After 3 years and 9 months, the copier is worth $30,750. After 5 years, the salvage value of the copier is $35,000. The domain of the function is 0 <= t <= 5.
a. To find the value of the copier after 3 years and 9 months, we need to plug in the value of t into the function V(t). Since 3 years and 9 months is equivalent to 3.75 years, we plug in 3.75 for t:
V(3.75) = 3400(3.75) + 18000
V(3.75) = 12750 + 18000
V(3.75) = 30750
Therefore, the copier is worth $30,750 after 3 years and 9 months.
b. To find the salvage value of the copier after 5 years, we need to plug in 5 for t into the function V(t):
V(5) = 3400(5) + 18000
V(5) = 17000 + 18000
V(5) = 35000
Therefore, after 5 years, the salvage value of the copier is $35,000.
c. The domain of this function is the set of all possible values of t. Since the function is defined for the first 5 years of use, the domain is 0 <= t <= 5.
d. To sketch the graph of this function, we can plot a few points and connect them with a line. For example, we can plot the points (0, 18000), (1, 21400), (2, 24800), (3, 28200), (4, 31600), and (5, 35000). The graph will be a straight line with a positive slope, starting at (0, 18000) and ending at (5, 35000).
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please help asap and show work
Answer:
(-3, -4)
Step-by-step explanation:
Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise or counterclockwise direction, produces a point that has the coordinates (−x,−y). Ari's error was that she rotated "N" by 90 degrees instead of 180 degrees, as the rule for a 90 degree rotation is (-y, x). Therefore, the correct coordinated for N' can only be (-3,-4)
Perform the following conversions. With math explanation
300 ft = m
130 cm = in
0.5hp = W
350psi = Pa
10 ????????/????????3 = ????????/m3
350 W = ????T????/ℎ
10,000 cal = ????
a)91.44 m
b)51.18 in
c)372.85 W
d)2383186.955 Pa
e)10000 ????????/m3
f)0.4667 T????/ℎ
g)41840 J
300 ft = m
1 ft = 0.3048 m, so 300 ft = 300 * 0.3048 m = 91.44 m
130 cm = in
1 in = 2.54 cm, so 130 cm = 130/2.54 in = 51.18 in
0.5hp = W
1 hp = 745.7 W, so 0.5 hp = 0.5 * 745.7 W = 372.85 W
350psi = Pa
1 psi = 6894.757 Pa, so 350 psi = 350 * 6894.757 Pa = 2383186.955 Pa
10 ????????/????????3 = ????????/m3
1 ????????/????????3 = 1000 ????????/m3, so 10 ????????/????????3 = 10 * 1000 ????????/m3 = 10000 ????????/m3
350 W = ????T????/ℎ
1 W = 0.00134 T????/ℎ, so 350 W = 350 * 0.00134 T????/ℎ = 0.4667 T????/ℎ
10,000 cal = ????
1 cal = 4.184 J, so 10,000 cal = 10,000 * 4.184 J = 41840 J
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1. IF HEIGHTS OF FEMALE COLLEGE STUDENTS ARE NORMALLY DISTRIBUTED WITH A MEAN OF 64 INCHES AND A STANDARD DEVIATION OF 10 INCHES, WHAT IS THE PROBABILITY OF RANDOMLY SELECTING A FEMALE COLLEGE STUDENT WITH A HEIGHT LESS THAN 63 INCHES.
2. WHAT IS THE PROBABILITY OF RANDOMLY SELECTING A FEMALE COLLEGE STUDENT WITH A HEIGHT BETWEEN 61 AND 69 INCHES?
3. WHAT IS THE PROBABILITY OF FINDING AN AVERAGE OF GREATER THAN 65 INCHES WITH A SAMPLE OF 35 FEMALE COLLEGE STUDENTS?
a)0.1587 (or 15.87%)
b)0.6827 (or 68.27%)
c)0.0228 (or 2.28%)
1. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height less than 63 inches is 0.1587 (or 15.87%).
2. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height between 61 and 69 inches is 0.6827 (or 68.27%).
3. Using the Central Limit Theorem, the probability of finding an average of greater than 65 inches with a sample of 35 female college students is 0.0228 (or 2.28%).
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A college entrance exam has a mean of 500 and a standard deviation of 100 in the population. A small liberal arts college has 100 applicants with a mean of 510. The college wants to determine whether its applicants have significantly higher scores than the general population of applicants. The data analyst obtains a t statistic of 1. 70 and a one-tailed probability of. 4. What would the probability be if the analyst performed a two-tailed test?
The probability when analyst performed a two-tailed test for the given one tailed probability is equal to 0.2.
Mean = 500
Standard deviation = 100
Number of applicants in art college = 100
Mean of the art college = 510
t-statistic = 1.70
One tailed probability = 0.4
Analyst performed a two-tailed test,
⇒ Probability value = 2(one-tailed probability value)
In a two-tailed test, deviations from the mean in both directions.
Probability of observing values are both higher and lower than the mean.
⇒ Probability for two-tailed test = Probability value for one-tailed test / 2
⇒Probability for two-tailed test = 0.4 / 2
⇒Probability for two-tailed test = 0.2
Therefore, the probability for a two-tailed test is equal to 0.2.
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Adina makes 53112 per year and is looking to find a new apartment rental in her city. She searched online and found an apartment for 1500 per month. The recommendation is to budget between 25% and 30% of your monthly income for rent. Can Adina afford this apartment based upon the recommended interval? Explain.
( i have to show my work )
What are the solutions for the equation 6x²-11x-7=0
The solutions for the equation 6x²-11x-7=0 are x = -1/2 and x = 7/3
How to determine the solutionIt is important to note that quadratic equations are defined as equations having the highest degree of x as 2.
From the information given, we have that the quadratic equation is given as;
6x²-11x-7=0
Now, multiply the coefficient of x squared with the constant value, then find the pair factors of the product that adds up to given the coefficient of x = -11
We have;
6x² - 14x + 3x - 7 =0
Group the expression in pairs
(6x² - 14x) + (3x - 7) = 0
Factor the expressions
2x(3x - 7) + 1(3x - 7) = 0
Then, we have;
(2x + 1) and (3x - 7) = 0
x = -1/2
x = 7/3
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The number of blueberry muffins that a baker makes each day is 30% of the total number of muffins she makes.
A. On Monday, the baker makes 42 blueberry muffins. What is the total number of muffins that the baker makes on Monday?
B. On Tuesday, the baker makes a total of 60 muffins. How many blueberry muffins does the baker make on Tuesday?
The baker makes a total of 140 muffins on Monday.
The baker makes 18 blueberry muffins on Tuesday.
What are percentages?
Percentages are a way of expressing a fraction or proportion out of 100. The term "percent" literally means "per hundred." Percentages are commonly used in many areas of everyday life, including finance, science, and statistics.
To express a number as a percentage, it is multiplied by 100. For example, 0.75 is equivalent to 75 percent, since 0.75 x 100 = 75. Similarly, 50 percent is equivalent to 0.5 or 1/2.
Percentages are commonly used to express changes and comparisons. For example, if a product's price increases from $100 to $120, this represents a 20 percent increase in price. If a person scored 80 out of 100 on a test, this represents an 80 percent score.
Percentages are also used to calculate percentages of a total. For example, if a person earned $40,000 out of a total company income of $500,000, their income represents 8 percent of the total income. Similarly, if a person wants to calculate a 20 percent tip on a $50 meal, they would calculate 20 percent of $50, which is $10.
In summary, percentages are a way of expressing a fraction or proportion out of 100, and are commonly used to express changes, comparisons, and percentages of a total in everyday life.
A. Let's assume the total number of muffins the baker makes on Monday to be x.
According to the problem, the number of blueberry muffins that the baker makes is 30% of the total number of muffins.
