Cesium-137 has a half-life of approximately 30 years. How much of a 40 g sample would be left after 90 years?

Of all the given options option 2) 2x-3y+7=0  is a linear equation in two variables.

A linear equation in two variables is an equation of the form ax + by = c, where a, b, and c are constants, and x and y are variables. These equations represent a straight line in a two-dimensional coordinate system, and the slope-intercept form of the equation is y = mx + b, where m = -a/b is the slope of the line, and b = -c/b is the y-intercept.

1. (x-1)(y+2)=0: This equation is not a linear equation in two variables as it is a product of two linear equations in one variable, therefore this is not a linear equation in two variables.

2. 2x-3y+7=0: This equation is a linear equation in two variables. The equation is in the form of ax + by + c = 0 where a, b, and c are constants and x and y are variables. This equation is a straight line in a 2D coordinate system and the slope and y-intercept can be calculated using a and b.

7x-3y+2z=0: This equation is not a linear equation in two variables as it has three variables (x, y and z) and it is not possible to graph this equation in a 2D coordinate system as it has three variables.

(y+x)^2-2=0: This equation is not a linear equation in two variables because it is a square of a linear equation. The equation is in the form of (y+x)^2 and we know that any equation in the form of (y+x)^n where n>1 is not a linear equation.

So the correct answer is option 2) 2x-3y+7=0.

Therefore, Of all the given options option 2) 2x-3y+7=0  is a linear equation in two variables.

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A. (6,1) and D. (5,1) are the solutions that satisfy the linear inequality 2x - 3y < 6.

A. 2(6) - 3(1) = 12 - 3 = 9 < 6

D. 2(5) - 3(1) = 10 - 3 = 7 < 6

The given linear inequality 2x - 3y < 6 can be solved by first isolating the variable y on one side of the inequality. This can be done by adding 3y to both sides of the inequality, resulting in 2x < 6 + 3y. Then, divide both sides of the inequality by 2, resulting in x < 3 + 1.5y. This is the equation of a line in the x-y plane, which has a slope of -1/2 and a y-intercept of 3. To find the solutions that satisfy the inequality, the coordinates of points that are located below the line must be found.

The coordinates of point (6,1) can be plugged into the equation of the line, resulting in 6 < 3 + 1.5(1), which is true, so (6,1) satisfies the inequality. The coordinates of point (5,1) can be plugged into the equation of the line, resulting in 5 < 3 + 1.5(1), which is also true, so (5,1) satisfies the inequality. The coordinates of point (2,-7) can be plugged into the equation of the line, resulting in 2 < 3 + 1.5

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The number of downloads that make site A the better deal is 31 downloads

An equation shows the relationship between numbers and variables in an expression.

Let y represent the total cost of download for x downloads.

For site A, there is a flat rate of $29 per month plus $0.80 per download, hence:

y = 0.8x + 29

For site B, there is a flat rate of $17 per month plus $1.19 per download, hence:

y = 1.19x + 17

For site A to be better then the total cost should be lower:

0.8x + 29 < 1.19x + 17

-0.39x < -12

x > 30.8

It would take 31 downloads for site A to be the better deal

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Answer:

y = -24

Step-by-step explanation:

Solve for y:

y/8 + 38 = 35

Put each term in y/8 + 38 over the common denominator 8: y/8 + 38 = y/8 + 304/8:

(y/8 + 304/8) = 35

y/8 + 304/8 = (y + 304)/8:

((y + 304)/8) = 35

Multiply both sides of (y + 304)/8 = 35 by 8:

(8 (y + 304))/8 = 8×35

(8 (y + 304))/8 = 8/8×(y + 304) = y + 304:

y + 304 = 8×35

8×35 = 280:

y + 304 = 280

Subtract 304 from both sides:

y + (304 - 304) = 280 - 304

304 - 304 = 0:

y = 280 - 304

280 - 304 = -24:

Answer: y = -24

The ratio of the midpoint of any given line segment is equal to 1 : 1.

As given in the question,

Therefore, the ratio of the midpoint for any given line segment is always equal to 1 : 1.

