Nancy left a bin outside in her garden to collect rainwater. she notices that 1 over 2 gallon of water fills 2 over 3 of the bin. write and solve an expression to find the amount of water that will fill the entire bin. show your work. explain your answer in words.

Using an exponential function, it is found that:

An exponential function is modeled by:

[tex]y = ab^x[/tex].

In which:

The parameters for this problem are given as follows:

a = 2, b = 2.

Hence the number of bacteria after x hours is given by:

[tex]y = 2(2)^x[/tex]

After 6 hours, the amount is:

[tex]y = 2(2)^6 = 2^7 = 128[/tex]

After 24 hours, the amount is:

[tex]y = 2(2)^{24} = 2^{25} = 33554432[/tex]

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Answer:

Step-by-step explanation:

43.55 + 18.62 = 62.17

The domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}

The function is given as

g(x) = –⌊x⌋ + 3

The above is a step function, and the domain is the set of input values it can accept

Step functions of the given form can accept any real value of x

Hence, the domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}

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Complete question

The graph of the step function g(x) = –⌊x⌋ + 3 is shown. What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}

Answer:

A

Step-by-step explanation:

Answer:

C. [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

When you convert a fraction division into multiplication, you convert the divisor into its reciprocal. The reciprocal of [tex]\frac{2}{7}[/tex] is [tex]\frac{7}{2}[/tex]. So you get your answer  [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex].

Total Saving of Ethan is = $4600

Saving after donating 20% = $4600-$920

                                              =$3680

What is Percentage ?

As a fraction of 100, a percentage is a number or ratio. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent sign ("percent") is frequently used to indicate it. A % has no dimensions and no associated unit of measurement.

How to calculate percentage?

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. The formula for percentage calculation is (value/total value)100%

Solution :

Let the Saving be 100%

Donated salary 20% = $920

finding 80% of the saving

Formula for percentage:

                                        [tex]\frac{value}{total value} *100[/tex]

                                        =[tex]\frac{20}{100} *920[/tex]

                                        = [tex]5*920[/tex]

                                        = [tex]4600[/tex]

Then the Total saving =$4600

The Total saving after donating 20% = $3680

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Answer: x=11

Step-by-step explanation:

The lines are parallel, which you can tell by the two arrows. 4x-8 is a corresponding angle to 3x+3, meaning they are congruent.

4x-8 = 3x+3

x=11

Answer:

x = 11

Step-by-step explanation:

these angles are corresponding angles so they are equal to each other.

4x - 8 = 3x + 3 Subtract 2x from both sides

x - 8 = 3   Add 8 to both sides

x = 11

Plug 11 back into the equations find the angle measurements

4(11) -8 = 36 degrees

3(11) + 3 =  36degrees

The total amount of fencing they need = 38x + 10.

Perimeter for the rectangular fencing of the home = 160 yards

Perimeter for the square fencing of the pool = 40 yards

Perimeter of a rectangle = 2(length + width)

Perimeter of a square = 4(side length).

Perimeter for the rectangular fencing of the home = 2(3 + 10x + 2 + 5x) = 2(15x + 5) = 30x + 10

Perimeter for the square fencing of the pool = 4(2x) = 8x

The total amount of fencing they need = 30x + 10 + 8x = 38x + 10.

If x = 5, then:

Perimeter for the rectangular fencing of the home = 30x + 10 = 30(5) + 10 = 160 yards

Perimeter for the square fencing of the pool = 4(2x) = 8x = 8(5) = 40 yards.

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Answer:

38
160
40

Step-by-step explanation:

The domain and the range of the function are given as follows:

b. Yes; domain: all re.al numbers; range: y greater-than-or-equal-to 0.

Since each input is related to only one output values, the graph is a function. It is defined for all values of x, assuming only non-negative values, hence the correct option is:

b. Yes; domain: all re.al numbers; range: y greater-than-or-equal-to 0.

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Answer:

Infinite solutions.

