Brad invested $2,500 in an account earning 3.4% annual interest that is compounded semi-annually. How long will it take the investment to triple?

(Round your answer to the nearest hundredth.)

Step-by-step explanation:

what is the. meaning of this

For diagram 5, X = 76° and from diagram 6 x = 80° in the given triangles

An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure. In geometry, triangle is a three-sided polygon that is classified into three categories based on its sides, such as:

Scalene triangle (All three sides are unequal)

Isosceles triangle (Only two sides are equal)

Equilateral triangle (All three sides are equal)

Find attachment to understand the explanation

∠A = ∠C ( base angles of an isosceles triangle)

∠A = x and ∠C = 76

Therefore ∠X = 76°

For diagram 6

interior ∠A + exterior ∠A = 180°

but exterior ∠A = 110°

interior ∠A = 180  - 110

interior ∠A = 70°

∠A = ∠C( base angles of isosceles ΔBAC) which is 70°

∠A + ∠B + ∠c = 180

∠B = 180 - 70 - 70

∠B = 40°

but ∠CBA + ∠CBD = 90 because ∠B = 90° and ∠CBA = 40°

∠∠CBD = 90 - 40

∠CBD = 50°

But ∠∠CBD = ∠BDC( base angles of isosceles Δ)

so that

∠BCD + ∠CBD + ∠BDC = 180°( angles in a triangle)

x + 50 + 50 = 180

x = 180 - 100

x = 80°

In conclusion the value of x in the first and second diagrams are 76° and 80° respectively

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New coordinates become (-2,8) (-2,-4) and (4,-4)

What do you mean by scale factor?

Magnification is defined as the scale ratio of a given original object and a new object that is a representation of it but of a different size (larger or smaller).

The new figure obtained is similar to the original figure

The expansion description should state how much the shape was expanded.

Suppose a triangle with the vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2.

As we know, if (x,y) point dilated by scale factor a then new coordinates become (ax, ay)

So, if triangle having vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2 then new coordinates become (-2,8) (-2,-4) and (4,-4)

Therefore, new coordinates become (-2,8) (-2,-4) and (4,-4)

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The volume of the smaller wedge cut from a sphere of radius 4 by two planes that intersect along a diameter at an angle of π/6 is 1/6.

What is volume ?

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

Consider that the tetrahedron is bounded by the coordinate planes and the plane 8 x+y+z=2

Evaluate the triple integral [tex]\iiint_E d V$.[/tex]

The lower boundary of tetrahedron is the plane z=0 and the upper boundary of tetrahedron is the plane z=2-8 x-y.

And the projection is y=2-8 x.

The x-limits are obtained by taking y=0 and z=0 in 8 x+y+z=2.

[tex]$$\begin{array}{r}8 x=2 \\x=\frac{2}{8} \\x=\frac{1}{4}\end{array}$$[/tex]

Therefore, the region becomes [tex]$R=\left\{(x, y, z) / 0 \leq x \leq \frac{1}{4}, 0 \leq y \leq 2-8 x, 0 \leq z \leq 2-8 x-y\right\}$[/tex].

Therefore, the integral becomes

[tex]$ \iiint_E d V=\int_0^{\frac{1}{4}} \int_0^{2-8 x} \int_0^{2-8 x-y} d z d y d x $[/tex]

[tex]$=\int_0^{\frac{1}{4}} \int_0^{2-8 x}[z]_0^{2-8 x-y} d y d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}} \int_0^{2-8 x}[2-8 x-y] d y d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[2 y-8 x y-\frac{y^2}{2}\right]_0^{2-8 x} d x . $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[2(2-8 x)-8 x(2-8 x)-\frac{(2-8 x)^2}{2}\right] d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[32 x^2-16 x+2\right] d x $[/tex]

[tex]$ =\left[32\left(\frac{x^3}{3}\right)-16\left(\frac{x^2}{2}\right)+2 x\right]_0 $[/tex]

