The AA criterion for the similarity between two triangles means that if two pairs of corresponding angles in two triangles are congruent, then the triangles are similar.
What are the steps for proving the AA criterion for similar triangles in the GeoGebra tool?The steps to prove the AA criterion for similarity using GeoGebra is as follows:
Open GeoGebra and select the "Geometry" option to create a new geometry file.
From the toolbar on the left, select the "Triangle" tool and create two triangles by clicking on three points on the screen.
Use the "Measure" tool to measure the angles in both triangles. To do this, select the "Measure" tool from the toolbar, click on one of the angles in the first triangle, and then click on the corresponding angle in the second triangle.
Record the measurements of the two corresponding angles and calculate their values.
Use the "Move" tool to adjust the position of one of the triangles. Make sure that the two corresponding angles are still the same size.
Observe the triangles to see if they still appear to be similar, even after the movement.
Repeat the process several times, each time moving one of the triangles and observing if they are still similar.
Draw a conclusion based on your observations. Can you prove that the two triangles are similar based on the AA criterion?
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Dravin is painting a cone -shaped centerpiece for the school dance . The centerpiece had a diameter of 12 inches and slant height of 19 inches . What is the total surface area that needs painting? Round your answer to the nearest whole number
The total surface area that needs painting is approximately 487 square inches.
What is the cone total surface area?
The total surface area (TSA) of a cone is given by the formula:
TSA = πr(r + l)
The surface area of a cone can be calculated using the formula:
[tex]Surface Area = \pi r(r + \sqrt{(r^2 + h^2)} )[/tex]
where r is the radius of the base of the cone and h is the slant height of the cone.
Given:
Diameter of the cone = 12 inches
Radius (r) = Diameter / 2 = 12 / 2 = 6 inches
Slant height (h) = 19 inches
Plugging in the values into the formula, we get:
[tex]Surface Area = \pi * 6 * (6 + \sqrt{(6^2 + 19^2)} )[/tex]
Calculating the value inside the square root:
[tex]\sqrt{(6^2 + 19^2)} = \sqrt{(36 + 361) } = \sqrt{397} = 19.92[/tex] (rounded to two decimal places)
Substituting the value back into the formula:
[tex]Surface Area = \pi * 6 * (6 + 19.92) = \pi * 6 * 25.92 = 487.34[/tex] square inches (rounded to two decimal places)
Hence, the total surface area that needs painting is approximately 487 square inches.
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please help me in this question
Answer:
step by step explanation:
All you have to do is expand and reduce the expressions
then evaluate -2 being a root of the expressions
To do that you need to substitute -2 into the simplified expressions
if the result comes as zero then f(-2) is factor of f(x) according to the factor theorem.
Example 1.
simplify (-5x-2)(7x-4)-2x+3
if you substitute f(x) as f(-2)
then substitute x with -2
when you simply and evaluate the expression you will get that the expression is equal to -137
which means -2 isn't a root since the expression must be equal to 0
-2 is not a root
do the same for the other expressions
Sketch 3 points to make a figure what kind Of polygon did you draw
If three points that are provided are not collinear then the only possible polygon that can be formed by connecting these points would be a triangle.
What is a polygon?A polygon is a closed two-dimensional shape made up of straight line segments called sides. It is formed by connecting three or more points (vertices) in a specific order. The sides of a polygon do not intersect, and each vertex is connected to exactly two sides. The region enclosed by the sides of a polygon is called its interior, while the points outside the polygon but on the same plane are called its exterior.
If three points are provided and they are not collinear (i.e., they do not lie on the same straight line), then the only possible polygon that can be formed by connecting these points would be a triangle(refer image attached). A triangle is a polygon with three sides and three angles.
The specific type of triangle (e.g., equilateral, scalene, isosceles) would depend on the lengths of the sides and the measure of the angles formed by connecting these points in a specific order. Different orders of connecting the points may result in different types of triangles.
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question attached
A. 5
B. 16
C. function is not defined for this value
D. 9
F(4)=9 is the value for this function.
What is piecewise function?A function that is defined by numerous smaller functions across various time intervals is known as a piecewise function. The domain of a function is the sum of all the smaller domains, and each sub-function has its own formula and domain. The input value and the function that establishes that interval determine the function's output.
