From greatest comparative advantage to least comparative advantage the list of toothpaste is Mint, Fresh, Sparkling, Bright White
To determine the comparative advantage of toothpaste companies in producing small tubes of toothpaste, we need to look at the opportunity cost of producing small tubes of toothpaste in terms of the production of large tubes of toothpaste. The company with the lowest opportunity cost of producing small tubes of toothpaste (i.e., the company that gives up the least amount of large tubes of toothpaste to produce small tubes of toothpaste) has the greatest comparative advantage in producing small tubes of toothpaste. We can calculate the opportunity cost by looking at the difference in the number of large tubes of toothpaste that each company could produce if they chose to produce only large tubes versus the number of large tubes they could produce if they chose to produce some small tubes as well.
So, using the data provided in the table, we can calculate the opportunity cost for each company as follows:
Sparkling:
Opportunity cost of producing small tubes of toothpaste = (200 large tubes/hour - 100 large tubes/hour) / 200 small tubes/hour = 0.5 large tubes per small tube
Bright White:
Opportunity cost of producing small tubes of toothpaste = (250 large tubes/hour - 100 large tubes/hour) / 250 small tubes/hour = 0.6 large tubes per small tube
Fresh:
Opportunity cost of producing small tubes of toothpaste = (250 large tubes/hour - 200 large tubes/hour) / 250 small tubes/hour = 0.2 large tubes per small tube
Mint:
Opportunity cost of producing small tubes of toothpaste = (150 large tubes/hour - 150 large tubes/hour) / 150 small tubes/hour = 0 large tubes per small tube
Therefore, the order of the companies from greatest comparative advantage to least comparative advantage in producing small tubes of toothpaste is: Mint, Fresh, Sparkling, Bright White
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Complete question
Toothpaste company |Large tubes |Small tubes
Sparkling |100 per hour |200 per hour
Bright White |100 per hour | 250 per hour
Fresh |200 per hour |250 per hour
Mint |150 per hour |150 per hour
'This table shows the production possibility schedule for several toothpaste companies. Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing small tubes of toothpaste.
What is the factored form of the polynomial? x2 − 15x 36 (x − 4)(x − 9) (x − 3)(x − 12) (x 4)(x 9) (x 3)(x 12)
Coefficients and indeterminates are both parts of polynomials. The polynomial [tex]x^{2}[/tex] - 15x + 36 has the components (x-3) (x-12).
To factor the polynomial [tex]x^{2}[/tex]- 15x + 36, we need to find two numbers whose product is 36 and whose sum is -15. These numbers are -3 and -12,
=[tex]x^{2}[/tex] -12x -3x + 36
now, we'll use x as the common term between the first two terms and 3 as the common term between the next two terms.
=x(x-12)-3(x-12)
=(x-12)(x-3)
so we can write the polynomial as (x - 3)(x - 12). This is the factored form of the polynomial.
To verify this, we can expand the expression (x - 3)(x - 12) using the distributive property, which gives us [tex]x^{2}[/tex]- 15x + 36. This confirms that the factored form is correct.
Factoring polynomials is an important skill in algebra as it helps simplify expressions and solve equations more easily. By factoring a polynomial, we can often find its roots, which are the values of x that make the polynomial equal to zero. This is useful in solving various types of problems in mathematics and science.
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Find a polynomial
of the smallest degree with
integer coefficients whose zeros include √2 and 2
A polynomial having integer coefficients and the lowest degree: p(x) = x² - (2 + √2)x + 2√2. Here, integer coefficients for x² is 1: x is - (2 + √2) and 2√2 is the constant.
Explain about the polynomial?Sums (including differences) of polynomial "contexts" are polynomials. Any variables there in expression has to have whole-number powers for it to be a polynomial term.
A polynomial term can also be a simple number. In particular, an expression must not contain any square roots of variables, any fractional and negative powers mostly on variables, and any variables in any fractions' denominators in order to qualify as a polynomial term.
