Erica earned a total of 67,160 last year from her two jobs. The amount she earned from her job at the store was 1,550 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college

Answer:

ln(d) = n can be rewritten in exponential form as d = e^n.

Step-by-step explanation:

The natural logarithm, denoted by ln, is the logarithm to the base e (approximately 2.718). The inverse of the natural logarithm function is the exponential function e^x. Therefore, when you take the natural logarithm of a number, you can raise e to the power of that number to get the original value.

ln(d) = n is the same as d = e^n

So, Ln(d)=n can be written as d = e^n

This is because e^n is the inverse function of Ln(d) and Ln(d)=n is the logarithm form of d = e^n

Answer:

1

Step-by-step explanation:

C•1/J

C•K/J

K=C×J

K=175

when J =15

then C is;

C=K/J

175/15

C=11.67

Answer:

Step-by-step explanation:

I do know give me brainliest first

Answer:

24 gift bags

Step-by-step explanation:

Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!

May I have heart, 5 star, and brainliest please?

Vertex: (4,1/6) Focus: (4,7/12) Directrix: x=2

On solving the provided question we can say that 1,000,000 nanometers =  1 millimeter; 1e-6 millimeter = nanometers

A nanometer, often known as a nanometer, is a unit of measurement that is one billionth of a metre and one thousandth of a picometre in the International System of Units. In scientific notation, a nanometer is represented by the numbers 1 109 m and 1/1000000000 metres. The prefix "nano" refers to one billionth, or 10-9, in the International System of Units. An nanometer is therefore one billionth of a metre. The metric unit of length known as a nanometer is one billionth of a metre (0.000000001 m). It is a small length unit, abbreviated as nm. One billionth of a metre or one billionth of a micrometre is what is known as a nanometer (nm), which is 109 metres. Atoms and the molecules they make up are measured using this scale.

1,000,000 nanometers =  1 millimeter

1e-6 millimeter = nanometers

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Answer:

[tex]y=-(x-6)^2+6[/tex]

Step-by-step explanation:

Vertex form of a parabola is expressed as: [tex]y=a(x-h)^2+k[/tex]

It's also important to note that the axis of symmetry is a vertical line which passes through vertex, so in this form, that axis of symmetry can be defined as such: [tex]x=h[/tex]

So if we're given the axis of symmetry we know the x-coordinate of the vertex.

Since we're given the axis of symmetry to be: [tex]x=6[/tex] then that means the x-coordinate of the axis of symmetry is six. Another important thing to note about the vertex is it's y-value is either a minimum or maximum depending on whether it's opening up or down. So when we're given the maximum height to be 6, that's the y-coordinate of the vertex.

So now we know the coordinates to the vertex: [tex](6, 6)[/tex]. Using this we can plug in some values into the vertex form: [tex]y=a(x-6)^2+6[/tex], but we still don't know the "a" value in front (besides that it's negative). Luckily we're given a point on the equation! We can plug in the coordinates given: [tex](7, 5)[/tex] into the vertex form as (x, y) to solve for the "a" value, so let's do that.

Original Equation:

[tex]y=a(x-6)^2+6[/tex]

Passes through the point (7, 5), so substitute it for (x, y)

[tex]5=a(7-6)^2+6[/tex]

Simplify inside parenthesis:

[tex]5=a(1)^2+6[/tex]

Square the one:

[tex]5=a+6[/tex]

Subtract 6 from both sides:

[tex]-1=a[/tex]

So now let's plug this back into our equation: [tex]y=-1(x-6)^2+6[/tex], although we don't have to explicitly put the one, and just put the negative sign which does the same thing: [tex]y=-(x-6)^2+6[/tex]

The amount of discount in dollars is 28.17

To find the amount of the discount, we need to multiply the original price by the percentage that was discounted.

Discount = Original Price x (Discount Percentage/100)

Discount = 46.95 x (60/100) = 28.17

So, the amount of discount in dollars is 28.17

We can start solving the problem by using the formula:

Hours worked = Total cost / Hourly wage

In this case, we know that Chris needs at least $320.00 for his class trip, and he earns $8 per hour working on the weekends. So, we can plug in these values into the formula:

Hours worked = $320.00 / $8.00

To solve this equation, we divide 320 by 8:

Hours worked = 40

So Chris needs to work 40 hours on the weekends to be able to go on the class trip.