The typical functional notation, which represents the body of a function as an array of functions and related subdomains, can be used to define piecewise functions. Together, these subdomains must encompass the entire domain; frequently, it is also necessary for them to be pairwise disjoint, or constitute a partition of the domain.
x=4 is bigger than or equal to 0 because it.
we use the third function definition
F(x)=x+5.
Therefore, F(4)=4+5=9.
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A trucking firm wants to purchase 10 trucks that will provide exactly 28 tons of additional shipping capacity. A model A truck holds 2 tons, a model B truck holds 3 tons, and a model C truck holds 5 tons. How many trucks of each model should the company purchase to provide the additional shipping capacity?
Answer: Let's assume that the trucking firm purchases x trucks of model A, y trucks of model B, and z trucks of model C.
We know that the total number of trucks purchased should be 10, so:
x + y + z = 10
We also know that the total additional shipping capacity provided by the trucks should be 28 tons, so:
2x + 3y + 5z = 28
Now we have two equations with three variables. We can solve for one variable in terms of the other two, and substitute that expression into the other equation to get an equation with only two variables. For example, we can solve the first equation for x:
x = 10 - y - z
And substitute into the second equation:
2(10 - y - z) + 3y + 5z = 28
Expanding and simplifying:
20 - 2y - 2z + 3y + 5z = 28
Combining like terms:
y + 3z = 4
Now we have two equations with two variables:
x + y + z = 10
y + 3z = 4
We can solve for y in the second equation:
y = 4 - 3z
And substitute into the first equation:
x + (4 - 3z) + z = 10
Simplifying:
x + 1z = 6
x = 6 - z
Now we have three equations with three variables:
x + y + z = 10
2x + 3y + 5z = 28
x = 6 - z
We can substitute the expression for x into the first equation:
(6 - z) + y + z = 10
Simplifying:
y = 4 - (6 - z)
y = z - 2
Now we have expressed all three variables in terms of z. We can substitute these expressions into the second equation and solve for z:
2(6 - z) + 3(z - 2) + 5z = 28
Simplifying:
12 - 2z + 3z - 6 + 5z = 28
Combining like terms:
6z + 6 = 28
Solving for z:
z = 3
Now we can use the expressions for x and y to find how many trucks of each model the company should purchase:
x = 6 - z = 3
y = z - 2 = 1
Therefore, the company should purchase 3 trucks of model A, 1 truck of model B, and 6 trucks of model C to provide exactly 28 tons of additional shipping capacity.
Step-by-step explanation:
What is the circumference of the circle? Use 3.14 for π
. Round your answer to the nearest hundredth. please help 100 points
Answer:
b)
Step-by-step explanation:
Becky can make a monthly payment of $530 for a car. If
the annual interest rate she qualifies for is 6% for 4 years,
what price could she afford for the car?
Becky can afford a car with a price of $20,858.33 or less, given her monthly payment of $530, and assuming an annual interest rate of 6% for 4 years.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To calculate the price that Becky can afford for the car, we need to use the present value formula for an annuity:
PV = PMT x [tex]((1 - (1 + r/n)^{(-nt))}[/tex] / (r/n))
where:
PV = present value of the car
PMT = monthly payment
r = annual interest rate
n = number of compounding periods per year
t = number of years
In this case, PMT = $530, r = 6% (or 0.06 as a decimal), n = 12 (since monthly payments are being made), and t = 4. Plugging in these values, we get:
PV = $530 x[tex]((1 - (1 + 0.06/12)^{(-12*4)})[/tex] / (0.06/12))
PV = $20,858.33
Therefore, Becky can afford a car with a price of $20,858.33 or less, given her monthly payment of $530, and assuming an annual interest rate of 6% for 4 years.
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At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Based on the data in the sample, we can estimate that 900 people in attendance would prefer mustard on a hot dog.
How to find the number of people that would prefer mustard on a hot dogAccording to the data provided, out of the 150 people surveyed, 27 people prefer mustard on a hot dog.
To estimate how many people in attendance would prefer mustard on a hot dog, we can use a proportion:
27/150 = x/5000
Where x is the number of people in attendance who would prefer mustard on a hot dog.
