The half-life of cobalt-60 (used in
radiation therapy) is 5.26 years (actual
data). How much of a 200 g sample of
cobalt-60 will remain after 26.3 years?

AnswEr :

Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .

⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]

⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.

[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]

Therefore ,

When , x = 2 ,

When , x = –7 ,

Answer:

Hi,

Step-by-step explanation:

If the "is" means is equal to

Let's say a-1, a, a+1 the 3 consecutive integers.

[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]

[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]

The two sets are : (0,1,2) and (4,5,6).

Answer:

Graph D

Step-by-step explanation:

Move the constant to the opposite side of the equation and group terms that include the same variable.

g(x) + 1 = x^2 + 2x

Finish the square. Remember to keep the equation balanced by using the same constants on both sides.

g(x) + 1 + 1 = x^2 + 2x + 1

g(x) + 2 = x^2 + 2x + 1

Rewrite as perfect squares

g(x) + 2 = (x + 1)^2

Equation in vertex form:
g(x) = (x + 1)^2 - 2

The vertex:

(-1, -2)

* This a minimum *

You need to find the least common multiple of 8 and 6.

[tex]8=2^3\\6=2\cdot3\\\\\text{lcm}(8,6)=2^3\cdot3=24[/tex]

Therefore, the answer is 24 days.

Answer:

good and right and keep trying your best

Answer:

10 m

Step-by-step explanation:

opposite = sin30° × 20 = [tex]\frac{1}{2}[/tex] × 20 = 10 m

The maximum value of the objective function is 330

The given parameters are:

Max w = 5y₁ + 3y₂

Subject to

y₁ + y₂ ≤ 50

2y₁ + 3y₂ ≤ 60

y₁ , y₂ ≥ 0

Start by plotting the graph of the constraints (see attachment)

From the attached graph, we have:

(y₁ , y₂) = (90, -40)

Substitute (y₁ , y₂) = (90, -40) in w = 5y₁ + 3y₂

w = 5 * 90 - 3 * 40

Evaluate

w = 330

Hence, the maximum value of the function is 330

Read more about objective functions at:

https://brainly.com/question/26036780

#SPJ1

Answer:

if a scale factor is less than 1 then your figure gets smaller

Step-by-step explanation:

The probability of Ryan winning a prize would be 0.71.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Ryan is on a game show. He will choose a box to see if he wins a prize.

The odds in favor of Ryan winning a prize are 5/7.

P(Ryan wins a prize) = 5/7 = 0.71

Thus, the probability of Ryan winning a prize would be 0.71.

Learn more about probability here;

https://brainly.com/question/11234923

#SPJ1

Hi student, let me help you out! :)

.  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We need to translate "five times the sum of a number and -23" into an algebraic expression.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So in this case we should add a number (let it be x) and -23:

[tex]\star~\large\pmb{x+-23}[/tex]

Which is the same thing as

[tex]\star~\large\pmb{x-23}[/tex]

Now we multiply this little expression by 5, which gives us

[tex]\star~\large\pmb{5(x-23)}[/tex]

The parentheses around the  expression indicate that we multiply 5 by the entire expression, and not just one term.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

a=11,b=7 Is the correct answer

Please mark me as brainliest

Answer:

a = 11 and b = 7

Step-by-step explanation:

Multiply numerical values 5 x (-4) then add exponents of like terms x⁷(x⁴) = x¹¹ then y²(y⁵) = y⁷

Explanation:

Pick any term. Subtract off the previous one to find the common difference.

And so on. You only need to pick one of those to show as your steps to your teacher. However, doing all three subtractions is a good way to get practice in seeing how we have an arithmetic sequence. The common difference must be the same each time.

We subtract 7 from each term to get the next term, i.e. we add -7 to each term to get the next one.

Answer:

There are 0 solutions to this problem because it cannot be re-arranged logically enough to come to a new conclusion.

Answer:

0

Step-by-step explanation:

If we try to solve this question, we get no solutions:

First we subtract 5 from both sides :

9x = 9x + 2

Now we subtract 9x from both sides :

0 = 0 +2

0 = 2 ❌

This is why this equation has no solutions

Hope this helped and have a good day

The y-intercept of g(x) is (0, -3) and there are no asymptotes for g(x).

The function is given as g(x) = 2x - 3 and we need to find the y-intercept and the asymptote of this function g(x).

Y-intercepts of a given function are the points on the y-axis that the given function passes through.

In y-intercept points we always have x=0.

