Given the speeds of each runner below, determine who runs the fastest.
\text{Frank runs 9 feet per second.}
Frank runs 9 feet per second.
\text{Tony runs 299 feet in 34 seconds.}
Tony runs 299 feet in 34 seconds.
\text{Zach runs 1 mile in 396 seconds.}
Zach runs 1 mile in 396 seconds.
\text{Will runs 675 feet in 1 minute.}
Will runs 675 feet in 1 minute.

Answer:b

Step-by-step explanation:

2 3/8 ÷ 1 1/4

Steps

19/8 x 4/5

= 19/10

= 1 9/10

So the answer to this is B.

answer:

3/8 is the slope, also stated as .4 (from 3.75)

the segment length is 8.5 (using the pythagorean theorem)

Step-by-step explanation:

Hope this help po, thank you.

Answer:

In the first step, there is an issue when distributing the -3 to the terms inside of the parentheses. When multiplying the -3 to the -5, you would get an answer of +15, not -15.

The full correct process is:

(4m + 9) - 3(2m - 5) = 4m + 9 - 6m + 15

                                = 4m - 6m + 9 + 15

                                = -2m + 24

You put C's value into your calculator, then push the TAN button to get your answer. Normally you round to 4 digits past zero. You didn't include any values so I can't give you an exact answer. Hope that helps!

Answer:

Step-by-step explanation:

To determine the approximate value of tan C, we need to know the value of angle C. If we have that information, we can use a calculator or a trigonometric table to find the value of the tangent function for that angle.

If angle C is not given, we cannot determine the value of tan C.

The angle between the two vectors < 8, 3 > and < 4, −3 > is 57.43°

Given: vectors < 8, 3 > and < 4, −3 >

To find the angle between two vectors, we can use the dot product method:

First, you will compute the dot product and magnitudes of both vectors. Thus,

Let a = < 8, 3 > and b = < 4, −3 >

a · b = <8, 3> ·<4, -3> = 8(4) + (3)(-3) =  32-9 = 23

|a| = √(8² + 3²) = √(64+9) = √73

|b| = √(4² + (-3)²) = √(16 + 9) = √25 = 5

By using the angle between two vectors formula using dot product,

θ = cos⁻¹ [ (a · b) / (|a| |b|) ]

θ = cos⁻¹ (23 / √73 · 5)

θ  = cos⁻¹ (23/42.72) = 57.43°

Therefore, the angle between the following two vectors is 57.43°

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The error term for the given rule is: [f''''(x) / 5] * h²[f''''(x) / 5] * h² is the error term for the given rule.

Error term = [f''(x) / 12] * h², therefore, the error term for the given formula is:

f''(x) = [f'(x + h) - f'(x)] / h[f'(a)

≈ 2.14f(a + h) – 3f(x) – f(x + 2h) / 2h]

Then we have to calculate the second derivative of f(x) to calculate the error term: f''(x) = [f'(x + h) - f'(x)] / hf''(x)

= [f(x + 2h) - 2f(x + h) + 2f(x - h) - f(x - 2h)] / (2h)²

So, the error term is: f''(x) / 12 = [f(x + 2h) - 2f(x + h) + 2f(x - h) - f(x - 2h)] / 12h² f'(a) ≈ 2.14f(a + h) – 3f(x) – f(x + 2h) / 2h has an error term of                    [f(x + 2h) - 2f(x + h) + 2f(x - h) - f(x - 2h)] / 12h².3-2.

Use the above formula to approximate f'(1.8) with f(x) In x using h= 0.1, 0.01 and 0.001.

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Frequency means how often a number or something appears.

so,

2

4

3

5

Answer:

5/7 or 0.71 is the answer

Answer: ooooooof

Step-by-step explanation:

The Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.

Exponential smoothing is a forecasting technique that takes into account both the historical demand and the trend of the data. It is calculated using the formula:

Forecast = α * (Demand / Seasonal Index) + (1 - α) * Previous Forecast

Initial forecast (Previous Forecast) = 417

α (Smoothing parameter) = 0.35

Demand for Year 4, Q1 = 307

Seasonal Index for Q1 = 0.762

Using the formula, we can calculate the Year 4, Q1 forecast:

Forecast = 0.35 * (307 / 0.762) + (1 - 0.35) * 417

        = 335.88

Therefore, the Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.