To solve for x, we can cross-multiply:
27 x 5000 = 150 x
Simplifying the equation, we get:
x = (27 x 5000)/150
x = 900
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a private student loan at 4.25%, but the rate for such a loan could be 12.59%. Under the same circumstances as Self Check 2 ($10,000 principal, no interest paid while in school) and a rate of 12.59%, what would the principal be when you make your first payment 51 months later? What are some recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations.?
The principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.
What is the principal?To calculate the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59%, we first need to calculate the amount of interest that has accrued over the 51 months.
Using the formula:
Interest = Principal x Rate x Time
where Principal = $10,000,
Rate = 12.59% per year,
Time = 51/12 years (since the interest is compounded monthly):
Interest = $10,000 x 0.1259 x (51/12)
= $5,307.13
So the total amount owed after 51 months would be:
Total amount owed = Principal + Interest
= $10,000 + $5,307.13
= $15,307.13
Therefore, the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.
As for recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations, one example is the Black Lives Matter movement, which has brought attention to systemic racism and police brutality in the United States. Another example is the #MeToo movement, which has raised awareness about sexual harassment and assault and has led to changes in workplace policies and cultural attitudes toward these issues.
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Write the equation in standard form for the circle with center (0,5) and radius 7.
Answer:
[tex]x^2+(y-5)^2=49[/tex]
Step-by-step explanation:
Recall the formula for the graph of a circle:
[tex](x-h)^2+(y-k)^2=r^2\\[/tex]
Where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and r is the radius.
We are given the vertex and the length of the radius.
Substitute the values:
[tex](x-0)^2+(y-5)^2=7^2=\\x^2+(y-5)^2=49[/tex]
Thus, the standard form is:
[tex]x^2+(y-5)^2=49[/tex]
Which choice is NOT equal to the others? Responses A −[[2/5]]−[[2/5]] B [[2/−5]][[2/−5]] C [[−2/5]][[−2/5]] D [[2/5]]
Answer:
B is the answer
Step-by-step explanation:
The expression that is not equal to the others is B [[2/−5]] The other expressions are A −[[2/5]], C [[−2/5]], and D [[2/5]].
Each of forty-nine moviegoers was asked, "What is your favorite movie type?"
Here are the results.
12 men and 10 women chose "Drama".
. 14 men and 13 women chose "Action".
Construct a two-way frequency table for the data.
The numbers in each cell represent the frequency of people who chose that combination of gender and movie type.
What is the frequency?
The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.
To construct a two-way frequency table for the data, we need to organize the responses by gender and movie type. The table is in the attached image.
The rows represent the gender of the moviegoers, and the columns represent the movie type.
The numbers in each cell represent the frequency of moviegoers who chose that combination of gender and movie type.
For example, there are 12 men who chose Drama as their favorite movie type, and there are 13 women who chose Action as their favorite movie type.
The total number of moviegoers who chose Drama is 22, and the total number who chose Action is 27. The total number of moviegoers is 49.
Hence, The numbers in each cell represent the frequency of people who chose that combination of gender and movie type. For example, 12 men chose Drama as their favorite movie type.
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Can someone help me with this problem? I need to find x and y
Answer:
x = √17
y = 10.1
Step-by-step explanation:
x² + 8² = 9²
x² = 81 - 64 = 17
x = √17
sin∅ = √17/9
∅ = 27.27°
9/y = cos(27.27)
y = 9/cos(27.27) = 10.13
y = 10.1
A bag contains 41 U.S. quarters and nine Canadian quarters. (The coins are identical in size.) If six quarters are randomly picked from the bag, what is the probability of getting at least one Canadian quarter? (Round your answer to one decimal place.
%
Answer:
The coins are picked without replacement.
The probability of picking at least one Canadian quarter is 1 minus the probability of picking 6 U.S. quarters:
[tex]1 - ( \frac{41}{50} )( \frac{40}{49} )( \frac{39}{48} )( \frac{38}{47} )( \frac{37}{46} )( \frac{36}{45} ) [/tex]
[tex] = 1 - .28296 = .71704[/tex]
So the probability of picking at least one Canadian quarter is about 71.7%.
PLEASE HELPPPPPP ME PLEASE
If the the a is greater than 1, compared to the parent function the C. Stretched vertically.
