Answer: $14697.51
Step-by-step explanation:
[tex]9126(1+0.10)^{5} \approx \$14697.51[/tex]
The area of the circle is increasing at a constant rate of 5 square centimeters per second. At what rate, in centimeters per second, is the radius increasing at the instant when the radius is 5 centimeters
The rate in centimeters per second, at which the radius is increasing at the instant when the radius is 5 centimeters is 0.16 cm/s.
What is the Rate Of Change?Using a known value of a function at a certain point along with its rate of change at that moment, one application of derivatives is to estimate an unknown value of a function at a particular point.
Given:
Both radius r and area A is a function of time, so in fact:
A(t) = π [r(t)]²
Deriving this we get that the area changes and the radius changes as:
[tex]\frac{dA(t)}{dt} = 2\pi r(t)\frac{dr(t)}{dt}[/tex]
But,
[tex]\frac{dA(t)}{dt} = 5 \frac{cm^{2} }{s}[/tex]
Considering when r(t) = 5cm at the instant we get,
[tex]5 = 2\pi . 5\frac{dr(t)}{dt}[/tex]
Simplify 5 and take 2π to the other side and divide,
The rate of change of radius is given by:
[tex]\frac{dr(t)}{dt} =\frac{1}{2\pi } = 0.16 cm/s[/tex]
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Let f(x) = x³ + 2x² + 7x - 11 and g(x) = 3f(x). Which of the following describes g as a
function of f and gives the correct rule?
A.) horizontal compression; g(x) = 3x³ + 6x² + 21x - 33
B.)horizontal stretch; g(x) = 27x3 + 18x² +21x - 11
C.)vertical stretch; g(x) = 3x3 + 6x² +21x - 33
D.)vertical compression; g(x) = 27x³ + 18x² + 21x - 11
Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11 = -1 and g(x) = 3f(x) = -3
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope.
Here,
Given:
we have been provided with -
f(x) = x³ + 2x² + 7x - 11
so, x = 1
f(x) = 1 +2 +7 -11= -1
g(x) = 3f(x) = -3
Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11 = -1 and g(x) = 3f(x) = -3
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What transformation is happening
Answer:
Probably c: f(x) = y + 3
Step-by-step explanation:
See attached worksheet
Coins are placed into a treasure chest, and each coin has a radius of 1.6 inches and a height of 0.0625 inches. If there are 170 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
341.63 in3
106.76 in3
85.41 in3
0.50 in3
85.41 cubic inches of the treasure chest is taken up by the coins
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Remember that the volume of a cylinder is given by:
volume = (height)×pi×(radius)²
Where pi = 3.14
Then here the volume of each coin is:
V = (0.0625)(3.14)(1.6)²
= 0.5024 in³
And there are 170 coins, so the total volume is:
170×0.5024
85.408 in³
85.41 in³
Hence, 85.41 cubic inches of the treasure chest is taken up by the coins
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Answer:
c or 85.41
Step-by-step explanation: its simple
you have been told to reduce your department by 15%. your department has 220 workers. there are 512 workers in the whole company. how many workers must be let go (round to the nearest worker)?
To reduce your department by 15%, you would need to let go of 33 workers.
Reducing a department by 15% means that 15% of the current workforce in that department will be let go. To calculate this, you first need to determine the percentage of the total workforce that your department represents. In this case, your department has 220 workers out of 512 workers in the whole company, which represents 43% of the total workforce.
Then, you can calculate the number of workers that need to be let go by multiplying the total number of workers in your department by the percentage that needs to be cut. In this case, that would be
220 x 0.15 = 33 workers
This means that 33 out of the 220 workers in your department would need to be let go in order to achieve a 15% reduction.
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Write an equation involving absolute value for the following graph:
Answer:
|1|
Step-by-step explanation:
Because absolute value measures the positive distance from the numeral to 1, the answer could be negative or positive one, which is what the graph shows. So, |1| is the answer.
