fixed manufacturing overhead was $1,026,260.
The actual labor- hours for the year turned out to be 41,200 labor-hours.
Estimated total manufacturing overhead
= $1,026,260 + ($6.25 per labor- hour X 46,000 labor - hours)
= $1,313,760
Predetermined overhead rate
= $1,313,760 / 46,000 labor-hours
= $28.56 per labor-hour
Hence, the predetermined overhead rate for the recently completed year was closest to $28.56 par labor - hour.
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-8w+(-4z)+2+6w+9z-7 ?