How to find the comparison ?The equation y = ax^2 + c represents a quadratic function where "a" is the coefficient of the x^2 term and "c" is a constant term. The parent function of this quadratic function is y = x^2.
If the equation of a quadratic function is given in the form y = ax^2 + c and "a" is greater than 1, then the graph of the function will be stretched vertically and the vertex will be shifted up or down depending on the value of "c".
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What is the perimeter of the trapezoid?
Use circle K for problems 11-13
After calculation we get
11) d. m/JML = 90 degrees, a. m/GMH = 45 degrees, b. mLH = 90 degrees, c. m/LKH = 45 degrees
12) a. AGKH is an isosceles triangle, b. Another triangle formed by two radii is an equilateral triangle.
13) a. m/GKH = 33.4 degrees, c. m/KHJ = 33.4 degrees, e. mJL66.8 degrees, b. m/KGH = 66.8 degrees, d. m/JKL = 113.2 degrees
What is quadrilateral?A quadrilateral is a geometric shape with four straight sides and four angles. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.
According to the given information:
a. Since m/LGH and m/GHJ are both 45°, GH is a bisector of ∠JGL. Therefore, m/GMH = 90° - 45° = 45°.
b. Since GH is a bisector of ∠JGL, m/LGH = m/HGL = 45°. Also, since LH is a straight line, m/LGH + mLH + m/HGL = 180°. Thus, mLH = 90° - 45° = 45°.
c. Since GH is a bisector of ∠LJK, m/GHK = m/JHK = 45°. Also, since LK is a straight line, m/LKH + m/JHK + m/LJK = 180°. Thus, m/LKH = m/LJK = (180° - 2*45°)/2 = 45°.
d. Since GH is a bisector of ∠JGL and JML is a straight line, m/JML = m/JGH + m/HGL = 45° + 45° = 90°.
a. AGKH is a quadrilateral with two sides that are radii of the circle. Since all radii of a circle are equal, AGKH is a kite. Furthermore, since the two radii AG and KH are perpendicular to each other, AGKH is also a rectangle.
b. Another triangle formed by two radii is AKJ, where AK and AJ are radii of the circle and KJ is a chord.
a. Since GH is a diameter of the circle and GKH is a right triangle with ∠GHK = 90°, m/GKH = 180° - 90° = 90°.
b. Since GH is a diameter of the circle and KJ is a chord, m/KGH = m/KJ = 1/2 * m/KHJ = 1/2 * (180° - 113.2°) = 33.4°.
c. Since GH is a diameter of the circle and KHJ is a right triangle with ∠KHJ = 90°, m/KHJ = 180° - m/GKH = 180° - 90° = 90°.
d. Since GH is a diameter of the circle and JKL is a right triangle with ∠JKL = 90°, m/JKL = 180° - m/KJ - m/JKH = 180° - 33.4° - 45° = 101.6°.
e. Since JL is a chord of the circle and ∠JGL is an inscribed angle that intercepts it, m/JGL = 1/2 * m/JL = 1/2 * (180° - m/JKL) = 1/2 * (180° - 101.6°) = 39.2°. Also, since GH is a diameter of the circle and GJL is a right triangle with ∠GJL = 90°, m/GJL = 90° - m/GHL = 90° - 45° = 45°. Therefore, m/JLH = m/JGL - m/GLH = 39.2° - 45° = -5.8°. Note that the negative value indicates that ∠JLH is a reflex angle.
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Translate in two ways each of these statements into logical expressions using predcates quantifiers and logical connective first let the domain consist of the students in your class and second let it consist of all people a) everyone in your class has a cellular phone
For all x, P(x) (using universal quantifier ∀) and It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
1. For all x in S, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
For all x, P(x) (using universal quantifier ∀)
It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
For all x in S, P(x) (using universal quantifier ∀)
It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
1. For all x, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
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50 Points! Multiple choice algebra question. Shen is simplifying the expression (3x^4+4x^2) (x^3-2x^2-1). Which of the following shows the correct product. Photo attached. Thank you!
So, multiple choice algebra questions. the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2[/tex].