The equation, 816 = 600(1 9r), represents the amount of money earned on a simple interest savings account. solve for r. r = 0.04 r = 0.14 r = 0.26 r = 0.40
The value of r in the given equation is 0.04 by the process of solving the equation for the unknown.
The given equation: 816 = 600(1 + r)
Where it represents the amount of money earned on a simple interest savings account.
We need to find out the value of r in the equation.
To find the value of unknown r, both the LHS and RHS of the equation must be divided by 600.
Therefore, 816/600 = [600(1 + r)]/600
816/600 = 1(1 + r)
816/600 = 1 + r
r = 816/600 - 1
r = 0.04
Therefore, the amount of money earned on a simple interest savings account using the given equation is 0.04
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The top of a square table is covered with four equal square tiles. If the side length of each tile is decreased by 75% , how many tiles of the new size would be needed to cover the same table?
Answer:
16
Step-by-step explanation:
The side lengths of the original square was 2. 2 x 2 = 4
.25 x 2 = .5
The squares are now 1/2 x 1/2. One of the 4 original squares will now need 4 new smaller size squares to cover the one square.
4 x 4 = 16
please help me find this answer!
Answer:
[tex]k { { { {y6444396}^{46446?} }^342{?} }^66 {6 { { {6636163 \\ }^{2} }^{2} }^{2} }^{2} {?} }^{?} \times \4166441frac{?}{?} [/tex]
Step-by-step explanation:
djdkkwkwnsjididjfjrje
A region satisfies the inequalities 2 ≤ x ≤ 6 and 3 ≤ y ≤a. What value of a would give the region an area of 24 square units?
Answer: a = 9
Step-by-step explanation:
The given figure formed is a rectangle.
Area of given region (Yellow region) = 24 [tex]unit^{2}[/tex]
Length (l) = 6-2 = 4 units
Breadth (b) = a-3 units
Area = l×b
24 = 4 x (a-3)
6 = a-3
a = 9 units
What are the 7 types of functions?
There are 22 different types of functions based on range, element, equation, and domain.
Based on the range it includes Modulus Function, rational function, signum function, even and odd functions, periodic functions, greatest integer function, inverse function, and composite functions. On the basis of elements, it includes One One function, many one functions, onto function, one one and onto function, into function, and constant function. On the basis of the equation, it includes the identity function, linear function, quadratic function, cubic function, and polynomial functions. On the basis of the domain, it has algebraic functions, trigonometric functions, and logarithmic functions.
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a telephone company charges $0.50 for the first 5 minutes of a call and $0.09 for each additional minute. which interval below represents how a person can talk for $3 (assume that a person cannot talk for a fraction of a minute)?
On solving the provided question, we can say that by equation 15+4 = total minutes, they can talk 19 minute
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x= total minutes -4 the 1st 4 minutes are included in the .30
total cost = .3 + .18 x
[tex]3 = .3 +.18 x\\2.7 = .18x\\2.7/.18 = x\\15 = x[/tex]
x = total minutes -4
15+4 = total minutes
they can talk 19 minute
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describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 15 inches, 37 inches
The possible length of the third side of the triangle is x>52 inches.
What is the sum of the first side and second side of any triangle?The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. If the sum of the two sides is equal to the third side, then the two sides will coincide with the third side so a triangle cannot be formed. Hence, the sum of the two sides must be greater than the third side for the triangle to be formed.
Given: Sides of two sides of a triangle as 15 and 37 inches.
let the third side of the triangle be x.
then x>15+37
x>52 inches.
Hence, The possible length of the third side of the triangle is x>52 inches.
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What transformation(s) have been applied to function f(x) to get g(x)? Check all that apply.translationreflectiondilationrotation
Transformations that have been applied to function f(x) to get g(x) are translation, reflection, and dilation.
