The levels of mercury in two different bodies of water are rising. In one body of water the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year.

For this case we have by definition of properties of powers that:

To multiply powers of the same base, the same base is placed and the exponents are added. Also:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Now, applying the above properties, we can rewrite the given expression as:

[tex]3 ^ {-3-5} = 3 ^ {- 8} = \frac {1} {3 ^ 8}[/tex]

ANswer:

[tex]\frac {1} {3 ^ 8}[/tex]

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For this case, we must simplify the following expression:

[tex]\frac {(x + 8)} {4} - \frac {(x + 5)} {4}[/tex]

They are fractions with the same denominator, they can be subtracted in the traditional way. We must bear in mind that the law of the signs of multiplication states:

[tex]- * + = -[/tex]

So:

[tex]\frac {(x + 8)} {4} - \frac {(x + 5)} {4} = \frac {x + 8-x-5} {4} = \frac {x-x + 8- 5} {4} = \frac {3} {4}[/tex]

ANswer:

Option C

Answer:

#3) 72; #4) 40,320; #5) 90.

Step-by-step explanation:

#3) The number of possible choices are found by multiplying the choices of flavors and the choices of toppings:

6*12=72.

#4) The ordering of 8 cards is a permutation, given by 8!=40,320.

#5) This is a permutation of 10 objects taken 2 at a time:

P(10,2) = 10!/(10-2)!=10!/8!=90.

P.S I had the same question once.

The number of choices which are possible for a single serving of frozen yogurt with one topping from a yogurt shop is 72.

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.

The number of possible ways to arrange is the n!. Here, n is the number of objects.

Let n is the total choices of selecting  6 different flavors of frozen yogurt and 12 different toppings. Thus,

n=6 x 12

n=72

These choice is equal to the possible choices for a single serving of frozen yogurt with one topping.

Thus, the number of choices which are possible for a single serving of frozen yogurt with one topping from a yogurt shop is 72.

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Answer:

1.5 pound of beans are in each bag

Step-by-step explanation:

12/8=1.5

1.5 pounds of beans are in each bag.

Diving 12 by 8 will give you 1.5, the total number of pounds in any given cup. You can check this by multiplying 8 by 1.5, which gives you one-and-a-half pounds.

Answer:

R= q+c over 5y

Step-by-step explanation: Good luck sweetie!!

well I know for a fact that the equation for a parabola is

[tex]ax^{2} + bx + c[/tex]

so obviously it is an equation for an ellipse, sadly I am not exactly sure whether the answer is b or c.(I'm leaning towards b)

hopefully I helped out by eliminating 2 options.

Brainliest people comment what the answer is!!!!

Have a great day

Answer:

Option d)

[tex]3x^2+y^2+6x-6y+3=0[/tex]

Step-by-step explanation:

we are given with the equation

[tex]3x^2+y^2=9[/tex]

Dividing both sides by 9 and simplifying we get

[tex]\frac{x^2}{3}+\frac{y^2}{9}=1[/tex]

[tex]\frac{x^2}{(\sqrt{3})^{2}}+\frac{y^2}{3^{2}}=1[/tex]

Which represents an ellipse. Hence we have an ellipse in our problem. And also  it is obvious that any translation or rotation of this ellipse will again result into en ellipse.

If we see the first two options , they are the equations of the parabolas hence they can not be answer to the problem.

Let us see the third equation.

It is

[tex]3x^2+y^2+3x-3y+3=0[/tex]

Let us transform this equation in perfect square form.

[tex]3x^2+3x+y^2-3y+3=0[/tex]

[tex]3(x^2+x)+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x^2+x+\frac{1}{4}-\frac{1}{4})+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x^2+x+\frac{1}{4})-3\times\frac{1}{4}+y^2-3y+\frac{9}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x+\frac{1}{2})^{2}+(y+\frac{3}{2})^{2}-3\times\frac{1}{4}-\frac{9}{4}+3=0[/tex]

[tex]3(x+\frac{1}{2})^{2}+(y+\frac{3}{2})^{2}=0[/tex]

Which represents the equation of an circle , Although Circle also comes in the category of an ellipse but it clearly not the same as we have in the problem in which the minor and major axis are different.

Hence this is also not our answer. So we have a clue that as the first three options are not correct , the right answer must be the forth one. Let us confirm it by converting it into a perfect square.