[tex]$ =32\left(\frac{\left(\frac{1}{4}\right)^3}{3}\right)-16\left(\frac{\left(\frac{1}{4}\right)^2}{2}\right)+2\left(\frac{1}{4}\right)-0 $[/tex]

[tex]$ =\frac{1}{6} $[/tex]

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The required answer for the given mathematical operation is 182.5

What are arithmetic operations?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given, 67.4 + 43 + 30 + 42.10

        = 110.4 + 30 + 42.1

        = 140.4 + 42.1

        = 182.5

Hence, the required answer for the given mathematical operation is 182.5

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The new 2 × 2 system of equation is

2y – 3z = 12

–3y – 8z = 7

What are linear equations ?

If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables. (The “three variables” are the x, the y, and the z.) The numbers a, b, and c are called the coefficients of the equation.

How do you solve linear equations with 3 variables?

Pick any two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method.

Given Equations:

x-y-2z=4 ............(1)

-x+3y-z=8 ..........(2)

-2x-y-4z=-1 ........(3)

Given Condition 1: use equation (1) with equation (2) to eliminate x

According to the condition,

x-y-2z=4 ........(1)

-x+3y-z=8 ......(2)

On adding (1) and (2), we get

(1-1)x +(-1+3)y +(-1-2)z = 4+8

2y - 3z = 12

Given Condition 2: use equation (1) with equation (3) to eliminate x

x-y-2z=4 .......(1)

-2x-y-4z=-1 ..(3)

on multiplying (1) both the sides with 2 , we get

2x - 2y -4z = 8

On adding with (3), we get

2x - 2y -2z = 8

-2x-y-4z=-1

-3y - 8z = 7

Thus, The new 2 × 2 system of equation is

2y – 3z = 12

–3y – 8z = 7

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Answer:

[tex]\textsf{Slope form}: \quad y=-\dfrac{4}{5}x-\dfrac{26}{5}[/tex]

[tex]\textsf{Standard form}: \quad 4x+5y=-26[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]5x-4y=1[/tex]

Rewrite in slope-intercept form:

[tex]\implies 5x-4y+4y=1+4y[/tex]

[tex]\implies 5x=1+4y[/tex]

[tex]\implies 5x-1=1+4y-1[/tex]

[tex]\implies 5x-1=4y[/tex]

[tex]\implies \dfrac{5}{4}x-\dfrac{1}{4}=\dfrac{4y}{4}[/tex]

[tex]\implies y=\dfrac{5}{4}x-\dfrac{1}{4}[/tex]

Therefore, the slope of the line is ⁵/₄.

If two lines are perpendicular to each other, their slopes are negative reciprocals.

Therefore, the slope of the perpendicular line is -⁴/₅.

Substitute the found slope -⁴/₅ and given point (1, -6) into the slope-intercept formula and solve for b:

[tex]\implies -6=-\dfrac{4}{5}(1)+b[/tex]

[tex]\implies -6=-\dfrac{4}{5}+b[/tex]

[tex]\implies b=-\dfrac{26}{5}[/tex]

Therefore, the equation of the perpendicular line in slope form is:

[tex]y=-\dfrac{4}{5}x-\dfrac{26}{5}[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]

Multiply both sides of the equation in slope form by 5:

[tex]\implies y \cdot 5=-\dfrac{4}{5}x\cdot 5-\dfrac{26}{5}\cdot 5[/tex]

[tex]\implies 5y=-4x-26[/tex]

Add 4x to both sides:

[tex]\implies 5y+4x=-4x-26+4x[/tex]

[tex]\implies 4x+5y=-26[/tex]

Therefore, the equation of the perpendicular line in standard form is:

[tex]4x+5y=-26[/tex]

Answer: 240 miles

Step-by-step explanation:

160m = 4 days

miles 40-1  days

        80-2

        120-3

         160-4

       200-5

          240-6

The estimated price of a new car in 4 years time if the inflation rate is 12.3% is 393050

In economics, "inflation" refers to a significant increase in the price of goods and services throughout an economy. This is why growing prices often cause inflation. Deflation, which is a sustained decline in the average level of prices for goods and services, is the reverse of inflation. The most common measure of inflation is the annualized percentage change in an index of general prices, also known as the inflation rate.

