How would the equation look if you sell 60
liters in one day?

Divide by 12 to go from the APR to the monthly interest rate

(9.5%)/12 = 0.7916667%

The decimal form is 0.007916667 approximately.

Multiply this with the starting balance $1367.90 and we get:

0.007916667*1367.90 = 10.8292 which rounds to 10.83

The interest payment for the 1st month is $10.83; which means the principal payment would be 400-10.83 = 389.17

This principal payment will then drop the balance from $1367.90 to 1367.90-389.17 = 978.73 dollars.

The value $978.73 is now the starting balance of the 2nd month. This process of...

is repeated until the balance is $0.

This is what the table would look like

[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6}\text{Month} & \text{Starting} & \text{Interest} & \text{Principal} & \text{Payment} & \text{Ending }\\& \text{Balance} & & & & \text{Balance}\\\cline{1-6}1 & 1367.9 & 10.83 & 389.17 & 400 & 978.73\\\cline{1-6}2 & 978.73 & 7.75 & 392.25 & 400 & 586.48\\\cline{1-6}3 & 586.48 & 4.64 & 395.36 & 400 & 191.12\\\cline{1-6}4 & 191.12 & 1.51 & 191.12 & 192.63 & 0\\\cline{1-6}\end{array}[/tex]

Many credit card companies and banks offer free calculators on their website, or you can find similar free calculators online elsewhere, that will quickly calculate a table like shown above. It is called an amortization table or amortization schedule.

With the exception of the 4th month, each row has the principal and interest add to the $400 monthly payment. The last row will have a payment of 1.51+191.12 = 192.63 dollars.

The total amount paid back would be 400+400+400+192.63 = 1392.63 dollars. This is the sum of the values in the "payment" column.

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Here's another way to determine the answer.

The monthly payment formula is

[tex]\displaystyle P = \frac{Li}{1 - (1+i)^{-n}}[/tex]

where,

In this case,

Let's solve for the variable n. We'll need logarithms to isolate the exponent.

Part 1

[tex]\displaystyle P = \frac{Li}{1 - (1+i)^{-n}}\\\\\\\displaystyle 400 = \frac{1367.90*0.007916667}{1 - (1+0.007916667)^{-n}}\\\\\\\displaystyle 400 = \frac{10.8292087893}{1 - (1.007916667)^{-n}}\\\\\\\displaystyle 400(1 - (1.007916667)^{-n}) = 10.8292087893\\\\\\[/tex]

Part 2

[tex]\displaystyle 1 - (1.007916667)^{-n} = 10.8292087893/400\\\\\\\displaystyle 1 - (1.007916667)^{-n} = 0.0270730\\\\\\\displaystyle -(1.007916667)^{-n} = 0.0270730-1\\\\\\\displaystyle -(1.007916667)^{-n} = -0.9729270\\\\\\\displaystyle (1.007916667)^{-n} = 0.9729270\\\\\\[/tex]

Part 3

[tex]\displaystyle \log((1.007916667)^{-n}) = \log(0.9729270)\\\\\\\displaystyle -n*\log(1.007916667) = \log(0.9729270)\\\\\\\displaystyle n = -\log(0.9729270)/\log(1.007916667)\\\\\\\displaystyle n = 3.4805965\\\\\\[/tex]

Each decimal value is approximate.

That value of n then rounds up to the nearest integer n = 4

We do not round to n = 3 since that would be one month short, as shown in the table above.

You can use a graphing calculator to quickly solve that equation for the variable n. It can be used as a way to visually confirm the answer.

Answer:

22mile=1sec

x=360sec

criss cross method

(x)(1)=360×22

x=7920miles

A function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f is f(x) = 3x^4/4 + 729/4.

In the given question, we have to find a function f such that f'(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.

The given function is f'(x) = 3x^3.

No integrating on both side,

f(x) = [tex]\int3x^3dx[/tex] + C

f(x) = 3x^4/4 + C

As given, the line 81x + y = 0 is tangent to the graph of f.

So, slope at point of tangent; f'(x) = -81

So, 3x^3 = -81

Divide by 3 on both side, we get

x^3 = -27

Taking cube root on both side, we get

x = -3

So putting the value of x in 81x + y = 0, we get

y = 243

Thus, f(x) passes through (-3, 243).

So, 243 = 3/4(81) + C

Multiply by 4 on both side, we get

972 = 243 + 4C

Subtract 243 on both side, we get

4C = 729

Divide by 4 on both side, we get

C = 729/4

So, f(x) = 3x^4/4 + 729/4

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Answer:

Step-by-step explanation:

If the car holds at most 14.5 gallons of gas and you use 1.5 gallons of gas on the way to the grocery store, the amount of gas you have left in your tank can be represented by the inequality:

[tex]14.5 - 1.5 < = x[/tex]

This inequality can be read as "14.5 minus 1.5 is less than or equal to the amount of gas you have left in your tank, x."