To simplify the given expression [tex](3x^4+4x^2) (x^3-2x^2-1)[/tex], we can use the distributive property of multiplication to multiply each term of the first expression by each term of the second expression. This gives us:
[tex](3x^4+4x^2) (x^3-2x^2-1) \\= 3x^4(x^3) + 3x^4(-2x^2) + 3x^4(-1) + 4x^2(x^3) - 4x^2(2x^2) - 4x^2(1)[/tex]
Simplifying each term, we get:
[tex]= 3x^7 - 6x^6 - 3x^4 + 4x^5 - 8x^4 - 4x^2[/tex]
So, the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2.[/tex]
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Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $6. If Kyd selects any other type of card, he pays North $3.
Kyd's expected value is positive and North's expected value is negative, Kyd has the advantage in this game
What is expected value?
Expected value is a concept used in probability theory to describe the average value or outcome of a random variable over many trials. It is calculated by multiplying each possible outcome of a variable by its probability, and then summing all of the products. This can help to estimate the most likely outcome or value of an uncertain event or situation.
The probability of selecting a face card from a standard 52-card deck is 12/52 or 3/13. The probability of selecting any other type of card is 1 - 3/13 or 10/13.
Kyd's expected value for this game can be calculated as follows:
(3/13) x (-$3) + (10/13) x $6 = $3.38
Therefore, Kyd's expected value for this game is $3.38.
North's expected value for this game can also be calculated as follows:
(3/13) x $6 + (10/13) x (-$3) = -$0.92
Therefore, North's expected value for this game is -$0.92.
Since Kyd's expected value is positive and North's expected value is negative, Kyd has the advantage in this game.
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nvrm i got it i am him
How to solve it and the answer
Answer: The answer is, y=18x
Step-by-step explanation: This is going up by 18 as the y axis increases by 9. Hope this helped :)
please help <3 gracias
The function evaluated in x = 2 is:
3f(2) =12
How to evaluate the function?Here we know that:
f(x) = x^2
And we want to evaluate the expression:
3f(2)
To do that replace x by 2.
3f(2) = 3*(2^2) = 3*4 = 12
That is the value of the expression.
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can u slove ASAP please
Answer:
B) 352
Step-by-step explanation:
45% = 0.45
640 x 0.45= 288
288 is how many students walked to school
So to find how many took the bus to school
640- 288= 352
State any domain restrictions for the expression below from least to greatest (for example: -2,-1,0,1,2), by using one answer box for each domain restriction, then simplify the expression in the last answer box. (81-x²) (x² + 2x − 63) 2x² - 6x 3x2 30x + 63 3x 81x² ÷
The domain restrictions on the function [tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex] are the x values -9, 0, 3, 4 and 9
From the question, we have the following function that can be used in our computation:
[tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex]
Next, we set the denominator to 0 and solve for x
So, we have
81 - x²: x = ±9
2x² - 6x: x = 0 and x = 3
x² + 2x - 6x: x = 0 and x = 4
Hence, the domain restrictions are the x values -9, 0, 3, 4 and 9
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Trangle ABC has an area 25 square feet and perimeter of 65.5 feet of triangle ABC is dilated by a factor of 5/2 to create now calculate the area of trangle DEF using the scale factor
So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.
What is dilation?the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.
In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.
For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.
Let's start by using the formula for the perimeter of a triangle:
[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]
We can also use Heron's formula to find the area of triangle ABC:
[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
where s is the semi perimeter of the triangle:
[tex]s = (AB + BC + AC) / 2[/tex]
We can use these equations to solve for the side lengths of triangle ABC:
[tex]AB + BC + AC = 65.5[/tex]
[tex]s = (AB + BC + AC) / 2[/tex]
[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
Solving for AB, BC, and AC gives us:
AB = 15
BC = 20
AC = 30.5
Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.
DE = AB * (5/2) = 37.5
EF = BC * (5/2) = 50
DF = AC * (5/2) = 76.25
Now we can use Heron's formula again to find the area of triangle DEF:
s = (DE + EF + DF) / 2 = 81.875
Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet
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Tyrone has $800 in a savings account that earns 10% annually. The interest is not compounded. How much will he have in total in 1 year?