Step-by-step explanation:

 y = 5 - 2x

 2x + y = 5  ---------(I)

 a₁ = 2  ; b₁ = 1  and c = 5

4x + 2y = 10

a₂ = 4  ; b₂ = 2   and c₂  = 10

[tex]\sf \dfrac{a_1}{a_2}=\dfrac{2}{4}=\dfrac{1}{2}\\\\\dfrac{b_1}{b_2}=\dfrac{1}{2}\\\\\dfrac{c_1}{c_2}=\dfrac{5}{10}=\dfrac{1}{2}[/tex]

⇒  [tex]\sf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=\dfrac{1}{2}[/tex]

So, the line are coincident and has infinite solutions.

Answer:

1025.76

Step-by-step explanation:

Formula for a right rectangular pyramid is (l*w*h)/3

The length and width are both 18.7, so we can plug that in. The height is 8.8.

It becomes:

(18.7*18.7*8.8)/3, which equals the answer above.

The weight of the puppy after the first month as described is; 26.65lbs.

Since, it follows from the task content that the initial weight of the puppy is; 20.5lbs and it gained 30% of this after 1 month, it follows that the weight of the puppy after one month is;

Weight = 20.5lbs × 130% = 26.65lbs.

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Answer:

Min: 32

Lower Quartile: 36

Median: 42

Upper Quartile: 47

Max: 53

Interquartile: 11

Step-by-step explanation:

The min. is just the lowest number.  The lower quartile is the number in the middle of the numbers below 42, the median is the number in the very middle, the upper quartile is the middle number above 41 and the interquartile is the upper quartile minus the lower quartile.  

The equation which could be used to find the length of the hypothenuse is; 5 squared + 8 squared = c squared.

It follows from the task content that the equation which could be used to find the length of the third side be determined.

Hence, since it follows from Pythagoras theorem that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides of a right triangle.

Hence, the required equation is; 5 squared + 8 squared = c squared.

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Answer:

The answer is A
5 squared + 8 squared = c squared

Step-by-step explanation:

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

This question is incomplete, the complete question is:

Which of the following is equivalent to 5 sqrt 13³ ?.

A) 13^2.

B)13^15.

C)13^(5/3).

D)13^(3/5)

Given the expression; 5 sqrt 13³

This can be represented as; ⁵√13³

To convert from radical form to exponential form, we use apply the radical rule;

[tex]\sqrt[n]{a^m} = a^{m/n}[/tex]

Hence,

[tex]\sqrt[5]{13^3} = 13^{3/5}[/tex]

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

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Answer:

  (d)  f(x) = -x²

Step-by-step explanation:

For the vertex of the quadratic function to be at the origin, both the x-term and the constant must be zero. That is, the function must be of the form ...

  f(x) = a(x -h)² +k . . . . . . . . . . vertex form; vertex at (h, k)

  f(x) = a(x -0)² +0 = ax² . . . . . vertex at the origin, (h, k) = (0, 0)

Of the offered answer choices, the only one with a vertex at the origin is ...

  f(x) = -x² . . . . . a=-1

Based on Cody Ray's credit card details and the unpaid-balance method, Cody Ray's unpaid balance is $144.44 and his previous balance is $144.44. His new balance is $147.04

His unpaid balance is:

= Purchases + Finance charge - (Payments + Credit)

= 376.90 + 17.54 - 250

= $144.44

Previous balance is the $17.54 finance charges.

New balance:

= Unpaid balance + Finance charge + New Purchases

= 144.44 + (144.44 x 1.8%)

= $147.04

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Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.                      

Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.

Pythagoras theorem, [tex]x^{2} + y^{2} = (12)^{2}[/tex]       --->(1)

Given,[tex]\frac{dx}{dt}= 2feet/second[/tex]   at x=3

Put x=3 in Pythagoras theorem equation (1)

[tex](3)^{2} + y^{2} = 144[/tex]

         [tex]y^{2} = 144 - 9[/tex]

        [tex]y^{2}[/tex]  =  135

        y = 11.61

Derive equation (1) w.r.t to 't'

[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]                ---->(2)

substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

[tex]2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0[/tex]

12 + 23.22 [tex]\frac{dy}{dt}[/tex]  = 0

                  [tex]\frac{dy}{dt}= \frac{-12}{23.22}[/tex]

                  [tex]\frac{dy}{dt} = -0.518[/tex]

Hence,  using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.  

