Your original purchase price was $825.00 plus 7% sales tax. You enter into an agreement where the interest (12.5% APR) is waived for the first 12 months provided you make the required monthly payments; otherwise the interest is accrued from the date of purchase. You miss the first payment due date. The late fee is $35.00. How much is the interest?

1. ≈ 33759 bees

The parent function for exponential functions is y = a(b^x), where "a" is the initial value and "b" is the growth rate. In this case, "x" is the number of days, and "y" is the number of bees after "x" days. We already know that the initial value is 20, so we can set "a = 20". Next, we know that after 5 days, there are 29 bees, which we can also plug into our equation: "x = 5" and "y = 29". Then, we end up with the equation 29=20(b^5) and solve for the growth rate, "b". To solve for "b", first divide both sides by 20, and then take the 5th root of both sides:

29 = 20(b^5)

29/20 = b^5

^5√(29/20) = ^5√(b^5)

^5√(29/20) = b

Now, we know the equation to this problem is y = 20((^5√(29/20))^x). We can plug in "x = 100" to find the number of bees after 100 days.

y = 20((^5√(29/20))^100)

y ≈ 33759 bees

2. No, you can't find the inverse of the function y=4x^2 + 12x + 9, because, for an inverse to be possible, it must pass the horizontal line test, which this function does not pass. The domain restriction necessary would have to make it so the function passes the horizontal line test, which would mean restricting half of the function from its vertex in this case. The x-value of the vertex (refer to the vertex formula) of this function is -12/8, so we can restrict the domain by only letting the domain be [-12/8, +infinity). Finding the inverse (switch "x" and "y", and solve for "y"):

x = 4y^2 + 12y + 9                                x:  [-12/8, +infinity)

x - 9 = 4y^2 + 12y

x - 9 = 4y^2 + 12y

(x - 9)/4 = y^2 + 3y

(x - 9)/4 + 2.25 = y^2 + 3y + 2.25

(x - 9)/4 + 2.25 = (y + 1.5)^2

√((x - 9)/4 + 2.25) = y + 1.5

√((x - 9 + 9)/4) = y + 1.5

(√(x) / 2) - 1.5 = y

(-3 + √(x))/2 = y

3a. To solve this problem, we have to find a way to use "log base5 of 3" and "log base5 of 8" to get "log base5 of 2".

First, we can exclude the logbase5 so the problem is easier to look at. We need to find a way to get "2" using "3" and/or "8" (cannot use subtraction/addition in this step, and using "3" and/or "8" is required with multiplication/division). Keep in mind the rules of logs with the same base.

8^1/3 = 2

Now, we put the logbase5 back in:

logbase5 of (8^1/3) = logbase5 of 2

From log rules, we can move the exponent "1/3" down:

1/3 * logbase5 of 8

We know that logbase5 of 8 = 1.2920

1/3 * 1.2920

approximately 0.4307

3b. As previously explained, we need to use "3" and "8" to get to "75/8" while keeping in mind the rules of logs.

First, we can simplify "logbase5 of (75/8)":

logbase5 of (75/8) = (logbase5 of 75) - (logbase5 of 8)

Now, ignore the "logbase5" and use provided values of "3" and "8" to get to 75. Note that we can use the number 5: logbasex of x= 1 [x^1 = x]

(5^2) * 3 = 75

Next, place the "logbase5" back in, and simplify

logbase5 of ((5^2) * 3) - logbase5 of 8

logbase5 of (5^2) + logbase5 of 3 - logbase5 of 8

2logbase5 of 5 + logbase5 of 3 - logbase5 of 8

2(1) + 0.6826 - 1.2920

approximately 1.3906

The rearranged formula with the x as subject is x = 2y - 10

Formula

Formula refers a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign.

Given,

Here we have the formula y = 1/2x + 5

Now, we have to rearrange the given formula in order to make x as the subject.

Here we we need to find the formula, as x the subject,

So, the given formula,

y = 1/2 x+ 5

We have to move the number 5 to the left hand side, then the sign of the number changes into negative,

So, it can be written as,

=> y - 5 = 1/2x

Here we need the value of x alone, so move the number that is in division to the LHS, then it will be changed as multiplication, then we get,

=> 2 (y - 5)  =x

When we expand it, then we get,

=> 2y - 10 = x

Therefore, the formula that has x as subject is 2y - 10.

