Suppose your city is building a new park, and issues bonds to raise the money to build it. You obtain a $1,000 bond that pays 5% interest annually that matures in 5 years. How much interest will you earn?

Answer:

90 km/h

Step-by-step explanation:

speed = distance/time

speed = 225 km / 2.5 h

speed = 90 km/h

Answer:

90km/hr

Step-by-step explanation:

To find the speed, take the distance and divide it by the time.

225 km/ 2.5 hours

90km/hr

Answer:

14

Step-by-step explanation:

We can divide 76,450 shavings by the average shavings per pencil, 5,425 to get an answer of 14.09... This can be rounded to 14.

Answer:

Step-by-step explanation

If f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.

What is a function?

A function is a mathematical object that assigns exactly one output to each input of a specified type. In other words, a function is a rule that takes in certain inputs (or "arguments") and produces a unique output. The inputs to a function are called the domain, while the set of possible outputs is called the range.

The given functions are f(x) = 3x and g(x)=x-2.

To find f(g(4)), we first need to evaluate g(4). The function g is defined as g(x) = x - 2, so g(4) = 4 - 2 = 2.

Next, we need to evaluate f(2), where f is defined as f(x) = 3x. So, f(2) = 3 * 2 = 6.

Therefore, f(g(4)) = f(2) = 6.

Hence, if f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.

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We have the product of 4 negative numbers, by the rule of signs, we can see that the product is positive.

Here we need to reember the rule of signs for the product, it is:

(-)*(-) = +

(+)*(+) = +

(+)*(-) = -

(-)*(+) = -

So the product between two negative numbers is positive, now let's look to our product.

(-1.2)*(-3.5)*(-2.7)*(-0.4)

We can rewrite this as:

(-1.2*-3.5)*(-2.7*-0.4)

The negative sings cancell, then we get:

(-1.2*-3.5)*(-2.7*-0.4)

(4.2)*(1.08)

Now we have the product of two positive numbers, this will be positive.

(4.2)*(1.08) = 4.536

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Answer:

100

Step-by-step explanation:

total angles of any triangle is 180

it tells you one of the base angles is 40, so 2 of them are 80

so the top one is 180-80 =100

The speed of the shadow at any time while the rock is in the air is given by v(1-s) / (H-h).

By the AAA congruency theorem, the two triangles are formed and are similar. Here, the ratio of their sides must be equal, and thus -

= H/d+s = h/s

= Hs = h(d+s)

= Hs = hd + hs

= Hs - hs = hd

= s(H-h) = hd

Differentiating both sides with respect to t -

= {s' (H- h)} + {sh'} = h'

Since we know that h' = v -

= {s' (H- h)} + {sv} = v

= s'(H-h) = v - sv

= s'(H-h) = v(1-s)

= s' = v(1-s) / (H-h)

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Answer:

39.9

Step-by-step explanation:

Rectangle: area = length × width

Semicircle: area = 0.5πr²

total area = 9 × 6 - 0.5 × 3.14159 × 3²

total area = 39.9

A rectangle having perimeter 26 m has a length of 8m and breadth of 5m.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

The value for perimeter of a rectangle is - 26 m

Let x be the length of the rectangle and y be the breadth.

The formula for perimeter of rectangle is 2(l + b)

From the given information, it is known that -

Perimeter = 2(x + y) = 26 m...(1)

Difference between the length and breadth = x - y = 3 m....(2)

Use the first equation to solve for one of the variables in terms of the other -

2x + 2y = 26

x + y = 13....(3)

Add equation (2) and (3) -

x + y + x - y = 13 + 3

2x = 16

x = 16/2

x = 8 m

Now substitute the value of x in equation (2) -

x - y = 3

8 - y = 3

y = 8 - 3

y = 5 m

Therefore, the length is 8 m and the breadth is 5 m.

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An equation that represents the linear function shown in the table or mapping diagram is y = -x/4 - 3.

