You are walking from home to a shoe store. You stop for a rest after 1/3 miles. The shoe store is actually 3/4 miles from home. How much farther do you have to walk? Write your answer as a fraction in simplest form.

Let's use the variable "x" to represent the number of 3-inch bolts that James bought.

We know that he bought a total of 16 bolts, so the number of 4-inch bolts he bought would be 16 - x.

The cost of the 3-inch bolts is 36 cents each, so the total cost of the 3-inch bolts would be 0.36x dollars.

Similarly, the cost of the 4-inch bolts is 42 cents each, so the total cost of the 4-inch bolts would be 0.42(16 - x) dollars.

We know that the total cost of all the bolts was $6.00, so we can set up the following equation:

0.36x + 0.42(16 - x) = 6.00

Simplifying and solving for x, we get:

0.36x + 6.72 - 0.42x = 6.00

-0.06x = -0.72

x = 12

Therefore, James bought 12 of the 3-inch bolts.

The end behavior of the given function is As x → –∞, f(x) → –∞, and as x → ∞, f(x) → –∞.

The term "end behavior" describes the behaviour or trend of a function's graph as its x-values go closer to positive or negative infinity. It explains how the function "ends" or acts when x is extremely large (positive infinity) or extremely small (negative infinity). The degree and leading coefficient of the polynomial formulation of the function can be used to predict the final behaviour. For instance, the left and right ends of the graph will both point upward for a function with an odd-degree polynomial and a positive leading coefficient (towards positive infinity).

For the function f(x) = -2∛x as x approaches negative infinity because the function has a negative coefficient in front of the cube root, which means that as x decreases significantly, the absolute value of the cube root increases. The function also approaches negative infinity as x approaches very big (positive) values and the cube root approaches very small absolute values. As a result, the function's final behaviour is that it approaches negative infinity as x gets closer to both negative and positive infinity.

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The end behavior of the given function is As x → –∞, f(x) → –∞, and as x → ∞, f(x) → –∞.

The term "end behavior" describes the behaviour or trend of a function's graph as its x-values go closer to positive or negative infinity. It explains how the function "ends" or acts when x is extremely large (positive infinity) or extremely small (negative infinity). The degree and leading coefficient of the polynomial formulation of the function can be used to predict the final behaviour. For instance, the left and right ends of the graph will both point upward for a function with an odd-degree polynomial and a positive leading coefficient (towards positive infinity).

For the function f(x) = -2∛x as x approaches negative infinity because the function has a negative coefficient in front of the cube root, which means that as x decreases significantly, the absolute value of the cube root increases. The function also approaches negative infinity as x approaches very big (positive) values and the cube root approaches very small absolute values. As a result, the function's final behaviour is that it approaches negative infinity as x gets closer to both negative and positive infinity.

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Answer:

The function f(x) = -2∛x represents a cube root function that is multiplied by -2.

As x approaches negative infinity, the cube root of x becomes more negative, and when it is multiplied by -2, it becomes more positive. Therefore, as x → –∞, f(x) → ∞.

As x approaches positive infinity, the cube root of x becomes more positive, and when it is multiplied by -2, it becomes more negative. Therefore, as x → ∞, f(x) → –∞.

Therefore, the correct answer is: As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞. D.

Answer:

The function f(x) = -2∛x represents a cube root function that is multiplied by -2.

As x approaches negative infinity, the cube root of x becomes more negative, and when it is multiplied by -2, it becomes more positive. Therefore, as x → –∞, f(x) → ∞.

As x approaches positive infinity, the cube root of x becomes more positive, and when it is multiplied by -2, it becomes more negative. Therefore, as x → ∞, f(x) → –∞.

Therefore, the correct answer is: As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞. D.

Answer: x=-5,y=3

Step-by-step explanation: Add the 2 equations together, 3x+x=4x, y+(-y)=0, and -12-8=-20. This leaves us with 4x=-20, so x=-5. Plug x back into the equation, so -5-y=-8, add 5 to both sides  so -y=-3, and y=3.

Answer:

Step-by-step explanation:

1

Answer:

Step-by-step explanation:

To solve this problem, we need to use the distance formula to find the length of each side of the triangle, and then apply the Pythagorean theorem to determine whether the triangle is a right triangle.

Let's label the three vertices of the triangle as A, B, and C, and their coordinates as follows:

A = (-2, 5)

B = (3, -1)

C = (1, 3)

The length of AB is:

AB = sqrt((3 - (-2))^2 + (-1 - 5)^2) = sqrt(25 + 36) = sqrt(61)

The length of AC is:

AC = sqrt((1 - (-2))^2 + (3 - 5)^2) = sqrt(9 + 4) = sqrt(13)

The length of BC is:

BC = sqrt((1 - 3)^2 + (3 - (-1))^2) = sqrt(4 + 16) = sqrt(20) = 2sqrt(5)

Now, we need to check whether the triangle is a right triangle. We can do this by checking whether the sum of the squares of the two shorter sides (AB and AC) is equal to the square of the longest side (BC). If it is, then the triangle is a right triangle.

AB^2 + AC^2 = 61 + 13 = 74

BC^2 = (2sqrt(5))^2 = 20

Since AB^2 + AC^2 is not equal to BC^2, the triangle is not a right triangle.

Therefore, the answer is: "The triangle is not a right triangle."

the total cost for the company including commission is $15,917

The commission is a sum of money that an employer pays as a fee or a percentage to an employee for completing a certain task or for generating new business by promoting the company's products or services. Incentives or sales commissions are other names for it. In general, anyone can earn a commission; it's not just for salespeople. The commission comes on top of the wage.

The company's policy, which ensures basic compensation and commission over a specific number of deal closures, determines the proportion of commission.

Equity ownership in a corporation is represented by shares. Shares are a type of financial asset that some businesses use to guarantee an equitable dividend distribution of any declared residual profits.

according to question,

total cost of 100 shares = 100*44.41 = $4441

total cost of 600 shares = 600*19.08 = $11448

broker charges for all 700 shares = 700*0.04 = $28

total cost acquired by the company is = $4441+$11448+$28

                                                               = $15917

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If the daily prices are $ 1.50 for children and $ 2.25 for adults, a total of 284 children and 255 adults swam at the public pool that day.

Let's assume that the number of children who swam in the pool is x, and the number of adults who swam in the pool is y.

From the problem statement, we know that the total number of people who swam in the pool is 539. Therefore, we can write:

x + y = 539

We also know that the total receipts for admission are $1017.00. The price for a child is $1.50 and the price for an adult is $2.25. Therefore, the total revenue can be expressed as:

1.5x + 2.25y = 1017

Now we have two equations with two variables. We can solve for x and y by using any method of solving linear equations. For example, we can use the substitution method to solve for x and y:

x + y = 539 → x = 539 - y

Substituting this value of x into the second equation, we get:

1.5(539 - y) + 2.25y = 1017

Simplifying and solving for y, we get:

y = 255

Substituting this value of y into the equation x + y = 539, we get:

x = 539 - 255 = 284

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Answer:

  √(205)/13

Step-by-step explanation:

You want sec(θ) when cot(θ) = 13/6.

Some calculators can figure this directly as ...

  [tex]\sec{(\cot^{-1}\dfrac{13}{6})}=\boxed{\dfrac{\sqrt{205}}{13}}[/tex]

Others need to make use of the trig relations ...

  tan(θ) = 1/cot(θ)

  sec(θ) = √(tan²(θ) +1)

or

  sec(θ) = 1/cos(θ)

The tangent of the angle is

  tan(θ) = 1/cot(θ) = 1/(13/6) = 6/13.

Then the secant is ...

  sec(θ) = √((6/13)² +1) = √(6² +13²)/13

  sec(θ) = √205/13

A calculator can get there from ...

  sec(θ) = 1/cos(arctan(6/13)) = √205/13

The New Area based on the information will be 168ft

Expanding the above equation, we get:

120ft² + 22x + x² = 240ft²

Rearranging and simplifying, we get:

x² + 22x - 120 = 0

Since the increase cannot be negative, we take the positive value of x:

x = 2

Therefore, the increase in both the length and width of the patio should be 2ft to double its area.

New Length = 10ft + 2ft = 12ft

New Width = 12ft + 2ft = 14ft

New Area = 12ft x 14ft = 168ft²

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Answer:

? = 13.7

Step-by-step explanation:

Right triangle equation A^2 + B^2 = C^2

7.6^2 + 11.4^2 =

57.76 + 129.96 = 187.72

find the square root of 187.72 by putting it in the calculator

187.72 = 13.70109485^2

Estimate = 13.7^2

The equation is Skateboard = Deck + Grip Tape + Trucks + Wheels + Bearings + Hardware + Assembly + Personalization.

Here's an equation that outlines my "recipe" for making a skateboard:

Skateboard = Deck + Grip Tape + Trucks + Wheels + Bearings + Hardware + Assembly + Personalization

Explanation of the equation:

Deck: The wooden or composite board that serves as the main body of the skateboard. It is typically made from layers of plywood or other materials, and its dimensions (length, width, concavity, etc.) can be customized based on personal preference.

Grip Tape: A sandpaper-like material that is applied to the top of the deck to provide traction for the rider's feet. It is usually made of adhesive-backed paper or fabric and comes in various designs and colors.

Trucks: Metal T-shaped components that are mounted on the underside of the deck and serve as the axle and suspension system of the skateboard. They consist of a baseplate, hanger, kingpin, bushings, and hardware, and are responsible for allowing the board to turn and pivot.

Wheels: Typically made of urethane or other durable materials, skateboard wheels come in various sizes, shapes, and hardness levels (durometer). They are attached to the trucks and provide smooth rolling and maneuverability.

Bearings: Small, round metal or ceramic components that fit inside the wheels and allow them to spin freely on the axle. They are crucial for reducing friction and enabling the wheels to roll smoothly.

Hardware: Nuts, bolts, and screws used to attach the trucks to the deck and assemble the skateboard. They are typically made of metal and come in different sizes and lengths.

Assembly: The process of putting together all the skateboard components to create a functional skateboard. It involves attaching the trucks to the deck using the hardware, installing the wheels and bearings, and applying the grip tape.

Personalization: This refers to any additional customization or personal touches that a skateboarder may choose to add to their skateboard, such as stickers, artwork, or modifications to the deck shape or truck settings, to make it unique and suited to their individual style.

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The missing dimensions of the triangular plot of land are:

i. b = 2.45

ii. A = 69.5

iii. C = 75.5^o

A cosine rule is a trigonometric function that can be used to determine the length of side, or measure of the internal angles of a none right angled triangle.

Cosine rule states that;

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B

To determine the missing values of the triangle in the attached diagram, we have;

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B

  = 4^2 + 7^2 - 2(4*7)Cos35^o

  = 16 + 49 -2(36*0.8192)

  = 65 - 58.9824

  = 6.0176

b = (6.0176)^1/2

  = 2.4531

b = 2.45

From sine rule,

a/ Sin A = b/Sin B = c/ Sin C

a/ Sin A = b/Sin B

4/Sin A = 2.45/ Sin 35

Sin A = 4* Sin 35/ 2.45

        = 0.9365

A = Sin^-1 0.9365

  = 69.47

A = 69.5

So to determine the value of C, we have;

A + B + C = 180^o

69.5 + 35 + C = 180

104.5 + C = 180

C = 180 - 104.5

   = 75.5

C = 75.5^o

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The function is transformed by horizontal translation to the right is applied first, followed by the vertical translation downward

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

y = 3ˣ

Let the transformed function be f' ( x )

y' = 3⁽ˣ⁻²⁾ - 4

Horizontal Translation: When compared to the basic function, y = 3x, the function's "(x-2)" inside the exponent of 3 causes a horizontal translation to the right of 2 units.

This results in a 2 unit shift along the x-axis of the function's graph.

Vertical Translation: In comparison to the base function y = 3x, the "-4" at the end of the function causes a vertical translation downward of 4 units.

This results in a 4 unit downward shift of the function's y-axis graph.

Hence , the function is transformed

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The output for an input of n is given as follows:

f(n) = -4 - 2n.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

For this problem, we have that when x increases by one, y decays by two, hence the slope m is given as follows:

m = -2.

Hence:

f(n) = -2n + b.

When n = 1, f(n) = -6, hence the intercept b is obtained as follows:

-6 = -2 + b

b = -4.

Hence the equation is:

f(n) = -2n - 4.

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The statement that describes the behavior of the function f(x) is: The graph approaches 0 as x approaches infinity.

The correct answer is an option (b)

Consider the function [tex]f(x) = \frac{2x}{1-x^2}[/tex]

Consider the limit of function f(x) as x approaches infinity (x → ∞)

[tex]\lim_{n \to \infty} f(x)\\\\= \lim_{n \to \infty} \frac{2x}{1-x^2} \\\\= \lim_{n \to \infty} \frac{2x/x}{(1-x^2)/x}\\\\ = \lim_{n \to \infty} \frac{-2}{x}[/tex]

= 0

This means that when x approaches infinity the term x² grows rapidly

So, 1 - x², which is in the denominator will decrease, become a large negative more rapid than the x in the numerator.

We can say that the function approaches zero.

Thus the correct statement is: The graph approaches 0 as x approaches infinity.

The correct answer is an option (b)

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The complete question is:

Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?

a) The graph approaches –2 as x approaches infinity.

b) The graph approaches 0 as x approaches infinity.

c) The graph approaches 1 as x approaches infinity.

d) The graph approaches 2 as x approaches infinity.