Given,

The cost of the car bought by a women=350000

Time=4 years

And inflation rate=12.3%

We know that,

Inflation rate=((B-A)/A)×100

Here A denotes the standing price

So, A=350000

B denotes estimated price

So, B=x

12.3=((B-350000)/350000)×100

43050=B-350000

B=393050

Therefore, the estimated price of a new car in 4 years time if the inflation rate is 12.3% is 393050.

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The volume of a cone is given by the formula:

V = (1/3) * π * r^2 * h

Where V is the volume, r is the radius of the base, and h is the height of the cone.

In this case, the base diameter and the height of the cone are both equal to x units, so the radius of the base is x/2 units. Therefore, the volume of the cone is:

V = (1/3) * π * (x/2)^2 * x

= (1/3) * π * x^3 / 4

= (π/4) * x^3

The correct expression for the volume of the cone is therefore O πx^3.

The expression that represents the volume of the cone in cubic units is:

V = (1/12) π x³

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h

We have,

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

V = (1/3) πr²h

where r is the radius of the base and h is the height.

Since the diameter of the base is equal to x, the radius is equal to half the diameter, which is x/2.

Also, we know that the height of the cone is also equal to x.

Substituting these values into the formula, we get:

V = (1/3)π (x/2)² x

Simplifying this expression, we get:

V = (1/3)π(x²/4)x

V = (1/12)πx³

Therefore,

The expression that represents the volume of the cone in cubic units is:

V = (1/12) π x³

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There is a 0.001 percent chance that this song will be played on no more than two of the seven days.

A probability simple definition is what?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Detailed explanation:

Since this is a combination issue, we must first determine the combination of 7 select 5, and then multiply that result by the chance of each possible outcome:

Pick 5 from a combination of 7:

C(7,5) = 7! / (5! * 2!) = 7*6/2 = 21

This figure indicates that there are 21 alternative ways that the five days we want to be allocated in the seven days could be used.

The likelihood of each event is now:

5 days of song playback: (0.15)5

The song wasn't played for two days: (0.85)2.

Therefore, the final likelihood is

P =(0.15)^5*C(7,5) * (0.85)^2 = 0.001

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Answer:

83 degrees

Step-by-step explanation:

17^2 = 8^2 + 16^2 - 2 * 8 * 16 * cos (X)

289 = 64 + 256 - 16 * 16 * cos(X)

289 = 320 - 256 cos(X)

289-320 = -256 cos(X)

- 31 = -256 cos(X)

31 = 256 cos(X)

31/256 = 256/256 cos(X)

0.121094 = cos (X)

x = arccos 0.121094

x = 83.04475538

The average rate of change of g(x) = 3x² - 8x from x= 1 to x = 6 is 13.

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

g(x) = 3x² - 8x

The intervals, x = 1 to x = 6

Calculate the values of g(6) and g(1) as shown below,

g(6) = 3 × 6² - 8 × 6

g(6) = 3 × 36 - 48

g(6) = 108 - 48

g(6) = 60

And, g(1) = 3 × 1² - 8 × 1

g(1) = 3 - 8

g(1) = -5

Calculate the average rate of change as shown below,

The average rate of change = [g(6) - g(1)] / x₂ - x₁

The average rate of change = [60 - (-5)] / 6 - 1

The average rate of change = 65 / 5

The average rate of change = 13

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At the local bunny-hop, the sum of geometric sequences showing the jumps performed by Mr. Meyering is 40

The Sequences of the jump include

20, 10, ...

The common ratio, r is calculated from

first term, a * common ratio, r = second term

20 * r = 10

20r = 10

r = 10/20

r = 1/2

hence r < 1

The sum of gp to infinity for r < 1 is

Sum = a/ (1 - r)

Sum = 20 / (1 - 1/2)

Sum = 20 / 1/2

Sum = 20 * 2

Sum = 40

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The value when 7 is divided by 292 is given as 0.023972(approximation)

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation may be used to quickly and simply fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will thus be 6 groups with 5 students each. The initial number, 30, which is obtained by multiplying 6 by 5 may be used to confirm this figure.

