Answer:
The average daily balance on Perry's credit card for the period beginning October 10 was $714, and the balance at the end of the cycle was $506. To calculate the balance due, we need to know the length of the billing cycle. Assuming a 30-day billing cycle, we can use the average daily balance method to calculate the interest charged. The formula for interest charged is: Average Daily Balance x APR x Days in Billing Cycle / 365. Plugging in the numbers, we get: $714 x 0.08 x 30 / 365 = $4.68. Adding this interest to the ending balance of $506, the total balance due is $510.68.
Canada had 12,968,000 visitors in 2002 while Mexico had 9,807,000 visitors. How many more people visited Canada?
Step-by-step explanation:
To find out how many more people visited Canada than Mexico, we need to subtract the number of visitors to Mexico from the number of visitors to Canada:
12,968,000 - 9,807,000 = 3,161,000
Therefore, 3,161,000 more people visited Canada than Mexico in 2002.
I am struggling to correct numbers 1, 3, 4, 5, and 7. I have been working for hours on this.
Answer:
Step-by-step explanation:
1. sinL = 3/5
3. cosL = 4/5
4. sinN = 4/3
5. cos32 = x/14
x = 14(cos32) = 11.9
7. tan75 = 17/x
x = 17/tan75 = 4.56 ≈ 4.6
Find the perimeter of a rectangle with w=5 and l=9
Answer:
28 units
Step-by-step explanation:
The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.
Substituting l = 9 and w = 5, we get:
P = 2(9 + 5) = 2(14) = 28
Therefore, the perimeter of the rectangle is 28 units.
You deposit $1000 each year into an account earning 8% compounded annually.How much will you have in the account in 10 years?
Answer:
If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.
Given,
Annual deposit = $1000
Rate = 8% compounded annually
Time(n) = 10 year
Amount = ?
As we know the formula ,
Amount = P(1+r/100)ⁿ
Amount = 1000(1+8/100)¹⁰
Amount = 1000(1+0.08)¹⁰
Amount =1000(1.08)¹⁰
Amount = 1000 × 2.15892
Amount = $2158.92
Hence, amount in 10year will be $2158.92
A particle moves along the x-axis so that its velocity at any time t ≥ 0 is given by
v(t) = (2(pi) − 5)t − sin(t(pi))
A. Find the acceleration at any time t.
B. Find the minimum acceleration of the particle over the interval [0, 3].
C. Find the maximum velocity of the particle over the interval [0, 2].
Answer:
A. To find the acceleration, we need to take the derivative of the velocity function with respect to time:
a(t) = v'(t) = 2(pi) - cos(t(pi))
B. To find the minimum acceleration, we need to find the critical points of the acceleration function in the interval [0, 3].
a'(t) = sin(t(pi))
The critical points occur when sin(t(pi)) = 0, which means t = 0, 1, 2, 3. We need to evaluate the acceleration function at these points and at the endpoints of the interval:
a(0) = 2(pi) - cos(0) = 2(pi)
a(1) = 2(pi) - cos(pi) = pi + 2
a(2) = 2(pi) - cos(2pi) = 2(pi)
a(3) = 2(pi) - cos(3pi) = pi - 2
The minimum acceleration occurs at t = 3, with a minimum value of pi - 2.
C. To find the maximum velocity, we need to find the critical points of the velocity function in the interval [0, 2].
v'(t) = 2(pi) - cos(t(pi)) = 0
The critical points occur when cos(t(pi)) = 2(pi). We can solve for t as follows:
cos(t(pi)) = 2(pi)
t(pi) = arccos(2(pi))
t = arccos(2(pi))/pi ≈ 1.58
We need to evaluate the velocity function at these points and at the endpoints of the interval:
v(0) = -sin(0) = 0
v(1.58) ≈ 1.69
v(2) = (2(pi) - 5)(2) - sin(2(pi)) = 4(pi) - 10
The maximum velocity occurs at t = 1.58, with a maximum value of approximately 1.69.
If f(x) =X+2/x^2 -9
and g(x)=11/x^2+ 3x
(a) find f(x) + g(x)
(b) list all of the excluded values
(c) classify each type of discontinuity
The sum of the two functions f(x) + g(x) is (x+2)/(x^2 - 9) + 11/(x^2 + 3x)
Function calculation.
(a) To find f(x) + g(x), we simply add the two functions together:
f(x) + g(x) = (x+2)/(x^2 - 9) + 11/(x^2 + 3x)
(b) To determine the excluded values, we need to look for values of x that make the denominators of the two functions equal to zero. The denominators are:
x^2 - 9 and x^2 + 3x
Setting these equal to zero and solving for x, we get:
x^2 - 9 = 0 => x = ±3
x^2 + 3x = 0 => x(x+3) = 0 => x = 0 or x = -3
Therefore, the excluded values are x = ±3 and x = 0.
