A tank has 15 gallons of water in it when water begins draining from the tank. (Recall that water weighs 8.345 pounds per gallon.)

Define a function f that determines the number of gallons of water in the tank, f ( w ) , in terms of the number of pounds of water that have drained from the tank since the tank started draining, w .

Answer:

Ten plus six hundredth plus 8 thousandth equals ten and sixty-eight thousandths

Step-by-step explanation:

0.06 is in the hundredth place

0.008 is in the thousandth place

Answer:

ten plus zero point zero six plus zero point zero zero eight

Step-by-step explanation:

The ten is 10 then plus + and then 0.06 plus + 0.008

To simulate the 20% probability of rain over three days, generate a random number between 1 and 100 for each day. Count the trials where all three numbers are between 21 to 100 as 'non-rainy' days. The experimental probability of no rain in three days is the ratio of 'non-rainy' trials to total trials.

Probability is a branch of mathematics that studies randomness and the chance of an event occurring. In this case, we can perform a simulation to experimentally determine the probability that it will not rain on the next 3 days even though there is a forecast of a 20% chance of rain.

One way to perform the said simulation is by using random numbers from 1 to 100. Why? Because probability can be expressed as a percentage, and the range from 1 to 100 encompasses all percentage possibilities (0% to 100%). So, for each day, we can generate a random number in this range. If the generated number falls in the range 1-20 (which represents the 20% predicted chance of rain), we consider that day as a 'rainy day'. If it falls in the range 21-100, we consider it a 'non-rainy day'.

We repeat this process for three days. The experimental probability of it not raining on all three days will be the ratio of favorable outcomes (all three numbers landing in the 'non-rainy day' range) to the total number of trials.

If we perform a large number of these three-day simulations, we'll have a good estimate of the experimental probability. The Law of Large Numbers ensures that as more trials are conducted, the experimental probability will approach the theoretical probability.

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To solve the given proportional equation, it simplifies to 5 = a/(a-9), leading to 4a = 45 after simplification and solving, with the solution being a = 11.25.

To solve the proportional equation 10/2 = a/(a-9), we first simplify and then solve for a. The equation simplifies to 5 = a/(a-9). By cross-multiplication, we get 5(a - 9) = a, which simplifies to 5a - 45 = a. Bringing all terms to one side gives 4a = 45, and dividing both sides by 4 gives a = 11.25. Therefore, the correct answer is a. 11.25.

I multiply 1200 times 5 and yet 6000 because it says what is the height

Properties of polygons.

Step-by-step explanation:

(1) Both pair of opposite sides are congruent.          Distance Formula

(2) Both pairs of opposite sides are parallel.            Slope Formula

(3) Diagonals are congruent .                                    Distance Formula

(4)  Diagonals bisect to each other.                          Midpoint Formula

(5) Diagonals are perpendicular.                               Slope Formula

(6)  Sides of polygon create a right angle.                Slope Formula

(7) A triangle is isosceles /equilateral.                      Distance Formula

Answer: 4.647

Step-by-step explanation:

The 4 in the hundredths place, or before the 6, is less than 5 so it will not round the 6 to a 7, therefore making it not round to 4.7

Answer:

17

Step-by-step explanation:

Let the number be x.

We know that 3x=51

If we divide both sides by three, we get x=17

17

act like there is a variable in there and youll get 17

Answer:

30 feet

Step-by-step explanation:

3 feet times 10 years would be 30. This is because for each yard, the player travels 3 feet.

Answer:

30 feet or 10 yards

Step-by-step explanation:

feet is 1 yard so

to get 10 yards

do 3 feet times 10 to make 30 feet

split 30 feet into yards

1 yard for every 3 feet

30 divided by 3 is 10 yards

The linear equation representing the value of the car as it depreciates over time is y = -3,000x + 25,635, where y is the value of the car and x is the age of the car in years.

To write a linear equation that describes the depreciation of the SUV over time, we define two variables: y represents the total value of the car at any time x, where x represents the age of the car in years.

The car is purchased for $25,635 and depreciates at a rate of $3,000 per year, which means that the value of the car decreases by a constant amount each year. We can write this situation as a linear function:

Linear Depreciation Equation:

y = -3,000x + 25,635

Here, the y-intercept is $25,635 (the value of the car at the time of purchase when x is zero), and the slope is -$3,000 (the rate at which the value of the car decreases per year).

the y-coordinate corresponding to x=4 is 12.

the equation y=3x represents a linear function. A linear function is a type of mathematical relationship where the graph of the function forms a straight line.

