The pair of figures is similar. Find x. Round to the nearest tenth if necessary.

The argument is valid by the law of detachment.

Answer:

The argument is valid by the law of detachment.

Step-by-step explanation:

We first verify that the first statement, "if p, then q" is correct.  If a parallelogram has a right angle, this means that the angle opposite that angle must also be right; this is because the opposite angles of a parallelogram are congruent.

This also means that the adjacent angle to this right angle must also be right; this is because the adjacent angles in a parallelogram are supplementary.

Thus "if p, then q" is true.

The law of detachment states that if I have two statements, one of the form "if p, then q" and the other "p", then the conclusion, "q," is valid.

for every 5 men there are 6 women

90 /5 = 18

18 *6 = 108 women

Answer:

108 women

Step-by-step explanation:

 82=6482=64choices for that.

Now, for the second one, we can't be in the row or column of that first one, so leaving us with 72=4972=49 choices.

Then so on, we have 62=3662=36 for the third one, 2525 for the fourth one, and so on ……

But, however, we have to remember the rooks are not labeled, thus it doesn't matter specifically about a specific rook's position.

Thus, we have a total of (8!)28!=40320(8!)28!=40320 ways.

x - 2/3 = 5/6

 the only step needed is to add 2/3 to 5/6

2/3 + 5/6 = 1 1/2

x = 1 1/2

Answer:

the value of x is [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

we need to solve value of x for expression [tex]x-\frac{2}{3}=\frac{5}{6}[/tex]

[tex]x-\frac{2}{3}=\frac{5}{6}[/tex]

Add both the sides by [tex]\frac{2}{3}[/tex]

[tex]x-\frac{2}{3}+\frac{2}{3}=\frac{5}{6}+\frac{2}{3}[/tex]

take L.C.M both the side and simplify

[tex]x=\frac{3}{2}[/tex]

Hence, the value of x is [tex]\frac{3}{2}[/tex]

Answer:

The station first give away all three prizes to 300th caller.

Step-by-step explanation:

A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller.

To get the answer we need to calculate L.C.M.  of 15, 25, 100.

15 = 3 x 5

25 = 5 x 5

100 = 2 x 2 x 5 x 5

LCM is = 2 x 2 x 3 x 5 x 5 = 300.

Hence, the station first give away all three prizes to 300th caller.

The time it takes the rock to hit the water is 6 seconds

Data;

To find the time it takes for the rock to hit the ground, we have to use the and assume that the given equation represents the height at which the rock attained.

[tex]f(x) = -16(x^2 - 3x -18)\\0 = -16x^2 + 48x + 288\\16x^2 - 48x - 288 = 0\\x^2 - 3x - 18 = 0[/tex]

Solving the above quadratic equation,

x = - 3 or x = + 6

The time it takes the rock to hit the water is 6 seconds

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To evaluate the ratio of 390mm to 13cm, we convert 13cm to 130mm and then simplify the ratio of 390mm to 130mm to its lowest terms, which is 3 : 1.

To evaluate the ratio of 390mm to 13cm, we first need to express these measurements in the same unit. Converting centimeters to millimeters is simple: there are 10 millimeters in 1 centimeter.

Therefore, 13cm is equivalent to 130mm. Now, we can write the ratio as 390mm : 130mm. To simplify this ratio to its lowest terms, we divide both numbers by the greatest common divisor, which is 130 in this case. The simplified ratio is therefore 3 : 1.

The generalized description is as follows: quantity (in old units)  imes conversion factor = quantity (in new units). One must remember to simplify the ratio by dividing both the numerator and the denominator by their greatest common divisor, finalizing the answer without the '1' in the denominator when it's the only figure present.

To find the law connecting w and t, we establish w as partly constant and partly inverse to t squared. Using given values, we find constants k and c and then solve for t when w is 46.

The problem states that w is partly constant and partly varies inversely as the square of t. Given two sets of values for w and t, we can establish the relationship between them. Since the variation is inverse with respect to the square of t, we can write the relationship as:

w = k / t2 + c

where k is a constant of variation and c is the constant part of w. To find these constants, we use the given data points (24, 4) and (18, 2). Substituting these into the equation, we get two simultaneous equations:

Solving these will give us the values of k and c, which then allows us to find t when w = 46.

To solve for t when w = 46, we plug this value into our established equation and solve for t. We'll end up with a quadratic equation in terms of t that we need to solve to find the time t.

Answer with explanation:

Total number of vacant seats = 4 seat

Number of students Looking for Seats = 12 Student

We have to fill the four Seats and there are 12 students.

First Seat can be filled in 12 ways,11 students are left,So, second seat can be filled in 11 ways ,Now,there are 10 students left ,So, third seat can be filled in 10 ways,Now there are 9 students left,so last seat can be filled in 9 ways.

Total number of ways of filling 4 seats if there are 12 number of students

               =12 × 11 × 10 × 9

              =132 × 90

             =  11880 ways

Or ,you can solve it directly by the concept of Permutation.

Total ways of filling 4 vacant seats if there are 12 students in all

           [tex]= _{4}^{12}\textrm{P}=\frac{12!}{(12-4)!}=\frac{12\times 11\times 10\times 9\times 8!}{8!}=12\times 11\times 10\times 9=11880[/tex]  

Answer:

The greatest perfect square that is a factor of 980 is 196.

Step-by-step explanation:

To find : What is the greatest perfect square that is a factor of 980?

Solution :

First we factor the number 980.

[tex]980=2\times 2 \times 5\times 7\times 7[/tex]

[tex]980=2^2\times 7^2\times 5[/tex]

[tex]980=(2\times 7)^2\times 5[/tex]

[tex]980=(14)^2\times 5[/tex]

[tex]980=196\times 5[/tex]

This clearly means that 196 is the required factor.

Therefore, The greatest perfect square that is a factor of 980 is 196.

We have that The Greatest perfect square of 980 is

x= 196

From the question we are told that

The greatest perfect square that is a factor of 980

Generally

Greatest perfect square

Where a  perfect square is a number that is written to given the product of two identical Numbers

Therefore

Greatest perfect square of 980 is

x= 196

Where

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980

Therefore

The Greatest perfect square of 980 is

x= 196

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Answer:

All the numbers are less than and equal to 18.

Step-by-step explanation:

To find : All numbers such that a third of a number increased by half that number is at least 3 less than that same number ?

Solution :

Let the number be 'x',

A third of a number is [tex]\frac{x}{3}[/tex]

Half that number is [tex]\frac{x}{2}[/tex]

3 less than that same number is [tex]x-3[/tex]

A third of a number increased by half that number is at least 3 less than that same number is written as,

[tex]\frac{x}{3}+\frac{x}{2}\geq x-3[/tex]

[tex]\frac{2x+3x}{6}\geq x-3[/tex]

[tex]\frac{5x}{6}\geq x-3[/tex]

[tex]5x\geq 6x-18[/tex]

[tex]5x-6x\geq -18[/tex]

[tex]-x\geq -18[/tex]

[tex]x\leq 18[/tex]

Therefore, all the numbers are less than and equal to 18.

The set of numbers such that a third of a number increased by half that number is at least 3 less than that same number are given as; x <= 18.

According to the question;

Let the numbers in question be represented as x.

In essence;

[tex] \frac{x}{3} + \frac{x}{2 } \geqslant x - 3[/tex]

[tex] \frac{5x}{6} \geqslant x - 3[/tex]

Therefore, the set of numbers such that a third of a number increased by half that number is at least 3 less than that same number are given as; x <= 18.

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The value 0.02% written as a decimal is 0.0002

Given the value to be written as a decimal :

To express as a decimal , divide 0.02 by 100

Now we have ;

Therefore, the value 0.02% written as a decimal is 0.0002

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x < -2 and y ≤ -x -2

The bank's likely response to Kevin's concern would be that checks are recorded on the date they are cashed, not on the date they are written, which explains the mismatch in dates Kevin observed. Balancing one's checkbook regularly is important for managing personal finances.

When Kevin has noticed that the dates on his check register do not match the dates on his account statement and contacts the bank, the bank's likely response will be "The date that the check is written is usually a few days before it is cashed. We record when it was cashed and you record when it's written." This is a common situation in personal finance and is related to the cash basis of accounting that most individuals use to manage their finances. The difference in dates arises because checks are processed and cleared by the bank on the date they are cashed, not on the date they are written. It's important for individuals to balance their checkbooks regularly to manage money, keep track of cash flow, and avoid overdraft fees.