The given zeros for the polynomial are-
√2 and 2
There are two zeros so, the smallest degree of polynomial will be 2.
Thus, Let p(x) be the 2 degree polynomial.
Then, general equation will be:
p(x) = (x - √2)(x - 2)
On expansion:
p(x) = x² -2x -√2x +2√2
On simplification:
p(x) = x² - (2 + √2)x + 2√2
Here, integer coefficients for x² is 1: x is - (2 + √2) and 2√2 is the constant.
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Use y=-10x+216 to predict the number of students who will drop out in 2012
I'm sorry, but I need more information to answer your question.
The equation y = -10x + 216 represents a linear relationship between two variables, where y represents the number of students who drop out and x represents the year. However, I don't have any information about the values of x for previous years or any other data that can be used to make a prediction for the year 2012.
If you have additional information, such as the number of dropouts for previous years, you can substitute those values into the equation and solve for the value of y in 2012.
chris rents a booth at a flea market at a cost of $75 for one day. at the flea market chris sells picture frames each of which costs him $6.00. if chris sells each picture frame for $13, how many picture frames must he sell to make a profit of at least $200 for that day?
Answer:
x ≤ 40
Step-by-step explanation:
-75-6x+13x ≤ 200
-75 is the cost of the booth a day
-6 is the intial cost of the paintings for Chris
x is the amount of paintings
13 is the price Chris sells the paintings for
200 is the profit needed
First thing you do is add like terms -75-6x+13x ≤ 200
add -6x and 13x
-75+7x ≤ 200
Now add 75 to both sides
7x ≤ 275
Now divide both sides by 7
x≤ 275
x≤ 39.2857142857
round up to x≤ 40 (because 39 paintings is not enough, 40 gives him $205 in profit while 39 only gives him $198 in profit)
Un número excede en 12 unidades a otro, si restáramos 4 unidades a cada uno de ellos, entonces el primero sería igual al doble del segundo. Halle los dos números
x - numero primero
y - numero segundo
x = y + 12
x - 4 = 2(y - 4)
x - y = 12
x - 4 = 2y - 8
- x + y = - 12
x - 2y = - 4
_______________
- y = - 16
y = 16
x = 16 + 12
x = 28
The radius of a circle is 14 cm. Find its area in terms of π.
Answer:
A≈615.75cm²
Step-by-step explanation:
A=πr2=π·142≈615.75216cm²
PLEASE HELPPP WITH MY MATHS ASSIGNMENT
a) The accumulated amount or future value of investing $150 on the first day of each month at 6% compounded monthly for 40 years is $274,152.43.
b) , The future value of the investment after 40 years at an annual interest rate of 4%, compounded semi-annually, is $9,054.60.
a)
N = 40 years * 12 months = 480 months
I% = 6% per year / 12 months = 0.5% per month
PV = $0 (since we are not investing any money initially)
PMT = $150
FV = ?
P/Y = 1 (payments made monthly)
C/Y = 12 (compounded monthly)
Using the formula for future value of an annuity:
FV = PMT * ((1 + I%)^(N) - 1) / I%
FV = $150 * ((1 + 0.5%)^(480) - 1) / 0.5%
FV = $274,152.43
Therefore, the accumulated amount or future value of investing $150 on the first day of each month at 6% compounded monthly for 40 years is $274,152.43.
b)
Given information:
PV (present value) = $900
I% (annual interest rate) = 4%
P/Y (payments per year) = 1 (since the investment is compounded semi-annually)
C/Y (compounding periods per year) = 2
N (number of periods) = 40 years * 2 (since interest is compounded twice a year) = 80
Using the compound interest formula:
FV = PV * (1 + (I%/C/Y))^(N*C/Y)
FV = $900 * (1 + (4%/2))^(80*2)
FV = $900 * (1.02)¹⁶⁰
FV = $900 * 10.06
FV = $9,054.60
Therefore, the future value of the investment after 40 years at an annual interest rate of 4%, compounded semi-annually, is $9,054.60.