The equation given is

[tex]3x^2+y^2+6x-6y+3=0[/tex]

[tex]3x^2+6x+y^2-6y+3=0[/tex]

[tex]3(x^2+2x)+y^2-6y+9-9+3=0[/tex]

[tex]3(x^2+x+1-1)+y^2-6y+9-9+3=0[/tex]

[tex]3(x^2+x+1)-3+y^2-6y+9-9+3=0[/tex]

[tex]3(x+1)^{2}+(y-3)^{2}-3-9+3=0[/tex]

[tex]3(x+1)^{2}+(y-3)^{2}-9=0[/tex]

[tex]3(x+1)^{2}+(y-3)^{2}=9[/tex]

Which certainly represents an ellipse. hence this is our correct answer.

Answer:

[tex]82,8m^2 = S.A[/tex]

Step-by-step explanation:

Area of a Rectangle: [tex]hb\:or\:wb = A[/tex]

Area of a Triangle: [tex]\frac{1}{2}hb; \frac{1}{2}bh, or\: \frac{hb}{2} = A[/tex]

Need to know

- Two small triangles

- Two big triangles

12m² = Rectangle

26,4m² EACH = Big Triangles

9m² EACH = Small Triangles

[tex]2[9] + 2[26,4] + 12 = 18 + 52,8 + 12 = 82,8[/tex]

So, the surface area of the rectangular pyramid is 82,8m².

* The answer is not 85,31 because this rectangular pyramid has two slant heights. If we ONLY had 9 as ONE SLANT HEIGHT, then the answer would have been 85,31, otherwise it is incorrect.

I am joyous to assist you anytime.

Answer:

in the graph

Step-by-step explanation:

the function g(t)= sin t is a periodic function with amplitude a0= 1 and period T0=2[tex]\pi[/tex]

For our case, the 5 that multiplies g (t) increases the amplitude so that a = 5 * 1 = 5 and  the 3 that multiplies the variable increases the period being T = 2[tex]\pi[/tex]*1/3 = 2[tex]\pi[/tex]/3

Answer:

The answer is B.

[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\[/tex]

[tex]\bf cos(x)cos\left( \cfrac{\pi }{7} \right)+sin(x)sin\left( \cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2}\implies cos\left( x-\cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2} \\\\\\ x-\cfrac{\pi }{7}=cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies x-\cfrac{\pi }{7}= \begin{cases} \frac{3\pi }{4}\\\\ \frac{5\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf x-\cfrac{\pi }{7}=\cfrac{3\pi }{4}\implies x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n} \\\\[-0.35em] ~\dotfill\\\\ x-\cfrac{\pi }{7}=\cfrac{5\pi }{4}\implies x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n}[/tex]

[tex]

d=295

t=120

s=d\div t= 295\div120\approx2.46\frac{\text{ft}}{\text{s}}

[/tex]

Answer:

DDDDDDDDDDD for sure...

D it might look as if it were B but if it was you would cross multiply so it’s definitely D

The volume of each sample is 0.10 liters of water from each water sample

Answer:

The name of the polygon is rectangle

Step-by-step explanation:

* Lets find the slope of the four sides and the length of two adjacent

 side to know what is the name of the figure

∵ The vertices are (1 , 3) , (3 , 4) , (5 , 0) , (3 , -1)

∵ The rule of the slope of a line which passes through the points

  (x1 , y1) and (x2 , y2) is m = (y2 - y1)/(x2 - x1)

- Let (x1 , y1) is (1 , 3) and (x2 , y2) is (3 , 4)

∴ m1 = (4 - 3)/(3 - 1) = 1/2

- Let (x1 , y1) is (3 , 4) and (x2 , y2) is (5 , 0)

∴ m2 = (0 - 4)/(5 - 3) = -4/2 = -2

- Let (x1 , y1) is (5 , 0) and (x2 , y2) is (3 , -1)

∴ m3 = (-1 - 0)/(3 - 5) = -1/-2 = 1/2

- Let (x1 , y1) is (3 , -1) and (x2 , y2) is (1 , 3)

