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There is no general rule that says a system of linear equations cannot have exact solutions that are integers greater than 1. The existence of such solutions depends on the specific coefficients and constraints of the system

It is not true that a system of linear equations cannot have exact solutions that are integers greater than 1. In fact, there are many systems of linear equations that have such solutions.

However, there are certain types of systems of linear equations that do not have integer solutions, or may not have any solutions at all. For example, if the coefficients of the variables in the equations are irrational numbers, then it is possible that the system has no integer solutions.

Furthermore, some systems of linear equations may have solutions that are not integers, but are instead fractions or irrational numbers. This is because the solutions to a system of linear equations are determined by the intersection points of the lines or planes that represent the equations, and these intersection points may not always fall on integer coordinates.

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To calculate the deposit, we need to add up the amounts of the two checks and the cash: $90.50 + $90.50 + $45.00 + $150.00 = $376.00. Therefore, the deposit is $376.00.

The problem asks us to calculate the deposit amount for two checks of $90.50 each, and cash of $45.00 and $150.00. To solve the problem, we simply add up the amounts of the checks and cash to find the total deposit amount. Adding $90.50 and $90.50 gives us $181.00, and adding this to the cash amounts of $45.00 and $150.00 gives us a total of $376.00. Therefore, the deposit amount is $376.00. This is the total amount of money that will be added to the account when the checks and cash are deposited.

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If A sheet of paper is 0.00005 meter thick, the thickness of a sheet of paper in nanometers is 50,000 nanometers. Option A is correct answer.

To convert the thickness of a sheet of paper from meters to nanometers, we need to multiply by the conversion factor of 1 meter / 1 x 10^-9 nanometers.

First, we need to convert the thickness of the paper from meters to nanometers. We can do this by multiplying the thickness in meters by the conversion factor:

0.00005 meter x (1 x 10^-9 nanometers / 1 meter) = 50 nanometers

It's important to understand the concept of scientific notation when dealing with extremely large or small numbers. In this case, we use scientific notation to express the size of a nanometer, which is a billionth of a meter. By expressing the conversion factor in scientific notation, we can easily move the decimal point to convert between units.

Therefore , the correct option is A.

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Complete question is:

A sheet of paper is 0.00005 meter thick. One nanometer is 1 x 10-meter. How thick is a sheet of paper in nanometers?

A. 50,000

B. 500,000

C. 50,000,000,000,000

D. 500,000,000,000,000

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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The required length for line segment K'N' is 9 units. So correct option is C.

A trapezoid is a two-dimensional geometric shape that is defined as a quadrilateral with one pair of parallel sides. It is also known as a trapezium in some countries. The other two sides of a trapezoid are typically non-parallel and can be of different lengths.

Trapezoids can be classified into two types: isosceles trapezoids and non-isosceles trapezoids. Isosceles trapezoids have equal lengths of the non-parallel sides, while non-isosceles trapezoids have unequal lengths.

The area of a trapezoid can be calculated using the formula: (base1 + base2) x height / 2, where base1 and base2 are the lengths of the parallel sides, and height is the perpendicular distance between the parallel sides.

The perimeter of a trapezoid can be calculated by adding the lengths of all four sides together. If the trapezoid is isosceles, the perimeter can be calculated using the formula: 2 x (side length) + (sum of the lengths of the parallel sides).

Trapezoids can also be used to solve problems in real-world situations, such as calculating the area of a trapezoidal roof or finding the distance between two parallel lines. They are also commonly used in geometry problems and proofs.

In summary, a trapezoid is a quadrilateral with one pair of parallel sides. It can be classified as isosceles or non-isosceles and can be used to calculate area and perimeter, as well as solve problems in geometry and real-world situations.

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The area of the segment is 28.92 unit square

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

Angle, θ = 50 degrees

Radius, r = 15 units

Using the above as a guide, we have the following:

Area of a segment =  (½) × r² × [(π/180)(θ – sin(θ)]

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

Area of a segment =  (½) × 15² × [(π/180)(15 – sin(15 degrees)]

Evaluate

Area of a segment =  28.92

Hence, the area is 28.92

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Yes we can say that 10 mm is a conversion factor because it is equals to 1 cm and that is what conversion factor is.

A millimetre is a unit of measurement smaller than a metre. Because of something called conversion factors, I know that a mm is smaller than a m.