Answer: $80
Step-by-step explanation:
If Tyrone's savings account earns a simple 10% annual interest and is not compounded, then the interest for one year can be calculated using the formula:
Interest = Principal × Rate × Time
where:
Principal = $800
Rate = 10% = 0.1
Time = 1 year
Interest = $800 × 0.1 × 1 = $80
Tyrone will earn $80 in interest in 1 year. To find the total amount in his account after 1 year, we add the interest to the principal:
Total amount = Principal + Interest
Total amount = $800 + $80 = $880
In 1 year, Tyrone will have $880 in total in his savings account.
Answer:
$880
Step-by-step explanation:
10% = .1
800 x .1 = 80
80 + 800= 880
A large production facility uses two machines to produce a key part for its main product. Inspectors have expressed concern about the quality of the finished product. Quality-control investigation has revealed that the key part made by the two machines is defective at times. The inspectors randomly sampled 35 units of the key part from each machine. Of those produced by machine A, 5 were defective. Seven of the 35 sampled parts from machine B were defective. The production manager is interested in estimating the difference in proportions of the populations of parts that are defective between machine A and machine B. From the sample information, compute a 98% confidence interval for this difference.
The range of the 98% confidence interval for the percentage of faulty components that differ between machines A and B is about between -0.2448 and 0.1305. (rounded to 4 decimal places).
How can you figure up a confidence interval for the proportional difference?Define the populations of interest and the characteristic you want to compare (e.g., proportion of success or failure).Collect random samples from each population and record the number of occurrences of the characteristic of interest in each sample.Calculate the sample proportions ([tex]p_1 \;and \;p_2[/tex]) by dividing the number of occurrences by the sample size for each population.Calculate the standard error (SE) of the difference in proportions using the sample proportions, sample sizes, and appropriate formula (SE = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex], where[tex]p_1 \;and \;p_2[/tex] are the sample proportions and[tex]n_1 \;and \;n_2[/tex] are the sample sizes for the two populations, respectively).Determine the appropriate critical value from the probability distribution (e.g., standard normal distribution for large sample sizes or t-distribution for small sample sizes) based on the desired confidence level.Calculate the margin of error (ME) by multiplying the standard error by the critical value (ME = critical value * SE).Construct the confidence interval by adding and subtracting the margin of error from the sample statistic (e.g., the difference in sample proportions, or the ratio of sample proportions).Interpret the confidence interval, stating that we can be [confidence level]% confident that the true population parameter falls within the calculated interval.Given:
Sample proportion from machine A ([tex]p_1[/tex]) = 5/35 = 0.14285714285714285
Sample proportion from machine B ([tex]p_2[/tex]) = 7/35 = 0.2
Sample size from machine A ([tex]n_1[/tex]) = 35
Sample size from machine B ([tex]n_2[/tex]) = 35
Standard error (SE) = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex]
= [tex]\sqrt{[0.14285714285714285 * (1 - 0.14285714285714285) / 35] + [0.2 * (1 - 0.2) / 35] }[/tex]
= 0.07058061453775912 (rounded to 11 decimal places)
Margin of error (ME) = Critical value * Standard error
= 2.660 * 0.07058061453775912 (using z-score for a 98% confidence level)
= 0.18765117789861733 (rounded to 11 decimal places)
Confidence interval (CI) = Sample statistic ± Margin of error
= [tex](p_1 - p_2) \pm ME[/tex]
= (0.14285714285714285 - 0.2) ± 0.18765117789861733
= -0.05714285714285715 ± 0.18765117789861733
The 98% confidence interval for the difference in proportions of defective parts between machine A and machine B is approximately -0.2448 to 0.1305 (rounded to 4 decimal places).
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What number is halfway between 10 and 17
Answer:
13.5
Step-by-step explanation:
10+17=27
27/2=13.5
Answer:
13.5
Step-by-step explanation:
What number is halfway between 10 and 17
tanya has a dog leash that is 4 yards long. she shortens the leash by 6 feet.what is the lenght of shortened leash
Answer:
2 yards or 6 feet long
Step-by-step explanation:
Each yard is 3 feet long.
If Tanya shortens the leash by 6 feet, that is 2 yards.
4-2=2
The leash is 2 yards (or 6 feet) long.
Answer:
6 foot
Step-by-step explanation:
1 yards = 3 foot
4 yards = 12 foot
We take
12 - 6 = 6 foot
So, the length of the shortened least is 6 foot.