Oil leaks from a tank. At hour t = 0 there are 360 gallons of oil in the tank. Each hour after that, 3% of the oil leaks out.
(a) What percent of the original 360 gallons has leaked out after 8 hours?
%
(b) if Q(t) = Q0e^kt the quantity of oil remaining after t hours, find the value of k.
k=
(c) What does k tell you about the leaking oil? Select all that apply if more than one statement is true
A. It tells what percent of oil remains after each hour.

B. It is the amount that the oil that leaks out each second.

C. Because it is less than one, we know the amount of oil in the tank is decreasing,

D. It tells by what percent of oil decays each hour.

E. Because it is negative, we know the amount of oil in the tank is decreasing.
F. It gives the continuous hourly rate at which oil is leaking.

G. None of the above

First, we need to follow the circumference of a circle formula, which is [tex]C = 2 \pi r[/tex]. Since we know the radius, we can plug 11 for the radius and 3.14 for pi.

The equation should now look like this: [tex]C = 2 * 3.14 *11[/tex]. Then, we multiply. After solving, the circumference of the circle is 69.08 centimeters.

An example of theoretical probability from the considered option is given by: Option 2: A spinner has 8 equal sections numbered 1 to 10. The probability of spinning the number 3 is 1/8

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]

where, [tex]P_e(E)[/tex]is denoting experimental probability of occurrence of E.

Probability which is derived theoretically, irrespective of what outcome comes, is called theoretical probability. Probabiltiy which is based on the outcomes of experiments performed is called experimental probability.

Suppose we want to find the probability of an event E.

Then, its theoretical probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Checking all the options to see which one gives theoretical probability:

This option uses what was observed from one result. Thus, 3/5 is experimental probability here, as there is no evidence of it being theoretical probability but enough support towards being experimental probability.

No experiment is done here, just the description of the setup of the random experiment.

Now, E = event of getting 3 on the spinner.

All spinner's parts are assumingly equally likely, we have:

Number of ways E can occur = 1

Number of ways spinner's outcome can come = 8

Thus, we get P(E) = 1/3

Thus, this option is demonstrating theoretical probability.

This is using experimental results to get the estimated probability.

Actually, assuming coin being fair, both the tail and heads being equally probable, if we take:

E = event of getting head, then as there are two results possible being Tail or Head (assuming only 2 results), and there is one way of getting head in one toss, so we get:
P(E) = 1/2 = 0.5

Thus, this option is demonstrating experimental probability instead of theoretical one.

It is using the data from one experiment. So its experimental probability. Sometimes we can get experimental probability = theoretical probability value, but still, there'd be difference of how you calculated it from the start. Usually, if calculated from experiment, then its experimental probability, and if calculated virtually and based on theories, it is theoretical probability.

Thus, an example of theoretical probability from the considered option is given by: Option 2: A spinner has 8 equal sections numbered 1 to 10. The probability of spinning the number 3 is 1/8

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Answer:

f(1) = 3

Step-by-step explanation:

f(t) = t² - 1t + 3

we want to find f(1)

all we have to do is replace the t's with 1 and evaluate

f(1) = (1)² - 1(1) + 3

evaluate exponent 1² = 1

f(1) = 1 - 1(1) + 3

multiply

f(1) = 1 - 1 + 3

subtract

f(1) = 3

Answer:

The correct answer is 7.5

Step-by-step explanation:

[tex] \tan(62) = \frac{x}{4} [/tex]

then you multiply by 4 and you get:

[tex] \tan(62) \times 4 = x[/tex]

Result:

[tex]x = 7.5[/tex]

An equation that can be used to determine j j, each bottle of juice costs 15.69 = 6j + 2.91

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Bashir bought snacks for his team's practice. He bought a bag of apples for $2.91 and a 6-pack of juice bottles.

The total cost before tax was $15.69.

An equation that can be used to determine j j, is how much each bottle of juice costs.

15.69 = 6j + 2.91

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Answer:

$54000

Step-by-step explanation: 3780 divided by the number of years he paid interest for, (6) gives you 630. If he pays 7% interest, you calculate what number 630 is 7% of (9000.) Therefore he takes out 9000 dollars a year. Meaning that in total, he borrowed 54,000 dollars. (9000 x 6)

Answer:

7x3 = 21

Step-by-step explanation:

It's simple math. One week is 7 days. So just multiply 7x3 and then that's equaled to 21.

