Engineers built an arch bridge across a river. The arch bridge


makes a parabola shape that has the equation


y=-0. 1(x – 5)2 + 12, where x and y are measured in


meters. If the bridge makes contact with both banks at a height


of 4 meters, how long is the distance between the two banks


of the river where the bridge is? Round your answer to the


nearest whole number.

Answer: Right/complementary angles

Step-by-step explanation:

Two angles that add up to 90 degrees are called complementary angles.

Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.

In other words, the sum of the measures of complementary angles is always 90 degrees.

Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.

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Answer:

240

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

Answer:

answer will be the integer only which was added to zero

The statement is True. The average of the draws, which is 71.3, is likely to estimate the average of the box.

However, it is also likely to be off by approximately 0.1 or so.

This is because the sample mean, in this case, serves as an estimate of the population mean.

Due to the sampling variability, the sample mean may not perfectly reflect the true average of the box.

The standard deviation (SD) of the draws, which is about 2.3, gives us an indication of the variability in the sample mean.

Therefore, while the 71.3 is a reasonable estimate, it is expected to have some degree of error or uncertainty around it.

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Answer: f(x)= log1/x, x≠0

Step-by-step explanation: trust

The functional model is a logical description of the functionalities (activities, events, procedures, and procedures) of the simulation model or content matter.

As per the given question, below is a list of values provided by a science teacher.

What function is responsible again for tables representing data that are

The chart with x and f(x) has been provided below.

The table shows that if \(x = \frac{1}{10}\)  then \(f(x) =1\)

Using the logarithm rule that is:

\(\log (10) = 1 \\\\\log (100) = 2.\)

Substituting the values of x in \(f(x)= \log \frac{1}{x}\)

When

\(x = \frac{1}{10}\\\\f(x)= \log \frac{1}{\frac{1}{10}}\)

We can write it \(f(x) = \log(10) = 1\)

If

\(x = \frac{1}{100}\\\\f(x)= \log \frac{1}{\frac{1}{100}}\)

We can write it \(f(x) = \log(100) = 2\)

Therefore, the final answer is "\(f(x)= \log \frac{1}{x} , x =/ 0\)".

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Answer:

1/3pi x r^2 / 4 x 2h

Step-by-step explanation:

Ummm I'm just clueless. :/

The lengths of the sides of the triangle with vertices A(2,-1,4), B(-2,3,9), and C(6,4,8) are approximately 10.63, 7.07, and 7.81 units.

To find the lengths of the sides of the triangle, we can use the distance formula in three-dimensional space. The distance formula is derived from the Pythagorean theorem, where the distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is given by:

d(PQ) = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

Applying this formula to our triangle, we can calculate the lengths of the sides as follows:

1. Side AB:

  AB = √((-2 - 2)² + (3 - (-1))² + (9 - 4)²)

     = √((-4)² + (4)² + (5)²)

     ≈ √(16 + 16 + 25)

     ≈ √57

     ≈ 7.55 units (rounded to two decimal places)

2. Side BC:

  BC = √((6 - (-2))² + (4 - 3)² + (8 - 9)²)

     = √((8)² + (1)² + (-1)²)

     ≈ √(64 + 1 + 1)

     ≈ √66

     ≈ 8.12 units (rounded to two decimal places)

3. Side CA:

  CA = √((6 - 2)² + (4 - (-1))² + (8 - 4)²)

     = √((4)² + (5)² + (4)²)

     ≈ √(16 + 25 + 16)

     ≈ √57

     ≈ 7.55 units (rounded to two decimal places)

Therefore, the lengths of the sides of the triangle ABC are approximately 7.55, 8.12, and 7.55 units.

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There are 10 keychains were made from 180 beads.

What is keychain?

A metal ring or chain known as a keychain, sometimes known as a key fob or keyring, is used to hang multiple keys on.

You can keep your keys organized on a key ring, which is a metal ring. Through the slots in your keys, you pass the ring.

Typically, it will be bigger than the split ring, and the polished stainless steel style is perfect for adding some lovely colors. The paint, which is a charming keychain in and of itself, gives the Carabiner Clip its lovely color.

Given:

The members of the art club are making keychains that require 18 beads a piece.

The art club adviser brought a bag with 250 beads for them to use.

There are 70 beads left in the end.

That is there are 250 - 70 = 180 beads are used.

Since each keychain requires 18 beads.

So, there are 180 / 18 = 10 keychains were made.

Here, there are 18 keychain were made.

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Answer:

9lbs

Step-by-step explanation:

12*.75=9

The factors of the given polynomials are found using factorization methods.

