Using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.
What is the percentage?A% is a mathematical figure or ratio that denotes a percentage of 100.
Ratios, fractions, and decimals are some of the numerous ways to represent a dimensionless connection between two numbers.
The symbol "%" is generally written after the integer to denote percentages.
A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics.
So, in the given situation we will use percentages to get what % of recyclable plastic is used as follows:
= 460/100 * 20
= 4.60 * 20
= 92 grams
Therefore, using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.
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NO LINKS!! URGENT HELP PLEASE!!!
Express the statement as an inequality part 7a^2
The statement, "t is not less than 7" as an inequality is E. t ≥ 7.
The statement, " the negative of z is not greater than 8" is A. - z ≤ 8 .
How to represent as inequalities ?The statement "t is not less than 7" means that t can be equal to 7 or greater than 7, so we can write this as:
t ≥ 7
Therefore, the correct inequality for the statement is t ≥ 7.
Similarly, the statement "the negative of z is not greater than 8" means that the opposite of z, which is -z, can be equal to -8 or less than -8, so we can write this as:
-z ≤ 8
Multiplying both sides of the inequality by -1 gives:
z ≥ -8
Therefore, the correct inequality for the statement is z ≥ -8.
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Answer:
e) The correct option is: t≥7
The phrase "t is not less than 7" means that t can be equal to 7 or any value greater than 7, but it cannot be less than 7. Therefore, we use the greater than or equal to a symbol (≥) to represent this statement.
here's an explanation of each option:
t = 7: This statement indicates that the value of t is exactly 7. If this statement is true, then t cannot be greater than or less than 7.t > 7: This statement indicates that the value of t is greater than 7. If this statement is true, then t can be any value that is greater than 7.t < 7: This statement indicates that the value of t is less than 7. If this statement is true, then t can be any value that is less than 7.t ≤ 7: This statement indicates that the value of t cannot be greater than 7, but it can be less than or equal to 7. If this statement is true, then t can be 7 or any value less than 7.t ≥ 7: This statement indicates that the value of t cannot be less than 7, but it can be greater than or equal to 7. If this statement is true, then t can be 7 or any value greater than 7.To express the statement t≥7 as an inequality in terms of 7a^2, we can simply multiply both sides by 7a^2, like this:t * 7a^2 ≥ 7 * 7a^2
Simplifying the right-hand side of the inequality, we get:49a^2
Therefore, the inequality in terms of 7a^2 is:t * 7a^2 ≥ 49a^2
Note that this inequality is equivalent to t ≥ 7, which is what we started with.
f) The correct option is:-z ≤ 8
The phrase "the negative of z is not greater than 8" means that -z cannot be greater than 8. In other words, -z is less than or equal to 8. To express this as an inequality, we use the less than or equal symbol (≤) and write "-z ≤ 8".
here's an explanation of each option:
Note that only the first option (-z ≤ 8) accurately represents the original statement "The negative of z is not greater than 8". The other options either represent a different statement or contradict the original statement.
The statement "the negative of z is not greater than 8" can be expressed as an inequality in terms of 7a^2 as follows:
-z ≤ 8
Since we cannot multiply or divide by a negative number when we are working with inequalities, we will multiply both sides of the inequality by -1. Remember that whenever we multiply or divide both sides of an inequality by a negative number, we must reverse the direction of the inequality symbol. So, we have:z ≥ -8
Multiplying both sides by 7a^2, we get:7a^2 * z ≥ -8 * 7a^2
Simplifying the right-hand side, we get:-56a^2
Therefore, the inequality in terms of 7a^2 is:7a^2 * z ≥ -56a^2
So, the statement "the negative of z is not greater than 8" can be expressed as the inequality 7a^2 * z ≥ -56a^2.
A 40" screen television at a popular electronics retailer is priced at $600. The wall mount for this sized television costs $29.99.
