When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of a radioactive isotope initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?

Answer:

y = 4x - 1.5

Step-by-step explanation:

We need to find the slope (m) and the y-intercept (b), if we are writing this in the slop intercept form of a line.

y =mx + b

The slope is the change in y over the change in x.

The two points give us the y's ad x's

The y's are: -1.5 and 2.5

The x's are: 0 and 1

[tex]\frac{-1.5 - 2.5}{0-1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4  A negative divided by a negative is a positive.

We have the slope.  The slope is the point (0,b).  We are given that point.

(o, -1.5)  The y-intercept is -1.5

y =mx + b

y = 4x - 1.5

The graph of the equation is attached to the solution.

We can graph the equation of the line by finding the x and y intercept of the line.

We know that the equation is in the slope intercept form.

Hence, we can write the y-intercept of the line as 2.

The coordinates of the point will be (0,2).

To find the x - intercept, we can put y = 0

0 = 2x + 2

-2 = 2x

x = -2/2 = -1

x = -1

The coordinates of the point will be (-1,0).

We can find another point on the line.

Let x = 1

y = 2(1) + 2

y = 2 + 2

y = 4

The coordinates of the point will be (1,4).

We can plot these points on the graph and get our graph.

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The given function F(x) is,

Take the limit of the function when x ix close to 2.

Hence, the function diverges.

Using proportions, two ways of writing the fraction of these books that you read is:

4/12 and 1/3.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication or division.

One example of application of proportions is for relative frequencies, as a relative frequency is given by the number of successes in the sample divided by the sample size.

In the context of this problem, it is found that:

Hence the relative frequency is:

4/12.

12 is divisible by 4, hence the fraction can be simplified as follows:

1/3.

The number of books is missing, and is of 12. (researching the problem on a search engine).

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Let

x -----> number of rides

y ----> the total cost

so

The linear equation that represents both situations are

y=40 -----> equation A

y=x+15 ----> equation B

equate both equations

40=x+15

solve for x

x=40-15

x=25

therefore

Average speed is 35.56 mph.

Calculating average speed involves dividing the whole distance travelled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time. Average speed refers to the average speed during the course of a journey.

We have to find the average speed of the whole journey.

First we have to find total distance for whole journey and then total time for whole journey.

Total distance for whole journey = 30 miles + 50 miles = 80 miles

Time for 30 miles = distance/speed = 30/40 = 3/4 hrs  = 0.75 hrs

Total time = 1.5 + 0.75 hrs = 2.25 hrs

Average speed =  total distance/ total time

= 80/2.25

= 35.56 mph.

The average speed is 35.56 mph.

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Solution

For this case we can do the following:

tan x = 35/30

And we can solve for x and we got:

And rounded to the nearest degree is:

49º

Solution:

Given that;

To find the amount in 5 years, we will apply the compound interest formula below

Substitute the values of the variables into the formula above

Hence, the answer is B

We are given

Therefore the value of x can be gotten by simplifying the above equation

Given that x is 5, we can proceed to find the value of the expression.

This implies that

Answer:

(I) y=10-6x. (ii) y=x/-2 - 3

The probability that, before the low fuel light comes on the car will travel is 0.2576

Given,

The average number of miles driven on a full tank of gas before its low fuel light comes on is ( μ )= 320

It follows the standard deviation of ( δ ) = 30

For the normal distribution,

P(X < x) = P( Z < x - μ / δ)

a)

P( X < 330) = P( Z < 330 - 320 / 30)

                   = P( Z < 0.3333)

                   = 0.6306

b)

P( X > 308) = P( Z > 308 - 320 / 30)

                  = P( Z > -0.4)

                  = P( Z < 0.4)

                  = 0.6554

c)

P( 305 < X < 325) = P( X < 325) - P( X < 305)

                             = P( Z < 325 - 320 / 30) - P( Z < 305 - 320 / 30)

                             = P( Z < 0.1667) - P( Z < -0.5)

                             = 0.5662 - ( 1 - 0.6915)

                             = 0.2576

d) P(X = 340) = 0

Since X is a continuous random variable (For normal distribution).

