The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the function of A(t)=14(2.71)^-.016*t, where t is the number of years since a government program was began to help clean up the lake. About how long will it take for the amount of pollutant to reach 7 parts per million?

Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the regular octagon is 8√58 units.

Perimeter is the sum of the length of the sides used to make the given figure.

For a regular octagon, the length of each side of the octagon is the same. Therefore, the length of a single side of the octagon is,

Length of the side of the octagon = √[(-4-3)² + (0 + 3)²] = √58

Now, the perimeter of the octagon is 8 times of√58.

Perimeter = 8 ×√58 = 8√58

Hence, the perimeter of the regular octagon is 8√58 units.

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Part A:

The greatest common factor is 2k

2k(2ck + 5k - 8c - 20)

Part B:

factor by grouping

2k(k - 4)(2c + 5) is the final factored form

Answer:

The hypotenuse is [tex]\sqrt{58}[/tex]

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

Taking the square root of each side

[tex]\sqrt{58} = \sqrt{c^2}[/tex]

[tex]\sqrt{58} =c[/tex]

The allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

Henry is working in a packed room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35

lbs. His tolerance is +/-5 lbs.

Weight of the bag = 35 lbs

Tolerance = ± 5 lbs

Allowable weights = 35 ± 5

= 35 + 5 = 40 lbs

= 35 - 5 = 30 lbs

Thus, the allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.

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Answer:

Find another point on the perpendicular line.

Step-by-step explanation:

Given an original line "m", and a point off the line "Q", in order to construct a second line "p", meant to be perpendicular to "m" through the point "Q", fundamentally, the only truly necessary step to construct a perpendicular line through is to find another point on the yet-to-be-found perpendicular line.

Most often, this is accomplished by exploiting the fact that "p" is the set of all points that are equidistant from any pair of points that are symmetric about "p".

Since the symmetry must be about "p", and we don't even know where "p" is, one often finds two points on "m" that are equidistant from "Q".

This can be accomplished by adjusting a compass to a fixed radius (larger than the distance from "Q" to "m"), and making an arc that intersects "m" in two places.  Those two places will be equidistant from "Q", and are simultaneously on line "m".  Thus, these two points, "A" & "B" are symmetric about "p".

Since "A" & "B" are symmetric about "p", they are equidistant from "p", and are on "m".  One could try to find the point of intersection between "p" and "m" through construction, but this is unnecessary.  We need only find a second point (besides "Q") that is equidistant from "A" & "B", which will necessarily be a point on "p", to form the line perpendicular to "m".

To do this, fix the compass with any radius, and from "A" make a large arc generally in the direction of "B", and make the same radius arc from "B" in the direction of "A" such that the two arcs intersect at some point that isn't "Q".  This point of intersection we can call point "T", and the line QT is line "p", the line perpendicular to the original line, necessarily containing "Q".

Answer:

[tex]\fbox {5 times}[/tex]

Step-by-step explanation:

Days where both will be done :

⇒ 2nd day × 3rd day

⇒ 6th day

Number of times in September :

⇒ The month has 30 days

⇒ Number of times = 30/6

⇒ Number of times = 5

Answer:

5 times

Step-by-step explanation:

• Calculate the lowest common multiple (LCM) of 2 and 3 to find the first day of the month in which she will do both:

LCM (2 and 3) = 2 x 3

                       = 6

This means, she will do both every 6th day.

• There are 30 days in September. To find how many days she will do both in September, we have to calculate how many 6-day blocks there are in 30 days:

⇒ 30 ÷ 6

= 5 times

Answer:

[tex] \frac{1}{4} [/tex]

Step-by-step explanation:

To find the gradient of the graph, we use the formula,

[tex]gradient \: (m) = \frac{(y2 - y1)}{(x2 - x1)} [/tex]

From the graph, we obtain values for x and y

x1 = 4, x2 = 8

y1 = 2, y2 = 3

Substitute the values into our formula.

[tex]m \: = \frac{(3 - 2)}{(8 - 4)} \\ = \frac{1}{4} [/tex]

Therefore, the gradient, m, =

[tex] \frac{1}{4} [/tex]

Note:-

Answer:

D

Step-by-step explanation:

the cordinate is at (-3,2)

Answer:

1764

Step-by-step explanation:

[tex]from \: the \: question \: rt {}^{2} \\ were \: r =9 \\ and \: t = 14 \\ rt {}^{2} = 9 \times (14) {}^{2} = 9 \times 196 = 1764[/tex]

Hii!

__________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ \leftharpoonup[/tex]

1764

[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]

Stick in the values: 9 for r and 14 for t, and simplify.