The equation y=3x is in slope-intercept form, where y represents the dependent variable (usually plotted on the vertical axis),

x represents the independent variable (usually plotted on the horizontal axis), and 3 represents the slope of the line.

To find the y-coordinate when the x-coordinate is 4 in the equation y=3x, we need to substitute x=4 into the equation and solve for y.

Substituting x=4 into the equation y=3x,

we get: y=3×4=12

So, when x=4, y=12.

Therefore, the y-coordinate corresponding to x=4 is 12.

This means that the point on the graph of y=3x where the x-coordinate is 4 has a y-coordinate of 12.

Answer:

55

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The two triangles [tex]\triangle MNP\sim \triangle RST[/tex].

Therefore the corresponding sides are proportional.

[tex]\frac{|ST|}{|PN|} =\frac{|TR|}{|MP|}[/tex]

From the diagram |MP|=4, |PN|=3, |MN|=5 |ST|=x and |TR|=12.

Let us substitute the values and solve for x.

[tex]\frac{12}{4}=\frac{x}{3}[/tex]

Multiply both sides by 3 to get:

[tex]3*\frac{12}{4}=\frac{x}{3}*3[/tex]

This implies that:

[tex]9=x[/tex]

Therefore x=9

Answer:

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

4x - 6x + 9 = 7

-2x + 9 = 7

-2x = -2

x = 1

y = 2(1)-3= -1

(1,-1)

Answer:

Option D:  - 6;  [tex]$ \textbf{-5}\frac{\textbf{5}}{\textbf{2}} $[/tex];   [tex]$ \textbf{-4}\frac{\textbf{1}}{\textbf{5}} $[/tex].

Step-by-step explanation:

The sequence is defined by:

[tex]$ A(n) = -6 + (n - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]

To find the first term of the sequence simply substitute n = 1.

First term of the sequence:

[tex]$ A(1) = -6 + (1 - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]

        [tex]$ = - 6 $[/tex]

Fourth term of the sequence:

[tex]$ A(2) = -6 + (4 - 1) \bigg ( \frac{1}{5} \bigg) $[/tex]

        [tex]$ = - 6 + 3\bigg( \frac{1}{5} \bigg) $[/tex]

        [tex]$ = \frac{- 30 + 3}{5} $[/tex]

        [tex]$ = \frac{-27}{5} $[/tex]

        [tex]$ = \frac{-25 - 2}{5} $[/tex]

        [tex]$ = - 5 - \frac{2}{5} $[/tex]

        [tex]$ = -5\frac{2}{5} $[/tex]   is the required answer.

Tenth term of the sequence:

[tex]$ A(10) = - 6 + (10 - 1) \bigg( \frac{1}{5} \bigg) $[/tex]

         [tex]$ = - 6 + 9\bigg( \frac{1}{5} \bigg) $[/tex]

         [tex]$ = \frac{-30 + 9}{5} $[/tex]

         [tex]$ = \frac{-21}{5} $[/tex]

         [tex]$ = \frac{-20 - 1}{5} $[/tex]

         [tex]$ = - 4 - \frac{1}{5} $[/tex]

         [tex]$ = -4\frac{1}{5} $[/tex]  is the required answer.

Answer:

5.85

Step-by-step explanation:

$40.95 / 7 =5.85

Final answer:

The scientist used 9/40 of a full bottle of solution.

Explanation:

To find out how much of a full bottle of solution the scientist used, we first need to calculate the amount that is left in the bottle. The bottle is currently 5/8 full, and the scientist used 2/5 of the solution. To calculate the amount left, we subtract the amount used from the initial amount:

Amount Left = Initial Amount - Amount Used

To subtract fractions, we need a common denominator. The common denominator for 8 and 5 is 40:

Amount Left = 5/8 - 2/5

To subtract the fractions, we need to have the same denominator, which is 40:

Amount Left = (5/8) * (5/5) - (2/5) * (8/8)

Amount Left = 25/40 - 16/40

Amount Left = 9/40

Therefore, the scientist used 9/40 of a full bottle of solution.

Answer:

i have no clue

Step-by-step explanation:

ask someone else

3 metres from one end to the third mark

Solution:

Total length of wood = 10 metre

Wood is marked into 10 equal length.

[tex]$\text{Length of each marking}=\frac{\text{Total length}}{\text{Number of marking}}[/tex]

                                     [tex]$=\frac{10}{10}[/tex]

                                     = 1 metre

Length of each marking = 1 metre

Number of metres from one end to third mark = 1 + 1 + 1 = 3 metre

The image of the marking is attached below.

