A savings account earns 6% simple interest per year. The principal is $800. What is the balance after 18 months?

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Circle

center (4 , 3)

radius = 5

equation of the circle = ?

Step 02:

equation of the circle

(x - h)² + (y - k)² = r ²

(h , k) ===> center

r ===> radius

(x - 4)² + (y - 3)² = 5²

(x - 4)² + (y - 3)² = 25

The answer is :

(x - 4)² + (y - 3)² = 5²

The difference of the polynomial is -40rt⁷+90s⁵t² +80r³s³. the correct option is D.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The given expression is (33r³s³-16rt⁷+72s⁵t²) - (24rt⁷ - 18s⁵t² – 47r³s³). The difference will be calculated as follows:-

Difference =  (33r³s³-16rt⁷+72s⁵t²) - (24rt⁷ - 18s⁵t² – 47r³s³).

Separate the like terms in the polynomial and solve accordingly.

Difference = (33r³s³+ 47r³s³-16rt⁷- 24rt⁷+72s⁵t²+ 18s⁵t² ).

Difference = 80r³s³- 40rt⁷+ 90s⁵t²  

Therefore, the difference of the polynomial is -40rt⁷+90s⁵t² +80r³s³. the correct option is D.

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Answer: AB ≅ CB

Step-by-step explanation:

In the given figure, we have ∆ABD ≅ ∆CBD

The CPCTC property of congruent triangles says that if two triangles are congruent then their corresponding parts ( angles and segments ) are congruent.

Since we have given that ∆ABD ≅ ∆CBD.

Therefore, the corresponding segments are congruent.

As segment AB is corresponding to segment CB. [First two letters]

Therefore, segment AB is congruent to segment CB.

Answer:

0.259

Step-by-step explanation:

There are some rules in determining what numbers are significant figures.

We can determine how many significant figures the number currently has.

There are currently seven significant figures. In order to round the number to three significant figures, we must round it to the thousandths place, or the 9.

The rounding rules are:

Since 0 is less than 5, the number rounded to 3 significant figures is 0.259.

Answer:

(a)  5/12

Step-by-step explanation:

to solve this problem you can make all fractions equivalent with 12 as the denominator

a) 5/12

b) 2/3 = 8/12      Multiply top and bottom by 4

c) 5/6 = 10/12     Multiply top and bottom by 2

d) 3/4 = 9/12       Multiply top and bottom by 3

if you compare numerators, the smallest one is the closest to zero, which would be (a) 5/12

Answer:

A 5/12

Step-by-step explanation:

first you need to round these all to /12 so a is 5/12

12/3 is 4 so multiply 4 by two which means b is 8/12

12/6 is 2 so multiply 5 by two which gives us c = 10/12

12/4 is 3 and multiply 3 x 3 which is 9 so d is 9/12

5 is the lowest decimal/fraction which makes it the closest to 0

Answer:

50% or 150/300

Step-by-step explanation:

There are five odd numbers every spin. If you spin 30 times, there are 300 different numbers, and 150 of them are odd.

In accordance with the definitions of rigid transformation and translation, the correct rule for the translation is defined by (x, y) → (x - 3, y + 4). (Right choice: A)

Mathematically speaking, transformations are rigid transformations that are modelled according to the following formula:

P'(x, y) = P(x, y) + (h, k)     (1)

Where:

Hence, a leftward translation indicates that h < 0. The correct rule for the translation is defined by (x, y) → (x - 3, y + 4).

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Answer:

a

Step-by-step explanation:

the picture

Answer:

6.0 ounces

Step-by-step explanation:

If the median of the given data is 12, then we need to arrange the numbers in ascending order:

Since the median is the middle value when the data is arranged in ascending order, v must be a number between 4 and 12 (exclusive) in order to maintain the median as 12.

Therefore, v could be any number greater than 4 and less than 12.

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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The questions that could be used to challenge each claim goes as follows.

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Answer:  The correct answer is x=18 and y=59

Step-by-step explanation:

Opposite angles are congruent:

(6x+13) = (7x-5)

Solve for x:

6x+13−7x=7x−5−7x

−x+13−13=−5−13

−x=−18

x=18

Plug x value in for y:

Y=180-(7x-5)

Y=180-(126-5)

Y=180-121

Y=59

A graph that represents the linear system of inequalities is shown in the image attached below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hours coaching and number of hours at the printing shop respectively, and then translate the word problem into algebraic equation as follows:

Since Mason coaches a swim team for $15 per hour, works at a printing shop for $18 per hour and wants to earn at least $125, a linear inequality to describe this situation is given by:

15x + 18y ≥ 125.