PMT (payment per period) cannot be calculated since no periodic payments are mentioned in the given information.
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Simplify to create an equivalent expression
2(-2-4p) + 2(-2p-1)
On solving the provided question we can say that Therefore, the simplified equivalent expression is -6 - 12p.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
[tex]2(-2-4p) + 2(-2p-1) = -4 - 8p - 4p - 2\\-4 - 8p - 4p - 2 = -6 - 12p\\[/tex]
Therefore, the simplified equivalent expression is -6 - 12p.
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Find the area of the trapezoid below.
Answer:
A = 18 cm²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 3 , b₁ = 8 , b₂ = 4 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (8 + 4) = 1.5 × 12 = 18 cm²
What do I do with the negative and what do I do with the x^2? Please help I’ve been stuck for a week.
(a + b) (x²-5) - (a + b) (3x + 5)
To answer your question about the negative, in the expression (a + b) (x²-5) - (a + b) (3x + 5), the negative sign in front of the second term indicates that you should subtract the second term from the first term.
how to solve quadratic equation ?
There are different methods to solve quadratic equations, but one of the most common methods is the quadratic formula:
Given a quadratic equation in the form of ax² + bx + c = 0, where a, b, and c are constants and a is not equal to zero, the quadratic formula is:
x = (-b ± sqrt(b² - 4ac)) / 2a
To solve the quadratic equation using the quadratic formula, follow these steps:
Write the quadratic equation in the standard form ax² + bx + c = 0.
Identify the values of a, b, and c in the equation.
Substitute the values of a, b, and c into the quadratic formula.
Simplify the expression under the square root sign.
Apply the plus-minus sign and simplify the numerator.
Divide the simplified numerator by the denominator.
Write the solution(s) in the form of x = value.
To simplify the expression (a + b) (x²-5) - (a + b) (3x + 5), you can factor out the common factor of (a + b) from both terms:
(a + b) (x² - 5 - 3x - 5)
Simplifying the expression within the parentheses:
(a + b) (x² - 3x - 10)
Now, you can factor the trinomial inside the parentheses by finding two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2:
(a + b) (x - 5) (x + 2)
So the final simplified expression is (a + b) (x - 5) (x + 2).
To answer your question about the negative, in the expression (a + b) (x²-5) - (a + b) (3x + 5), the negative sign in front of the second term indicates that you should subtract the second term from the first term.
And regarding the x^2 term, in the simplified expression (a + b) (x - 5) (x + 2), the x² term is represented by the (x - 5)(x + 2) part, which expands to x² - 3x - 10.
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=
(7−4n)⋅6 equation’s
Answer:
-17
Step-by-step explanation:
1st step =7-4 X 6
2nd step =7-24
3rd step =-17
The Jones’ family eats 572 bananas each year. How many do they average eating in one week
Answer:
10 / 11 bananas in one week, I believe.
Explain how a unit square area model shows that 0.1 of 1 is the same as 0.1 x 1.
A unit square is a square with sides of length 1 unit. When we talk about the area of a unit square, we mean the amount of space that the square covers, which is equal to 1 square unit.
To demonstrate that 0.1 of 1 is the same as 0.1 x 1 using a unit square area model, we can imagine dividing the unit square into 10 equal parts vertically and horizontally. This creates a grid of 100 smaller squares, each with an area of 0.01 square units.
Now, let's consider the expression 0.1 of 1. This means taking 0.1 times the area of a unit square. Since the area of the unit square is 1 square unit, 0.1 of 1 is equal to 0.1 times 1, which is 0.1.
Similarly, we can represent the expression 0.1 x 1 visually on the unit square area model by shading in 0.1 of the unit square, as before. Since 0.1 x 1 is also equal to 0.1, the shaded area will once again cover 0.1 square units, confirming that these two expressions are equal.
