A sample of a radioactive isotope had an initial mass of 110 mg in the year 1990 and decays exponentially over time. A measurement in the year 1993 found that the sample's mass had decayed to 90 mg. What would be the expected mass of the sample in the year 2002, to the nearest whole number?

√14 feet, A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. A point in a plane has specific coordinates, as we are aware. Any point's location on a plane can be described by an ordered pair of numbers, or coordinates, which are written as ((x,y)).

A coordinate can be expressed in one of three ways. a coordinate with an integer for degrees, a real number for minutes, and an integer for seconds (DMS). a coordinate that contains minutes (a real number) and degrees (an integer) (MinDec). a coordinate that merely contains degrees (real number).

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The sum of the numerator and denominator of the decimal is found as 111.

As for the given question;

The decimal number is given as;

0.12 bar

Decimal to fraction conversion

100(0.12 bar) = 12(0.12 bar)

99.(0.12bar) = 100(0.12bar) - (0.12 bar)

99.(0.12bar) = 12 × 0.12bar - 0.12bar

99.(0.12bar) = 12

0.12 bar = 12/99 (lowest fraction)

Thus, in the result the numerator is found as 12 and the denominator is found as 99.

Add = 12 + 99

Add = 111

Thus, the sum of the numerator and denominator of the decimal is found as 111.

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The graph of the linear equation:

y - 4 = (2/3)*(x + 2)

Can be seen on the image at the end.

Here we have the following linear equation:

y - 4 = (2/3)*(x + 2)

Isolating y, we get:

y = (2/3)*(x + 2) + 4

To graph the line, we just need to evaluate it in two different values of x so we get two points, once we get the points, we can graph them on a coordinate axis and then connect them with a line.

If we use x = 1 we get:

y = (2/3)*(1 + 2) + 4

y = (2/3)*3 + 4

y = 2 + 4 = 6

y = 6

Then we have the point (1, 6)

if x = 4 then:

y = (2/3)*(4 + 2) + 4

y = (2/3)*6 + 4

y = 4 + 4 = 8

So we have the point (4, 8)

Then the graph of the linear equation is the one you can see below:

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Work Shown:

p * q = 3p + 2q - 5

3 * 2 = 3(3) + 2(2) - 5

3 * 2 = 9 + 4 - 5

3 * 2 = 13 - 5

3 * 2 = 8

Using the simple interest formula, Mr. Solo received $26 interest.

In the given question we have to find how much interest Mr. Solo received.

The investment(P) = $325.

Interest rate(R) = 8%

Time(T) = 1 year

Finding the interest using the simple interest formula.

I = PRT/100

where I = interest

P = Principal Amount

T = Time

R = Interest Rate

Putting the value

I = 325*8*1/100

I = 26

Hence, Mr. Solo received $26 interest.

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Answer:

x = 3.5 hours

y = 1.5 hours

Step-by-step explanation:

There are two unknowns, x and y, both in umits of hours.  We need at least two equations before we start trying to solve this with substitution.  Looking at the information, this should be possible.

First, we know that Speed x Time = Distance.  

The distance covered by the cyclyst would be the sum of (12km/h)*x and (16km/h)*y, where x is the time, in hours, for the slower speed and y for the faster.  Together, the student travels 66 km.

The total distance of 66 km would be comprised of the two distances 12x and 16y:

 12x + 16y = 66 km  

For the second equation, we know that the total time is 5 hours.  That would be the sum of x and y:

 x + y = 5 hours

We now have 2 equations, so we stand a good chance of finding the answer.  Pick one of the equations and isolate one of the variables to one side.  Let's choose x + y = 5 hours, since that is easy to rearrange:

     x = 5-y

Now take the first equation and substitute the definition of x from above (5-y):

12x + 16y = 66

12(5-y) + 16y = 66

60-12y + 16y = 66

4y = 66-60

4y = 6

y = (6/4) or 1.5 h

The time spent at 16 km/h was 1.5 hours.

Use this value of y in either equation to find x.  Let's use x+y=5, since that will be easier:

x+y = 5 for y = 1.5

x+1.5 = 5

x = 3.5h

The time spent at 12 km/h was 3.5 hours

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

now let's consider the white, "cut-out" triangle on the left side.

the purple one angles at the top and bottom corner are 45°.

the withe outer angles at the same corners (they are the inner angles for the white triangle) are complementary angles (together they have 90°) to the purple ones, because due to the equal angles at the top and bottom we know the connection between the 2 45° angles (the white baseline) is at a 90° angle to the 45° to 135° sides.

so the 2 baseline angles of the left white triangle are also 45° (45+45 = 90).

and that means that the third white angle is

180 - 45 - 45 = 90°.

and because a full circle around the 3x° point must have 360° (as any full circle), we know that both angles (90° and 3x°) together are 360°.

360 = 90 + 3x

270 = 3x

x = 90°

3x = 270°

Answer:  y  =  160/q   -a

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.

A combination is a grouping of items where order does not matter. The formula of combination is

[tex]_{n}C_{r} = \frac{n!} {r! (n-r)!}[/tex]

Where

Given the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.

