Carl deposited $1220 in a bank that pays 9% interest, compounded monthly. Find the amount he will have at the end of 3 years.
a.
$3431.45
c.
$1549.40
b.
$1596.55
d.
$1334.44

Answer:

30.8% increase.

Step-by-step explanation:

17 - 13 |13| * 100% = 4 13 * 100 = 30.8%

I hope this helped you!

The volume of the given solid is equal to the triple integral of 1 over the region bounded by the coordinate planes and the plane 6x + 7y + z = 42. This can be written as:

[tex]$\iiint 1\, dV = \iiint 1\, dx\, dy\, dz$[/tex]

The region of integration is bounded by the coordinate planes x = 0, y = 0, and z = 0, and the plane 6x + 7y + z = 42. This is a right triangular prism with vertices (0,0,0), (6,0,0), and (0,6,42). To calculate the volume, we will use the triple integral in cylindrical coordinates, which can be written as:

[tex]$\iiint 1\, dV = \int0^{2\pi}\int0^6\int_0^{42/7} r\, dz\, dr\, d\theta$[/tex]

The volume of the given solid is given by:

[tex]$\frac{504\pi}{7}$[/tex]

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The two types of Angles of the triangle are  Acute Angle ( angle that are less than 90 degree) and Obtuse Angle ( angle between 90 and 180 degree ).

What are Angles ?

The Angle is defined as the geometrical shape that is constructed by joining two rays to each other at their end points.

The two types of angles of the triangle are Acute Angle and Obtuse Angle :

(i) Acute Angle :

An angle can be called as Acute if the measure of the angle is less than 90 degree .

(ii) Obtuse Angle :

an angle can be called as Obtuse if the measurement of the angle is greater than 90 degree and less than 180 degree .

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x=12

L||M means L will be parallel to M.

Two lines are parallel if their corresponding angles are the same.

Corresponding angles are shown below.

As the two angles given are corresponding, L||M when x+5 = 2x-7.

x+5 = 2x-7

x = 12

Therefore, the value of x which makes L||M is 12.

Answer:

x = 12

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ x + 5 = 2x - 7

Then the value of x will be,

→ x + 5 = 2x - 7

→ x - 2x = -7 - 5

→ -x = -12

→ [ x = 12 ]

Hence, the value of x is 12.

The required maximum volume of the box is 2ft³.

Volume is a measurement of how much space an object takes up.

We can calculate the amount of something needed to fill it, like water for a bottle, tank, or aquarium.

Amount of space that stuff takes up - that's what we mean when we talk about volume.

Stuff is anything that has mass and takes up room.

When scientists are measuring volume, they usually use cubic meters.

So, calculate as:

V=x·y²

2x+y=3

y=3-2x

V = x·(3-2x)² = x·(9-12x+4x²) = 9x - 12x²+4x

V ` = 9-24x+12x² = 3(4x²-8x+3) = 3(4x²-6x-2x+3)

= 3[2x(2x-3)-(2x-3)] = 3(2x-3)(2x-1)

When the most amount is present: V ` = 0

Then,

2x-3 = 0  

2x = 3              

x = 1.5 (That's wrong, 'cause y = 0.)

or: 2x-1 = 0

2x = 1

x = 0.5,  y = 3 - 2 · 0.5 = 3 - 1 = 2

V max = 0.5 · 2² = 0.5 · 4 = 2 ft³

Therefore, the required maximum volume of the box is 2ft³.

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Negation means negative of something , in logical mathematics negation is an expression opposite to another operation .

Examples of negation are ,

Logical operations are performed to check the trueness of an expression.

These are generally Boolean expressions or algebraic functions.

A negation of a basic assertion is made by  inserting the word "not" into the original statement. The truth value of the negation will always be the inverse of the truth value of the original assertion.

Under negation, what was true becomes false and the vice - versa.

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Answer:

65%

Step-by-step explanation:

39/60 X 100

(39 being the number of movies he rated very good, divided by the total number of movies he watched which is 60)

The estimated value of the multiplication is equivalent to 480.81.

Given is the expression as -

102.3 x 4.7

480.81

Therefore, the estimated value of the multiplication is equivalent to 480.81.

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Answer:

d which implies m/3 + 5 = 9

Answer: 25cm²

Step-by-step explanation:

Ok, so I haven't actually learnt this in school so I'm going to give it my best shot. (Don't be surprised if I get this wrong though.)

So, Quadrilaterals A and B are similar. They have the same angles. Therefore, (I'm thinking that) Quadrilateral B is just a scaled-up version of Quadrilateral A.

Here comes my theoretical part:

If one side of Quadrilateral B is 5 times longer than the same side of Quadrilateral A...

(Quadrilateral A is 3cm, and Quadrilateral B is 15cm).

... then the area of the entire Quadrilateral B should just be 5 times bigger than Quadrilateral A.

