evaluate (4xy+y)÷2 when x=3 and y=2

Answer: C

Step-by-step explanation:

the value of a remains the same

Step-by-step explanation:

1 ft = 12 in

so,

36 in = 36/12 = 3 ft

24 in = 24/12 = 2 ft

therefore, the area of the rectangle is

3×2 = 6 ft²

We know that the given expression 6x - x - 4 is (2) this is not equivalent to 7x − 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

It's possible to multiply, divide, add, or subtract with this mathematical operation.

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

So, the given expressions are:

7x - 4 and 6x - 4 - x

Now,

7x - 4 and 6x - x - 4

7x - 4 and 5x- 4

Then, we can easily say that the given expressions are not equivalent.

Therefore, we know that the given expression 6x - x - 4 is (2) this is not equivalent to 7x − 4.

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Complete questions:
Explain how you can tell if the expressions 7x – 4 and 6x – 4 – x are equivalent. Sample Response: 6x − x = 5x.

1. The new expression is now 5x − 4.

2. This is not equivalent to 7x − 4.

The multiple of 2 means any number that is completely divisible by 2.

A multiple in mathematics is basically that number which is formed by multiplying a particular number and it is completely divisible by that number.

If we talk about the number 2, then the multiple of 2 will mean that any number that is formed by multiplying 2 into it.

For example, 6 is a number which can be written as 2 x 3.

Here, 3 is multiplying two times and it becomes 6, so, it is a multiple of 2. Also, if any number is appearing in the table of 2 then it is a multiple of 2.

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As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

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if £1=1. 62USD then, £650 is equivalent to $1053 in US dollars and £450 is equivalent to $729 in US dollars.

To convert British pounds to US dollars, we can multiply the pound amount by the exchange rate of pounds to dollars.

£650 in USD:

£1 = $1.62, so we can write:

650 x 1.62/1 = 1053

Therefore, £650 is equivalent to $1053 in US dollars.

£450 in USD:

Using the same method, we can calculate the value of £450 in US dollars as follows:

450 x 1.62/1 = $729

Therefore, £450 is equivalent to $729 in US dollars.

The conversion of British pounds to US dollars is a common currency exchange process, as both currencies are widely used in international trade and finance. The exchange rate between the two currencies represents the value of one currency in terms of the other. In this case, the exchange rate of £1 to $1.62 means that one British pound is worth 1.62 US dollars. To convert a certain amount of British pounds to US dollars, we simply multiply the pound amount by the exchange rate. The resulting dollar amount reflects the value of the pounds in the equivalent US dollars. Exchange rates can fluctuate frequently due to various economic and political factors, affecting the value of currencies and international transactions.

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When the number"52" is divided by the number "2" , we get the answer as  26 .

The Division is defined as a mathematical operation , which is used to find the quotient of two quantities. It involves dividing a given number (the dividend) by another number (the divisor) to find the result (the quotient) .

We have to divide , the number 52 by 2 ,

It is represented as : 52/2 ;

Let the answer after performing division be = "x" ;

which means ; x = 52/2 ;

⇒ x = 26 ;

Therefore , On dividing 52 by 2 , the answer is 26 .

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To divide 52 by 2, we can use the long division method. The quotient is 26.

To divide 52 by 2, you can use long division method. Write 52 as the dividend and 2 as the divisor. Divide 5 (the first digit of the dividend) by 2 (the divisor), which gives you 2 as the quotient. Multiply the quotient (2) by the divisor (2), which equals 4. Subtract 4 from 5 to get 1. Bring down the next digit, which is 2. Repeat the process by dividing 12 by 2, which gives you 6 as the quotient. Multiply the quotient by the divisor to get 12, and subtract from the remaining digit 2, which gives you 0. Therefore, 52 divided by 2 equals 26.

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One gallon of water weighs around 3.78 kilograms (kg) or 8.34 pounds (lb) (kg). 

Based on the weight of water at ordinary atmospheric pressure and room temperature (about 68 degrees Fahrenheit or 20 degrees Celsius) (14.7 pounds per square inch or 1 atmosphere).

It's crucial to remember that water weight might change somewhat based on ambient temperature and pressure.

Water weighs slightly less at higher temperatures than it does at lower ones and vice versa. Similar to this, the weight of water increases somewhat at higher pressures while decreasing slightly at lower pressures.

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To show that a statement is false, we need to find a counterexample where the statement does not hold true. Here are the counterexamples for each statement:

The sum of any three odd numbers is even.

Counterexample: 1 + 3 + 5 = 9, which is an odd number. Therefore, the statement is false.

When an even number is added to the product of two odd numbers, the result will be even.

