How are sides RS and RT related to each other?

The half life of the substance is 828.37

The period of time it takes for one-half of a radioactive isotope to decay is known as the half-life. An individual radioactive isotope's half-life is unaffected by environmental factors and is independent of the isotope's starting concentration.

The amount of time needed for half of a radioactive sample's atomic nuclei to decay

Given:

As, The amount of a substance after t days is given by:

p(t)= [tex]p(0)[/tex][tex]e^{-kt[/tex]

Original amount after 300 days.

p(300)= 0.778p(0).

p(t)= [tex]p(0)[/tex][tex]e^{-kt[/tex]

0.778 = p(0)[tex]e^{-300k[/tex]

-300k= log (0.778)

-300k= -0.109020

k = 0.0003634

So, p(t)= [tex]p(0)[/tex][tex]e^{-0.0003634t[/tex]

This is t for which P(t) = 0.5P(0). So

0.5p(0)=  [tex]p(0)[/tex][tex]e^{-0.0003634t[/tex]

[tex]e^{-0.0003634t[/tex] = 0.5

log ( [tex]e^{-0.0003634t[/tex]) = log 0.5

-0.0003634 t = log 0.5

t= -0.30102999566/ -0.0003634

t= 828.37

Hence, the half life of the substance is 828.37

Learn more about half life here:

https://brainly.com/question/24228521

#SPJ1

The solution set of 6 ㏑ e = e ^ ㏑ 2x is 3

What is relation between Exponents and logarithms ?

Exponents and logarithms are inverse functions, you can use exponents to "undo" logarithms and use logarithms to "undo" logarithms. Exponents specify the number of times you must multiply a value, while logarithms specify which exponent to apply to obtain a certain value.

The given expression is,

6 ㏑ e = e ^ ㏑ 2x

we know, ㏑ (e) = 1 and e ^ ㏑(x)  = x

Put these values,

6 * 1 = 2x

Now, find x

6 = 2x

x = 3

Hence, the solution set of 6 ㏑ (e) = e ^ ㏑ (2x)  is 3

To read more about Exponents and logarithms.

https://brainly.com/question/28596269

#SPJ9

The sampling distribution of the sample mean will always have the same Mean as the original distribution.

Sampling distribution:

Sampling distribution means a probability distribution of a statistic that is obtained through repeated sampling of a specific population.

Given,

Here we have the statement "The sampling distribution of the sample mean will always have the same _________ as the original distribution."

Now, we have to find the missing word in the statement.

We know that, the mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. Simply said that the sample mean is equal to the population mean.

To know more about Sampling Distribution here.

https://brainly.com/question/13501743

#SPJ1

Answer:

4 pounds

Step-by-step explanation:

12/3=4 remember it says about!

Answer:

x<2

Step-by-step explanation:

8+3x<14

3x<6

3x/3<6/3

x<2

The interest on principle $775 over eight year at rate 1.47% is  $91.14

Simple interest is a interest which is only based on principle amount, it does not imply on yearly interest.

The given principle, p = $775 ,

Rate r = 1.47 %,

and Time = 8 year.

To find interest I, Use formula,

I=(p × r × t)/100,

I=775 ×1.47 ×8/100,

I = $91.14

So the interest is I = $91.14

To know more on Simple Interest:

https://brainly.com/question/28655726

#SPJ1

The value of f(-1) when f(x) is defined as given in the question is 0.

What is the substitution method?

One method for solving simultaneously linear equations using algebra is the substitution method. It involves changing the value of any one of the variables in one equation & applying it to another one.

Given, f(x) = 2x + 2  ......... (i)

Now, we need to find the value of f(-1), by substituting the value of x = -1 in above equation (i), then

f(-1) = 2*(-1) + 2 = -2+2 = 0

Hence, the required answer of f(-1) is 0.

To learn more about the substitution method

https://brainly.com/question/22340165

#SPJ1

The measurement of m∠1 and m∠3 is 52° when a is parallel to b.

According to the question,

We have the following information:

The line a is parallel to b and they are being cut a line m.

m∠6 = 128°

We know that when two parallel lines are cut by another line then the sum of consecutive interior angles is 180°. And we also know that vertically opposite angles are equal.

m∠1 and m∠3 are vertically opposite angles.

m∠3 and m∠6 are consecutive interior angles.

∠3+∠6 = 180°

∠3 = 180-128

∠3 = 52°

So, we have:

∠1 = ∠3 = 52°

Hence, the measurement of m∠1 and m∠3 is 52° when a is parallel to b.

To know more about measurement of m∠1 here

https://brainly.com/question/28736232

#SPJ1

a) The distance travelled on the cycle in the first 14 seconds is; 96 m

b) The acceleration in the first 4 seconds is; 2 m/s²

The velocity time graph for a cycle is as attached.

The distance covered will be the area under the curve.