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the girl will be scoring a total of 30 goals.

What is number line?

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

Given, the goal scored

3 times 2

4 times 1

and 5 times 4.

So the total goal scored will be 3*2=6

4*1=4

and 5*4=20

Score = 6+4+20=30

Hence the girl will be scoring a total of 30 goals.

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The mathematical relationship between force and work is that Work = Force x Distance.

The mathematical relationship between force and work is that Work is equal to the Force multiplied by the Distance. In other words, the work done by a force is equal to the force multiplied by the distance over which the force is applied. This can be expressed as the equation W = F x D, where W is the work, F is the force and D is the distance. This equation means that the amount of work done is proportional to the force applied and the distance over which it is applied. Thus, if the force is doubled, the work done will also double, and if the distance is doubled, the work done will also double. This equation can also be used to calculate the force required to do a certain amount of work. For example, if it is known that a certain amount of work must be done, then the equation can be rearranged to calculate the force needed to do that work.

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The answer is x = 2, y = -1.

The solution by the method of elimination goes as follows:

3x + 10y = -4        ...(i)

2x + 2y = 2          ...(ii)

Multiplying eq.(ii) by 5, we get

10x + 10y = 10      ...(iii)

Subtracting eq.(iii) from eq(i), we get

-7x = -14

x = -14/-7 = 2

Thus, x=2

Putting the value of x in eq.(ii), we get

2×2 + 2y = 2

2y = 2-4

2y = -2

y = -1

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Answer:b,c

Step-by-step explanation:i got it correct

James was able to save $15 by dividing $30 by 2. James and money equal 3/4 (money with sister) x/2 + 30 = 3/4 (x + 30) in the equation.

The statistic is said to be in its simplest form when cut into its smallest equivalent fraction. What to do to find the most basic form. Look for common factors in the denominator. Examine a fractional integer to verify if it qualifies as a real number. A statement having two equal sides and an equal sign in the middle is called an equation in algebra. The general form of almost any equation contains the quantities of all the variables in descending order. The conventional form of an equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditioned equations. An identity holds true regardless of the value given to the variables.

given

Sister's money saved should equal x.

James has saved only half as much money as his sister.

James saved x/2 in money.

They both saved a total of x + x/2 dollars.

If they each save thirty more

Then

sisters' money = x + 30

cash with James = x/2 + 30

Given that James will have saved half as much as her sister if they both save 30 more

thus,

James and money equals 3/4 (money with sister)

x/2 + 30 =3/4( x + 30 )

=> 4(x+30*2) /2 = 3x+90

=> 2x + 120 = 3x + 90

=> 3x-2x = 120-90

=> x = 30

James was able to save $15 by dividing $30 by 2. James and money equal 3/4 (money with sister) x/2 + 30 = 3/4 (x + 30) in the equation.

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The missing term is "zero" for the given equation.

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles. There are two types of supplementary angles.

As per the given figure, the required solution would be as:

8x - 3 + 4x + 3 = 180

Rearrange the likewise terms and apply the arithmetics operation,

12x + 0 = 180

We know that the sum of 3 and -3 is 0.

Compared to the given equation, we get the missing term as zero.

Thus, the required value is 0.

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Answer: hypotenuse-leg

Step-by-step explanation:

assuming you posted it on a math website

A 95% confidence interval for the mean is (3193, 2607).

Confidence interval in simple words is the range of values that the specific parameter lies within.

Confidence interval for mean is found by the formula,

CI = Х ± t [tex]\frac{s}{\sqrt{n} }[/tex]

where X is sample mean, s is the standard deviation and n is the sample size.

Sample mean = 2900

s = 1300

n = 55

Degree of freedom = n - 1 = 54

t value of degree of freedom 54 with the probability of exceeding the critical value as 1 - 95% = 5% = 0.05 is 1.674.

CI = 2900 ± (1.674)[tex]\frac{1300}{\sqrt{55} }[/tex]

   = 2900 ± 293.44

   = (3193.44, 2606.56)

   = (3193, 2607)

Hence the confidence interval is (3193, 2607).