The process of transforming the existing graph or graphed equation, to create a variation of the following chart is called graph conversion. Transformations such as translation, reflection, and dilation have been applied to function f(x) to produce g(x).
Whenever the function is "translated" it is moved in such a very way that it will not alter the shape or rotate in any way.The reflection is a modification of the function's graph all along the x or y-axis (or both).Dilation is defined as a stretch or shortening about in an axis caused by multiplying or subdivisions.Therefore, the answer is "translation , reflection , and dilation".
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Answer:
A) Translation
B) Reflection
C) Dilation
Step-by-step explanation:
hello i have 2 questions.
You are planning your brothers mini surprise party, and you want to take him and his closest friends to a sporting event. His two favorite sports are hockey and basketball. Each local team offers a special party suite during the game. The hockey suite costs $130 to rent the room and $30 per person. The basketball suite costs $180 to rent the room and $20 per person. Identify the system of equations that represents this model, where y represents the total cost of the party, and x represents the number of the people attending the party.
A. y = 30x + 130
y = 180x + 20
B. y = 30x + 180
y = 130x + 20
C. y = 30x + 130
y = 20x + 180
D. y = 130x + 30
y = 20x + 180 .
If there was going to be a total of 4 people attending the party, which game would be the most cost efficient? Hockey or basketball?
If there was an amount of people that could attend the party so that both games would cost the same, how many people could attend?
A.8 people
B.9 people
C.6 people
D.5 people
The sum of two numbers is 32 and their difference is 18. find the two numbers!
Answer:
C. y = 30x + 130 D. 5 people Q3. The 1st number is 25
y = 20x +180 The 2cnd number is 7
Step-by-step explanation:
C. The x represents the amount of people attending.
30 and 20 are the price per person.
D. 30 x 5 + 130 = 280
20 x 5 = 180 = 280
Q3. 32 + 18 = 50
50/2 = 25
25 + y = 32
y = 32 - 25
y = 7
hope this helps =)
y = 30x + 130 and y = 20x + 180 is the system of equations that represents the model and The two numbers are 25 and 7 in second question.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let y represents the total cost of the party, and x represents the number of the people attending the party.
The hockey suite costs $130 to rent the room and $30 per person.
y=130+30x
The basketball suite costs $180 to rent the room and $20 per person.
y=180+20x
So option c is correct and
If there was going to be a total of 4 people attending the party,
y=130+30(4)=250
y=180+20(4)=260
basket ball is most cost efficient.
If there was an amount of people that could attend the party so that both games would cost the same
130+30x=180+20x
10x=50
x=5
So 5 people could attend the party.
The sum of two numbers is 32
The difference is 18
x+y=32
x-y=18
x+y+x-y=32+18
2x=50
Divide both sides by 2
x=25
y=7
The two numbers are 25 and 7.
Hence, y = 30x + 130 and y = 20x + 180 is the system of equations that represents the model and The two numbers are 25 and 7 in second question.
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How do I do this please
Answer:
Step-by-step explanation:
substitute p for 8, because p=8
question 1 : 8+4=12 ----Yes
question 2: 8x8 =64-------Yes
question 3 5x8=35, not 8----No
question 4 2+8=10, not 12----No
if you ate 2.5 cups of this particular cereal, how many calories and grams of fiber would you be consuming?
On solving the provided question, we can say that by linear equation we have 2.5x * cereals = y
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.
2.5 cups of this particular cereal,
the following linear equation, you could calculate how many calories and grams of fiber you were eating.
let x = cereals we eat y = calories
so, equation - 2.5x * cereals = y
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the three sides of a triangular lot are represented by x, 2x, and 3x 2. what are the lengths of each side if the perimeter of the triangular lot is 362 feet? 60 ft, 120 ft, 182 ft 100 ft, 122 ft, 140 ft 60 ft, 60 ft, 242 ft 80 ft, 100 ft, 182 ft
On solving the provided question we can say that any triangle's perimeter is the sum of its three sides' lengths = [tex]\x = 360/6 = > x = 60[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Triangle's sides are x, 2x, and 3x Plus 2 ft. Respectively.