Formula for area of trapezium is;

A = (1/2)(sum of parallel sides) * height

Area for 0 to 14 sec is a trapezium formed with parallel sides as 14 and  10 while distance between them is 8 is solved as;

Area = (1/2)(14 + 10) * 8  

Area = 24 * 4  = 96  

Thus;

Distance covered = 96 m

Distance travelled on the cycle in the first 14 seconds is 96 m.

Therefore, the acceleration in first 4 seconds = (8 - 0)/(4 - 0)

= 8/4 = 2 m/s²

Read more about Velocity Time Graph at; https://brainly.com/question/10824584

#SPJ1

The option B is true which is m2=m1+3, s2=s1

From the given information,

The required correct answers are,

m2= m1 + 3

s2= s1

Hence,

Option b. is correct.

A standard deviation (or σ) is a proportion of how distributed the information is comparable to the mean. A low standard deviation implies information is grouped around the mean, and an elevated requirement deviation demonstrates information is more fanned out.

The standard deviation of a population or sample and the standard error of measurement (e.g., of the example mean) is very unique however related. The example implies the standard error is the standard deviation of the arrangement of implies that would be found by drawing an endless number of samples from the population and registering a mean for each sample. The mean standard error ends up equaling the population standard deviation partitioned by the square base of the example size and is assessed by utilizing the example standard deviation separated by the square foundation of the sample size.

To learn more about standard deviation, mean, median, and mode,

https://brainly.com/question/14747159

#SPJ4

Answer:

  m∠6 = 61°

Step-by-step explanation:

Given a transversal crossing parallel lines AB and CD, you want the measure of angle 6 given that angle 2 is 61°.

Where a transversal crosses parallel lines, corresponding angles and vertical angles are congruent. This has the effect of making all acute angles congruent, and all obtuse angles congruent.

Acute angle 6 is congruent to acute angle 2, which measures 61°. (They are "corresponding" angles.)

  m∠6 = 61°

Answer:

y = x-5

Step-by-step explanation:

-x + y = - 5

y = - 5 + x

y = x - 5

As per the dividing system, If every box gets the same amount, then the mass of fruit in each box is 10 kilograms.

Division

Division refers a process of splitting a specific amount into equal parts.

Given,

Felipe has 8 boxes.

He puts a total of 80 kilograms of fruit into these boxes.

Here we need to find the mass of fruit in each box, if every box gets the same amount.

While we looking into the given question, we have identify the following this,

Number of boxes = 8

Total weight of fruits = 80 kilograms.

And we also know that, each box must has same amount of weight.

Therefore, it can be calculated as, by dividing the total weight by the number of boxes, then we get,

=> 80/8

=> 10

Therefore, each box has 10 kilograms of fruits.

To know more about Division here.

https://brainly.com/question/21416852

#SPJ9

Answer:

double whatever you got

100 percent increase of 2 is 4

Step-by-step explanation:

hopes this helps please mark brainliest

Answer:

It means that whatever you have just doubled.

Step-by-step explanation:

If I have a total of 100 widgets, that is 100%.  If I have a 100% increase of that value, that means I now have 200 widgets.

The percentage value of puppies weighing over 6 pounds is 25%

What is Percentage?

Percentage is a relative number that represents the hundredth part of any quantity. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Solution:

Given that there are 12 puppies in total and 3 of them weighted above 6 pounds

To calculate the percentage we need to divide 3 by 12 and then multiply it by 100

= (3/12) * 100

= 25%

To learn more about Percentage from the given link

https://brainly.com/question/843074

#SPJ1

Answer:

False

A saver has much more positives. It means you'll have more money in your future :)

Answer:

-11

Step-by-step explanation:

3(-2)-5

-6-5

-11

h=-11

Answer:

m = - 3

Step-by-step explanation:

since the line passes through (1, 3 ) then the coordinates of the point make the equation true.

substitute x = 1, y = 3 into the equation and solve for m

3 = m + 6 ( subtract 6 from both sides )

- 3 = m

Answer:

3:10 ratio of mangos to rest of the fruits or 15:50 unsimplified

Step-by-step explanation:

There are 50 fruits in total with 15 of them being mangos. Simplify this (divide by both numbers by 5) to get 3:10

To write the point-slope form of the line that passes through (1, -5) and is parallel to a line with a slope of 1.

A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So if we have a slope of 1 or 1/1. our perpendicular line needs a slope of -1.

y - y1 = m(x - x1)

slope(m) = -1

(1,-5)...x1 = 1 and y1 = -5

now we sub...pay close attention to your signs

y - (-5) = -1(x - 1)....not done yet

y + 5 = -1(x - 1)...or it can also be written as : y + 5 = - (x - 1)

To learn more about parallel lines click here https://brainly.com/question/24607467

#SPJ4

The answer to the question is 5.

The calculation can be calculated as follows :

3√125

= 3√(5 x 5 x 5)

= 5

We can write 125 as 5 x 5 x 5.

Or 5 power 3.

The value of the cube root of 125 is 5.

