If tan A = 1/2, what is tan B?
Let A and B be the two non-right angles in a right triangle.

The number of seats in the first, second and third aircraft are 561 seats,  497 seats and 842 seats respectively

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Let F, S and T represent number of seats in the first, second and third aircraft respectively

We can set up three equations to represent the situation:

F = 64 + S   --- (1)

T = 2S - 152 --- (2)

F + S + T = 1900 --- (3)

Put (1) and (2) in (3):

F + S + T = 1900

(64 + S) + S + (2S - 152) = 1900

64 + S + S + 2S - 152 = 1900

4S - 88 = 1900

4S = 1900 + 88

4S = 1988

S = 1988/4

S = 497 seats

F = 64 + S

F = 64 + 497 = 561 seats

F + S + T = 1900

561 + 497 + T = 1900

1058 + T = 1900

T = 1900 -1058 = 842 seats

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The solution of the inequality is less than 1.75 which is shown on the diagram.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

5/8 > (1/2)x - 1/4

Simplify the inequality, then we have

5/8 > (1/2) x - 1/4

5/8 + 1/4 > (1/2) x

(5 + 2)/8 > (1/2) x

7 / 8 > (1/2) x

(1/2) x < 7 / 8

x < 7 / 4

x < 1.75

The solution of the inequality is less than 1.75 which is shown on the diagram.

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A rectangle that is scaled to be 4 times the size of the given rectangle would have the dimensions of 27.6 x 20.8.

When a rectangle is said to be scaled to be a certain number of times more than the size of another rectangle, it means that both rectangles will have the same shape and orientation, but their dimensions will be different.

This difference will come from the change that the scale factor brought about. In this instance, the scale factor is 4 times which means that the second rectangle will be 4 times the size of the first.

The first dimension would be :

= 6 . 9 x 4

= 27.6 units

The second dimension would be:

= 5 . 2 x 4

= 20. 8 units

The dimensions would then be:

27. 6  x 20. 8

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Answer:50%

Step-by-step explanation:

Answer:

Y=-8x-6 and x=-8x+

Step-by-step explanation:

Answer:

-2 is not a solution of the inequality 6g - 14 > 21.

Step-by-step explanation:

To determine if -2 is a solution of the inequality 6g - 14 > 21, we need to substitute -2 for g in the inequality and see if it is true.

6g - 14 > 21

6(-2) - 14 > 21

-12 - 14 > 21

-26 > 21

This inequality is not true. Because -26 is not greater than 21.

[tex]6g-14 > 21[/tex]

Substitute -2 for g:

[tex]6(-2)-14 > 21[/tex]

[tex]-12-14 > 21[/tex]

[tex]-26 > 21[/tex]

-2 is not a solution because -26 is not greater than 21.

According to the given information, there is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/55

From the question, we are to determine the statement that is true

From the given information,

There is 25 pounds of dog food in a bag.

and

There are approximately 2.2 kilograms in 1 pound.

If there are 2.2 kilograms in 1 pound

Then,

There would be x kilograms in 25 pounds

x = 2.2 × 25

x = 55 kilograms

Hence, there are 55 kilograms

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Step-by-step explanation:

930 = -20×|t - 15| + 1010

one solution is for (t - 15) > 0

930 = -20×(t - 15) + 1010

-80 = -20×(t - 15)

4 = t - 15

t = 19

that means 2019.

the second solution is for (t - 15) < 0

930 = 20×(t - 15) + 1010

-80 = 20×(t - 15)

-4 = t - 15

t = 11

that means 2011.

We can start solving the problem by using the formula:

Hours worked = Total cost / Hourly wage

In this case, we know that Chris needs at least $320.00 for his class trip, and he earns $8 per hour working on the weekends. So, we can plug in these values into the formula:

Hours worked = $320.00 / $8.00

To solve this equation, we divide 320 by 8:

Hours worked = 40

So Chris needs to work 40 hours on the weekends to be able to go on the class trip.

I hope this helps :)

Answer:

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

Chris earns $8 per hour and he needs at least $320.00 for his class trip.

If he works h hours, he will get 8h dollars.

Set up inequality:

Solving we get:

Chris needs to work at least 40 hours.

If you save RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent compounded annually, the future value or the amount you will accumulate after 5 years is RM5,637.09.

The future value is the compounded present value of the periodic deposits.

The future value formula or FV table can determine the accumulated future value of periodic investments.

We can also use an online finance calculator to determine the future value.

N (# of periods) = 5 years

I/Y (Interest per year) = 6%

PV (Present Value) = RM0

PMT (Periodic Payment) = RM1,000

Results:

Future Value (FV) = RM5,637.09

Sum of all periodic payments = RM5,000(RM1,000 x 5)

Total Interest = RM637.09

Thus, in 5 years, you will have an accumulated future value of RM5,637.09 in the savings account.

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The set of number that is correctly ordered from the question in the attachment is option D.