[tex]\twoheadrightarrow\sf 9\cdot14^2}[/tex]

[tex]\bullet[/tex] Square 14 first

[tex]\twoheadrightarrow\sf 9\cdot196}[/tex]

[tex]\bullet[/tex] Multiply the numbers

[tex]\twoheadrightarrow\sf 1764}[/tex]

[tex]\bullet[/tex] Great job! We found the answer

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

Answer:

3(4)² - 2(4) + 1 = 48 - 8 +1 = 41

x = 4

[tex] {3x}^{2} - 2x + 1 \\ \\ 3 \times {4}^{2} - 2 \times 4 + 1 \\ \\ 3 \times 16 -8 + 1 \\ \\ 48 - 8 + 1 \\ \\ 41.[/tex]

Answer:Angle C=68 degrees

Step-by-step explanation:

The solution is in the

Answer:

x/ 3x + 2

x approach 1

1/3 (1) + 2

1/ 5.

Answer: 14%

Step-by-step explanation:

Let's assume that there are 100 books in total.

So there are 60 fiction books and 40 nonfiction books.

10% of 60 is 6.

20% of 40 is 8.

So there are 14 books out of 100 that are worn.

This is 14%

39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:

We can write a mixed fraction in a fraction:

6 1/2 = 13/2

8 1/2  = 33/2

7 3/4 = 31/4

8 1/12 = 97/12

8 5/12 = 101/12

Adding all the fractions:

[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]

[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]

[tex]=23+\dfrac{64}{4}[/tex]

= 39 hours

Thus, 39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

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Answer: Choice C

As [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]

As [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]

Check out the diagram below.

========================================================

Explanation:

The leading term is the term with the largest exponent. That would be the term of [tex]-\text{x}^3[/tex]. The leading term directly determines the end behavior. The other terms will not play a role.

What this means is that the end behavior of [tex]\text{y} = -\text{x}^3 - \text{ax} + 3[/tex] is the exact same as the end behavior of [tex]\text{y} = -\text{x}^3[/tex]

As x gets really big in the positive direction, we'll have [tex]-\text{x}^3[/tex] get really small in the negative direction. For instance, x = 10 leads to [tex]-\text{x}^3 = -10^3 = -1000[/tex] and x = 100 leads to [tex]-\text{x}^3 = -100^3 = -1,000,000[/tex]

Therefore, as [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]

Visually the graph goes forever downward when we move to the right. We can consider this as "falls to the right".

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

The graph "rises to the left" because as [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]

Here's a small table to give numeric examples:

[tex]\begin{array}{|c|c|} \cline{1-2}x & y\\\cline{1-2}-1 & 1\\\cline{1-2}-10 & 1000\\\cline{1-2}-100 & 1,000,000\\\cline{1-2}\end{array}[/tex]

As x gets more negative, y becomes more positive. We have this opposite nature going on similar to the previous section.

This graph goes uphill when moving to the left.

Check out the graph below. In the diagram I used a = 2, but you could use any value of 'a' you want to get the same end behavior.

Answer:

[tex]\fbox {3(4a + 2) = 12a + 6}[/tex]

Step-by-step explanation:

⇒ 3(4a + 2)

⇒ 3(4a) + 3(2)

⇒ 12a + 6

Answer:

A) 3(4a + 2) = 12a + 6

Step-by-step explanation:

This is the correct answer because the distributive property is where you break up all the numbers and pretty much that is what you do in A.

3 * 4a = 12a

3 * 2 = 6

So then, as you can see, the answer would be 12a + 6.

This is another explanation, even though they are LITERALLY the same.

Apply the distributive property.

3 (4a) + 3 ⋅ 2

Multiply 4 by 3.

12a + 3 ⋅ 2

Multiply 3 by 2.

12a + 6

Brainliest pls

Answer:

70%

$571.41

Step-by-step explanation:

100% means 1, or a whole thing.

Since the discount is 30% of the original price, and the original price is 100% of the original price, then

100% - 30% = 70%

With a 30% discount, you actually pay 70% of the original price.

$399.99 is 70% of the original price.

399.99 / 70% = x / 100%

70x = 100 × 399.99

x = 571.41

The original price was $571.41.

-6 ≤ x < -2

Step-by-step explanation:

[ => this shows ≤ sign

) => this shows < sign

Answer:

[tex]P = A - I[/tex]

Step-by-step explanation:

Using the binomial distribution, it is found that the probabilities are:

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Exercise 1:

The parameters are:

n = 15, p = 0.4, x = 4.

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228[/tex]

Exercise 2:

The parameters are:

n = 12, p = 0.2, x = 2.

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835[/tex]

Exercise 3:

The parameters are:

n = 20, p = 0.05.

