Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

The half-life of bismuth-210 is given as follows:

5 days.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which the parameters are given as follows:

For this problem, we have that:

Hence the decay rate is obtained as follows:

[tex]6.64 = 122(1 - r)^{21}[/tex]

[tex](1 - r)^{21} = \frac{6.64}{122}[/tex]

[tex]((1 - r)^{21})^{\frac{1}{21}} = \left(\frac{6.64}{122}\right)^{\frac{1}{21}}[/tex]

1 - r = 0.8706

r = 1 - 0.8706

r = 0.1294.

Hence the function is given as follows:

y = a(0.8706)^t.

The half-life is the value of t for which:

y = 0.5a.

Hence:

0.5a = (0.8706)^t.

(0.8706)^t = 0.5

log((0.8706)^t) = log(0.5)

tlog(0.8706) = log(0.5)

t = log(0.5)/log(0.8706)

t = 5 days.

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w = 0  and z= -2  are the value in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

3w-4z= 8

2w+3z=-6

multiply both sides of the equation of a

  6w - 8z = 16

    3(2w +3z ) = - 6 * 3

calculate the quotient

         6w - 8z = 16

        3(2w +3z ) = - 6 * 3

    6w - 8z = 16

    6z + 3z = -18

substract the two equation

                  6w - 8z - (  6z + 3z) = 16 - (-18)

                            -17z = 34

                               z = -34/17

                                 z = - 2

put the value of z in equation

           6w - 8 * -2  = 16

          6w + 16  = 16

               6w = 0

                 w = 0

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Using the concept of rates and ratio, it will take approximately 0.12 days to finish 4 bananas

When comparing two or more similar amounts or numbers using the same units, a ratio is utilized. In spoken language, we state the ratio of one quantity "to" the second quantity, and it is frequently written with a colon. For instance, a class has a 3:4 (or 3:4) ratio of boys to girls. When comparing two quantities, for example, some issues may only give you two numbers, but other problems might have more than two. For example, the proportions of the various ingredients used in a recipe.

We can use the concept of ratio or proportions to determine the number of days they will consume 4 banana

4 days = 13 banana

1 day = x banana

Cross multiply both sides and solve for x

x * 4 = 13 * 1

4x = 13

x = 13 / 4

x = 3.25

Now, we can find the number of days it will take to consume 4 banana

1 day = 3.25 banana

x days = 4 banana

Cross multiply both sides and solve for x

4 * 1 = 3.25x

x = 4 / 3.25

x = 0.12 days

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A circle has a circumference of 91.688 millimeters. The above statement indicates that the circle's radius is 14.6 millimeters.

The radius of a circle or other curvy geometric object pertains to its length. It is the boundaries across another two-dimensional circular surface measured linearly in one dimension. The length of something like a circle's contour is referred to as its circumference, while the length of a form with straight sides is referred to as its perimeter.

Circumference of a circle = 91.688 millimeters

π = 3.14

Radius = ?

Therefore, cicumference of a circle = 2 * π * r

91.688 = 2 * 3.14 * r

r = 91.688/6.28

r = 14.6 millimeters.

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Therefore , the solution of  the given problem of percentage comes out to be percentage of b is 4301%.

In mathematics, a percentage is a number of ratio that is stated as a portion of 100. Also occasionally used are the abbreviations "pct.," "pct," with "pc." To denote it, though, the percent symbol "%" is frequently employed. The % amount has no dimensions. Because percentages contain a numerator of 100, they are effectively fractions. A number should be followed by the % sign (%) to show that it represents a percentage. For instance, someone would receive a 75% grade if you properly solved 75 out of 100 questions on a test. To determine percentages, divide the amount of money by the total, and then multiply the result by 100. The percentage is calculated by multiplying the ratio (value/total) by 100%.

Here,

a =2001/100 * (b+c)

and

b= 87/100*c

thus putting value of b in a

=>a = 2001/100*(87/100*c + c)

=> a= 2001/100 * 187/87 * b

=>a/b = 374187 / 8700 * 100 = 4301%

and

Now percentage of b is 4301%.