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A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. Answer parts a and b a. To what percent of its capacity is the large container filled? The container is filled to % of the maximum capacity. b. Some liquid will be poured from a full 16-ounce container until it is filled to the same percent of its capacity as the large container in part a. How many ounces of liquid must be poured from the full 16-ounce container? Explain When the 16-ounce container is % filled, it will contain ounce(s). So ounce(s) will need to be poured from the full 16-ounce container
We may conclude after answering the presented question that As a expression result, the huge container is at 87.5% of its full capacity.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
The big container is 8 ounces less than its maximum capacity of 64 ounces, which indicates it is 64 - 8 = 56 ounces full.
We may use the following formula to calculate the proportion of the container's capacity that is filled:
(Amount filled / Maximum capacity) x 100% = Percentage filled
Substituting the values yields:
% filled = (56 / 64) x 100%
87.5% of the spaces were filled.
As a result, the huge container is at 87.5% of its full capacity.
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4.5 Draw a diagram representing the scenario and find the requested value. A man is standing 270 feet from the base of a statue. If he man looks up at an angle of 34 degrees to see the top of the statue, how tall is the statuePlease round to the nearest whole foot.
Using the idea of the angle of elevation as it could be applied to the problem, the height of the statue is 182 ft
What is the angle of elevation?When gazing up at an object or point, the angle of elevation is the angle formed between the horizontal plane and the observer's line of sight. It is, in other words, the angle at which the line of sight of an observer is tilted upward from the horizontal plane.
The angle of elevation is an important concept in geometry and trigonometry and is used to calculate the height of objects, such as buildings, towers, or trees, or to measure the distance between two points.
We know that;
Tan 34 = x/270
x = 270 tan 34
x = 182 ft
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two step equations
find the value of the unknown variable in the equation
5(5p-1)= 20
Answer:
[tex] \begin{gathered} \mathfrak{\large\bold \bf \mapsto {\underline{ \boxed{ \sf{\ \: p \: = 1 }}}}} \: \purple \: \bigstar \\ \end{gathered}[/tex]
Step-by-step explanation:
[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5 ( 5p - 1) = 20 }}} \: \\ \end{gathered}[/tex]
[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5p - 1 = \frac{20}{5} }}} \: \\ \end{gathered}[/tex]
[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5p - 1= 4 }}} \: \\ \end{gathered}[/tex]
[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5p = 4 + 1 }}} \: \\ \end{gathered} \\ \\ \begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5p = 5 }}} \: \\ \end{gathered}[/tex]
[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ p \: = \frac{5}{5} }}} \: \\ \end{gathered}[/tex]
[tex]\begin{gathered} \large\bold \bf \mapsto { \pink{ \bf{\ p \: = 1 }}} \: \\ \end{gathered}[/tex]
[tex] \underline{ \rule{250pt}{7pt}}[/tex]
The solution to the equation 5(5p-1) = 20 is p = 1.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To solve this equation, we can follow these steps:
Simplify the left side of the equation by using the distributive property of multiplication:
5(5p-1) = 25p - 5
Solve for the unknown variable by isolating it on one side of the equation. In this case, we want to get p by itself, so we'll add 5 to both sides of the equation:
25p - 5 + 5 = 20 + 5
25p = 25
Finally, divide both sides of the equation by 25 to get the value of p:
25p/25 = 25/25
p = 1
Therefore,
The solution to the equation 5(5p-1) = 20 is p = 1.
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The perimeter of Aaron’s rectangular bedroom is 368 inches. His room is 8 feet wide. What is the area of Aaron’s bedroom?
The answer of the given question based on the area of Aaron’s bedroom is 8,448 inches².
What is Perimeter?Perimeter is total distance around boundary of two-dimensional shape. It is sum of the lengths of all sides of the shape. For example, the perimeter of a rectangle is found by adding the length and width of the rectangle and multiplying the sum by 2, while the perimeter of a circle is found by multiplying the diameter by π. Perimeter is usually measured in units like inches, feet, meters, or centimeters.