In order to write an equation that represents the linear function, we would use the point-slope form. Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear function representing the line which passes through the data points (-4, 6) and (8, 3) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 6 = (3 - 6)/(8 - (-4))(x - (-4))

y - 6 = (3 - 6)/(8 + 4)(x + 4)

y - 6 = -3/12(x + 4)

y - 6 = -x/4 - 9

y = -x/4 - 9 + 6

y = -x/4 - 3

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The numeric values of the function R(t) = 328 - 296e^(-0.004t) at t = 0 and t = 30 are given as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

R(t) = 328 - 296e^(-0.004t)

At t = 0, the numeric value is found replacing the lone instance of t by zero, hence:

R(0) = 328 - 296e^(-0.004(0))

R(0) = 32.

At t = 30, the numeric value is found replacing the lone instance of t by 30, hence:

R(30) = 328 - 296e^(-0.004(30))

R(30) = 65.47.

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It costs $6 to enter the fair, and each ride costs $2, thus the equation is x = 6+ 2y.

Its core idea is understood to be the number's minimal equivalent fraction. How to determine the simplest form. A fractional figure can be checked to discover if it is a prime number. A phrase having two equal sides and now an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in ranking in the general form of any equation.  Its general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Perhaps conditional equations of identities are categories for equations.

given

Suppose the total cost is x and there are y rides.

Each ride costs two dollars. Thus, the price of the rides will be:

= Number of rides * Price per ride

=> y * 2

=> 2 y

Thus, the final price will be:

Total price = Admission price + ride prices

Total cost: $6 plus $2. (Number of rides)

x = 6 + 2y

It costs $6 to enter the fair, and each ride costs $2, thus the equation is x = 6+ 2y.

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An inequality with two variables has a graph, which is a collection of points that shows all possible solution is x≤ 5 3/10.

The boundary line between the coordinate plane's two halves, one of which represents the inequality's solutions, is created by a linear inequality.

x + 1 1/2 ≤ 6 8/10 :

Solution : x ≤ 5 3/10

Decimal : x ≤ 5.3

Interval  notation : (-∝ , 53/10)

Steps:

x + 1 1/2 ≤ 6 8/10 :

Convert mixed Number to improper Fraction : 1 1/2  = 3/2

1 1/2

Convert mixed numbers to improper fraction ; a (b/c ) = a. c +b /c

1 1/2 = 1.2 + 1 /2

=3/2.

x + 1 1/2 ≤ 6 8/10 :

Convert mixed Number to improper Fraction : 6 8/10 = 68/10

6 8/10

Convert mixed numbers to improper fraction ; a (b/c ) = a. c +b /c

6 8/10 = 6.10 + 8 /10

=68/10

x+ 3/2 ≤ 68/10

Cancel the Common factor :2

x + 3/2 ≤ 34/5

Move 3/2 to the right side

x ≤ 53/10

Convert  improper Fraction  to  mixed Numbers: 53/10 = 5 3/10

53/10 = 5 Reminder 3

Convert to mixed Number : Quotient (Remainder / Divisor)

53/10 = 5 3/10

x≤ 5 3/10

x≤ 5 3/10.

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The smaller number is 25 and larger number is 37

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here; The sum of two numbers is 62 and 3 times the smaller number exceeds twice the larger number by one.

let the smaller number be x and the larger number be y then we have

x+y=62

3x-2y=1

Thus solving this system of linear equations by method of elimination we get

5y=185

y=37

∴ x=25

Hence, The smaller number is 25 and larger number is 37

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The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

the capacity of being divided. Math. the capacity of being evenly divided, without remainder.

Divisibility rules or Divisibility tests have been mentioned to make the division procedure easier and quicker. If students learn the division rules in Math's or the divisibility tests for 1 to 20, they can solve the problems in a better way. For example, divisibility rules for 13 help us to know which numbers are completely divided by 13. Some numbers like 2, 3, 4, 5 have rules which can be understood easily. But rules for 7, 11, 13, are a little complex and need to be understood in-depth.

Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.

Example: 10, 20, 30, 1000, 5000, 60000, etc.