Asymptotes are straight lines on the graph that meets the given function as it moves towards infinity.

Asymptotes occur only when the given function is a rational function or when one term of the function approaches zero as one term approaches infinity.

Find the y-intercept of g(x).

We have,

g(x) = 2x - 3

Since x = 0.

we get,

g(x) = 0 - 3

g(x) = -3 or y = -3

Thus the y-intercept of g(x) is (0, -3)

Find the asymptotes of g(x).

We see that g(x) is not a rational function and when x approaches infinity g(x) does not approach zero.

Hence we can say that g(x) has no asymptotes.

The y-intercept and asymptotes of g(x) are (0, -3) and no asymptotes.

Learn more about asymptotes of a given function here:

https://brainly.com/question/27861449

#SPJ5

To find the y-intercept of g(x), we set x = 0 and solve for y:g(0) = 2^0 - 3 = -2Therefore, the y-intercept of g(x) is (0, -2).To find the asymptote of g(x), we take the limit of g) as x approaches negative or positive infinity:lim x→-∞ 2^x - 3 = -3 (the asymptote is y = -3 as x approaches negative infinity)lim x→+∞ 2^x - 3 = +∞ (the graph of g(x) goes arbitrarily high as x approaches positive infinity, so there is no horizontal asymptote)Therefore, the asymptote of g(x) is y = -3.

Answer:

-10 6/11

Step-by-step explanation:

16/11−12/1=16/11+−12/1=16/11+−132/11=16+−132/11=−116/11

-116/11 = −10 6/11

Answer:

square root function; y = -√(x + 2) - 1

Step-by-step explanation:

the graph shown is a square root function

the parent of a square root function is y = √x

you transform this equation using y = a√(x - h) + k

it is reflected across the x axis so you put the negative before the a

since there is no dilation the a is blank

y = -√(x - h) + k

the h is the horizontal shift

it went 2 to the left so that is -2

that makes it y = -√(x - -2) + k

which is also y = -√(x + 2) + k

the k is the vertical shift

it went 1 down

that makes it y = -√(x + 2) - 1

that is your equation

Answer:

The problem is with the arrangement of the ratios

PQ is the whole line but PR is a part of it only so you need QR to the ratio of PR

Answer:

[tex]\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. To find f(0.5), substitute the x value in the function f(x) with 0.5

            f(x) = 30x + 5

          f(0.5) = 30*0.5 + 5

                    = 15 + 5

                    = 20

At 0.5 gigabytes of data used, the cost is  $20

2)  g(x) = 10x + 20

g(0.5) =  10*0.5 + 20

           = 5 + 20

           = 25

At 0.5 gigabytes of data used, the cost is $ 25.

3)          f(x) = 50

    30x + 5  = 50

Subtract 5 from both sides

            30x = 50 - 5

            30x = 45

Divide both sides by 30

                x = 45/30

             x = 1.5

If she chooses plan 'f', she could use 1.5 gigabytes.

         g(x) = 50

   10x + 20 = 50

            10x =50- 20

            10x = 30

                x = 30/10

              x = 3

If she chooses plan 'g', she could use 3 gigabytes.

4) Function 'g' would be better for a $50 monthly budget as she could get more gigabytes than function 'f'

If the diameter is d = 8, then we divide that in half to get the radius of r = 4.

If the radius is r = 9, then we double it to get the diameter of d = 18

The formulas are:

I'll let you determine the others.

Answer:

Step-by-step explanation:

Diameter is twice the radius.  d = 2*r

Radius is half the diameter r = d÷2

 1) d = 8

      r = 8÷ 2

      r = 4

2) r = 9

   d = 2*r

       = 2*9

   d = 18

3) r = 24

   d = 24*2 =48

4) d = 36

   r = 36 ÷2 = 18

5) d = 52

      r = 52÷2 = 26

Step-by-step explanation:

4a(a-x)+x(a-x)

[4a]2-4ax+ax-(x)2

(4a)2-3ax-(x)2

Answer:

4x^2 - 4x - 3

Step-by-step explanation:

f(x) = 2x - 1

g(x) = x^2 - 4

g(f(x)) = ?

[substitute the x of g(x) with f(x)]

g(x) = x^2 - 4

g(f(x)) = (2x - 1)^2 - 4

[solve]

[binomial * binomial = quadratic equation]

[use FOIL method (first, outer, inner, last)]

g(f(x)) = (2x - 1)(2x - 1) - 4

g(f(x)) = (2x*2x) + (-2x) + (-2x) + (1) - 4

[combine like terms]

g(f(x)) = 4x^2 - 2x - 2x + 1 - 4

g(f(x)) = 4x^2 - 4x - 3

Answer:

Step-by-step explanation:

we are given a right triangle and the measure of its two legs .

x represents the length of the hypotenuse.

