True, a contour line defines the outer edge or profile of an object, and can be used to suggest a volume in space.
Describe volume of object?It is the amount of space contained within the boundaries of an object and is typically represented by cubic units such as cubic centimeters (cm³), cubic meters (m³), or cubic inches (in³).
Volume can be calculated for various three-dimensional objects such as a cube, sphere, cylinder, or pyramid. The formula for finding the volume of an object depends on its shape. For example, the formula for the volume of a cube is V = s³, where s is the length of one of its sides. The formula for the volume of a cylinder is V = π²h, where r is the radius of the base, h is the height of the cylinder, and π is a mathematical constant approximately equal to 3.14.
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what is the smallest number that you can add to 17,438 that will make the sum divisible by 25?
Check the picture below.
Suppose that Y1 and Y2 are independent, standard normal random variables. Find the density function of U = Y1^2 +Y2^2.
The cumulative distribution function (CDF) of U is also well known and is given by:
F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)
where γ is the lower incomplete gamma function.
What is the chi-squared distribution?
The chi-squared distribution is a continuous probability distribution that is widely used in statistics and other fields.
The random variable U = Y1^2 + Y2^2 has a well-known distribution called the chi-squared distribution with two degrees of freedom. The density function of U is given by:
[tex]f(u) = (1 / (2 \times \pi)) \times e^{(-u/2)} \times (u/2)^{(1/2 - 1)}[/tex]
where e is the base of the natural logarithm and π is the mathematical constant pi. This distribution has a positive support on the interval [0, +∞).
The cumulative distribution function (CDF) of U is also well known and is given by:
F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)
where γ is the lower incomplete gamma function.
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Two houses are 1.5 inches apart on a map. The actual distance between the houses is 10.8 miles. What is the scale of the map?
Answer:
I inch = 7.2 miles
Step-by-step explanation:
Proportion method is applied:
1.5 inches on a map = 10.8 miles of actual distance
∴ 1 inches on the map = x miles of the actual distance
Cross-multiplication is applied:
(1.5 inches)(x miles) = (1 inch)(10.8 miles)
x needs to be isolated and made the subject of the equation:
x miles = [tex]\frac{(1 inch)(10.8 miles)}{1,5 inches}[/tex]
Inches in the numerator and denominator will cancel eachother out:
x miles = [tex]\frac{10.8 miles}{1.5}[/tex]
x miles = 7.2 miles
∴ Scale on the map:
1 inch = 7.2 miles
Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. - 6 x <5 f(x) = { -27 *"ax + b, 125
The values of a = 17 and b = - 56
that make the following piece wise defined function both continuous and differentiable everywhere.
What is continuous function?A continuous function in mathematics is one that doesn't change value unexpectedly due to discontinuities, or breaks in the function's continuity. A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap. Thus, there aren't any discontinuities—rapid changes in value.
conditions are:
1.
f(x) is continuous if,
[tex]\lim_{x \to \ 5^{-}}f(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f(x)[/tex] = f(5)
2.
differentiable if,
[tex]\lim_{x \to \ 5^{-}}f^'(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f^'(x)[/tex]
for 1st condition:
⇒ [tex]\lim_{x \to \ 5^{-}}f(x) = \lim_{x \to \ 5^{+}}f(x)[/tex]
⇒ [tex]\lim_{x \to \ 5^{-}}(-3x -6) = \lim_{x \to \ 5^{+}}(-2x^2+ax+b)[/tex]
⇒ (-3 × (-5) - 6) = - 2(5)² + a(5) + b
⇒ - 21 = - 50 + 5a + b
⇒ 5a + b = 29 ................... (1)
For 2nd condition:
⇒ [tex]\lim_{x \to \ 5^{-}}f^'(x) = \lim_{x \to \ 5^{+}}f^'(x)[/tex]
⇒ [tex]\lim_{x \to \ 5^{-}} \frac{d}{dx} (-3x - 6) = \lim_{x \to \ 5^{+}} \frac{d}{dx}(-2x^2 + ax + b)[/tex]
⇒ - 3 = - 4x + a
⇒ - 3 = - 4 (5) + a
⇒ a = 17
Substitute a = 17 in equation (1) we get:
5(17) + b = 29
or, b = - 56
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The complete question is as follows:
a robot building club organizes competitions by weight categories called classes each clas permit a percent error of 0.3% in the 5 kg class one robot weighs 4.925 kg
The weight of the robot is within the error limit of 0.3%.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a robot building club organizes competitions by weight categories called classes each class permit a percent error of 0.3%. In the 5 kg class one robot weighs 4.925 kg.