We can begin by converting the width of the room from feet to inches, since the given perimeter is in inches:
8 ft = 8x12 inch =96 inch
Let the length of the room be L. Then, the perimeter P is given by the formula:
P = 2L + 2W
Substituting the given values, we have:
368 = 2L + 2(96)
368 = 2L + 192
2L = 176
L = 88 inches
So, the length of the room is 88 inches. The area A of the room is given by the formula:
A = L x W = 88 x 96 = 8,448 inches²
Therefore, the area of Aaron's bedroom is 8,448 inches².
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The equation represents Function A, and the graph represents Function B: Function A f(x) = 6x - 1 Function B graph of line going through ordered pairs 1, 4 and negative 1, negative 2 and negative 2, negative 5 Which equation best compares the slopes of the two functions? (1 point) Slope of Function B = 2 x Slope of Function A Slope of Function A = Slope of Function B Slope of Function A = 2 x Slope of Function B Slope of Function B = − Slope of Function A
Option C : The slope of Function A is 6 and the slope of the line graphed in Function B, going through the ordered pairs (1, 4) and (-1, -2), is 3.
To compare the slopes of Function A and Function B, we need to determine the slopes of the line graphed in Function B and the slope of Function A, and then compare them using the answer choices provided.
The slope of the line going through the ordered pairs (1, 4) and (-1, -2) can be found using the slope formula:
slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(-1 - 1) = -6/-2 = 3
So the slope of Function B is 3.
The equation for Function A is f(x) = 6x - 1, which means its slope is 6.
Now we can compare the slopes using the answer choices provided:
Slope of Function B = 2 x Slope of Function A: 3 = 2 x 6 is not true
Slope of Function A = Slope of Function B: 6 = 3 is not true
Slope of Function A = 2 x Slope of Function B: 6 = 2 x 3 is true
Slope of Function B = − Slope of Function A: 3 = -6 is not true
Therefore, the equation that best compares the slopes of the two functions is "Slope of Function A = 2 x Slope of Function B".
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The equation represents Function A, and the graph represents Function B: Function A f(x) = 6x - 1 Function B graph of line going through ordered pairs 1, 4 and negative 1, negative 2 and negative 2, negative 5 Which equation best compares the slopes of the two functions? (1 point)
A. Slope of Function B = 2 x Slope of Function A
B. Slope of Function A = Slope of Function B
C. Slope of Function A = 2 x Slope of Function B
D. Slope of Function B = − Slope of Function A
What is the graph of the equation x=5
The graph of x=5 is a line parallel to the y-axis, with x-coordinate 5 at all points.
What is the vertical line?
A vertical line is a straight line that is perpendicular to the horizontal line and goes straight up and down in a two-dimensional coordinate system.
The graph of the equation x=5 is a vertical line passing through the point (5, y) for all values of y.
This is because no matter what value y takes, x will always be equal to 5.
Here's in image example of what the graph of x=5 would look like:
As you can see in the image attached, the line is vertical and intersects the x-axis at x=5.
Therefore, the graph of x=5 is a line parallel to the y-axis, with x-coordinate 5 at all points.
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2 [x² + 2x + 1] - x²-4x+4 = x²-3x
The solution for the equation given would be x = 2 and x = -1.
How to find the solution to the equation?To solve the equation 2[x² + 2x + 1] - x² - 4x + 4 = x² - 3x, we can simplify and rearrange the terms as follows:
2x² + 4x + 2 - x² - 4x + 4 = x² - 3x
x² - 3x + 6 = x² - 3x
2x² - 2x - 6 = 0
Dividing both sides by 2, we get:
x² - x - 3 = 0
We can then solve for x by factoring or using the quadratic formula. Factoring gives:
(x - 2)(x + 1) = 0
So, the solutions are x = 2 and x = -1.
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can someone please help me with ??!!
The statement "The value is decreasing $207 per year" best explains how the value is changing. This is because the function shows that the value is decreasing linearly with time, at a rate of $82 per year. Therefore, over t years, the value will decrease by 82t dollars. For example, after one year, the value will decrease by $82, and after two years, it will decrease by $164.
