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The dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.

The area of Rectangle is length times of width.

Area of rectangular pool = 6x² − 11x + 3

To factor the trinomial, we need to find two binomials that multiply together to give the trinomial 6x² − 11x + 3.

We use product-sum method of factoring to find the two binomials.

We need to find two numbers that multiply to 6 (the coefficient of the x² term) and add to -11 (the coefficient of the x term).

6x² − 11x + 3

6x² −2x-9x + 3

(2x − 1)(3x − 3)

Hence, the dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.

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The relationship between a statistic and a parameter is the same as the relationship between , Option(A) a sample and a population

The Population is defied as an entire group of individuals that we are interested in studying, while a sample is a subset of that population that we actually observe and collect data from.

A Parameter is defined as a numerical characteristic of a population, such as its mean or variance, whereas a statistic is a numerical characteristic of a sample, such as its sample mean or sample standard deviation.

The relationship between a sample and a population is similar to the relationship between a statistic and a parameter because a sample is used to estimate  information about the population, and a statistic is used to estimate  information about a parameter.

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Answer:

One equivalent ratio that compares the number of boys to the number of girls in Harold's class is 7:6. Another equivalent ratio is 14:12, and yet another equivalent ratio is 21:18. These ratios are equivalent because they represent the same relationship between the number of boys and girls, just with different scale.

Answer:

14:12

21:18

35:30

Step-by-step explanation:

An equivalent ratio is a ratio that represents the same comparison as another ratio, but with different values. To find equivalent ratios to compare boys to girls in Harold's class, we can multiply or divide both the numerator and denominator of the original ratio by the same value.

The original ratio of boys to girls is 7 boys to 6 girls, or 7:6. Here are three equivalent ratios:

14:12 (multiplying both the numerator and denominator by 2)

21:18 (multiplying both the numerator and denominator by 3)

35:30 (multiplying both the numerator and denominator by 5)

Answer:

3

Step-by-step explanation:

the square root basically means ___ multiplied by ___ equals the number in the square root, in this case being 9. the +/- symbol means that -3 multiplied by -3 equals positive 9 and positive 3 multiplied by positive 3 equals positive 9

In linear equation, $869,776  will her total payment for the home be .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.

The number is $6.74.

That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.

2. Amount borrowed

You will make a 22% down payment:

Thus the amount borrowed is $426,000 - $93,720 = $332,280

3. Monthly payment

Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:

4. Total monthly payments:

Multiply the number of payments by the monthly payment.

Number of payments = 20 years × 12 payments /year = 240 payments.

5. Total payment for the home.

The total payment for the home will be the down payment plus the amount paid to the bank:

$322,280 + $537,496 = $869,776

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Arianne's monthly mortgage payment will be $536.82.

A mortgage payment is generally made up of components like principal, interest, taxes and insurance. The interest is the cost of borrowing money. The amount of interest one pay is determined by your interest rate and your loan balance.

To calculate Arianne's monthly mortgage payment, we can use the following formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

First, we need to calculate the monthly interest rate: i = APR / 12 = 5% / 12 = 0.004167

Next, we can substitute the values into the formula: The computation of our monthly payment goes as follows:

= $90,000 [ 0.004167(1 + 0.004167)^360 ] / [ (1 + 0.004167)^360 – 1 ]

= $536.82.

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The probability of getting three or fewer heads on four flips of a fair coin is 0.75.

The fair coin is flipped four times. The sample space can be found as follows,

There will be 4 trial and each trial can have two outcomes so the total number of outcomes is 2x2x2x2.

Total possible outcomes are 16.

Now, the number of favorable outcomes when there will be 3 or less heads will be 6 because there has to be 3 heads in four position and that too without repetition.

So, the probability of event is,

P = Total favorable event/Total possible events

P(of three or fewer heads on four flips of a fair coin) = 6/8

So, probability of three or fewer heads on four flips of a fair coin is 0.75.

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Answer: i think it is 538.4

Step-by-step explanation:

The value of the length, x is 5√3

From the question, we have the following parameters that can be used in our computation:

Rise = 11

Length = x

Hypotenuse = 14

The value of the length , x is calculated as

x^2 = Hypotenuse^2 - Rise^2

Substitute the known values in the above equation, so, we have the following representation

x^2 = 14^2 - 11^2

So, we have

x^2 = 75

Take the square root of bpth sides and evaluate

x = 5√3

Hence, the value of x is 5√3

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90 degrees Fahrenheit is equal to approximately 32.2 degrees Celsius using conversion formula method.

To convert Fahrenheit to Celsius, the following formula can be used:

Celsius = (Fahrenheit - 32) x 5/9

Plugging in 90 degrees Fahrenheit, we get:

Celsius = (90 - 32) x 5/9

Celsius = 58 x 5/9

Celsius = 290/9

Celsius ≈ 32.2

Therefore, 90 degrees Fahrenheit is approximately 32.2 degrees Celsius.

