Is 10/11 rational or irrational? (10/11 = 0.909090)

The value of y is 1.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Let's simplify the left-hand side first:

4y - 7 + 2y = 6y - 7

Now let's simplify the right-hand side:

-3(y - 1) - 1 = -3y + 2

Now we can substitute these simplified expressions back into the original equation and solve for y:

6y - 7 = -3y + 2

Adding 3y to both sides, we get:

9y - 7 = 2

Adding 7 to both sides, we get:

9y = 9

Dividing both sides by 9, we get:

y = 1

Therefore, the solution is y = 1.

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Answer: B

Step-by-step explanation: B

The correct statement is B) The hypothesis is 'a number is a square number greater than 1.' This correctly identifies the 'if' part of the logical statement, whereas A), C) and D) are incorrect interpretations.

The given logical statement is 'If a number is a square number then it has at least one factor other than 1 and itself.' In examining the answer choices, 'B) The hypothesis is "a number is a square number greater than 1." correctly identifies the hypothesis or the 'if' part of the logical statement. A) is incorrect as it reverses the conditions and conclusions. C) is incorrect as the conclusion is the part following 'then' and D) is incorrect as 49, being a square number, upholds the conditions stated in the logical statement, and thus cannot be a counterexample.

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Answer:

810 feet.

Step-by-step explanation:

We are supposed to find the final altitude of the helicopter.

We have been given that a helicopter is flying at a altitude of 785 feet, this means that altitude of helicopter is positive.

Further, the helicopter descends 570 feet, this means that altitude of helicopter is [tex]-570[/tex].

Finally, the helicopter ascends 595 feet, this means that altitude of helicopter is [tex]595[/tex].

[tex]\text{Helicopter's final elevation}=785\text{ ft}-570\text{ ft}+595\text{ ft}[/tex]

[tex]\text{Helicopter's final elevation}=810\text{ ft}[/tex]

Therefore, the final elevation of helicopter is 810 feet.

Answer:

Cost:$ 920 each or $5,520

Total annual interest: $65 per bond and $390 total

Yield: 7.06%

Step-by-step explanation:

The cost of the bonds is given by the multiplication of the value of the bonds by 92 and divided by 100:

1000*92/100=920

So the cost of each bond would be $920

Then the interest that is payed by the bonds is based on its value which is $1000, so he receives 65 dollars per bond a year, that multiplied by the 6 bonds is equal to $390.

The yield is the real money paid to return interest rate relation, so you just have to take the percentage if 5,520 is the 100, how much is $390=

5520/100=390/x

x=39000/5520=7.06%

The expression representing Rose's stamp collection is given by R = (1/2)x - 7. It denotes that Rose's collection is 7 less than half of Van's stamp collection, where x represents the total number of stamps in Van's collection.

Let's denote Van's stamp collection as x. According to the given information, Rose's stamp collection is 7 less than half of Van's stamp collection.

Expression for Rose's stamp collection (R):

R = (1/2)x - 7

Here's the breakdown of the expression:

(1/2)x represents half of Van's stamp collection.

-7 signifies 7 less than half of Van's stamp collection.

This expression encapsulates the relationship between Rose's stamp collection and half of Van's collection, diminished by 7.

Hi there!

For the first one the answer is D. [tex] -\dfrac{9}{2} , -3, \dfrac{1}{2} , \sqrt{6} , 4.2 [/tex]

For the second one the answer is B. Irrational Numbers, Real Numbers

For the last one the answer is [tex] 9 < \sqrt{93} < 10 [/tex]

Your friend, ASIAX

The net change in the value of the account, when rounded to the nearest dollar, is $550.

To find the net change in the value of the account, you would sum up the amounts deposited, subtract the amounts withdrawn, and add the interest earned:

Net change = (Deposits - Withdrawals) + Interest earne

Net change = ($500 - $250) + $300

            = $250 + $300

            = $550

Therefore, the net change in the value of the account, when rounded to the nearest dollar, is $550.

The probable question maybe:

"What is the net change in the value of an investment account after depositing $500, withdrawing $250, and earning $300 in interest, when rounded to the nearest dollar?"

The greatest number of arrangements using every balloon is an illustration of the highest common factors (HCF).

The greatest number of arrangements you can make using every balloon is 8.

Given that:

[tex]White = 16[/tex]

[tex]Red = 24[/tex]

To determine the greatest number of arrangements, we simply calculate the HCF of 16 and 24.

We have:

[tex]16 = 2\times 2\times 2 \times 2[/tex]

[tex]24 = 2\times 2\times 2 \times 3[/tex]

The highest common factor is:

[tex]HCF =2 \times 2 \times 2[/tex]

[tex]HCF =8[/tex]

Hence, the greatest number of arrangements you can make using every balloon is 8.