I hope this helps :)

Answer:

----------------------------------------

Chris earns $8 per hour and he needs at least $320.00 for his class trip.

If he works h hours, he will get 8h dollars.

Set up inequality:

Solving we get:

Chris needs to work at least 40 hours.

If D and R are independent, then P(D or R) = 0.8412

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)

P(D) = 0.26 and P( R) = 0.26 , if D and R are independent, then,

P(D or R) = P(D) + P(R) - P(DnR)

then P(DnR) = P(D) × P(R) = 0.26×0.38 = 0.0988

P(D or R) = 0.26+0.38-0.0988

= 0.8412

Therefore the probability of P(D or R) if D and R are independent is 0.8412

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If a car radiator needs a 40% antifreeze solution the radiator now holds 49% of a 30% solution. The number of  liters that should be drained and replaced with 100% antifreeze to get the desired strength is 7 liters.

Let x represent the number of liters that should be drained

So, Let solve for x

x+.30(49-x)=.40× 49

x=14.7-.30x=19.6

.7x=19.6 - 14.7

.7x=4.9

x=4.9/.7

x = 7 liters need to be drained & filled with 100% antifreeze.

Therefore the number of liters is 7 liters.

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The final answer is N * 58 + 64.

What is the PEMDAS?

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).

The order of operations (PEMDAS) tells us to perform the following steps:

Parentheses: (4 x 12 - 40) to the power of 2 = (-8)^2 = 64

Exponents: N * 58 + 64

Multiplication and Division: from left to right

Addition and Subtraction: from left to right

Hence, the final answer is N * 58 + 64, since we do not know the value of N we can't solve it.

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The required expression is 21.29 × 38 = 809.02. has an exact value of the given product.

The estimate is a process, and it includes the rough over-calculation that makes one have a close value to the exact value.

here,
Given expression,
21.29 × 38 = (21 + 0.29) 38
Using distributive property,
               = 21× 38 + 0.29 × 38

               = 798 + 11.02
               = 809.02

The required expression is 21.29 x 38 = 809.02. has an exact value of the given product.

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Answer:

hope this would help you!

Answer:

a) The function is growth.

b) The growth rate in % is 4%. This can be determined by taking the natural logarithm of the coefficient (1.04) and multiplying it by 100.

ln(1.04)*100 = 3.98% ≈ 4%.

The relationship between the trigonometric ratios of the non-right angles in a triangle and the measures of the angles are;

1.) c.) They are reciprocals

2.) a.) They are equal

3. b.) They are complementary

The non-right angles in a right triangle are he two acute angles in the right triangle.

1) Complementary angles are angles that have a sum of 90°

Let A and B be two complementary angles, we get;

m∠A + m∠B = 90°

Let a and b represent the lengths of the opposite sides to the complementary angles ∠A and ∠B

Let side a represent the side opposite to the angle ∠A and let side b  represent the side opposite to the angle ∠B, we get

tan(A) = a/b tan B = b/a

Therefore, tan(B) is the reciprocal of tan(A)

The correct option is c,) They are reciprocals

2) Let r represent the length of the hypotenuse of the right triangle, we get;

sin(A) = a/r

cos(A) = b/r

sin(B) = b/r

cos(B) = a/r

The values, sin(A) = cos(B), and sin(B) = cos(A), therefore;

3) The sum of angles in the right triangle is 180°, therefore;

m∠A + m∠B + 90° = 180°

m∠A + m∠B = 180° - 90° = 90°

m∠A + m∠B = 90°

The sum of the two non-right angles in a triangle is 90°,  therefore, the two non-right angles re complementary.

The correct option is therefore; b.) They are complementary

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The sketch for slope is attached below.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Point               Slopes

(1, 1)                     (a) 3

_                        (b) -3

_                        (c) -5/2

_                         (d) Undefined

a) Now, using slope intercept form

y - 1= 3 (x-1)

y- 1= 3x- 3

y= 3x - 2

(b) Equation of a line has a slope -3 is given by

y - 1= (-3) (x-1)

y-1 = 3- 3x

y = -3x + 4

(c) Equation of a line has a slope -5/2 is given by

y - 1= (-5/2) (x-1)

y-1 = -5/2x + 5/2

y= -5/2x + 7/2

(d) The line parallel to y axis and passes through given point : x=1

"undefined" means the line is vertical.