Additionally, he cannot work for more than 20 hours a week;

x + y ≤ 20

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Answer:

4x-12

Step-by-step explanation:

original------------------------ 4(x-3)

Distribute--------------------- (4 x X) -  (4 x 3)

After Distrinuting----------4x-12

Hope this helps :P

Answer:

x=4

Step-by-step explanation:

Problem set up is: 5x-6=14

5x=20

x=4

Answer:

1.6

Step-by-step explanation:

1.6*5=8

8+6=14

Answer:

1 /2

Step-by-step explanation:

The theoretical probability is the possibility of an event occurring based on reasoning and not on the outcome of a trial or experiment. Hence, for the question above, the outcome of the tosses or trials would have no effect on the theoretical probability that a coin lands oon head or tail.

Theoretical probability of an event =

Favorable outcome / Total possible outcomes

Favorable outcomes = number of heads in a coin = 1

Total possible outcomes = number of faces on a coin = 2 (head and tail)

Therefore,

Theoretical probability of landing on head = 1 /2

Answer:

\(x {}^{3} \)

Step-by-step explanation:

\(\frac{(x {}^{5} )}{( {x}^{2} )}\)

\(x {}^{3} \)

Answer:

7/8

Step-by-step explanation:

A 55-gallon fish tank is a rectangular aquarium that measures approximately 48 inches in length, 13 inches in width, and 21 inches in height

A 55 gallon fish tank is a rectangular aquarium that holds approximately 55 US gallons (or 208 liters) of water. It typically measures 48 inches (122 cm) in length, 13 inches (33 cm) in width, and 21 inches (53 cm) in height.

The actual dimensions of a 55 gallon fish tank may vary slightly depending on the manufacturer. However, most tanks of this size have a similar shape and capacity.

Therefore, A 55-gallon fish tank is a rectangular aquarium with dimensions 45 inches × 13inches × 21 inches

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Answer:

a) 1, -1, 4, 2, 0, 5, 3 [ in the box ]

b) 2/9

c) 3/9 = 1/3

Step-by-step explanation:

negative score = -1 and -3

score more than 3 = 4, 5 and 7

The correct statement is the circle with radius of 20 in has a central angle of 0.25 radians that interprets an arc of 5 inches .

The Arc Length of the circle can be calculated by using the formula ,

Arc Length = (central angle in radians) × (radius) .

the central angle of the circle is = 0.25 radians ;

the radius and the arc length pair is given as :

(i) radius = 10 in and arc length = 25 in ;

Substituting the value of r = 10 in the formula ,

we get , Arc Length = 0.25 × 10 = 2.5 in ,

the option (i) is not correct .

(ii) radius = 20 in and arc length = 5 in ;

Substituting the value of r = 20 in the formula ,

we get , Arc Length = 0.25 × 20 = 5 in ,

the option (ii) is correct .

(iii) radius = 4 in and arc length = 16 in ;

Substituting the value of r = 4 in the formula ,

we get , Arc Length = 0.25 × 4 = 1 in ,

the option (iii) is not correct .

Therefore , the correct pair is that when radius of circle is 20in then the arc length is 5inches .

The given question is incomplete , the complete question is

A circle have a central angle of 0.25 radians and the  pair of radius and arc length of circle is given below , find the correct pair .

(i) radius = 10in and arc length = 25in

(ii) radius = 20in and arc length = 5in

(iii) radius = 4in and arc length = 16in

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The correct option is the first one:

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

The experimental probability is equal to the quotient between the number of times that a gold block was taken and the total number of trials, so it is:

E = 11/40 = 0.275

Multiply this by 100% to get the percentage:

0.275*100% = 27.5%

For the theoretical probability, take the quotient between the number of gold blocks and the total number:

T = 10/40 = 0.25

And multiply it by 100%

100%*0.25 = 25%

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

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Answer:

\(\dfrac{3x-1}{2x^2-3x}\)

Step-by-step explanation:

Given rational expression:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}\)

First, we need to eliminate the negative exponent in the numerator.