Hence 3 metres from one end to the third mark.

Answer: a,c

Step-by-step explanation:

Answer:

A .. C

Step-by-step explanation:

A unit fraction is a fraction with a numerator of 1 and a positive integer denominator. Identifying unit fractions involves ensuring the numerator is 1. Examples include 1/2, 1/3, and 1/5.

A unit fraction is a fraction where the numerator is always 1, and the denominator is a positive integer. This means that a fraction of the form 1/b, where b is a positive integer, qualifies as a unit fraction. For example, 1/2, 1/3, and 1/5 are unit fractions because the numerators are all 1.

When working with fractions, it's important to understand their components. The numerator (top number) represents how many parts you have, while the denominator (bottom number) tells you into how many equal parts the whole is divided. This rule helps identify unit fractions, as the numerator must always be 1.

To summarize, determining unit fractions is straightforward: check if the numerator is 1 and the denominator is a positive integer. If both conditions are met, you have a unit fraction.

Answer:

t = -8

Step-by-step explanation:

combine like terms, so -3t + 7t = 4t and 34 - 2 = 32

so 4t - 8 = 32 + 9t

then subtract 4t from both sides and subtract 32 from both sides. You will get: -40 = 5t.

Then divide both sides by 5 so you will get -8 = t

Answer: t= -8

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

180-78=102

102÷2=51

E=51

Answer:

14/3

Step-by-step explanation:

7       x           6

9                    1

7x6=42

9X1=9

42/9     or 14/3

The product of 7/9 and 6 is 14/3.

To find the product of 7/9 and 6, multiply the numerator (7) by the number (6) and keep the denominator (9) the same.

The calculation is as follows:

(7/9) * 6

= (7 * 6)/9

= 42/9

To simplify the fraction, divide both the numerator and the denominator by their greatest common factor, which is 3.

The simplified answer is: 14/3

Answer:

Distance [tex]=\sqrt{164}\ \approx12.80\ yards[/tex]

Step-by-step explanation

Pythagorean theorem :

In a right triangle

[tex](Hypotenuse)^2=(Perpendicular)^2+(base)^2[/tex]

From the diagram

[tex]perpendicular = 10\ yards\\\\Base = 8\ yards \\\\Hypotenuse = distance\ (d)\\\\(d)^2=(10)^2+(8)^2\\(d)^2=100+64\\(d)^2=164\\d=\sqrt{164}\ \approx12.80\ yards[/tex]

Answer:  yes

Step-by-step explanation:

Answer:

10 degrees

Step-by-step explanation:

Divide 360 by however many sides or angles are within the polygon.

360/x

360/36

10

Answer:

A(2,1) , B(-3,2) , C(-1,6)

Step-by-step explanation:

A translation of 2 units up means the y values will be shifted up 2 units

A (2,-1) -> A(2,1)

B (-3,0) -> B(-3,2)

C (-1,4) -> C(-1,6)

The vertices of the image of triangle ABC after a translation of 2 units up are A' (2, 1), B' (-3, 2), and C' (-1, 6), found by adding 2 to the y-coordinate of each original vertex.

The student has asked how to find the vertices of the image of triangle ABC after a translation of 2 units up. To do this, we simply add 2 to the y-coordinate of each vertex of the triangle. Here are the steps for the translation:

For vertex A (2, -1), the new position after translation is A' (2, -1 + 2) or A' (2, 1).

For vertex B (-3, 0), the new position after translation is B' (-3, 0 + 2) or B' (-3, 2).

For vertex C (-1, 4), the new position after translation is C' (-1, 4 + 2) or C' (-1, 6).

Therefore, the vertices of the image of triangle ABC after the translation are A' (2, 1), B' (-3, 2), and C' (-1, 6).

Answer:

$1910.1744

Step-by-step explanation:

To start we have to calculate how much the total will give us in one year,  for this we divide the number by 100 and multiply it by 102, so we will get that 2%  in one year

(1800 / 100) * (100 + 2) =

18 * 102

1836

Now we will repeat the procedure but instead of using the 1800 we will use the 1836 which will be what we will have when the first year ends.

(1836 / 100) * (100 + 2) =

18.36 * 102

1872.72

Finally we do the same with the new number

(1872.72 / 100) * (100 + 2) =

18.7272 * 102

1910.1744

So  in conclusion putting $1800 at the end of the 3 years we will get $1910.1744

$1910.1744 - $1800 = $110.1744

that is the exact amount of the profit that we will obtain.

Answer: no because 2 times -2 equals -4 and -4 - 1 = -5 not -3.