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The measurement of ∠1 =  136° and ∠2 = x = 44°, using Vertically opposed angles.

What is Vertically opposed angles?

Two lines intersecting at a point create vertical angles. Every time they are on an equal footing. Alternatively stated, four angles are created anytime two lines cross or intersect. Two opposed angles are equal and are referred to as vertical angles, as we can see. Due to their position opposite one another, they are also known as "Vertically opposed angles."

Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. The equality of the vertically opposed angles has been established.

∠x = 44

∠2 = x = 44

∠1 + ∠2 = 180

∠1 = 180 - 44 = 136°

Hence, The measurement of ∠1 =  136° and ∠2 = x = 44°.

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A) The explicit formula which model this situation will be;

⇒ an = $43,000 + $1,100n

Where, ''an'' be the construction worker's salary in the nth year.

B) The value of a₁₀ = $54,000

C) After 11 years her salary will be $55,100.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A construction worker's starting salary = $43,000.

And, Each year she receives a $1100 raise.

Now,

A) Let ''an'' be the construction worker's salary in the nth year.

So, We can formulate;

⇒ an = $43,000 + $1,100n

B) Since, The construction worker's salary in the nth year is,

⇒ an = $43,000 + $1,100n

Put n = 10, we get;

⇒ a₁₀ = $43,000 + $1,100 × 10

⇒ a₁₀ = $43,000 + $11,000

⇒ a₁₀ = $54,000

C) Let after n year her salary will be $55,100.

So, We can formulate;

⇒ an = $43,000 + $1,100n

⇒ $55,100 = $43,000 + $1,100n

Solve for n as;

⇒ $55,100 - $43,000 = $1,100n

⇒ $12,100 = $1,100n

⇒ n = 12,100 / 1,100

⇒ n = 11

Thus, After 11 years her salary will be $55,100.

Therefore, A) The explicit formula which model this situation will be;

⇒ an = $43,000 + $1,100n

Where, ''an'' be the construction worker's salary in the nth year.

B) The value of a₁₀ = $54,000

C) After 11 years her salary will be $55,100.

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The age of Molly is 24 years.

We have two persons. The names of the two persons are Wally and Molly. The age of Wally is 12 years. Billy has a cousin named Molly. The age of Molly is twice the age of Wally. It means that to find the age of Molly, we will multiply the age of Wally by two. Let the age of Molly be represented by the variable "x". A constant's value remains constant across time. A variable, on the other hand, changes its value depending on the equation. Variables are often written in alphabets or symbols. Constants are frequently written in numbers.

x = 2*12 = 24

Hence, Molly is 24 years old.

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Answer:

Step-by-step explanation:

8 10

Answer:Zn≅Zm implies (Z/2)n≅Zn/2Zn≅Zm/2Zm≅(Z/2)m.

Step-by-step explanation:

Answer:

Papina found 27 more shells than Camila.

Step-by-step explanation:

Let x = the number of seashells that Camila found.

That means that

4x = the number of seashells that Papina found.

Papina's shells + Camila's shells = 45

4x + x = 45

Combine like terms.

5x = 45

Divide by 5.

x = 9

Camila found x shells. That is 9 shells.

Papina found 4x shells.

4x

= 4(9)

= 36

Papina found 36 shells.

36 - 9

= 27

Papina found 27 more shells than Camila.

A deferred tax liability can arise when the tax return and the income statement report a revenue or expense in different years

A deferred tax liability is a balance-sheet entry that records taxes that are owed but are not due to be paid until a later date. The liability is postponed due to a timing difference between when the tax was accrued and when it is due to be paid.

On the balance sheet, deferred income tax appears as a liability. The most common cause of deferred income tax is a discrepancy between the IRS and GAAP depreciation methods. Income tax deferral can be classified as either a current or long-term liability.

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Answer:

Option B

Step-by-step explanation:

If 3 scoops = 6 quarts

Then we divide both sides by 3 to find :

1 scoop = 2 quarts

Now we multiply both sides by 6 :

6 scoops = 12 quarts

Now we multiply the 1 scoop equation by 9 to find the last value in the table :

9 scoops = 18 quarts

These values matches only table B

Hope this helped and have a good day

If you can give brainliest and check comments above

A. 136 in.
When spinning 180, you face backwards. When the initial spins, you can just think of it as moving the horn from the left hand to the right. That happens a second time. Two arms is equal to 68 in., so double of that is 136 in.