Solving for x, we get:

[tex]x > = 13[/tex]

So the amount of gas you have left in your tank is greater than or equal to 13 gallons.

Answer:

2/3 + -1/3 = positive 1/3

Answer:

To find the sum of 2/3 + (-1)/3, you can first convert the fraction to an equivalent fraction with a common denominator. In this case, the common denominator would be 3. 2/3 can be written as 2 x (3/3) = 2/3 and -1/3 can be written as -1 x (3/3) = -1/3. Then, you can add the numerators and the denominator will remain the same. So, the sum of 2/3 + (-1)/3 is 1/3.

The linear equation that represents the plant height is the one in the first option:

y = 14 + (3/2)x

We know that the initial height of the plant (this will be the y-intercept of the line) is 14cm, and we also know that the plant grows at a rate of 3/2 cm each day.

So, after x days, the plant is x times 3/2cm plus 14 cm of height, so the linear equation is:

y = 14 + (3/2)x

So the correct option is the first one.

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To find the total mass of all the worker bees in the hive, you need to multiply the mass of a single worker bee by the number of worker bees in the hive.

The mass of a single worker bee is 2 x 10^-4 kilograms, and there are 8 x 10^4 worker bees in the hive.

So the total mass of all the worker bees in the hive is (2 x 10^-4 kilograms) * (8 x 10^4 worker bees) = 0.16 kilograms.

In standard form, this is written as 1.6 x 10^-1 kilograms.

Answer:

To find the area of a triangle, we can use the formula:

Area = (base * height) / 2

To find the area of triangle ABC, we first need to find the base and the height.

Since angle B is 75 degrees, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle A: 180 - 75 - 90 = 15 degrees.

Then, we can use the fact that the measure of an angle in a triangle is proportional to the length of the side opposite that angle to find the length of side AC:

AC/AB = m∠A/m∠B

AC = (m∠A/m∠B) * AB

Substituting, we get:

AC = (15/75) * 12 = 3

Now that we know the base and the height of the triangle, we can use the formula to find the area:

Area = (3 * 12) / 2 = 18

Therefore, the area of triangle ABC is 18 square cm.

The probability of ending up with an orange hat is 1/12. It is because here are twelve possible outcomes.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

It is represented mathematically as;

Probability = Number of Expected outcomes / Total number of outcomes

From the question, we can have the following outcomes;

Clothing = 4

Colors = 3

Pr (pick a clothing) = 1/4

Pr (pick a color) = 1/3

Pr (picking an orange hat) = 1/4 x 1/3

Pr (picking an orange hat) = 1/12.

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It s true that a text file contains bytes of data that represent characters from a particular character set such as Unicode or ASCII. The correct option to this question is "True".

The text file contains texts that are represented by Unicode or ASCII. The Unicode or ASCII represents how the numbers, text, or other commands are displayed and written in a text file.

To represent text digitally in the text file, characters have their own unique character representation bit-pattern. These bit-pattern have a combination of 1s and 0s. And these patterns are represented by character codes that are either Unicode or ASCII.

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Answer:

maybe 16

I hope I helped

Step-by-step explanation:

joining m < 5 = m < 7

8x – 14 = 5x + 34

8x – 5x = 34 + 14

3x = 48

divide both sides by 3

x = 48/3

x = 16

The point where the tangent to the given equation is horizontal is [tex](x, y) = (-2, -5)[/tex].

To find the tangent of a curve, we have to find the first derivative of the function. Hence, the tangent of the given curve is given by

⇒ [tex]f'(x) = \frac{d{f(x)}}{dx} = \frac{d{x^{2}}}{dx} + \frac{d(4x)}{dx} - \frac{d(1)}{dx}[/tex]

⇒ [tex]f'(x) = 2x + 4[/tex]

Now, as the tangent is horizontal, that means the slope of the tangent is 0, hence setting [tex]f'(x) = 0[/tex] , we get the equation

⇒ [tex]f'(x) = 2x + 4 = 0[/tex]

Solving the equation obtained for the variable x,

⇒ [tex]2x = -4\\[/tex]

⇒ [tex]x = -2[/tex]

Now, putting the obtained value for x in the original equation, we get

⇒ [tex]f(x) = (-2)^{2} + 4(-2) - 1\\[/tex]

⇒ [tex]f(x) = -5[/tex]

Hence, the point where the tangent to the given equation is horizontal is [tex](x, y) = (-2, -5)[/tex].

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The measurement of angles △XYZ are ∠X = 59°, ∠Y = 89°, and ∠Z = 32°.

The measurement of angles △LMN are ∠L = 59°, ∠M = 89°, and ∠N = 32°.

What is angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that, △XYZ and △LMN are similar triangle.