So, 30% of x is equal to 42:
0.30x = 42
To solve for x, we can divide both sides by 0.30:
x = 140
Therefore, the baker makes a total of 140 muffins on Monday.
B. Let b be the number of blueberry muffins the baker makes on Tuesday.
According to the problem, the number of blueberry muffins is still 30% of the total number of muffins. So, we can set up the equation:
0.30(60) = b
Simplifying the left side:
18 = b
Therefore, the baker makes 18 blueberry muffins on Tuesday.
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Line f has a slope of -2 and line g has a slope of -8/4. What relationship do the lines have, based on their slopes?
A.) The lines intersect.
B.)The lines intersect to form right angles.
C.)The lines are parallel.
D.)No relationship can be determined.
The lines are parallel , based on their. So the C option is correct.
What is slope formula?
The formula to find the slope between 2 coordinates of a line is given by;
m = (y₂ - y₁)/(x₂ - x₁)
Line f has a slope of -2 and line g has a slope of -8/4. To determine the relationship between the lines based on their slopes, we can compare their slopes.
If two lines have the same slope, they are parallel. If two lines have slopes that are negative reciprocals of each other, they are perpendicular (and intersect to form right angles). Otherwise, the lines are neither parallel nor perpendicular and will intersect at some point.
The slope of line g can be simplified to -2, which is the same as the slope of line f. Therefore, the lines f and g have the same slope and are parallel (option C).
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Function g is a transformation of f(x) = 2x. Compare the graphs of the functions. Select all that apply.
x= 1 2 3 4 5
g(x)= 1/8 1/4 1/2 1 2
In response to the query, we have that The two graphs are oriented and coordinates have the same form in common. The moment where the two graphs come together (1, 2).
what are coordinates?A coordinate system is a technique used in geometry to precisely locate points or other geometry objects on a manifold, also including Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional sphere is located using a pair of numbers known as coordinates. The x and y positions are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second column represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.
f(1/x) = 2/(1/x) = 2x, where g(x) =
Hence, g(x) = f(1/x) is equivalent to f(x) = 2x.
The values of x and g(x) are as follows:
x= 1 2 3 4 5\sg(x)= 1/8 1/4 1/2 1 2
f(x) = 2x: (1, 2), (2, 4), (3, 6), (4, 8), (5, 10) (5, 10)
g(x) = f(1/x) = 2x: (1, 2), (1/2, 1), (1/3, 2/3), (1/4, 1/2), (1/5, 2/5)
The appropriate choices are thus:
A reflection of the graph of f(x) about the line y = x is the graph of g(x).
The two graphs are oriented and have the same form in common.
The moment where the two graphs come together (1, 2).
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Solve the equation. Don't forget to first simplify each side of the equation, if possible. 2(2z-3)=3(z+3)
The solution to the equation is z = 15.
To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.
On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:
2(2z) - 2(3) = 4z - 6
On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:
3(z) + 3(3) = 3z + 9
Now we can rewrite the equation as:
4z - 6 = 3z + 9
Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:
4z - 3z = 9 + 6
Simplifying gives us:
z = 15
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(a) Show the following o-fields are equal to each other: i. B= o({(-20,x); r < R}); ii. B2 = o({(-0,2); 2 € R}); [Note either of them can be taken as the definition of the Borel sigma field on the real line.]
The following o-fields are equal to each other because they both represent the Borel sigma field on the real line:
i. B= o({(-20,x); r < R})
ii. B2 = o({(-0,2); 2 € R})
Note that the Borel sigma field on the real line is the smallest sigma field containing all the open intervals on the real line. This means that any set that can be constructed from countable unions, intersections, and complements of open intervals is in the Borel sigma field.
In the first o-field, B= o({(-20,x); r < R}), the set {(-20,x); r < R} is an open interval on the real line, so it is in the Borel sigma field. Similarly, in the second o-field, B2 = o({(-0,2); 2 € R}), the set {(-0,2); 2 € R} is also an open interval on the real line, so it is also in the Borel sigma field.