∴ m4 = (3 - -1)/(1 - 3) = 4/-2 = -2

- The parallel lines have equal slopes

- The product of the slopes of the perpendicular lines is -1

∵ m1 = m3 and m2 = m4

∴ The sides contains points (1 , 3) , (3 , 4) and (5 , 0) , (3 , -1) are parallel

  and the sides contain points (3 , 4) , (5 , 0) and (3 , -1) , (1 , 3) are

  parallel

∵ m1 × m2 = 1/2 × -2 = -1

∴ The side contains points (1 , 3) , (3 , 4) is ⊥ to the line contains points

  (3 , 4) , (5 , 0)

∵ m3 × m4 = 1/2 × -2 = -1

∴ The side contains points (5 , 0) , (3 , -1) is ⊥ to the line contains points

  (3 , -1) , (1 , 3)

- Now lets find the length of the four sides by using the rule

 of the distance

- If a segment has two endpoints (x1 , y1) and (x2 , y2), then the length

 of the distance is √[(x2 - x1)² + (y2 - y1)²]

∵ The length of the side which contains points (1 , 3) and (3 , 4) is

 √[(3 - 1)² + (4 - 3)²] = √[4 + 1] = √5

∵ The length of the side which contains points (3 , 4) and (5 , 0) is

 √[(5 - 3)² + (0 - 4)²] = √[4 + 16] = √20 = 2√5

∵ The length of the side which contains points (5 , 0) and (3 , -1) is

 √[(3 - 5)² + (-1 - 0)²] = √[4 + 1] = √5

∵ The length of the side which contains points (3 , -1) and (1 , 3) is

 √[(1 - 3)² + (3 - -1)²] = √[4 + 16] = √20 = 2√5

∴ The four sides are not equal but each two opposite sides are equal

- From all above

# Each two opposite sides are parallel and equal

# Each two adjacent sides are perpendicular

∴ The name of the polygon is rectangle

Answer:

rectangle

Step-by-step explanation:

Answer:

It will take 4.858 years before the CD worth 8228.24

Step-by-step explanation:

* Lets revise the compound interest

- The formula for compound interest, including principal sum, is:

  A = P (1 + r/n)^(nt)

- Where:

• A = the future value of the investment/loan, including interest

• P = the principal investment amount (the initial deposit or loan amount)

• r = the annual interest rate (decimal)

• n = the number of times that interest is compounded per unit t

• t = the time the money is invested or borrowed for

- To find the time you can use the formula

  t = ln(A/P) / n[ln(1 + r/n)]

* Lets solve the problem

∵ P = $5600

∵ A = 8228.24

∵ r = 8/100 = 0.08

∵ n = 4

- Substitute all of these values in the equation of t

∴ t = ln(8228.24/5600) / 4[ln(1 + 0.08/4)] = 4.858 years

* It will take 4.858 years before the CD worth 8228.24

Answer:

FIGURE IT OUT THIS IS SUPER BASIC YOU REALLY NEED TO DO THIS BY YOURSELF

Step-by-step explanation:

girl slope intercept form is just when you isolate y and whatever you do to one side you do to the other you just minus the extra term which isn't y and then you divide whatever is multiplied to y on each term and it's that easy

Answer:

2. y = -8x + 9

3. y = -1/6x - 1/3

4. y = -4/3x + 3

Step-by-step explanation:

the goal for 2, 3, and 4 is to get them into y = mx + b form. to do this, we need to isolate y on one side of the equation

2. 8x + y = 9 < subtract both sides by 8x

y = -8x + 9

3. x + 6y = -2 < subtract x from both sides

6y = -x - 2 < divide both sides by 6 to get y alone

6y/6 = y

-x - 2 / 6 = -1/6 - 1/3

y = -1/6x - 1/3

4. 4x + 3y = 9 < subtract 4x from both sides

3y = -4x + 9 < divide both sides by 3 to get y isolated

3y/3 = y

-4x + 9/3 = -4/3x + 3

y = -4/3x + 3

Answer:

Step-by-step explanation:

If DMKT → FCBN, then

m∠D = m∠F, m∠M = m∠C, m∠K = m∠B and m∠T = m∠N

m∠K = 79° therefore m∠B = 79°.

Answer:

[tex]+2n^5 - 9n^2 + 5n[/tex]

Step-by-step explanation:

To solve the expression

[tex]-n(-2n^4+9n-5)[/tex]

first we will multiply -n with each term and then find their products.

When doing multiplication the powers will be added and co-efficient will be multiplied.