Now check
Find the difference.
(k^3-7k+2)-(k^2-12)=
The difference between the two expressions is:
(k³-7k+2)-(k²-12) = k³ - k² - 7k + 14
What is an expression?
We can begin by simplifying the left side of the equation:
(k³ - 7k + 2) - (k² - 12)
= k³ - 7k + 2 - k² + 12 // Distribution of the negative sign
= k³ - k² - 7k + 14 // Combining like terms
So the difference between the two expressions is:
k³ - k² - 7k + 14
An expression is a combination of one or more values, variables, and operators that can be evaluated to produce a result. Expressions can be as simple as a single number or variable, or they can be complex, combining multiple operators and functions.
What are variables?
A variable is a symbol or a named memory location that can hold a value. It is used to store and manipulate data during the execution of a program. Variables can be assigned different types of values, such as numbers, text, or Boolean (true/false) values. The value of a variable can change during the execution of a program, and it can be used in expressions and statements to perform calculations, make decisions, or control the flow of the program.
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Complete question is: (k³-7k+2)-(k²-12) = k³ - k² - 7k + 14
Solve these two questions fast for brainliest and 20 points
Sonya is approximately 47 feet away from Thomas. And
height of the kite above the ground is approximately 43 feet.
How to find the height?
To find the height of the kite above the ground, we can use trigonometry. Let's draw a diagram:
/|
/ |
/ | height (h)
/ |
/ |
/θ___|___
distance (d)
We know that the angle θ is 25°, the hand height is 3 feet, and the distance from the hand to the kite is 100 feet. We want to find the height of the kite above the ground, which we'll call h.
Using trigonometry, we can write:
tan(θ) = h / d
where tan(θ) is the tangent of the angle θ, and d is the distance from the hand to the kite. Solving for h, we get:
h = d * tan(θ)
Substituting the known values, we get:
h = 100 * tan(25°) ≈ 43.1 feet
So the height of the kite above the ground is approximately 43 feet.
2.Let's draw a diagram:
Sonya
|
|
66° | 48°
|
|
-----------o----------- Balloon
|
|
Thomas
We want to find the distance between Sonya and Thomas, which we'll call x. We know that the height of the balloon above the ground is 126 feet. We also know the angles of elevation from Sonya and Thomas to the balloon.
Let's first find the distance from Sonya to the balloon. We can use trigonometry again:
tan(66°) = 126 / d
where d is the distance from Sonya to the balloon. Solving for d, we get:
d = 126 / tan(66°) ≈ 50.5 feet
Now let's find the distance from Thomas to the balloon:
tan(48°) = 126 / (x + d)
where x + d is the total distance from Thomas to the balloon (the sum of the distances from Thomas to the point directly below the balloon, and from that point to the balloon). Solving for x + d, we get:
x + d = 126 / tan(48°) ≈ 97.5 feet
Finally, we can solve for x:
x = (x + d) - d ≈ 97.5 - 50.5 ≈ 47 feet
So Sonya is approximately 47 feet away from Thomas.
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Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement. Problems 5 & 6
5) Triangles QRN and MNL are not similar.
6) Triangle ECD is similar to triangle MNL
What is similarity of triangle?
Similarity of triangles is a concept in geometry that describes the relationship between two triangles that have the same shape but possibly different sizes. Two triangles are considered similar if their corresponding angles are congruent (equal in measure) and their corresponding sides are proportional (having the same ratio).
This can be expressed using the following notation: if triangle ABC is similar to triangle DEF, we can write it as:
∆ABC ~ ∆DEF
The symbol "~" means "is similar to."
5) To determine whether the two triangles QRN and MNL are similar, we can use the SSS~ (side-side-side) similarity criterion or the SAS~ (side-angle-side) similarity criterion.
Let's first check if the triangles satisfy the SSS~ criterion:
SSS~ criterion: If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.
