The value of a car in 2000 was $32,000 and it is decreasing in value at a rate of 16.3% per year.
a.) Write an equation that represents the situation for any amount of time from 2000.
b.) How much will the car be worth in 2035?

Answer:

t + 40 = 59

Step-by-step explanation:

We know

She has 59 tests to grade. So, it will be the total of the equation.

She already grades 40 on the tests.

t is the number of tests she has left to grade.

So, the equation is

t + 40 = 59

Answer:

Below

Step-by-step explanation:

From - 5/6  to zero on the line is  5/6

  then go another 23/12        now add them

      5/6 + 23/12     must have common denominator to add fractions

   5 / 6 = 10 /12

                10/12 + 23/12 = 33/12    = 2 9/12 = 2 3/4 units

Answer:

  (x+4)/(3x-3)

Step-by-step explanation:

You want to simplify the compound fraction ((x²/(x-1))/((3x²/(x+4)).

As with numerical fractions division by a fraction is the same as multiplication by its inverse. Common factors in the numerator and denominator cancel.

  [tex]\dfrac{\left(\dfrac{x^2}{x-1}\right)}{\left(\dfrac{3x^2}{x+4}\right)}=\dfrac{x^2}{x-1}\times\dfrac{x+4}{3x^2}=\dfrac{x+4}{3(x-1)}=\boxed{\dfrac{x+4}{3x-3}}[/tex]

The IV pump should be set at 25ml/hr.

Given is that 40 gm of magnesium sulfate is diluted in 1000 ml LR. After an initial loading dose, the nurse is to infuse a maintenance dose of 2 gm/hour.

Now, 40 gm of magnesium is diluted in 1000 ml.

So, 1 gm of magnesium will be present in (1000/40) ml = 25 ml.

Now, for 2 gm/hr, the pump should be set at 25 ml/hr.

Therefore, the IV pump should be set at 25ml/hr.

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Answer: 5 miles

if they go 10 miles in one hour, they would only go 5 miles in one half-hour.

Step-by-step explanation:

10 miles in 60 min, so you half that for the miles and minutes

half of 10 is 5 and half of 60 is 30

Answer:

h(x) = [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject , that is

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

[tex]\frac{y-1}{2}[/tex] = x

change y back to x with x the inverse function h(x)

h(x) = [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The average intensity of radiation between 10 meters and 50 meters from the source can be found using the following formula:

Average Intensity = (1 / (50 - 10)) * (Integral of r(x) from x=10 to x=50)

Using the formula for r(x), the integral of r(x) between 10 and 50 can be found as:

Integral of r(x) = -k * ln(x) evaluated at x = 50 and x = 10

Therefore, the average intensity of radiation between 10 and 50 meters from the source is given by:

Average Intensity = (1 / (50 - 10)) * (-k * (ln(50) - ln(10)))

This simplifies to:

Average Intensity = (1 / 40) * (-k * ln(5))

This is equivalent to choice c.

Average Intensity = 1/40 (-k/50 + k/10).

the solution of the given derivative will be y = k/2(1±√(1-4h/rk))

What is derivative?

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

dy/dt = 0

-r/k y²+ry-h=0

y = k/2(1±√(1-4h/rk))

Hence the solution of the given derivative will be y = k/2(1±√(1-4h/rk))

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On solving the provided question, we can say that the expression will be

an = a + (n-1)d => 20.75 = 5 + (n-1)1.75 => n = 10

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

Given that

a=5

d = 1.75

an = 20.75

the expression will be

an = a + (n-1)d

20.75 = 5 + (n-1)1.75

15.75 = (n- 1) 1.75

n-1 = 15.75/1.75

n- 1 = 9

n = 10

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Answer:

1) The math curriculum typically includes components such as number sense, arithmetic operations, algebra, geometry, data analysis and probability, among others. Problem solving and procedural fluency are emphasized as important skills to develop. Students may also receive instruction on missed mathematical concepts from previous grades to ensure they have a strong foundation for future learning.

2) Some specific types of mathematical instruction that are promoted include hands-on and concrete learning experiences, use of real-world problems, direct instruction, cooperative learning, and using technology to enhance learning. Additionally, promoting a growth mindset and a positive attitude towards mathematics is also emphasized.

3) Some specific procedures used to teach basic mathematical instruction include direct instruction, visual aids such as graphs and diagrams, manipulatives and hands-on activities, scaffolding, and systematic review and practice. Teachers may also use questioning techniques to encourage students to think critically and develop their problem-solving skills.

Step-by-step explanation:

The Simple Interest on Principal amount: $1,000 is $100.