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The formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is  M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .

in the question ,

it is given that the

formula to find , "gravitational  force" between two objects is

[tex]F_{g}[/tex] = (G*M₁*M₂)/r²

to express the formula in terms of M₁ ,

we first multiply both the sides by r² ,

on multiplying , we get

[tex]F_{g}[/tex]*r² = G * M₁ * M₂

On dividing both sides by G ,
we get

( [tex]F_{g}[/tex]*r² ) /G = M₁ * M₂

we have to find the formula for M₁ ,

we divide both sides  by M₂,

So , on dividing both  sides by M₂ , we get

( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) = M₁

hence M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ )

Therefore , the formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is  M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .

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If I'm not mistaken, the answer is 43.17

Plug in the values in the right positions. And simplify.

[tex] = \frac{1}{2} (12 \times \frac{1}{4} ) - \frac{1}{2} \\ = \frac{1}{2} (3) - \frac{1}{2} \\ = \frac{3}{2} - \frac{1}{2} \\ = \frac{2}{2} \\ = 1[/tex]

OPTION C IS THE ANSWER .

Answer:

mA = 69 degrees

Step-by-step explanation:

A complementary angle has a measure of 90 degrees.

(2x + 27) + (2x - 21) = 90

Simplify

4x + 6 = 90

-6

4x = 84

/4

x = 21

mA: 2(21) + 27 = 69

Answer:

A = 69°

Step-by-step explanation:

Complementary angles sum 90°

A + B = 90°

(2x + 27) + (2x-21) = 90°

4x + 27 - 21 = 90°

4x + 6 = 90°

4x = 90 - 6

4x = 84°

x = 84°/4

x = 21

Then A:

A = 2x + 27

A = 2*21  +  27

A = 42 + 27

A = 69°

B = 2x - 21

B = 2(21)  + 27

B = 42 - 21

B = 21°

Check:

69 + 21 = 90

Answer:

7

Step-by-step explanation:

Let x be the "integer."  We'll assume it is odd.

The next consecutive odd integer would be x+2.

(2(x+2) - x) =9    [When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9]

(2(x+2) - x) =9

(2x+4) - x) =9

x+4 =9

x = 5

The greater integer is x+2 or 7

Check:

If 5 is subtracted from 2 times the next consecutive odd integer, 7, is the difference 9?

2*7 - 5 = 9?

14 - 5 = 9?

14 - 5 = 9?  YES

The coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0)

Function translation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape.

Given is a triangle coordinate on x - y plane.

The rule (x, y) → (- x, - y) represents the rotation of a figure by 180 °.

Now, initially the coordinates of the triangle are -

(-2, 2) , (-3, 8) , (-7, 0)

After transforming the graph by the rotation of 180°, the new coordinates will be -

(2, - 2) , (3, -8) , (7, 0)

Plot the coordinates on the graph and you will get the rotated image.

Therefore, the coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0).

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For the given function

The sum of all angles = 360°

So,

So, the difference between x and y will be:

So, the answer will be:

∠x is 91° smaller than ∠y

The answer is not 1 so it is not that simple that you can divide it into 2 equal size subsets and ask whether the final sequence is in there. From what I got through his hints, it should be related to Central Limit theorem.

Given that,

One hundred coins are flipped, but the outcome is kept a secret. I am able to pose one yes/no query. I'll begin speculating on the outcomes of the coin toss following the response. I receive $1 for each accurate guess, and I lose $1 for each unreliable guess.

To find:

What is the most effective gaming approach and what is the highest possible return on investment

By Central Limit Theorem,

It is not straightforward to divide the response into two subsets of equal size and then check to see if the final sequence is present because the answer is not 1. His indications led me to believe that it should be connected to the Central Limit theorem.

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In this equation the solution for x in terms of a and b is 8.

