Austin takes1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is
/
radians per second.

Answer:

[tex]y(t)=\frac{1}{2}t^2+y_1t }[/tex]

Step-by-step explanation:

Refer to the attached image(s).

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Table of basic Laplace Transforms:}}\\1\rightarrow \frac{1}{s} \\t^n\rightarrow \frac{n!}{s^{n+1}}\\e^{at} \rightarrow\frac{1}{s-a}\\ \sin(at)\rightarrow\frac{a}{s^2+a^2}\\\cos(at)\rightarrow\frac{s}{s^2+a^2}\\e^{at}\sin(bt)\rightarrow\frac{b}{(s-a)^2+b^2}\\e^{at}\cos(bt)\rightarrow\frac{s-a}{(s-a)^2+b^2}\\t^ne^{at}\rightarrow\frac{n!}{(s-a)^{n+1}} \end{array}\right}[/tex]

The ratios with unit rates greater than 1 are:

3 1/5 pounds : 4 pounds

7 1/10 pounds : 9/10 pound

9/4 pounds : 3/4 pound

2 pounds : 1/3 pound.

A unit rate is the comparison of two quantities with a denominator of 1.

To determine if the unit rate is greater than 1, we need to compare the numerator to the denominator.

If the numerator is greater than the denominator, the unit rate is greater than 1.

Let's analyze each ratio:

3 1/5 pounds : 4 pounds:

The numerator (3 1/5) is greater than the denominator (4), so the unit rate is greater than 1.

7 1/10 pounds : 9/10 pound:

The numerator (7 1/10) is greater than the denominator (9/10), so the unit rate is greater than 1.

7/8 pound : 2 pounds:

The numerator (7/8) is less than the denominator (2), so the unit rate is not greater than 1.

9/4 pounds : 3/4 pound:

The numerator (9/4) is greater than the denominator (3/4), so the unit rate is greater than 1.

3 pounds : 1 1/2 pounds:

The numerator (3) is equal to the denominator (1 1/2), so the unit rate is not greater than 1.

2 pounds : 1/3 pound:

The numerator (2) is greater than the denominator (1/3), so the unit rate is greater than 1.

Therefore, the ratios with unit rates greater than 1 are:

7 1/10 pounds : 9/10 pound

9/4 pounds : 3/4 pound

2 pounds : 1/3 pound

3 1/5 pounds : 4 pounds

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Answer:

26 units

Step-by-step explanation:

AD = 9 -2 = 7 units long. BC is the same. so we have 2 X 7 = 14.

DC is 9 - 3 = 6 units long. AB is the same. so we have 2 X 6 = 12.

perimeter = 14 + 12 = 26 units

The approximate direction of the angle of the vector is determined as 45 degrees.

The approximate direction of the angle of the vector is calculated by applying the following formula for direction of a vector as follows;

The formula for the direction of a vector is given as;

tan θ = Vy / Vx

where;

The vector is given as;

V = 4i + 4j - 2k

The y component = 4, and the x component = 4

The direction of the vector is calculated as;

tan θ = 4 / 4

tan θ = 1

θ = arc tan (1 )

θ = 45⁰

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A linear model that shows the miles Martin has run as the input, and the total time, in minutes, he has been running as the output is: y = 11x - 5

The general formula for the equation of a line between two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

Using the coordinates as:

(5, 60), (9, 104) and (20, 225), we can say that the equation is expressed as:

(y - 60)/(x - 5) = (104 - 60)/(9 - 5)

(y - 60)/(x - 5) = 44/4

y - 60 = 11(x - 5)

y - 60 = 11x - 55

y = 11x - 5

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The retirement plans that potentially involve contributions from an individual's employer are I, III, and IV.

I - Traditional IRA: A Traditional IRA is an individual retirement account (IRA) that allows individuals to set aside money on a pre-tax basis. Contributions to a Traditional IRA may be made by an individual, or they may be made by an employer as part of an employee's retirement plan.

III - Pension Plan: A pension plan is a retirement plan organized by an employer that provides a guaranteed income to an employee after retirement. Employers typically make contributions to their employee's pension plan on their behalf.

IV - 401(k): A 401(k) is an employer-sponsored retirement savings plan. Contributions to a 401(k) plan can be made by an employee and their employer. Employers may match employee contributions, up to a certain percentage.

Therefore, the retirement plans that potentially involve contributions from an individual's employer are I, III, and IV.

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The number of more houses between the area 150m² and 200 m² than between 250m² and 300 m² is 8.