Since both o-fields contain sets that are in the Borel sigma field, they are both equal to the Borel sigma field on the real line. Therefore, B= o({(-20,x); r < R}) = B2 = o({(-0,2); 2 € R}).
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Mrs. Andretti is having new drapes made for her living room. The cost of the fabric is $15 per yard. The fee to make and hang the drapes is $250. She uses the expression 15x + 250 to calculate the total cost of the drapes. Mrs. Andretti states that x represents the total cost of the fabric. Is she correct? Responses Yes, x represents the total cost of the fabric. Yes, x represents the total cost of the fabric. No, x represents the total cost of the drapes. No, x represents the total cost of the drapes. No, x represents the total yards of fabric used. No, x represents the total yards of fabric used. No, x represents the total amount of fabric she already has.
Mrs. Andretti is right, of course. In the equation 15x + 250, x stands for the fabric's overall expense.
what is expression ?An expression in mathematics is a collection of numbers, variables, and operations that can be evaluated to create a value, including addition, subtraction, multiplication, and division. Expressions can be straightforward—like 3 + 4 or 5x—or complex—involving numerous factors and operations. From basic arithmetic to intricate functions and equations, a broad range of mathematical concepts can be represented by expressions.
given
The fabric's overall cost is indicated by the value x.
No, x stands for the drapes' total expense.
No, x is the overall number of yards of fabric used.
Mrs. Andretti is right, of course. In the equation 15x + 250, x stands for the fabric's overall expense.
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I’ve tried it so many times and can’t get the answer
Answer:
(364.0, 236.4)
Step-by-step explanation:
You want the vector 434∠33° written as an ordered pair.
Ordered pairThe "ordered pair" representation of a vector can take different forms. we're not sure the form your curriculum materials are asking for, so we'll show it a couple of ways.
(magnitude; direction) = (434; 33°) or maybe (434, 33)
(x, y) = 434·(cos(33°), sin(33°) ≈ (364.0, 236.4)
__
Additional comment
We like the form used in the problem statement above (434∠33°) for vectors expressed in polar form. For vectors expressed in rectangular form, many calculators work nicely with a complex number representation (364 +236.4i).
The ordered pair using a semicolon (;) separator is written that way to distinguish it from the (x, y) ordered pair. That form is used by some geometry software. A calculator may use [434, 33] or [364, 236.4] (for example), leaving it up to the user to remember what the pair represents.
Some authors use a combination of complex and polar representations like this:
A(cos(B) +i·sin(B)) = A·cis(B)
In this, the "cis" is a reminder of the "cosine + i·sine" complex number representation. It is also a longer way to write A∠B.
The second attachment shows our preferred calculator using our preferred vector notations. YMMV
→ Be sure your calculator is in "degrees" mode.
An umbrella was sold for rupees 279 in the off season at a loos for 7% find original price of umbrella
Answer:
300
Step-by-step explanation:
x(100%-7%)=279
0.93x=279
x=300
Answer this
………………..
The slope of the linear equation is; 0.5
The y-intercept of the Linear Equation is: 4.75
Yes the equation is proportional
What is the graph of the linear Equation?The equation we are given is expressed as;
y = ¹/₂x + 4³/₄
When x = 0,
y = ¹/₂(0) + 4³/₄
y = 4.75
When x = 1,
y = ¹/₂(1) + 4³/₄
y = 5.25
When x = 2,
y = ¹/₂(2) + 4³/₄
y = 5.75
When x = 3,
y = ¹/₂(3) + 4³/₄
y = 6.25
If we go on and on till x = 10, we will see the constant difference in y for every change in x is 0.5
Thus, slope = 0.5
y-intercept = 4.75
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RATIONAL EXPRESSIONS Solving a rational equation that simplifies to quadratic: Binomial... Solve for x 2-(5)/(x+7)=-(7)/((x-3)(x+7)) If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". x
X = 7 & -7/2
First, use the distributive property to simplify the equation:
2 - 5/(x+7) = -7/(x-3)(x+7)
2(x-3)(x+7) - 5(x-3) = -7(x+7)
2x2 + 7x - 6x - 15 = -7x - 49
2x2 -13x - 49 = 0
This equation can be solved by factoring the binomial:
2x2 -13x - 49 = 0
2x(x-7) - 7(x-7) = 0
(2x-7)(x-7) = 0
Therefore, the solution for x is x = 7 and x = -7/2.