Therefore , the solution of  the given problem of percentage comes out to be percentage of b is 4301%.

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The graph of the exponential function y = 200(1 + 0.05)ˣ starts with a curve and increases non-linearly or exponentially at any given time

Mathematical functions that rise or decrease in value at a rate proportional to their existing value are known as exponential functions. An exponential growth or decay function is another name for it. An exponential function is represented by the equation y = bx, where b denotes the base and x the exponent.

In this problem, we can use the basic form of an exponential function to represent this.

y = p(1 + r)ˣ

Substituting the values into the formula above;

y = 200(1 + 0.05)ˣ

The equation above is an exponential function that represents the growth over a period of time "x"

The graph of an exponential function curves from it's starting point and increases non-linearly steadily till it reaches it's peak.

Kindly find attached graph below

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The midpoint theorem is used in a variety of mathematical fields, but it is primarily used in geometry and algebra.

In geometry, the midpoint theorem is used to find the midpoint of a line segment, which is the point that is exactly halfway between the two endpoints of the segment. The theorem states that the coordinates of the midpoint of a line segment can be found by averaging the coordinates of the endpoints.

For example, if the endpoints of a line segment have coordinates (x1, y1) and (x2, y2), the coordinates of the midpoint would be ((x1 + x2)/2, (y1 + y2)/2).

In algebra, the midpoint theorem can be used to find the equation of a line when the coordinates of the endpoints of a line segment are known. The equation of a line can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.

The slope of the line can be found by taking the difference of the y-coordinates of the two endpoints divided by the difference of the x-coordinates of the two endpoints. The y-intercept of the line can be found by using the midpoint of the line segment and the slope of the line.

In Calculus, the midpoint theorem is used in optimization problems. Optimization problems are used to find the maximum or minimum value of a function.

The midpoint theorem is used to find the critical points of the function, which are the points where the function reaches its maximum or minimum value. The critical points are found by taking the derivative of the function and equating it to zero.

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Answer:

[tex]54,59,64,69[/tex]

Step-by-step explanation:

[tex]a_{n}=54+5(n-1)=54+5n-5=49+5n \\ \\ a_{1}=49+5(1)=54 \\ \\ a_2=49+5(2)=59 \\ \\ a_3=49+5(3)=64 \\ \\ a_3=49+5(4)=69[/tex]

The boundary line of the graph of an inequality in two variables is part of the solution when the line is a solid line

A mathematical statement stating the relationship in terms of greater than, larger than or equal to, less than, or less than or equal to between two numbers or algebraic expressions is known as an inequality.

Inequality representation using a solid line and a dotted line

Inequality plots that use the < or > symbols features a dashed line and  this shows the boundary lines are not a part of the solution.

An inequality marked with the symbol "or" such as greater than or equal to or less than or equal to is represented by a solid line boundary line and the region is included in the solution.

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The sorrect option: y - 4 = 5x - 10, is the equation of the line, in point-slope form.

The slope of the line;

Slope m = 5.

Passing points: (x1, y1) =  (-2, 4).

So, general equation of the line,

y - y1 = m(x - x1)

y - 4 = 5(x + 2)

y - 4 = 5x - 10

Thus, the equation of line, in point-slope form, that has a slope of 5 is found as : y - 4 = 5x - 10.

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The interest accumulation on the loan is equals to $526.50.

As a financial term, when an interest is added to the account balance, it is considered accrued. Interest accrues on loans such as a mortgage, savings accounts, student loans, and other investments.

In our calculation, we are using a simple interest because it is only an interest charge that borrowers pay lenders for a loan. It is calculated by using the principal only and does not include compounding interest.

Data

Loan = 4,050

Interest rate = 6.5%

Time = 2 years

To get our Interest, we will use the simple interest formula which is "S.I. = PRT/100". Where P is 4050, r = 6.5%, T= 2 years.

The interest accumulated is computed as follows:

= $4050 * 6.5% * 2 years

= $526.50

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This text describes a scenario where someone has taken out a loan of $4050. The loan has an interest rate of 6.5%, which means that the borrower will have to pay an additional 6.5% of the loan amount as interest. The loan is taken for a period of 2 years, which is the time frame during which the borrower has to repay the loan.