There are 6939.56 days in 19 lunar calendar new years with an extra month added in seven times.

"A lunar year is 12 lunar months, so 19 of these would be 228 lunar months. With the 7 extra months, the total period would be 235 lunar months of 29.530589 days each and is 6939.69 days.

We will notice that this is almost the same as 19 solar years of 365.24 days, which is 6939.56 days.

Now, you are referring to the Hebrew Calendar, a 19-year period that consists of 12 years of 12 months plus 7 years of 13 months,

Therefore,  19 years is the period after which the Hebrew and solar calendar dates will match up."

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Answer:

[tex] {\longrightarrow \pmb{\sf {\qquad \frac{1}{24} }}} \\ \\[/tex]

[tex] \: [/tex]

Step-by-step explanation:

It is given that the perimeter of an equilateral triangle is 1/8 unit and we have to find the length of each side of the triangle.

So, we know that,

[tex] \\ {\longrightarrow \pmb{\sf {\qquad 3a = Perimeter_{(Equilateral triangle) }}}} \\ \\[/tex]

Now, substituting the given values in the formula :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad 3a = \frac{1}{8} }}} \\ \\[/tex]

By doing cross multiplication we get :

[tex]{\longrightarrow \pmb{\sf {\qquad 3a(8) = 1(1) }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad 24a = 1 }}} \\ \\[/tex]

Dividing both sides by 24 we get :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad \frac{24a}{24} = \frac{1}{24} }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad a = \frac{1}{24} }}} \\ \\[/tex]

Therefore,

Answer:

the answer is a

Step-by-step explanation:

i literaly just tookthetest on edginuity

Answer:

a = 9

Step-by-step explanation:

First we substitute 1 into the quadratic equation :

(x+2)² = a

(1+2)² = a

(3)² = a

3×3 = a

a = 9

Hope you understood, hope this helped and brainliest please.

Answer:

$1,679.62

Step-by-step explanation:

129.60*12=$1,555.20

You then do 1,555.2*.08, and get:124.416

You then add the 2 together to find the amount needed to be paid back.

Answer:because each answers eachother

Step-by-step explanation:

Answer:

33.5 in^3

Step-by-step explanation:

The formula for a cone is (pi)(r^2)(h/3)

Since we need to use 3.14 for pi, we will plug in 3.14 for pi. It should look like this:  (3.14)(r^2)(h/3)

The radius is 2 and the height is 8. Plug in the numbers:

(3.14)(2^2)(8/3)

Simplify:

(3.14)(4)(2.66...)

Multiply:

(12.56)(2.66...) -> 39.4933...

Finally, 39.4933... is rounded to the tenths place:

39.5

Hope this helps :)

[tex]12b^2\sqrt[3]{2a}[/tex]

In word form, this is 12 b squared (RootIndex 3 StartRoot 2 a EndRoot

Or you could say 12b^2 times the cube root of 2a

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

Work Shown:

[tex]3b^2\sqrt[3]{54a}+3\sqrt[3]{2ab^6}\\\\3b^2\sqrt[3]{27*2a}+3\sqrt[3]{b^6*2a}\\\\3b^2\sqrt[3]{(3)^3*2a}+3\sqrt[3]{(b^2)^3*2a}\\\\3b^2\sqrt[3]{(3)^3}*\sqrt[3]{2a}+3\sqrt[3]{(b^2)^3}*\sqrt[3]{2a}\\\\3b^2*3*\sqrt[3]{2a}+3*b^2*\sqrt[3]{2a}\\\\9b^2\sqrt[3]{2a}+3b^2\sqrt[3]{2a}\\\\(9b^2+3b^2)\sqrt[3]{2a}\\\\\boldsymbol{12b^2\sqrt[3]{2a}}\\\\[/tex]

The idea here is that we break the cube roots into smaller pieces, so we pull out perfect cubes when factoring.

The sum of the expression is 12 b squared (Root Index 6 Start Root 2 a End Root) or 12b²∛(2a).

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

We have the expression,

3 b squared (Root Index 3 Start Root 54 a End Root) + 3 (Root Index 3 Start Root 2 a b Superscript 6 Baseline End Root).

In numerical form,

3b²∛(54a) + 3∛(2ab⁶)

To find the sum of the above expression:

we simplify the expression,

3b²∛(54a) + 3∛(2ab⁶)

= 3b²∛3³(2a) + 3∛(2a)(b²)³

= 9b²∛(2a) + 3b²∛(2a)

= 12b²∛(2a)

Therefore, the sum is 12b²∛(2a).

