How much would you need to save each month in an account earning 4.7% interest (compounded monthly) to have saved $10,000 in two years?

Answer:

       For the first picture:

[tex]\frac{1}{3} < \frac{2}{6}[/tex] is false because [tex]\frac{1}{3} x 2 = \frac{2}{6}[/tex]

[tex]\frac{1}{3} > \frac{2}{6}[/tex] is also false because [tex]\frac{1}{3} x 2 = \frac{2}{6}[/tex]

[tex]\frac{1}{3} =\frac{2}{6}[/tex] is true, so the 3rd is the correct option.

       For the second picture:

[tex]\frac{3}{6} ?\frac{1}{4}[/tex] using the LCM method, of 6 and 4 = 12

then it will be [tex]\frac{6}{12} > \frac{3}{12}[/tex] so the symbol will be > (1st option)

      For the third picture:

[tex]\frac{2}{5} =\frac{1}{2}[/tex] is false

[tex]\frac{2}{5} < \frac{1}{2}[/tex] is true, so the 2nd is the correct option.

[tex]\frac{2}{5} > \frac{1}{2}[/tex] is false

      For the forth picture:

The correct answer is the 3rd option ([tex]\frac{5}{8} > \frac{1}{2}[/tex])

Have a wonderful day! :-)

The angular speed of the wheel is 0.314 rad/sec and the linear speed of the car is 8.164 feet/second .

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ/ t

one revolution = 360°

180° = π

360° = 2π

3 revolution = 3× 2π = 6π

1 minute = 60 ×1 = 60s

angular speed = 6× 3.14/60

= 0.314 rad/s

The linear velocity =

V = wr

r = d/2

r = 52/2 = 26 feet

V = wr

V = 0.314× 26

V = 8.164 feet/second

Question: A Ferris wheel at a carnival has a diameter of 52 feet. Suppose it turns at a rate of 3 revolutions per minute. i. What is the angular speed of the wheel.

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At the end of two years if prices increase 5 percent the family needs to spend a total of $56227.50 on their annual living expenses.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Given that, the family spends $51,000 a year.

The first increase of 5% is given as:

A = (51000) (1 + 5/100)

A = 51000 (105/ 100) = 53550

For the second year increase:

A = 53550 (105 / 100) = 56227.50

Hence, at the end of two years the family needs to spend a total of $56227.50 on their annual living expenses.

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Answer:

A vertical line that passes through the coordinate (25, 0).

Equation of the vertical line is x = 25

Step-by-step explanation:

2x = 50

x = 25

Natural numbers: 0.1 Whole numbers: 0, Integers: -7, -3, 0, 1, Rational numbers: -7.2, -3.0, 0.1, 3.5,Irrational numbers: √5, √64, Real numbers: -7.2, -3.0, 0.1, √5, 3.5, √64.

Natural numbers are the positive integers, 1, 2, 3, 4, 5, and so on. They are also known as the counting numbers or the positive integers. They are the numbers used for counting and measuring. Natural numbers are the building blocks of mathematics, and are used in the formation of other number systems, such as integers, rational numbers, real numbers, and complex numbers.

Natural numbers are also used in the formation of equations and formulas, as well as in the counting of objects, in the measurement of distances, and in many other areas of mathematics. Natural numbers are an important part of everyday life, and are used in everything from telling time to counting money.

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Answer:

there is a 1 in 24 chance

Step-by-step explanation:

1(3)/6x4= 1/24

The total amount of acid in the final equation solution is 700% + 420% = 1120%, which is 40% of the total volume:

In arithmetic equations, the identical sign (=) is used to denote the equivalence of two assertions. It is demonstrated that using mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. For fact, the equal sign splits the number 12 into two separate parts, even if the answer is y + 6 = 12. It is possible to determine how many letters are also present on either end of this character.

Here,

Let x be the number of liters of pure acid solution needed, and y be the number of liters of 20% acid solution needed to make 28 liters of a 40% acid solution.

x + y = 28 (total volume of the solution)

100x + 20y = 40(28) (total amount of acid in the solution)

Simplifying the second equation, we get:

100x + 20y = 1120

Dividing both sides by 20, we get:

5x + y = 56

Now we can solve the system of equations by substitution or elimination. Here we will use the substitution method.

Solving the first equation for y, we get:

y = 28 - x

Substituting this expression for y into the second equation, we get:

5x + (28 - x) = 56

Simplifying and solving for x, we get:

4x = 28

x = 7

So the technician needs 7 liters of pure acid solution and 21 liters of 20% acid solution to make 28 liters of a 40% acid solution.

To check this answer, we can calculate the amount of acid in each solution and verify that the total amount of acid in the final solution is indeed 40%.

7 liters of pure acid solution contain 7 × 100% = 700% acid.

21 liters of 20% acid solution contain 21 × 20% = 420% acid.

The total amount of acid in the final solution is 700% + 420% = 1120%, which is 40% of the total volume:

1120% ÷ 28 liters = 40%

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The period of time during which the projectile is at least 240 feet above the ground is 3 seconds <= t <= 5 seconds.