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Marco pays $64  for credit card, $272 for Groceries and $672 for rent

percentage, a relative value indicating hundredth parts of any quantity.

Given that Marco budgets $1,600 a month for expenses.

According to the graph he pays 4% of credit card

Now let us find 4% of 1600

4/100×1600

0.04×1600

$64 Marco pays for credit card.

From graph, he pays 17% for groceries

17% of 1600

17/100×1600

0.17×1600=$272

$272 Marco pays for Groceries.

From graph, he pays 42% for rent

42/100×1600

0.42×1600=672

$672 Marco pays for Rent.

Hence, Marco pays $64  for credit card, $272 for Groceries and $672 for rent

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The division of the given polynomial would be (x^4) + 81.

What is the synthetic division?

Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.

To divide the polynomials using polynomial division, we will use the following steps:

Write the polynomials in descending order of exponents.

(2x^3 + x^4 - 6x^2 + 11x - 10) (x^2 + 2 - x)

Create a grid with the dividend on the left and the divisor on the right.

2x^3 x^4 -6x^2 11x -10

x^2 2 -x  

Bring down the leading coefficient of the dividend, which is 2x^3 in this case. Write it in the next row of the grid.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

Multiply the divisor (x^2 + 2 - x) by the leading coefficient (2x^3) and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

Subtract the second row from the third row and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

0 -x^4 -2x^2 11x -10

Divide the new leading term by the leading term of the divisor, which is x^2, and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

0 -x^4 -2x^2 11x -10

-x^2

So the final answer would be (-x^2) + (x^4 + 2x^2 - 11x + 10).

Hence, the division of the given polynomial would be (x^4) + 81.

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The distance from Earth to the Sun is 396 times larger than the distance from the Earth to the moon.

Scientific notation.

This is a mode of expressing large numbers of great power. Its helps in the simple expression of numbers so that some arithmetic operations can be performed as required.

In the given question, we have;

distance from Earth to the Sun = 1.47 X 10^11 meters

and

distance from Earth to moon = 3.71 X 10^8 meters

Thus,

to determine by how much is the distance between the Earth and Sun greater than that between the Earth and moon;

n = distance from Earth to the Sun/ distance from the Earth to the moon

  = 1.47 X 10^11/ 3.71 X 10^8

  = 3.962 x 10^2

n = 396

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Answer:

The circumference of a tire can be found by using the formula C = πd, where C is the circumference, and d is the diameter.

For the old bicycle with 12 inch diameter tires, the circumference is:

C = π * 12 = 12 * π inches

For the new bicycle with 16 inch diameter tires, the circumference is:

C = π * 16 = 16 * π inches

To find the difference in the circumference of the tires, we subtract the circumference of the old tire from the circumference of the new tire:

16π - 12π = 4π inches

So the difference in the circumference of the two tires is 4π inches.

It's around 12.56 inches.

Answer:

The quotient of two real numbers is not necessarily an integer. When dividing two real numbers, the result can be any real number, including a fraction or a decimal. It can be an integer only if the divisor is a factor of the dividend. In other words, if the remainder of the division is zero, the quotient is an integer.

Step-by-step explanation:

The gigabytes of music  downloaded in one hour is 19.8 gb per hour

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

Size =  75.24 gigabytes

Time = 3.8 hours

The rate is then calculated as

Rate = Size/Time

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

Rate = 75.24/3.8

Evaluate

Rate = 19.8

Hence, the rate is 19.8 gb per hour

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Answer: I believe 14.1 should be correct

Step-by-step explanation:

Given that we know one side length is 52 and the other is 21, we can use these values to create a scale.

52/21 = 2.4761, so we know that all sides will decrease by a scale of this value.

Given that, we can find the length of the MN. 35/2.4761 = 14.135

The question asks to round to the nearest tenth, so the answer should be 14.1. hope this helps!