Let -
{x} = 0.3% of 5
{x} = 0.3/100 x 5
{x} = 3/1000 x 5
{x} = 15/1000
{x} = 3/200
{x} = 0.015 .... Eq { 1 }
Now -
For the weight of the robot to be under the weight limit -
4.925 ≤ (5 - x)
4.925 ≤ (5 - 0.015)
4.925 ≤ 4.985 ..... Eq { 2 }
which is true.
Therefore, the weight of the robot is within the error limit of 0.3%.
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a 1.20 kg block is attached to a spring with spring constant 14.0 n/m . while the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 32.0 cm/s .
The amplitude of subsequent oscillations is 0.093 m.
What is Spring constant?The spring stiffness is quantified by the spring constant, or k. For various springs and materials, it varies. The stiffer the spring is and the harder it is to stretch, the bigger the spring constant.
Given that,
Mass of a block, m = 1.2 kg
Spring constant of the spring, k = 14.0 N/m
While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 32.0 cm/s or 0.32 m/s
We need to find the amplitude of the subsequent oscillations.
We can use the conservation of energy here. Initially, the kinetic energy of the block is maximum and then it gets converted to the potential energy of the spring.
Mathematically,
[tex]\frac{1}{2} mv^2=\frac{1}{2}kv^2[/tex]
A is the amplitude of subsequent oscillations.
[tex]A=\sqrt{(\frac{mv^2}{k} )} \\\\A=\sqrt{\frac{(1.2)(0.32)^2}{14} } \\\\A=0.093m[/tex]
So, the amplitude of subsequent oscillations is 0.093 m.
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What number should go in the space?
Multiplying by 1.15 is the same as increasing by _____%.
Answer: 115%
Step-by-step explanation:
100% = 1
10%=0.1
5%=0.05
100%+10%+5%=115%
1+0.1+0.05=1.15
Answer: 15
Step-by-step explanation:
x+x*15/100
x(1+.15)
1.15x
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter of his or her name, answer each of the following questions.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that the first student is a boy?
Answer: The sample space of possible outcomes is:
{SM, SJ, MJ, MS, JS, JM}.
There are 6 possible outcomes in the sample space, and 1 of these outcomes results in the first student being a boy (Franklin, represented by "F").
Therefore, the probability of the first student being a boy is P(A) = 1/6.
Step-by-step explanation:
An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modelled by the function p(x) = -x²+ 350x-6600 where p(x) is the profit in thousand Rupees and x is the number of automobiles made and sold. Answer the following questions based on this
model:
(i) When no cars are produce what is a profit/loss?
(ii) What is the break even point? (Zero profit point is called break even)?
(iii) What is the profit/loss if 400 cars are produced?
i) The profit/loss when no cars are produced is a loss of 6600 Rupees.
II) The break even point is at 20 cars
III) The profit/loss if 400 cars are produced is; a loss of 13400Rupees.
How to solve Profit functions?(i) When no cars are produced, x = 0.
Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;
p(0) = -0² + 350(0) - 6600 = -6600.
Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.
(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;
-x² + 350x - 6600 = 0
x = 20
Therefore, the break-even point is x = 20 cars. T
(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.
We find that p(400) = -400² + 350(400) - 6600
= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.
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I really need help with these questions pls?
Answer:
Top one is 3/8
Middle is 4/7
Bottom is 1/3
Step-by-step explanation:
PLS HELP me I am in need of help will mark brainiest
Answer:
Fourth option: √65/4
Step-by-step explanation:
Since the angles are similar, each of the angles of ΔEFG must be equal to each of the corresponding angles of ΔHIJ
Specifically, m ∠J in ΔHIJ = m∠G in Δ EFG
Let's first find ∠G
Since EFG is a right triangle,
tan(G) = EF/FG = √65/4
tan J must be the same as tan G = √65/4
This is the fourth option
The value of tanJ is in the right angled triangle HIJ√65 / 4
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Two triangles are similar if their corresponding angles are equal to each other.
Given that triangle EFG and triangle HIJ are similar, hence:
Angle G = Angle J
tanJ = tanG = √65 / 4
The value of tanJ is √65 / 4
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Solve, for 0 ≤ x < 360°, the equation
5 sinx - 5 cosx = 2
In response to the query, x is equal to 60°, 120°, 240°, and 300°. These four options are the answer to the equation.