Part A: If Jamie purchases the television and the wall mount and has a coupon for 30% off, how much will her subtotal be? Show all necessary work. (4 points)
Part B: If Jamie makes the purchase in a state with a 7% state sales tax, what will her final total be? Show all necessary work. (2 points)
Part C: The electronics retailer is extending a special offer to install the wall mount and television for free. However, Jamie decides to tip the installation specialist 10% of the original purchase price before the discount is applied. How much would her new total be, including tax, discount, and tip? Show all necessary work. (4 points)
The cost of the television and wall mount before discount is $600 + $29.99 = $629.99
After a 30% discount, the subtotal is:
$629.99 x 0.70 = $440.99
The sales tax is 7% of the subtotal:
$440.99 x 0.07 = $30.87
The final total is the subtotal plus the sales tax:
$440.99 + $30.87 = $471.86
The original purchase price before discount is $600.
10% of $600 is $60.
So Jamie decides to tip the installation specialist $60.
After the discount, the subtotal is $440.99 (as calculated in Part A).
The sales tax is 7% of the subtotal:
$440.99 x 0.07 = $30.87
The new total is the subtotal plus the sales tax and the tip:
$440.99 + $30.87 + $60 = $531.86
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A six sided dice is rolled. What is the probability of rolling a number greater than 2?
The probability of rolling a number greater than 2 is 2/3
Calculating the probability of rolling a number greater than 2?From the question, we have the following parameters that can be used in our computation:
Rolling a number cube once
Using the above as a guide, we have the following:
Sample space, S = {1, 2, 3, 4, 5, 6}
In the above sample space, we have
Outcomes greater than 2 = {3, 4, 5, 6}
So, we have
P(greater than 2) = n(Outcomes greater than 2)/n(Sample space)
Substitute the known values in the above equation, so, we have the following representation
P(greater than 2) = 4/6
When evaluated, we have
P(greater than 2) = 2/3
Hence, the probability is 2/3
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in the figure below lines m and n are parallel m2= 62 and m3=73
Answer: 135
Step-by-step explanation:
Each side of a square office is 3 meters long. It will cost $87.41 per square meter to replace the carpet in the office. What would be the total cost to replace the carpet?
As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.
what is a square?The geometric shape of a square has 4 equal ends and four equal, right-angled angles (90 degrees). It is an unusual instance of a rectangle with equal sides. The symbol "" is frequently used to denote a square, which is a two-dimensional figure. A square's area is equal to the sum of its sides doubled, or s2, where s denotes the width of a side. The circumference of a square, or 4s, where s is the height of a side, is the total of the lengths among all four sides. Many real-world uses for squares can be found in the fields of mathematics, architecture, construction, and design.
given
The square office's area is:
[tex]C = 9 \times $87.41 = $786.69[/tex]
A = s2 = 3 2 = 9 metres square
To completely replace the carpet, it would cost:
Cost per square meter equals C = A.
where a square meter costs $87.41. When we change the values, we obtain:
As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.
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A slow pitch softball diamond is actually a square 60' on side how far is it from home to 2nd base
Answer:
The distance from home to second base is approximately 84.85 feet in a slow pitch softball diamond that is 60 feet on each side.
Step-by-step explanation:
In a softball diamond that is 60 feet on each side, the distance from home to second base is approximately 84.85 feet. This is based on the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the distance from home to second base forms the hypotenuse of a right triangle with legs that are each 60 / sqrt(2) feet long. Using the Pythagorean theorem, we can calculate that the distance from home to second base is approximately 84.85 feet.
What are the factors of polynomial function g? G(x) = x^3 + 2x^2 - x - 2
To find the factors of the polynomial function g(x) = x^3 + 2x^2 - x - 2, we can use different methods such as long division, synthetic division, or grouping.
Using long division, we can divide g(x) by (x-1), which is a factor by the factor theorem:
x^2 + 3x + 2
___________________________
x - 1 | x^3 + 2x^2 - x - 2
- (x^3 - x^2)
--------
3x^2 - x
- (3x^2 - 3x)
----------
2x - 2
- (2x - 2)
--------
0
Therefore, we have factored g(x) as:
g(x) = (x - 1)(x^2 + 3x + 2)
We can further factor the quadratic term using factoring or quadratic formula to obtain the complete factorization of g(x).
The factors of polynomial function g(x) = x³ + 2x² - x - 2 are (x-1), (x+1), and (x+2).
This can be obtained by factoring the polynomial using the grouping method.