Answer:

[tex]\frac{10}{7}x^4[/tex]

Step-by-step explanation:

There is an exponent rule which essentially states: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

All this is doing is essentially cancelling out the terms, since you can think of it as: [tex]\frac{x^a}{x^b}\implies \frac{x*x*x...\text{ "a" amount of times}}{x*x*x...\text{"b" amount of times}}[/tex], and if you recall, multiplication and division cancel. So we cancel out "b" amount of x's, leaving us with "a - b" amount of x's. Which can also be expressed as: [tex]x^{a-b}[/tex]

We can use this logic to solve our problem: [tex]\frac{20x^6}{14x^2}[/tex], here we can separate this into two different fractions: [tex]\frac{20}{14}*\frac{x^6}{x^2}[/tex] and we can use basic division on the left side and our exponent rule on the right side. This gives us the following:  [tex]\frac{10}{7}x^{6-2}\implies \frac{10}{7}x^4[/tex] which is our solution!

The derivation of the function y = (4x+9x^2)(3x-7x^4) by the means of direct formulas is y = 12x^2 + 27x^3 - 28x^5 - 63x^6.

The direct formula method is a way to multiply two or more algebraic expressions together by applying the distributive property and combining like terms. It is also known as the "FOIL" method for multiplying binomials.

The direct formula method involves breaking down each expression into its individual terms and then using the distributive property to multiply each term in the first expression by each term in the second expression. After that, the resulting terms are combined according to the addition and subtraction rules of like terms.

To derive the function y = (4x+9x^2)(3x-7x^4) using the direct formulas method, we need to multiply the two expressions inside the parentheses:

y = (4x+9x^2)(3x-7x^4)

y = 4x3x + 4x-7x^4 + 9x^23x + 9x^2-7x^4

Using the distributive property, we can simplify the expression by combining like terms:

y = 12x^2 - 28x^5 + 27x^3 - 63x^6

y = (12x^2 + 27x^3) - (28x^5 + 63x^6)

So the final expression is y = 12x^2 + 27x^3 - 28x^5 - 63x^6

The direct formulas method uses the distributive property and the combination of like terms to derive the final expression of the function.

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According to the information, we can infer that the number of customers that buy package 1 is 16 customers.

To calculate how many customers buy package 1 we have to identify some important information such as:

To calculate this value, we have to divide 40 in 100, and then we have to multiply the result by 40.

According to previous information, the number of customers that buy package 1 is 16 customers. So, 24 customers buy package 2, 3 or 4. If we have to identify exactly how many buy an specific package we have to make the same procedure. For example package 3.

40 / 100 = 0.4

0.4 * 15 = 6

So, 6 customers buy package 3.

Note: This question is incomplete because there is some information missing. Here is the complete information:

TASK

Calculate how many customers buy package 1.

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The required solution of the given equation would be w = (x - 2y)/2 in terms of x and y.

What is an equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

2y + 2w = x

Solving the above equation in terms of x and y

As per the question, we have

2y + 2w = x

Subtract 2y both sides of the equation, and we get

2w = x - 2y

w = (x - 2y)/2

Thus, the required equation would be w = (x - 2y)/2.

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a) The linear combination of v, w by finding scalars c₁, c₂ such that c₁v + c₂w = b is [v w | b]

b) The graph of the equation is attached below.

c) The matrix representation is a useful tool for finding linear combinations of vectors, but it becomes more complex as the number of dimensions increase.

A linear combination of two vectors is when a third vector is expressed as a sum of the two vectors multiplied by scalars.

In R2, this can be represented using a parallelogram, where the vectors are drawn and the third vector is the diagonal of the parallelogram.

To find the scalars, we use the matrix representation [v w | b]. If the matrix gives a consistent system, it means that the third vector b can be expressed as a linear combination of the two vectors v and w.

In R3, the matrix representation is still used but it becomes more challenging to find a consistent system because there are more variables involved.

The vectors are graphed in 3D, and the third vector is found as the diagonal of a parallelogram that is now a parallelepiped.

However, it may not always be possible to find a consistent system in R3, as the third vector may not lie in the plane formed by the two vectors.

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The constants A and B for the differential equation are given as follows:

The solutions to the differential equation are given as follows:

This means that the roots of the characteristic equation are given as follows:

r = -8 and r = 8.

Considering that the leading coefficient is of 1, as 1 multiplies y'', the characteristic equation is given as follows:

(r + 8)(r - 8) = r² - 64.

Hence the differential equation is given as follows:

y'' - 64y = 0.

Hence the constants are given as follows:

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