Counterexample: 1 {square} 3 + 2 = 5, which is an odd number. Therefore, the statement is false.

When an odd number is squared and divided by 2, the result will be a whole number.

Counterexample: Let's take an odd number, say 3. If we square it, we get 3{square}2 = 9. If we divide 9 by 2, we get 4.5, which is not a whole number. Therefore, the statement is false.

In each of these cases, we have found a counterexample that shows that the statement is false. It is important to remember that just because a statement holds true for some examples, it does not necessarily mean it holds true for all examples. Finding counterexamples is an important tool in mathematical reasoning and can help us to refine and improve our understanding of mathematical concepts.

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Jane bought 4 pounds of jolly ranchers.

To calculate how many pounds of jolly ranchers Jane bought, we need to divide the total worth of jolly ranchers by the price per pound.
Determine the price per pound of jolly ranchers. This information is not provided in the question, so we will need to assume a price. Let's say that the price per pound of jolly ranchers is $2.50.
Divide the total worth of jolly ranchers by the price per pound.
$9.75 ÷ $2.50 = 3.9
Round the answer to the nearest whole number, if necessary. In this case, 3.9 rounds up to 4.

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Answer:

there is a chance of 33.33% that she picks a song of 2min and 13sec

Answer:B.

Step-by-step explanation:

The actually answer is B. Equal to the likelihood of choosing a song that lasts 3 minutes 15 seconds

Answer:

when they both are separated they form a right angled triangle 90°

To convert 1 teaspoon to 1 ml multiply the volume by the conversion ratio of  4.928922.

Add the volume to the conversion ratio to convert a teaspoon measurement to a millilitre measurement.

You may convert between teaspoons and milliliters using the following straightforward formula:

tablespoons in milliliters = 4.928922

One-third of a tablespoon's volume is represented by a teaspoon. [1] Although a teaspoon is roughly equivalent to 4.9 millilitres, on nutrition labels, a teaspoon is actually equal to 5 millilitres. 

The teaspoon is a common volume measurement in the US. Teaspoons can be written as tsp, although they can also be spelled as t, ts, or tspn.

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The  single natural logarithm for the expression 4 + ln 2 - ln 4 is ln(2). So, correct option is A.

To express 4 + ln 2 - ln 4 as a single natural logarithm, we can use the properties of logarithms to combine the terms.

First, we can use the rule that ln(a) - ln(b) = ln(a/b) to simplify ln 2 - ln 4:

ln 2 - ln 4 = ln(2/4) = ln(1/2)

Now, we can rewrite the expression as:

4 + ln(1/2)

We can use another logarithmic property, ln(a) + ln(b) = ln(ab), to write this as:

4 + ln(2^(-1))

Simplifying further:

4 - ln(2)

Therefore, 4 + ln 2 - ln 4 can be expressed as a single natural logarithm of:

ln(2^2 / 2) = ln(2)

So, the answer is (a) ln 2.

In general, when simplifying expressions involving logarithms, it's helpful to remember the logarithmic properties and rules, such as the product, quotient, and power rules, as well as the fact that ln(e) = 1. By applying these rules systematically, we can simplify complex expressions into simpler forms that are easier to work with.

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Answer:

a. 651

Step-by-step explanation:

To solve the problem, you can start by finding out how many students bike or walk to school by multiplying the total number of students by the percentage that bike or walk:

1860 x 0.45 = 837

Next, you can subtract the number of students who drive to school to find out how many students travel by bus:

1860 - 837 - 372 = 651

Therefore, the answer is 651, so the option (a) is correct.

Answer:

a. 651

Step-by-step explanation:

We first need to find the number of students that bike or walk.

We can do this by plugging the numbers into this equation:

[tex]\frac{is}{of} = \frac{percent}{100}[/tex]

We know that the percent is 45, and we know the total amount of students, 1860, so we are solving for is.

[tex]\frac{x}{1860} = \frac{45}{100}[/tex]  where x = is.

To solve this, we cross multiply:

1860(45) = 100x

83,700 = 100x

837 = x

Now we know that 837 students bike or walk, and 372 drive.

We can calculate how many students travel by bus by subtracting these numbers from the total number of students, 1860.

1860 - 837 - 372 = 651

Therefore, 651 students travel to school by bus.

Answer:

31.08 billion

Step-by-step explanation:

If the shoe sales for a certain company were 25.9 billion, and the sales are projected to increase by 20%, we can calculate the projected amount by adding the increase to the original sales:

Projected sales = Original sales + (Increase percentage × Original sales)

Plugging in the values we have:

Projected sales = 25.9 billion + (0.20 × 25.9 billion)

Projected sales = 25.9 billion + 5.18 billion

Projected sales = 31.08 billion

Therefore, the projected amount of shoe sales for the company is 31.08 billion.