Therefore, (I'm guessing), Quadrilateral B has an area of 25cm²

Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards

Multiplication is a mathematical operation that involves multiplying two or more numbers together. It is one of the four basic operations in mathematics, along with addition, subtraction, and division.

In this problem, we may require the use of some mathematical operators to find the solution to the problem.

1.

He currently has 216 cards, but he needs 15 sets of cards.

1 set of card = 72 cards

Let's calculate the number of sets he currently has.

1 set of card = 72 cards

x set = 216 cards

cross multiply both sides and solve for x.

x * 72 = 216 * 1

x = 216 / 72

x = 3 sets

He currently has 3 sets of cards.

Since he wants 15 sets of cards, we will need 12 more set of cards.

The number of cards can be calculated by multiplying 12 by 72

Number of cards = 12 * 72 = 864

He needs 864 more cards.

2.

1 set of card = $27

1 set = 72 cards

But she's bringing $9 to join, we can calculate the ratio of cards she will get.

1 / 27 = x / 9

x = 9 / 27

x = 1/3

She will get 1/3 of the cards bought which will be

72 * 1/3 = 24 cards

She will get 24 cards

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Answer:

y = 3x - 2

Step-by-step explanation:

See the attached worksheet.  Look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept.  The slope of the line can be determined by taking two points on the line to calculate the Rise/Run.  The points selected for this example are (0,-2) and (2,4).  This makes the Rise/Run (6/2), or 3.  The y-intercept, b, is -2 as per point (0,-2).

The equation for this (non)-prependicular line is thus y = 3x - 2.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{13}-\underset{x_1}{1}}} \implies \cfrac{ -4 }{ 12 } \implies {\Large \begin{array}{llll} - \cfrac{1 }{ 3 } \end{array}}[/tex]

Answer:1) 43 2)53 3)22 4)23

Step-by-step explanation:

well, maybe Pam has been eating the wrong chips or something, but if she's correct, that can only happen if both equations are exactly equal, are they?

[tex]\boxed{\cfrac{x}{16}=4}\implies x=(16)(4)\implies \cfrac{x}{4}=16 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x}{4}=16\implies x=(4)(16)\implies \boxed{\cfrac{x}{16}=4}\qquad \begin{array}{llll} \textit{yeap, Pam is correct}\\ \textit{she's Da Bomb} \end{array}[/tex]

Answer:

Step-by-step explanation:

12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12

Therefore , the solution to the given problem of inequality comes out to be 120d + 1,500 = 110d + 2,500.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right

Here,

Given : $1,500 a week to a wage

$55 per hour

Thus ,

Taking all the information in concern

We get,

where d is the is he number of hour

120d + 1,500 = 110d + 2,500

Therefore , the solution to the given problem of inequality comes out to br

120d + 1,500 = 110d + 2,500.

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If Jupiter is about 5.2 Astronomical Units (AU) from the Sun and Neptune is about 30.1 AU from the Sun, Neptune is about 5.79 times far from the Sun as Jupiter.

Therefore the answer is 5.79.

To find how many times as far from the Sun Neptune is as Jupiter, we need to divide the distance from the Sun to Neptune by the distance from the Sun to Jupiter.

Neptune is about 30.1 AU from the Sun and Jupiter is about 5.2 AU from the Sun, so:

= Distance from the Sun to Neptune / Distance from the Sun to Jupiter

= 30.1 / 5.2

= 5.79

So, Neptune is about 5.78 times as far from the Sun as Jupiter.

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Answer:

B

Step-by-step explanation:

180-152=28

t=180-(28+90)

t=62

Answer:

$899.54

Step-by-step explanation:

To find the cost of sod for a trapezoid shaped yard, we need to first find the area of the trapezoid. The formula for the area of a trapezoid is:

Area = (1/2) * h * (b1 + b2)

where h is the height of the trapezoid and b1 and b2 are the lengths of the bases.

Substituting the given values, we get:

Area = (1/2) * 46 ft * (78 ft + 111 ft)

= (1/2) * 46 ft * 189 ft

= 4274 ft^2

To find the cost of sod for this area, we need to multiply the area by the cost per square foot of sod. The cost will be:

Cost = 4274 ft^2 * $0.21/ft^2

= $899.54

So the cost of sod for this yard will be $899.54.

So, (2m + 4)(m + 5) is the factored form of 2m² +13m +20.

The factorial of a non-negative integer n, represented by n! is the product of all positive integers less than or equal to n. It is the mathematical operation that is applied to a non-negative integer.It is also used in many areas of mathematics, including calculus and number theory, as well as in many areas of science, including physics, chemistry, and computer science.

A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.

To factor a trinomial of the form "ax² + bx + c," we can use the following steps:

First, we need to determine two numbers that multiply to give us "c" and add to give us "b." In this case, the two numbers are 4 and 5 because 4 x 5 = 20 and 4 + 5 = 9, which is equal to "13m".