To do this, multiply the numerator by x / x:

\(\begin{aligned}(x^{-1}+3x-4) \cdot \dfrac{x}{x}&=\dfrac{ x^{-1}\cdot x+3x\cdot x-4 \cdot x}{x}\\\\&=\dfrac{1+3x^2-4x}{x}\end{aligned}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\dfrac{\frac{1+3x^2-4x}{x}}{2x^2-5x+3}\)

\(\textsf{Apply\:the\:fraction\:rule:}\:\dfrac{\frac{a}{b}}{c}=\dfrac{a}{b\cdot \:c}\)

                       \(=\dfrac{1+3x^2-4x}{x\cdot (2x^2-5x+3)}\)

                       \(=\dfrac{3x^2-4x+1}{x(2x^2-5x+3)}\)

Factor the quadratics in the numerator and the denominator:

\(\begin{aligned}\textsf{Numerator:}\quad 3x^2-4x+1&=3x^2-3x-x+1\\&=3x(x-1)-1(x-1)\\&=(3x-1)(x-1)\end{aligned}\)

\(\begin{aligned}\textsf{Denominator:}\quad 2x^2-5x+3&=2x^2-2x-3x+3\\&=2x(x-1)-3(x-1)\\&=(2x-3)(x-1)\end{aligned}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\dfrac{(3x-1)(x-1)}{x(2x-3)(x-1)}\)

Factor out the common term (x - 1):

                      \(=\dfrac{3x-1}{x(2x-3)}\)

Simplify the denominator:

                      \(=\dfrac{3x-1}{2x^2-3x}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\boxed{\dfrac{3x-1}{2x^2-3x}}\)

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Answer : true

Step-by-step explanation:

Answer:

Step-by-step explanation:

a+b=41

consecutive=>b=a+1

2a+1=41

2a=41-1=40

a=20 => b=20+1=21

Answer:

x >5

Step-by-step explanation:

4(x - 3) - 2(x - 1) >0

Distribute

4x -12 -2x +2 > 0

Combine like terms

2x -10 >0

Add 10 to each side

2x-10+10 > 10

2x>10

Divide each side by 2

2x/2 > 10/2

x >5

The answer is: [C]: " {x | x > 5} " .

__________________________________________

Explanation:

__________________________________________

Given: " 4(x − 3) − 2(x − 1) > 0 " ;

__________________________________________

Note the "distributive property of multiplication" :

__________________________________________

a(b+c) = ab + ac ;

a(b−c) = ab − ac ;

___________________________________________

So, given:

_________________________________________________

→ 4(x − 3) − 2(x − 1) > 0 ;

_________________________________________________

Let us simplify; and rewrite:

_________________________________________________

Start with:

______________________________________________________

→ -2 (x − 1) = (-2*x) − (-2 *1) = -2x − (-2) = -2x + 2 ;

______________________________________________________

Now, continue with:

→ 4(x − 3) = (4*x) − (4*3) = 4x − 12 ;

______________________________________________________

So, given the original problem:

______________________________________________________

→ 4(x − 3) − 2(x − 1) > 0 ;

______________________________________________________

Rewrite;

Replacing: "4(x − 3)" ; with: "4x − 12" ;

and replacing "− 2(x − 1)" ; with: " -2x + 2" ;

______________________________________________________

as follows: → " 4x − 12 − 2x + 2 " > 0 ;

______________________________________________________

On the "left-hand side", combine the "like terms", and simplify ;

______________________________________________________

+4x −2x = +2x ; −12 +2 = -10 ; and rewrite:

______________________________________________________

→ 2x − 10 > 0 ; Add "10" to EACH SIDE of the inequality;

______________________________________________________

→ 2x − 10 + 10 > 0 + 10 ;

______________________________________________________

to get: → 2x > 10 ;

______________________________________________________

→ Now, divide EACH SIDE of the inequality by "2";

to isolate "x" on one side of the inequality; & to "solve"/"simply" for "x" ;

_______________________________________________________

→ 2x / 2 > 10 / 2 ;

_______________________________________________________

→ x > 5 ; which is:

_______________________________________________________

→ Answer choice: [C]: " {x | x > 5} " .

_______________________________________________________

There are n - 2 (48) numbers between the sequence.

Perfect squares are numbers having a postive integers as its root without remainder

Given the sequences

\($1,4,9,16,25\ldots2500.$\)

The nth term of the sequence is expressed as:

g(n) = n²

Given that the last term is 2500. Substitute:

2500 = n²

n = √2500

n = 50

Hence there are n - 2 (48) numbers between the sequence.

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