In regression analysis, the variable being explained or predicted is called option (b) dependent variable.

The dependent variables are defined the variable the depends up on other variables. The independent variable(s) are the variables that are believed to have an influence on the dependent variable and are used to explain or predict the variation in the dependent variable.

The regression variable(s) refer to the variables that are included in the regression model as predictors, whether they are independent or dependent. The residual variable refers to the difference between the observed values of the dependent variable and the predicted values from the regression model.

Therefore, the correct option is (b) dependent variable

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The required answer for the expression -2/(1 + √3i) is Arg (z) = 2π/3. The required answer for the expression (√3 - i)⁶ is Arg (z) = π.

The principal argument is the angle created by the line joining the origin, z, and the positive real axis. A complex number with the expression z = x + i y has the argument form  [tex]\text{Arg}(z)=\tan^{-1}\frac{y}{x}[/tex] when x > 0.

a) Given z=2/(1 + √3i). First, simplify the given expression,

[tex]\begin{aligned}\frac{-2}{1+i\sqrt{3}}&=\frac{-2}{1+i\sqrt{3}}\times\frac{1-i\sqrt{3}}{1-i\sqrt{3}}\\&=\frac{-2(1-i\sqrt{3})}{1^2-(i\sqrt{3})^2}\\&=\frac{-2-2\sqrt{3}i}{4}\\&=\frac{-1}{2}-\frac{\sqrt{3}}{2}i\end{aligned}[/tex]

Now find, the arg of the above expression. Here, x is -1/2 and y is√3/2. We get,

[tex]\begin{aligned}\mathrm{Arg}(z)&=\tan^{-1}\frac{y}{x}\\&=\frac{\frac{\sqrt{3}}{2}}{\frac{-1}{2}}\\&=\tan^{-1}(-\sqrt{3})\\&=\frac{2\pi}{3}\end{aligned}[/tex]

The required answer is Arg (z) = 2π/3.

b) Given (√3 - i)⁶. We know that,

[tex]\begin{aligned}\sqrt{3}-i&=2\left(\frac{\sqrt{3}}{2}-\frac{1}{2}i\right)\\ &=2\times e^{\left(-\frac{\pi}{6}i\right)\end{aligned}[/tex]

Then,

[tex]\begin{aligned}(\sqrt {3} -i)^6&=2^6\times e^{-\pi i}\\&=-2^6\end{aligned}[/tex]

Here, x is -64 and y is 0. Then, tan⁻¹ (0) = 0 = π.

The required answer is Arg (z) = π.

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Answer:

The correct answer is B. 200 and 100. When y is inversely proportional to x, it means that the ratio of x to y remains constant. In this case, when x = 20, y = 400, which means that the ratio of x to y is 20/400. Since the ratio is constant, we can use that ratio to find the values of y when x = 40 and x = 80. When x = 40, y = (20/400) x 40 = 200 and when x = 80, y = (20/400) x 80 = 100.

The figure represents the four angles of a quadrilateral.

Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.

The angles are labeled t, q, r and s. The measure of angle t and q is 93 degrees, while the measure of angle r and s is 87 degrees. This means that the quadrilateral is a parallelogram since opposite angles of a parallelogram are equal. The measure of each of the remaining angles is 180 degrees minus the measure of the known angles, which means that angle t and q are 87 degrees and angle r and s are 93 degrees. The sum of the angles of a parallelogram is 360 degrees, which further confirms that the figure is a parallelogram.

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The slope of the line passing through the points (3,4) and (-4,-5) is 9/7.

The slope of a line passing through two points can be found using the slope formula, which calculates the change in the y-coordinate divided by the change in the x-coordinate between the two points. To find the slope of the line passing through (3,4) and (-4,-5), we plug the coordinates into the slope formula and simplify. The slope formula gives the rate at which the line rises or falls relative to its horizontal movement. A positive slope means that the line is rising from left to right, while a negative slope means that the line is falling from left to right. In this case, the slope is positive, indicating that the line rises from left to right.

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Answer:

100[tex]\pi[/tex]

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex]

The diameter is 20,.  The radius is 1/2 of the diameter.

A = [tex]\pi 10^{2}[/tex]

A = [tex]\pi 100[/tex]

Answer:

Step-by-step explanation: That is actually the hidden number that is on the other side of the circle so it says how or what numbers is on the hidden circle so good luck finding the number

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5

A fraction is a mathematical concept that represents a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator over a denominator, separated by a horizontal line, such as 1/2, 3/4, or 7/8.

Given that the volume of cylinder = πr^2h

Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively.

Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:

Volume of Cleopatra's clock = [tex]\pi r^2_ch_c[/tex]

Volume of Ptolemy's clock = [tex]\pi r^2_ph_p[/tex]

Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock.

We are given that after 2 hours of draining, both clocks have the same water height.

Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:

(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)

hc/hp = [tex](r_p/r_c)^2 * (5/4)[/tex]

After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:

[tex]r^2_ch_c/2 = r^2_ph_p[/tex]

Now, we can solve for the ratio of water heights after each clock has been draining for three hours:

Water height in Cleopatra's clock after 3 hours = [tex]h_c - (3/4)h_c = (1/4)h_c[/tex]

Water height in Ptolemy's clock after 3 hours = [tex]h_p - (3/5)h_p = (2/5)h_p[/tex]

hp= 1/10

Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:

hp/hc = 1/10/(1/4) = 2/5

And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:

hc/(2/5)hp = (1/4)/(2/5)(1/10)

= 5/4.

Hence,

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5

The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.

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Answer:

f(x) = (x + 3)(x - 4) / (x + 3)

Step-by-step explanation:

In order for a rational function to have a hole at x = 4 and a vertical asymptote at x = -3, the denominator must be equal to zero at x = 4 and the numerator must be equal to zero at x = -3. This can be accomplished with the following expression:

f(x) = (x + 3)(x - 4) / (x + 3)

Answer:

$0.07

Step-by-step explanation:

We know

It cost Nevaeh $5.39 to send 77 text messages.

How much does it cost to send one text?

We take

5.39 / 77 = $0.07 per text

So, it costs $0.07 to send one text.

It costs Nevaeh $0.07 to send one text message.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

To find out how much it costs to send one text message, we can divide the total cost by the number of messages:

Cost per message = total cost/number of messages

In this case, the total cost is $5.39 and the number of messages is 77, so:

Cost per message = $5.39 / 77 = $0.07

Therefore, it costs Nevaeh $0.07 to send one text message.

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Answer: The estimated probability of generating a 3 using the random number generator is 1/3, since there are 3 possible outcomes and each is equally likely.

The actual probability of generating a 3 is also 1/3, since the generator is equally likely to generate any of the 3 possible integers.

Therefore, the difference between the estimated and actual probability of generating a 3 is:

1/3 - 1/3 = 0

So there is no difference between the estimated and actual probability of generating a 3.

Step-by-step explanation:

Thus, only 6.25 grammes of the initial 200 grammes of Co-60 will be present after 26.3 years.

Any time energy is moved, radiation is created. A substance does not need to be radioactive in order to emit radioactivity. Radiation is not always released by element compounds. Alpha particles, light, and heat are all instances of radiation.

To solve this problem, we can use the exponential decay formula:

N = N0 * (1/2)^(t/T)

where:

N is the amount of Co-60 remaining after a time t

N0 is the initial amount of Co-60

t is the time elapsed since the initial measurement

T is the half-life of Co-60

We are given N0 = 200 g, T = 5.26 years, and t = 26.3 years. We can plug in these values to get:

N = 200 * (1/2)^(26.3/5.26)

Simplifying the exponent, we get:

N = 200 * (1/2)⁵

Evaluating the exponent, we get:

N = 200 * 1/32

N = 6.25

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The correct question is:

the half-life of colbalt-60 (used in radiation therapy) is 5.26 years (actual data). How much a of 200 g sample of colbalt-60 will remain after 26.3 years?

Answer:

Step-by-step explanation:

40 desks

2) The probability that in a cricket match, a batswoman did not hit a boundary, when she hits it 6 times out of 30 balls played, is 80%.

3) The probability of a family having:

i) 2 girls = 31.67%

ii) 1 girl = 54.27%

iii) No girl = 14.06%

iv) The sum of the probabilities = 1 or 100%

The probability refers to the likelihood that an expected event or outcome occurs when there are many possible outcomes.

We compute probability as the quotient of the the expected success and the total number of successes.

Probability lies between zero and one and is usually expressed as a decimal, fraction, or percentage.

The number of boundary hits = 6

The total number of balls the batswoman played = 30

The probability that the batswoman did not hit a boundary = 1 - 6/30

= 0.8 or 80%.

The chance that the batswoman hit a boundary = 6/30 = 0.2 or 20%.

The total number of families with 2 children = 1,500

The number of families with 2 girls = 475

The number of families with 1 girl = 814

The number of families with 0 girl = 211

The probability of a family having:

i) 2 girls = 475/1,500 = 0.3167 or 31.67%

ii) 1 girl = 814/1,500 = 0.5427 or 54.27%

iii) No girl = 211/1,500 = 0.1406 = 14.06%

iv) The sum of the probabilities = 1 or 100%

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