Using this method, we group the first two terms together and the last two terms together, resulting in (x²{2 + 2)(x-1) = 0. This gives us two possible roots, x = 1 and x = ±√2i.
However, as we are only interested in real factors, we only consider the real root of x = 1.
G(x) can then be divided by (x-1) using linear long division, yielding the quotient x² + 3x + 2. This quotient can then be factored as (x+1)(x+2). Therefore, the factors are (x-1), (x+1), and (x+2).
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pls!! :(( a golf ball has been hit off of the tee at an angle of elevation of 30 degrees and an initial velocity of 128 ft/sec
how long is the ball in the air (hang time)?
what is the maximum height of the ball?
how far, horizontally, does the ball travel in the air?
According to the information, the horizontal distance traveled by the ball is 443.404 feet.
How to calculate the distance traveled by the ball?We can use the kinematic equations of motion to solve for the hang time, maximum height, and horizontal distance traveled by the golf ball.
First, we need to resolve the initial velocity vector into its horizontal and vertical components. The vertical component will determine the maximum height and hang time, while the horizontal component will determine the horizontal distance traveled.
The initial velocity can be represented as:
v0x = v0 cos(theta) = 128 cos(30) = 110.851 ft/secv0y = v0 sin(theta) = 128 sin(30) = 64 ft/secwhere v0 is the initial velocity, theta is the angle of elevation, v0x is the horizontal component of the initial velocity, and v0y is the vertical component of the initial velocity.
Now we can use the kinematic equations to solve for the hang time, maximum height, and horizontal distance traveled.
Hang time (time in air):
We can use the vertical motion equation to solve for the time when the ball reaches its maximum height:
v = v0y - gt0 = 64 - 32tt = 2 secondsSince the ball will be in the air for twice the time it takes to reach its maximum height, the hang time is:
2t = 4 secondsMaximum height:
We can use the vertical motion equation to solve for the maximum height reached by the ball:
y = v0y t - 1/2 gt^2y = 64(2) - 1/2 (32)(2)^2y = 64 ftTherefore, the maximum height of the ball is 64 feet.
Horizontal distance traveled:
We can use the horizontal motion equation to solve for the horizontal distance traveled by the ball:
x = v0x t
x = 110.851(4)
x = 443.404 ft
Therefore, the horizontal distance traveled by the ball is 443.404 feet.
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An item is worth $240 now. This is 30% of what it was originally worth. What was it originally worth?
Where are the x-intercept(s) of the graph?
The x-intercept of the graph is (0,0).
What is an illustration of an x-intercept on a graph?
On a graph, the x-intercept is the point at which a line crosses the x-axis. At that time, the y coordinate has no value. The y-intercept is the point where the line crosses the y-axis. The x coordinate has no value. For example, y = x + 5 would intersect the x-axis at (-5, 0), forming the x-intercept.
From the figure, it is clear that the line crosses the X-axis at the origin, which means that x - coordinate 0 keeping y -coordinate is also zero.
Which means that the x-intercept of the graph is (0,0).
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anyone can help with these?
Answer:
m∠B=63 degrees
AC≈23.6 units
AB≈26.4 units
Step-by-step explanation:
since the measures of ∠A and ∠C are given, we add 90 (∠C) to 27 (∠A) and x (∠B) which equals 180 by triangle angle sum theorem.
after isolating the variable, m∠B=63 degrees
we then use law of sin to find AC and AB
since [tex]\frac{sin(A)}{a}[/tex] is already given, use that to find both AC and AB
the equation for AC would be: [tex]\frac{sin(27)}{12} =\frac{sin(63)}{AC}[/tex]
the equation for AB would be: [tex]\frac{win(27)}{12} =\frac{sin(90)}{AB}[/tex]
after isolating the variables, AC≈23.6 units and AB≈26.4 units
Lanzamos 1000 veces un dado de 6 caras. Calcula la probabilidad de obtener entre 400 y 500 veces un 6.
La probabilidad de obtener entre 400 y 500 veces un 6 en 1000 lanzamientos es de 0.
Calculando la probabilidadEste es un problema de distribución binomial con una probabilidad de éxito del evento (obtener un 6 en un lanzamiento de un dado de 6 caras) de 1/6.
