Sandy drove 55 miles per hour to Orlando. Write a function rule that relates the number of miles traveled to the hours driven. ​

Q1(A) Velocity of wind is 32.6 m/s. Q2(A) Drag force on the model car is 1828 N. Q3(A) the correct answer is Increased by a factor of 3^4.

Question 1A square section rubbish bin of height 1.25 m × 0.2 m × 0.2 m filled uniformly with rubbish tipped over in the wind. It has no wheels, has a total weight of 100 kg, and rests flat on the floor.

Assuming that there is no lift, the drag coefficient is 1.0, and the drag force acts halfway up, what was the wind speed in m/s?

Solution: Given, Height of square section rubbish bin, h = 1.25 m

Width of square section rubbish bin, w = 0.2 m

Depth of square section rubbish bin, d = 0.2 m

Density of air, ρ = 1.225 kg/m3

Total weight of rubbish bin, W = 100 kg

Drag coefficient, CD = 1.0

The drag force acts halfway up the height of the rubbish bin.

The velocity of wind = v.

To find v,We need to find the drag force first.

Force due to gravity, W = m*g100 = m*9.81m = 10.19 kg

Volume of rubbish bin = height*width*depth

V = h * w * d

V = 0.05 m3

Density of rubbish in bin, ρb = W/Vρb

= 100/0.05ρb

= 2000 kg/m3

Frontal area,

A = w*h

A = 0.25 m2

Therefore,

Velocity of wind,

v = √(2*W / (ρ * CD * A * H))

v = √(2*100*9.81 / (1.225 * 1 * 1 * 1.25 * 0.2))

v = 32.6 m/s

Question 2A large family car has a projected frontal area of 2.0 m2 and a drag coefficient of 0.30.

Ignoring Reynolds number effects, what will the drag force be on a 1/4 scale model, tested at 30 m/s in air?

Solution: Given,

Projected frontal area, A = 2.0 m2

Drag coefficient, CD = 0.30

Velocity, V = 30 m/s

Let FD be the drag force acting on the original car and f be the scale factor.

Drag force on the original car,

FD = 1/2 * ρ * V2 * A * CD;

FD = 1/2 * 1.225 * 30 * 30 * 2 * 0.3;

FD = 1317.75 N

The frontal area of the model car is reduced by the square of the scale factor.

f = 1/4

So, frontal area of the model,

A’ = A/f2

A’ = 2.0/0.16A’

= 12.5 m2

The velocity is same for both scale model and the original car.

Velocity of scale model, V’ = V

Therefore, Drag force on the model car,

F’ = 1/2 * ρ * V’2 * A’ * CD;

F’ = 1/2 * 1.225 * 30 * 30 * 12.5 * 0.3;

F’ = 1828 N

Question 3 The volume flow rate is kept the same in a laminar flow pipe but the pipe diameter is reduced by a factor of 3, the pressure drop will be:

Solution: Given, The volume flow rate is kept the same in a laminar flow pipe but the pipe diameter is reduced by a factor of 3.

According to the Poiseuille's law, the pressure drop ΔP is proportional to the length of the pipe L, the viscosity of the fluid η, and the volumetric flow rate Q, and inversely proportional to the fourth power of the radius of the pipe r.

So, ΔP = 8 η LQ / π r4

The radius is reduced by a factor of 3.

Therefore, r' = r/3

Pressure drop,

ΔP' = 8 η LQ / π r'4

ΔP' = 8 η LQ / π (r/3)4

ΔP' = 8 η LQ / π (r4/3*4)

ΔP' = 3^4 * 8 η LQ / π r4

ΔP' = 81ΔP / 64

ΔP' = 1.266 * ΔP

Therefore, the pressure drop is increased by a factor of 3^4.

Increased by a factor of 3^4

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Leo is approximately 13.928 km away from the starting point.

Given that Leo walked 7 km south and then 12 km east, we need to determine the distance from the starting point,

To determine the distance from the starting point, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the distance Leo walked south forms one side of a right triangle, and the distance he walked east forms the other side. The distance from the starting point will be the length of the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance from the starting point as follows:

Distance² = (7 km)² + (12 km)²

Distance² = 49 km² + 144 km²

Distance² = 193 km²

Taking the square root of both sides gives us:

Distance = √(193)

Distance ≈ 13.928 km

Therefore, Leo is approximately 13.928 km away from the starting point.