1. [tex]7\frac{1}{3}[/tex] = 7 + 0.3333

= 7.3333

2. 221 / 30 = 7.3666

3. 7.36 = 7.36363636

4. [tex]2.4\sqrt{3\pi }[/tex] = 2.4 * [tex]\sqrt{9.43}[/tex]

= 7.36999

We would have to arrange all of the values from their highest to the least values

7.36999, 7.3666, 7.36363636, 7.3333

[tex]2.4\sqrt{3\pi }[/tex],  221 / 30, 7.36 , 7.3333

Hence the last option is the answer. It shows how the solution is ordered from the greatest to the smallest value

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A finance charge includes Interest, fees, and principal, So the correct answer is Option (B) Interest, fees, and principal.

A finance charge is a fee incurred when using a credit or extending credit that already exists. A fixed rate or a percentage of borrowings may be used to calculate finance charges; the latter is more common.

A finance charge is usually made up of the cost of carrying the debt as well as any related transaction fees, account management fees, or late fees imposed by the lender.

Finance charges are a way for a lender to get paid for giving a borrower credit or access to funds. These costs could be one-time payments, like the origination fee for a loan, or they could be interest payments that could be repaid daily or monthly. A finance charge includes Interest, fees, and principal

Therefore,

A finance charge includes Interest, fees, and principal, So the correct answer is Option (B) Interest, fees, and principal.

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Answer: 7m-6m²-2mn

Step-by-step explanation:

Multiply each term in parenthesis by -2

Calculate product (2x3=6)

7m-6m²-2mn

Answer:

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

It is a combination of 3 rectangles.

All dimensions are given apart from the middle one. The missing dimension is:

The total area is:

Answer:

Step-by-step explanation:

Ben has a piece of plywood that measures 1 yard on each side, and he cuts it into 6 equal pieces.

The width of each piece is 1/3 yard, and the length of each piece is 1/2 yard.

To find the area of each piece that Ben cuts, we can multiply the width and length of each piece:

Area = (1/3 yard) x (1/2 yard)

Area = (1/3) x (1/2)

Area = 1/6 yard^2

So each piece that Ben cuts has an area of 1/6 yard^2.

The product 1/2x1/3 relates to the model in that it represents the area of the piece. In other words, the length and width are multiplied to find the area of the piece.

In this case, we can see that Ben cuts the plywood into 6 pieces of equal area, which is 1/6 of a square yard.

Mary paid Social Security tax of $4,378.325 in 2000. This is calculated by multiplying 7.5% by the amount of income over the maximum taxable income of  $4,378.325.

The theory used in this question is the marginal tax rate, which is the tax rate that applies to the income earned over the maximum taxable income. In this case, the marginal tax rate is 7.5%, which is the Social Security tax rate.

Step 1: Calculate the amount of income over the maximum taxable income.

Maximum taxable income: $53,000

Income earned: $61,711

Amount of income over the maximum taxable income: $8,711 ($61,711 - $53,000 = $8,711)

Step 2: Calculate the Social Security tax.

Social Security tax rate: 7.5%

Amount of income over the maximum taxable income: $8,711

Social Security tax paid: $4,378.325 ($8,711 x 0.075 = $4,378.325)

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Answer:

I know it

Step-by-step explanation: Btw did somone already answer this?

There are 10 and 26 candy bars of each size did he buy.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Diego brought 16 candy bars $25.

And, large candy bars cost $1.25 and regular candy bars cost $0.75.

Now, Let number of large candy bars = x

And, Number of regular candy bars = y

Here, Diego brought 16 candy bars.

Hence, We get;

⇒ x + y = 16  .. (i)

And, large candy bars cost $1.25 and regular candy bars cost $0.75.

Hence, We get;

⇒ 1.25x + 0.75y = 25  .. (ii)

Multiply by 1.25 in (i) and subtract from (ii),  we get;

⇒ 1.25y - 0.75y = 20 - 25

⇒ 0.5y = - 5

⇒ y = - 10

And, from (i);

⇒ x + y = 16

⇒ x - 10 = 16

⇒ x = 26

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The property used to simplify the expression is 12 × 47 = 12 × (40 + 7) is  distributive property.

The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.

In other words,  distributive property is a rule that states that you can distribute the terms of an expression.

Therefore, let's check the property used on the expression as follows:

12 × 47 = 12 × (40 + 7)

12 × 40 + 12 × 7

480 + 84

564

Hence, the property used on the expression is distributive property.

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Answer:

0.01 %

Step-by-step explanation:

The interest rate is the percentage of the principal (the amount borrowed) that is charged as interest over a certain period of time.

