The exact value of a number is often what is meant when the word absolute is used in mathematics.
The absolute value of a number is often what is meant when the word absolute is used in mathematics. For mathematicians, knowing the absolute value is essential. To display a number's absolute value, vertical bars are placed on either side of the number. The absolute value on a number line denotes separation from zero.
The absolute value of a negative number is a positive number. The absolute value of one positive number is equal to that of another positive number. No matter what its sign, a number's absolute value is always its non-negative value. For instance, 5 is also the absolute value of 5, as is the absolute value of -5.
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the eifell tower 324 m tall. the height was halved repeatedly to make a model around30 cm. what power of 2 was the height divided by
The power of two by which the height was divided is given as follows:
Tenth power of 2.
How to obtain the power of two by which the height was divided?The power of two by which the height was divided is obtained applying the proportions in the context of this problem.
The equation that relates the heights and the scale factor is given as follows:
New height = Old height / Scale factor.
The parameters for this problem are given as follows:
Old height: 324 m.New weight: 30 cm = 0.3 m, as 1 m = 100 cm.Then the scale factor is obtained as follows:
Scale factor = 324/0.3
Scale factor = 1080.
The tenth power of 10 is given as follows:
2^10 = 1024.
Which is close to 1080, and hence the height was divided by the tenth power of 2.
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the price of fuel may increase due to demand and decrease due to overproduction. marco is studying the change in the price of two types of fuel, A and B, over time.
the price f(x), in dollars, of fuel A after x months is represented by the function below:
f(x) = 2.27(0.88)^x
part A: is the price of fuel A increasing or decreasing and by what percentage per month? justify your answer
part B: the table below shows the price g(m), in dollars, of fuel B after m months:
m (number of months): 1 | 2 | 3 | 4
g(m) (price in numbers): 3.44 | 3.30 | 3.17 | 3.04
which type of fuel recorded a greater percentage change in price over the previous months? justify your answer
a) The price of fuel A is decreasing by a percentage of 12% per month.
b) The greater percentage decay is of type A fuel.
How to model an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the parameters are given as follows:
a is the initial value.b is the rate of change.For a decaying exponential function, we have that:
b = 1 - r, |b| < 1.
In which r is the decay rate.
For fuel type A, the decay rate is given as follows:
1 - r = 0.88
r = 0.12.
For fuel type B, the parameter b is given as follows:
b = 3.30/3.44
b = 0.96.
Hence the decay rate is of:
1 - r = 0.96
r = 0.04.
(which is a lower decay rate than the 0.12 of fuel type A).
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Find the equation of the tangent line to the curve f(x) = 4x^3 - 2x^2 + 3x - 10 when x=4
Answer:
Is your question complete? there's no y term
Answer:
Refer to the image attached.
Step-by-step explanation:
Tanner is building birdhouses in shop class, and he has a total of 495 nails on hand. A small birdhouse requires 25 nails and a large birdhouse requires 59 nails.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
An inequality in standard form that describes this situation is 25x + 59y ≤ 495.
How to write an inequality that represents this situation?In order to write an inequality that represents or describes this situation, we would assign variables to the number of nails required by the small birdhouse and large birdhouse respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the small birdhouse.Let the variable y represent the large birdhouse.Since Tanner has a total of 495 nails on hand and a small birdhouse requires 25 nails while a large birdhouse requires 59 nails, an inequality that represents or describes this situation can be written as follows;
25x + 59y ≤ 495.
In conclusion, we can reasonably infer and logically deduce that the total number of nails required by both the small birdhouse and large birdhouse is less than or equal to 495 nails.
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Give the domain and range. A relation. An arrow goes from 1 to negative 1, from 2 to 0, from 3 to 1. a. domain: {1, 2, 3}, range: {1, 0, 1} b. domain: {–1, 0, 1}, range: {1, 2, 3} c. domain: {1, 0, 1}, range: {1, 2, 3} d. domain: {1, 2, 3}, range: {–1, 0, 1} Please select the best answer from the choices provided A B C D
The domain and the range of the relation are given by the following option:
d. domain: {1, 2, 3}, range: {–1, 0, 1}.