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Complete question =

Leo walk 7km south then 12km east. How far is he from the starting point?

Answer: 3ft

Step-by-step explanation:

Step 1; 3x-9=23 5x

Step 2; 3x9=23 5x 3x+ 9=23- 5x

Step 3 ; 3x-9 3x4-9 = 3ft

3ft is the answer.

Answer:

29

Step-by-step explanation:

Answer: 9 minutes

Step-by-step explanation:

12 x 3/4(.75) = 9

Answer:

-4

Step-by-step explanation:

Slope (m) =  

ΔY

ΔX

=  

-4

1

= -4

θ =  

arctan( ΔY ) + 360°

ΔX

= 284.03624346793°

ΔX = 5 – 2 = 3

ΔY = -8 – 4 = -12

Distance (d) = √ΔX2 + ΔY2 = √153 = 12.369316876853

Answer:

B

Step-by-step explanation:

(4x^-2)^4

256x^-8

256 * 1/x^8

256/x^8

Answer:

Add and subtract the second term to the expression and factor by grouping.

2

x

3

(

3

x

−

1

)

(

x

−

1

)

Step-by-step explanation:

Answer:

3x⁴+2x²+8

Step-by-step explanation:

\(6 {x}^{5} + 4 {x}^{3} + 8x\)

\( = 2x(3 {x}^{4} + 2 {x}^{2} + 8)\)

The most the salon would be willing to pay that groomer is $25×4 = $100.

The unitary method is a technique that determines the worth of a single unit from value of multiple units, as well as the quality of multiple units from value of a single unit.

Some key features regarding the unitary method are-

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The test result suggests that networking is an effective strategy for finding a job after graduation, as the data indicate that most workers (more than 50%) secure their jobs through networking.

To test the claim that most workers get their jobs through networking, we can use a one-sample proportion hypothesis test.

Null hypothesis (H0): The proportion of workers who get their jobs through networking is equal to 0.50.

Alternative hypothesis (Ha): The proportion of workers who get their jobs through networking is greater than 0.50.

Using the given sample data and a significance level of 0.05, we can perform the hypothesis test.

Calculate the test statistic:

To calculate the test statistic, we can use the formula:

z = (p - P) / sqrt((P * (1 - P)) / n)

Where:

p is the sample proportion (61% or 0.61),

P is the hypothesized population proportion (0.50),

n is the sample size (703).

Substituting the values:

z = (0.61 - 0.50) / sqrt((0.50 * (1 - 0.50)) / 703)

z ≈ 4.69

Determine the critical value:

Since the alternative hypothesis is one-tailed (greater than 0.50), we need to find the critical value for a one-tailed test with a significance level of 0.05. Consulting the standard normal distribution table or using a statistical software, the critical value for a significance level of 0.05 is approximately 1.645.

Compare the test statistic with the critical value:

The test statistic (z = 4.69) is greater than the critical value (1.645).

Make a decision:

Since the test statistic is in the critical region, we reject the null hypothesis. This means that there is evidence to support the claim that most workers (more than 50%) get their jobs through networking.

Interpretation:

The result suggests that networking is an effective strategy for finding a job after graduation, as the data indicate that a majority of workers secure their jobs through networking. It implies that job seekers should focus on building and leveraging professional networks to enhance their job prospects.

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The eigenvalues in terms of α are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4, in increasing order. There are no critical values.

The given coefficient matrix is [[7/4, 3/4], [α, 7/4]]. To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where A is the coefficient matrix, I is the identity matrix, and λ is the eigenvalue.

Expanding the determinant, we get:(7/4 - λ)(7/4 - λ) - (3/4)(α) = 0

Simplifying and rearranging, we get: λ^2 - (7/2)λ + (49/16) - (3/4)α = 0

Using the quadratic formula, we get: λ = (7 ± sqrt(49 - 16α)) / 4

Therefore, the eigenvalues in terms of α are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4, in increasing order.

To find the critical values of α where the qualitative nature of the phase portrait changes, we need to examine the sign of the eigenvalues. If both eigenvalues are real and have the same sign, the phase portrait consists of either a stable node or a stable spiral. If both eigenvalues are real and have opposite signs, the phase portrait consists of either a saddle or an unstable node. If both eigenvalues are complex conjugates with positive real part, the phase portrait consists of a stable focus, and if both eigenvalues are complex conjugates with negative real part, the phase portrait consists of an unstable focus.

From part a), we know that the eigenvalues are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4. To determine the critical values of α where the nature of the phase portrait changes, we need to set each eigenvalue equal to zero and solve for α.

Setting (7 + sqrt(49 - 16α)) / 4 = 0, we get sqrt(49 - 16α) = -7, which is not possible since the square root of a real number is always non-negative. Therefore, there are no critical values of α where the nature of the phase portrait changes. Alternatively, we can examine the sign of the discriminant, which is 49 - 16α. If the discriminant is positive, the eigenvalues are real and have opposite signs, indicating a saddle or an unstable node. If the discriminant is zero, one of the eigenvalues is zero, indicating a degenerate case. If the discriminant is negative, the eigenvalues are complex conjugates with non-zero real part, indicating a stable focus or a stable spiral. In this case, the discriminant is always positive or zero, since α can take any value. Therefore, there are no critical values of α where the nature of the phase portrait changes.

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Answer:

The ratio of x-values to y-values in the table is 2:3

Step-by-step explanation:

8 / 12 = 2/3

10 / 15 = 2/3

12 / 18 = 2/3

Each has a ratio of 2 to 3.

Answer:

6 -> 4/10

7 -> s √144 in

8 -> 0.4

9 -> s = ∛999 in

10 -> d = 3

A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611

B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362

The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.

The formula for calculating the standard error of the mean is

SE = σ/√n

where SE is the standard error, σ is the population standard deviation, and n is the sample size.

For n = 30, SE = 4,000/√30 = 729.16

A. For a sample size of n = 60, SE = 4,000/√60 = 516.40

To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error.

For a range of +/- $500, the z-scores are

z = ($51,300 - $51,800) / 516.40 = -0.969

z = ($52,300 - $51,800) / 516.40 = 0.969

Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.

B. For a sample size of n = 120, SE = 4,000/√120 = 368.93

Following the same steps as above, the z-scores for a range of +/- $500 are

z = ($51,300 - $51,800) / 368.93 = -1.364

z = ($52,300 - $51,800) / 368.93 = 1.364

Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.

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The speed of the water wave is 2.0 meters per second.

The speed of a wave is calculated by dividing the distance traveled by the time it takes to travel that distance. In this case, the distance traveled by the water wave is 10.0 meters, and the time taken is 5.0 seconds.

To determine the speed, we use the formula:

Speed = Distance / Time

Substituting the given values, we have:

Speed = 10.0 meters / 5.0 seconds = 2.0 meters per second

Therefore, from the given information, we can determine that the speed of the water wave is 2.0 meters per second.

This information about the speed of the water wave is useful for various purposes. It allows us to understand how quickly the wave is propagating through the medium. It also helps in analyzing wave behavior, such as interference, reflection, or refraction, and studying the characteristics of the medium through which the wave is traveling. Additionally, the speed of the wave can be used in calculations involving wave frequencies, wavelengths, and periods.

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Answer: B (The cost of a notebook is $0.75, and the cost of a folder is $0.25.)

Step-by-step explanation:

No need for explanation. i know i’m right!!

Answer:

I believe it's A. but that's just what I think sorry I can't really back it up much

The answer is the third option, because the range is -6 and the third option says its greater than or equal to -2.

(a), the linear transformation T is not one-to-one because T(-3, -4, 1) = T(-3, -5, -3), which means that two different inputs map to the same output. In situation (b), it is not possible to determine whether T is one-to-one based solely.

a. To determine if T is one-to-one, we need to check if different inputs map to different outputs. Given T(0, -2, -4) = u, T(-3, -4, 1) = v, and         T(-3, -5, -3) = u + v, we can see that T(-3, -4, 1) = T(-3, -5, -3). This means that two different inputs (-3, -4, 1) and (-3, -5, -3) map to the same output u + v. Therefore, T is not one-to-one in this situation.

b. In this situation, we are given T(a) = u, T(b) = v, and T(c) = u + v. However, we do not have any information about whether a, b, and c are different or if u and v are different.  If T is one-to-one based on this information alone. To determine if T is one-to-one, we would need additional information or a specific description of the linear transformation.