Fahrenheit is a temperature measurement system developed by the German physicist Daniel Gabriel Fahrenheit in 1724.

The Celsius scale is widely used throughout the world for measuring temperature, and it is the standard unit of temperature used in most scientific research and international trade. In addition to measuring air temperature, Celsius is used to measure temperature in a variety of fields, including chemistry, biology, and engineering.

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The equations are solved and the old account balance for Account #4 is given by A = - $ 30

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Acc #    Old Acc Balance ($)      Trans Amount ($)      New Acc Balance($)

1                       352                                       -48                      304

2                      432                                      +80                      512

3                       75                                       -100                     -25

4                       -30                                        52                       12

5                      -10                                        -20                     -30

So , the old account balance for the account number 4 is -30

Hence , the equation is A = - $ 30

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0.08$/fl. Ounce

The first step in finding the unit price of a can of pineapple juice in dollars per fluid ounce is to determine the volume of juice contained in the can. If a can holds 4 cups of juice, then we need to convert that volume to fluid ounces. One cup is equal to 8 fluid ounces, so 4 cups is equal to 32 fluid ounces.

Next, we need to determine the price of the juice in dollars per fluid ounce. We are told that the can costs 2.56 dollars, so we need to divide that cost by the number of fluid ounces in the can to find the unit price.

So, the unit price of the juice in dollars per fluid ounce is:

2.56 / 32 = 0.08 dollars per fluid ounce

So, for each fluid ounce of pineapple juice, the cost is 0.08 dollars. This is the unit price of the juice in dollars per fluid ounce. It is important to note that this unit price is only valid for this specific can of juice and may not be the same for other sizes or brands of pineapple juice.

In conclusion, the unit price of a can of pineapple juice containing 4 cups or 32 fluid ounces, and costing 2.56 dollars, is 0.08 dollars per fluid ounce.

Answer:

Step-by-step explanation:

i don't know

Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.

To find the answer, we need to use the formula for permutations:

Permutations = n! / (n-r)!

Where:

- n is the total number of items

- r is the number of items to be arranged

- ! means factorial (e.g. 5! = 5 x 4 x 3 x 2 x 1)

In this case:

- n = 10 (the total number of plants)

- r = 3 (the number of plants to be arranged on the window ledge)

Plugging these values into the formula, we get:

Permutations = 10! / (10-3)! = 10! / 7! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (7 x 6 x 5 x 4 x 3 x 2 x 1) = (10 x 9 x 8) / 1 = 720

Therefore, Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.

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Answer:

Step-by-step explanation:

75%

Answer:

Area = 452 cm²

Step-by-step explanation:

[tex] = \frac{\pi }{4} {d}^{2} [/tex]

[tex] = \frac{\pi}{4} {(24)}^{2} = 452.39 \: cm²[/tex]

the matches are

-2(2x+5) ≤ -7(x+4)         x<=-6

4x-3x-1                          x<=-1

5(x-3)9(x+1)                   x>=-6

3(x-4)+5 2x-9                x>=-2

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

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The correct matching of the inequalities can be shown from the calculations below

Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.

Using the principle of inequalities we have;

1) -2(2x + 5) ≤ - 7(x + 4)

-4x -10 ≤ -7x -28

-4x +7x ≤ -28 + 10

3x ≤ -18

x ≤ -6

2) 4x - 6/2 ≥ 3x - 1

4x - 6 ≥ 6x - 2

4x - 6x ≥ -2 + 6

-2x ≥ 4

x  ≤ -2

3) 5(x - 3) ≤ 9(x + 1)

5x - 15  ≤ 9x + 9

5x - 9x  ≤ 9 + 15

-4x  ≤ 24

x ≥ -6

4) 3(x - 4) + 5 ≥ 2x - 9

3x - 12 + 5≥ 2x - 9

3x - 2x ≥ -9 + 12 -5

x ≥ -2

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x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

[tex]y=b_1x+b_0[/tex]

There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.

Given a collection of pairs (x,y) of numbers, there is a line [tex]y=b_1x+b_0[/tex] that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.

[tex]b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)[/tex]

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

[tex]y=b_1x+b_0[/tex]

specifying the least squares regression line is called the least squares regression equation.

Example,

Find the least squares regression line for the five-point data set

x = 2  2  6  8  10  

y=  0  1   2  3  3.

compute the table,

x   y     x2         xy

2  0     4           0

2  1      4            2

6   2   36       12

8   3   64        24

10  3   100    30

28  9   208    68   (sum)

[tex]S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125[/tex]

The regression line is y=0.34375x-0.125

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Answer:

The mass of 3.5 moles of Ca (Sodium)  is 140 g to two significant figures.

Answer:

7/10

Step-by-step explanation:

Here ya go!

The solution is, B = 245, is a Reflex Angle., when it is given that A=65.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

We know that, a ray is a line that continues on forever inn one direction with a point at it's start.

here, we have,

A = 65°

now,  B is a Reflex Angle ,

so, we know that Reflex Angle means the angle with value >180 to <270.

now, we get,

B = 180 + 65

  = 245

Hence, The solution is, B = 245, is a Reflex Angle.