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied.

Given:

Principal amount: $1,000

Interest rate: 10%

Time: 12 months

So, the Simple Interest

= P x R x T/100

= 1000 x 10 x 1 / 100

= 10000/100

= $100

and, Amount = P + I

Amount = $1100

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Answer:

x cube minus fourteen is equal to sixty-eight

In the triangle ABC the line segment bisecting AC is the median, i.e. BD.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

The triangle ABC is given.

In Δ ABC, the line segment AC is bisected, so -

AD = CD

The line segment from a vertex to the middle of the other side is what is meant by a median. When the vertex is an angle in an equilateral triangle or the non-congruent angle of an isosceles triangle, it is also an angle bisector.

Since line segment BD bisects AC.

Therefore, the median is BD.

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A graph which represents the function f(x) = -|x - 2| - 1 include the following:

In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).

Next, we would use an online graphing calculator to plot the given absolute value function f(x) = -|x - 2| - 1 as shown in the graph attached below.

By observing critically the graph (see attachment), the two ordered pairs (points) that fit on its axes include the following:

Ordered pair = (2, -1).

Ordered pair = (0, -3).

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The solution to the subtraction and addition of the given expressions are;

- 2x² + 9x - 23

3x² - 2x - 1

5y² - 7y + 5

(5x² + 3x - 9) - (7x² - 6x + 14)

= 5x² + 3x - 9 - 7x² + 6x - 14

= - 2x² + 9x - 23

(8x² - 11x + 6) + (-5x² + 9x - 7)

open parenthesis

= 8x² - 11x + 6 - 5x² + 9x - 7

= 3x² - 2x - 1

(14y² - 4y + 3) - (9y² + 3y - 2)

= 14y² - 4y + 3 - 9y² - 3y + 2

combine like terms

= 14y² - 9y² - 4y - 3y + 3 + 2

= 5y² - 7y + 5

Hence, the solution to the expressions are - 2x² + 9x - 23; 3x² - 2x - 1; 5y² - 7y + 5.

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Answer: 18.84

Step-by-step explanation: just multiply 3.14 by the radius

The height of the hyperbolic vase is 5.12 * 2 = 10.24 inches.

What is a hyperbola?

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows. These two sections are known as connected components or branches. A plane and both halves of a double cone connect to form a hyperbola, which is an open curve with two branches. The hyperbola will be symmetrical regardless of whether the plane is perpendicular to the cone's axis or not.

The eccentricity formula for a hyperbola is

[tex]e = \sqrt{1+\frac{b^2}{a^2} }[/tex]

e = 2.5

Given width at the narrowest point is 4 inches.

So the  value of a from the below figure is

a = ±2

So we can find b from the above eccentricity formula

2.5  = [tex]\sqrt{1+\frac{b^2}{2^2} }[/tex]

6.25 = 1 + b²/4

b²/4 = 5.25

b² = 21

b = ±4.6

So the equation of the hyperbola is

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

[tex]\frac{x^2}{4} - \frac{y^2}{21} = 1[/tex]

Now we are asked to find the height of the vase

The width at the top is 6 inches.

So take x = 3

Then we can find y from the above equation

[tex]\frac{3^2}{4} - \frac{y^2}{21} = 1[/tex]

y² = 26.25

y = 5.12 inches

Therefore the height of the hyperbolic vase is 5.12 * 2 = 10.24 inches.

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The modification that would have to  result in a net worth of $100,000 is: adding $1,000 in credit card debt. Option D

They currently have $101,000 in assets.

We have the value of the automobile plus the value of the recreational vehicle.

110000+27000 = 137000

When the medical expenses are subtracted from the net assets, we have

137000-8700 = 128300

When the loan sum is subtracted from net value, we have

128300-80000 = 48300

Savings and net wealth together provide us

48300+5000 = 53300

Retirement money added to net worth gives us

53000+50000 = 103300

After deducting the credit card debt from net value, we have

103300-2300 = 101000

We deduct $1,000 from this to create $100,000. Therefore, choice D is the best one.

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The slope of the line with the first two points (0, 1) and (-7, -3) is equal to 4.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-3 - (-7))/(1 - 0)

Slope, m = 4/1

Slope, m = 4.

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Mona always brings fabric samples with her when she holds client meetings. She likes to use them to help clients understand how her designs will look and

how different fabrics will go together.

Another reason that Mona MOST LIKELY brings along fabric samples is a) They allow the client to see and feel the texture of the fabric.

From the illustration above Mona brings product samples when she meets in a business meeting with her customers.