What does equation mean in its entirety?A mathematical equation is a statement that two amount or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is applied when several or more factors must be considered jointly in order to understand or explain the whole situation.
This equation can be solved using the trigonometric identity:
[tex]sinx = \sqrt{ (1 - cos^2x)}[/tex]
This identity can be used as a substitution in the equation:
5 sinx - 5 cosx = 2
5 [tex]\sqrt{(1 - cos^2x) }[/tex] - 5 cosx = 2
5 sqrt[tex](1 - cos^2x)[/tex]) = 7 + 5 cosx
Squaring both sides:
25([tex]1 - cos^2x[/tex]) = 49 + 70 cosx + 25 [tex]cos^2x[/tex]
25 - 25 [tex]cos^2x[/tex] = 49 + 70 cosx + 25 [tex]cos^2x[/tex]
0 = 74 + 45 cosx
45 cosx = -74
cosx = -74/45 = -2/3
The inverted cosine function can be used to determine that x = cos-1(-2/3). x must be within the range of 0° to 360°, hence x must be 300°.
5 sin - 5 cos - 5(-1/2) = 5 sqrt(3)/2 + 5/2 = 2 + 2.5 = 2.5
Since the left side of the equation is not equal to 2, x = 300° is not a solution to the equation.
We can repeat this process for the other solutions to the equation:
x = 60°, x = 120°, x = 240°, and x = 300°
These are the four solutions to the equation for 0° <= x < 360°.
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rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. what is $\frac{q}{p}$?
The expression 6j^2 - 4j 12 can be rewritten as [tex]$-24(j\frac{1}{2})^2 -12$[/tex]where , and [tex]$q=-12$[/tex]. Thus,[tex]$\frac{q}{p}=-24$[/tex].
The expression[tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex], where c, p, and q are constants. To do this, we can factor out a common factor from the expression. In this case, the common factor is j. Then, we can rewrite the expression as [tex]$j(6j - 12)$[/tex] which simplifies to [tex]$-24j^2 -12$[/tex]. Dividing both sides by j, we can rewrite the expression as [tex]$-24(j\frac{1}{2})^2 -12$[/tex] where [tex]$c=-24$[/tex], [tex]$p=\frac{1}{2}$[/tex] and [tex]$q=-12$[/tex]. Thus, [tex]$\frac{q}{p}=-24$[/tex]. To summarize, the expression [tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex] where c, p, and q are constants, and [tex]$\frac{q}{p}=-24$[/tex].
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hey thank for helping me
Answer: -1
Step-by-step explanation:
When the graph g hits g=2, the y is -1
In a group of 21 students, 8 students take Art courses, 7 students take Music courses. Two students take both courses. A student is chosen randomly from this group.
What is the probability that the student takes either Art or Music courses?
Cavalleria Pizza sells only pizza. They offer five types of crust, two types of cheese, four meat toppings and
four vegetable toppings. If you must order exactly one type of cheese, one meat topping and one vegetable
topping on your pizza, how many different pizzas can you order at Cavalleria Pizza?
Answer:
3?
Step-by-step explanation:
im not sure sorry
Given a simplified rate of (2), determine the percent change.
The percent change of an object is the ratio of its final value to its initial value.
What is meant by percent change?The percentage of an item's final value versus its starting value is its percent change. By dividing the difference in data by the starting value, you can get the percent change.
"Rate" simply refers to the quantity divided by another number, typically 100, 1,000, or another multiple of 10. A rate per 100 is known as a percentage.
Percentage Change is the difference that results from deducting the old value from the new value, dividing by the old value, and multiplying the result by 100 to represent it as a percentage. In most cases, multiplying a fraction by 100 results in a percent conversion.
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Angel read for 1/2 hour. Margo read 1/6 hour. Who read for the greater amount of time.
If the public debt in 2006 was 6,783,231,062,743.62 and the budget for 2007 was in deficit by 595,821,633,586.70 what was the public debt in 2007?
Answer: The public debt in 2007 would be 6,783,231,062,743.62 + 595,821,633,586.70 = 7,379,052,696,330.32
Step-by-step explanation:
Math 5th grade
Roshaun walks around the city park. The square park measures 61 1/4 yards on each side. How far does Roshaun walk?
Answer: 245 yds
Step-by-step explanation:
61 1/4 times 4 = 245
Simplify expression[5-6+1]
Answer: 0
Step-by-step explanation:
Using GEMDAS
- Grouping
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
[5-6+1]
= [-1+1] because you add/subtract from left to right
= [0] because -1+1=0.