What is time of projectile motion?

Vertical motion totally determines the time for projectile motion.

The height of the projectile above the ground after t seconds is given by s = -16t^2 + 128t. To find the period of time during which the projectile is at least 240 feet above the ground, we need to find the values of t for which s >= 240.

Solving for t:

-16t^2 + 128t >= 240

-16t^2 + 128t - 240 >= 0

t^2 - 8t + 15 >= 0

(t - 5)(t - 3) >= 0

So t must be between 3 and 5 seconds, inclusive.

Therefore, the period of time during which the projectile is at least 240 feet above the ground is 3 seconds <= t <= 5 seconds.

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Answer: A = 6

Step-by-step explanation: Here to help! So, if "a" wants to know the numerator of the fraction, all you have to do is to multiply 0.6 by 10, and that would get you 6/10. 6/10 is equivalent to 60% or 0.6. :))))

The phrase "3 over 1" would be used to describe the proportion of vehicles to trains. The (C) option is that.

A ratio in mathematics shows how many times one quantity is present in another.

For instance, if a dish of fruit's fully oranges and six lemons, the ratio of oranges and lemons is eight to six.

This ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons and oranges is 6:8.

Two quantities are compared to form a ratio.

An equality of two ratios is a percentage.

So, the following are some of the car models that Alex has collected:

There are 8 airplanes.

There are 4 trains in all.

There are 12 vehicles.

Consequently, the car-to-train ratio is 12:4.

This is further simplified to its most basic form:

= 12:4

= 3:1

Therefore, the phrase "3 over 1" would be used to describe the proportion of vehicles to trains. The (C) option is that.

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Complete question:

Alex has a collection of vehicle models. He built 8 model airplanes, 4 model trains, and 12 model cars. Write a ratio to represent the ratio of cars to trains.

A. 12:24 FAST HELP

B. 1:3

C. 3 over 1

D> 4 to 12

The perimeter of this parallelogram is equal to 236/10 or 23 6/10 meters.

In Mathematics, a parallelogram simply refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Mathematically, the perimeter of a parallelogram can be calculated by using this mathematical expression;

Perimeter = A + B + C + D

Where:

A, B, C, and D represents the length of sides of a parallelogram.

Substituting the given parameters into the perimeter of a parallelogram  formula, we have the following;

Perimeter = 3 3/10 + 8 5/10 + 3 3/10 + 8 5/10

Perimeter = 33/10 + 85/10 + 33/10 + 85/10

Perimeter = 66/10 + 170/10

Perimeter = 236/10 or 23 6/10 meters.

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Answer:

838,200

Step-by-step explanation:

960x5x184 =838,200

Answer:

Step-by-step explanation:

To find the equation of a line that is parallel to another line, we can use the same slope for both lines. The slope of the line with the equation -14x + 3y = -4 can be found by rearranging the equation into slope-intercept form:

y = -14/3x - 4/3

The slope of this line is -14/3.

To find the equation of a line that passes through the point (2,-6) with the same slope, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Where:

m is the slope of the line

(x1, y1) is a point on the line

Plugging in the values from the given information:

m = -14/3

x1 = 2

y1 = -6

y - (-6) = -14/3 (x - 2)

y + 6 = -14/3x + 14

So the equation of the line through the point (2,-6) that is parallel to the line with the equation -14x + 3y = -4 is:

y + 6 = -14/3x + 14.

Answer:

3/8 feet²

---------------------------

Area of the rectangle is the product of its two dimensions:

Substitute the dimensions and find the area:

Answer:

21.1 minutes

Step-by-step explanation:

Time for first mile + second + third

6.75+ 7.1+ 7.25

21.1 minutes or (21.1 * 60) seconds = 1266 seconds

The percentage of increase is given by the equation A = 85 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage change be represented as P

Now , the equation will be

The initial value be represented as A = 40

The final or increased value be B = 74

So , the percentage change P = [ ( | A - B | ) / A ] x 100

Substituting the values in the equation , we get

The percentage change P = [ ( 34 ) / 40 ] x 100

The percentage change P = 0.85 x 100

The percentage change P = 85 %

Hence , the percentage change is 85 %

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Answer:

i- 72000 * π radians per hour,  ii- 65,940 miles per hour.

Step-by-step explanation:

(i) To find the car's angular speed in radians per hour, we need to find the number of radians the wheel rotates in one revolution, then multiply that by the number of revolutions per second. The number of radians in one revolution is equal to the circumference of the wheel divided by the wheel's radius. The wheel's circumference is given by 2 * π * r, where r is the wheel's radius (18 inches / 2 = 9 inches). Then, the number of radians per revolution is:

2 * π * r / r = 2 * π

So, the number of radians per second is:

2 * π * 10 revolutions per second = 20 * π radians per second

Finally, to convert radians per second to radians per hour, we multiply by 3600 (the number of seconds in an hour):

20 * π * 3600 seconds/hour = 72000 * π radians per hour

(ii) To find the car's linear speed in miles per hour, we need to multiply the wheel's circumference by the number of revolutions per hour. The wheel's circumference is given by 2 * π * r, so the linear speed is:

2 * π * r * 10 revolutions per second * 3600 seconds/hour = 18 * π * 10 * 3600 miles per hour

The answer is approximately equal to 65,940 miles per hour.