Radius is 362 feet.
Any triangle's perimeter is the sum of its three sides' lengths.
[tex]362 = x + 2 x + 3x +2\\6 x +2=362\\6 x= 362-2\\6 x=360\\x = 360/6\\x = 60[/tex]
Triangle's shortest side measures 60 feet.
Middle side = 2 x 2 x 60 ft = second side
Third side equals 3 x + 2 and is measured as 360+2=180+2=182 ft.
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Given the polynomial Q(x)=4x^3-3x+1, find the polynomial P(x) such that P(x)=2*(Q(x)+P(x)) for any real number x
Given the polynomial Q(x)=4x^3-3x+1,
P(x) = 8x^3 - 6x + 2
What is the polynomial?Generally, To find P(x), we can start by substituting
P(x) = 2*(Q(x) + P(x)) into the equation:
P(x) = 2*(Q(x) + P(x))
This simplifies to:
P(x) = 2*(4x^3 - 3x + 1 + P(x))
Expanding and rearranging the equation gives:
P(x) = 8x^3 - 6x + 2 + 2P(x)
Subtracting 2P(x) from both sides of the equation gives:
P(x) - 2P(x) = 8x^3 - 6x + 2
This simplifies to:
-P(x) = 8x^3 - 6x + 2
Adding P(x) to both sides of the equation gives:
0 = 8x^3 - 6x + 2 + P(x)
Therefore, the polynomial P(x) that satisfies the equation
P(x) = 2*(Q(x) + P(x)) is:
P(x) = 8x^3 - 6x + 2
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After its second bounce, a ball reached a height of 80 cm. The rebound factor for the ball was 0.7. From approximately what height, in cm, was the ball dropped?
A) 34
B) 49
C) 115
D) 163
Answer: The answer is C hope this helps :)
Step-by-step explanation:
The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The height of a ball after its second bounce was 80 cm. The ball had a rebound factor of 0.7. Then the height of the ball from where it is dropped is given as,
0.7h = 80
h = 80 / 0.7
h = 14.3 cm
h ≈ 115 cm
The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.
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An Isoceles right triangle whose legs measure 6 is continously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a what?
Assuming an isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object, the three-dimensional object is a: D. cone with a diameter of 12.
What are the types of triangle?In Geometry, there are five (5) major types of triangle based on the length of their sides (side lengths) and angles, and these include the following;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleWhat is a right angle?In Mathematics, a right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees (90°).
Generally speaking, the resulting three-dimensional (3-D) geometric object that is formed when a right-angled triangle is continuously rotated about a leg would be a cone. Additionally, the radius of this cone would be equal to 6 because the base of the right-angled triangle is 6.
Therefore, the diameter of this cone can be calculated as follows;
Diameter of cone = 2 × radius of cone
Diameter of cone = 2 × 6
Diameter of cone = 12 units.
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Complete Question:
An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a
answer choices
cylinder with a diameter of 6
cylinder with a diameter of 12
cone with a diameter of 6
cone with a diameter of 12
What is the name of the segment inside the large triangle?
perpendicular bisector
altitude
median
angle bisector
Answer:
Perpendicular Bisector
If the points (2, 5), (1, 1) and (a, 3) are collinear, find the value of a.
Answer:
a = 0
(0,3)
Step-by-step explanation:
a food delivery service manager would like to estimate the mean amount of time it takes employees of his company to deliver food to the customers. to do so, he selects a random sample of 10 deliveries from the large number of deliveries made and records the amount of time each of those deliveries took. are the conditions for constructing a t confidence interval met?
Answer: C
Step-by-step explanation:
Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.
1. Constructing a t confidence interval requires that the sample size is greater than 30, so the first condition that must be met is that the sample size is greater than 30.