[tex]-n(-2n^4+9n-5)​\\-n(-2n^4) -n(+9n) -n(-5)\\+2n^5 - 9n^2 + 5n[/tex]

Slope=5

Y-intercept=-7

Answer:

The amount in the account at the end of the 2nd quarter is $1537.73 ⇒ 2nd answer

Step-by-step explanation:

* Lets revise the compound interest

- Compound interest can be calculated using the formula

 A = P (1 + r/n)^(nt)

Where:

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the annual interest rate (decimal)

• n = the number of times that interest is compounded per unit t

• t = the time the money is invested for

* Now lets solve the problem

# P = $1500

# r = 5/100 = 0.05

# n = 4 ⇒ quarterly compound

# t = 1/2 ⇒ two quarters means 1/2 year

∴ A = 1500(1 + 0.05/4)^(4 × 1/2) = $1537.73

* The amount in the account at the end of the 2nd quarter is $1537.73

Answer:

Step-by-step explanation:

Put the coordinates of the points to the inequalities:

y ≤ x - 5; y ≥ -x - 4

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

(-5, 2) → x = -5, y = 2

2 ≤ -5 - 5

2 ≤ -10   FALSE

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

(5, -2) → x = 5, y = -2

-2 ≤ 5 - 5

-2 ≤ 0   TRUE

-2 ≥ -5 - 4

-2 ≥ -9   TRUE

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

(-5, -2) → x = -5, y = -2

-2 ≤ - 5 - 5

-2 ≤ -10   FALSE

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

(5, 2) → x = 5, y = 2

2 ≤ 5 - 5

2 ≤ 0    FALSE

Final answer:

Option b) (5, -2) is the only point that satisfies both inequalities, y ≤ x − 5 and y ≥ −x − 4, making it the correct answer.

Explanation:

The goal is to determine which point lies in the solution set of the given system of inequalities:

y ≤ x − 5

y ≥ −x − 4

Let's evaluate each option given for the system of inequalities:

(−5, 2): Plugging into the inequalities, y = 2 is not less than or equal to x − 5, because 2 is not ≤ (−5 − 5).

(5, −2): y = −2 is less than or equal to 5 − 5, and is also greater than or equal to −5 − 4. Therefore, (5, −2) satisfies both inequalities.

(−5, −2): y = −2 is not less than or equal to −5 − 5, thus not in the solution set.

(5, 2): y = 2 is not less than or equal to 5 − 5, hence it does not satisfy the first inequality.

The only point that satisfies both inequalities is option b) (5, −2).

Answer:

7 years

Step-by-step explanation:

A = P (1 + r)^(n)

where A is the final amount, P is the initial amount, r is the interest rate, and n is the number of times of compounding.

Compounded quarterly means compounded 4 times per year.  So the effective interest rate per compounding is:

r = 0.07 / 4

r = 0.0175

Given that A = 8000 and P = 5000:

8000 = 5000 (1 + 0.0175)^n

1.6 = 1.0175^n

log 1.6 = n log 1.0175

n = (log 1.6) / (log 1.0175)

n ≈ 27.1

Rounding up to the nearest whole number, it takes 28 compoundings.  Since there's 4 compoundings per year:

t = 28 / 4

t = 7

It takes 7 years.

Answer:

B: 3z-4

Step-by-step explanation:

First you start with PEMDAS. Parenthesis first.

Distribute 4 to (2z-1)

You get 8z-4

Next combine like terms such as 8z and -5z.

You get 3z because 8-5 is 3.

then you add on the negative four and get 3z-4.

Answer:

b

Step-by-step explanation:

i got it right on edge :)

Answer:

The correct option is B.

Step-by-step explanation:

It is given that Alondra took out a car loan for $22,500 that has a 0% APR for the first 24  months and will be paid off with monthly payments over 5 years.

We know that

1 year = 12 months

Using this conversion we get

5 year = 60 months

It means total number of months in 5 years is 60. For first 24  months the APR is 0%. So, the number of months will Alondra be charged interest is

[tex]60-24=36[/tex]

Therefore the correct option is B.

A) The probability of selecting a hockey card, keeping it out, and then selecting another hockey car is 1/9

B) The probability of selecting a hockey card, keeping it out, and then selecting a football card is 1/4

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

A box has 3 hockey and 6 football cards.