Histogram is a graphical representation of discrete or continuous data. In other words, it is a graphical representation of distribution of data.

Therefore, the histogram has number of houses on the y-axis and area on the x -axis,

The histogram relates the number of houses to the area of the houses in square metres.

Therefore, let's find how many more houses have an area between 150m² and 200 m² than between 250m² and 300 m²?

Hence,

Houses between 150m² and 200 m²  = 9

Houses between 250m² and 300 m² = 1

Finally,

difference between them = 9 - 1 = 8 houses

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The volume of the figure is V = 5,730.265 cm³

Given data ,

Let the figure be represented as V

Now , the figure consists of a cone and hemisphere

So , V = Volume of cone + volume of hemisphere

where height = 14 cm

And , radius r = 12 cm

On simplifying , we get

V = ( 1/3 ) πr²h + ( 2/3 )πr³

V = ( 1/3 ) ( 3.14 ) ( 12 )² ( 14 ) + ( 2/3 ) ( 3.14 ) ( 12 )³

V = 2,111.15026 + 3,619.1147369

On further simplification , we get

V = 5,730.265 cm³

Hence , the volume is V = 5,730.265 cm³

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The complete question is attached below :

Find the volume of the figure. Use 3.14 for . 12 cm 14 cm

Answer:

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

Divide the total amount by the cost per piece:

Since the carpenter can only buy whole pieces of wood, they can buy 30 pieces.

The equation represents a cosine function that is horizontally shifted, vertically shifted, and scaled with specific values for amplitude, period, phase shift, and midline adjustment.

The equation and description of the interactive widget graph. It appears that the equation you've shared represents a periodic function, specifically a cosine function, with some transformations applied to it.

The general form of a cosine function is given by:

f(x) = A * cos(Bx - C) + D

In your equation, the parameters have specific values:

A = 2

B = 5π/5 = π

C = 5/(2π) = 5/2π

D = -4

The parameter A determines the amplitude of the cosine function, which controls the vertical range of the graph. In this case, it is 2, so the graph will oscillate between 2 units above and 2 units below the midline.

The parameter B affects the period of the function. Since B = π, the period of the cosine function will be 2π/B = 2π/π = 2. This means that the graph completes one full cycle (i.e., goes through one peak and one trough) over an interval of length 2.

The parameter C introduces a phase shift or horizontal translation to the graph. The value of C, 5/2π, determines how much the graph is shifted horizontally. Specifically, it is shifted 5/(2π) units to the right.

The parameter D is the vertical shift or midline adjustment. With D = -4, the entire graph is shifted downward by 4 units.

The movable point mentioned in the widget likely allows you to change the value of x and observe how it affects the position of the extremum point and the intersection points with the midline.

Overall, the equation represents a cosine function that is horizontally shifted, vertically shifted, and scaled with specific values for amplitude, period, phase shift, and midline adjustment.

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The probability of obtaining a success given that X is less than 5, P(X < 5) is 0.8906.

The probability of obtaining a success is calculated as follows:

Given data:

X has a binomial distribution with n = 6 trials and p = 0.5, the probability of obtaining a success.

Using the binomial distribution function:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = k) = [tex](_nC_k) * p^{k} * (1 - p)^{(n - k)}[/tex]

Therefore;

P(X < 5) = (₆C₀) * 0.5⁰ * 0.5⁶ + ( 1) * 0.5¹ * 0.5⁵ + (₆C₂) * 0.5² * 0.5⁴ + (₆C₃) * 0.5³ * 0.5³ + (₆C₄) * 0.5⁴ * 0.5²

P(X < 5) = 0.015625 + 0.09375 + 0.234375 + 0.3125 + 0.234375

P(X < 5) = 0.8906

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Note that the rule that describes the transformation shown is: (x,y) → (x+7,-y)(Number 2)

We have,

A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure. The Pre-Image is the original shape of the item, and the Image is the final shape and location of the object after the transformation.

Thus, with regard to the transformation above,

At Point A: The original coordinate of point A was (-6,-6).

The coordinate after the transformation is A'(1,6), which eliminates option 3.

At Point B:

The original coordinate of point B was (-2,4).

After the transformation, we have B'(5,-4), which eliminates option 1 and option 4. It is therefore right to state that (x,y) → (x+7,-y) is the correct representation of the transformation.

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Full Question:

The missing options are:

Which rule describes the transformation shown?