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Use the Distributive
Property to express
24 + 36
Answer:
60
Step-by-step explanation:
24 + 36 = 60
You can use the Gold Digger for the distributive property! * Factor as if you want to find the Greatest Common Factor.
Your favorite restaurant is at the intersection of Second Street and Washington Boulevard.
Second Street is on y =
-4
x + 4.
3
Washington Boulevard is on 7y = 3x -9. With the help of this map, can you figure out the
name of this eatery?
19-8
Answer:
To find the name of the restaurant, we need to find the intersection point of the two streets.
The equation of Second Street is y = (-4/3)x + 4/3.
The equation of Washington Boulevard is y = (3/7)x - 3/7.
To find the intersection point, we can set the two equations equal to each other:
(-4/3)x + 4/3 = (3/7)x - 3/7
Multiplying both sides by 21 (the least common multiple of 3 and 7) to eliminate fractions, we get:
-28x + 28 = 9x - 9
Bringing all the x terms to one side and all the constants to the other side, we get:
-37x = -37
Dividing both sides by -37, we get:
x = 1
Substituting this value of x into either equation, we can find y:
y = (-4/3)(1) + 4/3 = 0
Therefore, the intersection point of Second Street and Washington Boulevard is (1,0), which means the restaurant is located at that point.
Step-by-step explanation:
Two cheeseburgers and one small order of fries contain a total of 1420 calories. Three cheeseburgers and two small orders of fries contain a total of 2290 calories. Find the caloric content of each item.
One cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Two cheeseburgers and one small order of fries contain a total of 1420 calories.
Three cheeseburgers and two small orders of fries contain a total of 2290 calories.
let the number of Calories in one cheeseburgers be x and in one fries be y.
So, the system of Equation is:
2x + y = 1420
3x + 2y= 2290
solving the above two equation
x= 550 and y= 320
So, one cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.
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The math coach is delivering boxes of books to classrooms. She has 495 books to deliver. Each box contains 15 books. She has already delivered 4 boxes. Write an equation, where b is the number of boxes of books, that the math coach still needs to deliver.
Answer:
The math coach has delivered 4 boxes of books, so the number of boxes she still needs to deliver is b. Each box contains 15 books, so the total number of books she still needs to deliver is 15b. She has 495 books to deliver in total. Therefore, we can write the equation:
15b = 495 - 4(15)
Simplifying the right-hand side:
15b = 495 - 60
15b = 435
Dividing both sides by 15:
b = 29
So the math coach still needs to deliver 29 boxes of books.
Which rational number has a different value than the others?
A. 44%
B. 22/50
C. 0.44
D. 4/9
help plsssssssssssssssssss
Answer: Third answer option, [tex]\sqrt{3} *\sqrt{12}[/tex]
Step-by-step explanation:
Both 3 and 9 are not irrational numbers, so the first option is incorrect.
The [tex]\sqrt{3}[/tex] is irrational, but 0 is not, so the second option is also incorrect.
The [tex]\sqrt{3}[/tex] and [tex]\sqrt{12}[/tex] are both irrational. Let us see if they result in a rational number when multiplied together;
[tex]\sqrt{3} *\sqrt{12} =\sqrt{3*12} =\sqrt{36} =6[/tex]
They do, so this answer option is correct.