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Answer:

171

Step-by-step explanation:

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Answer:

45 minutes

Step-by-step explanation:

Assume task completed in total x hours

[tex]\frac{x}{10} + \frac{3}{8} + \frac{3}{12} = 1 \\ 12x + 45 + 30 = 120 \\ 12x = 45 \\ x = \frac{15}{4} = 3 \frac{3}{4}[/tex]

So q will take 45 more minutes

Answer:

Runner B

Step-by-step explanation:

speed = distance ÷ time

Runner A: 1 ÷ 8 = 0.125m/ms

Runner B: 2 ÷ 10 = 0.2m/ms

Runner C: 3 ÷ 20 = 0.15m/ms

Runner D: 5 ÷ 30 = 0.17m/ms

Runner B has the highest speed so he is the fastest runner.

The Algebraic equations (x - 20)² and x² - 20 have an equal value My number is 6.

Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.

I think of a number, if I subtract 10 from my number, then square the result, I get the same answer as if I square my number, then subtract 20 from the result.

Let the number be x.

If I subtract 20 from my number that is x - 20 then square the result that is (x-20)².

And if I square my number that is x² then subtract 20 from the result that is x² - 20.

Both the result are the same then we have

         (x - 20)² = x² - 20

x² - 20x + 100 = x² - 20

  -20x + 100 = -20

                  x = 6

My number is 6

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Answer:

it is related by 35 because you are adding 35.

Step-by-step explanation:

#1

[tex]\\ \rm\Rrightarrow \dfrac{WX}{UV}=\dfrac{HI}{FE}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{WX}{16}=\dfrac{10}{8}[/tex]

[tex]\\ \rm\Rrightarrow WX/2=10[/tex]

[tex]\\ \rm\Rrightarrow WX=20[/tex]

Again

#2

[tex]\\ \rm\Rrightarrow \dfrac{WX}{UT}=\dfrac{HI}{FG}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{20}{20}=\dfrac{10}{FG}[/tex]

[tex]\\ \rm\Rrightarrow FG=10[/tex]

Answer:

WX = 20

FG = 10

Step-by-step explanation:

If EFGHI ~ VUTXW

then:

The only pair of sides that both have measures is EF and VU

EF = 8

VU = 16

VU/EF = 16/8 = 2

Therefore, VUTXW is enlargement of EFGHI by a scale factor of 2.

As HI = 10

⇒ WX = 10 × 2 = 20

As UT = 20

⇒ FG = 20 ÷ 2 = 10

Answer:

$ 8.10

Step-by-step explanation:

3.60   *   2.25  =

Answer: b: 10, 16, 23, 28, 32

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

its B !

Answer:

$4,014.68

Step-by-step explanation:

A = $4,014.68

A = P + I where

P (principal) = $3,000.00

I (interest) = $1,014.68

First, convert R as a percent to r as a decimal

r = R/100

r = 6/100

r = 0.06 rate per year,

Then solve the equation for A

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

A = 3,000.00(1 + 0.06/1)^(1)(5)

A = 3,000.00(1 + 0.06)^(5)

A = $4,014.68

Answer: n2.4

Step-by-step explanation:

Average age=6⋅1+4⋅2+3⋅3+5⋅46+4+3+5=4318=2.38888...=2.4

The average age of a child attending this daycare is 2.4 years old.

The expression 14e - 16 is an algebraic expression, and the factored expression is 2(7e - 8)

The expression is given as:

14e - 16

Express both terms as a product of 2

14e - 16 = 2 * 7e - 2 * 8

Factor out 2 in the expression

14e - 16 = 2 * (7e - 8)

Remove the product sign

14e - 16 = 2(7e - 8)

Hence, the factored expression of 14e - 16 is 2(7e - 8)

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Answer:

you just need two points to graph it.

x=0, you get y=0; which is the origin.

x=1, y=4.

you should get something like this:

Step-by-step explanation:

Answer:

m<7

m is greater than 7, i hope that helps

Answer:

m<7

Step-by-step explanation:

-5+20m+3<18m+12

Group like terms

20m-18m<12+5-3

2m<17-3

2m<14

2m÷2<14÷2

m<7

hope this helps *_*

pls brainliest