The forecasted demand for Year 4, Q1 using exponential smoothing is 335.88.

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Answer:

8

Step-by-step explanation:

Using Euler's method with a time step of 0.3, the first two approximations for the solution to the initial value problem y'(t) = t + y, y(0) = 5 are u1 = 6.5 and u2 = 8.035.

Using Euler's method, we can approximate the solution to the initial value problem y'(t) = t + y, y(0) = 5 with a time step of Δt = 0.3 as follows:

At t = 0, y = 5

Using the formula: y1 = y0 + f(y0,t0)Δt, where f(y,t) = t + y

y1 = 5 + (0 + 5)0.3 = 6.5

Using the formula again with y1 and t1 = Δt:

y2 = 6.5 + (0.3 + 6.5)0.3 = 8.035

Thus, the first two approximations u1 and u2 are 6.5 and 8.035, respectively.

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Answer:

The expected value of x ; E(x) = 1

Step-by-step explanation:

F(x) = 1/8 for 0 ≤ x ≤ 4

To prove that it is a probability density function we will find E(x )

attached below is the required prove

It is proven that F(x) = 1/8 for 0 ≤ x ≤ 4 is  probability density function

The expected value of X = 1

Answer:

1. Square root of 8 over 2 (1.41)

2. 2

3. Square root of 7 (2.65)

Answer:

10cm

Step-by-step explanation:

Assuming the shape is a rectangle since it's already stated that it's a parallelogram, and the area is stated, we can use the Pythagorean theorem to find the length

\(a^{2} +b^2=c^2\), where c will be the length

isolate c

\(c^2=a^2+b^2\)

\(c=\sqrt{a^2+b^2}\)

substitute for a and b

\(c=\sqrt{8^2+6^2}\)

\(c=\sqrt{64+36}\)

\(c=\sqrt{100}\)

\(c=10\)

To solve the equation in part a and determine the mystery weight, we used the following properties of equality:

Addition property: This property states that if we add the same number to both sides of an equation, the equality is preserved. In this case, we added 23 grams to both sides of the equation to isolate the variable.

Subtraction property: This property states that if we subtract the same number from both sides of an equation, the equality is preserved. In this case, we subtracted 8 grams from both sides of the equation to isolate the variable.

Multiplication property: This property states that if we multiply both sides of an equation by the same number, the equality is preserved. In this case, we multiplied both sides of the equation by 3 to isolate the variable.

Division property: This property states that if we divide both sides of an equation by the same number (excluding 0), the equality is preserved. In this case, we divided both sides of the equation by 2 to isolate the variable.

By using these properties of equality, we were able to manipulate the equation and isolate the variable to determine the mystery weight.

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The probability that at least one household has their TV set tuned to the game is 1 - (1-0.22)^33, which is approximately 0.993.

To solve this problem using the direct method, we can use the fact that 22% of TV sets were tuned to the game. This means that the probability of a randomly selected TV set being tuned to the game is 0.22.

To find the probability that at least one of the 33 households surveyed had their TV set tuned to the game, we can use the complement method. The complement of the event "at least one household has their TV set tuned to the game" is "none of the households have their TV set tuned to the game".

Using the complement method, we can find the probability of this event by taking the probability that no households have their TV set tuned to the game, which is (1-0.22)^33.

So, the probability that at least one household has their TV set tuned to the game is 1 - (1-0.22)^33, which is approximately 0.993.

If I had to do this by hand, I would use the complement method, as it involves simpler calculations.

To find the probability that at least one TV set among the 33 households surveyed is tuned to NBC Sunday Night Football, we can use either the direct method or the complement method.

1. Direct Method:
The direct method requires calculating the probabilities of 1, 2, 3, ..., 33 households watching the game, and then summing up these probabilities. This method can be tedious and time-consuming, especially when done by hand.

2. Complement Method:
The complement method is generally easier and quicker, as it involves calculating the probability that none of the 33 households is watching the game and then subtracting this probability from 1.

Given that 22% (0.22) of the TV sets in use were tuned to the game, the probability that a household is not watching the game is 1 - 0.22 = 0.78.