What is equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Sol- As per the question given that- ax-3= bx+5------(equation 1)

Let ax=3-----(equation 2)

And bx =5------(equation 3)

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

(ax)+(bx)= 3+5

(ax)+(bx)=8

x(a+b)+y(a+b)=8

(x+y)+(a+b)=8

1×(a+b)=8

Thus

a+b=8

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Using the information of the factors f ( x ) are

The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include

The given function is substituted in the several equations given but the equations that yielded the desirable result of f ( x ) = 0 are:

Therefore they are the correct choice

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Answer:  m=1/5

Step-by-step explanation:

Answer:

x-intercept (-2,0)

y-intercept (0,-3)

Step-by-step explanation:

to find the x-intercept we set y=0

so 3x=-6

x=-2

to find the y-intercept we set x=0

so 2y=-6

y=-3

Solution:

Let the score for the seventh test be represented below as

The mean score t be attained after the sevent tests is

The scores from the 6 tests are given below as

To figure out the seventh score, we will do the calculation below

Hence,

The final asnwer is

The value of x in the right triangle is 15√2.

A right triangle is a triangle that has one of its angles as 90 degrees.

The sides of a right triangle can be named base on the angle position. This includes hypotenuse side, opposite side and adjacent side.

Therefore, the side x of the right triangle can be found using trigonometric ratios as follows:

cos 45 = adjacent / hypotenuse

cos 45° = x / 30

cross multiply

30 cos 45° = x

Therefore,

x = 30 × 1 / √2

x =  30 / √2 × √2 / √2

x = 30√2 / 2

x = 15√2

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- 5 < x < 5

Number line:

The coordinates of the point C on the line AB such that AC is 2/3 the length of AB is (3,6) .

In the question ,

it is given that

the coordinates of the end points of A and B is A(-1,2) and B(5,8) .

also AC = 2/3(AB)

So , AC/AB = 2/3

and given that point C is on the line AB , hence AC+CB=AC

2+CB=3

So , CB=1

hence AC/CB = 2/1

so , the point C divides the line AB in the ration 2:1 .

and we have the coordinates of end points ,

that is x₁[tex]=[/tex] -1 , y₁=2 and x₂=5 , y₂ = 8 and the ratio m=2 and n=1 .

Substituting the above values in the section formula ,

which states that the coordinate of point C will be

((m*x₂+n*x₁)/(m+n)  ,  (m*y₂+n*y₁)/(m+n))

= ((2*5+1*(-1))/(2+1) , (2*8+1*2)/(2+1))

= ((10-1)/3 , (16+2)/3)

= (9/3 , 18/3)

= (3,6)

Therefore , The coordinates of the point C on AB such that AC is 2/3 the length of AB is (3,6) .

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Answer:

A. [tex]9n - 190 = 5n[/tex]

Step-by-step explanation:

Dora earning 5 dollars per song is represented by [tex]5n[/tex].

Gary earning 9 dollars a song but paying the $190 fee is represented by [tex]9n - 190[/tex] because the fee from the coffee shop is subtracted from his total earnings.

Answer:

Angles gh, fh,  and jh are perpendicular :)

Step-by-step explanation:

perpendicular is when line touch and they make a 90* angle and the three angles that i have listed all touch and make 90*

The proof of (g/n)/(g/m) isomorphic to g/m from the first isomorphism theorem is as shown below.

Let a group g with normal subgroups m and n. Furthermore, n is a subset of m.

Proof: We have to prove (g/n)/(m/n) ≅ g/m           (1)

g/m and g/n are valid because m and n are normal in g. As normality satisfies the intermediate subgroup condition, n is normal in m. because normality is image-closed m/n is a normal subgroup in g/n. Under the quotient map by n, the normal subgroup m of g is sent to a normal subgroup m/n of g/n. Thus the L.H.S of the statement to prove makes sense.

To describe the isomorphism from the left side to the right side

φ: g/n \to g/m

ψ(gn) = gm

So, a coset of n is taken by the map and it gives the corresponding coset of m. This is well-defined, because if h∈ n, thus h∈ m, hence (gh)m = g(hm) = gm.

The map is a homomorphism. So we observe that it maps the identity element to the identity element, keeps group multiplication preserved, and also preserves the inverse map.

Also, the map is surjective because any coset gm is present as the image of gn under ψ.

Lastly, we need to find the kernel of the map which is given by the set of gn such that gm = m. This is those cosets of n that are in m, and this is the same as the coset space m/n. Thus the kernel of the map is exactly g/m. Thus, the surjective homomorphism ψ: g/n → g/m has kernel m/n. And now by the first isomorphism theorem

(g/n)/(m/n)≅g/m     where ≅ shows isomorphism

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