A grocer wants to create a 40 pound mixture of almonds and cashews that will sell for $12.50 per pound. The almonds sell for $10 per pound and the cashews sell for $14 per pound. How many pounds of each should the grocer use?
The grocer should use 15 pounds of almonds and 25 pounds of cashews to create a 40 pound mixture that will sell for $12.50 per pound.
To create a 40 pound mixture of almonds and cashews that will sell for $12.50 per pound, the grocer should use a combination of both almonds and cashews that will give him the desired price. We can use a system of equations to solve for the amount of each ingredient the grocer should use. Let x be the amount of almonds and y be the amount of cashews.
The first equation is the total weight equation: x + y = 40The second equation is the total cost equation: 10x + 14y = 12.50(40)Solving for x in the first equation gives us: x = 40 - y
Substituting this value of x into the second equation gives us: 10(40 - y) + 14y = 12.50(40)
Simplifying and solving for y gives us: 4y = 100 -> y = 25
Substituting this value of y back into the first equation gives us: x + 25 = 40 -> x = 15
Therefore, the grocer should use 15 pounds of almonds and 25 pounds of cashews to create a 40 pound mixture that will sell for $12.50 per pound.
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Evaluate each logarithm by using properties of logarithms and the following facts.
loga(x) = 3.1 loga(y) = 5.8 loga(z) = 1.1
(a) loga (xy)
(b) loga (x/z)
(c) loga (y7)
(d) loga (square root y)
Please explain how to figure these out. Thank you ! Any help is appreciated!
We can use the properties of logarithms to evaluate each expression. The properties of logarithms include:
1) loga (xy) = loga (x) + loga (y)
2) loga (x/z) = loga (x) - loga (z)
3) loga (x^p) = p loga (x)
4) loga (square root x) = (1/2) loga (x)
Using these properties, we can evaluate each expression as follows:
(a) loga (xy) = loga (x) + loga (y) = 3.1 + 5.8 = 8.9
(b) loga (x/z) = loga (x) - loga (z) = 3.1 - 1.1 = 2
(c) loga (y^7) = 7 loga (y) = 7 * 5.8 = 40.6
(d) loga (square root y) = (1/2) loga (y) = (1/2) * 5.8 = 2.9
Therefore, the answers are:
(a) loga (xy) = 8.9
(b) loga (x/z) = 2
(c) loga (y^7) = 40.6
(d) loga (square root y) = 2.9
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Student Edition. Geometry. Volume 2 < 75 of 350---> 5. BLUEPRINTS Ezra is redrawing the blueprint shown of a stage he is planning to build for his band. By what percentage should he multiply the dimensions of the stage so that the dimensions of the image are the size of the original blueprint? What will be the perimeter of the updated blueprint? (Example 2) 10 units 4 units 8 units Long Description 10 units 2 units
Ezra should increase the stage's dimensions by the following factor in order to make the picture half the size of the original blueprint:
50%.
The modified blueprint will have a perimeter that is half that of the original layout.
What is a dilation?When the scale factor is multiplied by the coordinates of an image's vertices, the result is a dilatation, which alters the side lengths of a figure.
The scale factor of the dilation is supplied as follows because, for this issue, we want the updated stage's dimensions to be half those of the original stage.
k = 1/2.
Given that both the perimeter and the side lengths have the same unit, 50%, or half of the original stage's perimeter, will be represented by the updated stage's perimeter.
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A toy rocket is launched from the top of a building 128 feet tall at an initial velocity of 236 feet per second. a) Give the function that describes the height
A toy rocket is launched from the top of a building 128 feet tall at an initial velocity of 236 feet per second.
a) Give the function that describes the height of the rocket in terms of time t.
b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet.
c) For what time interval will the rocket be more than 845 feet above ground level?
d) After how many seconds will it hit the ground?
The function that describes the height of the rocket in terms of time t is h(t) = -16t² + 236t + 128
The maximum height is 962.125 feet.