It is the real solution of the equation x3 = 125.

The number 125 is called a perfect cube number since its cube root value is a whole number.

Read more about cube root here

https://brainly.com/question/12726345

#SPJ1

The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Since the aspect ratio of 4:6 is closer to that of an 11-inch by 14-inch frame (which is approximately 1:1.5) than the aspect ratio of 3.5:5 (which is approximately 7:10).

By minimizing the difference in aspect ratio between the photo and the frame, you will minimize the loss of the edges of the picture when trying to fit it into the frame.

The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize the loss of the edges of the picture when trying to fit it into an 11-inch by 14-inch frame.

Learn more about the Ratio here:

brainly.com/question/1504221

#SPJ2

They are congruent by SAS as follows if I understand you correctly:

Since x is shared by both NR and AG, it must be at their intersection.

Because it lies in the middle of both, NX = XR and AX = XG.

We join point A to point N and point R to point G to complete the triangles (any 2 points define a line).

Due to the fact that there are two triangles on either side of the point X, angle AXN is perpendicular to angle RXG. Angle AXN is equal to angle RXG because the vertical (opposite) angles formed by two intersecting lines are equal.

The following is how the SAS evidence of congruency is established:

Angle RXG in triangle RXG and angle AXN in triangle AXN are congruent (vertical angles)

Triangles AX in AXN and XG in RXG are congruent (midpoint X of line AG created these).

Triangle RXG and triangle AXN's NX and XR are congruent.

By SAS, triangles are congruent. this means they have two corresponding sides that are congruent and the angle between those 2 corresponding sides is congruent also.

To know more about congruency, visit;

https://brainly.com/question/7888063

#SJP9

Kate bakes 20-inch by 18-inch pan of cornbread and divide it into 2 in x 2 in pieces. The number of pieces is 90.

The problem can be solved using associative property in multiplication and division. That is the factors can re-group and it will not change the product.

The given problem can be translated into an algebraic expression:

(20 x 18) : (2 x 2)

Let

length of cornbread pan = 20

wide of cornbread pan = 18

To cut the cornbread 2 inches by 2 inches means we divide the length by 2 inches and the wide by 2 inches. Hence, the algebraic expression can be re-group into:

(20 x 18) : (2 x 2) = (20 : 2) x (18 : 2)

                           = 10 x 9 = 90

Hence, the pan contains 90 pieces of cornbread.

Complete question:

Kate bakes 20-inch by 18-inch pan of cornbread. the cornbread is cut into pieces that measure 2 inches by 2 inches. how many pieces of cornbread does the pan contain?

Learn more about associative property here:

https://brainly.com/question/28435728

#SPJ4

If a clock shows the hour hand between 6 and 7 and the minute hand at 10. It means : D.50 minutes after 6, E. 6:50

Each of the section time of an analog clock is 5 minutes. Since the hour hand is between 6 and 7 and the minute hand is on 10 ,  it implies that :

5 minutes × 10 minutes

= 50 minutes after 6

Or

6: 50minutes

Therefore the correct option is D and E.

Learn more about time here:https://brainly.com/question/24051741

#SPJ1

Four fifth times and eight ninth times would be simplified as 32/45.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.

To simplify four-fifth times and eight-ninth times, we have to use the fractions,

Simplifying, we get

                           [tex]=\frac{4}{5}* \frac{8}{9}\\\\=\frac{4*8}{5*9}\\\\\=\frac{32}{45}[/tex]

Hene, four fifth times and eight ninth times would be simplified as 32/45.

To learn more about fractions visit:

https://brainly.com/question/78672

#SPJ9

The multiplied form of the Algebraic expression is 10x -0.8[tex]x^{2}[/tex]

An algebraic expression is a mathematical statement that contains a combination of numbers, symbols, variables and mathematical operators.

These expressions may be linear, quadratic or polynomials and the numbers in front of each term is called coefficient while the symbols or letters are called variable

2x( 5 - 0.4x)

we multiply each term in the bracket by 2x

2x  x 5  - 2x x 0.4x = 10x - 0.8[tex]x^{2}[/tex]

In conclusion, 2x(5 - 0.4x) reduces to 10x - 0.8[tex]x^{2}[/tex]

Learn more about Algebraic expression: https;//brainly.com/question/2164351

#SPJ1

As we can conclude from the graphical method that this system has no common intersection point they have no solution.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given system of equations are x + 2y = 4, 3x + 6y = 6, 3x - y = 5 and

6x - 2y = 10.

The graphical representation of these equations are attached in the image below.

As we can observe , 3x - y = 5(green line)  and 6x - 2y = 10(purple line) are coinciding with each other so they have infinite no. of solutions.

x + 2y = 4(red) and 3x + 6y = 6(blue) are parallel to each other and hence have no solution.

And in together all these 4 lines have no common intersection point so they have no solution.

learn more abut the system of equations here :

https://brainly.com/question/24065247

#SPJ5