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Answer:

Step-by-step explanation:

The domain is all of the x's in the graph. The graph starts at 3 (look at the x-axis) and just gets bigger from there. So the answer is that the domain is all the x's that are 3 and bigger...

That is written [3, infinity) in interval notation or in set notation that is:

{x|x>= 3} that is the 3rd answer in your screen.

The given statement "For a sample with a standard deviation of s = 8, a score of x = 42 corresponds to z = -0.25. The mean for the sample is m = 40." is False because the calculated z-score does not match the given value.

To calculate the z-score, we use the formula z = (x - m) / s, where x is the score, m is the mean, and s is the standard deviation. Substituting the given values, we have z = (42 - 40) / 8 = 0.25. However, the given statement states that the z-score is -0.25, which is incorrect. Therefore, the statement is false.

The correct z-score for x = 42 with a mean of m = 40 and standard deviation of s = 8 is 0.25, not -0.25.

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Answer:

9x⁶y⁴

Explanation:

The area of a rectangle is equal to:

So, dividend both sides by the length, we get that the width can be calculated as:

Then, replacing the expression for the Area and the length, we get:

Now, we will use the following property:

It means that when we divide two numbers with the same base, we subtract the exponents. So, the width is equal to:

Therefore, the expression that represents the width of the rectangle in yards is: 9x⁶y⁴

Answer:

Explanation:

Here, we want to solve the given equation for L

What that means is that we want to make L the formula subject. Hence, we are to simply isolate L on one side of the equation

To do this, we have to divide both sides by the values attached to L:

Answer:

The answer is \(\sqrt{x} 101\)

Step-by-step explanation:

Answer:

D.\(\sqrt{101}\)

Step-by-step explanation:

The formula is = \(\sqrt{(x2-x1)^{2}+(y2-y1)^{2}\)

So, x1=-2 ; y1=3; x2=8; y2=2

putting these values in the formula the result will be \(\sqrt{101}\)

Hope, this helps you.

Answer:

I think the answer is A. 25.6 units.

Answer:

27.3 units to the nearest tenth

Step-by-step explanation:

Count all the box in the triangle

Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

A proportional relationship exists when each pair of data values is related in the same way, by multiplying by a factor. A proportional relationship can be identified by looking at data, an equation, or a graph. A proportional relationship with a constant of proportionality k between two quantities y and x is represented by the equation y = kx.

They pass through the source. They are linear (straight lines) and pass through the origin as well. The x to y ratio is a proportionality constant. For example, consider the following number pairs with a ratio of 2.5: 5 and 2; 10 and 4; 100 and 40; 2.5 and 1. These number pairs are all proportional to one another.

Note that an overview was his as the information is incomplete.

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Answer: 11

Step-by-step explanation:

Just go through the order of operations. (PEMDAS)

Evaluate the exponent first,

X=3

3^1=3

then multiply 2 and 3, which gives you 6

then finally add 5

this gives you the answer of 11

Answer:

stop cheating

Step-by-step explanation:

get smart

The statement "If limₓ→ₐ f(x) and limₓ→ₐ g(x) don’t exist, then lim ₓ→ₐ [f(x)+g(x)] does not exist" is false.

In general, the sum of two limits exists if and only if both individual limits exist. However, the individual limits of f(x) and g(x) not existing does not guarantee that the limit of their sum does not exist.

There are cases where the limit of the sum can still exist even if the individual limits do not exist. One example is the limit of f(x) = x and g(x) = -x as x approaches 0. The individual limits do not exist at x = 0, but the limit of their sum f(x) + g(x) = x + (-x) = 0 does exist at x = 0.

For example, consider the functions f(x) = sin(1/x) and g(x) = -sin(1/x). Both f(x) and g(x) do not have a limit as x approaches 0 because they oscillate between -1 and 1 infinitely. However, if we consider the sum f(x) + g(x), the oscillations cancel each other out, and the limit of the sum as x approaches 0 is 0.

Therefore, the statement is false.

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Answer:

Step-by-step explanation:

i posted this on accident

Answer:

24

Step-by-step explanation:

What you have here is a permutation, seeing as each element can only be used once.

We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter

However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.

Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.

Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.

Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter

The way to calculate how many permutations we have without repetition is using factorials

N!

Where N is the number of elements you have.

In this case, it would be 4!

4! is 4 * 3 * 2 * 1

Which equals 24

If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on