How to obtain the domain and the range of the relation?The domain of a function is the set that contains all the input values, which are the values from which the arrow departs.
The range of a function is the set that contains all the output values, which are the values from which the arrow arrives.
Considering these definitions and the description of the set, the correct option is given by option d.
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Which of the following method solves initial values problem by using sloped at two points ?
A. Euler method
B. Heuns method
C. RK method
D. picards method
The method that solves initial values problem by using sloped at two points is Heuns method.
Therefore the answer is B. Heuns method.
The Heun's method, also known as the improved Euler method, is a numerical method used to solve initial value problems for ordinary differential equations. It is a second-order method, which means that it uses the slope at two points (the starting point and one other point) to estimate the solution at a future point.
Heun's method is an explicit method which is an extension of the Euler method, by using the slope at the midpoint between the current and the next steps to improve the accuracy of the solution.
Euler method is a first-order method which estimates the solution at a future point by using the slope at one point only.
RK method is a family of methods that ranges from first-order to fourth-order method, but it uses a combination of the slopes at different points to estimate the solution.
Picard's method is a method of solving differential equations that is based on the idea of repeatedly applying a function to an initial value until a fixed point is reached. It's a method that does not use slopes.
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round 6 978 781 641 to nearest 100
Answer:mm
Step-by-step explanation:
Answer:
Step-by-step explanation: 6 978 781 600
Marcel just started her own business making cookies. She sells the cookies in boxes, charging $15.00 per box. It costs her $50.00 to buy the supplies. She wants to calculate how many boxes she must make to earn a profit of at least 245.00.
Answer:
Step-by-step explanation:
To calculate how many boxes of cookies Marcel needs to make to earn a profit of $245.00, we need to use the following formula:
Profit = (Revenue - Expenses) / Number of boxes
We know that the revenue is $15.00 per box and the expenses are $50.00. We also know that the profit should be at least $245.00.
So we can substitute these values into the formula and solve for the number of boxes:
$245.00 = ($15.00 - $50.00) / x
Where x is the number of boxes.
To solve for x, we'll need to multiply both sides of the equation by x:
$245.00*x = ($15.00 - $50.00)
$245.00*x = -$35.00
x = -$35.00/$245.00 = -0.142857143
The number of boxes is a negative value which is not possible, so Marcel will not earn a profit of $245.00. She will need to increase her revenue or decrease her expenses to reach a profit of $245.00.
PLEASEEEE HELP!!!
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
Answer:
The two spaceships will meet in 4 hours.
Step-by-step explanation:
We can start solving the problem using the formula for distance, velocity, and time which is
Distance = Velocity x Time
Let x be the number of hours it will take for the two spaceships to meet.
The distance that the first spaceship travels is 110,000 x x km
The distance that the second spaceship travels is 90,000 x (x+1) km, since the second spaceship started 1 hour later.
The total distance that the spaceships travel is equal to the distance between the space stations, so we can set up the equation:
110,000x + 90,000(x+1) = 710,000
Solving for x, we can find that x = 4 hours.
So the two spaceships will meet in 4 hours.
how to prove the median of a trapezoid is parallel to the bases and equal in length to the average of their lengths?
The median of a trapezoid is parallel to the bases and equal in length to the average of their lengths. This is due to the midpoint theorem and the definition of the average.
The median of a trapezoid is a line segment that connects the midpoints of the non-parallel sides of the trapezoid. By the definition of a trapezoid, the two parallel sides (the bases) are of equal length.To prove that the median of a trapezoid is parallel to the bases and equal in length to the average of their lengths, we will make use of the midpoint theorem and the definition of the average.First, let's look at the midpoint theorem: If two points are the midpoints of two sides of a trapezoid, then the line connecting them is parallel to the bases. Now, let's look at the definition of the average: The average of two numbers is equal to the sum of the numbers divided by two.Now, let's apply these two concepts to the median of a trapezoid. As stated above, the median of a trapezoid connects the midpoints of the non-parallel sides of the trapezoid. By the midpoint theorem, the line connecting the midpoints of the non-parallel sides of the trapezoid is parallel to the bases. Next, we need to prove that the median of a trapezoid is equal in length to the average of the lengths of the bases. We can do this by noting that the length of the median of a trapezoid is equal to the sum of the lengths of the bases divided by two. This is because the median line segment connects the midpoints of the bases, so the length of the median is equal to half the sum of the lengths of the bases.Therefore, we can conclude that the median of a trapezoid is parallel to the bases and equal in length to the average of their lengths.Learn more about median here
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Which statement comparing milliliters and liters is true?
200 milliliters > 3 liters
500 milliliters 4 liters
3,000 milliliters < 4 liters
4,000 milliliters < 3 liters
The correct statement is 3000 ml<4l
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Option 3 as 3000 ml<4 liters
we know that 1 liter=1000 ml
Thus 4 liters=4000 ml
Hence, Option C is the correct statement.
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A can of motor oil weighs 31 ounces. When one half of the oil in the can has been poured
out of the can and the remaining can and oil weighs 16 ounces how much does the can
weigh?
The value weight of the can is 1 ounce
What is subtraction?To subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less. The minuend, subtrahend, and difference are parts of a subtraction problem.
The total weight of the can and oil is 31 ounces .
When ½ of the the oil is poured the weight of the can and oil is 16 ounces.
Therefore the weight of ½ of oil is 31-16 = 15 ounces
if ½ of the oil weighs 15 ounces
full oil will weigh 15× 2 = 30 ounces
the weight of the can = 31-30 = 1ounce
Therefore the weight of the can is 1 ounce
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Sandy used a virtual coin toss app to show the results of flipping a coin 80 times, 800 times, and 3,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 80 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 800 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 3,000 flips
Answer:
Sandy's experimental probability was closest to the theoretical probability in the experiment with 3,000 flips.
In probability, as the number of trials increases, the experimental probability is expected to converge to the theoretical probability. This is known as the Law of Large Numbers. Since the experiment with 3,000 flips had the most number of trials, it is most likely that the experimental probability was closest to the theoretical probability in this experiment. The larger the sample size, the more likely it is to reflect the true probability of the coin being a fair coin.
Q7 a and b is confusing, is there any chance someone could help?
Answer:
a. 12 sides
b. Not possible
Step-by-step explanation:
a.
[tex]d=\frac{1}{2} n(n-3)[/tex]
[tex]\frac{1}{2}n^{2}-\frac{3}{2} n=54[/tex]
multiply by 2
[tex]n^{2} -3n=108[/tex]
equation
[tex]n^{2} -3n-108=0[/tex]
factor
[tex](n-12)(n+9)[/tex]
[tex]n-12=0\\n=12[/tex]
b.
[tex]n^{2} -3n=33[/tex]
[tex]n^{2} -3n-33=0[/tex]
The roots of the equation are decimal numbers
The number of sides must be integer
So there is no polygon with 33 diagonals.
Hope this helps
What is a infinitely many in math?
In mathematics, having an infinitely large amount or cardinality is referred to as having an infinity many.
Endless sets actually have an infinite number of components. If a set has continuity on both sides or is unbounded from start to finish, we can refer to it as infinite. For instance, the set of whole numbers W = 0, 1, 2, 3, etc. is an infinite set since it has an unlimited number of items. The set of real numbers is one of the uncountably infinite sets. Dots are used to symbolize the elements of an infinite set to denote the set's infinity.
There are some properties of infinite many solutions.
The superset of an infinite set is also infinite.
The subset of an infinite set may or may not be infinite.
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in the xyxyx y plane a line that has the equation y cy cy equals c for some constant ccc intersects a parabola at exactly one point if the parabola has the equation y x 2 5xy x 2 5xy equals minus x squared plus 5 x what is the value of ccc
The value of c can be found by solving the equation yc^2 = -x^2 + 5x.
What is square?Square is a two-dimensional shape with four equal sides and four equal angles of 90 degrees each. It is a regular polygon and is one of the most common shapes in mathematics. Squares can be found in nature, architecture, and art. They are used to divide and organize space, and are often used as a form of measurement in areas such as geometry, construction, and engineering.
After rearranging the equation, we can solve for c by using the quadratic formula. c = (x^2 - 5x)/(x^2). Therefore, the value of c is (x^2 - 5x)/(x^2).
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Can a 3x3 matrix have infinite solutions?
Yes, a 3x3 matrix can have infinite solutions. This is because if the determinant of the matrix is zero, the system of equations has an infinite number of solutions.
A 3x3 matrix is a system of three equations with three unknowns.
For a system of linear equations to have a unique solution, the determinant of the matrix must not be zero. If the determinant of the matrix is zero, then the system of equations has an infinite number of solutions.
Therefore, a 3x3 matrix can have infinite solutions if the determinant of the matrix is zero.
Yes, a 3x3 matrix can have infinite solutions. This is because if the determinant of the matrix is zero, the system of equations has an infinite number of solutions.
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Can 1.5 cm 2 cm and 2.5 cm be the sides of right-angled triangle?
Yes, it is possible to draw a right angled triangle with sides 1.5cm , 2cm , and 2.5cm.
As given in the question,
In the given triangle,
Measure of the side length of the given triangle are :
1.5cm , 2cm , and 2.5cm
In this triangle longest side is equal to 2.5cm.
Given triangle is right angled triangle check whether Pythagoras theorem satisfied the measure of the sides of the triangle.
Hypotenuse represents the longest side.
( Hypotenuse)² = ( Side 1 )² + ( Side 2)²
Right hand side
= ( 1.5 )² + ( 2 )²
= 2.25 + 4
= 6.25
= ( 2.5 )²
= Hypotenuse²
It satisfied the Pythagoras theorem.
Therefore, the given sides of the triangle represents it is a right angled triangle.
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A circle has a diameter of 7.6 cm
workout the circumferences of the circle
give your answer correct to 3 significant figures
The circumference of the circle is 23.864
In order to calculate the circumference of a circle, you need to multiply the Diameter of the circle with value of π (pi) which is 3.14.
In the given question,
given, d = 7.6cm
formula : C = d x π
therefore, C = 7.6 x 3.14 = 23.864cm
Write the answer correctly to 3 significant figures.
Alternatively, Circumference can also be calculated by using the value of the radius of the circle. We know, Radius = Diameter/2
Therefore, C = ( 2 x r ) x π
Symbols:
π = pi ( value = 3.14)
d = diameter
r = radius
C = circumference
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In ΔEFG, g = 4.3 cm, e = 9.1 cm and ∠F=116°. Find the length of f, to the nearest 10th of a centimeter.
The length of f in the triangle is 11.6 cm
What is cosine rule?In trigonometry, the Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
Cosine rule is therefore given as:
f² = g²+e²-2bccos F
f² = 4.3²+9.1²-2×4.3×9.1cos116
f² = 18.49+82.81-78.26(-0.44)
f² = 101.3+34.43
f² = 135.73
square root both sides
f = √135.73
f = 11.6 ( nearest tenth of centimeter)
therefore the length of f is 11.6cm
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chris and jacob are friendly competitors who sit in the back of the class. both are about to take the act. they agree that if one of them scores 5 or more points better than the other, the loser will buy the winner a pizza. suppose that they have the same ability so that each of their scores vary normally with mean 24 and standard deviation 2. what is the probability that the scores differ by 5 or more points in either direction?
0.0764 is the probability that the scores differ by 5 or more points in either direction
What is probability?The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
According to the information, the mean and standard deviation of "X" are:
μ(X) = 24
σ (X) = 2
We have to find the probability the scores differ by 5 or more points on either direction.
Consider X₁ and X₂ as the random variable, which showing the scores of Leon and Fred.