Podemos utilizar una aproximación normal para la distribución binomial si el número de ensayos es grande y la probabilidad de éxito es moderada.
La aproximación normal para una distribución binomial se define como:
Z = (X - μ) / σ
donde X es el número de éxitosμ es el valor esperado de Xσ es la desviación estándar de X.El valor esperado de X es:
μ = n * p = 1000 * 1/6 = 166.67
La desviación estándar de X es:
σ = √(n * p * (1-p)) = √(1000 * 1/6 * 5/6) = 11.79
x = 400: z = (X - μ) / σ = (400 - 166.67) / 11.79 = 19.79
x = 500: z = (X - μ) / σ = (500 - 166.67) / 11.79 = 28.27
La probabilidad de obtener entre 400 y 500 éxitos se puede calcular utilizando la tabla de distribución normal estándar o una calculadora de probabilidad normal.
P(400 ≤ X ≤ 500) = P(19.79 ≤ z ≤ 28.27) = 0
Por lo tanto, la probabilidad de obtener entre 400 y 500 veces un 6 en 1000 lanzamientos es de aproximadamente 0.
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y’all which one is it cus ion kno
Gabriella is 53 5/6
inches tall. Sheila is 1 1/3
inches shorter than Gabriella and Jane is 1 1/4
inches shorter than Sheila. How tall is Jane?
at a store 40% of all the refrigerators are silver. there are 50 silver refrigerants at the store . how many refrigerants are at the store?
Answer:
125
Step-by-step explanation:
50 refrigerators are 40% of all the refrigerators in the store.
5 refrigerators are 4% of refrigerators in the store
125 refrigerators are 100% of refrigerators in the store
therefore there are 125 refrigerators at the store.
Y=2x to the power of 2 plus 4x minus one
What angle(s) on the Unit Circle make this equation true?
-√3 csc(2θ) = 2
a. Using only the graph of the given equation on Desmos, what angle(s) on the Unit Circle make this equation true? You must include a detailed, labeled screenshot as your explanation or detailed, labeled drawing of the graph as you solution.
b. Even though Desmos found the angle(s) that make the equation true in part (a), you must now show why the angle(s) are true. Provide a clear, convincing argument why the angles you stated in part (a) are true without the use of Desmos in anvway.
The angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer.
How to calculate the valueFrom the information, the following can be deduced:
-√3 csc(2θ) = 2
csc(2θ) = -2/√3
sin(2θ) = -√3/2
We know that sin(2θ) = 2sin(θ)cos(θ) by the double-angle identity for sine,
2sin(θ)cos(θ) = -√3/2
2sin(θ)cos(θ) = -√3/2
sin(θ)cos(θ) = -√3/4
sin(θ)cos(θ) = sin(π/3)sin(θ)
cos(θ) = sin(π/3)
θ = π/6 + 2πn, 5π/6 + 2πn
Therefore, the angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer
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[tex]\left\{\frac{1}{2^n}\:+\:\frac{\left(-1\right)^n}{n+1}\::\:n\:\:N\right\}[/tex]
Find max, min, sup and inf
The maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is 1/6.
The given sequence is: [tex]{1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}[/tex]
To find the maximum and minimum values of the sequence, we can start by taking the first few terms and looking for patterns:When [tex]n = 1,[/tex] the sequence evaluates to: [tex]1/2 + (-1)^1 / 2 * 2 = 0[/tex]
When [tex]n = 2,[/tex] the sequence evaluates to: [tex]1/4 + (-1)^2 / 3 * 2 = 1/6[/tex]
When [tex]n = 3,[/tex] the sequence evaluates to: [tex]1/8 + (-1)^3 / 4 * 2 = 7/96[/tex]
When [tex]n = 4,[/tex] the sequence evaluates to: [tex]1/16 + (-1)^4 / 5 * 2 = 17/240[/tex]
It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.
Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.
The maximum value occurs at n = 2, where it evaluates to 1/6.
To find the supremum and infimum of the sequence, we can start by considering the upper and lower bounds of each term separately.The term [tex]1/(2 ^ n)[/tex] has a lower bound of 0 and an upper bound of 1.