What is the probability that no two adjacent people will stand?

First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.

The number of arrangements according to the number of people standing.

Case 1: 0 people standing = 1 arrangement.

Case 2: 1 people standing = [tex]_{8}C_{1}[/tex] = [tex]\frac{8!} {1! 7!}[/tex] = 8 arrangements.

Case3: 2 people standing = [tex]_{8}C_{2}[/tex] = [tex]\frac{8!} {2! 6!}[/tex] = [tex]\frac{7 \times 8} {2}[/tex] = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.

Case 4: 3 people standing = [tex]_{8}C_{3}[/tex] = [tex]\frac{8!} {3! 5!}[/tex] = [tex]\frac{6 \times 7 \times 8} {6}[/tex] = 56 arrangements. In this case, three people standing are next to each other = [tex]_{8}C_{1}[/tex] = 8 arrangements. Two people standing are next to each other and the third person is not = [tex]_{8}C_{1} \times _{4}C_{1}[/tex] = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.

Case 5: 4 people standing but no two adjacent people = 2 arrangements.

The number of arrangements that no two adjacent people will stand.

n(A) = 1 + 8 + 20 + 16 + 2 = 47

The probability that no two adjacent people will stand is

P(A) = n(A)/n(S)

P(A) = 47/256

Hence, the probability that no two adjacent people will stand is 47/256.

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a.  I would rather compound annually at 5 % interest

b.  I would increase the simple interest rate if i were to change my answer

Since you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually, we need to determine the amount of each type of interest after 10 years.

Since  you have $200 to invest for 10 years at  7% simple interest, using the simple interest formula for the amount, we have

A = P(1 + rt) where

Substituting the values of the variables into the equation, we have

A = P(1 + rt)

A = 200(1 + 0.07 × 10)

A = 200(1 + 0.7)

A = 200(1.7)

A = 340

Also, since  you have $200 to invest for 10 years at  5% interest compounded annually, using the compound interest formula for the amount, we have

A' = P(1 + r)ⁿ where

Substituting the values of the variables into the equation, we have

A' = P(1 + r)ⁿ

A' = 200(1 + 0.07)¹⁰

A' = 200(1.07)¹⁰

A' = 200(1.9672)

A' = 393.43

Since A' = $393.43 > A = $340, i would rather compound annually at 5 % interest

To change my answer, I would increase the simple interest rate if i were to change my answer

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Answer:

We may use the logarithm formula,

N = ln(EV/SV) ÷ ln(1+r), where (1+ r) is the value of 1 plus interest for 1 year.

EV is end value, SV is start value.

EV is 20000, SV is 12000, interest is 5.6% semi annual

(1+r) is obtained as,

Step-by-step explanation:

The capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter are I, N, O and S.

It is possible to rotate clockwise or counterclockwise. If an item needs to be rotated, there are several methods for doing so:

When the capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter: I, N, O and S.

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The length of the given isosceles triangle legs is 1.9 feet.

A linear equation is a equation that has degree as one.

To find the solution of n unknown quantities n number of equations with n number of variables are required.

Given that,

The perimeter of an  isosceles triangle is 4.9 feet.

And, legs of the triangle are 0.3 foot less than twice the base.

Suppose the base of the triangle be x.

Then, its legs are 2x - 0.3.

As per the question the expression for the perimeter of the triangle is,

2x - 0.3 + 2x - 0.3 + x = 4.9

=> 5x - 0.6 = 4.9

=> 5x = 5.5

=> x = 1.1

Thus, the legs can be found by substituting x = 1.1 in 2x - 0.3 as below,

2 × 1.1 - 0.3

= 1.9

Hence, the length of one of the triangle’s legs is 1.9 feet.

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Answer:

x = -20

Step-by-step explanation:

x/4 + 8 = 3

subtract 8 from both sides:

x/4 + 8 - 8 = 3 - 8

x/4 = -5

multiply both sides by 4:

4(x/4) = 4(-5)

x = -20

We utilize the z statistic to find the probability percentage. Calculating the z value and then looking up the p value using the common probability tables is the process to follow. The z score formula is:

Z = (x - )/ ( / sqrt(n)

where,

Standard deviation equals 2

sample size, n With n = 5, calculating the z and p values:

The tables show that p(5) = 0.8686.

For n = 6, calculate the z and p values as follows:

The tables show that p(6) = 0.8888.

If both days to occur, the probability that each day will last no more than 11 minutes is as follows:

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The reflection of point produce an image at the same coordinates, (0, k) is a reflection of the point across the y-axis.

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting a figure in a line or a point.

Every point of a figure is translated to an image across a fixed line via a reflection. The fixed line is referred to as the reflection line.

Given:

A point has the coordinates (0, k).

The rule for a reflection of a point across the x-axis is:

(x, y) ----> (x, -y)

and, the reflection is (0 , -k)

The rule for a reflection of a point across the y-axis is:

(x, y) ----> (-x, y)

and, the reflection is (-0 , k) or (0, k).

