A sample of radium has a weight of 1.5 mg and a half-life of approximately 6 years.

a. How much of the sample will remain after 6 years?

Your salary in x years is modeled an the exponential growth

The equation that determines your salary in x years is y = 45000(1.05)^x

The model of the exponential growth is given as:

y = a(1 + r)^x

From the question, we have:

Initial salary, a = 45000

Raise, r = 5%

So, the equation becomes

y = 45000(1 + 5%)^x

Evaluate the sum

y = 45000(1.05)^x

Hence, the equation that determines your salary in x years is y = 45000(1.05)^x

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Answer:

See below, please

Step-by-step explanation:

[tex](2x + 9) + (4x - 3) = 90[/tex]

[tex]6x + 6 = 90[/tex]

[tex]6x = 90 - 6 = 84[/tex]

Hence

[tex]x = 14[/tex]

Answer:

152 hundred

Step-by-step explanation:

164 hundred - 12 hundred = 152 hundred

Please rate!

Answer:

1.52

Hope this helps :)

Step-by-step explanation:

step one:

put them as decimals which would be 1.64 and 0.12

step two:

subtract which would be 1.64 - 0.12

step three:

solve your answer would be 1.52 or 152 hundredths

[tex]❖\qquad\qquad\huge\underline{{\sf Answer}} \qquad \normalsize❖[/tex]

Let's simplify ~

[tex]\qquad \sf  \dashrightarrow \: \cos(x) \times \tan(x) \times \csc(x) [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cancel{ \cos(x) }\times \dfrac{ \cancel{ \sin(x)} }{ \cancel{ \cos(x) }} \times \dfrac{1}{ \cancel{\sin(x)} } [/tex]

[tex]\qquad \sf  \dashrightarrow \:1[/tex]

The equivalent value is 1

Answer:

134

Step-by-step explanation:

Gabriel has 56 cards and divides them evenly among 8 friends, which means each person has 56/8= 7 cards.

So Marcus has 127 + 7 = 134 cards

Answer:

8

----

125

Step-by-step explanation:

(2/5)³

2      2     2          8

--- x --- x ---  =  ---------

5      5     5         125

I hope this helps!

Answer:

1/16

Step-by-step explanation:

Place x=0 and you can see [tex]\frac{0}{0}[/tex] indefinitness. So you can apply the l'hosptial rule. Its basic you should

[tex]\lim_{x \to \ 0} \frac{g(x)}{f(x)} = \\[/tex]  [tex]lim_{x \to \ 0} \frac{g'(x)}{f'(x)}[/tex] so apply the derivative

[tex]\frac{\frac{1}{x-4} +\frac{1}{\sqrt[4]{(1-x})^3 } }{2x}[/tex] and replace the x=0 and you'll see same answer [tex]\frac{0}{0}[/tex] re-apply the l'hospital rule and answer

[tex]\frac{\frac{-1}{(x-4)^2} + \frac{3}{16\sqrt[4]{(1-x)^7} } }{2}[/tex] and replace the 0 you can see the answer [tex]\frac{1}{16}[/tex]

Answer:

first you distribute the five making it 10x-30+20=10

second you combine like terms making it 10x-10=10

third you isolate the variable making it 10x=20

Finally you divide both terms by ten giving you x=2 as your answer.

Answer:

5 startrood 3 endroot units .

The length of YA from the figure is 10√3 units

According to the pythagoras theorem;

YZ² = AZ² + YA²

Given that YZ = 2AZ, hence;

20²  = 10² + YA²

YA²  = 400 - 100
YA²  = 300

YA = √300

YA = 10√3 units

Hence the length of YA from the figure is 10√3 units

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Step-by-step explanation:

the area of a rectangle is

length × width

that is in our case

(x + 3) × 4.5 = 4.5x + 4.5 × 3 = 4.5x + 13.5

remember, when multiplying 2 expressions, you multiply every term of one expression by every term of the other expression and then you add all these individual results up by considering the signs, of course.

Answer:

120

Step-by-step explanation:

6p3 = 120

The number of the different combinations of the teams will be 26.

A permutation is an act of arranging objects or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.

Given that for a class activity, a teacher put students into teams of 5. The teams were made up of 2 students randomly chosen from group A and 3 students randomly chosen from group B. If group A has 4 students and group B has 6 students,

The number of possible combinations will be calculated as,

C = ⁶C₃ + ⁴C₂

C = ( 4 x 3 ) / 2 + ( 6x 5 x 4 ) /( 3x 2 )

C = 6 + 20

C = 26

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Answer:

d = 3

Step-by-step explanation:

According the figure:

Answer Check Below:

⇒ 10 + 3 = 13

⇒ 13 + 3 = 16

⇒ 16 + 3 = 19

Answer:

$3

Step-by-step explanation:

B for question 12

B for question 13

Step-by-step explanation:

U = Union

n= intercestion

B'= not b

A"= not a

so AnB'

should be B

if 2.50 = 1

2.50x8=

20

1×8 =

8

should be $8

Answer:

x ≤ 45

Step-by-step explanation:

x + 35 ≤ 80

  - 35    -35

x ≤ 45

I hope this helps!