The question being asked is about the interest that will be accumulated on this loan. Interest accumulation refers to the increase in the amount of money that the borrower owes due to the interest that is being charged on the loan.

In this case, we need to calculate the total amount of interest that will be charged over the 2-year period, based on the loan amount and interest rate.

To calculate the interest accumulated on this loan, we can use the following formula:

Interest = Principal * Rate * Time

Where:

- Principal = the amount borrowed (in this case, $4050)

- Rate = the interest rate (in this case, 6.5% or 0.065 as a decimal)

- Time = the length of the loan in years (in this case, 2 years)

Plugging in the values, we get:

Interest = $4050 * 0.065 * 2

Interest = $527.25

So the interest accumulated on this loan is $527.25. This means that the borrower will have to pay back a total of $4577.25 ($4050 + $527.25) over the 2-year period.

Around 100 hours will take for both vats to contain the same amount of liquid.

How do you calculate the rate of evaporation of a liquid?

The equation indicates that the evaporation rate,

W = (95+0.425*V)*(Pw-Pa)/Y, where W is the evaporation rate, V is the air velocity at the water surface,  Pw is the saturation vapor pressure at water temperature.

To find out how many hours it will take for both vats to contain the same amount of liquid, we need to compare the rates at which the liquid is evaporating from each vat.

We can set up the following equation:

(35 - x) / 0.25 = (40 - x) / 0.35

where x is the amount of liquid in both vats at the time they reach the same level.

We can then solve for x by multiplying both sides by 0.25 and 0.35 and then subtracting one equation from the other:

35 - x = 40 - x

x = 5

So, both vats will contain 5 liters of liquid at the time they reach the same level.

To find out how many hours it will take to reach this point, we can use the rate of evaporation for either vat.

For Vat A:

35 - 5 = 30 liters

30 liters / 0.25 liters/hour = 120 hours

For Vat B:

40 - 5 = 35 liters

35 liters / 0.35 liters/hour = 100 hours

So, It will take around 100 hours for both vats to contain the same amount of liquid.

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The solution for f(-3) - 2 in the function when the function f(x) = 4 − (x + 3)⁵ is 2

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

f ( x ) = 4 − ( x + 3 )^5

To make the equation legible, we need to rewrite it

So, we have the following representation

f(x) = 4 − (x + 3)⁵

Also from the question, we have

f(-3) - 2

This means that the value of x is -3, and we calculate f(x) when x = -3

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

f(x) - 2 = 4 − (x + 3)⁵ - 2

So, we have the following equation

f(-3) - 2 = 4 − (-3 + 3)⁵ - 2

There are constants to add or subtract to both sides of the equation

However, there is no factor to multiply or divide from both sides of the equation

So, we have the following representation

f(-3) - 2 = 4 − (0)⁵ - 2

Solving further, we have

f(-3) - 2 = 4 - 2

Evaluate the difference

f(-3) - 2 = 2

Hence, the solution is 2

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Complete question

Given that f ( x ) = 4 − ( x + 3 )^5

Find f(-3) - 2

Hint: find f(-3) first and then subtract 2.

When one side and one angle of a right angled triangle are given as 19 and 35°, respectively, the value of b is calculated using trigonometric ratios as 13.03.

Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

given

one side = 19

angle = 35°

one angle = 90° as right angle triangle

another angle = 35°+ 90° + x = 180°

= 125° + x = 180°

x = 55°

[tex]\frac{a}{sinA} = \frac{b}{sinB}[/tex]

19 / sin55° = b / sin35°

b = 13.03

When one side and one angle of a right angled triangle are given as 19 and 35°, respectively, the value of b is calculated using trigonometric ratios as 13.03.