……………………………………………………………………

Then (by applying the Pythagorean theorem) we obtain :

[tex]x=\sqrt{24^{2}+7^{2}}[/tex]

  [tex]=\sqrt{576+47}[/tex]

  [tex]=\sqrt{625}[/tex]

  [tex]=25[/tex]

Answer:

Step-by-step explanation:

for any variable to be eliminated in a simultaneous equation, the one of the coefficients must be the same in the two equations. and:

FOR OPTION A

if the first equation is multiplied by 3 , we will be having 12x-27y= 24 as the new equation 1 and since the cofficient of y or x are different in equation 1 and 2, no variable can be eliminated.

FOR OPTION B

if the second equation is multiplied by 2, our new equation 2 will be 4x+6y= 48. here, the cofficient of x in the two equations are now the same but since we're going to add, 4x+4x = 8x which does not eliminate x

FOR OPTION D

if the second equation is multiplied by three, our new equation 2 becomes 6x+9y= 72 and subtracting,-9y -9y= -18y which does not eliminate y

Answer:

84.

Step-by-step explanation:

mean = total of the values  / number of numbers

If the total of the numbers = T:

14 = T / 8

T = 8*14 = 84.

The surface area of the given shape is 285.01 ft²

From the question, we are to calculate the surface area of the given shape.

The given shape in the diagram is a cone.

The surface area of a cone is given by the formula,

[tex]S = \pi r(r+l)[/tex]

Where S is the surface area

r is the radius

and [tex]l[/tex] is the slant height

First, we will calculate the slant height of the cone

[tex]l^{2}=9^{2} +5.6^{2}[/tex] (Pythagorean theorem)

[tex]l^{2}=81+31.36[/tex]

[tex]l^{2}=112.36[/tex]

[tex]l}=\sqrt{112.36}[/tex]

[tex]l=10.6 \ ft[/tex]

∴ The slant height is 10.6 ft

Now, for the surface area

[tex]S = \pi \times 5.6(5.6+10.6)[/tex]
[tex]S = \pi \times 5.6(16.2)[/tex]

[tex]S = 90.72\pi \ ft^{2}[/tex]

[tex]S = 285.0053 \ ft^{2}[/tex]

S ≅ 285.01 ft²

Hence, the surface area of the given shape is 285.01 ft²

Learn more on Calculating surface area of a cone here: https://brainly.com/question/27812847

#SPJ1

Answer:

increasing to the certain point

Step-by-step explanation:

Potato head

I'll focus on question 10 only. Let me know if you need me to answer the others.

We have the population with this set of numbers: {2,4,6,8,10}

There are 5 values in that set.

Now consider having slots labeled A,B and C to represent the three placeholders for the numbers.

There are 5*4*3 = 20*3 = 60 permutations and 60/(3*2*1) = 60/6 = 10 combinations.

Therefore, we have 10 different subsamples of 3 items.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6000\\ P=\textit{original amount deposited}\\ r=rate\to 9.5\%\to \frac{9.5}{100}\dotfill &0.095\\ t=years\dotfill &2 \end{cases} \\\\\\ 6000=P[1+(0.095)(2)]\implies \cfrac{6000}{1.19}=P\implies 5042.02\approx P[/tex]

The domain is [tex]x \le 5[/tex] and the range of the function is [tex]f(x) \ge - 3[/tex]

The function is given as:

[tex]f(x) = \sqrt{5 - x} - 3[/tex]

The radicand must be at least 0.

So, we have:

[tex]\sqrt{5 - x} \ge 0[/tex]

Square both sides

[tex]5 - x \ge 0[/tex]

Rewrite as:

[tex]5 \ge x[/tex]

Solve for x

[tex]x \le 5[/tex]

This means that the domain is [tex]x \le 5[/tex]

For the range, we have; [tex]\sqrt{5 - x} \ge 0[/tex]

This means that:

[tex]f(x) \ge 0 - 3[/tex]

[tex]f(x) \ge - 3[/tex]

Hence, the range of the function is [tex]f(x) \ge - 3[/tex]

Read more about domain and range at:

https://brainly.com/question/10197594

#SPJ1

Answer:

B

Step-by-step explanation:

A dog might be around
b) 25 kgs