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Answer: $4.20

Step-by-step explanation:

The bag contains $4.20. We know that 18% of the coins are pennies and 36% are dimes. There are 50 coins total, so 18% of 50 is 9 pennies and 36% of 50 is 18 dimes. Since there are 2 more nickels than pennies, there must be 11 nickels. 9 pennies plus 11 nickels plus 18 dimes equals 38 coins. To calculate the total amount of money, we multiply 38 by the value of each type of coin: 9 pennies x $0.01 = $0.09, 11 nickels x $0.05 = $0.55, and 18 dimes x $0.10 = $1.80. Adding these together, we get $0.09 + $0.55 + $1.80 = $2.44. Therefore, the bag contains $4.20.

Answer: There are 9 pennies, 18 dimes, and 11 nickels and 12 quarters

so in total, the bag has $11.2

Step-by-step explanation:

18% of 50 = 9

36% of 50 = 18

There 2300 different combinations of 3 people could you choose.

The sequence of the results is irrelevant when calculating the overall outcomes of an event using combinations.

Given:

We have to select 3 people from 25 people.

n= 25, r=3

So, the number of different combination is

= C(n, r)

= n!/ r! (n-r)!

= 25! / 3! (25- 3)!

= 25! / 3! x 22!

= 25 x 24 x 23 /3 x 2

= 25 x 23 x 4

= 2300

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Answer:

Step-by-step explanation:

Put ' - 3' whre 'x' is and compute the answer

f(-3) = 3 (-3) - 7

      = -9 - 7 = - 16

Two lines that form a right angle at their point of intersection are perpendicular to each other.

The negative reciprocal is equal to the slope of the perpendicular lines. A transversal line is a line that is perpendicular to two parallel lines. Equal pairs of alternate angles and matching angles are created in the case of the transversal line.

When two lines intersect at a right angle, they are perpendicular to each other. The junction is referred to as the point of perpendicularity. The perpendicular lines form a 90-degree angle, and they can be used to create a coordinate system or used in geometric constructions. Such lines are called perpendicular lines.

Correct Question :

Two lines that form a right angle at their point of intersection are called what?

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The principal for Account A is $150, and we do not have enough information to find the principal for Account B. Account A earned the most interest the first month because it has a higher monthly interest rate.

The principal for Account A can be found using the formula for simple interest:

I = Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Rearranging the formula to solve for P, we get P = I / (rt).

For Account A, the interest is $9.45, the interest rate is 3.6%, or 0.036, and the time is 21 months, or 1.75 years.

Plugging these values into the formula, we get:

P = $9.45 / (0.036 × 1.75) = $150

So the principal for Account A is $150.

For Account B, we do not have enough information to find the principal. We know the interest rate, but we do not know the interest or the time.

To determine which account earned the most interest the first month, we can compare the monthly interest rates.

The monthly interest rate for Account A is 3.6% / 12 = 0.3%, and the monthly interest rate for Account B is 2.4% / 12 = 0.2%.

Since the monthly interest rate for Account A is higher, it earned the most interest the first month.

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The value of x is  15√2

The value of the side y is 30

The sum of angles in a rectangle is 360 degrees

To determine the value of the variable, x

Let's use the trigonometric identity, cosine

cos = adjacent/hypotenuse

substitute the values

cos 45 = 15/x

Find the value

1/√2 = 15/x

cross multiply

x = 15√2

For y, we have;

sin 45 = y/15√2

1/√2 = y/15√2

Make y subject

y= 15√2 /√2

y = 60/2

y = 30

Hence, the values are 30 and 15√2

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The percentage of decrease is 20%

First, if we have an initial value A, and we increase it by x (a percentage in decimal form) then the new value will be:

A' = A*(1 + x)

Whle a decrease is written as:

A' = A*(1 - x)

In this case we have an increase of the 25%, it is written as:

A' = A*(1 + 0.25)

A' = A*1.25

IF we pass the factor to the other side, will get:

(1/1.25)*A' =  A

(0.8)*A' = A

Now we want to write the coefficient on the left in the form (1 - x)

We will get:

0.8 = 1 - 0.2

0.2 is the percentage (in decimal form) decreased  from A' to get A. Then the answer is 20%.

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A) The scale factor is 2.

B) The measure of m<C is 67.17.

C) The measure of m<Z is 75.96

D) The length of AD is 4 unit.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A) The scale factor is

= CB/ XY

= 5/ 2.5

= 2 unit

B) We’re given the measurement of angle XYZ, which is also the measurement of angle y.

Since angles in similar triangle are equivalent, if y(67.17)=c, then c must be equal to 67.17.

C) The measure of angle Z is equivalent to 75.96

D) The length of AD

= 2 x WX

= 2 x 2

= 4 unit

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