Consider the polynomials given.

x⁴ - 8x² + 16 = (x²)² - 8x² + 16

Using the factorization method,

                   = (x² - 4)(x² - 4)

                   = (x² - 2²)(x² - 2²)

                   = (x - 2)(x + 2)(x - 2)(x + 2) [By difference of squares formula]

The factor is x - 2.

x⁴ - 16 = (x²)² - 4²

          = (x²- 4)(x² + 4)

          = (x² - 2²)(x² + 4)

          = (x - 2)(x + 2)(x² + 4)

The factors are x - 2 and x² + 4.

x⁶ - 8 = (x²)³ - 2³

        = (x² - 2) (x⁴ + 2x² + 4)

        = (x² - 2) ((x²)² + 2x² + 4)

Factor is x² - 2.

x⁴ + 2x² - 8 = (x²)² + 2x² - 8

                  = (x² + 4) (x² - 2)

The factors are x² - 2 and x² + 4

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Answer:

Smaller factor/larger figure = 3/6 = ½

Step-by-step explanation:

Scale factor of similar figures is usually the ratio of one to the other.

In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.

Length of smaller figure = 3

Corresponding length of larger figure = 6

Scale factor = smaller figure/larger figure = 3/6

Simplify

Scale factor = ½

Scott will therefore need 221 minutes to complete 52 kilometers at his current pace.

Long-distance travel refers to a journey between two locations that are far apart. The best option for long-distance travel is the train because it is dependable and affordable. Communication that takes place over a long distance is referred to as long-distance. His lover in Colorado gave him a long-distance call.

We may construct a proportion to calculate how long it will take Scott to complete 52 kilometers at the same speed:

52 km/m at 20 km/85 min.

We can cross-multiply to find the value of m:

20 km * m equals 85 min * 52 km.

Simplifying:

20m = 4420

20 divided by both sides:

m = 221

Scott will therefore need 221 minutes to complete 52 kilometers at his current pace.

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Answer: \(108^{\circ}\)

Step-by-step explanation:

Given

The top left and right corners measures \(72^{\circ}\) and the bottom right corner measures \(108^{\circ}\).

Suppose the missing corner measures \(x\)

So, the sum of the four angles of parallelogram is \(360^{\circ}\)

\(\therefore x+72^{\circ}+108^{\circ}+72^{\circ}=360^{\circ}\\\Rightarrow x=360^{\circ}-252^{\circ}\\\Rightarrow x=108^{\circ}\)

Therefore, the missing angle is \(108^{\circ}\).

\(Hi!\)

\(Let's\) \(set\) \(up\) \(a\) \(proportion\)\(:\)

\(\frac{7.5}{1} =\frac{1}{?}\)

\(7.5(?)=1\\\)

\(? = \frac{1}{7.5}\)

\(Hope\)  \(this\)  \(helps!\) \(:D\)

Answer:

-8x-4 is the answer using distributive property.

Answer:

-8x -4

Step-by-step explanation:

8 (-x -(1/2))

Distribute

-8*x + 8*-1/2

-8x -4

Answer:

R(-2,-1)

S(-1,-5)

T(2,-3)

Step-by-step explanation:

First, you flip all coordinates to their exact points, just of the other side of the y-axis.

Then, you just gotta graph it and rotate it 180* around the origin.

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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The probability distribution of X is 0.5, 0.25, 0.25, and 0.125. Mean value ∑ X × P (X) = 1.875. Standard Deviation of X = 1.0533

a) For a fair coin,

P(H) = P(T) = 0.5

Outcome  X                            Probability

T                  1                                  0.5

HT              2                       0.5×0.5 = 0.25

HHT          3                       0.5×0.5×0.5 = 0.125

HHHT          4                           0.5×0.5×0.5×0.5 = 0.0625

HHHH          4                           0.5×0.5×0.5×0.5 = 0.0625

So, probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X     P(X)    X×P(X)         X2×P(X)

1     0.5     0.5          0.5

2     0.25      0.5               1

3     0.125    0.375         1.125

4     0.125       0.5            2

sum 1     E(X) = 1.87

c) Variance = E(X²) - E(X)²

= 4.625 - 1.875²

= 1.1094

Standard Deviation of X = √ Variance

= √1.1094

= 1.0533

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Answer:

  (a)  5024 ft³

Step-by-step explanation:

You want the difference in volumes of two cones with height 16 ft, where the larger has diameter 40 ft and the smaller has diameter 20 ft.

The volume of a cone is given in terms of its radius as ...

  V = π/3(r²h) . . . . . . r=radius; h=height

The radius is half the diameter, so the formula with diameter is ...

  V = π/3(d/2)²h = π/12d²h

The two given cones have the same height, but different diameters. The difference in volumes will be ...