I don’t believe I can solve the 2nd question

The maximum value of the quadratic function F(x) = -3x² + 18x + 3 is 30 when x = 3

The quadratic equation is given as

F(x) = -3x² + 18x + 3

The above function is a quadratic function

As a general rule, a quadratic function has the following representation:

F(x) = ax² + bx + 3

This means that: a = -3

The value of a for a quadratic function must be less than 0 for the function to have a maximum

This means that the function has a maximum value because -3 is less than 0

Solving further, we have

F(x) = -3x² + 18x + 3

Differentiate and set to 0

-6x + 18 = 0

So, we have

x = 3

Substitute x = 3 in F(x)

F(3) = -3(3)² + 18(3) + 3

Evaluate

F(3) = 30

This represents the maximum value

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Answer:

Step-by-step explanation:

10$ for cheese pizza
15$ for peproni pizza

he sold 64 pizza in which 3 of them are of cheese
so therefore,

64-3=61
61*10 = 610
3*15  =  45

           ---------

           $655

In order to find the standard error of two samples, the following are needed:

1: Find the mean. .

2: Find each score's deviation from the mean. ...

3: Square each deviation from the mean.

4: Find the sum of squares.

5: Find the variance.

6: Find the square root of the variance.

The standard error is a statistical term that refers to the degree to which a sample distribution accurately represents a population using standard deviation.

A statistic's standard error is the standard deviation of its sampling distribution or an estimate of that standard deviation. The standard error of the mean is used when the statistic is the sample mean.

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To determine the standard error of two samples the following procedure are followed

First, determine the mean.

second: Calculate the variation between each score and the mean

third: Square each variation from the mean

4th: Determine the sum of the variance

5th: Determine the variance by dividing the sum in 3 by 1 less the number of sample

6th: Calculate the standard deviation by variance's square root

7th: find the square toot of the number of samples

lastly: divide the standard deviation by result of step 7

The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error.

It reveals how much the sample mean would change if you conducted the same study again with fresh samples drawn from a single population.

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Y=21,000(1.20)*. D=anan1 d = a n a n 1 is the formula for figuring out the common difference of an arithmetic series, where d is the common difference and an a n is the nth term. A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d".

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Answer:

[tex]5\frac{1}{3}[/tex]

Step-by-step explanation:

3 5/9 x 1 1/2

32/9 x 3/2

96/18

16/3

5 1/3

Hopes this helps please mark brainliest

The height that the Kite C can fly after the string on Kite C is tripled is 59.917 feet.

Given,

The length of the string on Kite C = 28 3/4 feet = 21.75 feet

The depth of the Kite C = -6 2/3 feet = -5.333 feet

The string on Kite C is tripled = 21.75 × 3 = 65.25 feet

We have to find the height of the Kite C can fly;

Here,

The first height that the Kite C can fly;

Length + depth = 21.75 + (- 5.333) = 16.417 feet

Now,

The height that the Kite C can fly after the string on Kite C is tripled;

Tripled length + depth = 65.25 + (-5.333) = 59.917 feet.

That is,

The height that the Kite C can fly after the string on Kite C is tripled is 59.917 feet.

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Answer:

pretty sure it is c

Step-by-step explanation:

Match up the sides for example 4 and 24 are on the same side

so 36 gets matched up with x

If you need a better explanation, comment on my answer lol

Hope it helps Have a good day : )

Answer:

The first one

Step-by-step explanation:

Answer:

y = 8/9 x - 4

Step-by-step explanation:

y-4 = 8/9(x-9)

y-4 = 8/9 x -8

y = 8/9 x +4 -8

y = 8/9 x -4

Answer:

y=8/9x-4

Step-by-step explanation:

4=8/9(9)+2

4=72/9+2

4=8+2

4=10

10-4=6

2-6=-4

4=8/9(9)-4

4=8-4

4=4

Hopes this helps please mark brainliest

The coordinate of the point on the directed line segment from (- 10, 2) to (-3,-5) will be;

⇒ (x , y) = (- 6, - 2)

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The two points are;

(- 10, 2) and (- 3, 5)

And, The partitions the segment into a ratio of 4 to 3.