Simply said, a conversion factor is a number that may be multiplied or divided to convert one set of units to another. Hence, when we need to translate 10 millimetres to centimetres, we utilise a conversion factor.

The mm to m conversion factor is:

10 mm = 1 cm

We can simply compute the conversion of 10 mm to m now that we know the conversion factor by multiplying 0.001 by the amount of millimetres we have, which is 10.

10 x 0.1 = 1 cm

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The minimum number of x intercepts is 1.

( Table attached)

What is the x-intercept?

The intersection of a function or equation's graph with the x axis is known as the x intercept. This can be compared to a point having a value of 0.

For any given curve, the x-intercept is a coordinate that is plotted on the x-axis. To put it another way, the x-intercept is the value of the x coordinate at the point where the graph crosses the x-axis, or we can say that it is the value of the x coordinate at a point where the value of the y coordinate equals zero.

The minimum number of x intercepts is 1.

With a positive leading coefficient an odd degree polynomial will start negative and end positive. With a negative leading coefficient an odd degree polynomial will start positive and end negative.

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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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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.

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 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:

X Y

2 2

4 12

6 30

8 56

The time 10 pm can be expressed in military time as 2200 hours .

In military time, the hours of the day are expressed in a 24-hour format,

The time starts from 0000 (midnight) hours and goes up to 2359 (11:59 PM) hours.

To convert a time from the standard 12-hour clock to military time, we add 12 hours to any time in the afternoon or evening .

In this case , to convert 10 PM to military time, we add 12 hours to the time ;

⇒ 10 PM + 12 hours = 22:00 hours or 2200 hours ;

Therefore, 10 PM in military time is 2200 hours.

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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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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 solution to the system of linear equation by substitution method is as follows :  x = 1 and y = -3

6x − 9 = y

y = −3x

let's substitute the value of y in the first equation as follows;

6x - 9 = -3x

add -3x to both sides of the equation

6x + 3x - 9 = -3x + 3x

9x - 9 = 0

add 9 to both sides of the equation

9x - 9 + 9 = 0 + 9

9x = 9

divide both sides by 9

x = 9 / 9

x = 1

let's find y by substituting the value of x in the second equation

y = -3x

y = -3(1)

y = -3

Therefore, x = 1 and y = -3

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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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Answer:c

Step-by-step explanation:

Answer:

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

Answer:

Option 3: about 14 inches

Step-by-step explanation:

The notebook paper is in the form of a rectangle of length

[tex]l = 11[/tex] inches and width [tex]w = 8.5[/tex]  inches

The diagonal of such a rectangle is given by the Pythagorean formula
[tex]d = \sqrt{l^{2} + w^{2}}[/tex]

Substituting the values of [tex]l[/tex] and [tex]w[/tex]:

[tex]d = \sqrt{11^{2} + 8.5^{2}}\\\\d = \sqrt{121 + 72.25}\\\\d = \sqrt{193.25}\\\\d= 13.9014\;inches[/tex]

This corresponds to Option 3: about 14 inches

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?

54 centimetres, rounded to two decimal places, is comparable to around 21.26 inches.

The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.

It is the unit of length.

Furthermore, length is measured in centimetres,

Used in the International System of Units,

This is the metric system's present configuration.

There are 21.26 inches in 54 cm (centimeters).

To convert centimeters to inches,

You can use the following conversion:

1 inch = 2.54 cm

Therefore,

To convert 54 cm to inches,

You can divide 54 by 2.54:

54 cm / 2.54 = 21.26 inches

So 54 cm is equivalent to approximately 21.26 inches,

Rounded to two decimal places.

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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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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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The number 1.07  × 10⁸ in standard form is 107,000,000.

To write 1.07 × 10⁸ in standard form, we need to move the decimal point to the left or right such that there is only one non-zero digit to the left of the decimal point.

In this case, we have 1.07 × 10⁸, which means we have a value of 1.07 times 10 raised to the power of 8. To convert this to standard form, we need to move the decimal point 8 places to the right since 10 is being raised to the power of 8.

1.07 × 10⁸ = 107,000,000

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Answer:

Step-by-step explanation:

40 desks

Answer:

0.80*c = 20

Step-by-step explanation:

"80% of c is 20" can be written as:

  0.80*c = 20

80% of c is 0.80*c

"is" can be written as "="

Put these two together to obtain:

  0.80*c = 20

The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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