The rocket reaches its maximum height at 14.75 seconds.
The rocket will hit the ground after 14.88 seconds.
a) The function that describes the height of the rocket in terms of time t is given by:
h(t) = -16t² + 236t + 128
b) To determine the time at which the rocket reaches its maximum height, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:
t = -b/2a = -236/(2*-16) = 7.375 seconds
The maximum height is then found by plugging this value of t back into the function:
h(7.375) = -16(7.375)² + 236(7.375) + 128 = 962.125 feet
c) To find the time interval during which the rocket is more than 845 feet above ground level, we need to solve the inequality:
-16t² + 236t + 128 > 845
Rearranging and factoring gives:
-16t² + 236t - 717 < 0
(4t - 59)(-4t + 12) < 0
The solutions to this inequality are t = 59/4 and t = 12/4. Therefore, the rocket will be more than 845 feet above ground level for the time interval 12/4 < t < 59/4, or 3 < t < 14.75 seconds.
d) To find when the rocket will hit the ground, we need to solve the equation:
-16t² + 236t + 128 = 0
Using the quadratic formula gives:
t = (-236 ± √(236² - 4(-16)(128)))/(2(-16))
t = (-236 ± 244.28)/(-32)
The two solutions are t = 14.88 seconds and t = -0.51 seconds. Since time cannot be negative, the rocket will hit the ground after 14.88 seconds.
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6. Construct a golden spiral that involves a golden rectangle with length 4 meters
1:1.618 (the golden ratio).
To construct a golden spiral that involves a golden rectangle with length 4 meters, first draw a 4 meter long line. Divide it into two segments, such that the longer segment has a ratio of 1:1.618 (the golden ratio) to the shorter segment.
Draw a right angle at the end of the shorter segment. This creates a square that has a side length of 4 meters. Draw an arc centered at the intersection of the two line segments with a radius equal to the shorter segment and connect the ends of the arc. This creates a golden rectangle with a length of 4 meters.
Draw a quarter circle at each corner of the golden rectangle and connect the endpoints. This creates a spiral, and it is a golden spiral if the ratio of the lengths of the two line segments is 1:1.618 (the golden ratio).
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Which piecewise function represents the graph?
Answer:
A
Step-by-step explanation:
trust
PLEASE HELP
An insurance company monitors accidents at rock concerts.
When someone is injured while dancing in a mosh pit,
"moshing", the company collects information about the
victim. Some statistical data about the ages of those injured
is shown below..
N Mean
66 20.136
StDev Min Q1 Median Q3 Max
5.099 13 17
19
22 47
Using the data above, which of these ages is considered an
outlier?
22.0
19.0
29.5
25.5
The measure that is considered an outlier is the data-set is a measure of 29.5.
What is the interquartile range of a data-set?The interquartile range is calculated as the difference between the third quartile and the first quartile.
The values that are outliers are given as follows:
At least 1.5 IQR below Q1.At least 1.5 IQR above Q3.The quartiles for this problem are given as follows:
Q1 = 17, Q3 = 22.
Hence the IQR is of:
IQR = 22 - 17
IQR = 5.
Meaning that the outliers are given as follows:
Values that are at most 17 - 1.5 x 5 = 9.5.Values that are at least 22 + 1.5 x 5 = 29.5.More can be learned about interquartile range at brainly.com/question/12323764
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an international company had 19700 employes in one country that is 22.9 percent of there employs, how many employies do they have in all
Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.
What formula is used to calculate a percentage?We must first divide the value by the whole sum, and then multiply the result by 100 to get the percentage.
Let's use algebra to solve the problem.
If 19,700 employees represent 22.9% of the company's total number of employees, we can write:
0.229 = 19,700 / Total number of employees
To find the total number of employees, we can isolate the variable on one side of the equation:
Total number of employees = 19,700 / 0.229
Using a calculator, we get:
Total number of employees = 86,026.2
Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.
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