Since the triangles are similar, thus the measurement of triangles are similar.

Therefore,

∠X = ∠L, ∠Y = ∠M, ∠Z = ∠N.

∠Y = ∠M = 89° and ∠Z = ∠N = 32°.

The sum of all interior angles of triangle is 180°.

∠X + ∠Y + ∠Z = 180°

∠X + 89° + 32° = 180°

∠X + 121° = 180°

Subtract 121° from both sides:

∠X  = 59°

∠X = ∠L = 59°.

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The equation that represents the number of time a cricket chirp (y) given the temperature (x) in degree Fahrenheit is y = 0.23 x + 40

Steps to translate a word problem into an equation or a function:

- Assign the unknowns to variables

- Identify which one is independent variables, which one is dependent variables. The independent variable will become the input while the dependent variable will become the output.

In the given problem, there are two variables:

- temperature in the air (in Fahrenheit)

- number of time a cricket chirp

From the problem, we can conclude that the number of time a cricket chirp depends on the temperature of the air. Hence,

independent variable =  temperature in the air (in Fahrenheit)

dependent variable = number of time a cricket chirp

Let:

y =  number of time a cricket chirp

x =  temperature in the air (in Fahrenheit)

It is said: The number of chirp per minute is equal to 0. 23 times the temperature of the air, in degree Fahrenheit, plus forty.

We can translate it into an equation:

y = 0.23 x + 40

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The illustrated volume of the cylinder is 769cm³.

One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In many contemporary branches of geometry and topology, a cylinder can also be defined as an infinite curvilinear surface.

It should be noted that the formula for finding the volume of a cylinder is πr²h

where π = 3.14

r = radius

h = height

Let's assume that the height is 5cm and radius is 7cm. The volume will be:

V = πr²h

Volume = 3.14 × 7² × 5

Volume = 769cm³

Note that your information was incomplete and an overview was given.

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Answer:y=7.5x

Step-by-step explanation:

In the 9th grade HMH Math book for teachers, it explains that you must divide 150 by 20 and put it in the equation.

Answer:

Step-by-step explanation:

Answer is B.

Function 1: slope is 2

Function 2: (-5 + 4)/(2-1)= -1/1= -1

Answer: Sofia needs to order an additional 100 - 24 = 76 pieces of sushi.

Since each roll contains 12 pieces, Sofia needs to order 76 / 12 = 6 additional rolls of sushi.

At a cost of $8 per roll, Sofia will need to pay an additional 6 * $8 = $48 for the additional sushi.

Step-by-step explanation:

Answer:

Read carefully below

Step-by-step explanation:

In general, the inverse of a function f(x) is a function g(x) such that f(g(x)) = g(f(x)) = x for all values of x in the domain of f(x) and g(x). To find the inverse of a function, we need to switch the input and output variables and solve for the new output variable.

In this case, we are given the function -2f(x+5)-4. To find the inverse of this function, we need to switch the input and output variables and solve for the new output variable, which we will call y. We can do this by first moving all the terms to one side of the equation, and then solving for y:

-2f(x+5) - 4 = y

-2f(x+5) = y + 4

f(x+5) = (y + 4) / -2

This is the inverse function of -2f(x+5)-4. However, keep in mind that not all functions have inverses. In particular, a function must have the property that it is one-to-one (i.e. it maps unique inputs to unique outputs) in order to have an inverse. It is not clear from the given information whether the function -2f(x+5)-4 is one-to-one, so it is possible that it does not have an inverse.

Answer:

2,3 and 7

Step-by-step explanation:

168 = 2x2x2x3x7

= 2²x3x7

Answer:

m = -21.

Step-by-step explanation:

To solve this equation, we can use the distributive property to expand the left side and the right side of the equation:

19(2m - 16) = 13(2m + 4)

38m - 304 = 26m + 52

Then we can combine like terms on both sides of the equation to obtain:

38m - 26m = 52 - 304

12m = -252

Finally, we can divide both sides of the equation by 12 to find the value of m:

12m / 12 = -252 / 12

m = -21

Therefore, the value of m that satisfies the equation is m = -21.

Step-by-step explanation:

5.

y = 3

yes, that's it for this here too.

it means that any value for x is valid, and all have the assigned y value 3.

6.

remember, the usual equation for a line is

y = ax + b

"a" being the slope, "b" the y-intercept (the y-value when x = 0).

we see the y-value for x = 0 is 3. that is "b".

for the slope we need 2 points and calculate the x- and y- coordinate differences.

always look for points with integer coordinates.

I see e.g. (0, 3) and (3, 2).

x changes by +3 (from 0 to 3).

y charges by -1 (from 3 to 2).

the slope "a" = -1/+3 = -1/3

the equation is then

y = (-1/3)x + 3

7.

we do exactly the same things.

we see the y-value for x = 0 is +1. that is "b".