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The value 120 in the linear function represents the y - intercept

In this problem, the 120 in the equation y = 120 - 15x represents the initial amount of money that Ahmed starts with from his summer job.

It is the y-intercept of the linear equation, which means that when x = 0, y = 120. This means that if Ahmed does not subscribe to the PlayStation Plus Extra subscription for any months, he will have $120 left from his summer job.

It can be interpreted as the starting point or the base point of Ahmed's savings.

It's important to note that the y-intercept of a linear function is the point where the function crosses the y-axis, it gives the value of the dependent variable (y) when the independent variable (x) is equal to zero.

It also indicates that the amount of money Ahmed has is decreasing by 15 dollars per month of subscription, since the coefficient of x is -15.

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Therefore , the solution of the given problem of inequality comes out to be  Rosa's age is 17 .5 and her fathers age is 52.5 years.

In mathematics, an inequality is a relationship of linear solution or integers without the equal sign. Inequity inevitably leads to imbalance. When two numbers are not equal, there is an inequality between them. Between equality and inequality, there are differences. In instances when the variables aren't similar or equal, I've used the most common symbol (). There are many inequalities that may be utilised to compare values regardless of how small or huge they are.

Here,

Given :

Let Rosa age = x

Rosa's father age =  3x

and

=> 3x -x < 35

=> 2x < 35

=> x <35/2

=> x < 17.5

Thus , Rosa's age is 17 .5 and her fathers age is 3*17.5 = 52.5 years

Therefore , the solution of the given problem of inequality comes out to be  Rosa's age is 17 .5 and her fathers age is 52.5 years.

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The function x3 + 4x²-3x - 12 in factored form knowing that one of the roots is -4 [tex]$$(x-4)\left(x^2+3\right)$$[/tex]

Group the first two terms and the last two terms.

[tex]$$\left(x^3-4 x^2\right)+3 x-12$$[/tex]

Factor out the greatest common factor (GCF) from each group.

[tex]$$x^2(x-4)+3(x-4)$$[/tex]

Factor the polynomial by factoring out the greatest common factor, x-4.

[tex]$$(x-4)\left(x^2+3\right)$$[/tex]

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Answer:

Step-by-step explanation:

blb

The price per pound that was paid for the apples is $0.85 per pound

An equation shows the relationship between numbers and variables in an expression.

Unit rate is the ratio of two quantities. The denominator of a unit rate is always equal to one.

The apples are 3.4 lbs and their total price is $2.89. hence:

The price per pound is gotten by dividing the total price of apples by the weight of the apple

Price per pound = $2.89 / 3.4 lbs = $0.85 per pound

The price per pound is $0.85 per pound

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Answer:

13

Step-by-step explanation:

a) The required equation is h(t)=10−8×sin⁡(2×π×t/12). b) The sandbar at the latest at 7:00 pm. c) Captain Highliner will be able to return to the harbour at the earliest at 7:00 am.

a) The depth of water over the sandbar can be expressed as a function of time, t, in hours, using the following equation:

h(t)=10−8×sin⁡(2×π×t/12)

This equation describes a sinusoidal function with a period of 12 hours, a maximum value of 10 metres (at high tide) and a minimum value of 2 metres (at low tide).

b) To find the latest time of day that Captain Highliner will be able to get his trawler over the sandbar, we need to find the time when the depth of water is at least 4 metres.

We can do this by setting h(t) equal to 4 and solving for t:

4=10−8×sin⁡(2×π×t/12)

6=8×sin⁡(2×π×t/12)

3/4=sin⁡(2×π×t/12)

The value of sin⁡(2×π×t/12) is positive between 0 and 6 hours, and negative between 6 and 12 hours. Therefore, the only solution to this equation is t=3/4×12=9 hours.

This means that Captain Highliner will be able to get his trawler over the sandbar at the latest at 10:00 am + 9 hours = 7:00 pm.

c) To find the earliest time of day that Captain Highliner will be able to return, we need to find the time when the depth of water is at least 4 metres.