The term [tex]((- 1) ^ n)/(n + 1) / n * N[/tex] has a lower bound of [tex]-1/4[/tex] and an upper bound of [tex]1/4[/tex].
Therefore, the supremum of the sequence occurs when [tex]n = 1[/tex], where the sequence evaluates to [tex]1/2[/tex].
The infimum of the sequence occurs when [tex]n = 2[/tex], where the sequence evaluates to [tex]1/6.[/tex]
In summary, the maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is [tex]1/6.[/tex]
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Suppose the odds for a bet are 11: 1. Your friend tells you that he thinks the odds are too generous. Select all of the odds that are less generous.
Select all that apply.
4:1
6:1
19:1
18:1
In the ratio, the odds that are less generous is C) 19:1 and D)18:1.
What is ratio?
When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.
Here odds for bets are 11:1.
That means if for every $1 you bets, you may wins $11.
There are [tex]\frac{1}{1+11}=\frac{1}{12}=8.33\%[/tex] chance of this happens.
If the friends thinks odds are too generous , then the odds that less than generous are,
=> for 4:1 then [tex]\frac{1}{1+4}=\frac{1}{5}= 20\%[/tex]
=> For 6:1 then [tex]\frac{1}{6+1}=\frac{1}{7}= 14\%[/tex]
=> For 19:1 then [tex]\frac{1}{19+1}=\frac{1}{20}=5\%[/tex]
=> For 18:1 then [tex]\frac{1}{18+1}=\frac{1}{19}=5.2\%[/tex]
Hence the odds that are less generous is C) 19:1 and D)18:1.
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A flagpole is 12 feet fall. Its shadow is
11 feet long. How far is it from the top of the flagpole to the end of its shadow?
Step-by-step explanation:
You are looking for the hypotenuse of a right triangle with legs of 12 and
11 feet
Using Pthagorean theorem
hypot^2 = 12^2 + 11^2
hypot^2 = 265
hypot = sqrt (265) = 16.28 ft
please help pleaseee i need dis good grade
Answer:62.8 units
Step-by-step explanation:
solve as a fraction -2 1/3 - (-5) = ?
Answer:
-2 1/3 - (-5) = -2 1/3 + 5
To add these two numbers, we need to find a common denominator. The common denominator of 3 and 1 is 3.
-2 1/3 can be written as -7/3 using the rule that a mixed number is equal to the sum of the whole number and the fraction.
So, we have:
-7/3 + 5
To add these two fractions, we need to find a common denominator. The common denominator of 3 and 1 is 3.
-7/3 can be written as -7/3 x 1/1 = -7/3.
So, we have:
-7/3 + 15/3 = 8/3
Therefore, -2 1/3 - (-5) = 8/3.
How many more calories should a person on a 2000 cal diet eat for veggies then from carbs
Hence, a person on a 2000 calorie diet should eat more calories approximate ratio of 200-300 calories from vegetables and 900-1300 calories from carbohydrates.
What is the calories?A calorie is a measurement, just like a teaspoon or an inch. Calories are the amount of energy released when your body breaks down (digests and absorbs) food. The more calories a food has, the more energy it can provide to your body
How many calories take a person in vegetables and carbohydrates?The number of calories a person should consume from vegetables versus carbohydrates depends on various factors such as age, gender, activity level, body composition, and overall health status. However, in general, it is recommended that a person on a 2000 calorie diet should consume more calories from vegetables than from carbohydrates.
The United States Department of Agriculture (USDA) recommends that adults consume 2.5 to 3 cups of vegetables per day, depending on their age, gender, and level of physical activity. On a 2000 calorie diet, this would amount to approximately 200-300 calories from vegetables.
For carbohydrates, the recommended intake varies depending on the individual's energy needs, but it generally accounts for 45-65% of their total calorie intake. This equates to 900-1300 calories from carbohydrates on a 2000 calorie diet.
Therefore, a person on a 2000 calorie diet should eat more calories from vegetables than from carbohydrates, with an approximate ratio of 200-300 calories from vegetables and 900-1300 calories from carbohydrates.
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Need help on this please
Answer:
Step-by-step explanation:
(-50, -20), (-60, 40)
(40 + 20)/(-60 + 50) = 60/-10= -6
y - (-20) = -6(x - (-50))
What 4×4/3 in its simplest form
Answer:
5 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{4}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{16}{3}[/tex]
You can re-write [tex]\frac{16}{3}[/tex] as
[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] I wrote it like this because every [tex]\frac{3}{3}[/tex] is equal to 1.
1 + 1 + 1 + 1 + 1 + [tex]\frac{1}{3}[/tex] = 5[tex]\frac{1}{3}[/tex]
Helping in the name of Jesus.
any help? i dont seem to understand which radius of circle is.
First of all, radius is half the diameter. Radius is from the center-most point of a circle straight to the edge.
Answer:
The area of the whole object is 1,237.68 m^2 (meters squared).
Step-by-step explanation:
The circles are equal to:
π * d = a
3.14 * 12 = a
37.68 = a.
Now, since the circles are half in the rectangle, it would be easier to calculate the rectangle using these halves, so the total of the half-circles outside the rectangle is equivalent to a whole circle, or 37.68. Now, let's calculate the rectangle:
20 * (30 * 2) = a
20 * 60 = a
1200 = a.
The whole area is equivalent to the area of the two half-circles and the area of the rectangle:
37.68 + 1200 = a
1237.68 = a
Two angles lie along a straight line. If m∠A is five times the sum of m∠B plus 7.2°, what is m∠B?
As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.
what is angle ?Thus according their size or measurement, angles can be categorised. An oblique angle is larger than 90 degrees but far less than 180 degrees, a straight angle is exactly 90 degree, a right angle is turned 90 degrees, and an acute angle is less than 90 degrees. Reflex angles are angles that are higher than 180o but a little less than 360 degrees, and complete angles are angles that measure exactly 360 degrees. Geometry, trigonometry, physics, engineering, and many other branches of mathematics and science all make use of angles.
given
The total of the two angles, which are along a straight line, is 180 degrees. Let's refer to the angle B's measurement as x.
The information provided in the problem can then be used to create an equation as follows:
m∠A = 5(m∠B + 7.2°)
Due to the fact that the two angles are perpendicular to one another, we may replace mA with 180 - mB:
180 - m∠B = 5(m∠B + 7.2°)
The right side is being widened:
180 - m∠B = 5m∠B + 36
Simplifying and putting all the mB words to one side:
6m∠B = 144
m∠B = 24
As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.
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A cow is tethered to one corner of a square barn, 8 feet by 8 feet, with a rope 130 feet long. What is the maximum grazing area for the cow?
The maximum grazing area for the cow is approximately 53,343.08 square feet.
How to Find the maximum Grazing Area?The maximum grazing area for the cow can be found by imagining a circle with radius equal to the length of the rope (130 feet) centered at the corner of the barn where the cow is tethered. The grazing area is the portion of the circle that lies outside the barn.
Since the barn is 8 feet by 8 feet, it covers a square area of 64 square feet. The radius of the circle is 130 feet, so the area of the circle is π(130)^2 square feet.
To find the maximum grazing area, we need to subtract the area of the barn from the area of the circle.
Area of circle = π(130)^2 square feet = 53,407.08 square feet
Area of barn = 64 square feet
Maximum grazing area = Area of circle - Area of barn
= 53,407.08 - 64
= 53,343.08 square feet (rounded to two decimal places)
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Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
The equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
How to solveWe can observe from the table that the number of books collected increases by 10 for each week.
Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:
b = mw + c
where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).
The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):
10 = 10 * 1 + c
c = 0
Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).
Weeks (w) Books Collected (b)
1 10
2 20
3 30
4 40
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
Find the value of x. Write your answer in simplest form.
76√2
The value of x which is the hypotenuse of the triangle is 107.48
How to find missing side of a right angle triangle using Pythagoras theorem[tex]\dfrac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{Hyp = x}[/tex]
[tex]\text{opp} = 76\sqrt{2}[/tex]
[tex]\text{adj} = \text{x}[/tex]
substitute into the equation[tex]\text{x}^2 = (76\sqrt{2})[/tex]
[tex]\text{x}^2 = 11552[/tex]
[tex]\text{x}^2 = \sqrt{11552}[/tex]
[tex]\text{x} = 107.48[/tex]
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