A container holds 44 cups of water. how much is this in gallons

Answer: Therefore, the population will exceed 100,000 in the year 2005 + 10.73 ≈ 2016.

Step-by-step explanation:   a) The population of the town in 2005 is given by the formula, where t = 0 since 2005 is the starting year:

P = 50,000(1.15)^0 = 50,000

Therefore, the population of the town in 2005 was 50,000.

b) We need to find the value of t when the population P exceeds 100,000:

100,000 = 50,000(1.15)^t

Divide both sides by 50,000:

2 = 1.15^t

Take the natural logarithm of both sides:

ln 2 = ln (1.15^t)

Apply the power rule of logarithms:

ln 2 = t ln 1.15

Divide both sides by ln 1.15:

t = ln 2 / ln 1.15

Using a calculator, we get:

t ≈ 10.73

Answer:

David share is 36 sweets

Step-by-step explanation:

let Lucy share be x

let David share be y

Lucy has 27 more

x=y+27

total sweet is x+y

y+27 +y= 2y+27

total ratio = 4+7=11

David share=

\(y = \frac{4}{11} \times (2y + 27)\)

\(11y = 4(2y + 27)\)

\(11y = 8y + 108\)

\(11 y- 8y = 108\)

\(3y = 108\)

y=108/3= 36

Answer:

8

Step-by-step explanation:

the degree is the highest exponent value

Given:

Point G is on line segment FH. FG = 8 and GH = 11.

To find:

The length of FH​.

Solution:

Point G is on line segment FH. So, by segment addition property, we get

\(FH=FG+GH\)

Substitute FG = 8 and GH = 11.

\(FH=8+11\)

\(FH=19\)

Therefore, the length of FH​ is 19 units.

Length of FH is 19 unit

Given that;

FH is a line segment

Length of FG = 8 unit

Length of GH = 11 unit

Find:

Length of FH

Computation:

Length of FH = Length of FG + Length of GH

Length of FH = 8 + 11

Length of FH = 19 unit

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The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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The length of the real life plane is 8000 centimetres.

The scale model as a ratio is  1:2000.

A model of a plane has a length of  4 cm. The real life plane has a model of 80 m.

The length of the real life plane in centimetres is as follows:

1 metre = 100 centimetres

80 metres = ?

cross multiply

length of the real life plane in cm = 80 × 100

length of the real life plane in cm = 8000 centimetres

The scale model can be calculated as follows;

scale model = 4 / 8000

scale model = 1 / 2000 = 1:2000

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The distance traveled is 1190 m. We can evaluate using the speed and time formula.

Given Speed = 30mph

Time = 3.5 hr

We know that

Speed = Distance / Time

340 = distance /3.5

Distance = 1190m

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Answer: I'm assuming you want to know how much surface area his fence is, so 40

Step-by-step explanation: First we can divide 15 by 3 to get 5, and then multiply 5 by 8. This gives us 40, which is our answer.

Hope this helps :)

Answer:

ok whats the question tho is it the total length of the fence if it is its 40 pretty sure

Step-by-step explanation:

3/8 of the fence lets say x, equals 15 feet

divide 15 by 3/8 to find x which is 40

Answer:

You could talk on the phone for 200 minutes at night, or 40 minutes during the day.

For every 5 minutes you reduced your night time talking, you could talk during the day for 1 minute.

Step-by-step explanation:

0.50d + 0.10n < $20

0.50d < $20 --> d < 40 minutes

0.10n < $20 --> n < 200 minutes

50,000 because 8 is larger than 5 so you round up to 5 in the ten thousands place.

The total amount after forty years with interest compounded every twenty years is ₹ 56,444.61 and the total interest earned is ₹ 6,444.61.

To find the total amount and total interest after forty years with interest compounded every twenty years, we can use the formula of compound interest

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

Where

A = total amount

P = principal amount = ₹50,000

r = annual interest rate = 0.5%

n = number of times interest is compounded per year = 1 (compounded every 20 years)

t = time in years = 40

Using this formula, we can calculate the total amount and total interest as follows

Total amount = P(1 + r/n)^(nt) = 50000(1 + 0.005/1)^(12) * (1 + 0.005/1)^(12) = ₹ 56,444.61

Total interest = Total amount - Principal = ₹ 56,444.61 - ₹ 50,000 = ₹ 6,444.61

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The distance  from Link to the Octorok  is 10.63 units.

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below:

distance = √( (x₂ - x₁)² + (y₂ - y₁)²)

Here we want to find the distance from Link to the Octorok so Link can attack, so we need to get the distance between the points (-4, -5) and (3, 3).

The distance will be:

distance = √( (3 + 4)² + (3 + 5)²)

distance = √( (7)² + (8)²)

distance = √113

distance = 10.63

The distance is 10.63 units.

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Answer:

49÷0.20= 245

He has to be able to have a number of text each month to be able to switch so 0.20 for each text he sends each month so you have to divide from 49.

Answer:

$4.73

Step-by-step explanation:

just do 20 minus 15.27

Answer:

A = bh

Step-by-step explanation:

Area = base × height

Area = base · height

A = bh

Answer:

250 girls

Step-by-step explanation:

Add the ratio together (2+5=7), then do 350÷7=50

50 is one part of the ratio so to find how many girls, you would do 50x5=250

9514 1404 393

Answer:

Step-by-step explanation:

The figure and its image are symmetrical about the origin, so the following three transformations are equivalent:

  1. reflection across the origin

  2. rotation 180° about the origin

  3. reflection across both x- and y-axes, in either order

__

The figure itself has left-right symmetry, so only one reflection is necessary to map the figure to its image: reflection across a horizontal line. Following that reflection, the image can be put into place by an appropriate translation. One such pair of transformations is ...

  4. reflection across the x-axis and translation 6 units right, in either order

Answer:

\(\frac{5.23}{9} = 0.581111\)

Step-by-step explanation:

5.23 / 9 = 0.5811111

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .

a. Input variables: hours worked as a cashier, payroll clerk, and assistant.

The total amount earned each week is the output variable.

b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:

Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)

c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).

d. The equation describing the total money earned each week is as follows:

(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y

This expression is simplified as follows:

y = 190 + 9x - 70 + 7x

y = 16x + 120

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.

g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:

y = 16x + 120 + 0

y = 16x + 120

As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.

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Answer:

119/30

Step-by-step explanation:

14/3-7/10

Answer:

$2

Step-by-step explanation:

To find the unit cost, divide the entire price of all the songs (22), by how many songs you bought (11)

22 Dollars / 11 Songs   =    2 Dollars / Song   (2 Dollars per Song)

Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

Answer:

23552

Step-by-step explanation:

23, 92, 368...   is a geometric sequence.

first term = a = 23

common ratio = r = 2 term ÷ first term = 92 ÷ 23 = 4

nth term = \(ar^n^-^1\)

6th term = \(23*(4)^6^-^1\)

\(=23*4^5\)

\(=23*1024\)

\(=23552\)

Hope this helps :)

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The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Given,

The points which the line passes, (x₁, y₁) = (7, 6)

Slope of the line, m = 0

We have to find the equation of the line:

We know that,

y - y₁ = m(x - x₁)

So,

y - 6 = 0(x - 7)

y - 6 = 0

y = 6

That is,

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

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Answer:

0.4 hours

Step-by-step explanation:

or 24 minutes :D

If the image distance is greater than the object distance, then according to the magnification ratio, the image height must also be equal to the object height.

The student is solving the quadratic equation by completing the square.

Answer:

$27.20 is the answer. just multiply and then add

Answer:

It will cost her $23.1 to send the little packages and, $4.10 to send one big package.

Step-by-step explanation:

Its very easy multiply the cost which is $3.30 times the amount which is 7 and that your answer $23.1. Than do the same for the big package multiple $4.10 times 1 and you get $4.10.