D = X₁ - X₂
According to the information the two scores are independent
The mean of μ(D) = 0
The standard deviation σ(D) = 2.828
Let's standardize D = -5
z = [x - μ(D)] / σ(D)
z = - 1.77
Let's standardize D = 5
z = [x - μ(D)] / σ(D)
z = 1.77
Using a table of typical normal probabilities as a guide:
= P (D ≤ -5) or P (D ≥ 5)
= P (z ≤ -1.77) + P (z ≥ 1.77)
= P (z ≥ 1.77) + P (z ≥ 1.77)
= 2P (z ≥ 1.77)
= 2(1 - P (z ≤ 1.77))
= 2 (1 - 0.9618)
= 0.0764
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In the triangle shown, for $\angle A$ to be the largest angle of the triangle, it must be that $m
The least possible value of n−m, expressed as a common fraction is 17/6.
By Triangle Inequality Theorem,
(x + 4) + 3x > x + 9
So 4x + 4 > x + 9
3x > 5
x > 5/3
If angle A is the largest angle, the side opposite to angle A will be the largest length, so
x + 9 > x + 4 (which is possible for all values of x)
and x + 9 > 3x
2x < 9
x < 9/2
Therefore 5/3 < x < 9/2. So m = 5/3 and n = 9/2
So calculating value of n - m
n - m = 9/2 - 5/3
= 27/6 - 10/6
= 17/6
--The question is incomplete, the complete question is as follows--
"In the triangle shown, for ∠A to be the largest angle of the triangle, it must be that m<x<n. What is the least possible value of n−m, expressed as a common fraction?"
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when mr. adams calculated his students' algebra test scores, he noticed that two students had extremely low scores. which measure of central tendency is affected most by the scores of these two students?
Mean has been affected most by the scores of these two students.
A bunch of scores is averaged to form the mean. The total scores were divided by the total scores. When population samples are tiny, the mean is susceptible to extreme scores.
When you add up all the individual scores and divide that total by the number of students, you obtain the mean, which is the arithmetic average score.
The average performance of a group of students on a test is represented by their mean scale score. A mean scale score is derived specifically by summing together the scores of each individual student and dividing that amount by the number of scores. It is additionally known as an average.
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Find the area of the following figure. Pictures are not drawn to scale. Round answers to the nearest tenth.
The area of the trapezoid is 210 squared '
How to find the area of a trapezoid?
The area of a trapezoid be be calculated using the formula:
A = 1/2(a+b)h
where:
a is the length of one of the parallel sides of the trapezoid
b is the length of the other parallel side of the trapezoid
h is height is the distance between the two parallel sides (perpendicular to the bases)
a = 12', b = 18 + 5 = 23' and h = √(13²-5²) = 12'
A = 1/2(a+b)h
A = 1/2(12+23)12
A = (35)6
A = 210 squared '
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What is the area of triangle abc?
Therefore , the solution of the given problem of triangle comes out to be area of triangle = 0.25 unit square.
What does a triangle actually mean?Triangles are polygons because they have four sides or more. Its form is simple and geometric. An angle square with the letters ABC is known as a triangle. When the sides remain not collinear, Euclidean geometry generates a singular plane or square. Having three parts and three corners makes a triangle a polygon. The corners of a triangle are where the three sides meet. Angles in a triangle add up at 180 °.
Here,
Given:
So , the vertices are of unit length :
=> Area of triangle = 1/2 * b*h
=> Area of triangle = 1/2 * 1 * 0.5
=> Area of triangle = 0.25 unit square.
Therefore , the solution of the given problem of triangle comes out to be area of triangle = 0.25 unit square.
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how many gallons will daniel need? help please thank you
Measure wall height from floor to ceiling. Exclude baseboards and moldings. Measure length of each wall including doors and windows.
What exactly is the wall formula?Walls. Use the basic formula of Length x Width = Area to determine the area of a wall. Then, using the same approach, calculate the individual area of windows and doors. After you’ve taken all of these measurements, deduct the area of the windows and doors from the overall wall area. Methods of longwall and shortwall Long walls are those that run the length of the room, whereas short walls are those that run perpendicular to the length of the room.
