A Sporting goods company makes footballs with an alligator logo. Of the 8,750 footballs produced in one week, 77 were defective

Therefore, the value of the car in 2018 was approximately $13,197.36. Rounded to two decimal places, this is $13,197.36.

A decimal is a way of representing a number that is based on powers of ten. It is a number expressed in the base-ten system, which means that each digit in the number represents a power of 10. The decimal point separates the whole number part of the decimal from the fractional part of the decimal.

To model the depreciation of the car over time, we can use the formula:

f(t) = a(1 - r)^t

where:

After t years, f(t) is the car's worth.

a is the initial value of the car, which is $28,750.

r is the annual depreciation rate, which is 12% or 0.12 (expressed as a decimal).

t represents how long it has been since the car been acquired.

Substituting the given values, we get:

f(t) = 28,750(1 - 0.12)^t

To find the value of the car in 2018, we need to substitute t = 6 (since 2018 is 6 years after 2012) and evaluate the function:

f(6) = 28,750(1 - 0.12)^6

Simplifying,

f(6) = 28,750(0.88)^6

Evaluating using a calculator, we get:

f(6) ≈ 13,197.36

Therefore, the value of the car in 2018 was approximately $13,197.36. Rounded to two decimal places, this is $13,197.36.

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The value of the car in 2018 was approximately $14,303.22.

What is exponential functions?

An exponential function is a mathematical function of the form f(x) = [tex]a^{x}[/tex], where a is a positive constant and x is the input variable. The base a is usually a positive real number, but it can also be a complex number.

The initial value of the car is $28,750, and it depreciates by 12% each year. This means that the value of the car after t years can be modeled by the exponential function:

f(t) = [tex]28750(1 - 0.12)^{t}[/tex]

Simplifying the expression inside the parentheses:

f(t) = [tex]28750(0.88)^{t}[/tex]

To find the value of the car in 2018, we need to substitute t = 6, since 2018 is 6 years after 2012:

f(6) = [tex]28750(0.88)^{6}[/tex]

Using a calculator, we get:

f(6) = [tex]28750(0.497^{1})[/tex]

f(6) = 14,303.22

Therefore, the value of the car in 2018 was approximately $14,303.22.

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Answer:

The vertex of a quadratic function of the form f(x) = ax^2 + bx + c is located at the point (-b/2a, f(-b/2a)).

In this case, the quadratic function is f(x) = -2x^2 + 12x - 9, so we can use the formula above to find the coordinates of the vertex:

x-coordinate of vertex = -b/2a = -12/(2*(-2)) = 3

To find the y-coordinate of the vertex, we can evaluate the function at x = 3:

f(3) = -2(3)^2 + 12(3) - 9 = 9

Therefore, the coordinates of the vertex are (3, 9). The x-coordinate of the vertex is 3, and the y-coordinate of the vertex is 9.

The answer is an option (D) f(x) = One-half (one-half) superscript x.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

To determine the exponential function represented by the values in the table, we need to look for a function of form f(x) = abˣ that passes through the given points.

Let's plug in the x and f(x) values from the table into the general formula:

When x = -2, f(x) = 16 gives us 16 = ab⁻²

When x = -1, f(x) = 8 gives us 8 = ab⁻¹

When x = 0, f(x) = 4 gives us 4 = ab⁰

When x = 1, f(x) = 2 gives us 2 = ab¹

When x = 2, f(x) = 1 gives us 1 = ab²

We can rewrite the equations as:

16 = a/b²

8 = a/b

4 = a

2 = ab

1 = ab²

We can solve for a and b by using a system of equations:

From the equation 4 = a, we get a = 4.

Substituting a = 4 into the equation 2 = ab, we get b = 2/a = 1/2.

Therefore, the exponential function represented by the values in the table is:

f(x) = 4(1/2)ˣ

Hence, the answer is an option (D) f(x) = One-half (one-half) superscript x.

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Answer:

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

2(5) + 3(3 - 5) + (3)^2

10 + (9 - 15) + 9

19 - 6 = 13

The calculated value of the rocket’s greatest height is 324 feet

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

h(t) = -16t² + 144t

Differentiate the height function and set the differentiated equation to 0

So, we have

32t = 144

This gives

t = 144/32

So, we have

t = 4.5

Substitute t = 4.5 in the above equation, so, we have the following representation

h(4.5) = -16(4.5)^2 + 144(4.5)

Evaluate

h(4.5) = 324

Hence, the rocket’s greatest height is 324 feet

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Complete question

A rocket is launched in the air. Its height in feet is given by h(t) = −16t² + 144t where t represents the time in seconds after launch.

What is the rocket’s greatest height?

The total amount of interest earned on the account is $1049.15.