Hailey goes to a store an buys an item that price of a dollars, so the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.

The amount of discount that Hailey receives is 35% of the original price, which is 0.35a. Therefore, the discounted price she pays is a - 0.35a = 0.65a.

The amount of tax that is added to the discounted price is 8% of the discounted price, which is 0.08(0.65a) = 0.052a.

So the total amount that Hailey paid at the register is the discounted price plus the tax:

total amount = discounted price + tax

total amount = 0.65a + 0.052a

Simplifying this expression, we get:

total amount = 0.702a

Therefore, the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.

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Answer:

Step-by-step explanation:

The surface area of a cube is given by the formula:

SA = 6s^2

where s is the length of an edge.

Substituting s = 6.44 cm into the formula, we get:

SA = 6(6.44 cm)^2

SA = 6(41.4736 cm^2)

SA = 248.8416 cm^2

Therefore, the surface area of the cube is 248.8416 cm^2.

The building is, 246 feet tall.

Since, We know that;

Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.

To determine the height of the building, we have;

height of pole = 7 ft

total length of the building's shadow = 167 ft

the length of the shadow of the pole = 4.75 ft

Let the height of the building be represented by h. On comparison, we have;

4.75/ 167 = 7/h

4.75h = 167 x 7

        = 1169

h = 1169/ 4.75

h  = 246.11

Hence, The building is 246 ft. tall.

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The simplified expression is given as follows:

7/x³.

Where the coefficients are:

The expression in this problem is defined as follows:

x³(1/4 x³)(28x^-9).

To obtain the coefficient c, we must multiply the coefficients of each expression, as follows:

c = 1 x 1/4 x 28

c = 7.

When two terms with the same base and different exponents are multiplied, we keep the bases and add the exponents, hence:

3 + 3 - 9 = -3.

The negative exponents goes in the denominator, hence the simplified expression is given as follows:

7/x³.

Meaning that the exponent is of e = 3.

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Answer:

The correct answer is D. purchase price: $117, advertised price: $293.

Step-by-step explanation:

Answer:

the second one is x= -1

*this stuff is genuinely easy. I'm in 10th grade and all you have to do is put it in the calculator. If you have a tinspire like me you could make the x into a 1 in the calculator, put the whole thing in graph and it'll trace the answer for you. If your teacher wants to see work then maybe don't do that but let me know and I'll send the work for you.

If the normally distributed heights have mean as 69, then the probability that he can fit through the doorway without bending is 0.9938.

In "Normal-Distribution", probability refers to the likelihood of a continuous random variable falling within a certain range of values

We first convert the height of the doorway and the height of the male passenger to z-scores by using z = (x - μ) / σ,

where:

x = height (doorway height or male passenger height)

μ = mean of the male height,

σ = standard deviation of male height,

For the doorway height:

⇒ [tex]Z_{doorway}[/tex] = (76 - 69.0)/2.8 = 2.50,

For a male passenger:

⇒ [tex]Z_{male}[/tex] = (x - 69.0)/2.8,

To find the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the proportion of the "male-population" that has a height less than or equal to the height of the doorway;

⇒ P([tex]Z_{male}[/tex]  ≤  [tex]Z_{doorway}[/tex] ) = P([tex]Z_{male}[/tex]  ≤ 2.50) and

We know that the value of P(z ≤ 2.50) is 0.9938,

Therefore, the required probability is approximately 0.9938.

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The given question is incomplete, the complete question is

An airliner carries 350 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in,

If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.

Step-by-step explanation:

A(n) discount is an amount returned after purchase or deducted from the purchase price.

Angle or arc HGJ is measured at 275 for given figure.

Arcs may be created from the circumference of a circle. It is referred to as the curved line that connects two locations on a circle's perimeter and splits it into segments. The length of an arc is inversely proportional to the angle it makes at the centre of the circle.

When the central angle rises, so does the arc's length, and vice versa. Arcs are commonly used to depict and compute measurements of circles and circular objects in geometry, trigonometry, and physics.

For given problem,

mHGJ= 360° - mJH = 360°-( mJl + mlH ) =  360°-(30°+55°)

         = 360°-85° = 275°

Hence, arc or angle HGJ= 275 degrees

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The calculated value of the perimeter of the scaled rectangle is 120 inches

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

Perimeter =  48 in

Scale factor = 2.5

Using the above as a guide, we have the following:

Perimeter of the scaled rectangle = Perimeter * Scale factor

Substitute the known values in the above equation

Perimeter of the scaled rectangle = 48 * 2.5

Evaluate

Perimeter of the scaled rectangle = 120

Hence, the perimeter of the scaled rectangle is 120

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