For any given number, to check if it is divisible by 13, we have to add four times of the last digit of the number to the remaining number and repeat the process until you get a two-digit number.  Now check if that two-digit number is divisible by 13 or not. If it is divisible, then the given number is divisible by 13.

For example: 2795 → 279 + (5 x 4)

→ 279 + (20)

→ 299

→ 29 + (9 x 4)

→ 29 + 36

→65

Number 65 is divisible by 13, 13 x 5 = 65.

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The order in which you shoot the scenes will not matter in terms of the final outcome of the movie.

The mathematical property that one can use to answer this question is scheduling.

From the information, in order to produce the movie, one needs to shoot a scene for a high-speed chase and need to shoot a scene for a bank robbery.

Here, the film production crew will be putting the movie together. However, it may impact the logistics of the production process and the scheduling of the crews. It is not a mathematical property that I used to answer this question. It is simply a matter of logistics and scheduling.

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The graph of the inequality y > -10 is given by the image presented at the end of the answer.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality for this problem is given as follows:

y > -10.

Which means that the solution is the numbers that are greater = to the right of -10, with an open interval.

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If Bob is able to produce more donuts than Sue in one day, that means that Bob has an absolute advantage in the production pf donuts.

Absolute advantage is when a particular person is able to produce more amount of product than the other with the same amount of input of resources, for example, time. Comparative advantage on the other hand is based on the opportunity cost.

Comparative advantage is basically the ability to produce a good or a service for an opportunity cost which is lower than that of a competitor. Since, Bob is able to produce more donuts than Sue, Bob has an absolute advantage over Sue.

--The given question is incomplete, the complete question is

If Bob can produce more donuts in one day than Sue can produce in one day, then:

a. Bob has a comparative advantage in the production of donuts.

b. Sue has a comparative advantage in the production of donuts.

c. Bob has an absolute advantage in the production of donuts.

d. Sue has an absolute advantage in the production of donuts."--

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On solving the system of linear equations 3x + 3y = 45 and x + 2y = 24, the cost for each shirt is obtained as $6, and cost for each pair of pants is obtained as $9.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Let the cost of shirts be x and the cost of pair of pants be y.

The number of shirts bought by person A = 3

The number of pair of pants bought by person B = 3

The total cost for person A = $45

The equation for person A is -

3x + 3y = 45....(1)

The number of shirts bought by person B = 1

The number of pair of pants bought by person B = 2

The total cost for person B = $24

The equation for person B is -

x + 2y = 24....(2)

Multiply equation (2) by 3 -

3(x + 2y) = 24 × 3

3x + 6y = 72....(3)

Subtraction equation (1) from equation (3) -

3x + 6y - (3x + 3y) = 72 - 45

3x + 6y - 3x - 3y = 27

3y = 27

y = 9

Substitute the value of y in equation (2) -

x + 2(9) = 24

x + 18 = 24

x = 24 - 18

x = 6

Therefore, the cost of shirts and pants is x = 6 and y = 9 respectively.

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50 fishing lures are carved in a week.

A) Big Lake Bob

Production Possibilities Schedule:

Fishing Lures    Duck Decoys

100                          0

90                          5

80                         10

70                         15

60                       20

50                       25

40                       30

30                       35

20                       40

10                       45

0                       50

50 fishing lures are carved in a week.

25 duck decoys are crafted in a week.

This implies that Big Lake Bob forgoes 10 fishing lures for every 5 duck decoys he carves.

Large Lake Schedule of Bob's productivity potentials

B) Bob's potential for production The schedule is a table of numbers that shows the various combinations of two items that can be created using the restricted resources (labor hours, capital, materials, etc.) and technology in Bob's economy.

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We can apply the order of four transformations to the graph of f(x) in order to sketch the graph of g(x): A 3-unit horizontal shift to the left : The graph becomes f(x-3 ) as a result, with a vertical asymptote at x = 0 rather than x = 3.

2. To move from f(x) to g(x), four transformations are used:

A three-unit horizontal shift to the left: The graph thus shifts by a factor of -2 three units in the direction of the left  A vertical stretch.