Simple interest is interest that is just based on the principal. It does not account for any interest accrued in prior periods and is determined as a percentage of the principal. If your principal is $1,000 and your yearly interest rate is 5%, for instance, you would make $50 in simple interest after a year ($1,000 0.05).

Contrarily, compound interest is calculated on the principal amount in addition to any prior quarters' interest. This means that interest is calculated on the new amount after the principal and interest earned during each period have been added.

The compound interest is given by the formula:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

Rearranging for P we have:

[tex]P = A / (1 + r/n)^{(nt)}[/tex]

Substituting the value of r = 3.2%, n = 2 and t = 6 we have:

[tex]P = 6049.15 / (1 + 0.032/2)^{(2*6)}[/tex]

P = 5000

Here, P is the initial balance.

Now, for interest we have:

I = A - P

Substituting the values:

I = $6049.15 - $5000

I = $1049.15

Hence, the total amount of interest earned on the account is $1049.15.

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The measure of the angle NSR is equal to 113 degrees

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

The circle

Using the angle of intersecting chords theorem, we have following equation

NSR = 1/2(Sum of major and minor arcs NS)

So, we have

NSR = 1/2 * (176 + 50)

Evaluate

NSR = 113

Hence, the angle is 113 degrees

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7 is the area of one face of the three-dimensional figure .

What exactly is a three-dimensional figure?

Objects or shapes with three dimensions—length, breadth, and height—are referred to as three-dimensional objects or solid figures in geometry. The height of a three-dimensional object is the same as its thickness or depth, in contrast to a two-dimensional shape, which lacks height.

area of base = 5 cm²

total surface area = 26 cm²

26 = 3 * area of one face  + 5

26 - 5 =  3 * area of one face

21/3 =  3 * area of one face

   area of one face  = 7

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one face of the three-dimensional figure has a surface area of 16/3 square centimeters.

The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface. It's also expressed in square units.

Let A represent the area of one of the three-dimensional figure's faces.

The overall surface area of the figure, including the base, is 26 square centimeters, according to the problem description. The total area of the base and the three similar faces is 26 - 5 = 21 square centimeters.

Because the three faces are identical, the total area of the three faces is 3A. As a result, we can write:

3A + 5 = 21

Subtraction of 5 from both sides yields:

3A = 16

By dividing both sides by three, we get:

A is equal to 16/3 square centimeters.

As a result, one face of the three-dimensional figure has a surface area of 16/3 square centimeters.

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Answer:

A. When x = 3, h(x) = 16 is false.

B. When x = 4, h(x) = 8 1/3 is true.

C. When x = 9, h(x) = 10 is true.

D. When x = 10, h(x) = 10 1/3 is true.

E. When x = 12, h(x) = 12 is false.Therefore, the true statements are B, C, and D.

There are 715 ways to select four people from a group of six men and seven women to attend a conference.

Combinations in mathematics relate to the various ways that a group of things can be chosen, regardless of the order in which they are chosen. Combinations are a form of counting problem where a smaller subset of the objects in the bigger set are selected.

The combination is given by the formula:

C(n,r) = n!/(r!(n-r)!)

The total number of people = 13.

The number of ways we can choose 4 people from the given 13 people are:

C(13,4) = 13!/(4!9!) = (13x12x11x10)/(4x3x2x1) = 715

Hence, there are 715 ways to select four people from a group of six men and seven women.

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The complete question is:

the total cost for a Mug Club member who refills their cup 120 times in one year is $309.

How to solve?

If a customer purchases a Mug Club membership, they pay $75 for the mug and then refill it for $1.95 per refill. If they refill their mug 120 times in one year, the total cost would be:

$75 (for the initial purchase of the mug) + $1.95 x 120 (for the 120 refills)

= $75 + $234

= $309

Therefore, the total cost for a Mug Club member who refills their cup 120 times in one year is $309.

Cost refers to the amount of money or resources that are required to produce or obtain a good or service. It can include expenses such as materials, labor, rent, utilities, and other expenses incurred in the production or acquisition of a product or service.

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The limit of the given expression when we put the values of n and k is: γ = 0

We want to find the limit of the function as n tends to infinity:

lim n → ∞ [tex]\lim_{n \to \infty} \Sigma \frac{1}{k} - In (n)[/tex] for k = 1

n → ∞ simply means that n is approaching zero. Thus, we can simplify our expression when we put the limit for n to get:

1/k - 1

At k = 1, we have:

(1/1) - 1  = 0

Thus, γ = 0

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Formula for the concentration after n steps is [tex]C(n) = C(0) * (0.86)^n[/tex] and

after 11 steps, the mixture contains less than 9% vinegar.

What is concentration?

Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.

a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:

[tex]C(1) = C(0) * \frac{1 - 0.14}{1}[/tex]

where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:

C(2) = C(1) * [tex]\frac{1 - 0.14}{1}[/tex]

Substituting the formula for C(1), we get:

C(2) = C(0) * [tex](\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})[/tex]

or, more generally:

[tex]C(n) = C(0) * (0.86)^n[/tex]

b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:

[tex]C(0) * (0.86)^n < 0.09[/tex]

Dividing both sides by C(0), we get:

[tex](0.86)^n < 0.09[/tex]

Taking the natural logarithm of both sides, we get:

n * ln(0.86) < ln(0.09)

Dividing both sides by ln(0.86), we get:

n > ln(0.09) / ln(0.86)

Using a calculator, we get:

n > 10.7

Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.

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An answer choice that is equivalent to the product below include the following: B. 3√10.

In this scenario and exercise, you are required to determine the correct and most accurate answer choice that is equivalent to the product of the given mathematical expression.

In this scenario and exercise, the simplest form of the given expression √3 × √5 × √6​ can be determined or calculated by simplifying it as follows;

Expression = √3 × √5 × √6

Expression = √3 × √5 × √(3 ×2)

Expression = √3 × √5 × √3 × √2

Expression = 3 × √(5 × 2)

Expression = 3 × √10

Expression = 3√10.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The t-value is given as follows:

t = 1.82.

The equation for the t-value is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 86.3, \mu = 83.5, s = 7.2, n = 22[/tex]

Hence the t-value is given as follows:

[tex]t = \frac{86.3 - 83.5}{\frac{7.5}{\sqrt{22}}}[/tex]

t = 1.82.

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When editing a speech, you should look for these components:

The act of editing speech involves more than just correcting grammar and spelling errors as its also involves analyzing the rhetorical strategies used, ensuring that the level of formality is appropriate for the audience and occasion and making sure that the main idea and supporting details are clearly presented and organized.

An effective editing can help to strengthen the message of the speech and increase its impact on the audience. Therefore, it is important to consider all of these components when editing a speech.

Full question "Which of the following components should you look for when editing in speech rhetorical strategies main? Idea and supporting detail grammar and spelling errors level of formality"

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The sample in this study is D. The students who complete the survey.
This is because the dance committee is only collecting data from those students who are surveyed, which represents a smaller group within the entire population of the school.

The sample in this study refers to the specific group of individuals who are selected to participate in the survey or study.

In this case, the dance committee at Northeast Middle School is choosing the theme for the spring dance and conducts a poll to ask students about their choices.

They ask every 10th student entering the cafeteria to complete a survey.

Therefore, the sample in this study is the students who complete the survey.

They are the specific group of individuals who are selected to participate in the survey and provide information about their preferences for the spring dance theme.

D. The students who complete the survey.

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Answer:

The students who complete the survey

Step-by-step explanation:

On solving the query we can say that The slant height, along with the function cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

You are informed that the cone in this scenario has a volume of 4.5 cubic inches. Using the aforementioned calculation, you can determine the radius if you know the cone's height.

Alternately, you may use the Pythagorean theorem to calculate for the radius if you know the cone's slant height. The slant height, along with the cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.

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Answer: 1728 cubic meters

Step-by-step explanation: 12 x 12 x 12 V= LxWxH

For the deviation between each data value and the mean in column 3, there are around 1320.511 squared deviations in all.

To find the sum of the squared deviations in column 3, add up all the values in that column.

x x − x (x − x)²

50 50 − 40.545 (9.455)² = 89.397

28 28 − 40.545 (-12.545)² = 157.377

37 37 − 40.545 (-3.545)² = 12.567

30 30 − 40.545 (-10.545)² = 111.197

58 58 − 40.545 (17.455)² = 304.677

38 38 − 40.545 (-2.545)² = 6.477

39 39 − 40.545 (-1.545)² = 2.387

59 59 − 40.545 (18.455)² = 340.587

47 47 − 40.545 (6.455)² = 41.667

34 34 − 40.545 (-6.545)² = 42.837

26 26 − 40.545 (-14.545)² = 211.557

To find the sum of the squared deviations, add up the values in column 3:

x − x² = 89.397 + 157.377 + 12.567 + 111.197 + 304.677 + 6.477 + 2.387 + 340.587 + 41.667 + 42.837 + 211.557 = 1320.511

Rounded to three decimal places:

x − x² ≈ 1320.511

Therefore, the sum of the squared deviations in column 3 is approximately 1320.511.

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The value of x from the given equation is 8/15.