So, the probability of selecting a hockey card, keeping it out, and then selecting another hockey card

= 3/9 x 2/8

= 6/72

= 1/9

and,  the probability of selecting a hockey card, keeping it out, and then selecting a football card

= 3/9 x 6/8

= 18/72

=1/4

Learn more about probability here:

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Final answer:

The probability of selecting a hockey card, keeping it out, and then another hockey card is 1/12, whereas the probability of selecting a hockey card and then a football card is 1/4.

Explanation:

The probability of selecting a hockey card, keeping it out, and then selecting another hockey card from a box containing 3 hockey and 6 football cards is calculated as follows. First, the probability of picking one hockey card (Event A) would be 3 out of the total of 9 cards, or 3/9. Then, since the card isn't replaced, there are now 2 hockey cards left out of 8 total cards. So, the probability of picking another hockey card (Event B) after the first pick would be 2/8.

The probability of both events A and B occurring is found by multiplying the two probabilities together:

P(A and B) = P(A)  imes P(B) = (3/9)  imes (2/8) = 1/12.

For selecting a hockey card and then a football card, the initial probability of picking a hockey card remains 3/9. After a hockey card has been picked and kept out, there are still 6 football cards left out of 8 total cards. The probability of now picking a football card would be 6/8.

The probability of picking a hockey card first and then a football card is therefore:

P(Hockey and then Football) = P(Hockey)  imes P(Football) = (3/9)  imes (6/8) = 1/4.

Answer: Option B

No solutions

Step-by-step explanation:

We have the following system of equations

[tex]2x - y = -6[/tex]    (1)

[tex]-4x + 2y = -9[/tex]   (2)

To solve the system using the substitution method, solve the first equation for the variable y

[tex]y=2x+6[/tex]

Now substitute the value of y in the second equation

[tex]-4x + 2(2x +6) = -9[/tex]

[tex]-4x + 4x +12=-9[/tex]

[tex]12=-9[/tex]

2 is not equal to -9, the system is inconsistent. The system has no solution

Answer:

No solution

Step-by-step explanation:

Given equations are 2x-y=-6 and -4x+2y=-9.

Now we need to solve that system of equation using substitution method.

solve 2x-y=-6 for y

2x-y=-6

-y=-6-2x

y=6+2x

Plug this value of y into other equation -4x+2y=-9

-4x+2(6+2x)=-9

-4x+12+4x=-9

12=-9

Which is a false equation.

Hence there is no solution to the given system.

Answer:

B

Step-by-step explanation:

To find the correct one plug in 4 into x and if you get 3, that's the correct one.

A. y(4) = -4^2 + 4*4 + 4 = -16 + 16 + 4 = 4 X

B. y(4) = -4^2 + 8 * 4 - 13 = -16 + 32 - 13 = 3

For this case we have the following functions:

[tex]m (x) = \frac {x + 5} {x-1}\\n (x) = x-3[/tex]

By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex](m * n) (x) = m (x) * n (x)\\(m * n) (x) = \frac {x + 5} {x-1} (x-3)\\(m * n) (x) = \frac {(x + 5) (x-3)} {x-1}[/tex]

By definition, the domain of a function is given by the values for which the function is defined.

The domain of m(x) is given by all reals except 1.

The domain of n(x) is given by all reals.

While the domain of [tex](m * n) (x)[/tex] is given by:

All reals, except the 1. With [tex]x = 1[/tex], the denominator is 0 and the function is no longer defined.

Answer:

Domain of[tex](m * n) (x)[/tex] is given by all reals except 1.

For this case we must find the value of the variable "x" of the following expression:

[tex]4(10^{5x})=200[/tex]

We divide both sides of the equation by 4:

[tex]10 ^ {5x} = \frac {200} {4}\\10 ^ {5x} = 50[/tex]

We find ln on both sides of the equation to remove the exponent variable:

[tex]ln (10^{5x}) = ln (50)\\5x * ln (10) = ln (50)[/tex]

We divide both sides of the equation between 5 * ln (10):[tex]x = \frac {ln (50)} {5 * ln (10)}[/tex]

In decimal form we have:

[tex]x = 0.33979400[/tex]

ANswer:

[tex]x = 0.33979400[/tex]

Here is a table that will help you understand. And the answer.