1. (x,y) → (-y, x+7)

2. (x,y) → (x+7,-y)

3. (x,y) → (-x, y+7)

4. (x,y) → (y+7, -x)

Through the work that was shown, you have

     999x = 393

If you divide both sides of the equation by 999, you'd have

     [tex]x=\dfrac{393}{999} = \dfrac{131}{333}[/tex]

So, [tex]0.\overline{393} =\dfrac{131}{333}[/tex]

The factored form of the expression is  (x+3) (x-6), which is equivalent to choice C. x-6 , is one of the factors.

To factor a quadratic expression like this, we want to find two numbers that multiply to the constant term (-18) and add up to the coefficient of the x term (-3).

In this case, those numbers are -3 and 6, because (-3) * 6 = -18 and (-3) + 6 = 3.

Then, we can use those numbers to split the middle term into two terms:

x²-3x-18

=x²+3x - 6x-18

=x(x+3) -6(x+3)

=(x+3) (x-6)

So the factored form of the expression is (x+3) (x-6),

which is equivalent to choice C. x-6 , is one of the factors.

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The distance between the boat and the diver is D = 276.5 feet

Given data ,

A scuba diver is 356 feet under the water's surface.

And the diver establishes a 39° angle of depression with her boat.

Therefore, using the trigonometric relationships, we can

tan θ = opposite / adjacent

On simplifying , we get

tan 39° = D / 356

Multiply by 356 on both sides , we get

D = 276.5 feet

Hence , the distance is therefore 276.5 ft.

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The surface area of the box which is a rectangular prism would be = 24 square inches. That is option D.

To calculate the area of the given box the formula that should be used is the formula of the area of a rectangular prism. That is;

Area of rectangular prism = length×width×height

Where:

length = 4 inches

width = 3 inches

height = 2 inches

Area = 4×3×2 = 24 square inches

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Answer:

1

Step-by-step explanation:

6c - 2c = 4

      4c = 4

        c = 4/4

        c = 1

With regard to Neotraditionism, Denis' influence to write the first state  what was not objective comes from the desire to "put an end to all kind of naturalism and illusion" "Purely Plastic Art"

In order to create truly original works of art that went beyond what they saw as stagnating traditions of representation and illusionism both Denis and Kandinsky had their own unique visions for what constituted true artistic expression

Denis wanted to create a "purely plastic art" that would transcend nature altogether (Denis, 1890).

While Kandinsky believed that color held within it an almost mystical power capable of evoking deep emotions: "Color is...the soul is...the artist is..." he wrote poetically (p. 44).

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The number of times two yellow cards occurred in 400 simulations of the repeated experiment. will be 64.

The probability of getting yellow is calculated as,

P(YY) = 2/5 x 2/5

P(YY) = 4/25

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

The expected value is calculated as,

E(YY) = 400 x 4/25

E(YY) = 64

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The correct interpretations of the slope and y-intercept are:

For each increase in speed of 1 mph, an additional 46.4 calories are predicted to be burned.

About 71.9 calories are burned at rest.

These interpretations are based on the regression equation given as

ŷ = 71.9 + 46.4x,

where ŷ represents the predicted calories burned and x represents the speed in miles per hour.

The slope of 46.4 indicates that for each 1 mph increase in speed, there is an additional predicted burn of 46.4 calories.

The y-intercept of 71.9 suggests that at a speed of 0 mph (resting), approximately 71.9 calories are burned.

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The value of the area of a triangle is equal to 133 in^2.

We are given that;

Dimensions= 19in 13in

Now,

To determine the area of a triangle, we can use the formula A = (1/2) bh, where b is the base and h is the height.

The base and the height are the sides that are perpendicular to each other. For example, the area of a right triangle with base 12 in and height 9 in is;

A = (1/2) * 12 * 9

A = 54 in^2.

To find the area of the given triangle, we need to identify the base and the height. The base could be any side of the triangle, but the height must be perpendicular to it. In this case, we can choose the side with length 19 in as the base, and the side with length 14 in as the height. Using the formula, we get:

A = (1/2) * b * h

A = (1/2) * 19 * 14

A = 133 in^2

Therefore, by the area, the answer will be 133 in^2.

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ln|sec(x)tan(x)| + C is the integral value of ∫sec²x/tanx dx

We can start by using the identity sec²(x) = 1 + tan²(x) to rewrite the integrand as:

sec²(x)/tan(x) = (1 + tan²(x))/tan(x)

= tan(x)/tan(x) + tan³(x)/tan(x)

= 1 + tan²(x)

Now we can make the substitution u = tan(x) to get:

∫sec²x/tanx dx = ∫(1 + tan²(x)) dx

= ∫(1 + u²) du

= u + (1/3)u³ + C

= tan(x) + (1/3)tan³(x) + C

= ln|sec(x)tan(x)| + C,

Therefore,  ln|sec(x)tan(x)| + C is the integral value of ∫sec²x/tanx dx

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Answer:

48

Step-by-step explanation:

Volume of triangular prism =1/2 bhl

=1/2 (4cm)(6cm)(4cm)

=48

Janna would be use 30 marshmallows and 45 graham crackers to make 15 s'mores.

