A $9070 investment earns interest at
3.3% per year compounded
semiannually over 17 years. Use the
compound interest formula to
calculate the value of this investment
to the nearest cent.

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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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

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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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

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 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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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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Answer:

164

Step-by-step explanation:

c = number of caps

t = number of t-shirts

c + t = 278

8c + 7t = 2110

   -7c - 7t = -1946

+   8c + 7t = 2110

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

      c         = 164

Answer: 164

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 best buy is at the campus canteen. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

According to mathematicians, all real numbers may be described by the four basic operations, often known as "arithmetic operations." The phrases quotient, product, sum, and difference are produced by the four mathematical operations of division, multiplication, addition and subtraction, respectively.

We are given that a can of tab costs Rs. 7.20 at Timber City.

So, the cost of 6 packs will be

6 (7.20) = Rs. 43.20

But, on promotion, the cost is Rs. 39.60.

So, the discount is

D = Rs. 43.20 - Rs. 39.60

D = Rs. 3.60

Similarly,

A can of tab in the campus canteen costs Rs. 7.50.

So, the cost of 6 packs will be

6 (7.50) = Rs. 45

But, on promotion, the cost is Rs. 39.

So, the discount is

D = Rs. 45 - Rs. 39

D = Rs. 6

Hence, the best buy is at the campus canteen.

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Answer:

Step-by-step explanation:

The expression (2x + 3y)² - 9 can be fully factorised as follows:

(2x + 3y)² - 9 = (2x + 3y + 3)(2x + 3y - 3)

= (2x + 3y + 3)(2x + 3y - 3)

The expression is now fully factorised.

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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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).

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: 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:

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:

Answer:

Step-by-step explanation:

why do you need help if you already did it?

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:

Below

Step-by-step explanation:

Convert football field to inches

   100 yd  * 36 in/yd = 3600 inches

now multiply by the conversion factor:

    3600 inches  *  2.54 cm / in = 9144 cm

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]

Answer:

x cube minus fourteen is equal to sixty-eight

Answer: 18.84

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

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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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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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]

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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