This is a step to provide a clearer picture to potential customers so they can see Mona's products in more detail.

So the most appropriate choice is option A, namely Mona's reason is also to provide potential consumers with experience and knowledge about the texture of the fabrics sold by Mona.

This can also help to improve the quality of business relationships.

Providing samples of new products will further enhance the business relationship between us and customers. Impress them with what we have given them. Give them something special on birthdays or other special days for them, that way your business bond and them will get stronger and closer.

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The number of food items they need to have on hand is:

Nachos = 1165

Hamburgers = 1700

Chicken strips = 50

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of fans surveyed = 250

Nachos= 58,

Hamburgers = 85

Chicken strips = 33

The percentage of each item.

Nachos= 58/250 x 100 = 23.2%

Hamburgers = 85/250 x 100 = 34%

Chicken strips = 33/250 x 100 = 13.2%

Now,

If,

Number of fans surveyed = 5000

Nachos = 23.2% of 5000 = 23.3/100 x 5000 = 1165

Hamburgers = 34% of 5000 = 34/100 x 5000 = 1700

Chicken strips = 13.2% of 5000 = 13.2/100 x 5000 = 50

Thus,,

Nachos = 1165

Hamburgers = 1700

Chicken strips = 50

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Answer:

y = - [tex]\frac{3}{4}[/tex] x + 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = - [tex]\frac{3}{4}[/tex] , then

y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation

to find c substitute (8, 9 ) into the partial equation

9 = - [tex]\frac{3}{4}[/tex] (8) + c = - 6 + c ( add 6 to both sides )

15 = c

y = - [tex]\frac{3}{4}[/tex] x + 15 ← equation of line

The function h as a composition of two functions f and g are;

[tex]f(x)=\sqrt[7]{x} \\\\ g(x)=x^6-4[/tex]

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Functions are formed by composing two or more functions in a way that one's output is another's input are called composite functions. They are also called function of functions.

From the information given we can deduce that the functions are:

[tex](f\circ g)(x)=\sqrt[7]{x^6-4}[/tex]

The simplification of the function gives the individual function as;

[tex]f(x)=\sqrt[7]{x} \\\\ g(x)=x^6-4[/tex]

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Answer:

The width of the rectangle is approximately 8.904 yards, and the length of the rectangle is 24.71 yards.

Step-by-step explanation:

Let x be the width of the rectangle, then the length of the rectangle is 4x - 18.

The area of the rectangle is x * (4x - 18) = 630, so we can solve for x:

x * (4x - 18) = 630

Expanding and rearranging the equation:

4x^2 - 18x - 630 = 0

Using the quadratic formula, we can find the solutions for x:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 4, b = -18, and c = -630.

x = (18 ± √(18^2 - 4 * 4 * -630)) / (2 * 4)

x = (18 ± √(18^2 + 2520)) / 8

x = (18 ± √(324 + 2520)) / 8

x = (18 ± √2844) / 8

x = (18 ± 53.23) / 8

Since width can't be negative, x must be positive, so:

x = (18 + 53.23) / 8

x = 71.23 / 8

x = 8.904

The length of the rectangle is 4 * 8.904 - 18 = 24.71 yards.

Answer:

Step-by-step explanation:

why do you need help if you already did it?

The p-value from the data is 0.5289

To test whether the average score improvement of the GRE prep company's students is different than 100, we can use a two-sided t-test.

First, we need to set up our null and alternative hypotheses:

Null hypothesis (H0): The true mean score improvement of the GRE prep company's students is equal to 100.

Alternative hypothesis (Ha): The true mean score improvement of the GRE prep company's students is different than 100.

We will use a significance level of α = 0.05, which means we will reject the null hypothesis if the p-value is less than 0.05.

Next, we can calculate the sample mean and sample standard deviation of the data:

Sample mean (x) = 98.16

Sample standard deviation (s) = 8.88

We have a small sample size (n = 10) and the population standard deviation is unknown, so we will use a t-test. The t-statistic for a two-sided test is given by:

t = (x - μ) / (s / sqrt(n))

where μ is the hypothesized population mean (in this case, 100).

Substituting the values, we get:

t = (98.16 - 100) / (8.88 / sqrt(10)) = -0.655

Using a t-table with 9 degrees of freedom (n-1), we find that the two-tailed p-value for t = -0.842 is 0.5289.

Since the p-value (0.5289) is greater than the significance level (0.05), we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that the true mean score improvement of the GRE prep company's students is different than 100.

Therefore, based on the given data, we cannot reject the claim of the GRE prep company that the average score improvement of their students is equal to 100.

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