  V2 -V1 = (π/12)((d2)²h) -(π/12)((d1)²h) = (πh/12)((d2)² -(d1)²)

  V2 -V1 = 3.14(16 ft)/12 × ((40 ft)² -(20 ft)²) = 3.14·16/12·1200 ft³

  = 3.14·1600 ft³ = 5024 ft³

The difference in volumes of the two cones is 5025 cubic feet.

Answer:

D. 8/15

Step-by-step explanation:

13/23 = .565217

11/20 = .55

9/17 = .52941176

8/15 = .53333333

Answer:

The question is asking what is the volume of water in the full pool.  It is 70 liters.

Step-by-step explanation:

Let P represent the volume of a full pool.

"2/5 of a kiddy pool was filled with water" can be written as:

(2/5)P.

"After pouring out 5/7  of the amount of [I assume from the 2/5P] water in the pool" can be written as:

(2/7)(2/5)P, or (4/35)P       [This represents the amount of water remaining in the pool after the above shenanigans.]

The we are told that when 62 liters are added back to the pool, it is full.  That can be written as:

62 + (4/35)P = P  [Add 62 liters to what was remaining. ((4/35)P), and we'll have P, a full pool, for a cool fool. [sorry]

62 = (31/35)P

P = 62(35/31)

P = 70 liters

Answer:

C. The answer I think is C.

The equivalent regular expression for the given DFA using Arden's theorem is (a+b)(a+bb+ba(a+b))*.

1. Start with the given DFA and its transition table:

  State | Input a | Input b

  ------|---------|---------

  1     | 3       | 2

  2     | 1       | 2

  3     | 2       | -

2. Apply Arden's theorem, which states that for a DFA with a single final state, the regular expression for that state can be obtained by substituting the regular expressions for the other states into the equation: R = S + RP, where R is the regular expression for the final state, S is the regular expression for the current state, and P is the regular expression for the next state.

3. Begin with state 1:

  - Substitute the regular expression for state 3 into the equation:

    1 = 3a + ε

  - Since state 3 has no outgoing transition for input b, it is represented as ε (empty string).

4. Move to state 2:

  - Substitute the regular expression for state 1 into the equation:

    2 = 1(a + b) + 2a + 3b

  - State 1 is represented as (a + b) from the previous step.

  - Note that 1 is substituted because it is the regular expression for the state itself.

5. Move to state 3:

  - Substitute the regular expression for state 2 into the equation:

    3 = 2b

  - State 2 is represented as b from the previous step.

6. Substitute the obtained regular expressions back into the previous equations until no new substitutions are made:

  - In this case, there are no new substitutions to be made.

7. The resulting regular expression for state 1 is (a + b)(a + bb + ba(a + b))*.

Therefore, the equivalent regular expression for the given DFA using Arden's theorem is (a + b)(a + bb + ba(a + b))*.

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Answer:

8,2 and 0,4 are the points you need on the graph

Step-by-step explanation:

Answer:

Step-by-step explanation:

The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint. In this case, the x-coordinate moves from 4 to 2, or down by 2, so the new x-coordinate must be 2-2 = 0.

Answer:

x

Step-by-step explanation:

Answer:

Step-by-step explanation:

See image

Answer:

A because we need the amount of time she played soccer for so we need to add the 2 days together

Step-by-step explanation:

The question asks to find the limits of the products of two functions f(x) and g(x) under different conditions.

To find the limit of the product of two functions f(x) and g(x), we can use the product rule of limits. The product rule states that the limit of the product of two functions is equal to the product of their limits, as long as the limits exist.

a. Limit of f(x)g(x) as x approaches a:

limit[f(x)g(x)] = limit[f(x)] x limit[g(x)] as x approaches a. If both limits exist, then their product will be the limit of the product.

b. Limit of f(x)/g(x) as x approaches a:

limit[f(x)/g(x)] = limit[f(x)] / limit[g(x)] as x approaches a. If the limit of g(x) is not equal to zero, then we can use this rule.

c. Limit of g(x)/f(x) as x approaches a:

limit[g(x)/f(x)] = limit[g(x)] / limit[f(x)] as x approaches a. If the limit of f(x) is not equal to zero, then we can use this rule.

d. Limit of [f(x)g(x)] / [f(x) + g(x)] as x approaches a:

We can use L'Hôpital's rule to evaluate this limit. Taking the derivative of both the numerator and denominator with respect to x, we get:

[f'(x)g(x) + f(x)g'(x)] / [f'(x) + g'(x)]

Taking the limit as x approaches a, we can again use the product and quotient rules of limits.

Therefore, the limit of [f(x)g(x)] / [f(x) + g(x)] as x approaches a is:

limit[[f(x)g(x)] / [f(x) + g(x)]] = [limit[f(x)] x limit[g(x)]] / [limit[f(x)] + limit[g(x)]] as x approaches a.

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