(c) To classify the type of discontinuity at each of the excluded values, we need to examine the behavior of the function as x approaches these values.
At x = ±3, the denominators of both functions become zero, which means that the function is undefined at these values. This creates a vertical asymptote, which is a type of infinite discontinuity.
At x = 0, the denominator of g(x) becomes zero, but the denominator of f(x) does not. This creates a removable discontinuity, because we can define f(0) separately to make the function continuous at this point. Specifically, we can set f(0) = 2/(-9) = -2/9 to remove the discontinuity.
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[tex]65y - 147y[/tex]
Math problem.
I need help.
Answer: 82y
Step-by-step explanation:
147y - 65y = 82y
Just perform simple subtraction
The perimeter of a movie screen is 70 meters it is 23 meters wide how tall is it
Answer:
height = 12 m
Step-by-step explanation:
We can assume from the problem that the movie screen is rectangular and the formula for perimeter (P) of a rectangle is
P = 2h + 2w, where l is the length and w is the width.
Thus, we can plug in 70 for P and 23 for w and solve for h:
[tex]70=2h+(2*23)\\70=2h+46\\24=2h\\12=h[/tex]
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The scale factor of PQRS to JKLM is 4/5.
The scale factor of JKLM to PQRS is 5/4.
The value of w, x, and y are 20, 12.5, and 20 respectively.
The perimeter ratio is 4:5.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor of PQRS to JKLM = 15/12
Scale factor of PQRS to JKLM = 5/4 or 1.25.
Scale factor of JKLM to PQRS = 12/15
Scale factor of JKLM to PQRS = 4/5 or 0.8.
For the value of w;
15/12 = 25/w
15w = 12 × 25
w = 20
For the value of x;
15/12 = x/10.
12x = 150
x = 12.5
For the value of y:
15/12 = y/16
12y = 15 × 16
y = 20
Perimeter ratio = 12 : 15 = 4:5
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the graph y = arctan x is transformed to y = a arctan(b(x-c)) + d by a horizontal compression of 1/2 and translation of pi/3 units down. the new equation is:
y = 1 arctan(1/2(x-0)) - [tex]\frac{\pi }{3}[/tex], which simplifies to y = arctan(1/2(x-[tex]\frac{\pi }{3}[/tex])). So correct option is B.
Describe Equation?An equation is a mathematical statement that uses symbols and mathematical operations to show that two quantities are equal. Equations are used to represent a wide range of relationships and can be used to solve problems and make predictions.
The original equation is y = arctan x. To horizontally compress the graph by 1/2, we need to replace x with 2x. The equation becomes y = arctan(2x).
To translate the graph down by [tex]\frac{\pi }{3}[/tex] units, we need to subtract [tex]\frac{\pi }{3}[/tex] from y. The equation becomes y = arctan(2x) - [tex]\frac{\pi }{3}[/tex].
So far, we have y = arctan(2x) - [tex]\frac{\pi }{3}[/tex]. To match the form y = a arctan(b(x-c)) + d, we need to further transform the equation.
We can write 2x as 1/2(4x), so the equation becomes y = arctan(1/2(4x)) - [tex]\frac{\pi }{3}[/tex].
Comparing this with y = a arctan(b(x-c)) + d, we have a = 1, b = 1/2, c = 0, and d = -[tex]\frac{\pi }{3}[/tex].
Substituting these values, we get y = 1 arctan(1/2(x-0)) - [tex]\frac{\pi }{3}[/tex], which simplifies to y = arctan(1/2(x-[tex]\frac{\pi }{3}[/tex])).
Therefore, the answer is B. y= arctan(1/2(x-[tex]\frac{\pi }{3}[/tex])).
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The complete question is:
The equation y = 1 arctan(1/2(x-0)) -π/3 can be written as y = arctan(1/2(x-π/3)).
What is equation ?
An equation is a mathematical statement that proves the equality of two quantities by using symbols and mathematical procedures. Equations can be used to express a wide variety of relationships, solve issues, and generate predictions.
The first formula is y = arctan x. We must swap out x for 2x in order to horizontally compress the graph by half. y = arctan is the new formula.(2x).
We must deduct π/3 from y in order to scale the graph downward by π/3 units. Y = arctan(2x) -π/3 is the new equation.
y = arctan(2x)-π/3 is what we now have. We need to further alter the equation so that it has the form y = an arctan(b(x-c)) + d.
Since 2x can be written as 1/2(4x), the equation changes to y = arctan(1/2(4x)) -π/3.