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So on solving the provided question, we can say that by equation Shayna : [tex];5x + 10y = $175[/tex] and Brenda : [tex]9x + 4y = $147[/tex]; cost =   [tex]$11/ft^2[/tex] of grass, $12/geranium

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation, that will be formed are

Shayna : [tex];5x + 10y = $175[/tex]

Brenda : [tex]9x + 4y = $147[/tex]

[tex]5x + 10y = $175 \\ 5x = $175 - 10y\\(5x/5) = ($175/5) - (10y/5) = > x = $35 - 2y\\9x + 4y = $147 = > 9($35 - 2y) + 4y = $147\\ $315 - 18y + 4y = $147\\$315 - $147 = 18y - 4y \\ $168 = 14y = > y = $12\\ 5x + 10y = $175 = > 5x + 10($12) = $175 = > 5x + $120 = $175 \\5x = $175 - $120 = > 5x = $55 = > x = $11[/tex]

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When a polynomial is to be divided by a linear expression and the leading coefficient (first number) must be a 1, synthetic division is used. Any polynomial equation, regardless of degree, can, for instance, be divided by x + 1, but not by x2+1.

Additionally, the binomial must be of degree 1; synthetic division cannot be used to divide by a binomial such as x2 + 1. Here are the steps for performing synthetic division on a polynomial by a binomial.

To get the quotient and the remainder, write down the coefficients and divide them by the linear factor's zero. Q(x) + (R/(x - a)) = (P(x)/(x - a)).

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She will make $ 10130 more per year as an accountant than a public relations expert by frequency .

Frequencies are arranged into visual displays known as frequency distributions in order to make the information more understandable. Absolute or relative frequencies, such as ratios or percentages, can be shown in a frequency distribution. A frequency distribution can be shown using a graph or a frequency table. In a frequency distribution, the precise number of observations and the percentage of observations falling inside each range may both be shown. The distribution in the latter case is known as a relative frequency distribution. An observation's frequency is the frequency with which it appears in the data. For example, the frequency of the number 9 in the following list of integers is 5. (because it occurs 5 times). 1,

given

$58,020 Public Relations Specialist

$68,150 for an accountant

How much more will she make working as an accountant compared to a public accountant? $68,150 - $58,020, or $ 10130.

She will make $ 10130 more per year as an accountant than a public relations expert.

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The dimensions of each side of the square will be 4 centimeters long.

To determine the smallest possible square that can be formed from the tiles without cutting or overlapping them, you will need to find the greatest common divisor (GCD) of the two dimensions of the tile (20 cm and 12 cm).

The GCD represents the largest size of a square that can be formed without cutting or overlapping the tiles.

The GCD of 20 and 12 can be found using the Euclidean algorithm:

Divide 20 by 12. The quotient is 1 and the remainder is 8.

Divide 12 by 8. The quotient is 1 and the remainder is 4.

Divide 8 by 4. The quotient is 2 and the remainder is 0.

Since 4 is the last non-zero remainder, it is the GCD of 20 and 12.

Thus, each side of the square will be 4cm long.

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Answer:

(n+5)(n-2)

Step-by-step explanation:

n^2+3n-10

(n+5)(n-2)

The value of m in the linear pair with an array is 101°, using supplementary rule.

Two lines converge at a single point to generate a pair of linear angles. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair always has an angle total of 180 degrees.

When two lines cross, they generate a linear pair, which is two nearby angles. The numbers 1 and 2 form a linear pair in the figure. The same goes for 2 and 3, 3 and 4, and 1 and 4. In a linear pair, the two angles are always supplementary, which implies that their sum total is 180 degrees.

 79° + m = 180°

          m = 180° - 79°

          m = 101°

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Complete question:

What is the value of m?

79° + m = 180°

Answer: Let one of the number be X and the other no will be x +18, this is as per given sum.

By sum,

Step-by-step explanation: x + x + 18 = 128

or, 2 x = 128 - 18 = 110

Therefore x = 55 & the other no will be 55 + 18 = 73

Hence, 55 & 73 are the two numbers.

The equation that represents the relationship between the number of fruit Tyler ate and Han ate is x = y + 34

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Also a linear equation can be defined as an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The number of fruits Tyler ate is represented by x

The number of fruits Han ate is represented by y

Han ate 34 less than tyler, this means that y = x-34

and also making x the subject,

x = y + 34

Therefore the equation that represents the relationship between the number of fruits Tyler ate and Han ate is x = y+34

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The value of r when y = 18 is 17.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given the equation which is linear having the exponent of the variable equals 1.