Hello!

Let's solve this inequality.

x+35≤80

Subtract 35 from both sides:

x≤80-35

x≤45

It means "less than or equal to"

So all numbers less than or equal to will make this inequality true.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

Answer:

' =9 93/107 days

Step-by-step explanation:

1/11+1/24

one day =35/264

35/264 -1/32

=107/ 1056- fraction of rem in a day

1 day= 107/1056

x = 1

=107/1056x=1

x=1÷107/1056

1056÷107

=9 93/107 days

Answer:

XZ is longer than XY

Step-by-step explanation:

First we can notice all of the answers consist of knowing the lengths, so we must now find the lengths for each segment. To do this, we must use the pythagorean theorem.

(1, -1) and (-5, -5)

-5- -1 = -4

-5-1 = -6

-4^2+-6^2 = c^2

16+36 = c^2

52 = c^2

7.21110255 = c

So, the length of XZ is 7.21110255 units long

(1, -1) and (8, -2)

8-1 = 7

-2--1 = -1

7^2+-1^2 = c^2

49+1 = c^2

50 = c^2

7.07106781 = c

So, the length of XY is 7.07106781 units long.

XZ is longer than XY

Answer: First train speed shall be 42 mi/hr

Second train speed shall be 84 mi/hr

Yes it is the valid answer, it gets annoying when almost everyone enters the wrong answer for a good laugh. Either way, hope this helps! Have a spectacular day.

Step-by-step explanation:

What is the 1st train's head start in miles?

Let +s+ = the speed of the 1st train in mi/hr

From 2PM to 4PM is 2 hrs

+d%5B1%5D+=+s%2A2+

---------------------

Let +d+ = distance the 2nd train travels until

it overtakes the 1st train

From 4PM to 6PM is 2 hrs

Start time when the 2nd train leaves

---------------------

Equation for 1st train:

(1) +d+-+2s+=+s%2A2+

Equation for 2nd train:

(2) +d+=+%28+s%2B42+%29%2A2+

--------------------

Substitute (2) into (1)

(1) +%28+s%2B42+%29%2A2+-+2s+=+s%2A2+

(1) +2s+%2B+84+-+2s+=+2s+

(1) +2s+=+84+

(1) +s+=+42+

and

+s%2B+42+=+42+%2B+42+

+s+%2B+42+=+84+

------------------

The 1st train's speed is 42 mi/hr

The 2nd train's speed is 84 mi/hr

---------------------------

check:

(2) +d+=+%28+s%2B42+%29%2A2+

(2) +d+=84%2A2+

(2) +d+=+168+

and

(1) +d+-+2s+=+s%2A2+

(1) +d+-+2%2A42+=+42%2A2+

(1) +d+=+84+%2B+84+

(1) +d+=+168+

Answer: D

Step-by-step explanation:

21=7+6+neither-5

7+6=13-5=8

21-8=13

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

To obtain $4000 after two years, let A = 4000 and t = 2.

Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.

Substitute and solve for P:

[tex]\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}[/tex]

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

[tex]\displaystyle A = Pe^{rt}[/tex]

Where e is Euler's number.

Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:

[tex]\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}[/tex]

In conclusion, about $3692.47 should be deposited.

Jose's rectangle must have equal and parallel opposite sides

The coordinates of the other points could be C(7,5) and D(7,1)

The coordinates are given as;

A = (2,5).

B = (2,1).

To form a rectangle, each of the remaining points must have the same y-coordinates as points A and B.

So, we have:

C = (x,5)

D = (x,1)

Also, the remaining points must have the same x-coordinates.

i.e.

Cx = Dx

From the list of options, we have:

C(7,5) and D(7,1)

Hence, the coordinates of the other points could be C(7,5) and D(7,1)

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Answer:

2.4 kg

Step-by-step explanation:

1.5 divided by 5 is 0.3 and 0.3 multiplied by 8 is 2.4

Why did you ask this, but also answer it?- Lol thank you for the points though I guess...

Answer:

thank you they are all correct!

Step-by-step explanation:

The amount of oxygen in the flask through the intake tube illustrates proportions

The flask 99.35% will contain of oxygen after 5L have passed through the intake tube

To do this, we make use of the following representations

So. we have the following derivative

dP = dV - P * dV

Divide through by dV

dP/dV  = 1 - P

Next, we set up the integral

[tex]\int\limits^x_{0.040} \frac {1}{1 - P}dP= \int\limits^5_0 {dV}[/tex]

Integrate both sides

[tex]-\ln(|P - 1|)|\limits^x_{0.04} = 5[/tex]

Expand

-ln(|x - 1|) + ln(|0.04 - 1|) = 5

Evaluate the difference

-ln(|x - 1|) + ln(|-0.96|) = 5

Express as a fraction

ln(0.96/|x - 1|) = 5

Express both sides as exponents with a base of 2

e^ln(0.96/|x - 1|) = e^5

Solve for x

x = 1 - 0.96/e^5

Evaluate the difference

x = 0.9935

Express as percentage

x = 99.35%

Hence, the flask 99.35% will contain of oxygen after 5L have passed through the intake tube

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Answer:

3

Step-by-step explanation:

substitute x = - 2 into the expression

3x² - 9

= 3(- 2)² - 9

= 3(4) - 9

= 12 - 9

= 3

Answer:

B

Step-by-step explanation:

[tex]\sin{x}=\frac{5}{13}, \cos{x}=\sqrt{1-(\frac{5}{13})^2}=\frac{12}{13}[/tex]

[tex]\sin{y}=\frac{8}{17}, \cos{y}=\sqrt{1-(\frac{8}{17})^2}=\frac{15}{17}[/tex]

[tex]\cos(x+y)=\cos{x}\cos{y}-\sin{x}\sin{y}\\=\frac{12}{13}\times\frac{15}{17}-\frac{5}{13}\times\frac{8}{17}\\=\frac{140}{221}[/tex]

The computation of the percentage shows that the kilograms of seed that won't be watered is 12 kilograms.

Your information is incomplete. Therefore an overview will be given. Let's assume that the watered squares are 35 while the total squares are 50.

Then, the percentage of the watered squares will be:

= 35/50 × 100

= 70%

Therefore, the percentage of the unwatered squares will be:

= 100% - 70%

= 30%

Then, the kilograms of the seed that won't be watered will be:

= Percentage of unwatered seed × Entire kilograms of seed

= 30% × 40kg

= 12kg

In conclusion, the seed that won't be watered is 12 kg.

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Answer:

[tex] \frac{4(x - 5)(x + 7)(x - 12)}{(x + 1)(x)(x - 12)} [/tex]

Step-by-step explanation:

A rational function is

[tex] \frac{p(x)}{q(x)} [/tex]

where q(x) doesn't equal zero.

If p is a asymptote, or hole at that value, then we will use

[tex](x - p)[/tex]

Step 1: We have asymptote as 0 and -1 so our denomiator will include

[tex](x - 0)(x - ( - 1)[/tex]

Which is

[tex](x)(x + 1)[/tex]

So our denomator so far is

[tex] \frac{p(x)}{x(x + 1)} [/tex]

Step 2: Find Holes.

Since 12 is the value of the hole,

[tex](x - 12)[/tex]

is a the binomial.

This will be both on the numerator and denomator so qe have

[tex] \frac{(x - 12)}{x(x + 1)(x - 12)} [/tex]

Step 3: Put the x intercepts in the numerator.

Since 5 and -7 is the intercepts,

[tex] \frac{(x - 12)(x - 5)(x + 7)}{x(x + 1)(x - 12)} [/tex]

Step 4: Horinzontal Asymptotes,

Multiply the numerator and denomiator out fully,

[tex] \frac{ {x}^{3} - 10 {x}^{2} - 59x + 420 }{ {x}^{3} - 12 {x}^{2} + x - 12} [/tex]

Take a L

look at the coefficients,

Notice they have the same degree,3, this means if we divide the leading coefficents, we will get our horinzonral asymptote.

Multiply the numerator by 4.

[tex] \frac{4(x - 12)(x - 5)(x - 7)}{x(x + 1)(x - 12)} [/tex]

Above is the function,

Explanation:

The distributive property tells you that multiplication distributes over addition. In equation form, it looks like ...

  a(b +c) = ab +ac

__

The parentheses are a grouping symbol. In the above equation, they indicate that the sum (b+c) is to be treated as a group. When it is multiplied by 'a', everything in the group is multiplied by 'a'.

In the real world, there are many ways things are grouped. Baseball cards are packaged together with bubble gum; Cracker Jacks® are packaged together with a prize; left gloves are packaged together with right gloves; a bicycle is a package that has a frame, 2 wheels, a seat, handlebars. If you purchase a number of any of these packages, each of the items in the package is part of your purchase that number of times.

For example, 3 bicycles will have 3 frames, 3×2 = 6 wheels, 3 seats, 3 sets of handlebars. In algebraic form, this might look like ...

  3(f +2w + s + h) = 3f +6w +3s +3h

__

Using the distributive property to eliminate parentheses is like regrouping the contents of the packages so like items are grouped together. In our above example, the 3 frames were grouped together when we considered that part of the group of 3 bicycles. The multiplier multiplies every member of the group.

__

The reverse of the distributive property tells us we can regroup items into sets. It tells us we can take 3 frames, 6 wheels, 3 seats, and 3 handlebars and group them together in a way that makes 3 bicycles, each having a frame, 2 wheels, a seat, and handlebars.

  3f +6w +3s +3h = 3(f +2w + s + h)

Often, we're asked to choose the multiplier to be the greatest common factor (GCF) of the numbers of things in the group. That makes each group as small as possible. The multiplier only needs to be a common factor, not necessarily the greatest common factor.