We have a = 1, b = 1/2, c = 0, and d = π/3- when y = an arctan(b(x-c)) + d is compared to this.
The result of substituting these numbers is y = 1 arctan(1/2(x-0)) -π/3, which may be written as y = arctan(1/2(x-π/3)).
y= arctan(1/2(x-π/3)), hence the solution is B.
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A cabinet was ordered from a carpenter with a volume of 1.08 m³. He wrote down the following measurements: 1.2 m wide and 1.8 m high, but forgot to write down the depth. Therefore, the depth measurement is
The depth of this cabinet is equal to 0.5 m³.
VolumeVolume is a three-dimensional measure that indicates the space occupied by an object. It is a physical quantity that expresses the amount of space an object occupies in three dimensions - length, width and height.
Note that this cabinet has the shape of a parallelepiped, and its volume is found by multiplying its dimensions. Calculating the depth measurement, we have:
1,08 m³ = 1,2 m * 1,8 m * p
p = 1,08 m³/(1,2 m * 1,8 m)
p = 1,08 m³ / 2,16 m³
p = 0,5 m
An old building was demolished. 5 dump trucks are used to
transport a total of 2 tons of rubble. How much rubble did each
truck carry?
-15>-11+w solve inequality for W
Answer:
Starting with:
-15 > -11 + w
Add 11 to both sides:
-15 + 11 > w
Simplifying:
-4 > w
Therefore, the solution for the inequality -15 > -11 + w, when solved for w, is:
w < -4
Please HELP DUE IN AN HOUR
Answer:
It is not true (equal sign with a slash in it) one side’s 23 and the other side is 20
Which two statements best describe Michael’s height while on the two roller coasters?
It switches between negative and positive every 40 seconds. it switches between positive and negative every 80 seconds. So correct statements are B and E.
Describe Algebra?Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.
Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.
As a result, every 40 seconds it alternates between negative and positive.
B is accurate.
We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.
As a result, every 80 seconds it alternates between positive and negative.
E is accurate.
The complete question is:
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Simplify the expression to a polynomial in standard form
(x−3)(2x^2 −5x−5)
Answer:
Step-by-step explanation:
To simplify the expression, we can use the distributive property of multiplication:
(x−3)(2x^2 −5x−5) = 2x^3 −5x^2 −5x −6x^2 +15x +15
Next, we can combine like terms:
2x^3 −5x^2 −6x^2 −5x +15x +15 = 2x^3 −11x^2 +10x +15
Therefore, the simplified polynomial in standard form is 2x^3 −11x^2 +10x +15.
In ΔVWX, v = 33 inches, w = 57 inches and ∠X=147°. Find ∠W, to the nearest degree.
How many total blocks does Ben need to walk north and east to get from his home to the playground and home again?
Domain is now called the ____________ which means before a change
Answer:
Step-by-step explanation:
Domain is now called the "source" which means before a change or transformation. In mathematics, the term "source" is often used to refer to the set of all possible inputs or values that can be fed into a function or transformation, before any changes or transformations take place. The set of all possible outputs or resulting values from the function or transformation is called the "range" or "codomain".
What is the surface area of an ice cube that has 4 cm sides?
TA
4 cm
4 cm
The surface area of an ice cube with 4 cm sides is 96 square centimeters.
What is surface area?It is a measurement of the sum of all the areas of the faces, sides, and any other surfaces of an object. For example, a cube has six square faces, each with the same area.
According to question:To find the surface area of an ice cube with 4 cm sides, we need to add up the areas of all six faces. Each face is a square with side length 4 cm, so the area of each face is:
Area of one face = (side length)² = 4 cm × 4 cm = 16 cm²
Since there are six faces on a cube, the total surface area of the ice cube is:
Total surface area = 6 × (area of one face) = 6 × 16 cm² = 96 cm²
Therefore, the surface area of an ice cube with 4 cm sides is 96 square centimeters.
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A solid metal cone has radius 1.65 cm and slant height 4.70 cm. Find the angle the, slant height makes with the base of the cone.
Answer:
Step-by-step explanation:
We can use trigonometry to find the angle between the slant height and the base of the cone.
The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).
Using the Pythagorean theorem, we can find the height of the cone:
height^2 = (slant height)^2 - (radius)^2
height^2 = (4.70 cm)^2 - (1.65 cm)^2
height^2 = 19.96 cm^2 - 2.72 cm^2
height^2 = 17.24 cm^2
height = sqrt(17.24) cm
height = 4.15 cm (rounded to two decimal places)
Now we can use trigonometry to find the angle between the slant height and the base of the cone.
tan(angle) = opposite / adjacent
tan(angle) = height / radius
tan(angle) = 4.15 cm / 1.65 cm
tan(angle) = 2.515
Taking the inverse tangent (or arctan) of both sides, we get:
angle = arctan(2.515)
angle = 70.32 degrees (rounded to two decimal places)
Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.