10r - 9y = 8

We have to find the value of r when value of y = 18.

Substituting y = 18 in the equation,

10r - (9 × 18) = 8

10r - 162 = 8

10r = 170

r = 170/10

r = 17

Hence when the value of y = 18, then the value of r = 17.

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27 logs Teresa can keep the fire going for 444 hours with 666 logs instead of having to maintain it for 181818 hours.

The unit technique is a strategy for addressing issues that entails first figuring out the price of a specific unit, then multiplication that value to figure out the needed value. Simply put, the unit method is employed to derive a single unit value from a multiple that is supplied. For example, 40 pens could cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, abstract algebra, mathematical analysis, or mathematical skills of matrices or operators.

given

6 logs in 4 hours

18hrs= ?x

then you multiply and cross.

so,18x6= 4x

4x/4=108/4

x=27 logs

27 logs Teresa can keep the fire going for 444 hours with 666 logs instead of having to maintain it for 181818 hours.

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840 cubes can be placed in the given cuboid.

Now, According to the question:

We know that,

Volume of cuboid = l × b × h

Volume of cuboid = 84cm × 60cm × 36cm

Volume of cuboid = 181,440[tex]cm^3[/tex]

Side of the cube = 6 cm

Volume of the cube = side³

= 6³

= 216 cm³

Required number of cubes = volume of cuboid / volume of the cube

= 181,440/216

= 840

Thus, 840 cubes can be placed in the given cuboid.

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The complete question is this:

A box measure 84cm by 60cm by 36cmthe box is completely filled with identical cube. How many small cubes with side 6 cm can be placed in the given cuboid?

The volume of the cube before it was melted is greater than 49cm^3

The amount of melted liquid left after making the cone is 49 cm^3.

A cone is a three-dimensional shape that has a circular base and a single vertex or point. The amount of liquid remaining after making a cone can be calculated by comparing the volume of the cone to the volume of the cube.

The volume of a cone can be calculated using the formula:

V = (1/3) * pi * r^2 * h

Where V is the volume of the cone, pi is a mathematical constant (approximately 3.14), r is the radius of the circular base, and h is the height of the cone.

However, we don't have information about the radius or height of the cone, we only know the volume of melted liquid left after making the cone is 49 cm^3.

We can use this information to determine the volume of the cube before it was melted and compare it with the volume of the cone.

The volume of a cube can be calculated using the formula:

V = s^3

Where V is the volume of the cube, s is the length of one side of the cube.

Let's call Vc the volume of the cube before it was melted and Vcon the volume of the cone

Vc - Vcon = 49 cm^3

Therefore, the volume of the cube before it was melted is greater than 49cm^3

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Answer: Your answer is x = 8  for c and m = -12 for b

Step-by-step explanation:

c.

-8x = -64

-8x - 8 these cancel out

-64 - 8

64/8 = 8

x = 8

b.

-8 + m = -20

m - 8 = -20

m - 8 + 8 = -20 + 8 (add the -20 + 8 because the 8's cancel out)

m = -12

The slope of the given equation [tex]y = -5x^5[/tex] is [tex]-25x^4[/tex].

To find the slope of the equation [tex]y = -5x^5[/tex], you need to take the derivative of the equation with respect to x. The slope of the equation represents the rate of change of y with respect to x, that is how y changes as x changes.

The derivative of [tex]y = -5x^5[/tex] can be calculated using the power rule, which states that if f(x) = [tex]x^n[/tex] then f'(x) = [tex]nx^{(n-1)}[/tex], the slope of the equation is [tex]-55x^4[/tex].

So, the slope of the equation [tex]y = -5x^5[/tex] is [tex]-25x^4[/tex].

Here, note that this equation represents a polynomial function of degree 5, which means that it is a function that has the highest power term of [tex]x^5[/tex]. Also, the slope of a polynomial function is always a polynomial function of one degree lower than the original function.

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