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

A simple main effect analysis looks at the mean difference at each level of the independent variable.

Given With a simple main effect, the analysis examines.

Simple effects are also called the main effects of design of experiments. The main effect can be defined as the effect of the explanatory variables measured on a particular criterion or response variable of the study. It's easy to say that what happens within the level of the explanatory variables is the difference. In a factorial experiment, the simple main effect is that one independent variable is at a specified level of another. The main effect of one independent variable is averaged across the levels of the other independent variable. For a simple main effect, the results are analyzed as if a separate experiment was performed at each level of the other independent variables.

Therefore, a simple main effect analysis looks at the mean difference at each level of the independent variable.

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Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:

p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.

Hence, out of 44,000 adults, the expected number is found as follows:

0.4412 x 44000 = 19,413.

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The median value of x is 2.

According to the statement

we have given the values of x at some points then

and we have to find the median for the x.

We know that the median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.

and after put the values in this formula we get our median value for x.

So,

we have given that the f(x) is 0.2 when x is from -1 to 0

and f(x) is 0.2 +1.2x when x is grater than 0 but less than 1

and f(x) is 0 when x is less than -1 or grater than 1

From these statements it is clear that the the f(x) is only exist when the x lies in between from the -1 to 1.

So, the total value of x becomes is -1,0,1

Then according to the median formula

median = (n + 1) ÷ 2

median = (3+1) / 2

median = 2.

So, The median value of x is 2.

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Step-by-step explanation:

x=8-y

2x-y=7

2(8-y)-y=7

16-2y-y=7

-3y=-9

y=3

x=8-y

x=8-3=5

Answer:

Hello

Step-by-step explanation:

Méthode par combinaisons linéaires:

[tex]\left\{ \begin{array}{ccc|c|c}x+y&=&8&1&-2\\2x-y&=&7&1&1\\\end {array} \right.\\\\\\\left\{ \begin{array}{ccc}3x&=&15\\-3y&=&-9\\\end {array} \right.\\\\\\\boxed{\left\{ \begin{array}{ccc}x&=&5\\y&=&3\\\end {array} \right. }\\[/tex]

Proof:

5+3=8 and 2*5-3=7

Answer:

the answer is 22

Step-by-step explanation:

12,15,22,37,49

since 22 is in the middle its the median (make sure you put the #'s from least to greatest)

Answer:

22

Step-by-step explanation:

22, 37, 49, 15, 12

First put the data set from least to greatest.

12, 15, 22, 37, 49

The median is the middle number of the data. In this case, the median is 22.

Hope this helps!

The missing number for the subtraction of matrices is 4.

The subtraction of two matrices of the same size is really direct. You just need to subtract the elements that are in the same position, then:

[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right] \\\\B = \left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]\\\\A - B = \left[\begin{array}{ccc}a_{11} - b_{11}&a_{12}-b_{12}\\a_{21} - b_{21}&a_{22}-b_{22}\end{array}\right][/tex]

Then the missing therm will just be equal to the difference between the last two elements of each matrix:

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

The missing number is 4.

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The Surface area of the triangular prism with the net shown below is 106 cm²

An equation is an expression that shows the relationship between two or more variables and numbers.

Surface area of the triangular prism = 2(0.5 * 5 * 3) + (7 * 3) + 2(7 * 5) = 106 cm²

The Surface area of the triangular prism with the net shown below is 106 cm²

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The total cost in 5 hours is $225

Given that the charges of a supply fee of an artist is $50

The charges per hour classes is $35

The total cost is expressed by c

The number of hours expressed by h

We need to calculate the total cost in 5 hour lesson

As per the given statement ,

C= 50 +35h

Where h is the number of hours

h = 5 hours

C = 50 + 35h

C = 50 + 35(5)

C = 50 +175

C = $225

The total cost in 5 hours is $225

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Answer:

sum

Step-by-step explanation:

example

2+3=5