Rachel ran 3 miles when she was training for a race. How many feet did she run?
15,840 feet
5,280 feet
10,560 feet
14,840 feet
To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:
3 miles x 5,280 feet/mile = 15,840 feet
Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.
Can someone please help me!!!
The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).
What is vertex?Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.
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In a restaurant, there are 5 managers, 15 servers, 10 cooks and 15 other personnel. If a person is selected at random, what is the probability that the person is either a manager or a cook?
Answer:
0.33
Step-by-step explanation:
There are a total of 5 + 15 + 10 + 15 = 45 people in the restaurant.
The probability of selecting a manager or a cook is the sum of the probabilities of selecting a manager and selecting a cook, since these events are mutually exclusive (a person cannot be both a manager and a cook at the same time).
The probability of selecting a manager is 5/45, since there are 5 managers out of 45 people in total.
The probability of selecting a cook is 10/45, since there are 10 cooks out of 45 people in total.
Therefore, the probability of selecting either a manager or a cook is:
P(manager or cook) = P(manager) + P(cook)
P(manager or cook) = 5/45 + 10/45
P(manager or cook) = 15/45
P(manager or cook) = 1/3
So, the probability that the person selected at random is either a manager or a cook is 1/3 or approximately 0.333
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23 x _ = 23 x 4
(help me)
Answer:
4
Step-by-step explanation:
To solve for the missing value in 23 x _ = 23 x 4, you can use the property of equality to divide both sides by 23. This will give you _ = 4. Therefore the missing value will be 4.
Hope this helped :)
Answer: the answer is 4
Step-by-step explanation: u can divide both sides with 23 and that leaves u with x=4
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For problems 6 and 7 set up a proportion and solve.
6. The ratio of the birth weight to the adult weight of a male black bear is 3:1000.
7. The measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.
What is an angle?An angle is an abstract concept in geometry which is formed by two lines or rays that meet at a common point. An angle is measured in degrees and can be classified by its size as acute, right, obtuse, or reflex. An angle can also be formed by three points or two intersecting planes.
6. The average birth weight is 12 ounces. The average adult weight is 12 x 1000 = 12000 ounces. Since there are 16 ounces in 1 pound, the average adult weight of the male black bear is 12000/16 = 750 pounds.
7. The measures of the angles in a triangle are in the extended ratio 2:15:19.To find the measure of each angle, we can set up an equation using the extended ratio. Let x be the measure of the first angle, then 15x and 19x will be the measures of the other two angles. This can be written as: 2x + 15x + 19x = 360°. Solving this equation, we get x = 36°. Therefore, the measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.
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PLEASE PLEASE HELP ME!!!!!!!!
The parallelogram H’I’J’K is a dilation of the parallelogram HIJK. What is the scale factor of the dilation?
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
PLEASE LOOK AT PICTURE!!!!!!
Answer: 1/3, proper, 1 1/3, not proper.
In the image below, arc AB has a measure of 32 degrees.
What is the measure of the inscribed angle that intercepts it? (Angle ACB)
Therefore , the solution of the given problem of angles comes out to be the engraved angle ACB is 16 degrees in size.
An angle meaning is what?Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.
Here,
A circle's inscribed angle has a measure that is half that of the interrupted arc. As a result, the inscribed angle ACB intersecting arc AB with a measure of 32 degrees will have a measure of:
=> Angle ACB = 32 / (1/2)
=> ACB = 16 degree angle
As a result, the engraved angle ACB is 16 degrees in size.
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A pyramid has a height of 5 inches and a volume of 60 cubic inches. Which of the following figures could be the base for this pyramid?
Select 3 answers that apply.
A a hexagon with an area of 36 square inches
11 a right triangle with one leg 5 inches and the hypotenuse 13 inches
ca circle with radius 4 inches
Da 4-inch by 9-inch rectangle
a 3-inch by 4-inch rectangle
a square with side length 6 inches
E
The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:
A hexagon with an area of 36 square inches (option A)A 4-inch by 9-inch rectangle (option D)A 3-inch by 4-inch rectangle (option E)How do we calculate?The formula to find the base of a pyramid given its height and volume,
Volume of pyramid = (1/3) * Base area * Height
Substituting in the given values, we have:
60 = (1/3) * Base area * 5
Base area = 36 square inches
In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.
The following figures have a base area of 36 square inches:
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If Big Bun won 5 out of 25 matches, what percent did he win? A 25% B 20% C 15% D 10%
Answer:20%
Step-by-step explanation:
5(100)/25=20