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5 7/9  - 4 1/3

covert 1/3 to 9ths 3 x 3 = 9 so 1/3 = 3/9

5 7/9 - 4 3/9 = 1 4/9 meters

The student is asking about fractions. In a fraction, the denominator (bottom number) represents the total number of equal parts the whole is divided into, while the numerator (top number) signifies the parts we're considering. When multiplying, the numerators and denominators multiply separately to form the new fraction.

The student is referring to the concept of fractions. In a fraction, the number on the bottom (the denominator) is the total number of equal parts into which a whole is divided, and the number on the top (the numerator) is the number of those parts we are considering. To clarify by using an example, let’s take 2/4. In this scenario, the denominator is 4, which means our whole is divided into 4 equal parts. The numerator is 2, which shows that we're referring to 2 out of those 4 parts. When multiplying fraction, the numerators multiply to create the new numerator and denominators multiply to create the new denominator. Hence, 2/4 multiplied with 3/4 would produce 6/16.

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Ten less than five times a number cubed in the mathematical from will be 10 - 5x³.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

Ten less than five times a number cubed.

Let the number be 'x'. Then the cube of the number x will be x³.

Then the five times a number cubed will be given as,

5x³

Ten less than five times a number cubed. Then the expression is given as,

⇒ 10 - 5x³

Ten less than five times a number cubed in the mathematical from will be 10 - 5x³.

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The simplified form of [tex]\frac{6}{18}[/tex] is [tex]\frac{1}{3}[/tex].

To simplify the fraction [tex]\frac{6}{18}[/tex], follow these steps:

Find the greatest common divisor (GCD) of the numerator and the denominator. The numerator is 6 and the denominator is 18. The greatest common divisor of 6 and 18 is 6.

Divide both the numerator and the denominator by their GCD.

When we divide the numerator 6 by 6, we get [tex]\frac{6}{6} = 1[/tex].

When we divide the denominator 18 by 6, we get [tex]\frac{18}{6} = 3[/tex].

Write the simplified fraction: After dividing both parts by 6, the fraction [tex]\frac{6}{18}[/tex] simplifies to [tex]\frac{1}{3}[/tex].

The product of the numbers will be 120. And the product 3 × 40 = 3 × 4 tens.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

According to the commutative property of integer multiplication, changing the order of something like the operands or the integers has no impact on the outcome of the multiplication.

a x b = b x a

Similarly, the product of the numbers 3 and 40 can be written as,

3 × 40 = 3 × 4 tens

The product of the numbers will be

3 × 40 = 120

The product of the numbers will be 120.

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Final answer:

To find the perimeter of Jill's room in the scale drawing, convert the actual room measurements using the scale and then calculate the perimeter based on the scaled dimensions. The perimeter on the drawing is 12 inches.

Explanation:

The question asks us to calculate the perimeter of a room in a scale drawing. Jill's room measurements are 12.5 feet in length and 11.5 feet in width, with a scale of 0.5 inch equals 2 feet. To find the perimeter on the drawing, we first convert the actual measurements into scale measurements:

Scale for Length: 12.5 feet / 2 feet = 6.25; then 6.25 × 0.5 inch = 3.125 inches.

Scale for Width: 11.5 feet / 2 feet = 5.75; then 5.75 × 0.5 inch = 2.875 inches.

Next, we calculate the perimeter of Jill's room on the drawing:

Perimeter = 2 × (Length + Width) in the drawing.

Perimeter = 2 × (3.125 inches + 2.875 inches) = 2 × 6 inches = 12 inches.

Therefore, the perimeter of Jill's room on the drawing is 12 inches.

By using algebra to model the problem, we find that the pharmacist had 36 prescriptions for tranquilizers.

In the given problem, we need to find out the number of prescriptions for tranquilizers. We know that the pharmacist has 4/3 as many prescriptions for antibiotics as tranquilizers. We also know that the total number of prescriptions for both the drugs is 84. We can make a mathematical model out of this information and solve for the number of tranquilizer prescriptions.

Let us suppose the number of tranquilizer prescriptions is x. Then the number of antibiotic prescriptions would be 4/3*x. Together, these prescriptions add up to 84.

So, we can write the equation: x + 4/3*x = 84

To make the equation simpler we can multiply the entire equation by 3 which transforms the equation into: 3x + 4x = 252

Combining like terms gives us: 7x = 252

Finally, dividing both sides of the equation by 7 gives us the solution: x = 252 / 7

So, x = 36

Therefore, we conclude that the pharmacist had 36 prescriptions for tranquilizers.

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The equivalent fraction of 8/9 with the denominator 18 is 16/18.

To write the fraction 8/9 as an equivalent fraction with the given denominator 18, we have to find a number that we multiply by 9 (the original denominator) to get 18. This number, in this case, is 2. What we do to the bottom of a fraction, we should also do to the top, therefore we would also multiply the numerator (8) by the same number (2). So, the equivalent fraction is 8 * 2 / 9 * 2 = 16 / 18.

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