The sides of triangles QRN and MNL are:
QR = QN + RN = 56 + 48 = 104
RN = 48
QN = 56
MN = ML + NL = 60 + 70 = 130
NL = 70
ML = 60
We can see that the ratios of the corresponding sides are not equal:
QR/MN = 104/130 = 0.8
RN/NL = 48/70 = 0.686
QN/ML = 56/60 = 0.933
Since the ratios of the corresponding sides are not equal, the triangles QRN and MNL are not similar by the SSS~ criterion.
Now let's check if the triangles satisfy the SAS~ criterion:
SAS~ criterion: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.
We can see that the included angles are not congruent, since we don't have any angle measures given. Therefore, we cannot use the SAS~ criterion to determine similarity.
Since the triangles do not satisfy either the SSS~ or SAS~ similarity criterion, we can conclude that they are not similar by either criterion.
6) In triangle ECD, we have:
angle ECD = 180 - angle CED - angle CDE
= 180 - (angle MNL + angle LNM) - angle CDE (since MNL is given as similar to ECD)
= 180 - (angle MNL + angle LNM) - angle CDM (since triangle CDM is similar to triangle LNM)
= 180 - 45 - 36 = 99 degrees
Similarly, in triangle MNL, we have:
angle MNL = 180 - angle LNM - angle MLN
= 180 - angle LNM - (angle ECD + angle CDE) (since MNL is given as similar to ECD)
= 180 - angle LNM - (angle CDM + angle CDE) (since triangle CDM is similar to triangle LNM)
= 180 - 36 - 45 = 99 degrees
Therefore, the triangles have two congruent angles: angle ECD is congruent to angle MNL, and angle CED is congruent to angle MLN.
Next, we need to check if the corresponding sides are proportional. We can do this by finding the ratios of the corresponding sides:
EC/MN = 96/36 = 8/3
CD/NL = 64/45
ED/ML = 80/54 = 40/27
If we simplify these ratios, we get:
EC/MN = 8/3
CD/NL = 64/45 = 16/9
ED/ML = 40/27
Since the ratios of the corresponding sides are not equal, the triangles are not similar by SSS~ or SAS~.
However, we can see that the triangles are similar by AA~, since they have two congruent angles. Therefore, a valid similarity statement would be:
Triangle ECD is similar to triangle MNL by AA~.
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The sum of the interior angles of an octagon is:
0000
1080°.
180°.
360°.
720⁰.
Answer:
1080°
Step-by-step explanation:
Let n = the number of sides
(n-2)180
(8-2)180
6(180) = 1080
Helping in the name of Jesus.
what is the minimum vertical ceiling height to play indoor volleyball?
Answer:
USA Volleyball specifies a minimum ceiling height of 23′ for nationally sanctioned competition.
Step-by-step explanation:
its height regulation of how tall the ceiling should be
Jozef "accidentally" broke his piggy bank to find a total of 42 dimes and quarters. If the coins totaled $8.25, how dimes did he have in his piggy bank? How many quarters?
Therefore, Jozef had 15 dimes and 27 quarters in his piggy bank.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.
Here,
Let's use the following variables to represent the number of dimes and quarters in Jozef's piggy bank:
d: the number of dimes
q: the number of quarters
We know that Jozef has a total of 42 dimes and quarters, so we can write the equation:
d + q = 42
We also know that the total value of the coins is $8.25. We can express this value in cents as:
10d + 25q = 825
We can simplify this equation by dividing both sides by 5:
2d + 5q = 165
Now we have two equations with two variables:
d + q = 42
2d + 5q = 165
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for q:
q = 42 - d
Now we can substitute this expression for q into the second equation:
2d + 5(42 - d) = 165
Simplifying and solving for d, we get:
2d + 210 - 5d = 165
-3d = -45
d = 15
So Jozef had 15 dimes in his piggy bank. We can use the first equation to find the number of quarters:
15 + q = 42
q = 27
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For a role-playing game, Nikia randomly selects a team card and a character card. The teams are air, fire, land, and water. The characters are healer, spy, and thief. Nikia's favorite team is air and her favorite character is spy. How many outcomes are there? (Hint-Use a tree diagram, table, or list)
Answer:
To determine the number of outcomes for Nikia's random selection of a team card and a character card for a role-playing game, we can use a tree diagram, table, or list.