I see e.g. these points : (0, 1) and (3, 2).

x changes by +3 (from 0 to 3).

y changes by +1 (from 1 to 2).

the slope "a" is +1/+3 = 1/3.

the equation is

y = (1/3)x + 1

8.

and again the same things.

we see the y-value for x = 0 is +3. that is "b".

I see e.g. these points : (0, 3) and (-3, 0).

x changes by -3 (from 0 to -3).

y changes by -3 (from 3 to 0).

the slope "a" is -3/-3 = 3/3 = 1.

the equation is

y = x + 3

The equivalent expression to {(2 3/10)⁴ ÷ (9/10)⁵}⁴ is "2 and three tenths raised to the sixteenth power divided by nine tenths raised to the twentieth power".

The correct answer choice is option B

Exponents refers to the power to which a number, expression or symbol is to be raised. For instance, 4²; the exponent is 2 which is a power.

{(2 3/10)⁴ ÷ (9/10)⁵}⁴

= (2.3⁴ ÷ 0.9⁵)⁴

Multiply the powers

= 2.3¹⁶ ÷ 0.9²⁰

It can also be written as

(2.3)¹⁶ / (0.9)²⁰

Consequently, the expression which is equivalent to 2 and three tenths raised to the fourth power divided by nine tenths raised to the fifth power, all raised to the fourth power is (2.3)¹⁶ / (0.9)²⁰

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Answer:

I am 100% sure it is b

Step-by-step explanation:

I have proof( i did the test) and took a picture

Answer:

y= 6

Step-by-step explanation:

9³ = 3^y

3²^³ = 3^y

3⁶ = 3^y

therefore

y=6

Given the prime factorization of 90. The number that complete thi prime factorization is 2 × 3² × 5.

Factor tree

  90

   /\

2  45

     /\

  3  15

       /\

    3   5

The prime factorization

90 = 2 × 3 × 3 × 5

     = 2 × 3² × 5

So, the number that complete thi prime factorization is 2 × 3² × 5.

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Using the provided information we get,

a) Optimal quantity of city beautification projects is three.

b) 3124 city beautification is a public good because it is rival in consumption and non-excludable. So, Correct option is option (C).

The fictional city of Hurstville is trying to determine how many urban beautification projects it has. The city has two types of citizens, ones who appreciates beauty more than other type.

The average cost of each project = $400

We have given that

The combined marginal benefit curves are determined by horizontally adding up the in the individual marginal benefit curves. So, the optimal quantity of benefication projects is at the point where MSB is equal to MSE. Thus, the optimal outputs is 3 projects.

The city beneficiation is a public good because it is non-trivial in consumption and non-excludable.

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The percent increase  from last year to this year is 7.94%

From the question, we have the following parameters that can be used in our computation:

Initial height = 63 inches

New height = 68 inches

The percent change from last year to this year is then calculated as

Percent change = (New height - Initial height)/Initial height * 100%

Substitute the known values in the above equation, so, we have the following representation

Percent change = (68 - 63)/63 * 100%

Evaluate

Percent change = 7.94%

Hence, the percentage increase is 7.94%

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The required values of the z-score as per the corresponding blood pressure readings are: z-score = 1.267 when reading is 142, z-score = 0.6 when reading is 130, and z-score = -1.2- when reading is 103.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

Normally distributed with a mean of 121 and a standard deviation of 15.

As per the given question, we have

mean ц = 121

standard deviation σ = 15

For X₁ = 140

z-score = (X₁ - ц )/σ

z-score = (140 - 121)/15

z-score = (19)/15 = 1.267

For X₂ = 130

z-score = (X₂ - ц )/σ

z-score = (130 - 121)/15

z-score = (9)/15 = 0.6

For X₃ = 103

z-score = (X₃ - ц )/σ

z-score = (103- 121)/15

z-score = (19)/15 = - 1.2

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Answer:

let x as hotdog and x + 42 as soda

x + x + 42 = 250

2x + 42 = 250

2x + 42 - 42 = 250 - 42

2x = 208

x = 104

sodas sold: x + 42 = 104 + 42 = 146 sodas

hotdogs sold: x = 104 hotdogs

Step-by-step explanation:

Answer:

104 hot dogs sold

146 sodas sold

Step-by-step explanation:

s=number of sodas. h=number of hotdogs

s+h=250

s=h+42  ==> there were 42 more sells for soda than compared to hot dog

h+42+h=250  ==> plugin h+42 for s

h+h+42=250 ==> simplify

2h+42=250 ==> solve for h

2h+42-42=250-42 ==> isolate h by subtracting 42 on both sides

2h = 208

h = 208/2

h = 104 hot dogs sold

s=104+42  ==> plug in 104 for h in s=h+42

s = 146 sodas sold