Answer is 0
What is the answer to x in this equation 4x+4=12?
Answer:
x=2
Step-by-step explanation:
4x+4=12
-4 -4
_______
4x=8
_____
4 4
x=2
what are some services offered by the banks and credit unions
Step-by-step explanation:
mortgages, lines of credit, checking and savings accounts, auto loans and the convenience of electronic banking and Automated Teller Machines (ATMs)
Step-by-step explanation:
Banks and credit unions offer a variety of financial services, including:
Checking and savings accounts
Personal loans
Mortgages
Credit cards
Investment products (e.g. mutual funds, individual retirement accounts (IRAs))
Foreign currency exchange
Online and mobile banking
Wire transfers
Automated teller machines (ATMs)
Insurance products (e.g. life, auto, homeowners)
Wealth management services
Small business banking services.
Note that the exact services offered may vary depending on the institution.
A parking lot is arranged with 9 parking spots in the first row, 15 parking spots in the second row, and 21 parking spots in the third row. If a person is aiming to park in first row, what is his probability in decimal form of getting a parking spot?
Answer:
21+15+9=45/4=that the answer
An emergency plumber charges $65 as a call out few plus an additional $75 per hour. He arrives at the house at 9:30 and works to repair a water tank. The total repair bill is $196.25. Use the variable t for the number of hours.
Answer:
Step-by-step explanation:
Answer:
Around 11:15 am
Step-by-step explanation:
Let h represents the number of hours the plumber works
Since the plumber charges $65 fee plus $75 per hour, the bill can be calculated by:
→ bill = 65 + 75h
Since the bill is $195.25
→ 195.25 = 65 + 75h
→ 75h = 130.25
→ h = 1.74
1.74 implies that the plumber worked almost 1 hour and 45 minutes. Since the plumber started at 9:30, the repair was completed around 11:15 am.
There are 80 people at the movie theater today 2/5 of the people are eating popcorn one for eating chocolate candy and the rest are eating record twist how many people are eating record toys
The people that are eating record toys are 48
How many people are eating record toysFrom the question, we have the following parameters that can be used in our computation:
People at the movies = 80
People are eating popcorn = 2/5
Using the above as a guide, we have the following:
Record toys = (1 - People are eating popcorn) * People at the movies
Substitute the known values in the above equation, so, we have the following representation
Record toys = (1 - 2/5) * 80
Evaluate
Record toys = 48
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Imagine that your instructor chose to use the Keep the Highest scoring method in Grade it Now mode. Here are your scores:First attempt: 2/10Second attempt: 10/10Third attempt: 3/10What would be your final score?
The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.
What is mode?In statistics, the value that consistently appears in a particular set is referred to as the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.
The scores at different attempts are:
First attempt: 2/10 = 0.2
Second attempt: 10/10 = 1
Third attempt: 3/10 = 0.3
The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.
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Solve with the box method
The polynomial n² + 6n - 1 can be factored as,
(n + 3 + √10)(n - 3 + √10)(3n - 2).
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, A product of two polynomials (n² + 6n - 1)(3n - 2).
Now, The quadratic expression n² + 6n - 1 can be factored as,
n² + 6n - 1.
[- 6 ± √(36 + 4)]/2.
= [- 6 ± √40]/2.
= [- 6 ± 2√10]/2.
= - 3 ± √10.
Therefore, (n² + 6n - 1)(3n - 2)
= (n + 3 + √10)(n - 3 + √10)(3n - 2).
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Fill in the Blank: Solve the following system of linear equations graphically. Then, fill in the blanks below with the solution.
Equation #1: y=14x−2
Equation #2: y=x+1
The solution to the system of equations is the ordered pair (
,
)
The solution to the system of equations is (13/3, 16/3).
The graph is given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
y = 14x - 2 _____(1)
y = x + 1 ______(2)
Now,
The graph of the equation is given below.
Now,
From (1) and (2).
14x - 2 = x + 1
14x - x = 1 + 2
13x = 3
x = 13/3
And,
y = x + 1
y = 13/3 + 1
y = 16/3
So,
The solution is (13/3, 16/3)
Thus,
The solution is (13/3, 16/3).
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please help with finsing the lemgth of x
Answer:
x = 5
Step-by-step explanation:
You want the length of x in the figure showing similar triangles.
ProportionThe bottom edge of the triangle is 2/3 of the left edge.
The similar triangles have the same ratio of side lengths. That means x is 2/3 of (3+4.5):
(2/3)(7.5) = 5
The length x is 5 units.