Next, consider which unit of measurement is most appropriate for measuring a wall. Very tiny units such as inches, centimeters, and millimeters can be ruled out. We can also eliminate.
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nikki has to travel a total of 351 miles. she travels the first 216 miles in 4 hours. it takes her 2.5 hours to travel the rest of the way. is she going faster, slower, or the same speed for the second part of her trip? (hint: how far did she travel on the second part of her trip?)
Nikki's speed during the second part of her trip is the same as her speed during the first part of her trip, 54 miles/hour.
Nikki has to travel a total of 351 miles, and she travels the first 216 miles in 4 hours. The second part of her trip is the remainder of the distance she needs to travel, so we can calculate it by subtracting the distance she traveled in the first part from the total distance:
Second part of the trip = 351 miles - 216 miles = 135 miles
It takes Nikki 2.5 hours to travel the second part of her trip. To calculate her speed, we can divide the distance she traveled by the time it took her:
Speed = Distance / Time
Speed for the second part of the trip = 135 miles / 2.5 hours = 54 miles/hour
To compare her speed during the first and second parts of the trip, we can calculate the speed of Nikki during the first part of the trip:
Speed for the first part of the trip = 216 miles / 4 hours = 54 miles/hour
Nikki's speed during the second part of her trip is the same as her speed during the first part of her trip, 54 miles/hour.
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The four triangles at right are placed in a bag. If you reach into the bag without looking and pull out one triangle at random, what is the probability that: Homework Help ✎
The triangle is scalene?
The triangle is isosceles?
At least one side of the triangle is 6 cm?
Probability of scalene triangle, isosceles triangle and at least one side of the triangle is 6 cm are 1/4, 1/2 and 1/2 respectively
How to determine the probability of having a scalene triangle?Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.
A probability of 0 means that an event is impossible, a probability of 1 means that an event is certain to occur.
A scalene triangle is a triangle with no equal sides.
An isosceles triangle is a triangle with two equal sides.
An equilateral triangle is a triangle with all 3 sides equal.
Check the attached image to see how I labeled the triangles
Triangle 1 is isosceles (two sides with 6 cm each)
Triangle 2 is scalene
Triangle 3 is isosceles (two sides with 10 cm each)
Triangle 4 is equilateral (three sides with 4 cm each)
Probability (Scalene triangle) = 1/4
Probability ( isosceles triangle) = 2/4 = 1/2
Probability ( At least one side is 6 cm) = 2/4 = 1/2
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The grain silo pictured above has a radius of 1.7 m. How much paint is required to
completely cover the sides and top of the grain silo once?
The amount of paint required for the grain silo is calculated to be
106.61 m²
How to find the paint required to cover the grain siloThe figure is made up of 2 objects a cylinder and the conical cover. Therefore, we solve for total surface area TSA of the cylinder and the cone and add
TSA for cylinder
= 2πr (h + r)
where
h = 6.2 m
r = 1.7 m
= 2π * 1.7 (6.2 + 1.7)
= 26.86π
TSA for cone
= πr (l + r)
where
l = slant height = 1.9 m
r = 1.7
= π * 1.7 (1.9 + 1.7)
= 6.12π
how much paint required = TSA for cone + TSA for cylinder
how much paint required = 6.12π + 26.86π
how much paint required = 32.98π
how much paint required = 103.61 m²
the thickness of the painting will say the volume of paint
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The total was $29.00 after adding a $4.00 tip to the bill for a family of five, each of whom ordered a hot dog. What was the price of a hot dog?
A. 4 - 5x = 29; $5.00
B. 4 + 5x = 29; $5.00
C. 29 - 5x = 4; $5.00
D. 5x = 29 = 4; $5.00
Answer: The answer is B
Step-by-step explanation:
4( the tip) +5 (# of family) * x( unknown cost of hot dog) = 29 (total)