You must first define the function and its domain before you can plot its graph. We can begin by sketching the piecewise linear graph of f(x) = |x|, which has a slope of 1 for x greater than 0 and -1 for x less than 0 in order to sketch the graph of g(x) = -2|x-3|+1. The vertical asymptote is shown by the x axis. For all real numbers, the definition of the f(x) graph exists.

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Answer:

3/4 of a tank of gas

Step-by-step explanation:

18 1/2-17 3/4= 3/4

or the easiest way for me is to change the faction to decimals

18.5-17.75= 0.75 which is 3/4

Answer:

12,000

Step-by-step explanation:

How can we do this?

We can do this by taking the number 11,900,

11,900

looking at the hundredths place,

11,900

and figuring out if it is closer to 10, or 0. 9 is closer to 10, so we round up.

12,000

Therefore, 11,900 rounded to the nearest thousand is 12,000.

The complete expression of the algebra is;

4a(-2a³ + 4a + 3) + 2a(3a³ - 2a + 7) = -2a⁴ + 12a² + 26a

We are given the expression as;

4a(-2a³ + 4__ + 3) + 2a(__a³ - 2a + _) = -2a* + 12a² + 26a

Expanding the left hand side gives;

-8a⁴ + __(16a) + 12a + __(2a⁴) - 4a² + __(2a)

Grouping like terms gives;

-8a⁴ + __(2a⁴) + 12a + __(2a) + __(16a) - 4a²

Factorizing out exponents gives;

a⁴(-8 + __(2)) + a(12 + __(2)) + a²((16/a) - 4)

Comparing this with the right hand side gives;

a⁴(-8 + __(2)) = -2a*  -----(1)

((16/a) - 4)a² = 12a²    -----(2)

(12 + __(2))a = 26a   ----(3)

From eq 1, we can see that;

* = 4

From eq 2;

((16/a) - 4) = 12

16/a = 12 + 4

a = 16/16

a = 1

From eq 3;

(12 + __(2)) = 26

___ * 2 = 26 - 12

___ = 14/2

___ = 7

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Answer:

31.81

Step-by-step explanation:

the dotted line ² = (22²-16²)

x = sq root of [dotted line²  +(44-16)² ]

= sq root of [22²-16²+28²]

31.81

We can see here that Side AC is the longest side. A. Side AC.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

We see here that triangles that have an angle of 90° are usually known to be right angle.  The angles in a triangle are equal to 180°.

We see here that the above answer. This is because the side opposite to the largest angle is the longest angle.

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The answers include the following below:

This is referred to as the discounted price at which goods or services are being sold.

Since we were told that the discount is 15%, then the sale price will be (100-85)% of $30 which is 85% of $30.

This therefore means that the equation to find the sale price will be 85/100 × 30 = 0.85(30).

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Answer:

see below

Step-by-step explanation:

Step 1

5(x – 3) = x + 13

Step 2

See if x is a solution

5 (6-3) ?= 6+13

5 (3) ?= 19

15 ?= 19

Step 3

This is not true so it is not a solution

Step 4

5(x – 3) = x + 13

Distribute

5x-15 = x+3

Subtract x from each side

5x-x -15 = x+13-x

4x-15 = 13

Add 15 to each side

4x-13+13 = 15+13

4x =28

Divide each side by 4

4x/4 = 28/4

x = 7

7 is a solution

Answer:

First you substitute 6 for x!

5(6 - 3) = 6 + 13

6 - 3 = 3

The equation is now:

5 * 3 = 6 + 13

5 * 3 = 15

6 + 13 = 19

The result is:

15 = 19 which is not a true statement.

x is not equal to 6.

Now lets try 7.

5(7 - 3) = 7 + 13

7 - 3 = 4

7 + 13 = 20

5 * 4 = 20

Thus: x = 7

Step-by-step explanation:

Hope it helps! =D

Answer:

The biologist goes to his 150 favorite hiking places and looks at an acre along each trail: Random Sampling.

The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list: Stratified Sampling.

The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population: Stratified Sampling.

The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations: Cluster Sampling.

The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres: Random Sampling.