To find the interest rate, we can use the formula:

Interest Rate = Interest / Principal x Number of days / 365

We know that the principal is 600$, the interest is 14.25$ and the number of days is 90

so we can substitute the values into the formula:

Interest Rate = 14.25 / 600 x 90 / 365

Interest Rate = 0.02375 * 90 / 365

Interest Rate = 0.0104

Rounded to the nearest thousandth, the interest rate is 0.010 or 0.01 %

The respective answers are 5 and 4

Addition in math is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

Given: 5 means 5+0+0 which equals to 5

4 means 4+0+0+0 which equals 4

Hence the respective answers are 5 and 4

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Answer:

Newton's 3rd law of motion

Step-by-step explanation:

Newton's 3rd law of motion states that for every force in nature there is an equal and opposite reaction.

So, assuming the people are both pushing with the same force, their forces are basically canceling each other out, and a net force of 0 is acting uponm the box, which explains why it is not moving.

The gain percentage is 12.5%

First, let`s find the Cost price (C.P) of the sofa.

Let C.P of the sofa be x.

Now, according to the question:

x+ 7% of x=Rs.3852

x + (7/100 * x) = 3852

x + 0.07x = 3852

1.07x = 3852

x=3852/1.07,

x = Rs 3600.

Now the dealer sells it for Rs 4050.

so, the Formula for gain% is=(Selling price-Cost price/Cost price)x100

Gain %= (4050-3600/3600)x100

Gain%=(450/3600)x100

Gain%=(450/36)

i.e = 12.5%.

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The equation, 6(-2 + 4) = -12 + 24, illustrates E. the Distributive Property of Multiplication over Addition.

In this mathematical property, the multiplication of two or more addends by a number results in the same value as multiplying each addend individually by the number and then adding the products together.

For instance, 6(-2 + 4) = -12 + 24

= 12

OR:

6(-2 + 4) = 6 x 2

= 12

In this situation, we can either multiply the numbers in parenthesis individually by 6 or sum the parenthesis and then multiply the sum by 6.  Either way yields the same result, showing that multiplication is distributive.

Thus, in the equation, the property illustrated is Option E, not the commutative properties of addition and multiplication, the inverse properties of addition and multiplication, the associative properties of addition and multiplication, or the identity properties of addition and addition multiplication.

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Answer:

a. To find the cost to surround the forest with a fence, we first need to determine the perimeter of the forest. The problem tells us that the perimeter is 45 yd. To convert this to feet, we can use the conversion factor of 3 feet per 1 yard. So, the perimeter in feet is:

45 yd x (3 ft/1 yd) = 135 ft

Next, we need to multiply the perimeter by the cost per foot to install fencing. We're told this cost is $6 per foot, so we can calculate the cost as:

135 ft x $6/ft = $810

b. To determine which region costs more to prepare, we need to calculate the cost per square yard for both the grassland and the forest. We're told that the cost to prepare 1 square yard of grassland is $15 and the cost to prepare 1 square yard of forest is $25.

To find the total cost for the grassland, we'll multiply the area of grassland with the cost per square yard:

2400 yd x $15/yd = $36,000

To find the total cost for the forest, we'll multiply the area of forest with the cost per square yard:

60 yd x $25/yd = $1,500

We can see that the grassland cost $36,000 to prepare while the forest cost $1,500 which means Grassland costs more to prepare.

The correct option is A.

"The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%."

First, let's find the theoretical probability.

We know that there are:

For a total of 40 marbles.

The theoretical probability of randomly pulling a gold marble is equal to the quotient between the total number of gold marbles and the total number of marbles, it is:

P = 10/40

P = 1/4 = 0.25

For the experimental probability, we need to take the quotient between the number of times that the outcome of the experiment was a gold marble and the total number of times that the experiment was performed.

The experiment was performed 40 times and 11 times we got the gold marble, then:

E = 11/40  = 0.275

Then the correct statement is A:

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Answer: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

Step-by-step explanation:

Answer:

I think so the answer is a)y=x³+2x²-1

The side of the square in terms of the perimeter is P/4.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

P = 4s

Where s is the side of the square and P is the perimeter of the square.

Now,

The side of the square.

P = 4s

Divide 4 into both sides.

s = P/4

Thus,

The side of the square is P/4.

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Id the base BCDE of the pyramid is a horizontal square w side lengths 12cm . The size of the angle between AB and the base of the pyramid is 62 degree.

Side of square of base BCDE =12cm

Area of base =12² =144cm²

Volume of pyramid = 768cm³

1/3 a² × h= 768

1/3 × 144 × h =768cm³

h =768 × 3 /144

h =16 cm

BD² =BC² +CD²

BD² = 12² + 12²

BD² = 288

BD =√288 cm

BD = 16.97cm

BD = 17cm

So,

BF = 1/2 BD

BF = 1/2 × 17

BF =8.5cm

So since ΔABF  is angle between AB  and base of pyramid

tan <ABF = Tan-1 (16/8.5) = 62°

Therefore the size of the angle between AB and the base of the pyramid is 62 degree.

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Answer:

C. 2 ≤ x

Step-by-step explanation:

EDGE