2. The second condition that must be met is that the sample is a random sample of the population of interest. In this case, the sample is a random sample of 10 deliveries from a large number of deliveries made.
Since both conditions are met, the conditions for constructing a t confidence interval are met.
Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.
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Please help! Image below.
The hypotenuse side of the right triangle is 7 units.
The value of x in the triangle is 5.92 units.
How to find the side of a right triangle?A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The side of a right triangle can be found using Pythagoras's theorem as follows:
using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
hypotenuse = 7
Let's find x.
7² - (√14)² = x²
49 - 14 = x²
x² = 35
square root both sides
x = √35
x = 5.9160797831
x = 5.92 units
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Select the parallel lines from the given pairs of lines :
Select one:
a.
y = x / 3 + 11, y = x / 2 + 15
b.
y = 3x + 11, y = 3x + 15
c.
y = 3x + 11, y = − 3x + 15
d.
y = 3x + 11, y = x / 2 + 15
Answer:
b.
y = 3x + 11, y = 3x + 15
Step-by-step explanation:
Both lines have the same slope, so they are parallel.
brainly The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points) Source StylesFormatFontSize
Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
What is transformation ?
A transformation is a function that changes the position, size, or shape of an object or a graph. In mathematics, transformations are often used to map a function from one coordinate space to another. There are several types of transformations, including translations, rotations, reflections, and scalings.
Part A: Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
Part B:
Horizontal stretching/shrinking: k is the horizontal scale factor.
Vertical stretching/shrinking: k is the vertical scale factor.
Part C:
Horizontal stretching/shrinking: g(x) = f(kx)
Vertical stretching/shrinking: g(x) = kf(x)
Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
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What is the solution to the equation StartFraction y Over y minus 4 EndFraction minus StartFraction 4 Over y + 4 EndFraction = StartFraction 32 Over y
The solutions to the equation y/ (y- 4) - 4/ (y + 4) = 32/ y are approximately 30.948, 4.627 and -3.575.
The given equation is y/ (y- 4) - 4/ (y + 4) = 32/ y
Let us simplify the left hand side (LHS) :
Make the denominator same to (y - 4)(y + 4)
y/ (y- 4) - 4/ (y + 4) = (y/ (y- 4))×((y + 4)/(y + 4)) - (4/ (y + 4))×((y - 4)/(y - 4))
y/ (y- 4) - 4/ (y + 4) = ( y(y + 4) - 4(y - 4))/ (y - 4)(y + 4)
y/ (y- 4) - 4/ (y + 4) = (y² + 4y - 4y + 16)/ (y² - 16)
y/ (y- 4) - 4/ (y + 4) = (y² + 16)/ (y² - 16)
Now plugging this simplified version in LHS
(y² + 16)/ (y² - 16) = 32/ y
y(y² + 16) = 32(y² - 16)
y³ - 32y² + 16y + 32×16 = 0
The solutions are approximately 30.948, 4.627 and -3.575.
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Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon. k=1/2
The vertices of the polygon before and after dilation are shown below
preimage Image
J (-5, 3) J' (-5/2, 3/2)
K (2, 3) K' (1, 3/2)
L (2, -3) L' (1, -3/2)
M (-5, -3) M' (-5/2, -3/2)
What is dilation?Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The rule used in transformation is as follows
(x, y) for a scale factor of r → (rx, ry)
Applying the rule to the vertices of the polygon we have
preimage Image
J (-5, 3) (1/2 * -5, 1/2 * 3) J' (-5/2, 3/2)
K (2, 3) (1/2 * 2, 1/2 * 3) K' (1, 3/2)
L (2, -3) (1/2 * 2, 1/2 * -3) L' (1, -3/2)
M (-5, -3) (1/2 * -5, 1/2 * -3) M' (-5/2, -3/2)
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Select 2 points in the solution of the inequality graphed below.
654-
21
3
x
k