Now,

Since, We know that;

The The coordinate of the point on the directed line segment from

(x₁, y₁) to (x₂, y₂) that partitions the segment into a ratio of m₁ to m₂ will be;

⇒ x = (m₁ x₂ + m₂ x₁) / (m₁ + m₂)

⇒ y = (m₁ y₂ + m₂ y₁) / (m₁ + m₂)

Hence, The coordinate of the point on the directed line segment from

(- 10, 2) to (-3,-5) will be;

x = (4×-3 + 3×-10) / (4 + 3)

x = (-12 - 30) / 7

x = - 42/7

x = - 6

And,

y = (4×-5 + 3×2) / (4 + 3)

y = (-20 + 6) / 7

y = - 14/7

y = - 2

Thus, The coordinate of the point on the directed line segment from

(- 10, 2) to (-3,-5) will be;

⇒ (x , y) = (- 6, - 2)

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Sara calculated the unit rate as dollars per orange whereas Sara's friend Daniel calculated unit rate as oranges per dollar.

What is unit rate?

One of a given object constitutes a unit. The cost of only one of an item is its unit rate. With one as the denominator, this is written as a ratio. For instance, you would move 7 yards on average every second if you covered 70 yards in 10 seconds.

Sara said there was a ratio of 12 to 8, so the unit rate was $1.50 per orange, it means she is calculating the unit rate as dollar per oranges.

Whereas, his friend Daniel, he thought the ratio would be 8:12, so the unit rate would be 8/12 oranges per dollar.

In this way both the unit rates are correct.

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The amount you need to sell the job if you want to make 15% net margin, based on the costs, is $7, 857.26

First, find the total cost for the project:
= Equipment + cost of labor + overhead

Cost of labor and equipment:

= 4, 200 + ( 16 x 32 per man- hour)

= $ 4, 712

The total cost is then:
= 4, 712 x ( 1 + 45%)

= $6, 832.40

The amount to sell for is:
= Total cost x ( 1 + net margin)

= 6, 832.40 x ( 1 + 15%)

= $7, 857.26

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The coordinates of point P along QR so that the ratio of QP to PR is 1 to 4 is P(6,3).

It is the comparison of one quantity with another. For example, if your weight is 30 kg and your father's weight is 90 kg, then the ratio of weight is 1:3.

Given:

The coordinates of Q = (8,4),

The coordinates of R = (-2, -1),

The ratio of QP/PR = 1/4,

Calculate the coordinates of the P by the following formula,

P(x, y) = [(mx₂ + nx₁) / m + n , (my₂ + ny₁ ) / m + n]

Here m and n are ratio and m/n = 1/4

Substitute the values,

P(x, y) = [1 × (-2) + 4 × 8] / 1 + 4 , [1 × (-1) + 4 × 4] / 1 + 4

P(x, y) = (6,3)

Therefore, the coordinates of point P along QR so that the ratio of QP to PR is 1 to 4 is P(6,3).

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Answer:

O Liquid water warms and changes to water vapor.​

Step-by-step explanation:

Answer:

5 and 11

Step-by-step explanation:

x =2

fx=3x-1

3(2)-1

6-1

= 5

when x= 4

fx=3x-1

3(4)-1

12-1

11

f(x) =5 and 11

Answer:

5 and 11

Step-by-step explanation:

Input the values of x in the function and solve using basic mathematical operations.

[tex]f(2)=3(2)-1=6-1=5\\\\\\f(4)=3(4)-1=12-1=11[/tex]

The distance between each tick mark on this number line= 1/5 units

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

5 equal spaces between 0 and 1 shows,

5 equal spaces= 1 unit

1 equal space = x units

Do the cross multiplication.

5*x=1*1

5x=1

x=1/5

So, the distance between each tick mark on this number line= 1/5 units

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Answer:

1/5 is the answer

The graph that represents the given table is graph 2

The table is given,

At x = 0

The value of y = -2

The y intercept of the line is -2

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

The two points are (0, -2) and (1, -3.5)

The slope of the line m = [tex](\frac{y_2-y_1}{x_2-x_1} )[/tex]

Substitute the values in the equation

The slope of the line = -3.5 - (-2) / 1 - 0

= -1.5 /1

= -1.5

The slope of the line is negative and the y intercept of the line is negative, the correct graph is graph 2

Hence, the graph that represents the given table is graph 2

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The length longer of the green caterpillar than the orange caterpillar is 2 1/2 inches.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the green caterpillar was 4 inches long and the orange caterpillar was 1 1/12 inches long.

The difference in length will be:

= 4 - 1 1/2

= 2 1/2 inches.

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