The rule for a reflection of a point across the line y = x is:

(x, y) ----> (y, x)

and, the reflection is (k, 0).

and, The rule for a reflection of a point across the line y = -x is:

(x, y) ----> (-y, x)

and, the reflection is (-k, 0)

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Using the principle of proportional relationship, the total recommended daily amount of fiber is  34.4 grams

Let x be the recommended daily amount ( in grams ) of the fiber,

So, 32% of x = [tex]\frac{32}{100}x[/tex] = 0.32x

According to the question,

11 grams is 32% of the recommended daily amount of fiber,

That is, 0.32x = 11

x = 11/0.32 = 34.4 grams

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Step-by-step explanation:

when we say "a/b of c", we mean mathematically :

a/b × c

so,

a)

x = 1/5 × 15 = 15/5 = 3

b)

x = 3/4 × 48 = 3×48/4 = 3×12 = 36

Answer:

Step-by-step explanation:

a) 1/5 of 15 = ?

→ 1/5 of 15

→ (1/5) × 15

→ 15/5 = 3

So, answer is 3.

b) 3/4 of 48 = ?

→ 3/4 of 48

→ (3/4) × 48

→ 144/4 = 36

So, answer is 36.

Answer:

2.43

Step-by-step explanation:

The quotient is the answer to a division problem.

67.98/28 = ~2.42785714286

To round to the nearest hundredth, leave 2 decimal digits remaining. If the thousandth place (3rd decimal digit) is greater they or equal to 5, add 1 to the hundredths digits.

7 [tex]\geq[/tex] 5

2.42+0.01

2.43

The required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

The quadratic function is defined as a function containing the highest power of a variable is two.

The quadratic function is given in the question:

2y² + 2y - 5 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 2, b = 2 and c = -5

Using the quadratic formula to solve the above quadratic function

[tex]y = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of a = 2, b = 2 and c = -5 in the above formula

[tex]y=\dfrac{-2\pm \sqrt{2^2-4\cdot \:2\left(-5\right)}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-2\pm \:2\sqrt{11}}{2\cdot \:2}[/tex]

Separate the solutions as:

[tex]y=\dfrac{-2+2\sqrt{11}}{2\cdot \:2},\:y=\dfrac{-2-2\sqrt{11}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

Therefore, the required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

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The slop m is ( 2-3).The slope formula, or the ratio of the change in the y values to the change in the x values, is m is equal to subtraction of y2 and y1 and divide by subtraction of x2 and x1  The initial point's coordinates are x1 and y1, respectively.

The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1). The initial point's coordinates are x1 and y1, respectively.

(10, 7) and (3, 1).

m=(y2-y1)/(x2-x1).

3-1 / 7-10= 2/-3

The slop m is ( 2-3)

When determining the slope of a straight line without its equation, there are three steps. The first point's coordinates are x1 and y1. Step one is to locate the line's first two points. Step 2: Decide which will be (x1, y1) and which will be (x2, y2). Step 3: Determine the slope using the slope equation.

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The proportional relationship between the number of books on shelf and how much shelf space the books takes up is 1 inch

What is proportionality?

The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.

When two or more parameters are directly or indirectly proportional to one another, the relationship is written as a = kb or a = k/b, where k denotes the direction of the relationship between the two variables. The proportionality constant, k.

As we know [tex]\frac{y}{x}[/tex] = constant of proportionality

So, [tex]\frac{y}{x}[/tex] will be

[tex]\frac{2}{2} = \frac{11}{11} = \frac{13}{13} = \frac{16}{16}[/tex] = 1

∴ it is 1 inch per book

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Pieces of data such as $18,000 and $350,000 represent outliers in this chart in standard deviation .

How to interpret a standard deviation?

In this chart, there are outliers. The main outliers are $18,000 and $350,000. This is because we know the mean or average is $63,423, and therefore values that are too different from this average are considered outliers.

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There is 2.1 miles distance between the last water stop and the end of the race.

Total miles Julio will run = 13.1 miles

Distance at which water stops are location = 2.75

Total number of water stops in full race of 13.1 miles = 13.1 / 2.75

=4.764

so , there are 4 stops in the runs for drinking water every 2.75 miles

Distance from starting point of race and last water stops = 4 × 2.75 = 11 miles

Distance between the last water stop and the end of the race = 13.1 - 11

= 2.1 miles

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The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.

Here,

When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).

Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.

As a result, 186 outcomes or triplets are possible and satisfy this property.

Hence, the required probability is 186/216=31/36.

The required probability is 31/36 for three dice rolls to produce triangle sides.

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Answer:

-3.2

Step-by-step explanation:

-5(x+1)-9=2

first simplify by distributiom

-5(x)-5(1)-9=2

simplify the multiplication

-5x-5-9=2

add the numbers

-5x-14=2

now to get x by itself on one side we undo in reverse order and move the -14 over to the other side so add 14 to both sides to cancel the -14

-5x=2+14

simplify

-5x=16

now divide both sides by -5 to get x by itself

-5x/-5=16/-5

simplify

x=-3.2 or as a fraction, [tex]-\frac{16}{5}[/tex]