For all 33 households not to be watching the game, the probability is (0.78)^33 ≈ 0.00038.

Now, to find the probability that at least one household is watching the game, we subtract this probability from 1:

1 - 0.00038 ≈ 0.99962.

So, the probability that at least one of the 33 households is tuned to NBC Sunday Night Football is approximately 0.99962.

If you had to do this by hand, the complement method would be the preferred approach, as it requires fewer calculations and is more straightforward.

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Explanation

8 x 5 means 8 in 5 places

Answer: 40

Answer:

The answer rounded to the hundredth is 45.96.

A linear equation in the form y = mx + c has slope m Any line parallel to 3x + 9y = 5 has the same slope 3x + 9y = 5 → 9y = -3x + 5 → y = (-3/9)x + 5/9 → y = -⅓x + 5/9 &

Box B has the smaller range of masses, with a range of 49 grams, compared to Box A's range of 97,649 grams.

The question asks which of the boxes has the smaller range of masses and what is the value of this range in grams (g).
To find the range, we need to subtract the smallest value from the largest value in each box.
In Box A, the smallest value is 4 and the largest value is 97653. So, the range in Box A is 97653 - 4 = 97649 g.
In Box B, the smallest value is 2 and the largest value is 8762. However, we are given that key 35 represents a mass of 53 g and key 51 represents a mass of 51 g. So, the actual largest value in Box B is 51. Therefore, the range in Box B is 51 - 2 = 49 g.
Comparing the ranges, we can see that the range in Box B (49 g) is smaller than the range in Box A (97649 g).

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The congruent triangles in this problem are given as follows:

Triangles A and B.

Two figures are classified as congruent if their side lengths are the same.

If we rotate triangle B 180º over it's base, we have that it will have a similar format to triangle A, and also with the same side lengths.

Hence the congruent triangles in this problem are given as follows:

Triangles A and B.

With triangle C, no rotation would make it like A and B, with the same side lengths, hence it is not congruent to any of the triangles in this problem.

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Answer: 15

Step-by-step explanation:

Answer:

opens upwards

Step-by-step explanation:

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

• if a > 0 then parabola opens upwards

• if a < 0 then parabola opens downwards

given

y = 5x² - 17x - 12

with a = 5 > 0

then parabola opens upward

Answer:B

Step-by-step explanation:

Given

Height of building \(h=30\ m\)

Angle of depression \(\theta =45^{\circ}\)

Suppose distance of Point A from base of building be  \(x\)

From diagram we can write

\(\Rightarrow \tan \theta =\dfrac{h}{x}\)

\(\Rightarrow \tan (45^{\circ})=\dfrac{30}{x}\)

\(\Rightarrow 1=\dfrac{30}{x}\)

\(\Rightarrow x=30\ m\)

So, point A is \(30\ m\) from base of building

Answer:

\(\dfrac{x}{x + 1}\\\\\text{which is the first answer choice }\)

Step-by-step explanation:

We are given
\(f(x) = x^2 - x\\g(x) = x^2 - 1\\\\\text{and we are asked to find $ \left(\dfrac{f}{g}\right)\left(x\right)$}\)

\(\left(\dfrac{f}{g}\right)\left(x\right) = \dfrac{f(x)}{g(x)}\\\\\\= \dfrac{x^2-x}{x^2 - 1}\)

\(x^2 - x = x(x - 1)\text{ by factoring out x}\\\\x&2 - 1 = (x + 1)(x - 1) \text{ using the relation $a^2 - b^2 = (a + 1)(a - 1)$}\)

Therefore,

\(\dfrac{x^2-x}{x^2 - 1} = \dfrac{x(x-1)}{(x + 1)(x - 1)}\)

x - 1 cancels out from numerator and denominator with the result
\(\dfrac{x}{x+1}\)

So

\(\left(\dfrac{f}{g}\right)\left(x\right)$} = \dfrac{x}{x + 1}\)

Answer:

They are supplementary.

Step-by-step explanation:

A linear pair consists of two opposite angles whose non-common sides create a straight line. If a linear pair consists of two angles, then they are supplementary

Answer:

hello there I am from India!