The probability is:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Using the binomial formula for each value and adding them:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841[/tex]

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The applied factory overhead is $6,939 and  the over-or underapplied factory overhead amount for October is $461.

1. Applied factory overhead:

Predetermine overhead rate=Fixed overhead/Machine hours

Predetermine overhead rate=16,920/36,000

Predetermine overhead rate=0.47

Applied overhead=Machine hours×Rate

Variable=2700×2.10 per hour= $5,670

Fixed=2700×0.47 per hour=$1,269

Total overhead applied=$6,939

($5,670+$1,269)

2. Under applied overhead

Total overhead applied $6,939

Less Total factory overhead   $7,400

Under applied overhead -$461
($6,939-$7,400)

Therefore the applied factory overhead is $6,939 and  the over-or underapplied factory overhead amount for October is $461.

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The solution of the given equation 4(3x - 4) - 7( 2x + 3) = 3 is -20.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is;

4(3x - 4) - 7( 2x + 3) = 3

To solve;

4(3x - 4) - 7( 2x + 3) = 3

Solve the parentheses using the distributive property;

12x - 16 - 14x - 21 = 3

we need to get the like terms together;

12x - 14x -16 - 21 = 3

-2x - 37 = 3

Add 37 both sides, we get;

-2x = 40

Divide both sides by -2

x = -20

Hence, the solution of the given equation is -20.

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Answer:

Step-by-step explanation:

[tex]9~km/h=\frac{9 \times ~1000}{1 \times 60 \times 60}=\frac{5}{2} m/s}[/tex]

Answer:

49 + 28 = 7(7 + 4)

Step-by-step explanation:

49 bags of soil one week

28 bags of soil the next week

49 + 28 bags of soil purchased in total

Find the GCF (Greatest Common Factor) of 49 and 28.

49/7 = 7

28/7 = 4 (GCF is 7 since it is the largest number that can divide both 49 and 28 equally)

Factor out the GCF + rewrite division above (optional for visualization)

49/7 = 7 -> 49 = 7 * 7

28/7 = 4 -> 28 = 7 * 4

49 + 28 = 7(7 + 4)

Let me know if you have any questions!

Marlon's weight is 39.3 pounds with a mean weight of 40 pounds and a standard deviation of 1.3 pounds.

We know that the formula for calculating a z-score is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Given that mean weight = 40 pounds.

and standard deviation = 1.3 pounds.

Also given that Marlon is heavier than 30% of boys his age on average, according to measurements.

The z value of 30% is -0.524.

We can put this value in the formula.

-0.524 = (x - 40)/1.3

i.e. (-0.524) * 1.3 = x - 40

i.e. - 0.6812 = x - 40

i.e. x =  40 - 0.6812 = 39.3188

Therefore, we can conclude that Marlon's weight is 39.3 pounds with a mean weight of 40 pounds and a standard deviation of 1.3 pounds. So, the last option is correct.

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The value of c is 81/64 for the expression a perfect square trinomial.

An expression can be defined as a mathematical statement that consists of variables, constants and mathematical operators simultaneously.

It is given that an expression

x² +9/4x +c is a perfect square polynomial

c =?

(a+b)² = a² +2ab+b²

2ab = 9/4

b = 9/8

c = b² = 81/64

Therefore the value of c is 81/64 for the expression a perfect square trinomial.

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Answer:

   5

Explanation:

Data Set : {11, 13, 9, 4, 6, 5, 8, 10}

Arrange ascendingly: {4, 5, 6, 8, 9, 10, 11, 13}

Quartiles:

Interquartile Range: Q3 - Q1 = 10.5 - 5.5 = 5

Proper ascending ordered set

Q1

Q3

IRQ

Answer: There is no mode.

Step-by-step explanation:

The mode is the number that appears the most in a given set of data. Each number in this data set is repeated twice. Therefore, there is no mode.

I hope this helped!! :)

Answer:

1, 2, 3, 4

or none

Step-by-step explanation:

Mode is the value or values in the data set that occurs most frequently.

example:

For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6.

in 1, 1, 2, 2, 3, 3, 4, 4 all numbers occur the same amount of times, therefore they all (or none) are the mode

hope this helps:)

Answer:

when (-1, -4) is substituted into the first equation it's true

when (-1, -4) is substituted into the second equation it's true

the ordered pair (-1, -4) is a solution to the systems of equation

Step-by-step explanation:

original equation

x-y=3

multiply both sides by 7

7x-7y = 21

add 7y to both sides

7x=7y + 21

substitute into second equation

(7y+21)-y=-3

simplify

6y+21=-3

subtract 21 from both sides

6y=-24

y=-4

substitute y into original equation

x-(-4) = 3

cancel out negative signs

x+4=3

subtract -4 from both sides

x=-1