Next, we can factor the trinomial into the form (ax + b)(cx + d) by grouping the middle term and the constant term together.

So, the factored form of the trinomial is (2m + 4)(m + 5)

So, (2m + 4)(m + 5) is the factored form of 2m² +13m +20.

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Answer:

The answer is 18

Step-by-step explanation:

22½ = [(22 × 2) + 1] ÷ 2 = 45/2

1 ¼ = [(1 × 4) + 1] ÷ 4 = 5/4

Now,

45/2 ÷ 5/4

45/2 × 4/5

(45 × 4) ÷ (2 × 5)

180/10 = 18

Thus, 18 people are at Chrissy's birthday party.

When these equations are solved, the value of x is 4 and the value of y is 3. Therefore, the value of x + y = 7.

To solve the system of equations, we will use the elimination method.

First, we multiply the first equation by 3 and the second equation by 5.

3(3x + 5y = 9)

5(5x + 3y = 7)

Then, we add the equations together:

9x + 15y = 27

25x + 15y = 35

Now, we subtract the second equation from the first to eliminate the x terms:

-16y = -8

y = 0.5

Next, we plug this value for y into one of the original equations and solve for x:

3x + 5(0.5) = 9

3x = 8.5

x = 2.83

Finally, we plug the values of x and y into the original equation to verify that they are correct:

3(2.83) + 5(0.5) = 9

So, the value of x is 2.83 and the value of y is 0.5. Therefore, the value of x + y = 2.83 + 0.5 = 3.33.

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1/7 is the probability that the product is an odd number.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                   Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Total Cards are 7

2 cards out of 7 cards can be selected in ⁷C₂   = 21  ways

Product would be odd if both cards are odd

3 , 5 , 7  are odd cards

2 cards out of 3 Can be selected   in ³C₂  = 3  ways

( 3 , 5) , ( 3 , 7) , ( 5 , 7)

Hence probability  the product of the numbers on the 2 cards  is odd number

= 3/21

= 1/7

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Meri will need 696 yards of wood to make 12 birdhouses, as each birdhouse requires 58 yards of wood.

Meri is making birdhouses and each birdhouse needs 58 yards of wood. To find out the total length of wood needed for making 12 birdhouses, we can use the formula:

length of wood per birdhouse x number of birdhouses = total length of wood

So, in this case, we can substitute the given values in the formula:

58 yards x 12 birdhouses = 696 yards

This means Meri needs 696 yards of wood to make 12 birdhouses.

This equation works because it uses the concept of the unitary method, where we find the total length of wood by multiplying the number of birdhouses by the length of wood used in each birdhouse, this way we are able to find the total amount of wood needed.

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Yes, the rate 4.8 laps every 8 minutes; 3.6 laps every 6-minute form a proportion.

A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:

1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

4.8 lap every 8 minutes will be equal to (4.8/8) = 0.6 lap a minute.

3.6 lap every 6 minutes will be equal to (3.6/6) = 0.6 lap in a minute.

Here, as the value of the ratio of both the quantities are same so the given values are said to be in Proportion.

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When  C.I. is given as 80% then the margin of error will be 1.9591% as calculated from the given data.

We are given that the first margin of error (MOE) is 3%.

Also,  confidence interval

first C.I.=95%

second C.I.=80%

Therefore , MOE at 80% will be ,

The formula for proportion is given as (P),

P=x/n , here 64%.

The values are same or constant as in general, this means standard deviation is also constant

Now formula for MOE is given by

MOE = Z x ( SD ) / √n

where ,  Z is value for confidence interval

MOE ∞ Z-value

So we can say that ,

MOE = k x Z ( where k = proportionality constant).

So , for 95 % Z=1.96 and for 80% Z=1.28

MOE then calculated will be , 1.95% .

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To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.

To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.

The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.

For example reduce the ratio 225: 125: 25

The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.

If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.

Now divide each number by 5 and see what we get.

225/5: 125/5: 25/5

45: 25: 5

When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.

Now divide each number by 5 again and get a final ratio of 9: 5: 5.

45/5: 25/5: 5/5

9: 5: 1

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The area of the figure is 51.63 m²

A composite figure is figure that is made up of two or more different shapes.

The composite figure in the given image is made up of a rectangle, semicircle and a triangle. Therefore, the area of the composite figure will be the sum of the areas of the shape it is made of. Thus:

Area of figure = area if rectangle + area of semicircle + area of triangle

Area of figure = LW + 1/2πr² + 1/2bh

Area of figure = (6 × 5) + (1/2 × 3.14 × 3²) + (1/2 × 3 × 5)

Area of figure = 30 + 14.13 + 7.5

Area of figure = 51.63 m²

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