The names of the phrases connected with the division process are referred to as division parts. The division is made up of the following four components: dividend, divisor, quotient, and remainder.

In the problem 7 is the Dividend and 292 is the divisor so

[when we add decimal 0 is added to the number and for each 0 in the quotient 0 is also added to the number if the zero is after the decimal]

      292 ) 700( 0.023972

              - 584                

                 1160

                - 976    

                  2840

                 -2628    

                    2120

                   -2044  

                       760

                      - 584

                         176

7 divided by 292 is 0.023972 (approx.)

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The probability of the flights at the airlines at least 4 of the next 5 are overbooked from the given histogram is equal to 0.446.

Histogram is attached.

As given in the question,

Required histogram is attached.

From the attached histogram,

Histogram is attached.

The probability of 4 overbooked flights for the given airlines 'P (4) =  0.332

The probability of 4 overbooked flights for the given airlines 'P(5)' = 0.114

Required probability of at least 4 for the next 5 flights of the given airlines

= P ( x ≥ 4 ) upto next P(5)

= P(4) + P(5)

= 0.332 + 0.114

= 0.446

Therefore, the probability of at least 4 upto next 5 flights of the given airlines from the given histogram is equal to 0.446.

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Answer:

[tex]a_n=9n+26[/tex]

Step-by-step explanation:

An explicit formula for a sequence allows you to find the nth term of the sequence.

To determine if the sequence is arithmetic or geometric, calculate the differences between the terms:

[tex]35 \underset{+9}{\longrightarrow} 44 \underset{+9}{\longrightarrow} 53[/tex]

As the first differences are the same, the sequence is arithmetic with a common difference, d, of 9.

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Substitute a = 35 and d = 9 into the formula to create an explicit formula for the nth term of the sequence:

[tex]\implies a_n=35+(n-1)9[/tex]

[tex]\implies a_n=35+9n-9[/tex]

[tex]\implies a_n=9n+26[/tex]

All the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.

What is rigid motion?

A geometric figure is moved by rigid motions, but its size and shape remain unchanged. It generates visuals that make sense.

Rigid transformation comes in four different varieties.

1. translate 2. reflect. 3. Rotation 4. Gliding reflection

Here,

We have a series of rigid motion maps ΔNEM  onto ΔCDE.

We have to find the correct statement, so we concluded that all the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.

Hence, ΔNEM and ΔCDE are congruent.

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The total area of the space will be equal to 175 square meters.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Elizaveta painted 35 square meters of wall space. This represents 20% of the total area.

The total area will be calculated as,

20% of area = 35 square meters

100% of the area = ( 35 x 100) / 20

100% of the area = 175 square meters

Therefore, the total area of the space will be equal to 175 square meters.

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Elizaveta painted 35 m2 of wall space. This represents 20% of the total area.

What is the total area of the walls to be painted?f ^(4) 2

Answer:

The total amount of the sales tax: $3.00

The total amount paid: $47.25

Step-by-step explanation:

Tip (In $): 6.75

Sales tax: 3.00

The total amount of food (before additional fees): 37. 50

So, to find the amount (in dollars) of the sales tax and tip, we must use this formula:

Amount = whole number * part percent/100

So, plugging in the numbers to the formula, it would look like this:

37.50 * 18 / 100
That is how to find the tip, you would do the same to find the sales tax. Then, when you get both amounts, you add them to 37.50 (the total before the fees) and get $47.25.

Therefore, the new volume comes out to be 787.22 cm3.

The volume of a substance is a measurement of how much space it occupies. Matter is a term used to describe a physical substance that has mass and occupies space. In physical disciplines like chemistry, cubic meters are the standard unit of volume (m3). This yields other units like the litre (L) and milliliter (mL) (mL).