The perimeter of the square is 12√2 units

A square is a quadrilateral that has all it's sides equal and all it's angles equal. The sum of interior angles of a square is 360°. This means that each angle of a square is 90°.

The perimeter of a square is obtained by adding all the sides.

Therefore the perimeter of a square = 4l

A (-1,4) and B ( 2,7)

line AB = √2-(-1))² + (7-4)²

AB = √ 3²+3²

AB = √9+9

AB = √18 units

therefore since the sides of a square are equal, the perimeter = 4× √18

= 4×3√2

= 12√2 units

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Answer:

Option A. 12√2 units

Step-by-step explanation:

Below is a function which takes some number of degrees, positive or negative, and returns the reduced equivalent in the interval [0 , 360 )

Below is a Python function that takes an angle in degrees and returns its equivalent in the interval [0, 360):

def deg_reduce(degrees):

   return degrees % 360

The % operator in Python is the modulo operator, which returns the remainder of a division. By using degrees % 360, the function returns the reduced equivalent of degrees in the interval [0, 360).

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Shaded region in venn diagram is the common area of set A and set B. It represent A∩B.

How to present a set can also be expressed with a picture or diagram called a Venn Diagram. The Venn diagram was introduced by a British mathematician named John Venn (1834 – 1923).

Instructions for creating a Venn diagram include:

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Answer:

Step-by-step explanation:

The formula for the area of a triangle is:

1/2×base×height

If you know the area of the triangle and height you can apply the area formula:

A=1/2×base×height

in reverse to calculate the length of the base:

b=2A/h

given, h=60dam

A=18

so, b=2×18/60

b=36/60

b=0.6

The answer is 0.6

Answer:

1.55 x [tex]10^{15}[/tex]

or 1,550,000,000,000,000

Step-by-step explanation:

2.5 x 1.034 x [tex]10^{3}[/tex] x 6 x [tex]10^{11}[/tex]

15.51 x [tex]10^{14}[/tex]

1.551 x [tex]10^{15}[/tex]

If knowing the probability of an event occurring is known then it can be turned into one's favour as well as it can be obstructed if not in favour.

A way to determine the likelihood of something occurring is through probability. Many things are hard to predict with 100 percent certainty. We can only predict the likelihood of an event occurring or how likely it is using it. A probability can be between 0 and 1, with 0 signifying an impossibility and 1 signifying a certainty.

If the likelihood of an event occurring is known, one can attempt to influence the outcome in accordance with the likelihood.

The possibility of altering the likelihood that the event will go in one's favour is another useful tool.

Therefore, being aware of the probability can be beneficial.

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The next two elementary row operations that should beRow4=Row4-4*Row3. This will make the element zero. The second step is we divide 8 by -2 to get 4th unknown as d=8/(-2)=-4.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

Presently 3rd element in Row 3 is the pivot element,

For solving the matrix, we need to make 3rd element of fourth row as zero,

Hence, we do the operation Row4=Row4-4*Row3.

This will make the element zero.

The second step is we divide 8 by -2 to get 4th unknown as d=8/(-2)=-4.

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The volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis is 8π/3 cubic units.

The volume of the solid generated by revolving this region about the x-axis can be found using the method of cylindrical shells. The volume is given by:

V = ∫[0, 2] 2πx(2 - 2√x) dx

Evaluating the definite integral:

V = π ∫[0, 2] (4x - 4x^(3/2)) dx

= π [2x^2 - 4/3 x^(3/2) ] |_0^2

= π [4 - (4/3)(2^(3/2))]

= 8π/3.

Therefore, the volume of the solid generated by revolving the region bounded by the lines y = 2 and y = 2√x and the x-axis about the x-axis is 8π/3 cubic units.

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--The question is incomplete, answering to the question below--

"Find the volumes of the solids generated by revolving the regions bounded by the lines and curves about the x-axis

y=2√x, y=2, x=0"

Answer:8k

Step-by-step explanation:i did the test and got it write

H is a subgroup of G since it is closed under the group operation, contains the identity element and inverses of its elements.

A subset H of a group G is a subgroup of G if it satisfies the following three properties:

1. Closure: H is closed under the group operation, that is, if α, β∈H then αβ∈H.

2. Identity element: H contains the identity element e of G.

3. Inverses: For each element α∈H, its inverse (or reciprocal) α−1 is also an element of H.

In this case, the subset of G consisting of elements of finite order (H) satisfies all of these three properties. Since H is closed under the group operation, if α, β∈H then αβ∈H. The identity element of G, e, is also an element of H since the order of the identity element is always 1, which is finite. Finally, for each element α∈H, its inverse α−1 is also an element of H since the inverse of a finite order element is also of finite order. Therefore, by satisfying all of the three properties of a subgroup, H is indeed a subgroup of G.

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