Since, We know that;

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

We have to given that;

Janna wants to make s'mores at the backyard campfire.

The table below shows the parts of marshmallows to graham crackers to make s'mores.

S'mores  Marshmallows  Graham Crackers

4                   8                           12

15

That means, the rate is,

8/4 = 2 Marshmallows for each S'mores,

And 12/4 = 3 Graham Crackers for each S'mores.

Therefore, 30 marshmallows and 45 graham crackers to make 15 s'mores.

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Janna wants to make s'mores at the backyard campfire. The table below shows the parts of marshmallows to graham crackers to make s'mores.

S'mores Marshmallows Graham Crackers

4 8 12

15

At this rate, how many marshmallows and graham crackers will Janna use to make 15 s'mores?

Janna will use 17 marshmallows and 21 graham crackers to make 15 s'mores.

Janna will use 16 marshmallows and 24 graham crackers to make 15 s'mores.

Janna will use 25 marshmallows and 48 graham crackers to make 15 s'mores.

Janna will use 30 marshmallows and 45 graham crackers to make 15 s'mores.

The vertices of the image after a dilation with the origin as its center and a scale factor of 2 are having coordinates A' = (12, 8), B' = (4, 8), C' = (12, -4) and D' = (4, -4)

To dilate a figure with the origin as the center, we only need to multiply each coordinate by the scale factor. In this case, the scale factor is 2.

So, for vertex A(6, 4), we have:

x-coordinate after dilation: 2 × 6 = 12

y-coordinate after dilation: 2 × 4 = 8

Similarly, for vertex B(2, 4), we have:

x-coordinate after dilation: 2 × 2 = 4

y-coordinate after dilation: 2 × 4 = 8

For vertex C(6, -2), we have:

x-coordinate after dilation: 2 × 6 = 12

y-coordinate after dilation: 2 × (-2) = -4

Finally, for vertex D(2, -2), we have:

x-coordinate after dilation: 2 × 2 = 4

y-coordinate after dilation: 2 × (-2) = -4

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The expression that represent the perimeter of the triangle is 3d² - 4d + 1.

The perimeter of any two-dimensional figure is simply the distance around the figure.

Hence, the perimeter of the triangle is the sum of all its 3 side lengths.

From the diagram:

Side length 1 = ( d² + 3 )

Side length 2 = ( 4d² + 3d - 2 )

Side length 3 = ( -2d² - 7d )

Hence, the perimeter of the triangle will be:

Perimeter = side length 1 + side length 2 + side length 3

Plug in the expressions

Perimeter = ( d² + 3 ) + ( 4d² + 3d - 2 ) + ( -2d² - 7d )

Collect and add like terms:

Perimeter = d² + 3 + 4d² + 3d - 2 + -2d² - 7d

Perimeter = d² + 4d² - 2d² + 3d - 7d + 3 - 2

Perimeter = 3d² - 4d + 1

Therefore, the perimeter is 3d² - 4d + 1.

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The estimated cost of printing Sarah's 300-page book is $6.50.

The estimated cost would be $20.00.
1. The y-intercept for the trend line is 5.00. The real-world meaning of this point is that the base cost for printing a book, regardless of the number of pages, is $5.00.
2. To find the slope of the trend line, use the formula (y2 - y1) / (x2 - x1). With the y-intercept (0, 5) and the given point (200, 6), the slope is (6 - 5) / (200 - 0) = 1 / 200 = 0.005.
3. The real-world meaning of the slope is that for each additional page in the book, the printing cost increases by $0.005 or half a cent per page.
4. Using the slope and y-intercept, the equation for the trend line in slope-intercept form is y = 0.005x + 5.
5. To estimate the cost of printing Sarah's 300-page book, substitute x = 300 into the equation: y = 0.005(300) + 5. So, y = 1.5 + 5 = 6.5. The estimated cost of printing Sarah's 300-page book is $6.50.

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Answer: If we resolve, 10 to the power of 5 means 100,000.

Step-by-step explanation:

The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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Answer:

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

The sum of (-2) and (-4) is:

The difference of (-2) and (-4) is:

The product of the sum and difference is: