given the length of a vector and its angle measured from the y-axis, which trigonometric function can be used to calculate its y component?

a. A speed of 40 mph is 1.5 standard deviations below the mean.

b. The minimum speed of a driver that will be ticketed is approximately 49.36 mph.

The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.

a) We can use the z-score formula to find out how many standard deviations away from the mean a speed of 40 mph is:

z = (40 - 46) / 4 = -1.5

This means that a speed of 40 mph is 1.5 standard deviations below the mean.

b) To find the minimum speed of a driver that will be ticketed, we need to find the z-score that corresponds to the 80th percentile (since we want to find the speed for the upper 20th percentile):

z = invNorm(0.8) ≈ 0.84

Using the z-score formula again, we can solve for the speed:

z = (x - 46) / 4

0.84 = (x - 46) / 4

x - 46 = 3.36

x ≈ 49.36 mph

Therefore, the minimum speed of a driver that will be ticketed is approximately 49.36 mph.

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Answer:

125 people

Step-by-step explanation:

P( green) = number of green / total

                = 25/120

                 =5/24

Multiply this probability by 600

5/24 * 600 =125

Answer:

out of 120 people 25 people has chosen green

out of 1 people green will be chosen by 25/120 people

out of 600 people green colour will be chosen by( 25/120)×600 people =25×5=people

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

Answer:

y=1

Step-by-step explanation:

you can use those points to find the slope

use the equation \(\frac{y_{1} - y_{2}}{x_{1}-x_{2}}\) then plug in the numbers

so (1-1)/(-8-7) = 0/15 so the slope is zero meaning it is a horizontal line which we can tell logically because the y coordinates of both points are 1.

so if you plug those numbers into the formula y=mx+b where m is slope and b is the y intercept then

you get y=0*x+1

then 0*x is just zero and it goes away so the equation for this line is y=1

Hope this helps! :)

The equation of the line that passes through the points (-8, 1) and (7, 1) will be y = 1.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

The two points are given below.

(-8, 1) and (7, 1)

Then the equation of the line that passes through the points (-8, 1) and (7, 1) will be given as,

(y - 1) = [(1 - 1) / (7 + 8)](x - 7)

y - 1 = 0

y = 1

The equation of the line that passes through the points (-8, 1) and (7, 1) will be y = 1.

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Answer:

i don't wanna tell u the wrong answer but I think it is A

Because it says 8 neclaces for EACH of her two friends

So i divided 11.52 by 16

So i got 0.72 I am sorry if it is wrong  Have a great day!

Therefore, at the given point (1, 1, 2, 4), ∂u/∂t = (ln(2) / 2) × ∂t/∂u, and ∂t/∂u cannot be determined from the given equation.

To calculate the partial derivatives ∂u/∂t and ∂t/∂u using implicit differentiation of the given equation, we'll differentiate both sides of the equation with respect to the variables involved, treating the other variables as constants.

Let's break it down step by step:

Given equation: (-2ln(-x) = ln(2)(tx - v) × 2ln(w - uv) = ln(2)

We'll differentiate both sides of the equation with respect to u and t, treating x, v, and w as constants.

Differentiating with respect to u:

Differentiate the left-hand side:

d/dt (-2ln(-x)) = d/dt (ln(2)(tx - v))

-2(1/(-x)) × (-1) × dx/du = ln(2)(t × du/dt - 0) [using chain rule]

Simplifying the left-hand side:

2(1/x) × dx/du = ln(2)t × du/dt

Differentiating with respect to t:

2ln(w - uv) × d/dt (w - uv) = 0 × d/dt (ln(2))

2ln(w - uv) × (dw/dt - u × dv/dt) = 0

Since the second term on the right-hand side is zero, we can simplify the equation further:

2ln(w - uv) × dw/dt = 0

Now, we substitute the given values (1, 1, 2, 4) into the equations to find the partial derivatives at that point.

At (1, 1, 2, 4):

-2(1/(-1)) × dx/du = ln(2)(1 × du/dt - 0)

2 × dx/du = ln(2) × du/dt

dx/du = (ln(2) / 2) × du/dt

2ln(w - uv) × dw/dt = 0

Since the derivative is zero, it doesn't provide any information about ∂t/∂u.

Therefore, at the given point (1, 1, 2, 4):

∂u/∂t = (ln(2) / 2) × ∂t/∂u

∂t/∂u cannot be determined from the given equation.

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Answer: 7 necklaces

Step-by-step explanation: So we're looking at 3blue+2red is less than or equal to the 22 blue beads and 15 red beads. The closest you could get is using 21 blue beads and 14 red beads which is 7 necklaces.

There will be 2 beads left over.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of blue and red beads in a necklace.

= 3 blue beads and 2 red beads

Number of blue beads = 22

The number of necklaces that can be made from the blue beads.

= 7

3 x 7 = 21

One blue bead remains.

Number of red beads = 15

The number of necklaces that can be made from the blue beads.

= 7

2 x 7 = 14

One red bead remains.

Thus,

There will be 2 beads left over.

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Any combination of translation, rotation, and reflection would result in a geometric figure that is exactly the same size and shape as dilate DEF by factor 3.

Dilation is a transformation that changes the size of a geometric figure but preserves its shape. When a figure is dilated by a factor of 3, all of its dimensions are multiplied by 3, and the resulting figure is three times as large as the original. To obtain a figure that is exactly the same size and shape as dilate DEF by factor 3, we need to apply a combination of transformations that preserves both the size and shape of the figure. Translation, rotation, and reflection are examples of such transformations. Translation involves moving the figure without changing its size or shape. Rotation involves turning the figure around a fixed point without changing its size or shape. Reflection involves flipping the figure across a line without changing its size or shape.

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Answer: $52.50

Step-by-step explanation: Divide 28.00 by 8. It would equal $3.50, and that's how much per gallon. Multiply 3.50 by 15. So, the final answer is $52.50.

Answer:

$5.90

Step-by-step explanation:

49.50-20= 29.50  Divide that by 5 and you get 5.90. Hope this helps.

Answer:

3x^2+4x^2

Step-by-step explanation:

Answer:

Whether a net force acts on the object.

Step-by-step explanation:

Newtons first law states that an object will remain at rest unless it is acted upon by an imbalanced force.

Answer: 660,000 milligrams

Step-by-step explanation:

330 x 2 = 660

convert grams to milligrams by multiplying the mass by 1,000

Answer:

660,000

Step-by-step explanation:

hope this helps!

A slow-moving barge moves through the sea at a speed of 4 km/h. It travels 8 miles upstream in the same amount of time as a barge traveling 24 miles downstream with the current. The current moves at a 2 km/h rate.

Let’s start by using the formula for distance, rate, and time:

Distance = rate x time

Let’s assume that the rate of the current is r km per hour.

Going upstream (against the current), the effective rate of the barge is:

4 – r km per hour

Going downstream (with the current), the effective rate of the barge is:

4 + r km per hour

We are told that the time it takes the barge to travel 8 miles upstream is the same as the time it takes to travel 24 miles downstream. Using the formula, we can set up the following equation:

8 / (4 – r) = 24 / (4 + r)

We can simplify this equation by cross-multiplying:

8(4 + r) = 24(4 – r)

Expanding and simplifying, we get:

32 + 8r = 96 – 24r

Adding 24r and subtracting 32 from both sides, we get:

32r = 64

Dividing both sides by 32, we get:

R = 2

Therefore, the rate of the current is 2 km per hour.

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The sequence's numbers are all multiples of 30. Every number can be divided by 30.

If two integers are divided equally, leaving no remainder, then we say that one integer divides the other (we sometimes say, "with no remainder," but that is not technically correct). Mathematicians express this more explicitly as follows: If a and b are integers (with a not zero), then a divides b if c is an integer such that b = ac. Sequence: 1 51, 2 52,....., n 5n,....n 5n=n(n 4 1)=n(n1)(n1)(n+1)(n 2 +1)

At n=1, n 5, n=0, n=1, 2, 3, etc. Not attainable

Atn=2,n 5 −n=30 ∴ The sequence's numbers are all multiples of 30. Every number can be divided by 30.

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As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).

In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.

The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.

The third set of data is 24, 25, 25, 25, 26, 26.

The median is the middle value, which is also (25+25)/2 = 25.

The mode is the value that appears most frequently, which is 25.

Therefore, the mode and median are the same, fulfilling Marjane's requirement.

Therefore, the correct option is (c).

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We fail to reject the null hypothesis and there is no significant evidence for the manager to conclude that the standard deviation has decreased at the α = 0.01

What is standard deviation?

The standard deviation is a statistic that expresses the degree of variation or dispersion among a group of data. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

The null and alternative hypotheses are:

\(H_{0} :\) α = 0.004

\(H_{a} :\) α < 0.004

Under null hypothesis, the test statistic is:

\(x^{2} = \frac{(n-1)s^{2} }{\alpha ^{2} }\)

   = (29 - 1)0.0036² / 0.004²

   = 22.68

Now the critical value of x² at 0.01 level of significance for

df = n-1

  = 29 - 1

 = 28

\(x_{critical} ^{2}\) = 48.278

Since the test statics

x² = 22.68 is less than the critical value

\(x_{critical} ^{2}\) = 48.278

∴ we fail to reject the null hypothesis and there is not significant evidence for the manager to conclude that standard deviation has decreased at α = 0.01

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Answer:

Yes! Because they are in proportion: 1x9 = 9, 2x9 = 18 therefore, 1:2 and 9:18 are equivalent. Similar to equivalent fractions - you need to multiply both numbers by the same number. Hope this helped!

Step-by-step explanation:

If you need further help, let me know!

- profparis

It is true that we use a bode plot to show filter characteristics because the use of logarithms creates plots that can be approximated with straight lines.

We use a bode plot to display the frequency response of a filter. The frequency response of a filter is a complex function, and its plot can be difficult to analyze. However, by using logarithmic scales on the frequency and amplitude axes, we can transform the complex function into a simpler form that can be approximated with straight lines. This simplification is particularly useful because it allows us to easily identify the characteristics of the filter, such as its cutoff frequency, bandwidth, and phase shift. Therefore, the use of logarithmic scales is essential in creating a bode plot, and it is why we use this type of plot to show filter characteristics.

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Answer:

0.0108 kg

Step-by-step explanation:

Jiri is on a special diet

Over 5 days he eats 0.054

Therefore the food consumed in a day can be calculated as follows

5 days= 0.054

1 day= 0.054/5

= 0.0108kg

To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:

ΔL = I * Δω

where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.

To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:

Δω = ωt0 - ω0

Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.

The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:

I = (1/2) * m * r^2

where m is the mass of the cylinder and r is the radius of the cylinder.

By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.

It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.

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Answer:

2500 children and 2500 adults

The number of children is 2500 and the number of adults that attended the game is also 2500.

Let us consider that, number of children be x and number of adults be y that attend game.

Since, total 5000 people attend the game.

               \(x+y=5000\\\\x=5000-y..........(1)\)

It costs $3 for children and $7 for adults and the total takings at the door was $25000

              \(3x+7y=25000 .............(2)\)

Substitute value of x from equation 1 into equation 2.

           \(3(5000-y)+7y=25000\\\\15000-3y+7y=25000\\\\4y=10000\\\\y=10000/4=2500\)

So that, \(x=5000-2500=2500\)

Thus, the number of children is 2500 and the number of adults that attended the game is also 2500.

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According to data from the Pew Research Center, there were approximately 10.5 million unauthorized immigrants living in the United States in 2017. This number represents around 25% of the total foreign-born population in the country. In conclusion, out of the 41.3 million foreign-born individuals in the U.S., about 10.5 million are considered unauthorized immigrants.

Unauthorized immigrants, also known as undocumented immigrants, are individuals who enter the United States without legal permission or overstay their visas. They are not eligible for most government benefits and are often subject to deportation if caught.

The Pew Research Center estimates that there were 41.3 million foreign-born individuals living in the United States in 2017, which includes both authorized and unauthorized immigrants. Of this population, around 10.5 million were unauthorized immigrants.

Unauthorized immigration is a complex and contentious issue in the United States, with many different opinions on how to address it. Understanding the size and characteristics of this population is an important part of any discussion or policy debate.

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We are given the relationship:

a. It's required to find a relationship where r is a function of t. To do that, we need to solve the equation for r.

Subtract 4t:

Divide by 7:

b. We use the function found in part a and evaluate it for t=-7:

Thus, f(-7) = 6

c. Solve f(t) = 18

Again, we use the function from part a and solve the equation:

Multiplying by 7:

Subtract 14 and then divide by -4:

t = -28

Answer:

mean is 3 median is 3 and mode is also 3

Step-by-step explanation:

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