Here,

When the height was raised here by 13 inches, it was equivalent to adding an additional 13 levels, each measuring 56.23 cm3, to the prism that already existed.

Your new volume would therefore be: => 56.23 cm3 + 13 (56.23 cm3) = > 787.22 cm3.

therefore, the new volume comes out to be 787.22 cm3.

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Answer:

C. 38 = x + 23

Step-by-step explanation:

X represents the amount she still needs to bake for the party.

38 represents the total amount of cookies she needs to bake.

Because she already made 23 cookies, you add to X

[tex]6\frac{5}{6}-4\frac{1}{3}[/tex] Showing my work using the mixed fraction the answer is [tex]=\frac{5}{2}[/tex]

What do you mean by mixed fraction?

A fraction represented by a quotient and a remainder is a mixed number

Fractions represent parts of a whole.

How can I convert an improper fraction to a mixed number?

Divide the numerator by the denominator.

Keep the denominators the same, take the quotient as an integer, and the remainder as the numerator of the correct fraction.

Given expression:

[tex]6\frac{5}{6}-4\frac{1}{3}[/tex]

⇒ [tex]\frac{41}{6}-\frac{13}{3}[/tex]

⇒ [tex]\frac{41-26}{6}[/tex]

= 15/6

= 5/2

Therefore, [tex]6\frac{5}{6}-4\frac{1}{3}=\frac{5}{2}[/tex]

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Based on given question question, following are the answers of blanks based on Midpoint Theorem.

1.) Definition of midpoint

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side.

2.) ∠ECD ≅ ∠BCA [Vertically opposite angle]

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines. They are also called vertically opposite angles as they are situated opposite to each other.

3.) ∠D ≅ ∠A [Alternate interior angle]

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.

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Answer:

Step-by-step explanation:

The risk of getting a cold is calculated by dividing the number of people who have a chance of getting a cold by the total number of people. In this case, the risk of getting a cold is 4 people / 20 people = 20%. Therefore, the risk of getting a cold is 20%.

Answer:

a)  $153,850

b)  $779.54

c)  $873.54

Step-by-step explanation:

[tex]\begin{aligned}\textsf{Loan amount}&=\textsf{Cost of property}-\textsf{Down payment}\\&=181000-(181000 \times 0.15)\\&=181000-27150\\&=153850\end{aligned}[/tex]

Therefore, the loan amount is $153,850.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Monthly Payment Formula}\\\\$PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}$\\\\where:\\\\ \phantom{ww}$\bullet$ $P =$ loan amount \\\phantom{ww}$\bullet$ $i =$ interest rate per month (in decimal form) \\\phantom{ww}$\bullet$ $n =$ term of the loan (in months) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the  Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.045}{12}\left(1+\frac{0.045}{12}\right)^{360}}{\left(1+\frac{0.045}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{153850 \cdot 0.00375\left(1.00375\right)^{360}}{\left(1.00375\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=779.5353492[/tex]

Therefore, the monthly payments would be $779.54.

Given:

Substitute the given values into the Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.055}{12}\left(1+\frac{0.055}{12}\right)^{360}}{\left(1+\frac{0.055}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=873.5433786[/tex]

Therefore, the monthly payments would be $873.54.

Step-by-step explanation:

A)20+10x=y

B)20+10(3)=y

20+30=y

y=50

The mass of the substance that would remain after 50 years is 49 Kg

We know that the term radioactive decay has to do with the breakdown of a radioactive substance and such  a break down can be modelled by the use of a mathematical function as we can see here.

The mathematical function that we can be  able to use for the modeling is given as;  m(t)=120e^-0.018t where t is the time that is taken in years.

After 50 years we are going to have;

m(t)=120e^-0.018(50)

m(t)= 49 Kg

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Missing parts;

A certain radioactive material decay in such a way There’s a mass in kilograms remains after T years is given by the that the mass in kilograms remains after T years is given by the function m(t)=120e^-0.018t

How much mass remains after 50 years? Round to 2 decimal places.