The given equation is 17/3 - 3/4 x= 1/2 x+5

17/3 - 3/4 x= 1/2 x+5   (Given)

17/3 - 3/4 x -17/3= 1/2 x+5 -17/3 (Subtraction property of equality)

-3/4 x = 1/2 x -2/3

-3/4 x -1/2 x = 1/2 x -2/3 -1/2 x (Subtraction property of equality)

-5/4 x=-2/3

-5/4 x × 4/5=-2/3 × 4/5  (Multiplication property of equality)

x= 8/15

Therefore, the value of x from the given equation is 8/15.

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Answer:

Step-by-step explanation:

It is given that length and width of a rectangle is 11 cm and 10 cm.

We know the formula of Perimeter of rectangle

[tex]:\implies \: [/tex] Perimeter = 2(L + B)

Where 'L' denote the length of the rectangle and 'B' denotes the breadth of the Rectangle.

Now Let's substitute the value of Length= 11 cm and Breadth = 10 cm in the above formula .

[tex]:\implies \: [/tex] 2(11 + 10)

[tex]:\implies \: [/tex] 2 × 21

[tex]:\implies \: [/tex] 42 cm

Henceforth The perimeter of the rectangle is 42 cm

The perimeter of a rectangle is calculated by multiplying by 2 the sum of its length and width. So, in this case, the rectangle's perimeter is 42 cm.

The subject of this question is on calculating the perimeter of a rectangle. The formula for finding the perimeter of a rectangle is 2*(length + width). Applying the values given, that is length = 11 cm and width = 10 cm.

So, the perimeter of a rectangle = 2*(11 + 10) cm = 2*21 cm = 42 cm

Therefore, the correct option is OC. 42 cm.

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The statement that must be true is c is the least common multiple of A and B, is D. c ≥ b and c ≥ a.

The rationale behind this lies in the fact that finding the least common multiple (LCM) of two numbers necessitates determining a value that is commensurate with both figures, yet simultaneously represents their most diminutive shared multiple.

To expound further, It is the minimal positive integer among all feasible ones that can be divided entirely without any leftover remainder by all supplied integers. Thus, this computation allows you to determine the minimum possible factorization required to obtain each number while preserving its numerical integrity.

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The length of JK is 42 units, which can be calculated using the theorem that states JK × JL = ML × JN, with the given lengths of KL, LM, and MN.

Length is a measurement of how long or extended an object or distance is, typically measured in units such as meters, centimeters, feet, or inches.

A theorem is a statement or proposition that has been proven to be true through deductive reasoning or a mathematical proof, and is often used as a basis for further reasoning and conclusions.

According to the given information:

To find the length of JK, we can use the theorem which states that the product of the lengths of the segments of a secant is equal. In other words, JK × JL = ML × JN. We are given the lengths of KL, LM, and MN, and we know that KL + LM + MN = JL + JN.

We can use this information to solve for JK. First, we need to find JL and JN. We can do this by subtracting KL and MN from LM to get JL = LM - KL and JN = LM - MN. Substituting these values into the equation JK x (LM - KL) = KL × (LM - MN), we can solve for JK.

JK = (KL × (LM - MN)) / (LM - KL) = (14 × (17 - 14)) / (17 - 14) = 14 × 3 = 42.

Therefore, the length of JK is 42.

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The surface area covered with stickers is 169.4 cm².

How to calculate the surface area of the paperweight?

We need to find the area of each face and then add them up for calculate the surface area of the paperweight,

We know,

Area of the rectangular base [tex]= length \times breadth = 17 cm \times 11 cm = 187 \: {cm}^{2} [/tex]

Area of the triangular top = (1/2) x base x height = (1/2) × 15 cm × 8 cm × 7 cm / √((15/2)² - (8/2)²) = 42 cm²

Area of the front and back faces (which are rectangles) [tex]= 2 \times length \times height = 2 \times 17 cm \times 10 cm = 340 \: cm²[/tex]

Area of the left and right faces (which are trapezoids) [tex]= ( \frac{1}{2} )(a+b) \times h \times 2 = ( \frac{1}{2} )(15 cm + 8 cm) \times 7 cm \times 2 = 91 {cm}^{2} [/tex]

Area of the bottom face (which is a rectangle) [tex]= length \times breadth = 17 cm \times 11 cm = 187 cm²[/tex]

Total surface area = 187 cm² + 42 cm² + 340 cm² + 91 cm² + 187 cm² = 847 cm²

To find the surface area covered with stickers, we need to calculate 20% of the total surface area:

Surface area covered with stickers [tex]=20\% \: of \: 874 \: {cm}^{2} = 0.2 \times 847 \: {cm}^{2} = 169.4 \: {cm}^{2} [/tex]

Therefore, the surface area covered with stickers is 169.4 cm² approximately.

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Answer:

63

Step-by-step explanation:

given the sight of the angle it should be 63, correct me if I'm wrong.

Answer:

The Correct answer is B

x≥4.5