We can use the same equation as before:

4=10−8×sin⁡(2×π×t/12)

6=8×sin⁡(2×π×t/12)

34=sin⁡(2×π×t/12)

The value of sin⁡(2×π×t/12) is positive between 0 and 6 hours, and negative between 6 and 12 hours.

Therefore, the only solution to this equation is t=3/4×12=9 hours.

This means that Captain Highliner will be able to return to the harbour at the earliest at 10:00 am + 9 hours + 12 hours (to complete one full tidal cycle) = 10:00 pm + 9 hours = 7:00 am the next day.

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Answer:

a1 = 3

a2 = 3 + 2 = 5

a3 = 5 + 2 = 7

a4 = 7 + 2 = 9

The value of f is 0.6.

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant.

A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.

Given that,

0.25(4f-3) = 0.05(10f - 9)

=> f - 0.75 = 0.5f -0.45

Rearranging the equation and combining like terms we get

f - 0.5f =  -0.45 + 0.75

=> 0.5f = 0.30

=> f = 0.30/0.5

=> f = 3/5

=> f= 0.6

Therefore, the value of f is 0.6.

Correct question: Simplify and solve the following linear equation: 0.25(4f-3) = 0.05(10f - 9)

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Answer:

Step-by-step explanation:

1/6 attended in the morning.

1/3 attended in the afternoon.

1/6 + 1/3

1/6 + 2/6 = 3/6

3/6, or 1/2 attended in the morning and afternoon combined.

a) If 1/2 attended in the morning and afternoon combined, then the other 1/2 attended in the evening.

b) 1/2 of 30 = 15, so 15 parents attended in the evening.

The quotient of (3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) is 3x^3 + 6x^2 + 8x + 24.

To find the quotient of (3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) we can use polynomial long division method.

First, divide 3x^4 by x and write down the quotient (3x^3)

Now, we multiply (x - 2) by 3x^3 and subtract it from 3x^4 - 4x^2 + 8x - 1

(3x^4 - 4x^2 + 8x - 1) - 3x^3(x - 2)

= 3x^4 - 4x^2 + 8x - 1 - 3x^4 + 6x^3

= 6x^3 - 4x^2 + 8x - 1

Now, we divide 6x^3 by x and write down the quotient (6x^2)

Now, we multiply (x - 2) by 6x^2 and subtract it from 6x^3 - 4x^2 + 8x - 1

(6x^3 - 4x^2 + 8x - 1) - 6x^2(x - 2)

= 6x^3 - 4x^2 + 8x - 1 - 6x^3 + 12x^2

= 8x^2 + 8x - 1

Now, we divide 8x^2 by x and write down the quotient (8x)

Now, we multiply (x - 2) by 8x and subtract it from 8x^2 + 8x - 1

(8x^2 + 8x - 1) - 8x(x - 2)

= 8x^2 + 8x - 1 - 8x^2 + 16x

= 24x - 1

Now, we divide 24x by (x - 2) and write down the quotient (24)

Remainder is

24x - 1 - 24(x - 2) = 47

Finally, we have found that the quotient of the polynomial division is 3x^3 + 6x^2 + 8x + 24 and the remainder is 47. So the final answer is

(3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) = (3x^3 + 6x^2 + 8x + 24)(x - 2) + 47

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Answer:

Probability of there being two heads would be 1/4.

Math:

1/2 * 1/2 = 1/4.

Hope this helps^^

A system of linear equations has infinite solutions when the graphs are the exact same line.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We know that;

Let the system of equations of two lines.

So, When the graphs are the exact same line, then a system of linear equations has infinite solutions.

Thus, A system of linear equations has infinite solutions when the graphs are the exact same line.

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The probability of the spinner is P(not yellow) = 37.5%.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

If the spinner is spun once, the probability of not landing on yellow (sections 2 and 3) is equal to the probability of landing on purple (sections 1 and 8), blue (sections 4, 5, and 6), or orange (section 7).

The total probability of these sections is 1- (2/8) = 1-(1/4) = 3/4.

So P(not yellow) = 3/4 = 37.5%.

Hence, the probability of the spinner is P(not yellow) = 37.5%.

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