There are four possible teams: air, fire, land, and water. Once a team card is selected, there are three possible character cards: healer, spy, and thief. Therefore, the total number of outcomes is the product of the number of options for each selection, which is:
4 (number of team options) x 3 (number of character options) = 12
So there are 12 possible outcomes for Nikia's random selection of a team card and a character card. However, since Nikia has specified that her favorite team is air and her favorite character is spy, the number of outcomes that would satisfy her preferences is:
1 (air team) x 1 (spy character) = 1
Therefore, only one outcome would satisfy Nikia's preferences.
Let f(x)=\sqrt(x) and g(x)=5\sqrt(x). Find (f-g)(x).
your messageConvert to number of atoms 294 grams AuTo convert 294 grams of Au to the number of atoms, we need to use the Avogadro's number, which is 6.022 x 10^23 atoms/mole. First, we need to find the number of moles of Au in 294 grams: 294 grams Au / 196.97 g/mole = 1.49 moles Au Next, we can calculate the number of atoms: 1.49 moles Au x 6.022 x 10^23 atoms/mole = 8.97 x 10^23 atoms Au Therefore, there are approximately 8.97 x 10^23 atoms of gold in 294 grams.PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!This figure is a rectangle with a semicircle on the shorter side.What is the perimeter of this figure?Use 3.14 for pi.A. 20.28 ftB. 30.28 ftC. 46.28 ftD. 74.24 ftTo find the perimeter of the figure, we need to add up the lengths of all the sides. Let's call the length of the rectangle "L" and the width "W". The rectangle has two sides of length L and two sides of length W, so the perimeter of the rectangle is: 2L + 2W The semicircle has a diameter equal to the width of the rectangle (W), so the circumference of the semicircle is: 1/2 (pi) W To get the total perimeter, we need to add the circumference of the semicircle to the perimeter of the rectangle. Since the semicircle only covers half of the width of the rectangle, we only need to add one width (W) to the perimeter of the rectangle. So the total perimeter is: 2L + 3W + 1/2 (pi) Wevaluate C(4,2)C(4,2) represents the number of ways to choose 2 items from a set of 4 distinct items. The formula for C(n,r) is n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. Plugging in the values for C(4,2), we get: C(4,2) = 4! / (2! * (4-2)!) = 24 / (2 * 2) = 6 Therefore, there are 6 ways to choose 2 items from a set of 4 distinct items.Let f(x)=\sqrt(x) and g(x)=5\sqrt(x). Find (f-g)(x).(f-g)(x) represents the difference between f(x) and g(x). So we can write: (f-g)(x) = f(x) - g(x) Substituting the given expressions for f(x) and g(x), we get: (f-g)(x) = sqrt(x) - 5sqrt(x) To simplify this expression, we can factor out sqrt(x) as a common factor: (f-g)(x) = sqrt(x) * (1 - 5) Simplifying the expression in the parentheses, we get: (f-g)(x) = -4sqrt(x) Therefore, (f-g)(x) = -4sqrt(x)
Hi can someone help me with my math hw? can you solve it on paper pls?
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\\ \end{cases} \\\\\\ A = 50000(1 + 0.05)^{t} \implies A=50000(1.05)^t \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{in 2017, 7 years later}}{A=50000(1.05)^7\implies A\approx 70355} \\\\\\ \stackrel{\textit{in 2020, 10 years later}}{A=50000(1.05)^{10}\implies A\approx 81444} \\\\\\ \stackrel{\textit{in 2030, 20 years later}}{A=50000(1.05)^{20}\implies A\approx 132664}[/tex]